First published
1989
Revised from the 1985 Russian edition
Translated from the Russian by V. Afanasyev
Ha allZAUUCKOM!l3blKe
Printed
in the Union
of Soviet Socia/ist Repub/ics
ISBN 5-03-000073-9
@ H3~aTeJIbCTBO «He~pa», 1985 @ English translation, Mir Publishers, 1989
Contents
Preface Chapter One. Subject-Matter of Mine Surveying. I.I. Subject-Matter 1.2. Brief Notes on History of Mine Surveying
9
Historical
Notes
Chapter Two. General Figure of the Earth, Systems of coordinates, Control and Survey Underground Nets and Surface Surveys 2.1. General Figure of the Earth 2.2. Geographic System of Coordinates 2.3. System of Plane Rectangular Coordinates 2.4. National System of Rectangular Coordinates 2.5. Geodetic Reference Nets 2.6. National Geodetic Nets 2.7. Geodetic Bridging Nets 2.8. Geodetic Survey Nets 2.9. General Data on Surveys
10 10 12
16 16 17 .18 19 22 23 26 28 29
Chapter Three. Graphical Documentation in Mine Surveying 3.1. General 3.2. Classification of Drawings and Rules of Mapping 3.3. Drawing Materials. Technology and Rules for Making and Storage of Mining Graphical Documentation 3.4. Mechanization ,of Graphical Work 3.5. Processes and Materials for Reproduction of Mining Graphical Documentation
33 33 35
Chapter Four. Connection Surveys 4.1. General 4.2. Orientation of Underground Survey via Horizontal or Inclined Adit 4.3. Geometric Orientation 4.4. Orientation down One Vertical Shaft 4.5. Sequence and Organization of Work for Orientation down One Vertical Shaft 4.6. Plumbing Surface Points onto Oriented Mine Level 4.7. Connection to Plumb Line Points in Orientation down One Vertical Shaft 4.8. Horizontal Connection Survey via Two Vertical Shafts 4.9. Horizontal Connection Survey with Use of Gyrocompasses 4.10. Vertical Connection Surveys
39 39
36 36
37
41 41 42
42 44
46 49 58 7n
Contents
6
Chapter 5.1. 5.2. 5.3. 5.4. 5.5. 5.6.
Five. Horizontal Surveys of Underground Workings General on Underground Mining Surveys Horizontal Underground Surveys Underground Reference Nets of Plan Control Construction of Underground Reference Nets Survey Nets Types of Station Points of Reference and Survey Nets. Their Fixation 5.7. Theodolites 5.8. Tests and Adjustments of Theodolites 5.9. Centring of Theodolites and Signals 5.10. Measurements of Horizontal Angles 5.11. Measurements of Inclination Angles 5.12. Measurements of Side Lengths of Theodolite Traverses 5.13. Distance Measurements by Light Range Finders 5.14. Detailed Survey of Underground Workings 5.15. Office Analysis of Results of Underground Theodolite Survey and Calculation of Point Coordinates 5.16. Accumulation of Errors in Underground Theodolite Surveys
74 74 7~
81
82 84 92 93 98 104 107 III III 112 116
Chapter Six. Vertical Surveys in Underground Workings 6.1. General 6.2. Levels 6.3. Levelling Staffs 6.4. Geometric Levelling in Underground Workings 6.5. Office Analysis of Results of Geometric Levelling 6.6. Errors in Geometric Levelling 6.7. Trigonometric Levelling 6.8. Errors in Trigonometric Levelling
121
Chapter Seven. Surveys of Preparatory and Stope Workings 7.1. General 7.2. Instruments for Surveys of Preparatory and Stope Workings 7.3. Surveys of Stope Workings in Coal Fields 7.4. Surveys of Underground Chambers and Cavities 7.5. Surveys of Preparatory Workings 7.6. Surveys of Blast Holes 7.7. Orientation of Sublevel Workings 7.8. Measurements of Mining Workings and Reserves of Mineral In Stocks
142
Chapter Eight. Special Surveys in Underground Workings 8.1. Assigning Directions to Underground Workings 8.2. Surveying of Workings Driven from Two Ends 8.3. Preliminary Estimation of Accuracy of Face Connection
167
Chapter Nine. Surveying in Mine Construction 9.1. General 9.2. Surveying at Mine Camp 9.3. Surveying in Construction of Mine Hoists 9.4. Survey Work During Sinking of Vertical Shafts 9.5. Survey Work for Arranging of Shaft Equipment
188 188 193 195 218 221
121 122 133 134 137 137 138 140
142 143 148 150 154 155 157
167 181 185
7
Contents 9.6. Survey Work During Driving of Shaft Workings 9.7. Survey Work During Driving of Vertical Shafts by Special Methods 9.8. Survey Work During Deepening of Vertical Shafts
228 229 234
Chapter Ten. Surveying in Quarries 10.1. General 10.2. Reference and Survey Nets and Surveying Work 10.3. Mine-Surveying Coverage of Drilling and Blasting Work 10.4. Survey Work for Transport Servicing 10.5. Survey Work in Trenching 10.6. Survey Work in Open-Cast Mining with Conveyer Bridges 10.7. Calculations of Volumes of Extracted Overburden Rock and Mineral in Quarries 10.8. Reclamation of Land 10.9. Survey Work in Open-Cast Mining of Placer Deposits
238 238 238 260 262 263 264
Chapter Eleven. Rock Disturbance and Protection of Structures 11.1. Introductory Notes I 1.2. General Data on Rock Disturbance I 1.3. Rock Displacement Parameters I 1.4. Factors Responsible for Rock Displacement I 1.5. Monitoring Rock Displacement. Observation Stations I 1.6. Calculations of Rock Displacement I 1.7. Measures for Protecting Surface Structures I 1.8. Construction of Safety Pillars
266 269 270
Surface 272 272 274 275 280 283 287 290 291
Chapter Twelve. Stability of Quarry Flanks 12.1. Principal Causes and Kinds of Rock Deformation 12.2. Factors Affecting Flank Stability 12.3. Mine-Surveying Observations on Rock Mining Deformations in Open-Cast Mining 12.4. Stability of Working Benches and Flanks of Quarries 12.5. Measures for Controlling Landslides 12.6. Artificial Strengthening of Rock Massif
295 295 296
Chapter Thirteen. Mine-Surveying Control of Mining Safety 13.I. Role of Mine-Surveying Service in Mining Safety 13.2. Control of Mining Work near Old Workings 13.3. Examples of Calculation and Construction of Dangerous Zones 13.4. Construction of Zones of Elevated Rock Pressure 13.5. Construction of Dangerous Zones for Mining Work in Seams Liable to Coal, Gas and Rock Bursts
309 309 309 311 315
Chapter Fourteen. Mine-Surveying Control of Geological ration 14.1. Brief Data on Geological Exploration 14.2. Mine-Surveying Control of Geological Work 14.3. Topographic Basis of Geological Exploration 14.4. Transfer of Plan of Exploratory Workings into Nature 14.5. Layout of Exploratory Ditches 14.6. Geodetic Control of Geophysical Prospecting Methods
300 303 305 306
318
Explo324 324 325 327 328 334 336
8
Contents 14.7. Mine-Surveying Work in Geophysical Prospecting 14.8. Barometric Levelling of Geological Observation Objects Chapter Fifteen. Mine-Surveying Work for Mineral Extraction in Water Areas of Seas and Oceans 15.1. General 15.2. Brief Data on Geomorphology of Ocean Bottom Relief 15.3. Characteristics of Some Solid Minerals 15.4. Mine-Surveying Service of Geological Prospecting and Mining in Water Areas 15.5. Marine Mine-Surveying Reference Nets 15.6. Special Mine-Surveying Work in Water Areas 15.7. Routine Mine-Surveying Work in Water Areas 15.8. Determination of Plan Coordinates of Floating Vessels 15.9. Depth Measurements 15.10. Calculation of Volumes of Extracted Rock Index
340 345
349 349 350 351 351 353 355 356 358 358 360 362
Chapter One Subject-Matter of Historical
1.1. Subject-Matter M odern mine surveying is a branch of the mining science and industry which is concerned with surveys on the land surface and underground during the prospecting and extraction of mineral deposits and the construction of mining plants; the results of surveys are then used for plotting the plans of mining workings and bedding conditions of deposits and also for the solution of various problems of the mining geometry. At the early period of its existence, mine surveying could be characterized simply as underground geodesy. In some countries, it is still called in this way (for instance, 'geodesie souterraine' in France). In the course of its progress, however, mine surveying has become a complex discipline which includes not only the methods and techniques of the survey work (mine surveying proper), but also the estimation of the accuracy of measurements and calculations based on the method of least squares and the theory of probability; geodetic and mine-surveying instrumentation; mining geometry; studies of displacements and pressure of rocks (mining geomechanics),etc. All these aspects of mine surveying have the same objectives: to ensure safe and efficient exploitation of mineral deposits on the bases of the instrumental measurements performed under particular mining and geological conditions of a mining plant. Modern mine surveying has to cope with more diversified and complex problems. The quality and productivity of the survey work
Mine Surveying. Notes
have increased drastically due to the realization of the latest achievements of science and engineering. There is a trend to form specialized mine-surveyor teams for making a particular kind of survey work at a number of mining plants (for instance, mine-surveying groups for the orientation of mines with the use of gyrocompasses or for surveying of open-cast pits by aerial and ground stereophotogrammetry). The prime task of minesurveying service, as earlier, is however the compilation of plans of mining enterprises which are required for the normal exploitation of mineral deposits and represent the current state of deposits and underground or surface workings and structures and buildings on the land surface. Certain progress has been made recently in the methods and techniques of mine surveying. New solutions have been proposed for the orientation and construction of underground reference nets. High-precision theodolites and light range finders have come into use for the construction of reference nets. New instruments and methods have been proposed for the surveys of quarries. Serious investigations have been completed in the field of mine surveying in the construction and reconstruction of mines. In particular, special methods have been suggested for the survey work during mounting of hoisting machines on tower head-frames and the construction of mine shafts. Laser instruments are finding ever wider use for direction assigning and control in vertical and horizontal workings, arrangement of equipment of vertical shafts, track laying in horizontal
1.1. Subject-Matter
workings, mounting of conveyers, laying of pipelines, etc. An essential progress has been done in the methods and instruments for plotting the mining graphical documentation and in the materials for making mine-surveying plans and sections. Field measurements and office work in mine surveying are now carried out with the use of diverse and rather intricate instruments and devices, in particular, highprecision optico-mechanical systems and electronic devices. Among many achievements in this field, it is worth to mention small-sized mine-surveying gyrocompasses, optical range finders, devices for measuring the curvature of boreholes, self-adjusting levels, apparatus for the stereophotogrammetric surveys of open-cast pits and underground workings, coded theodolites with direct input of measured results into electronic computers, special-purpose electronic computers for mine surveying, desk calculators, etc. Mine surveying also has to solve an important group of problems associated with the investigation of the configurations of lodes and their representation in special graphs and with the determination of the optimal regimes of extraction of minerals for obtaining the final product having the specified concentrations of useful and waste components. This branch of mine surveying, called mining geometry, helps the mine surveyor in controlling measures for the preservation of mineral deposits and efficient extraction of minerals. Another important concern of mine surveying relates to the studies of mechanical processesin rock massifs and in the elements of working systems, which are induced by mineral extraction operations (mining geomechanics).The investigations of rock displacements and rock pressure have been especially fruitful in the last 20-25 years. Regulations have been worked out for the protection of surface structures, collieries and ore
11
mines against rock displacements. Methods have been developed for preliminary calculations of land surface deformations in underground mining of coal fields, which have made it possible to introduce certain radical measures for the protection of structures against the harmful influence of underground workings. Conditions have been formulated for safe extraction of minerals from deposits beneath water basins. In open-cast mining, methods for the calculation of inclination angles of pit flanks and measures for artificial strengthening of slopes have been suggested. A division of mining geomechanics is concerned with the studies of the effects of rock bursts. The mechanisms of appearance of rock bursts have been investigated thoroughly on the scientific basis and measures for preventing them have been developed. Mine surveyors carry out the investigations of rock pressure in permanent, preparatory and stope workings in coal and ore deposits. As an engineering discipline, mine surveying is based on the concepts of fundamental sciences, such as mathematics, physics, mechanics, and philosophy. Measurements and calculations in mine surveying are carried out by the conventional techniques adopted in geodesy. Mine surveying is also associated closely with geodetic instrumentation, geology, mining, production management, etc. Mine surveyors have to participate in all stages of the operation of mining plants from the exploration of a mineral deposit and up to the abandonment of a mine after it has been worked out, and to perform specific survey work at all these stages. . Exploration of mineral deposits. In the exploration of mineral deposits, the mine surveyor makes land surveys, determines and transfers into nature the positions of exploring workings (pits, ditches, adits, etc.), makes the surveys of exploring workings, assaying points, seam outcrops, bedding elements of mineral deposits and enclosin2 rock: and
12
Ch.
1. Subject-Matter
compiles (together with geologists) the graphical documentation representing the shape and bedding conditions of a deposit. Minesurveying plans and sections plotted by the results of geological prospecting are used for the calculations of mineral reserves and design of mining plants. Design and construction of mining plants. At the stage of mining plant design, the mine surveyor participates in construction surveying: the determination of the boundaries of mine fields according to the current regulations on land allotment; design of working systems and surface structures; development of measures for the protection of surface and underground structures against harmful influence of underground workings; compilation of the graphs of work organization and plans of mining work for the periods of construction and exploitation of a mining plant; and the calculations of the losses and industrial reserves of minerals. At the stage of mining plant construction, the mine surveyor is engaged in a wide circle of problems associated with transferring the design data into nature (levelling of a pay-out area, layout of the centres and axes of shafts and mining complexes, location of roads, etc.). He performs control on the construction of hoisting complexes, sinking and equipment of shafts, driving of permanent workings, etc. Exploitation of deposits. The role of the mine surveyor at the stage of exploitation is extremely important and includes the following operations: surveying of workings; assigning of directions to workings; compilation of plans by the results of surveys; control of the mining work in accordance with the design specifications and safety regulations; surveys for the connection of surface and underground reference nets; continuous control of the completeness of mineral extraction; observations on rock displacements and rock pressure; development of measures for the protection of structures, natural objects and mining workings against the harmful effect of
of
Mine
Surveying
mining operations; reclamation of land; planning of the preparatory and stoping mining work; development of quarterly, annual and perspective plans of the mining work; and calculations of the balanced and industrial reserves, losses, and dilution of minerals. When a mine is to be abandoned, the mine surveyor has to determine whether the mineral has been extracted completely, to survey underground workings, and to prepare complementary mining plans. He also arranges the field books of underground surveys and mine orientations and prepares the main plans of the mining work for storage. 1.2. Brief Notes on History of Mine Surveying Mine surveying actually appeared as soon as Man learned to do the underground mining work. Historical manuscripts, archeological findings, and other materials have given evidence that people of the antiquity were quite familiar with the art of construction of fairly intricate mines and other underground objects. It may be referred, for instance, to a 3500-years old Egyptian parchment showing a mine, which has been found in Italy. It is also known that Romans drove an adit about 6 km long to drain water from a lake. More than 100 vertical and inclined shafts were sunk for driving the adit, some of them being to a depth more than 100 m. This is a clear evidence that Romans were experienced well in mine surveying. The first description of methods of underground surveying that has survived to our times belongs to Heron of Alexandria (lst century B. C.). These methods included various measurements, plumbing, and construction of chains of regular geometrical figures (for instance, similar triangles) on the surface and underground, by means of which it was possible to orient underground workings.
1.2.
Brief
Notes
on History
In the 16th century A. D. when the magnetic needle compass came into use, mine surveying became more efficient and accurate. At that time, Agricola (Georg Bauer, 1494-1555),a famous German scientist, published the book De re metallica libri XII where Chapter V was devoted to the surveys of mining workings by means of a compass with the circle divided into 12 sectors and by other methods. In particular, he described the method of measuring the depth of a mine or the length of an adit by means of an inclined cord and plumb bobs. Mine surveyors of those times still could not calculate the coordinates of the angular points of surveys. Initially, there were no survey plans, and the mine surveyor contented himself with making the same survey on the surface as underground (in a mine) and could decide on the development of the mining work relative to the boundaries of allotment by the positions of survey points on the surface. The plans of the mining work came into common use in Germany at a substantially later time, in the 17th century. At the end of that century, two kinds of the mining work plans were employed: those plotted in the plane of a seam or vein and those made as projections onto a vertical plane. The mining work plans of that period were however oriented by a magnetic meridian. Only from the mid of the 18th century when the phenomenon of magnetic declination was discovered (August Beyer, Von Bergbau Grundlicher Unterricht, 1749),mine surveyors were obliged to abandon the use of the magnetic meridian and change to the orientation of mine surveys by an astronomic meridian. In Germany, the compass with sight vanes was designed in the 16th century and the suspension compass, in the 17th century. These instruments (the latter in combination with a suspension semicircle) were for many centuries the most common mine-surveyor's
of Mine
Surveying
13
instruments and are sometimes used in modem mine-surveying practice. With the suspension compass and suspension semicircle, it was easier to construct underground surveying nets; instead of a number of triangles, it was now sufficient to layout a broken line in an underground working by means of a cord. Practical mine surveying was given a strong impetus in the 1840's when work was undertaken to drive long adits near Freiberg and Harz in Germany. Prof. Weissbach and mine surveyor H. Borchers, who participated in the work, proved the applicability of theodolites and level instruments for mine surveying. These adits had a large length, intersected many mines, and were driven from many points by meeting faces. To perform this work, a detailed triangulation was carried out on the surface, which provided a single coordination network for all the mines involved. Levelling surveys carried out together with triangulation made it possible to relate all points to a single elevation system. Roughly at the same time, the methods of precise orientation of underground surveys were developed. In the 19th century, theodolites and levelling instruments came into wide use in mine-surveying practice in Germany. New mine-surveyor's instruments appeared, such as box compass, mirror compass, projecting plates, and large-Iength tapes for measuring the depths of mine shafts. In the second half of the 19th and the beginning of the 2Oth century, well equipped works for ~aking mine-surveyor's instruments were put into operation in Germany (Hildebrandt, Fennel, Zeiss). New methods of mine surveying and estimation of observed results were developed, in particular, the method of connection surveys with connection triangles, method of symmetrical junction, and the method of range lines with the use of the Weiss sleigh. Studies were carried
14
Ch
Subject-Matter
out on the effect of air currents on the positions of plumb bobs in the orientation of deep shafts (Wilski's hypothesis). In the first half of the 2Oth century, gyroscopic instruments came into use for the orientation of underground surveying nets. The first attempts for mine orientation by gyroscopes were undertaken in 1913-14 in Poland and Germany. At the beginning of the 192O's,a mine-surveying gyroscope was designed and manufactured in Germany, but turned out to be inefficient. Wide application of gyroscopic orientation dates to 1947 (Germany). The earlier makes of mine-surveying gyroscopes had certain drawbacks (large mass and dimensions, uncertain readings, etc.). In recent years, successful work on the design of gyrocompasses, gyrotheodolites and gyroscopic attachments has been completed in a number of countries. Gyrotheodolites have been employed efficiently for the orientation of underground surveying nets. In the post-war years, many mine-surveying instruments were improved, and new instruments based on utterly nowel operating principles were developed, such as highprecision theodolites, self-adjusting levels, coded theodolites, optical and radio range finders, and laser instruments. Much work has been done on the development of instruments for stereophotogrammetric surveys which are finding wide use in many countries for underground surveying. In recent time, the mine-surveying office work has been largely mechanized by the application of desk calculators, electronic computers, etc. Programs for solving minesurveying problems in powerful electronic computers have been worked out. Mine surveying is essentially an information science,and accordingly it has started to widely employ various automatic systems for data collection, storage, processing and transmission. In modern mine surveying, there is a strong trend to increase the observations on
of Mine
Surveyin
rock displacements in underground and open-cast mining. The movements of the Earth's surface under the effect of underground workings were noticed already in the 15th and 16th centuries, but attracted a keen interest of mine surveyors in the 18th century and especially in the 19th century in Belgium where the mining work began to endanger surface buildings and water-supply system in Liege. In the second half of the 19th century, the investigations of the laws of rock subsidence and caving were started, which resulted in the hypothesis of normals proposed by Toilliez in 1838. Another hypothesis was suggested by Gonot in 1858, according to which the displacement of a worked-up rock layer proceeded along the normals to the seam. In 1885, H. Fayol proposed the hypothesis of cupola based on the idea that the zone of rock subsidence was confined by a cupola (dome-shaped) space. At the end of the last century, J. Jicinsky marked in his works that the process of rock displacement should be influenced by the thickness of a seam, dipping angle, depth of the mining work, and properties of overlying rock. Of large significance for understanding properly the process of rock subsidence was the hypothesis suggested by R. Hausse (the end of the 19th century), which considered two zones of rock subsidence: the cave-in zone and bend zone. In the first quarter of this century, the problem of rock displacements was investigated by a number of researchers. 0. Donahue determined a number of subsidenceangles. A. Goldreich discovered certain differences in the subsidence of bed rock and detrital deposits. H. Briggs found the correlations between the angles of rupture and the compression and rupture resistance of rocks and established that subsidence angles in hard and brittle rocks are steeper than in those having a lower strength. In recent time, much attention has been given to the methods of prediction of rock
1.2.
Brief Notes
on History
deformations. One of the first methods was proposed by Keinhorst and Bals and based on the assumption that a portion of worked-out area confined by subsidence angles acted by a definite law on each point of the Earth's surface. The progress of mine surveying owes much to the contributions of Russian and Soviet scientists. The first in Russia mining regulations were issued by v. Tatishchev in 1734. In 1763, M. Lomonosov published his book On M easurements of M ines, the first publication in the country which dealt thoroughly with all aspects of mine surveying of that time and was a part of the fundamental work Principles of M etallurgy or Mining. Lomonosov gave the descriptions of the suspension compass and suspension semi-circle, measuring rod, instruments for plotting mine-surveying drawings, etc. and solutions of various mine-surveying problems, in particular, the method of location of the surface of a vertical shaft to be connected to a system of horizontal underground workings. In 1773, a mining school was founded in St. Petersburg (now the Leningrad Mining Institute). It had a mine-surveying class where students obtained profound training in the subject. A major event in the history of mine surveying in this country was the publication, in 1847, of the book The Art of Mine Surveying written by P. Olyshev, professor of the St. Petersburg mining school (1817-1896). The author gave the description of a theodolite with an eccentric telescope and of a geodetic level, proposed the procedure for the calculation of the coordinates of theodolite traverses, and solved the problem of driving an underground working by meeting faces. The introduction of theodolite surveys into the mine-surveying practice and the preparation of mine plans by point coordinates were of extreme importance for further progress in
of Mine
Surveying
15
the methods and techniques of underground surveys. Another important stage in the development of mine surveying is associated with the name of Prof. V. Bauman (1867-1923),author of a number of fundamental works, such as A Course in the Art of Mine Surveying (in three volumes), On the Problem of Faults. Shifts and Other Types of Displacement of Veins and Seams. On the Problem of Evaluation of M ineral and Ore Deposits, etc. An exceptionally great contribution to the mine-surveying science was done by I. Bakhurin (1880-1940).He worked out a number of issues in the theory of errors and the method of least squares and their applications for the estimation of accuracy and equation of mine surveys. Bakhurin was concerned with practically all aspects of mine surveying: survey control of workings driven by meeting faces;theory of cumulative errors in underground polygons; theory of random errors and method of least squares; theory of physical (in particular magnetic) and geometric orientation of mines; errors of orientation via one or two vertical shafts; mine-surveying instrumentation; rock displacements; etc. The results of his studies were~ummarized in the book A Course of Mine-Surveying Art (1932). The progress of mine surveying in this country is also associated with the name of Prof. P. Sobolevsky (1868-1949) who is responsible for a new branch of mine surveying which has later formed into an individual discipline, mining geometry. The development of mine surveying in recent time, and especially in the last two or three decades of the total scientific and engineering progress, has been associated with the improvement of existing and design of principally novel instruments, systems and techniques of field and office work. The scientific and applied aspects of mine surveying are being developed intensively. Minesurveying problems are solved with wide use of electronic computers and automatic devices.
Chapter Two General
2.1. General
Figure Control
Figure
of the Earth, Systems of Coordinates, and Survey Underground Nets and Surface Surveys
of the
Earth
The physical surface of the Earth is far from having a simple shape. Of the total area of the Earth's surface equal to 510 mln kIn2, 71 per cent fall on the bottom of seas and oceans and 29 per cent, on the land. Both the oceanic bottom and the continents have an intricate relief, especially the former. As has been found by investigations, the Ocean in some places has depths more than 10 kIn. Some regions of the land reach altitudes up to 7-8 km. The analysis of the depth of the Ocean and altitudes of the land on the basis of l-kIn height intervals has demonstrated that their distribution has two distinct peaks: one at altitudes of loo m above the level of the Ocean and the other at roughly 4.5 kIn below that level. It has been concluded on that basis that the surface of the Earth consists of two sharply distinct morphological elements: continents and oceans, the natural boundary between these elements being at a depth around 1.5 km below the level of the ocean. Further, the local irregularities of the surface relief make the shape of the Earth's surface extremely complicated so that the figure of the Earth can hardly be described mathematically. Noting that the surface of water of the Ocean has a rather simple shape and occupies almost 3/4 of the Earth's surface, it would be reasonable to assume the figure of the Earth as the body confined by the water surface of the Ocean. When determining the position of a point on the physical surface of
the Earth, this point is usually related to the general figure of the Earth which is understood in geodesy and mine surveying as the figure obtained by mental continuation of the still water surface of the Ocean. The surface obtained in this way is called the level surface. Its principal property consists in that the potential of the force of gravity on that surface is the same in all points, i. e. the surface is always perpendicular to an upright (vertical) line, and therefore, is horizontal everywhere. In the general case, it is possible to draw an infinite number of level surfaces at different distances from the Earth's centre, but one of these surfaces, i. e. that coinciding with the mean level of the Ocean and continued at that level under the continents, forms a figure that is taken as the general figure of the Earth and called the geoid. Since the direction of an upright line may depend on a number of factors, the geoid has a complicated structure. The principal among these factors is that the force of terrestrial attraction is variable, since the Earth's radius diminishes at the poles and since the rocks of the Earth's mantle have different density. The variations in the force of gravity are mainly due to the former reason (smaller radii of the Earth at the poles), though the latter reason may have an essential effect in some cases. The geoid has flattened portions (oblateness) near the poles, and its shape is too complicated for mathematical description. The results of satellite observations have shown that the oblateness, expressed as the difference between the lengths of an equatorial and polar diameter. attains 42 km
2.2.
Geographic
System
of
17
Coordinates
by the formula: a=(a-b)/a
Fig. 2.1
Ellipsoid
pI of revolution
of spheroid
770 m. It has also been established by satellite observations that the Earth has a pyriform (pear-Iike) shape: the South pole has turned out to be nearer by 45 km to the Earth's centre than the North pole. In addition, the South pole is located 25 m 80 cm below the surface of oblated sphere, whereas the North pole protrudes by 18 m 90 cm above that surface. Measurements have also demonstrated that the Earth has 'recesses'and 'ridges' which are traced clearly against the profile of the complicated figure of the geoid. The largest 'recesses'are located to the south-west of India (depth 59 m) and near the Antarctic continent (30 m). The highest ridges are located near New Guinea (57 m) and in France (35 m). It has also been established that the Earth's equator is not circular, but elliptical with one of its 'diameters' being larger by 200 m than the other. In view of these circumstances, the idea of using the geoid as the basis for geodetic calculations has been renounced. Among regular mathematical surfaces, the one that can approximate most closely the geoid surface is an ellipsoid of revolution obtained by the rotation of an ellipse on its minor axis. This figure is called the Earth's ellipsoid, or spheroid. The dimensions of the Earth's ellipsoid (Fig. 2.1) can be characterized by the lengths of its major and minor half-axes, a and b, and by the oblateness a which can be deteri:nined 2-1270
When plotting the portions of the Earth's surface on maps and plans, an important matter is to choose the proper dimensions for the ellipsoid which will approximate the geoid and onto whose surface the physical surface of the Earth with all its natural and artificial details will be projected. Many attempts have been made to determine the dimensions of an ellipsoid to approximate most closely the geoid (the first in 1800 by J.-B.J. Delambre, a French mathematician). An ellipsoid of particular dimensions and oriented uniquely in the Earth's body, onto whose surface the results of topographic, geodetic and mine surveying work are transferred in a country, is called a reference ellipsoid (local ellipsoid). 2.2. Geographic System of Coordinates The positions of points on the surface of the Earth or spheroid are determined by means of geographic coordinates, i. e. geographic latitude
Fig.
2.2
Geographic
system
of coordinates
18
Ch. 2. Systems
of Coordinates,
The longitude is the dihedral angle between the plane of Greenwich (zero) meridian and the meridional plane of a point p and the latitude is the angle made by a vertical line in a point p to the plane of equator. The plane passing through the centre of the Earth and perpendicular to the axis of rotation is called the equatorial plane. The plane passing through a vertical line and the axis of rotation of the Earth (or parallel to the latter) is the plane of a geographic ( astronomic) meridian. The lines of intersection of the planes of geographic meridians with the Earth's surface are called meridians. The lines formed by the intersection of planes drawn perpendicular to the axis of rotation of the Earth with the Earth's surface are called parallels of latitudes, or simply parallels. The network of meridians and parallels applied on the surface of the Earth ellipsoid represents the coordinate axes of the geographic system of coordinates. If the geographic coordinates are determined by astronomic observations (independently in any point on the Earth's surface), they are conventionally called astronomic geographic coordinates «p, /I.).The positions of points on the Earth's surface can also be determined by means of geographic coordinates obtained by geodetic observations and related to a normal to the ellipsoid surface; tt.ese are termed geodetic geographic coordinates and denoted as B (latitude) and L (longitude). Since the surface of the geoid does not coincide with that of the ellipsoid, normals drawn to the surface of the latter turn out to deviate from the directions of upright lines. The magnitude of deviation may be equal to 3-4" on the average. Noting that the difference of latitudes of 1" on the Earth's surface corresponds to a linear distance of 31 m, the positions of points on the Earth's surface, when given in astronomic and geodetic geographic Foordinates, may differ by 100 m on the average.
Nets and Surface
Surveys
In the general case, when the deviations of upright lines are neglected, geodetic and astronomic coordinates are replaced by the generalized concept of geographic coordinates. In geographic coordinates, longitudes can be reckoned: (I) eastward and westward of the Greenwich meridian, from 00 to 180°, and are called respectively easterly and westerly longitudes; easterly longitudes are considered to be positive and westerly ones, negative or (2) only eastward of the Greenwich meridian, from 0° to 360°, and are always called easterly longitudes. Latitudes may vary from 0° to 90° and are reckoned north and south of the equator. The former are considered positive and the latter, negative. 2.3. System of Coordinates
Plane
Rectangular
Geographic coordinates are expressed in angular values. They are inconvenient for engineering calculations in geodesy and mine surveying. Besides, the linear measurements of angular values turn out to be different in various portions of the Earth's surface. For these reasons, a system of plane rectangular coordinates seemsto be more convenient for land and mine surveying and solving various engineering problems when their results should be plotted on maps and plans. Such a system can largely simplify topographic and mine surveying, adjustment of reference nets, calculations of coordinates of reference points, processing of the results of surveys, etc. The plane system of coordinates also ensures precise coincidence of plans of adjacent areas, etc. The initial lines in a system of plane rectangular coordinates (Fig. 2.3) are two mutually perpendicular lines xx-yy lying in a horizontal plane and called respectively the axis of abscissae (x-axis) and the axis of ordinates (y-axis}. In contrast to mathe-
2.4.
National
System
of Rectangular
Coordinates
19
Fig. 2.3 System of plane rectangular coordinates
matics, the axis of abscissaein land and mine surveying plans is arranged vertically and coincides with the direction of a meridian. The intersection of these axes is the origin of coordinates (point 0). The coordinate axes divide the plane of a drawing into four quadrants which are numbered clockwise beginning from the guadrant in the north-east section (see Fig. 2.3). The abscissax and ordinate y of points are the lengths of the perpendiculars drawn from these points onto the coordinate axes. The signs of coordinates depend on the quadrant in which the points are located. The abscissae of the points located in the first and fourth quadrant are positive and of those in the second and third quadrant are negative. The ordinates of the points in the first and second quadrant are positive and of those in the third and fourth quadrant are negative. ,.
In land and mine surveying, the portions of the Earth's surface measuring up to 10 km in radius are considered to be flat (distortions along the length are not more than 1 cm and angular distortions, not more than 0.1"). The larger areas of the Earth's surface are depicted, to minimize distortions, in special projections in which the Earth ellipsoid is conventionally developed on a plane. In addition, the projection on a plane is done in such a way as to provide the coincidence of both geographic and rectangular coordinates. 2.4. National System of Rectangular Coordinates When the territories of a substantial area are to be represented in topographic maps, the surface of the reference ellipsoid must be
20
Ch. 2. Systems
of Coordinates,
developed in a plane. This procedure cannot however be done without cutting and folding the spherical surface being developed. The problem is solved by using an auxiliary surface which can be easily developed in a plane, such as a cylinder or cone. The portions of the reference ellipsoid are projected onto an auxiliary, geometrically regular surface (cylinder or cone) and this is then developed without folds and cuts. For more convenience, the auxiliary body is supposed to be tangent to the reference ellipsoid, and the network of meridians and parallels of the reference ellipsoid is transferred (projected} onto the surface of the body to form a cartographic grid on the map. Mter the cartographic grid has been transformed onto the auxiliary tangent figure, the latter is cut and developed in a plane. The method by which the image of the Earth's surface is transferred from the sphere onto the plane is called a cartographic projection. Cartographic projections involve certain distortions of geographic objects relative to their shape on the reference ellipsoid. By the nature of distortion, modern cartographic projections can be divided into equiangular (equal-angle), equivalent (equal-area) and their derivatives. In equiangular projections, angles are not distorted, and therefore, projected figures retain their similarity to the original ones. In equivalent projections, the areas remain equal, but the angles are distorted, and therefore, the outlines of figures are distorted too. In derivative projections, both angles and areas are distorted, but only moderately. Cartographic projections are studied by mathematical cartography where they are considered on a formalized basis as certain analytical relationships between the coordinates of points on tM.esurface of a reference ellipsoid and the coordinates of their projections on a plane. In the general form, these relationships can be written as x = f1 «p, 1..) and y = f2 «p, 1..);they correlate the rectan-
Nets and Surface
Surveys
gular coordinates of points on a plane and the geographical coordinates on the reference ellipsoid. 2.4.1. Gauss Conformal
Projection
Among many requirements set forth to cartographic projections for topographic maps, the principal one is that projection distortions should not exceed the errors of corresponding geodetic measurements. This condition is approached most closely in the conformal projection proposed in 1820 by C. F. Gauss of Germany. It is based on the theory of plane conformal coordinates, which makes It possible to obtain almost undistorted images of the terrestrial ellipsoid on a plane. The essence of the Gauss conformal projection consists in that the terrestrial ellipsoid is enveloped by a tangent cylinder whose axis is perpendicular to the minor axis of the ellipsoid. With this arrangement of the cylinder, it touches the ellipsoid along a meridian which is a common line of both figures (Fig. 2.4). Other meridians, when transferred (projected) onto the cylinder, will be increased in length. With moving father from the tangent (central) meridian, i. e. from the centre of zone, lengths will be distorted more and more, and their distortions can be determined by the formula: L\l=l
, y2 2R2
where 1is the length of a section on the Earth ~phere; y is the length of an arc from the central meridian to the given section; and R is the Earth's radius. With the use of the Gauss conformal projection, the surface of the terrestrial ellipsoid is represented on a sheet of paper in the form of individual figures as those shown in Fig. 2.5, which are called zones. As has been established, the optimal zone for transferring onto a tangent cylinder is a spheroidal
2.4.
National
System
of Rectangular
dihedron included between two meridians with the longitude difference 6°. Thus, the surface of the Earth is divided into 60 zones, a tangent cylinder being drawn to the central (axial) meridian of each zone. The surface of the spheroid within the limits of a particular zone is projected conformally onto the surface of the cylinder. 2.4.2. Zonal System of Rectangular
Coordinates
21
of a zone (see Fig. 2.6). Ordinates calculated from this new origin are called reduced ordinates. If, for instance, the ordinates of two points of the eighth zone relative to the central meridian are Yl = 23730.00 m and Y2 = -102280.00 m, the reduced ordinates will be: Yl = 23730.00 + 500000.00 = 523730.00 m Y2 = -102280.00 + 500000.00= 397720.00m
Coordinates
The origin of coordinates in each zone is taken at the intersection of the central meridian of that zone with the equator (Fig. 2.6). The central meridian is the x-axis, and the image of the terrestrial equator perpendicular to the central meridian is the y-axis. The x-coordinates of points to the north of the equator are considered positive and of those to the south, negative. The y-coordinates of points to the east of the central meridian are positive and of those to the west, negative. The longitude of the central meridian is found by the formula: Lo = 6N -3°, where N is the zone number. The western boundary meridian of the. first zone coincides with the Greenwich meridian. In order to eliminate negative ordinates, the origin of coordinates is transferred by 500 km to the west from the central meridian
Since the same numerical coordinates may exist in all 60 zones, it has been agreed to relate the coordinates to a particular zone by
Fig.
2.6
Zonal
system
of rectangular
coordinates
22
Ch. 2. Systems
of Coordinates,
writing the number of a zone before a coordinate. In the cases considered above, the ordinates of points located, say, in a zone No.8, should be written as follows: Yl = 8523730.00 m and Y2 = 8397720.00 m An important problem in mine surveying is how to choose properly the directions of coordinate axes. In the Cartesian rectangular system, the Z-axis is always vertical and directed upward, whereas the axes Ox and Oy are perpendicular to each other and lie in the horizontal plane. The orientation of these two axes must not be arbitrary. If the direction of one of these axes is specified, this will uniquely determine the direction of the other axis. In land and mine surveying, the Ox-direction is usually chosen (oriented in the horizontal plane) so as to satisfy the following conditions: (a) the direction of Ox-axis must be easily and precisely reproducible and (b) the direction of Ox-axis at various mining enterprises must permit the coincidence of plans of individual mines and larger enterprises. The following cases of orientation of the Ox-axis for mine surveying plans are possible: (a) orientation by a magnetic meridian; and(b) orientation
. by an astronomic
meridian;
(c) orientation by the central meridian within each zone of the national system of coordinates. Orientation by (a) and (b) cannot satisfy the requirements given above, since the magnetic azimuth is not constant in time and space, and the astronomic azimuth is not constant in space. On the contrary, the central meridian retains its orientation and position within the limits of a zone. Thus, the orientation of the x-axis should be preferably done relative to the central meridian of a zone.
Nets and Surface
Surveys
In some cases, however, the x-axis can be temporarily oriented relative to the magnetic or astronomic meridian. In exceptional cases when the survey work is carried out in an uninhabited region, is not large in scope, and there are no triangulation points, the x-axis can be oriented by the direction of a magnetic needle, though orientation by the astronomic meridian is more preferable in such cases. Mine survey plans obtained with this orientation can be used for many years. In contrast to magnetic declination, meridian convergence remains constant in time. In some kinds of mine surveying work, a conditional system of coordinates can be adopted, with the Ox-axis directed arbitrarily, for instance, along a line fixed by survey points. The conditional systems of coordinates are used in the mine survey servicing of construction of shafts and hoisting complexes, orientation of mines via two shafts, and in a number of other cases. 2.5. Geodetic
Reference
Nets
The mine survey servicing of mining enterprises is unfeasible without a network of reference points whose positions on the land are determined with a high precision. The measurements on the surface and underground involve errors which are accumulated if surveys are being done on individual areas not associated with one another. When represented on general mine survey plans or topographic maps, these areas will then be distorted to such an extent that the results of surveys become useless. In that connection, mine surveying is carried out by the principle 'from the general to particular', i. e. by providing first a general geodetic net on the territory of a country and then reference survey nets for surveying of individual small isolated areas. Points established on the surface and having precisely fixed coordinates are called reference (control) points. or base stations.
2.6.
National
Points ensuring the correct horizontal representation of the land surface are called plan (planimetric) control points, or horizontal control points. Those which can characterize the vertical relief of the land surface are called elevation (height) control points. A system of reference (control) points established on the territory of a country makes up a geodetic net. Geodetic nets can be divided into national nets, bridging (densification) nets, and survey nets. Mine survey nets on the territory of economic interests of mining enterprises consist of the P9ints of the national geodetic net and geodetic nets of mine surveying and topographic surveying carried out for servicing of mineral prospecting and construction and exploitation of mining enterprises. Some kinds of geodetic work on the land surface are carried out by mine surveyors. They include: the development of the existing mine survey reference nets as required for the surveys of mines and quarries; surveys of the pay-ore areas of mining enterprises; periodical layout, survey and levelling during the construction of minIng enterprises and exploitation of deposits in order to reflect current variations on mine survey plans; surveys of rock dumps and stocks of mineral; surveys for determining the volume of earth-moving work, for the reconstruction of railway tracks and other structures; surveys for observing rock displacements, stability of structures, etc. 2.6.
National
Geodetic
Nets
A national geodetic net may consist of triangulation, trilateration, polygonometric and levelling nets. A plan (horizontal) geodetic reference net is mainly constructed by the method of triangulation, i. e. by laying out triangles on the land surface. In each triangle, all three angles are measured, which ensures a reliable control of angular field measurements. For deter-
Geodetic
Nets
mining linear dimensions, the length of one side of a triangle is measured (taped) and the lengths of the other two sides are calculated. The triangles of a net are arranged in a certain order, and their shape should be close to equilateral where possible. The vertexes of triangles are fixed on the land by special station markers fastened in the ground. A metallic or wooden beacon (tower) is constructed above a station marker. It carries a cylinder at the top whose axis should be coincident with that of the marker. The cylinder serves as the sighting target when making observations from other points. The triangulation method makes it possible to determine the horizontal (plan) coordinates for the vertexes of triangles. Triangulation rows which consist of triangles with an average side length of 20-25 km form firstclass triangulation chains up to 200.km long (Fig. 2.7). Triangulation chains are laid off in submeridional and sublateral directions so as to form the closed polygons of a peripheral length up to 1000 km. The side lying at the intersection of several chains (ab in Fig. 2.7) is a common of these chains and called the initial side. Initial sides must be measured with a high accuracy. Since it is practically impossible to measure lines 20-25 km in length on the land surface, it is common practice to measure not an initial side, but a transverse side around 6 km long (ed in Fig. 2.7), which is called the triangulation base. In the base figure adbe, all interior angles are measured, and the length of the initial side is calculated by the known angles and the known length of the base line. In first-class triangulation, the latitude and longitude of the points at the ends of the initial side and the astronomic azimuth of that side are additionally determined by astronomic observations. The territory within polygons of first-class triangulation chains is filled in with a continuous network of second-class triangulation triangles with the lengths of sides ran-
24
Ch. 2. Systems
of Coordinates,
Nets and Surface
Surveys
Class 1 chain
(i
/\
.~ .0= "
,
11
: la u
~
b
~1
~2
C!J3
~4
Fig. 2.7 Development of triangulation network: 1, 2, 3. 4-triangulation second, third, and fourth class
ging from 7 km to 20 km depending on the pattern of terrain. In second-class triangulation, base lines are measured in one of every 20-25 triangles. As in the first-class triangulation, the latitudes and longitudes and astronomic azimuth of base lines are determined by astronomic observations. Further densification of a plan control geodetic net is carried out by third- and fourth-class triangulation. The characteristics of reference nets constructed by Ist-4th class triangulation are given in Table 2.1. In poorly accessible regions and densely
points of respectively first,
built-up territories, a geodetic net consists of polygonometric traverses in the form of broken lines representing closed or open polygons (Fig. 2.8). In that case, field work consists in measuring the angles in turning (change) points and the lengths of all polygonometric sides. Polygonometric nets are usually constructed by laying off the main and diagonal polygons having common change points (5 and 19 in Fig. 2.8). The required accuracy of polygonometric nets can be characterized by the data given in Table 2.2.
2.6.
National
Geodetic
25
Nets
Table 2.1 Triangulation class
Side length, km
Mean angular error (by triangle misclosures),
s
Permissible triangular misclosure, m
Mean ing
measurerror
base
(clos-
ing)
sides
of
Mean measuring error of base
1 2 3
Fig. 2.8 Polygonometry: 5, 19-common tion points; K, L, M -triangulation points
junco
Polygonometry as a method for the construction of geodetic nets has become popular in recent years, with the appearance of high-precision light and ratio range finders,
which have largely facilitated linear measurements, the most labour-consuming procedure in land and mine surveying. Another popular method for the construction of planimetric geodetic nets is trilateration. Its essencereduces to the construction of a network of triangles (as in triangulation) and measuring of the lengths of their sides (rather than angles). The latter are calculated from the known lengths of three sides. With the known angles and the measured length of one side (which is taken as the base line), the lengths of the other sides are calculated, after which the coordinates of trilateration points are determined. In trilateration, lengths are measured by means of range finders which can ensure a high accuracy of linear measurements (up to 1/400000). The elevation (height) control of various land and mine survey operations is ensured by levelling nets which may be of class I, II,
26
Ch. 2. Systems
To
be with
II III IV
of Coordinates.
performed highest
precision
500-600 150-200 25
s.JL IO.JL 20JL
III and IV. First- and second-class levelling nets are the main basis for establishing the general system of elevations for the entire territory of the country. Third- and fourthclass levelling nets are the basis for topographic surveys and for the solution of various problems associated with geodetic and mine survey servicing of civil and industrial construction objects. The general characteristics of national levelling reference nets are given in Table 2.3. The permissible misclosure (mm) of traverses in local geodetic reference nets constructed by technical levelling is equal to 50JL ' where L is the length of a traverse line, km. Fundamental bench marks of a natural levelling net should be established with a density ensuring that every subdivision map plotted on a scale 1/5000 include at least one bench mark. With topographic surveys on a scale 1/2000, the density of fundamental bench marks should be such as to allow one bench mark for one-four map sheets. First-class levelling is carried on the land along the directions essential for the national economy and defence of the country and relates to the most precise kinds of geodetic work. Accordingly, it must be carried out with the use of the most precise instruments. In modern levelling, random and systematic
Nets and Surface
Surveys
errors do not exceed 0.05 mm per kilometre of the levelling line. Second-class levelling is carried out by running polygons connected to the points of first-class levelling and attaining a length of 500-600 km. The main object of second-class levelling is to provide the precise basis for third- and fourth-class levelling. In levelling nets of class II, the perimeters of polygons and the lengths of level lines should not exceed 40 km and the lengths of lines between junction points, 10 km. In third-class levelling lines, the lengths of lines between higher-class levelling points shoud not exceed 15 km and of those between junction points, 5 kill. The lines of levels should be connected with one another at every 3 km in built-up territories or at every 5 km in free territories. The height marks of triangulation and polygonometric points of all classes and of points of local plan reference nets are perrnitted to be determined by class IV levelling. Trigonometric levelling is permissible for the determination of the heights of reference net points in exceptional cases,such as in mountainous regions. The levelling lines of all classesare fixed on the land by means of ground and wall bench marks. The bench marks in the levelling nets of class I, II and III must be spaced at intervals of 5-7 km. Fourth-class levelling is done by wall and ground bench marks and polygonometric stations. Wall and ground bench marks are established with intervals not more than 300 ill in built-up areas and not more than 0.5-2 kill in free territories. In levelling lines run through settlements, at least one bench or wall mark should be established in a settlement. 2.7.
Geodetic
Bridging
Nets
Geodetic bridging (densification) nets are developed on the basis of geodetic net points and serve for the surveys of land surface on
2.7.
Geodetic
Bridging
27
Nets
Table 2.4 Parameter
First order
Triangulation Side length of triangles, km Maximum relative error for base side Maximum misclosure of triangle Mean measuring error from triangle misclosures Maximum length of chain of triangles, km
0.5-5.0 1/500000 ::!:20" ::!:5" 5
Second order
0.25-3.0 1/20000 :1:40" :1:10" 3
Trilateration Side length of triangles, km Maximum relative error of side measurement Minimum angle of triangles Maximum length of chain of triangles, km
0.5-5.0 1/20000 20° 5
Polygonometry Maximum length of traverses, km Maximum perimeter of polygonometric traverses in free networks, km Length of side of traverse, km Maximum length of traverse from nodal point to highest-class or highest-order point, km Maximum number of sides in traverse Maximum relative misclosure of traverse Mean measuring error of traverse
scales 1/5000 to 1/500 and for performing various kinds of mine survey work. Planimetric geodetic bridging nets can be constructed as analytical nets or polygonometric nets of the first or second order. Their main characteristics are given in Table 2.4. Analytical nets can be formed by triangulation as a continuous network or chains of triangles or intersections (bearings). Analytical bridging nets of the first order can be developed on the basis of geodetic reference nets of classes I, 2, 3 and 4; those of the second order can be developed on the basis of reference nets of all classes and a firstorder analytical net. The analytical nets of the first order may have the sides from 0.5 km to 5 km long and those of the second order, from 0.25 km to 3 km long. The angles
0.25-3.0 1/10000 20° 3 3
15 0.12-0.60
3 15 110000 :t5"
9 0.80-0.30 2 15 1/5000 :t10"
of triangles should be not smaller than 30°, and the number of triangles in a chain should be not more than 10. If the territory to be surveyed has no available points of geodetic plan control (of any class), it is permissible to develop the independent survey nets of the first or second order for land and mine surveying. In that case, it is required to measure at least two base sides separated from each other by at least 10 triangles. The polygonometry of the first and second order can be developed in the form of individual traverses or a system of traverses with junction points belonging to the national geodetic referencenet or first-order analytical net. Of special significance are approach mine surveying points in reference nets. The ap-
28
Ch. 2. Systems
of Coordinates.
proach points must ensure the possibility of running a hanging traverse with the number of sides not more than three to a mine shaft. Approach points should be located at distances not more than 300 m from the collar of a shaft. It is possible to use the points of triangulation, trilateration and polygonometric nets of class 1-4 or of first-order analytical nets as approach points. The pay-ore area of a mining enterprise should have at least three elevation bench marks with their heights measured by levelling of a class not worse than four.
Nets and Surface
Surveys
Table 2.5 Contour interval height, m
Level line length in technical levelling, km
0.5 1.0 2.0 5.0
3 10 15
Levelline length in trigonometric levelling, km
2 5
and on territories where linear measurements are complicated, the base points of a Planimetric and elevation survey nets are survey net can be deterniined analytically by constructed on the basis of points of a constructing a chain of triangles; by the geodetic reference net. In exceptional cases, methods of intersections and resections; or by when the area to be surveyed is not more constructing a central system of geodetic than 20 km2 for surveys on a scale of 1/5000 rectangles. or 10 km2, 1/2000, they can be based on the The angles in triangles should, as a rule, be points of a survey net only. not smaller than 30°. Side lengths should be Planimetric survey nets are developed by not less than 150 m. A direct intersection is running theodolite, tacheometric or plane- made from three points and a resection, by table traverses or can be constructed analy- four initial points. The misclosures of tritically. angles should be not more than I '. The The number of points of a survey net is relative error of initial sides in triangle chains determined by the scale of a survey map and should not exceed 1/2000. In closed areas, the should be equal, together with the points of a base points of a survey net can be deterniined geodetic reference net, to at least four points conveniently by running individual theodoper square kilometre of the territory for a lite traverses or a system of theodolite trascale 1/5000, 10 points for a scale 1/2000 or verses in which the points of a geodetic 16 points for a scale 1/1000. The errors of the reference net serve as junction points. location of survey net points relative to the Elevation survey nets are constructed by nearest points of a geodetic reference net geometric, technical and trigonometric should not exceed the accuracy of a surveying (geodetic) levelling. Geometric levelling is scale (i. e. should be not more than:!: 0.1 mm usually employed in areas with the height of on the scale of the map). contour interval of relief up to I m and Survey nets consist of base points and trigonometric levelling, with greater contour additional points, i. e. points determined in interval heights. The lengths of level lines the survey net proper. Each survey sheet supported by the levelling points of class I-IV should include at least three base points fixed and of closed level lines should not exceedthe by fundamental marks for a scale of 1/5000, values given in Table 2.5. at least two such points for a scale 1/2000 or one point for a scale 1/1000. In open areas 2.8.
Geodetic
Survey
Nets
2.9.
General
Data on Surveys
2.9. General Data on Surveys The results of survey work on the surface are used for plotting maps and plans required for mineral prospecting, solution of problems of design and construction of mining enterprises, and for safe and efficient exploitation of deposits. These plans and maps, drawn on a scale 1/5000-1/500, should show all objects specified by the rules of compilation of topographic maps, as well as the specific objects of a mining enterprise, such as fall-throughs and cones of influence formed owing to mineral extraction; rock outcrops on the surface; boundaries of miDing allotments, etc. The scale of surveying is chosen depending on the kind of mining work to be carried out in the area. For instance, for detailed prospecting and exploitation of large-sized deposits, the surveys of the land surface should be made on a scale of 1/5000 for a simple relief with vertical contour intervals of 1 m or 2 m or 1/2000 for an intricate (mountainous) relief with 2-m contour intervals. For the deposits of small size and for the large deposits of an intricate geological structure, the recommended scale of surveying is 1/2000. The surface of small-sized deposits and of moderate-sized ore bodies of an irregular shape should be surveyed on a scale of 1/1000 or 1/2000 with vertical contour intervals of 0.5 m or 1 m. The land surveys for making construction projects and for the construction of mining enterprises should be carried out on the following scales: (a) 1/5000 with I-m or 2-m vertical contour intervals, for the development of engineering projects; (b) 1/1000 with 0.5-m vertical contour intervals (or in exceptional cases, 1/500), for making working drawings; and (c) 1/1000 or 1/2000 with vertical contour intervals of 0.5 m or 1 m, for the design and construction of mining enterprises and settlements.
29
Land surveys must be car:ried out with such an accuracy that the mean error of positions of clearcut objects and land contours on maps and plans is not more than :1:0.5 mm or, for mountainous regions, :1:0.7 mm. The mean errors of surveying should not exceed 1/4 of the height of contour interval for flat-relief areas (with angles of dip up to 2°) or 1/3 for a rugged relief. The mouths of shafts, pits, adits and other mining workings should be shown on plans and maps with an error of location not more than 1 m in plan and 0.3 m in elevation irrespective of the survey scale. Survey nets serve as the basis for terrestrial surveys which can be carried out by various methods and instruments. Aerophotogrammetric survey (aerial surveying) is a progressive method for making topographic maps and plans. It is carried out by making large-sized photographs by means of a special aerial photographic camera mounted on board an aircraft. Recently, special survey aircraft have been employed for the purpose, which are equipped with perfect photographic cameras, navigation instruments, and an on-board computer which controls automatically the photographic process, i. e. the frequency of taking photographs and the exposure. The variations of the terrain relief are detected by a radar system. When taking aerial photographs, the aircraft flies forth and back along straight courses (flight lines or strips) so that each next photograph overlaps the preceding one (forward overlap) by 60 per cent and the photographs of adjacent flight lines (side overlap) by 40 per cent. Aerial photographs obtained in this way are processed by office analysis for compiling topographic plans and maps. To ensure the specified accuracy of topographic plans, aerial surveying must be carried out to meet the following requirements: 1. The optical axis of a camera must not
30
Ch. 2. Systems
of Coordinates,
Nets and Surface
Surveys
according to Table 2.6 depending on the kind of relief and the purpose of topographic plan. In tacheometric surveying, the instrument is set up at a fixed point called a station o o (Fig. 2.9) to measure the spatial polar coor"' dinates of so-called picket points on the terrain: an inclination angle v, inclined distance S to a picket point, and a horizontal angle 13between the initial direction and the direction onto the picket point. A staff is set up on picket points for surveying details. A picket for surveying of details is called a contour picket and that for relief surveying; an elevation picket. If the picket is used both for detailed and relief surveying, it is called an elevation-contour picket, or staff point. The distances from the instrument to the staff points and between the staff points depend on the scale of surveying and vertical deviate during exposures from the vertical contour interval (Table 2.7). The instruments axis by more than 2-3°. for tacheometric surveys are called tacheo2. The axes of flight lines must be parallel meters. straight lines. Plane-table surveying is made by means of 3. The flight altitude must not deviate by a plane table and ruler (Fig.2.10). Planemore than 3 per cent from the specified value. table surveying differs from other methods in On-the-ground stereophotogrammetry finds that a topogrgphic plan is plotted directly wide application for surveying a rugged- during surveying (in the field). At present relief terrain and open-cast quarries. It is time, plane-table surveying is used only for perfllrmed by means of a phototheodolite, large-scale surveys of very small areas of tho: combination of a theodolite and phototerrain. graphic camera. The camera is set up succesA plane table (see Fig. 2.10) has a table 1, sively at two ends of a photographic base line tripod 4, and a base 3 which connects the to make two photographs which constitute a table with a tripod head. The table is fastened stereo-pair. The stereo-pair is examined in a on a metallic base (Fig. 2.11) consisting of a stereoscope to construct a topographic plan. base plate 1, sighting device (with tangent Tacheometric surveying is a kind of to- screw 2), three foot screws 3, a clamp 4, three pographic survey employed on small areas or screws 5 for clamping the plane table, and a under intricate relief conditions. It consists in base housing 6. The tangent screw 2 serves determining the elevation and plan locations for rotating the plane table within small of points of terrain by measuring vertical and limits in the horizontal plane. The table base horizontal angles and distances between the is attached to the tripod head by means of an points. The results of tacheometric survey are attachment screw 5 (see Fig. 2.10). The plane processed for plotting the topographic plan table is levelled (horizontally) by means of of the terrain in which the relief is depicted by foot screws. horizontal lines with the vertical contour The ruler (2 in Fig. 2.10) is used for the intervals between horizontal sections taken graphical construction of horizontal di-
2.9. General
Fig.
2.9
Scheme
1/5000
of tacheometric
2
0.5 0.5
Data on Surveys
31
surveying
200 200 150 150 100 100
300 300 200 200 150 150
350 300 250 200 200 150
120 100 70 50 40 30
32
Ch. 2. Systems
of Coordinates,
Nets and Surface
Surveys
5 6
4 "--2
Fig. 2.10 Plane table with ruler: I-table; 2ruler; 3- plane-table base;4- tripod; 5- attachment screw; 6-additional ruler; 7-circular level; 8cylindrical level; 9-vertical tangent screw; 10-clamp; ll-cylindrical level of vertical circle; l2-telescope level; 13-telescope; 14-telescope sighting device; 15-stand
rections on the plane table and measuring distances and inclination angle in particular directions. At present time, nomogram rulers are employed, which make it possible to calculate elevations and horizontal distances upon sighting the device (telescope) at a vertical staff. In plane-table surveying, it is essential to determine the elevations of summits, water
3 Fig. 2.11 Plane-table metallic base: 1- base plate; 2-tangent screw; 3-foot screws; 4-clamp; 5 -plane-table clamp screws; 6 -plane-table housing
sheds, basins, etc. and all points where the steepnessof slope changes. The elevations of the characteristic points of precipices, caverns, dip pits, etc. should be indicated rounded-off to 0.1 m. In addition to the horizontal lines of the relief, each square decimetre of a plan on a scale 1/5000 should also give the elevations of at least five characteristic points of the topography (summits of hills, road crossings, rock outcrops, etc.). The elevation marks of each plan sheet should be copied on tracing paper; if a plan is plotted in the office, its contour lines should also be copied on tracing paper.
Chapter
Graphical
3.1.
Documentation
General
For proper functioning of a mining enterprise, it is essential to have a file of graphical documents, in particular, mine-survey drawings compiled by the results of geological, topographic and mine surveys. A characteristic feature of mining graphical documentation is that the information contained in it varies continuously in time and space, which is caused by the dynamics of mining production, variations of geological conditions, and some other circumstances. Mine-survey drawings are used in the design, construction and exploitation of mining and associated enterprises. In particular, they are used in the design of geological prospecting and mining operations, underground and surface structures, compilation of plans of aeration, power supply, water drainage and haulage in underground workings and OI) the surface, solution of problems of protection of structures and natural objects against harmful effect of mining activity, problems of safety, accounting for the motion of mineral reserves,mining output, mineral losses, and many other problems of interest in mining. In that connection, mine-surveying drawings must have the required completeness and accuracy. Besides,they must be clear and easily readable and measurable. This is ensured by the application of modern drawing materials and instruments, advanced methods of preparation and complementation of
Three
in
Mine
Surveying
graphical documents, and high skill of draftsmen. Mine-surveying service plays the major part in the compilation of mining graphical documentation since this is based on the measurements and calculations made by mine surveyors. . In mining practice, the following definitions and concepts associated with mining graphical documentation are in use. Projections are graphical representations of particular spatial objects on the plane of drawings. In mine surveying, orthogonal projections are preferably used, especially their variety, projections with numerical (hypsometric) data. Orthogonal projections may be made on horizontal, vertical or inclined planes. For more clear representation, axonometric and affine projections are also employed. Plans are drawings of orthogonal projections of objects onto a horizontal plane. They are widely used for the representation of the Earth's surface and mining workings. Survey plans usually contain the elevation marks (height coordinates) of particular points or are constructed in isohypses; in the latter case, they are essentially projections with numerical data. Vertical projections are drawings of objects projected onto a vertical plane. Such documents are often compiled for steeply dipping seems(veins) and similar elements when horizontal projections would involve large distortions. If the strike of a deposit varies sharply, it can be projected onto a number of
34
Ch. 3. Graphical Documentation
vertical planes each of them being arranged parallel to the strike of individual portions of a deposit. In some cases, projections onto the plane of a seam are employed. Sections are the representation of the details of an object, which are located in a certain section plane. In mine-surveying practice, the most common types of sections are geological sections and sections of mining workings which depict the enclosing rock, some details of a working, supports, and other objects. In sections, objects and details may be projected onto vertical, horizontal or inclined planes. Vertical geological sections are most often confined to the lines of exploratory or mining-production workings. Profiles are graphs depicting, in a vertical section, only the contour or part of the contour of an object considered, for instance, the terrain relief, rocks in the roof or foot of a working, haulage tracks, etc. Sketches are rough drawings of objects which are made by hand, i. e. without the use of rules and other drawing instruments. For instance, a mine surveyor makes sketches in the field book when carrying out instrumental surveys or taping of mining workings, measuring the reserves of a mineral in store, etc. Scales. Objects are depicted in mine-surveying plans by diminishing the results of natural (field) measurements. The degree of diminution of a line in a plan is determined by the scale, i. e. a dimensionless fractional number in which the numerator is unity and the denominator shows how many times a line depicted in the plan Can be laid off along the corresponding horizontal distance in the terrain. This is what is called the numerical scale of lengths, or simply numerical scale. Consequently, s/S = I/M, where M is the denominator of the numerical scale. In plans, numerical scales are written as
in Mine Surveying
simple fractions, for example, 1/500, 1/1000, 1/2000, 1/10000, etc. Thus, if a numerical scale 1/1000 has been adopted for a plan, this means that horizontal distances on the terrain will be diminished on the plan to onethousandth. It is distinguished between large and small scales: the larger the denominator, the smaller the scale. A plan drawn on a larger scale can depict more details of the locality. The scale of a plan or map is chosen according to specifications and depending on where the plan will be used. Using numerical scales, horizontal distances on the terrain can be transformed into lines on a plan and vice versa. For instance, if the horizontal distance of a line on the terrain is equal to 174.30 ill and the scale of plan is 1/2000, the length of the corresponding line on the plan will be 174.3: 20 = = 8.71 cm; if a line on a plan made on a scale 1/5000 is equal to 10.2 cm, the horizontal distance on the terrain corresponding to that line will be 10.2 x 50 = 510 ill. Distances on plans can be measured with an accuracy permitted by the resolving power of man's eye, which is usually taken equal to 0.1 mm (with the critical angle of vision 60" and the distance of best vision to an object 250 mm, the resolution is equal to 0.073 mm, or roughly 0.1 mm). The corresponding horizontal distance in nature (on the terrain) is called the accuracy of scale. For the scales 1/500, 1/1000, 1/2000, 1/5000, and 1/10000, the accuracy is respectively equal to 0.05 ill, 0.1 ill, 0.2 ill, 1 ill, and 2.5 ill. The scale of a plan is chosen according to the dimensions of an object in nature and by considering the accuracy of the scale so that the finest details on the plan can be by a factor of 5-10 larger than 0.1 mill. For instance, if individual derails of construction objects on the site of a mining enterprise have sizes of an order to 1 ill, the mOSt suitable scale for their depiction will be 1/2000 or 1/1000.
3.2.
3.2.
Classification and Rules of
Classification
of Drawings
of Drawings Mapping
As regards their compilation, all mine surveying drawings can be divided into primary (originals) and secondary (copies, duplicates, and reproductions). Primary drawings are mapped directly by the results of a survey, which are recalculated to a single coordinate system. If a particular object cannot be surveyed directly (this mainly relates to underground workings), it is permissible to map it on an original drawing on the basis of descriptive information or another graphical documentation; an appropriate note should then be made on the drawing. Original (primary) drawings are the main technical and juridical documents for solving various problems of. mining geometry. They are prepared on a special base in a system of plats, which ensures their preservation and non-deformability and provides certain convenience in use. Original graphical documentation should have an accuracy characterized by the data of Table 3.1. Table 3.1 Error
in:
Maximum value, mm
Mutual arrangement of intersection points of a rectangular coordinate grid Position of stations of a control or survey net relative to the coordinate grid Mutual arrangement of the nearest stations of a control or survey net Position of conspicuous points relative to the nearest stations of a control or survey net Mutual arrangement of the nearest conspicuous points
:to.2
::1:0.6
and Rules of Mapping
35
Survey objects are depicted on maps and plans in their actual shape and in a size according to the map scale. Conventional signs are used in mining graphical documentation for objects which cannot be drawn in their actual shape on the drawing scale. In cases when a drawing contains the elements of terrestrial surface and underground workings and their geological characteristics, terrestrial elements are drawn in the flfSt place, then the elements of underground workings, and lastly the elements of geological characteristic are drawn. The contours of the elements of an object, which lie in the plane of a drawing are drawn in solid lines and those which are beyond that plane, in dotted lines. The contours of elements determined on the basis of description information are drawn in dotted lines. Secondary drawings are prepared by reproducing (copying) the original drawings. They must be complemented and corrected when a need arises and can be used for various practical purposes, for instance, for the compilation of exchange and calendar plans of mining work development, special plans for accounting the reserves,mines stock and loss of a mineral, plans of mine ventilation, plans for the prevention of accidents, etc. The main requirements to secondary graphical documents are that they should contain all the essential information as required by the purpose and that this information should be drawn clearly. Graphical documentation should preferably be drawn on the scales: 1/500, 1/1000, 1/2000, 1/5000 or 1/10000; the scale 1/25000 is recommended for cartograms and general charts, and scales 1/5, I/lO, 1/20, 1/50, I/lOO and 1/200, for small objects.
36
Ch. 3. Graphical Documentation
3.3. Drawing Materials. Technology and Rules for Making and Storage of Mining Graphical Documentation Up to a recent time, all mining graphical documentation was made on a paper base: original plans of mining workings on highquality drawing paper glued on a reinforcing substrate (aluminium plates, cloth, etc.) and secondary plans, on light-sensitive paper (copy paper) or tracing paper. At present, synthetic drawing materials (based on lavsan or therylene) are being used widely for making mining graphical documentation. They have a higher durability and strength, can withstand multiple corrections, retain stable dimensions under atmospheric influence, and possess a better transparency. Synthetic drawing films are manufactured in a number of varieties with different physico-mechanical properties of the drawing surface, depending on their application and the method of fixation of the image (by ink, graphite or synthetic pencil, engraving, diazotype copying, printing, etc.). Polyethylene terephthalate (1avsan) film (glossy, double-oriented) is employed for making various copies with the application of silverless light-sensitive layers. Mechanically matted lavsan is widely used in drawing. The glossy drawing surface of the lavsan film requires no matting additives if special inks are used for drawing. The film is highly transparent and ensures a high quality of copies. On the other hand, its white surface ensures a high contrast of drawings. An offset lavsan film is suitable for making offset plates by electrographical and photomechanical methods or by drawing. A plate made by the photomechanical method can be used for making up to 10000 copies. A templet drawing film possessesthermoadhesive properties, which makes it possible to mount various templets on it.
in Mine Surveying
Reinforced paper is a combination of lavsan and conventional paper, i. e. a lavsan film is sandwiched between two paper layers. It combines favourably the drawing properties of paper and high physico-mechanical properties of lavsan. Reinforced paper is manufactured in various versions with various kinds of paper and different thickness of lavsan film and has a number of applications. The matter of storage of originals made on plastic materials deserves special attention. They should be kept in an isolated room at a temperature within + 16° to + 20°C and air humidity 50-80 per cent. The best method of storage of originals (plats) is to keep them in the suspended state. General charts made on plastics can in exceptional cases be kept in rolls (rolled together with spacing paper where possible). 3.4.
Mechanization of Graphical
Work
In modern practice, graphical work is largely facilitated and made less labour-consuming by the use of principally novel engineering means which make it possible to 'mount' drawings from unified standard prefabricated graphical elements. The first to be named among these means are decalcomania means (decals),i. e. multiply repeated paint images of alphabet letters, digits and conventional signs applied onto a film material. The draftsman chooses the required sign, places the film on the drawing, and rubs at the other side of the film with a hard object. In this way, the paint image is detached from the film and transferred onto the drawing. Decals can be restored multiply by repeated rolling with a special paint. Decals are used widely for making inscriptions on drawings, compiling plans from conventional symbols, schemes of electric circuits, for marking of documents, catalogue cards, etc.
3.5.
Processes
As has been shown by experience, decals can be used both in specialized and nonspecialized production of graphical documents. They can be manufactured in any design institution or enterprise provided with photoprocessing laboratory equipment. Templets, i. e. applications of standard elements, conventional signs, inscriptions, etc. have also found wide use in modern drawing practice. The method of templets has many advantages and largely accelerates the drawing process, since drawings are compiled from individual standard elements. Templets are produced in a number of varieties differing from one another in the type of substrate (paper, thin cardboard, film, foil, etc.), the method of application of the image, and the principle of fixation of templets on a substrate. Adhesive templets are the most popular; they have an adhesive layer on the back side, which is protected by non-sticking paper. The latter must be removed before applying a templet into its place in a drawing. Such templets have however certain drawbacks: they can be used only 4-5 times; it is difficult to move a templet on the substrate in the case of variation design; templets taken off from the substrate are liable to twisting; etc. These drawbacks have been eliminated in a new method of templet mounting which uses templets prepared on a polyethylene terephthalate film base with the working (contact) layer made of a material fusible at 80-120°C. As the fused layer solidifies, it fixes firmly the templet on a substrate (paper or film). Templets are mounted by means of a thermal handle. For temporary fixation of a templet on a drawing, it suffices to touch the templet with the handle in a single point. For final fixation of a templet, the handle is applied in four or more points. Mter mounting the templets, the required textual and graphical additions are made in the drawing by using decals. The final original drawing is checked and reproduced by diazotype co-
and Materials
37
pying; microfilm copies can also be made when needed. All used templets and substrates can be restored. Templets are detached from the film base and the latter is cleaned from the traces of a pencil and ink, and from decals. Restored materials can be used anew. 3.5.
Processes and Materials for Reproduction of Mining Graphical Documentation
The principal processes for the reproduction of drawings of mining graphical documentation are diazo type copying, electrophotography, and offset printing. Diazotype copying is the most popular processfor the reproduction of original drawings made on transparent materials. The originals are reproduced on diazo-paper and diazo-film. Light-sensitive diazotype materials are manufactured industrially in a wide range and differ from one another in the kind of a light-sensitive layer and base and methods of development. Diazotype copying is performed in rotary copying machines and copying frames. Electrophotography is among the most advanced modern processes of reproduction of graphical images. It is distinguished favourably by high productivity, facsimile reproduction of images, simple technology, and possibility of copying of opaque originals. Electrophotographic process is based on the use of certain semiconductors whose conduction changes under the effect of light. When a layer of photosemiconductive material is exposed to light, there forms a latent electrostatic image in it, which is developed by a powder material whose particles are attracted to the portions of the selenium layer, that carry induced electrostatic charges. Offset printing is the most efficient and simple process of the reproduction of docu-
38
Ch. 3. Graphical Documentation
ments and has been for a long time in use in cartographic engineering. Offset printing ensures a higher quality of printed graphical documentation than is possible in diazotype copying on map paper and is well suitable for making multicolour prints. In addition, it requires much less labour for manual painting and offers the possibility for making multicolour composite prints, for printing in or eliminating some graphical elements, etc. Offset printing of maps at map-making agencies is carried out from colour-separated originals (separation drawings or simply separations) which are prepared directly at mining enterprises. Colour separations, as the name implies, describe the graphical situation in a single colour, for instance, red, black, etc. and are used for making corresponding colour-separated printing plates. Colour-separated drawings should meet very high requirements: (a) they are drawn on synthetic transparent materials 70-100 ~m thick; thinner films are preferable, since they diminish the parallactic effect during copying onto printing plates; (b) the films must be without dents, folds, scratches, etc. and have no spots, marks, pencil lines, etc.; (c) line elements, especially inscriptions and shadings, should be well filled with ink, without clearances and breaks; the shaded
in Mine Surveying
elements of a large area should be filled with ink at least three times and checked on an illuminated screen so that their optical density is sufficiently high; and (d) linear dimensions in colour-separated drawings should not differ from the originals by more than :to.15 mm at sides and :to.20 mm along diagonals; the arrangement of the whole situation in a plan should satisfy the same accuracy standards. The process of preparation of colour-separated originals by illumination drawings consumes much time and labour and is insufficiently accurate. In a novel process, colour-separated originals are prepared by diazotype copying of contour images made on tracing paper, synthetic drawing films, etc. Synthetic drawing materials are finding ever wider use and accordingly, in various novel technological schemes and processes. For instance, transparent materials with thermo-adhesive properties have largely simplified the process of preparation of general charts at mining enterprises. Transparent plats of the original documentation are diazo-copied on the film and mounted by the thermotemplet method on a base as fragments of a general chart. The latter is diazocopied on cartographic paper or diazo-film. Later, the obsolete fragments of the general chart can be replaced by new ones.
Chapter
Connection
4.1
General
The object of connection survey (orientation) is to ensure underground surveying in the coordinate system adopted on the Earth's surface. Connection survey is essential for mining work expansion, correct location of underground workings relative to objects on the surface, protection of surface structures, determination of the depth of mining work, construction of boundaries for safe mining, combined working of adjacent seams, and connection of underground workings. Connection surveys are carried out rarely, mainly before constructing a new mine and later, for preparation of new mining levels. Connection survey belongs to the most critical kinds of surveying work and must be done with the highest accuracy and under reliable control. A distinction is made between the horizontal and vertical connection surveys. Horizontal connection survey has to tackle two problems: (a) orientation of underground ;surveys, i. e. determination of the direction angles of the initial sides of an underground survey net and (b) centring, or plumbing, of an underground survey, i. e. determination of the coordinates x and y of the initial points of an underground survey net. Vertical connection survey is carried out for transferring a height mark from the Earth's surface down into the mine. Depending on the method of opening a deposit, connection surveys can be run via horizontal, inclined or vertical workings or shafts.
Four
Surveys
Connection survey via horizontal or inclined workings is carried out by running polygonometric traverses or geometric or trigonometric levelling traverses through the workings. Connection surveying (orientation) via vertical workings is done by special methods which can be divided into geometric and physical. The geometric methods of orientation of underground survey employ plumb bobs (plummets) sunk into vertical shafts of mines. The coordinates of plummets and the direction angles of plumb:-connecting lines are determined by'measurements on the Earth's surface. The physical methods include the magnetic, gyroscopic, and optical method. The magnetic method utilizes the ability of a magnetic needle to line up along a line of the magnetic field of the Earth. Though being rather simple, it has an essential disadvantage; owing to local magnetic disturbances, the orientation of the magnetic needle is subject to unpredictable variations in particular places. For that reason the magnetic method is not popular and employed only in rare cases when its low accuracy is sufficient for orientation of underground workings. The gyroscopic method uses a pendulum gyroscope (gyrocompass) whose axis performs harmonic oscillations about an equilibrium position which coincides with the plane of astronomic meridian on the station point of the instrument. Modern high-precision gyrocompasses are reliable instruments
40
Ch. 4. Connection
for gyroscopic orientation of underground sides of reference survey nets, because of which the gyroscopic method has found wide use as being the most precise and least labour-consuming. The optical method of orientation of underground survey is not very popular, since the available instruments have an insufficient resolving power in deep mines where the atmosphere may often be moist and dust-laden, and thus fail to ensure the required accuracy of measurements. In modern mine surveying practice, orientation of underground workings is mainly performed by the gyroscopic or geometric method (via one or two vertical shafts). Errors incurred in connection surveys cause subsequent errors in the determination of points of underground survey nets. If the coordinates x, y of an initial point 1 are found with errors (Fig. 4.la), these will be carried over without change into the coordinates of all subsequent points of an underground survey net. Therefore, an error 1-1' of the planimetric position of the initial point which has appeared on centring, will result in a parallel displacement of points 1-6 into positions 1'-6'. An error in the determination of the height mark (z) of an initial point gives a similar effect.
(a)
f:; :-1=::$;~' 2'
3'
~2
4'
5'
6,
04 , ~ 3
1
"'0-5
6 5'
(b)
~ a=C~~---~ ---, 2' ,
m(X '02
3
4'
---0 3
--0-4
,...0 5
Fig. 4.1 Effect of centring error (a) and orientation error (b) on positions of points of underground theodolite traverse
Surveys
An angular error of orientation (orientation error) gives a different effect. If the direction angle of the initial side is found with an error m" (Fig. 4.1b), the net 1-5 will be turned into the position 1-5'. The root-mean square displacement of the last point will be: M = (mJp')s (4.1) where m" is the rms error of orientation, minutes; p' is the number of angular minutes in a radian (p' = 3438'); and s is the length of the closing side of a traverse. This formula shows that the effect of an orientation error on the planimetric positions of points increases in proportion to the distance from the initial point. For that reason, orientation is the most critical part of connection survey and must be performed with the highest accuracy. In order to avoid appreciable errors, orientation must be done twice by the same method or different methods. Discrepancies in the results of orientation of one and the same side of a traverse should not exceed the following permissible values: (a) 3' for direction angles in geometric orientation; (b) 2' for direction angles in gyroscopic orientation; and (c) 5 cm for planimetric position of the initial point in the plumbing of a survey net via vertical workings. In order to satisfy these requirements, the root-mean square error m" of a single orientation must not exceed l' in the geometric method and 40" in the gyroscopic method of orientation. To minimize the effect of an orientation error on the positions of distant points in underground survey nets, it is recommended to make gyroscopic orientation of intermediate sides of nets in mines where field wings exceed two metres in length. Thus, the maximum rms displacement M of a point of an underground survey net, as calculated by formula (4.1) with due consideration of the error of orientation
4.3.
Geometric
(carried out twice), will be: M=
x 2000 m=
fi
4.2.
41
If a mine is entered by two adits, the theodolite traverse must be run to closure. In mines opened by inclines with the dipping angle of more than 70°, direction angles must be transferred only by using gyroscopic orientation.
0.4 m
x 3438'
Orientation Survey via or Inclined
Orientation
of Underground Horizontal Adit
If a deposit is opened by a horizontal entry (adit) or an inclined entry (incline), the underground survey can be oriented by running a polygonometric traverse from the surface into the mine (Fig. 4.2). If only one adit or incline is available, the traverse is run from an approach station on the surface, say, B, to the first side of the underground survey net. A back traverse line is run usually through other, temporarily established points. The polygonometric traverse run to a side CD in the figure makes it possible to calculate the direction angle aCD of the side and the coordinates of a point C: aCD= a AB+ 131+ 132+ ...+ 13n:!: 180°.n Xc = xB + /1 cos aB1
4.3.
Geometric
Orientation
Connection survey with the use of plummets can be performed via one, two or more vertical shafts. In any case it has to handle two problems: the problem of projection and that of connection (junction). The procedure of projection consists essentially in that a straight-Iine segment is transferred by means of two plumb bobs from the surface onto the mine level to be oriented. The projection procedure should be carried out so that the line segments on the surface and in the mine lie in the same vertical plane. The junction procedure includes two steps: connection on the surface and connection in the mine. The former determines the coordinates of the plummets and the direction + 12cosa12 + ...+ IncosanC angle of the line that is projected from the Yc = YB + /1 sin aB1 surface, and the latter is done to transfer the direction angle and plumb-line coordinates + 4sina12 + ...+Insinanc to the first (fixed) side of an underground where 131'132'..., 13nare the measured angles; theodolite traverse. n is the number of measured angles; aB1' ..., There are several methods of junction anCare the direction angles of sides; and /1, 4. which differ from one another in the shape of In are the measured lengths of sides. junction figures at plumb-bob lines. With all :~
//I
ri ri
%, ?:1
D
~ ""~
~2~~,(///////////// B 11 ~~---0--
1
~ ~ Fig.
4.2
Orientation
via
adit
'
2
13
3
---0---
~n-~
n
In
~. //j
C
42
Ch. 4. Connection
methods of junction, however, the matter of projection is tackled essentially in the same way.
Surveys
nection survey via a vertical shaft. This method is the most labour-consuming and requires certain special techniques, but the instruments and appliances employed in it, as 4.4. Orientation well as some of the operations described down One Vertical Shaft below, are typical for all kinds of geometric This kind of orientation is carried out by orientation, in particular, for connection means of two plummets hung from the sur- surveys via two or more vertical shafts. The preparatopy stageincludes the following face through the shaft onto the mine level to be oriented. The procedure requires careful operations. I. Approach points are established on the preparatory work, long-term outage of hoisurface at a distance not more than 300 m sting vessels in the shaft, and certain special safety measures. The procedure must be per- from the shaft collar. Existing stations of a formed in a clearly correlated sequence and geodetic net of class I to 4 in the vicinity of with coordinated actions of all the specialists the shaft can be used as approach points. The engaged in it. For that reason, the chief coordinates and direction angles of approach mining surveyor has to work out a detailed points must be determined with an accuracy plan of the organization and methods of corresponding to analytical or polygonometric nets of the first order. The approach surveying work which specifies, in particular, points should be established so that the the required outage time of hoisting means in hanging polygonometric traverse of the sethe shaft and the essential safety measures; the plan is to be approved by the chief cond order to be run immediately to the shaft engineer of the mining enterprise. Before collar between the initial point for direct starting the work, all members of the survey connection of plumb lines and an approach team are instructed by the chief mining point contains not more than three sides. surveyor in their duties and in details of the This traverse should be run twice or be closed or else be tied to higher-order station plan. The survey work of orientation down one points. 2. A number of (at least four) permanent vertical shaft can be divided into two stages: (I) the preparatory stage which includes station points (marks) are established in the the operations and steps that should be workings of the mine level to be oriented, so performed before stopping the hoist in the that the coordinates x, y and direction angle transferred into the mine can be fixed to shaft and (2) the main stage which covers the ope- them. 3. A set of instruments, appliances and rations of centring and orientation to be carried out when the shaft hoist is stopped. fixtures is prepared for accomplishment of As a rule, the main fan of the mine is switched connection survey work with the specified off for the time when observations of plum- accuracy. The survey instruments and appliances must be tested and adjusted before met oscillations are to be carried out. starting the work. The mass of plummets and the type and diameter of wire are chosen 4.5. Sequence and Organization depending on the depth of the shaft and the of Work for Orientation speed of air in it. down One Vertical Shaft 4. The points are chosen for hanging the This section will describe in detail the plumb bob lines in the shaft so as to obtain sequence and organization of work for con- the largest distance between the plummets
4.5.
Sequence
and Organization
of Work
43
and the most favourable figures for solving 3. Small plumb bobs (of a mass of 3-5 kg) the connection problem. Places are assigned on wires are passed through the holes in the for the construction of platforms for winches, top platform along the shaft to the level to be scales, guide pulleys, projection and centring oriented so as to avoid large swings. Practiplates, plummet dampers (dash-pots), etc. so cally both plumb bobs are sunk simultaneousas to ensure the stability of plummets during ly with a speed of 1 mjs. It should be checked the entire time of observations. If there is that the wires have no -knots, bends, etc. along enough place in the underground workings the entire length. near the shaft and the mining operations in 4. Upon sinking the plumb bobs, the team the shaft will not be interfered, some of these underground replaces them by the main procedures (construction of platforms for larger plummets and places these into dashwinches, arrangement of winches and guide pots. pulleys, closure of the sump, etc.) can be 5. Centring plates with scales, mirrors and carried out at an earlier stage. other devices are placed on the platforms on 5. Building materials are prepared for the the underground level to observe the oscillaclosure of the shaft, construction of plattions of plummets. If the strings of freely forms, attachment of fixtures in the shaft and hanging plummets are stable (their oscillaon the mine level to be oriented. Vessels with tions do not exceed 0.4 mm), the centring viscous liquid for plummet damping and plates can be aligned immediately with the other devices are prepare,d for the work. plummets. 6. Auxiliary workers (shaft fitters, carpen6. It is checked that the plummet strings ters, hoist operators) to be engaged in the do not touch the shaft walls. This can be connection survey work are instructed in the done by two methods: (a) a light ring cut out job, and a reliable telephone service is estab- of cardboard or another available material is lished between the working teams on the 'mailed down' along the wire, i. e. is let to surface and in the mine. slide down to the bottom or (b) the distances At the beginning of the main stage of between the plummets as measured on the survey work, the performers and the auxiliary surface and in the mine are compared; the personnel in the shaft and at the hoist are discrepancy between them must not exceed placed under the authority of the survey 2mm. work supervisor, usually the chief surveyor of 7. Observations of plummet oscillations the mine. Persons not engaged in survey are carried out to determine the central work are strongly prohibited to be present in positions of the plummets, after which the the underground workings and shaft building plummets are fixed in the centring plates and and on the platforms. The performers are the free positions of the plummet wires are divided into two teams or groups: one for checked again by comparing the distances work on the surface and the other, on the between the plummets as measured on the level to be oriented. surface and in the mine. The operations at the main stage are 8. All linear and angular parameters of the carried out roughly in the following sequence. connection triangles are measured on the I. Wood platforms are constructed on the surface and in the mine. shaft collar and in the shaft proper. Small 9. Upon finishing the cycle of observaholes are provided in the platforms for pas- tions, a check measurement of the distance between the plummets on the surface and in sing through plummets. 2. Winches, guide pulleys, centring plates, the mine is made again. If the discrepancy is etc. are fastened on the platforms. within the permissible value, it is now pos-
44
Ch. 4. Connection
Surveys
level being oriented do not usually lie in the same vertical plane with the plumb line points 01, O2 on the surface (Fig. 4.4). In other words, it is impossible to form a vertical plane in a shaft that would pass through all four points indicated. The rootmean square error for this case can be found by the formula: Au" = p'e/c
(4.2)
where e are the rms linear deviations of the points of both plummets on the level being oriented from the respective points on the surface and c is the distance between the ~
///////////;"J;!;;;///////////////////; Fig. 4.3 Plummet arrangement for orientation through vertical shaft: 1 -hand winch; 2- guide pulleys; 3 -centring plates; 4- guard platform; 5-plummet;
6~dash-pot
sible to start disassembling of .the surveying equipment. The main plummets are replaced by lighter plumb bobs and these are lifted to the surface. During lifting the plumb bobs, the work of all kinds in the shaft and near it and on the platforms is prohibited. With properly organized work and good coordination between the working teams, the main stage of surveying can be completed in 8-12 hours. The principal scheme of arrangement of plummets for orientation via a vertical shaft is shown in Fig. 4.3. 4.6.
plummets. Since the permissible discrepancy between two independent orientations is not more than::!: 3', the rms error of an orientation should be not more than 1'. If the rms error of surface connection and connection in the mine is taken to be not more than::!: 30", the rms error of projection, Au, should not exceed the following value: Auperm= J Au; + Au; ~ 42" To ensure this accuracy of projection, the rms linear deviations e should not exceed 0.4, 0.6, 0.8, I, and 1.2 mm for the distances between the plumb lines respectively 2, 3, 4, 5, and 6 m. This accuracy can only be attained by observing the rules listed in Sect. 4.7. It is essential to choose the distance between the plumb lines as close as possible to the shaft diameter. For handling successfully the problem of projection, of special importance is the observation of mean (central) positions of plummets on the oriented level. Observations of
Plumbing Surface Points onto Oriented Mine Level
Owing to the effects of various external forces, plumb line points 0'1, o~ on the mine
Fig.
4.4
Determining
angular
projection
error
4.6. Plumbing Surface Points onto Oriented Mine Level
N
".I
5.
~" ~
.4 '5 ~ ::;:::
2
-3
4.
5.
A 7 4 '5 Fig. 4.5 Centring plate with scales: 1- body; 2-mirror socket; 3-pyramid; 4-clamp screws; 5- pyramid-adjusting screws; 6- slit for plumb bob string; 7- plate-fastening sockets; 8 -plumb bob; 9-plug; M, N -scales
Fig. 4.6 Observation of pl~mmet oscillations scales by means of two theodolites
on
45
plummet oscillations can be made by two linear scales, a centring plate (Fig. 4.5.), eyepiece scales, and other devices. Irrespective of the type of instrument used for the purpose, the problem consists essentially in observing the motions of oscillating plummets in two vertical planes and determining their mean positions in each plane. These points are then fiXed. Figure 4.6 shows the scheme of observation of a plummet 01 by using two theodolites. The extreme points of positions of plummets are fixed by reading off on the scales at the exterior or interior edge of the plummet wire. The number of readings to fix the extreme position of the wire shou)d be not less than 11-13. The reading on the scale N 1 corresponding to the mean position of the plummet is calculated by the formula: N 1mean = 0.5 (I;IN./n + I;rN./n) (4.3) I I where IN. is an extreme left reading on the scale N; for the first plummet; rN. is an extreme right reading on the scale N ;; and n is the number of observations of extreme positions of the plummet 01 on the scale N 1. Similar observations and calculations are done on the scale M l' Observations of the mean position of the second plummet O2 are carried out simultaneously by using two other theodolites. The plumb line points are fixed according to the calculated data on their mean positions, the distance between them is measured as accurately as possible and compared with the distance between the plumb line points as measured on the surface. The observers should try to place the instruments and scales so that the angle y will be close to 90°, The accuracy in the determination of the mean position of a plummet will not be worsened if the angle y ranges between 45° and 135°. If the space available is too restricted, it is recommended to observe the oscillations of a plummet by means of a mirror and theodolite. This method is more intricate and time-
~
46
Ch. 4. Connection o
Scale N
~
oc
~
~Ni.
plate by means of two mutually perpendicular pairs of screws 5 (see Fig. 4.5).
~
4.7. , ... "
~
Surveys
W
Connection to Plumb Line Points in Orientation Down One Vertical Shaft
~
III
Fig. 4.7 Observation of plummet oscillations two scales by using mirror and theodolite
on
consuming. The principal scheme of determining the mean position of a plummet by means of a mirror and theodolite is shown in Fig.4.7. The reading on the scale N I corresponding to the mean position of a plummet is calculated by the formula N1mean= (N1 + N2 + ...+N1)/i
(4.4)
where N1 = (IN + 2,N + IN )/4 I I 2 N 2 = (IN + 2,N + IN )/4, etc. 2 2 3 i = (nr -I) + (n, -1) In these formulae, IN. IN. IN. and 'N ' 'N . 'N. are the left ind fight readings 6fth~ extreme positions of the plummet O Ion the scale N I; and nr and nl is respectively the number of right and left readings. In order to observe the oscillations of the plummet on the scale M I' the theodolite is sighted on the mirror which is arranged at an angle of 45° to this scale. Then a reading M I meancorresponding to the mean position of the plummet on the scale M I is taken. According to the readings N I mean !and M I mean' the plummet 0 I is fixed rigidly in the centring
The root-mean square error of transferring the direction angle from the initial side of a traverse to the plumb-connecting line and from the latter to the traverse side of an underground reference net on the mine level being oriented, should not exceed 30" for each of these two procedures. Considering this requirement and the possibilities of arrangement of plummets in a shaft, one chooses the connection method that is most suitable for the purpose. Among these methods, the method of connection triangle is most popular (Fig. 4.8.). Two points fixed earlier on the surface and in the shaft, say, A and C. and two points projected by plummets, 01 and O2, form two connection triangles: AO1O2 on the surface and CO1O2 in the shaft. The connection triangles will have a favourable form and ensure the specified accuracy of connection if the angles a and 'Yof the surface triangle and the angles P1 and 'Y1of the underground triangle do not exceed 2-3° and the ratios a/c and, b1/C1 are as small as possible. The connection procedure is started upon finishing the projection, and the observations and measurements on the surface and in the shaft are usually carried out concurrently. Before making the connection work, it is required to determine the expected errors in calculated angles, m« and m{i1 by the formulae: m« = (a/c)m1" m{i1= (b1/cJm1'1 (4.5) It is then permissible to solve the connection problem by the method of connection triangle if the expected errors of angles a and Pi do not exceed :t20". It is required to measure all the three sides a, b, and c of a
4.7. Connection to Plumb Line Points
Fig. 4.8 Junction by method of connection triangle
triangle AO1O2 and the angles 0, E, and yon the surface at a point A and the sides a1, b1, and c1 ofa triangle CO1O2 and the angles 01, El and Yl at a point C in the shaft. The rIllS errors of the measured angles at points A and C must not exceedm = 7". The differences of the measured angles1 points A and C (see Fig. 4.8), ° -(E -Y) and 01 -(El -YJ, must not exceed :!:20". These angles are adjusted by distributing the discrepancies, obtained by the reiteration method, equally between all the angles. Each side of connection triangles is measured at least five times by a steel tape at a constant tension, taking readings with an accuracy of up to a miliimetre. The arithmetic mean of these measurements is taken as the final result. The discrepancy between the individual readings must not exceed:!: 2 mm and the root-mean square error of the final length of a side must be not more than :!: 0.5 mm. The results of these field measurements are then used for calculations in office analysis. The solution of connection triangles and the calculations of the direction angle and the coordinates of the points of the initial side CD in the mine are carried out as follows. If the acute angles a and ~1 do not exceed 20°, use can be made of the sine fofIllulae: sin a = (a/c) sin Y, sin ~ = (b/c) sin Y
sinal =(al/cJsiny
Sin~l
=
(b1/cJsin
(4.6) Yl
If a or 131is less than 2°and 13or a1 is more than 178°, the angles can be calculated by the
approximate
formulae:
a = (a/c)y,
13 =
at = (a1/C
Iyl'
(b/c)y
Pi
=
(b1/c
If a or ~l exceeds 20°and ~ or al is smaller than 160°, the angles can be found by the formulae of sides: for the surface triangle: tan {a/2) = J(P -b)(P
-c)/[jJ(P
-a)]
tan (~/2) = J"iii=--a)(P -c)/[jJ(P
-b)]
and for the underground triangle: tan {afl)
,(4.8)
= J(Pl --bJ(P
CJI[P1
(Pi
aJ]
tan (fil/2) = J(P1 -aJ(p1
.'.'.CJI[P1 (P1 -hJ]
where P = (a + b + c)/2 and P1 ~ (a1 + b1 + cJ/2 Mter the angles have been calculated, a check is done by. adding the angles for each triangle, The sum of angles must not differ by more than 10" from 180°, The discrepancy (within the permissible value) is distributed evenly between the calculated angles. Before solving the connection triangles, the linear measurements are checked by colilparing the measured distance between the plummets to its value calculated by the formula: c=
Ja2
+b2
2abcos'Y
48
Ch. 4. Connection
Table 4.1. Solution
of Connection
Triangle
Surveys
with Angles a < 20° and p > 160'
Survey place m
(tana )
=
-m
2
Ot
2 +
) 2
m tan
.tany
ap"
--.!!.
y b
a
{3~
A
/1
b
2
a
3 4
b c
+
5.0313 8.0510 3.0220
12
a
II
13 5
y
1047'45"
22
tan a
177°07'31"
23 24
tan a/tan y tan a
1°04'00"
-m
0.031 1.63 3.8
,
tany
a sin a ~ -siny c
13
~
180000'00"
t2.4" 25
( ~m
):
tany ma
sin
13 =
18
m.
14.44
:to.29 mm 26
b -siny
y
tan ap'
0.000060
a 27 tanap"~
6
siny siny
8 9 10
c sinn
sin
13
131
0.018826
0.006229
16
19
mb
m"
:!:0.3
mm
28
0.050150 2°52'29"
17
20 21
( tanap"~)2
0.38
0.14
m
tan ap" -=C
0.000040
29
mc
:!: 0.23 mm
30
mc c
0.00010
31
m;
14.99
0,019
32
m,
:1::3.8"
b
0.031341
a
tany
( tan ap"~)2
0.41
4.8.
Horizontal
Connection
Survey
via
Vertical
49
Shafts
Table 4.1 (Continued) Calculation
of length of line c
.;.,c = a2 + b2 -2abcosy
1 2 3 4 5 6 7
y cosy a b ab 2ab 2ab cos y
1°04'00"
8
02
0.999827
9
b2
5.0313
10
2 Ccalc
8.0510
II
Ccalc
40.5070 81.0140
12
81.0000
13
The permissible discrepancy is not more than 3 mm for the surface triangle and 5 mm for the underground triangle. The direction angle of an underground side (see Fig. 4.8) is calculated by two polygons (one through plummet 01 and the other, plummet O2) using the following formulae: aCD= aBA + I: + (a + aJ + 1:1-3 x 180° (4.10) x 180°
aCD= aBA + 0 -(P + PJ + 01 -3
(4.11) The coordinates of the initial point C in the shaft are calculated by two polygons (see Fig. 4.8): x'c=xA+hcosaAO 1 +h1cosao 1c (4.12) Yc=YA+hsinaAo
Xc
=
+hlsinao.c
1
xA
+
acosaAo
+
2
(4.13)
1
a1cosao
c
2 Yc=YA+asinaAo
(4.14)
2 +a1sinaoc
2
(4.15)
The direction angles of the initial underground side CD, as transferred by two polygons, should be fully coincident, and the coordinates of a point C may have discrepancies within the accuracy of side measurement, i. e. up to 2 or 3 mm. If it is impossible to make a check by a different connection survey, orientation through one vertical shaft is repeated upon placing the plummets into new positions. The final result is found 4-127(!
25.3140 64.8186 9.1326 3.0220
Cmeas Ccals--Cmeas
3.0220 0.0000
as the arithmetic mean of two connection surveys. The calculations for connection triangles are made in table sheets. A table sheet for a case when the angles a are smaller than 200 and 13are larger than 160° is shown in Table 4.1. The method of connection triangle is simpler in measurements and calculations than the other methods available, ensures a high accuracy if the triangles are stretched, and for these reasons has found wide practical application. Other methods of connection through a single shaft, for instance, the method of connection rectangle with two- or single-sided connection schemes,the method of symmetrical connection, etc., will not be discussed here, since they are substantially more labour-consuming and therefore came out of use a few decades ago. 4.8.
Horizontal Connection Survey via Two Vertical Shafts
The analysis of the total error of connection survey, including the projection and connection errors, shows that with the connection through a single vertical shaft the projection error, which is the principal error in this kind of survey and depends mainly on
50
Fig.
Ch. 4. Connection
4.9
Orientation
via
two
vertical
shafts
the distance between the plummets, cannot always be diminished to the permissible value. In the orientation via two vertical shafts, however, the angular error of projection is not as critical, since the distance between the plummets is substantially greater. For that reason, the connection survey via two vertical shafts is the most accurate and reliable among all kinds of geometric orientation. For instance, with the distance between the plummets of 50 mm and a linear error of projection of 2 mm, the angular error, according to formula (4.2), will be: l1a" = p".: = 2 x 206265 = 8" c
Surveys
50000
i. e. is substantially smaller than the errors caused by other factors. In view of this circumstance, with the distance between the plummets of 50 m or more, it is permissible to perform connection on an underground level to freely hanging plummets. In the scheme of orientation via two vertical shafts, as shown in Fig. 4.9, the geometric connection between the sui:face and un-
derground survey nets is effected by means of the plummets hung in two shafts. Connection survey via two vertical shafts contains the following main stages: (I) projection of plumb line points 01 and O2 from the surface onto the mine level to be oriented. The main instruments and appliances, the order to plummet hanging in shafts, etc. are essentially the same as in the orientation via a single vertical shaft; (2) connection to the plummets on the surface and in the mine. The connection on the surface can be performed by one of the two schemes as follows: (a) if the distance between the shafts is not large, theodolite traverses with the number of sides not more than three (A-I-01 and A11-02) are run from one and the same point (A) to the plummets; (b) if the shafts are at a large distance from each other, an approach point is established at each of them, so that theodolite traverses with the number of sides not more than three can be run from these points to the plummets. The connection to the plummets in the
4.8.
Horizontal
Connection
mine is performed by running a theodolite traverse between the plumb line points (011-2-3-4-5-02). The accuracy of theodolite traverses oil the surface must correspond to first- or secondorder polygonometry and that on the level being oriented, to the accuracy of underground reference n(;ts. The underground traverse between the plummets should be stretched where possible, i. e. be of the least feasible length, and include as few points as possible. In Soviet practice, technical instructions on mine surveying specify that the root-mean square error of the direction angle of a plumb-connecting line relative to the nearest side of the reference net on the surface should be not more than 20". That is why, before making the connection survey, it is essential to estimate preliminarily the accuracy of the direction angle of the plumb-connecting line and that of the direction angle of the side of the underground reference net, so that the rillS error of the underground direction can be within the permissible limit of 1'.
Survey
via Vertical
Shafts
51
4.8.1 .Estimating the Accuracy of Direction Angle of Plumb-Connecting Line on the Surface Let side 1-1' be the initial side from which a polygonometric traverse with a junction point 2 has been run (Fig. 4.l0a). The rootmean square error of the direction angle of a plumb-connecting line can be found by the formula: . M~o
o = 1 2
v
(4.16)
where mp = 10" is the rms error of angular measurements; 11is the coefficient of influence of random errors in length measurements; Si are the lengths of sides of a polygonometric traverse from the junction point to plumb line points 01 and O2 (in the case considered, the side lengths S2-01'S2-3'and S3-0J;
(b)
Fig. 4.10 Preliminary estimation of accuracy of survey work: (a) for direction angle of plumb-colJnecting line on surface; (b) for direction angle of side of underground survey net
52
Ch. 4. Connection
Table
provided that ~ = 0.001 m1i2, mfl = 20", and c=115m. The calculation is done in the following sequence.
4.2
R,
Vertexes
2 2 3
R:
49 6724 144
7 82 12
[R;iJ
=
6917
Sides
.2 Ipi Sism
18 1 26
2-01 2-3 3-02
[sisin2
Surveys
I.
The
root-mean
square
errors
Ma
of fl
direction angles of traverse sides incurred by the errors of angular measurements are determined by the formula:
= 45 Ma
= (mfl/c)J[Ji"!]
(4.17)
fl
is the distance between the plummets (here c = 75 m); Ry. are the projections onto the line 0 102 of 'the distances from the plumb line points 01 and O2 to the points of traverses run from the junction point to these plummets (here: Ry , Ry .and Ry ); p" = = 206265"; and n is the nfImber ofrJeasured angles between the approach point and junction point (here n = 2). The magnitudes of Ry. are taken from the survey plan; the terms s; sin2
where mfl is the rms error of angular measurements; Ry is the projection onto the line 0102 of the distances from each plummet to the points of the traverse section which connects the plummet with the side in question (including one point of that side). The values of Ry are determined on the survey plan (Table 4.3). Substituting the numerical values into formula (4.17), we obtain: for the first side of connection traverse (I-II):
M
"pVIl-VIlI
20J23650 115
=
27'
-102 x 6917
4 x 1010 x I x 10-6
752+
x 45
752
\I -+2 x
4.8.2.
102 =
25"
Estimating the Accuracy of Connection by Connecting Polygon
Suppose that a polygonometric traverse has been run through points I, II, III, IJ-: J-: n, nI, and nII (see Fig.4.10b). It is required to find the error of direction angles of the first, last, and middle side of the traverse
2. The root-mean square errors M~ of the direction angles of traverse sides incu;red by errors in linear measurements of side lengths are found by the formula: Ms = (J.1/c) p" j;;"Sj;;;-;p-;
(4.18)
where Si are the lengths of traverse sides and
4.8.
Horizontal
Connection
Survey
via Vertical
Shafts
53
Table 4.3
for the first side of traverse (I-II):
traverse (Fig. 4.11 ): Side 01-1 sisin2
I-II II-III 52 8 VII-VIII 5
III-IV 0
VIII-O2 0
M. = 0.001/115 x 2 x 105 Jill
IV-V 0
[sisin2
=
JM;.
+
M;
(4.19)
..
Fig. 4.11 Double projection connecting polygon
for the last side (VII-VIII): M ~VII-VIII = V /272 ~I + T 202 ~v = 34" and for the middle side (IV -V):
= 20"
3. The root-mean square errors of the direction angles of traverse sides relative to the p1umb-connecting line 0102 are calculated by the formula: M«
M ~1-II= V /362 :Ju + T 202 ~v = 42"
of side length of
M ~IV-V= V /122 l~ + T 202 ~v = 23" On the basis of these preliminary calculations of errors, the work superviser (chief surveyor) chooses the techniques and instruments which can ensure the specified accuracy of mine surveying. The entire complex of angular and linear observations on the surface and in the mine is carried out before hanging the plummets into the shafts. Mter hanging the plummets, their points are connected by measuring the angles at the first and last points of the connecting polygon and the distances from these points to the plummets. The coordinates x, y of the plummets O 1 and O2 on the surface are determined by the results of measurements of the approach polygons (seeFigs. 4.9 and 4.10a). All lengths measured on the surface and in the mine are corrected for calibration, temperature, angle of dip, tape sag, and reduction of lengths to the surface of reference ellipsoid and the
Ch. 4. Connection
54
plane of Gauss projection. The last two corrections are found by the formulae: ASel= (y/2R)s, Aspr = -(H/R)s where y is the mean ordinate of the connection survey region; R is the mean radius of the Earth; H is the absolute elevation; and s is the measured length of the traverse side. The calculated coordinates are used for determining the direction angle of a plumbconnecting line, Qo 0 and the distance bel 2 tween the plummets, c, by the formulae: tanaOlO2
=
(Y°2
-YOl)/(XO2
c = (XO2 -XOl)/COS = (yO
2
-Yo
-XOl)
(4.20)
UOlO:
)/sin 1
Uo O 1 2
(4.21)
or
1, (X
X
02 -01
y--'2 )2
),22 +.,--(y
02 -01
In calculations by formula (4.20), the value of c obtained for the larger increase of coordinates is taken as the final value, whereas that calculated for the smaller increase is used as a check value. Then the coordinates of points of the underground connection polygon are calculated in the conventional system of coordinates. As a rule, the point 01 is taken as the origin of the conventional coordinate system and the axis of abscissaeis directed.along the first side, 01-1. In that case, x'o = y'o = 0 d ' 0 1 1 an
ao1-1= . After that the direction angle of a plumb-connecting line, a' o o , and the dis1 2 tance between the plummets ID the mine, c', are determined in the conventional coordinate system: tana'o o = y'o jx'o 1 2 2 2 ., a o o = x ,o , j sm c,o o = Yo
12
2
12
(4.22)
j cos a,o o
2
12 (4.23)
It is now essential to compare the plummet distances as calculated by the coordinates of the unified system on the surface (c) and in
Surveys
the conventinnal system in the mine (c'). The discrepancy A c = c' -c must not exceed the permissible value A Cperm which can be found by the formula: Acperm = 2 (mi/p2/[R~;J
+ ~2(SiCOS2
where Rx. are the distances from the points of , the underground polygon to the plumbconnecting line 0102; I.. = 5 x 10-5 is the coefficient of influence of systematic errors of linear measurements; and mfJ is the rootmean square error of angular measurements. Other terms are the same as in the preceding formulae. The values of R x. are determined on the surveying plan. , If the discrepancy is within the permissible value, all lengths of the underground connection polygon are corrected according to the formula: Asi = -(AC/C)Si (4.25) Then, corrections are determined for the direction angles of the underground connection polygon in order to recalculate this polygon into the coordinate system on the surface. These corrections are found by the formula: Aa
=
ao
o 1
-a' 2
o
o 1
(4.26) 2
The direction angles of the sides of an underground connection polygon will be: ai=ai+Aa
(4.27)
It is now possible to calculate the coordinates of all points of the underground connection polygon from the measured lengths of sides, corrected lengths of sides, and corrected direction angles. The coordinates of a plummet 01 on the surface are taken as the initial coordinates. The r;oordinates of a plummet O2 obtained by the recalculation of the underground connection polygon and on the connection on the surface
Table 4.4. Calculation of Direction Angle and Length of Plumb-Connecting Line in the Coordinate System Adopted on the Surface and in the Conventional Coordinate System Surface coordinate system tan a = Y02 -Y01 Xo -X 2 01
L\y
Ay 0102
L\x
b 13211.868 13325.417 -113.549
YO2 YO1 A.y
9
XOl dx tan
a
a
Conventional
tana' =
coordinate
y' , 02- Y01 x '°
-X ,
, 0,
77810.278 77938.922 -128.644 -128.644 -15.095 -113.549 98.454 1.306641 307°25'39"
YOl +XOl dx+dy
11
64 598.410 64613.505 -15.095 7.522292 262°25'39"
XOl
=
13
dx+dy L\x
14
dy
15 16
L\x-dy tan (a + 45'
17
a+45°
I1x
cosa
c
YO2 +XO2
10
12
3 4 6 7 8
= sina
a 1 2 5
=c
18 20
Ay sin a
22
c
19 21 23 24
-113.549 0.991279 114.548
-15.095 0.131781 114.546 114.548
~x cosa c Cc
system
dy' A uX
.ix'
+ .iy'=
(Y~2 + X~2)
,
cosa' -(y'
+ 01
x'
) 01
Ax' + Ay' tan(a'
25 26 29
YO2 YO1 Ay'
27 28
XO2
30 31 32
tan a'
XOl ':\X' a'
2.224 0.000 2.224
+ 45°) =
33
YO2 + XO2 YO1 + XOl
-114.515 0.000
34 35 36 37 38
-114.515 0.010421 178°53'15"
39 40 41
dx' + dy' dx'
+ dy' dx' dy'
dx'
-dy'
tan (a' + 45°) a' +45°
.,
.-,
-112.291 0.000 -112.291 -112.515 -114.515 2.224
42 44 46
sina'
43 45
d.x' cosa'
-114.515 0.999812
-116.739 0.981898 223°53'15"
47 48
c' c'c
114.537 114.537
da= =a-a'
49 50 51
a
262°25'39"
a'
178°53'15"
da
83°32'24"
Ay'
c'
2.224 0.019416 114.545
"' .:= .. .c CI1
= ... ; ~ > Q ~ E..~ .-=
>, .D ~ Q)
Q)U
= C\SC\S .,g Ou .. = a. .C O .. ~
CI1
..
Q)
~ a. .c CI1 = .~ ~ "3 :i. ..Q) U U C\S tri"E. ..,. >, a. -;.. .c ..=
E-
., e. '" c
'E o o u
"
g~
-"' '"" .:"' .-'" """, '"'"
u.-
'-~ 00 "' ';j "U =0= -;..2 >
.:
-;8 -.0 =0= -0 "'00 Z,-
,",,~ ..,,~
...2.
°uoo.' u"o:
1:1 u ' "' " 0= " .=.9"01, Q-o=
'"
.. B 9 "' ~ .J:: u .., ~
><
...
'<:
tj 8
tj = ';J
8 ~ ~ "' "' ~ ... .. t.s ~ = o S Q) ~ >. "'
2 t.s = ;,s .. o o u Q) -5
.5 "' ;:; S S ~ "E.
." ~ ~
'0 "'
U
:p; 0 O
'; =
Q)
~"O/)CQ. 00 Q "00
~
, "' 0~.5
0, \0
~
on O ~ M -0
M "' M 00 N '-0
~ ""' N M M -
N
~ N N ~ aN t'"I t'"I
""' 0'\ "'") N '0 """ '0
N O O
~ M .r; ..,. I
~ N ..., -
\0 V) \0 ,..; .." I
""' t"'; +
00 00 00 r'") 00 ~ N N
$ ~ +
-0 -.r
~
1-
<=! ""' N
N 00
I
::!:
N I
O
00 N
M
~ M -
Ir) o o ..t I
rrV) 0'1 0'1 O
N 00 ""' o O
-0 ",.
0\ O
'-0 rrr-.: I
~ ...; +
..,. r-. N ~ ~ ~ 0
1/") 0\ 00 00 00 O
~ 0
~ M ~ 01 "'
00 ~ O 00 M ~ 0
""' 0\ 0; "'
1-
01~ -0 -
~
00 00 00 N Ir) o O
~ \r) -t
O M
00 01")
00 0; ~
~ 00 (:7\ (:7\
-
00 00 \0 ; V
o 0
;
00 ~
~
\Q r'"\
0\ v
M O O 00 'r\
ID M
\Q \Q N O M
>
~ N
M
~ '"" .". N
11-
~
11-
'"'"'
'r) 00
O 1'N 0\ 0\ 0\
"'1' \0 \0 "' \0 ~ 0
,..., Ir\ ~ N ~ o O
""
Ir) 0\ N "t'
tr) tr)
>
~
0 0
> -
O ~
-
~ M N
10
~ "'
00 0\
-0 ~
~ N
-0 00
r"': Ir)
..., 0r-0Ir) "! 0
~oo c~
M 00 00 N 00 ID
~
~ = ~ O .. 01) .. 0) O)~ u =
;. "'
'2T ~N "' I 0,; -1i1i 00 ~O)O) ...;. ° "' ~::.::.
:i -o
1'0 0 -6
~ ~ ~ ~ ~ ~
~ ~ 0: ~
~ -.1-
rO O -0
Ir\ Ir\ :!:
~ N "i N
" c
1"-8! o
0
0N "'! a+
0\ "'" tr) tr) tr) 1-
100 -0
~ N Ir\ 0
8 o
~ O ~
~ 0
M 0\ O ." ."
0
~
= >
N N
O
0\ ""'
00 -0 O N "'
>
"" ~ 0 "' "'
~
~ Ir) ~
""' ""' N r..: ""' .,.,
.q. $ N Ir) I IC rN 16 I
00 0N -
\C .,.,
'"") .,., .,., v \C
""' N
N Ir\ Ir\ O -0 :76:76
000 00\ \O1r)
1aI ~ 0;
'0 a0; Ir\ +
~ "' r-O
~ ""' Ir) 0\
00 "' ""' 0 -
~ 0
00 O 0\ I,)
"'" r-r--:
~ 00 00 O
N ." I." ~ 0
-'rl -N 0-,.."
~c;i
-0 t')
.., 'C N
00 ..,
+
O M
N N N
~= 00'1") 00'1") 0\0(")
-\0 N-
O "' M
00
-\0 \ON N,,",
> -
=0 >
-
'Ooo r-'O r-oo r-.:...: MMM """'"'
~o 00-~
:1;
0 r'"\ -0 00 0\
oM 00 M 0~ 0
~ ""' r.: ""' N ""' -
ci
r~ rr~ 0
00 0 -c
~ N ""'
~~ ~rNr0""~ -~
"'" O 0\
~ ~ 0
-Co:t' I -
00
0
:!:
§; ~ I 00 01 M O "' -
""'-
C!
O \Q O
$
""' N .,., ...; oN 00 N -0 Ir)
.,., 0 .,., M
~
0 II") ~
~ O N +
\Q ~ 1"-~ +
~ N ..,. 1-
'0 ~
E ~ N ~.
::0 :z
~ "'
~ >, "'
=
00 M ~ '-0 Ir) N M -
M N ~ ~ +
0
00
~
N 1.0 N
"" "" ~
'00 N '00 00 00 C7) 0
r-aNr~a""\0 ~-
O M
"'" 0
0
00 00 ~ M "1"
-.1--.1NOJ")
r-", NN 00-
O r'"\ r'"\ -
0 0 ~ N 000 0-
:;:; N 0
~ "'" 0
~ I...;
o 0
0~
"' '-0 M 000
'0 '0 !"'j M IJ")
'0 '"'"'
"' ""' 1"-0 N
~
1M ~ 1-
N ~
N M
1-
>
~ N
M QO
>
00 ""'
:::
t' "' ~ I
~ , ,
5: "' M M
N
'I" M N ...; 'I" M M
r'"I -
-
...r'"I O O
C
.-.,., "tj
(,)
8 ~ ;3 "' ..:: t "' ~ ~ -5
.5 ~ ~ ~ >
~ (,) .t: v § = 0 ~ 0 0, bi) .5 'g =
0
= 0 (,) '0 "' = .0 0, "tj = "' "' v E E ;3 '"5. '"' ~ -0; = :0 ... 0 o U
Ir\Ir\ 0\0\ 00 """'"' --
~~ Ir)Ir) ...;...; ---
~~
58
Ch. 4. Connection
can be used for checking. The discrepancy between them must be within the accuracy of calculations. If other methods have not been used for orientation, connection survey via two vertical shafts must be carried out twice. The final result is taken as the arithmetic mean of two procedures. It is recommended to make the connection survey via two vertical shafts in combination with gyroscopic orientation of the sides adjoining the plummets. An example of calculation for orientation via two vertical shafts is given in Tables 4.4 and 4.5. If a mine field is opened by three or more vertical shafts connected by underground workings, it is recommended to make connection survey through the shafts with the use of redundant measurements. 4.9.
Horizontal Connection Survey with Use of Gyrocompasses
The wire of a plummet hanging in a shaft is subject to the action of a number of factors which tend to deviate it from the vertical position. The most important among these factors are air currents in the shaft and underground workings, and abundant water drip (downpour). These factors have been investigated and can be accounted for by special formulae. These factors have however become less important with the appearance of gyroscopic instruments which can determine the direction angles of any traverse side in a mine with an accuracy to 10-20". In that connection, geometric methods of orientation now have only a limited application, mainly in the construction of new mines. Repeated orientations in exploited mines are mostly carried out by means of gyrocompasses. Further, the essential disadvantage of geometric orientation via a single shaft by means of two plummets is that the distance between the plummets is too short and a direction angle
Surveys
cannot be transferred underground with a sufficiently high accuracy. A practical merit of gyroscopic orientation is that the direction angle of one or several sides of an underground survey net can be determined with a high accuracy in any place of the mine field and at any distance from the shafts. These circumstances have predetermined wide popularity of the connection survey method in which the coordinates x. y of an initial point of an underground polygon are determined by means of a plummet sunk into the shaft, (the problem of projection), and direction angles are then measured by the gyroscopic method. Under production conditions, the problems of centring and projection are tackled separately and in the following sequence. The projection problem is solved by means of a plummet hung in the vertical shaft. The method and equipment in this case are essentially the same as in orientation via a single shaft by means of two plummets. It should be noted, however, that, since the direction angle of the initial traverse side will then be determined by the gyroscopic method, the projection can be carried out in a simplified way without spending time for the stabilization of a plummet, determination of its central positions on scales,etc. on the surface and in the mine. A polygonometric traverse of an accuracy of not less than second-order is run on the surface from the initial side 31-32 to the centring point, i. e. the plummet point ° (Fig. 4.12). The angle ~A at a point A and the distance from that point to the plumb line 0, IAO' are measured in the shaft; the direction angle of a side A-B (IlAB) is then determined by the gyroscopic method. The direction angle of a side O-A is calculated by the formula: IlAO = IlAB -~A :J: 180° (4.28) and the coordinates of the first point (A) of an underground side, by the formulae:
4.9.
Horizontal
Connection
Survey
by Gyrocompasses
59
4.9.1. Theoretical Principles of Gyroscopic Orientation
Level950 m Fig. 4.12 Solving projection problem for determining initial point coordinates of underground polygon
XA =
Xo +
loAcosuoA
(4.29)
YA = YO+ loAsin aoA This method is used especially widely at mining enterprises with large mine fields and block-type vertical shafts located at a distance of 5-6 km from the main shafts. The connection survey made by this method increases substantially the accuracy and reliability of the survey reference net in the entire wing of a mine.
Mine surveying has in recent time become less labour-consuming and more accurate due to the appearance of reliable small-sized and explosion-proof gyrocompasses. The operating principle of a mine-surveying gyrocompass is based on the daily rotation of the Earth and the property of a free gyroscope to rotate freely in three mutually perpendicular planes (Fig. 4. 13). A gyroscope is called balanced if its centre of gravity coincides with the suspension point O (the point of intersection of the three axes). Balanced gyroscopes in which there is no friction in the suspension supports are called free. Free gyroscopes can exist only theoretically. Practically, the centre of gravity is always displaced somewhat relative to the suspension axis and there always is friction, though slight, in suspension supports. A free gyroscope (Fig. 4.13a) comprises a massive spinning disc, or rotor 2, which is suspended in two gimbals. The rotor is mounted in the inner gimbal 4 and outer gimbal 7 on bearings 1,3, and 5. This system allows the rotor to rotate freely on the
(a)
y
Fig. 4.13
Free gyroscope (a) and pendulum gyrocompass (b)
60
Ch. 4. Connection
Surveys
principal (spin) axis x, rotation axis of the inner gimbal y (sensitivity axis), and rotation axis of the outer gimbal z (precession axis). As the disc is rotating simultaneously on the three axes, the suspension point O remains immobile, and the x axis acquires stability and do~s not react to rotation of a base 6, in other words it retains a stable orientation in space. If the moment of an external force is applied to the x axis of a quickly rotating gyroscope, this axis turns (precesses)in the plane perpendicular to the force applied. The angular velocity of precession, O>pr'is directly proportional to the moment of external force M ex and inversely proportional to the rotating velocity H of the gyroscope:
E Fig.
4.14
Components
of Earth's
,x rotation
The principal axis x of a gyrocompass set up to a point O at a latitude
pr,=M ex/H (4.30) position continuously relative to the horizon If one of the degree of freedom of a plane under the action of Earth's daily rotation, so that its north end will rise gyroscope is restricted, the centre of gravity, which develops an additional pendulum load continuously above the horizon. The principal axis is acted upon by the moment of the on the sensitivity axis y, will displace downward along the z axis into a point O 1. This force of gravity of the pendulum weight, system is called a pendulum gyrocompass which is applied in a vertical plane and tends (Fig. 4.13b). A weight Q causes the x axis to to turn the axis in the horizontal plane adopt a position parallel to the horizon towards the meridian. The angular velocity of rotation of the plane. With quick rotation of the system, the x axis is arranged in the meridional plane. horizon plane, 0)3' around the sensitivity axis The daily rotation of the Earth, when obser- y, which underlies the operating principle of a ved from the North pole, is seen to occur gyrocompass, is called the useful component of Earth's rotation and can be determined by anticlockwise (Fig. 4.14). As the Earth rotates with an angular velocity 0>,the horizon plane the formula: rotates in space with an angular velocity 0>1 0)3 = O)cos2 around a vertical line. plane at (1= 00, then 0)3 = 0. At (1 = 90°, 0)3 The angular velocities 0>1and 0>2depend on has the maximum value. The angular velocity 0)3 also depends on the latitude of the station the local latitude 1= o>cos2= o>sin1, determines variations in the attains a maximum. In all positions, except for that at (1 = 0, height of the Sun and stars above the horizon the principal axis x of a pendulum gyroline and the vertical component 0>2,variacompass develops a moment of the gravity tions of their azimuthal positions.
4.9.
Horizontal
Connection
force (guide moment of gyrocompass): Mg = H 0) cos
sine
Survey
by Gyrocompasses
61
external force, M ex' and the maximum guide moment
Mg
(at
a =
900)
and
can
be found
m~x by the formula: E = Mex/ M g
(4.36) max
The correction E is introduced with a proper sign when calculating the gyroscopic azimuth of a side being oriented. 4.9.2. Mine Surveying
Gyrocompasses
There are several types of gyrocompasses which can be divided into three groups by the
(4.34)
If the gyromotor is brought into rotational motion, the gyrocompass axis will perform continuous harmonic oscillations about an equilibrium position coinciding with the meridional plane. The axis of symmetry of harmonic oscillations relative to the meridional plane is called the axis of the equilibrium of a gyrocompass and the positions in which the velocity of motion of the axis is equal to zero and the motion is reversed are called the points of the gyrocompass axis. The time during which the gyrocompass axis performs a single elliptic oscillation and returns into the initial position is called the period of continuous oscillations of a gyrocompass which is expressed by the formula: T= 21t.JH/MO)
cos
(4.35)
Under the action of friction forces, however\ the oscillations of the gyrocompass axis are gradually attenuated, the amplitude of oscillations A i decreases,and the pattern of motion of the axis changes from elliptical to that along a twisting helix. This results in a deviation of the gyrocompass axis by an angle E from the meridional plane. The magnitude of E depends on the moment of an
Fig. 4.15 General view of gyrocompass type MVT2: l-angle-measuring unit; 2-rotatable housing; 3- base; 4- foot screws; 5 -connecting cable; 6-power supply unit; 7-instrument casing; 8gyro attachment; 9-endless micrometer screw
",,' -2
4~
59
~1
4 5
5.2
I II
~.y
/9 c-I0 ! .11 ~
:~ ~ 45-
--12 ---13 1-14 -15
4342414039 383736 35 34-
3332-
Fig. 4.16 Gyrocompass type MVT2: 1- autocollimator; 2-illuminating unit; 3-illuminating lamp; 4-illuminating prism; 5-eyepiece; 6-upper rectangular prism; 7- objective; 8 -lower rectangular prism; 9-rectangular prism; 10-upper clamp of torsion suspension; 11- connector assembly; 12 fixed mirror; 13-SE mirror; 14-protective glass; 15-torsion suspension; 16-cable; 17-brushes; 18-collector; 19-cable coupler; 20-1ocking device; 21- gyro attachment fastening; 22- band-type current lead; 23-sensitive element; 24-magnetic screen; 25- gyromotor; 26 ~ gyro unit casing; 27~arrester head; 28-base; 29-base-tuming mechanism; 30-fixed bisector; 31-central hair line; 32-scale; 33-movable bisector; 34-theodolite
-18 ---19 -20 -21 -22 -23 24 -25 -26 -27 -28 -29 -30
---31 Fig. 4.17 Gyrocompass type MVT4: 1-explosion-proof glass;2- illuminating lamp; 3- illuminating mirror; 4 -illuminating prism (upper); 5 -illuminating prism (lower); 6-eyepiece; 7-hair cross; 8-upper rectangular prism; 9-lower rectangular prism; 10- objective; 11- worm screw; 12-rhombic prism; 13-protective glass; 14-sensitive element; 15-torsion suspension; 16-locking device; 17-lower clamp of torsion suspension; 18-locking clamp pin; 19-top of locking device; 20-current lead; 21-transducer; 22-damper; 23-top cover of gyro unit; 24-operating mode switch; 25-switch cam; 26-lock; 27-gyro unit; 28-storage battery; 29-battery fastening; 30-balance weights; 31-lower damper; 32- magnetic screen; 33- bottom cover of gyro unit housing; 34- gyro unit housing; 35- button spring; 36, 37 -connecting ring of gyro unit housing; 38 -lower nut of arrester; 39- SE rod; 40- upper cover of gyro unit; 41- tripod leg; 42, 43- tripod head; 44-locking device sleeve; 45-SE mirror; 46, 47-fixed casing of base; 48-control device and upper clamp of suspension; 49- scale; 50- fixed bisector
4.9.
Horizontal
Connection
design, method of centring, and suspension of a sensitive element. I. Gyrocompasses with liquid suspension and electromagnetic centring. 2. Gyrocompasses with liquid suspension and electromagnetic centring on needle, in explosion-proof or common embodiment. 3. Gyrocompasses with torsion suspension, such as types MVT2, MVT4, and MVB4M developed in this country, which are smallsized, reliable and high-precision instruments relatively simple in manufacture and operation. The gyrocompass type MVT2 (Fig. 4.15) is intended for the orientation of underground sides in connection surveys and especially for measuring the direction angles of traverse sides in the construction of mine survey reference nets. It belongs to the best instruments in the world designed for mine surveying. The mass of the instrument together with the power supply unit and tripod is 33 kg. The time of start is 30 minutes and the accuracy of measurement of direction angles is 20-30". The gyrocompass is positioned by means of a base 3 having a housing 2 which can be rotated around the vertical axis by means of an endless micrometer screw 9. The rotatable housing carries at the top an angle-measuring unit 1 which is essentially an optical theodolite, and at the bottom a gyro attachment 8 in which a sensitive element with gyromotor is suspended from a torsion. The instrument is power supplied from an electric storage battery arranged in an explosion-proof casing. The torsion is made of three strips connected together at flat sides, which makes it possible to obtain a low specific torque. The oscillations of the axis with the sensitive element (SE) about the meridional plane are observed by means of a mirror mounted in the top portion of SE and rigidly fixed to the axis. The standards of the theodolite carry an autocollimator to observe the oscillations of
Survey
by Gyrocompasses
63
the SE mirror. The sensitive element can be fixed in the non-working state by an arrester. The observations of forced oscillations consist essentially in taking readings on the circle in the points of reversion and determining the actual position of equilibrium. The design of a gyrocompass type MVT2 may be seen in Fig. 4.16. The gyrocompass MVT 4 (Fig. 4.17) has been developed on the basis of type MVT2 and has principally the same design. In recent time, a mine surveying gyrocompass type MVB4M (Figs. 4.18 and 4.19) has been developed in this country. The designers have managed to reduce the mass and dimen-
Fig.
4.18
MVB4M
General
view
of
gyrocompass
type
64
Ch. 4. Connection
Surveys
sions of the instrument and the time for determining a gyroscopic azimuth roughly by 50 per cent compared with the gyrocompass type MVT2. In contrast to MVT2, the new gyrocompass is intended not only for basic geodetic surveying, but also for everyday (current) mine surveying associated with the construction of underground reference nets and for measuring horizontal angles. Like MVT2, the instrument type MVB4M is a pendulum gyrocompass with torsion suspension and comprises a gyro unit, goniometer with multi-faced mirror, and power supply unit (transducer and storage battery) arranged in a common housing which is mounted on a tripod for operation and replaced into a casing for transportation. Tests have shown that the gyrocompasses types MVT2 and MVB4M ensure roughly the same accuracy of orientation. Horizontal angles can be measured by the gyrocompass type MVB4M with an accuracy of engineering theodolites. Technical characteristics
of gyrocompasses MVT2
Error
of
determination
gyroscopic Time side, fors
Fig. 4.19 Gyrocompass type MVB4M: 1- gyro unit cover; 2-storage battery; 3-torsion suspension; 4~transducer; 5-catch; 6-current lead; 7- arrester; 8 -locking device; 9- SE magnetic screen; 10- gyromotor; 11-multi-faced mirror; 12~measuring unit casing; 13-mirror for vertical sighting of telescope; 14-rectangular prism; 15-vertical sighting head; 16-teleobjective; 17pentaprism; 18-fixed mirror; 19-photographic objective; 20- hinged mirror; 21- graticule of scale microscope; 22-eyepiece; 23-light filter; 24-illuminating prism; 25-illuminating lamp; 26-illuminating unit; 27- fixed mirror scale; 28- magnetic screen on gyro unit housing; 29-arrester pinion; 30 -lower sleeve of arrester; 31 ~ upper sleeve of arrester; 32- sensitive element; 33 -lower clamp of suspension; 34 -pin with balance weights; 35- upper clamp of suspension; 36- protective cap of upper clamp
azimuth
of
determination
gyroscopic Number
min
starts
without
Mass recharging, of instrument at
least. set
for Number point,
operation kg. of units
a of
azimuth, of
MVB4M
of
at in
..
ready
30
40
20
15
15
10
station the
set.
.
37 3
19 2
The principal design feature of the gyrocompass type MVB4M which distinguishes it from type MVT2 and determines the scheme of gyroscopic azimuth of a side, is the provision of a goniometer with multi-faced mirror; this has made it possible to diminish substantially the mass and dimensions of the instrument.
4.9.
Horizontal
Connection
Survey
by Gyrocompasses
65
In the modern mining practice where mine fields and dangerous zones are continuously increasing and it is impossible to ensure permanent planimetric positions of points of a reference net, an efficient method for decreasing the influence of angular errors in nets and increasing the reliability of surveying is the introduction of reference nets with gyroscopic polygons in which the direction angles of all sides are determined by the gyroscopic method, i. e. by means of gyrocompasses.
side; Go is the gyroscopic azimuth of the initial side; and Yo is the meridian convergence in the station point of the gyrocompass on Earth's surface. The gyroscopic azimuths of sides on the surface and in the mine must be measured twice. The difference between the two observations must not exceed 2'. Their arithmetic mean is taken as the final result. The formula for determining a gyroscopic azimuth is as follows: G = (N -N 0) + E (4.38)
4.9.3. Gyroscopic
where N is the reading on the gyrocompass circle corresponding to the direction onto a point on the surface or at the underground side being oriented; N 0 is the circle reading at the equilibrium position of the sensitive element; and E is the correction for twisting of the torsion suspension. The junction direction N on the surface or of an underground side is determined twice, at the beginning and end of a start and at two different positions of the vertical circle. The difference between the two measurements should not exceed 30". The final result is found as the arithmetic mean of the two observations. The difference between the direction angle ao and gyroscopic azimuth Go of a side BC on the surface constitutes the gyrocompass correction 0. A start in the mine determines the gyroscopic azimuth G of an underground side DE to be oriented. The direction angle of DE is: a = G + 0- Y (4.39)
Orientation
This kind of orientation can be carried out either independently or in combination with other methods. It is obligatory in opening a deposit by means of inclined shafts with angles of dip more than 70°. At least two sides at each mining level must be oriented by the gyroscopic method. In the reconstruction and construction of mine survey reference nets, a side is oriented gyroscopically in each section. The direction angle of an oriented side must be measured independently twice, the discrepancy between the two observations being not more than 2'. The principal diagram of the determination of direction angles by the gyroscopic method is illustrated in Fig. 4.20. In the gyroscopic orientation of a side, it is recommended to make four starts of the gyrocompass, the first and the fourth being done on the surface at one and the same side with a known direction angle and the second and third, at the oriented side in the mine. The first start before sinking into the mine and the fourth, after completion of observations in the mine, are performed in order to determine the gyrocompass correction (0} which can be calculated by the formula: 8 = no -Go + Yo (4.37) where no is the direction angle of the initial ,-17711
where Y is the meridian convergence for the underground station point of a gyrocompass. Substituting from formula (4.37) into (4.39), we obtain: a = ao + G- Go + 01' (4.40) where 01'is the difference of meridian convergencesfor the gyrocompass station points on the surface and in the mine, which can be
Ch. 4. Connection
66
Surveys
c IT
, 'g
"io
si
c ..,..0
Ili 1
o
-1
1--
c'
~;I
'Y
c;
r
y
Fig. 4.20 Determination of direction angles of sides by gyroscopic method: BC and DE-respectively initial and oriented sides; B and D-station points of gyrocompass on surface and in mine; Ao and A -astronomical azimuths of initial and oriented sides; no and n-direction angles of initial ~nd oriented sides; Cg and C;:-directions of gyroscopic meridians; Go and G-gyroscopic azimuths of initial and oriented sides; L" and C'-directions of astronomical azimuth in points B and D; o-gyrocompass correction; 't-measuring unit constant; Yo and y-meridian convergences in points B and D; x and y -rectangular plane coordinates
4.9.
Horizontal
Connection
Survey
by Gyrocompasses
67
Fig. 4.21 Determination of gyroscopic azimuth of a side: DE-oriented side; A1. A2, A3' A4 -amplitudes of gyroscopic wobbling of sensitive element; Cg-djrection of gyroscopic meridian; N 1. N 2. N 3' N 4 -circle readings corresponding to reversion points of gyrocompass axis; No-circle reading at equilibrium position of gyrocompass axis; G-gyroscopic azimuth of side DE; E-twisting angle of suspension
found by the formula: 01'= 1.10YO -I.1Y
(4.41)
where Yo and yare the ordinates of station points B and D of the gyrocompass on the surface and in the mine, km (to be found graphically on the plan) and 1.10 and 1.1 are the coefficients depending on latitude (to be found in tables). 5.
If the ordinates of gyrocompass station points on the surface and in the mine do not exceed 10 km, then ~o = ~ and formula (4.41) takes the form: 01'= ~o (yo -y) (4.42) The equilibrium position N o of the sensitive element (Fig. 4.21) is found from the observations of four successive points of
68
Ch. 4. Connection
Surveys
Table 4.6. Determination of Equilibrium Position of Oscillating Sensitive Element Reversion points
mean intermediate values
readings
h 10
2 3 4
mean inter. mediate values
readings
divisions 30 35 39 44
30 00 30 00
9 II 9 II
22 24 22 24
38 18 42 28
10 10
23 23 23
28 28 35
divisioru
19.4
41.6 41.9
63.8 20.5 63.4
N o =
10
23
31
no
=
41.7
Table 4.7. Calculation of Junction Direction Junction direction 8
N'
8
10
24
10
36
10
30
8
N"
8
10
08
9
57
10
0.2
N = 8°10'16'
Table 4.8. Calculation of Error for Twisting of Torsion and Suspension
'I',
41.7
N
10
24
15
45.0
N~
10
44
52"
Ho
10
'l'c
+0
2'52"
"',
-0
02
52
07
'Vc
+0
20
40
23
31
D
20
40
20.2
+0
00
53
4.9.
Horizontal
Connection
Table 4.9. Calculation or Gyroscopic Azimuth
Survey
69
by Gyrocompasses
Table 4.11. Calculation of Meridian Convergence
N
8
10
16
No
10
23
31
+99.1
+99.3
357
46
45
-1.3
-1.5
E
+0
00
53
G
357
47
38
N -N
o
~ 0.
36.5
-0'50"
36.5 .0'55"
Table 4.10. Calculation of Gyrocompass Error Initial sides
points. The correction for twisting of the torsion and suspension is calculated by the formula: E = '11/D (4.44)
Polyamy-Novy 12, 35
40,43
Starts
G~
7
35
l6
Go
17
35
29
B
+0
23
4(j
17
35
22
17
35
35
+0
24
10
where N l' N 2' N 3' and N 4 are the readings on the gyrocompass circle at reversion
where D is a coefficient determined as the ratio of the specific guide moment to the specific torque of the torsion and '11:is the twisting angle of the torsion: '11= '11 t + '11 c (4.45) Here '11 t is the zero of torsion suspension determined by the formula '11 t = t (no -nc); t = 52" is the scale value of an autocollimating telescope; no is the suspension zero; and nc is the scale reading of an autocoltimating telescope corresponding to the positiQn of a fixed bisector in the determination of the suspension zero; the term '11 c can be found as the difference of circle readings N c -N o corresponding respectively to the mean value of oriented direction and the equilibrium position of the sensitive element, i. e.: '11 c = N c -N o (4.46) In practice the results of observations and calculations of direction angles in gyroscopic orientation are recorded in a record book (Tables 4.6-4.12).
70
Ch. 4. Connection
Surveys
4.10.
Vertical
Connection
Surveys
km. The height mark transfer should be made independently twice. If the dipping angles of opening workings exceed 5-8°, height marks are transferred by trigonometric levelling. The procedure requires the use of theodolites with the vertical circle accuracy of not worse than 30". Height differences at each side of a traverse line are determined twice: in the forward and back direction. The height mark transfer is performed independently twice. The difference in heights, mm, in this case must be not more than L\h = :t 10~
(4.47)
where nl' n2 is the number of sides in the first and second trigonometric levelling line. Most coal mines are opened by vertical shafts where height marks can often be transferred by means of a long steel tape or length-measuring winch. 4.10.1. Transferring a Height Mark into a Mine by Means of Steel Tape In this method of height mark transfer (Fig. 4.22), the hand winch 4 with a measuring steel tape 7 wound onto its drum "is placed on a temporary platform 3. The tape with a light weight (3-5 kg) is let to sink onto the pit bottom level; then the light weight is replaced by a standard weight 2 corresponding to that with which the tape has been standardized. Measurements are made as required by surveyor's levels 6, set up on the surface and in the mine. Level readings are taken on a staff 1 (asur)set on an initial bench mark R.ur and on a tape 5 (n...r). At the pit bottom level, readings are taken from the station point of the surveyor's level on the tape 5 (nm) and on the staff 1 (llm) set on an underground bench mark Rm. During levelling, air temperature is measured at the surface (t sur)and at the pit bottom level (tm). Then, the position of the tape is
changed by lor 2 m along the height and the horizons of the instruments are changed to make another series of observations. The height difference for each series of observations is found by the formula: hmeas = nsur-nm + asur-am (4.48) The values of hmeasas calculated by two series of measurements must not exceed the permissible deviation L1h = (10 + 0.2H), mm, where H is the depth of a shaft, m. Upon averaging of hmeas'the following corrections are determined: (a) for tape standardization, L1/1, which is taken according to the tape certificate; (b) for thermal expansion of the tape
72
Ch. 4. Connection
Al2 = al(t -to), m, where a is the temperature coefficient of linear expansion of the tape (for steel, a = 1.2 x 10-5); t = 0.5(tsur + tm) is the average temperature of air in the mine; to is the temperature at which the tape has been standardized; and 1 = nsur-nm is the interval measured by the tape in the mine, m; (c) for elongation of the tape under the action of its own mass A13= fyg/2E, m, where y is the density of the tape metal (for steel, y = 7874 kg/m3); 9 = 9.81 m/s2 is the acceleration due to gravity; 1 is the length of the hanging portion of the tape, m; and E is the elastic modulus of the tape metal (for steel, E = 2.5 x 1011Pa); (d) for elongation of the tape due to the different mass of the weights used in standardization and measurements Al4 = 100[(P -Po)/EF], m, where P is the mass of the standard weight, kg; P o is the mass of the weight used in the tape standardization, kg; and F is the cross-sectional area of the tape, mm2. The elevation of a bench mark in the mine, Rm, is determined by the formula: H m = H sur+ hmeas (4.49) where H suris the elevation of the initial bench mark on the surface and h meas is the measured height including all corrections. 4.10.2. Transferring a Height Mark into a Mine by Means of the Measuring .Winch The measuring hand winch shown in Fig. 4.23 has a drum 3 with a steel wire wound onto it. As the handle 5 is turned, a system of rollers 4 rotates the drum and a measuring disc 2 which makes one full turn per metre of unwound wire. The number of full turns is indicated by a counter 1, whereas incomplete turns are indicated with an accuracy to 1 mm on the scale provided at the rim of the measuring disc. In order to measure the depth of a shaft.
Surveys
4
2
~I~iilli~ 5
3
4
Fig. 4.23 Measuring winch
the wire is let to slide over a length measure 1 and a guide pulley 2 into the shaft, and readings are taken on the scales at the beginning and end of the procedure (Fig. 4.24). In depth measurements, aweight-staff 3 with centimetre marks is attached to the end of the wire and the check staff 4 is fastened lor 2 m above the weight-staff (in the top position of the wire, the check staff is not shown in the figure). This scheme of height transfer is much similar to the scheme with the use of steel tape. An observer on the top platform takes the following readings: N sur on the counter and measuring disc scale; tsuron the thermometer of the measuring disc; Asuron the scale of the weight-staff by means of the surveyor's level placed at the station point on the surface; and asur on the staff set up on the initial bench mark Rsurby means of the surveyor's level at the station point on the surface. Then the check staff is lowered onto the level glass of the levelling instrument and all observations are reneated.
4.10. Vertical Connection Surveys
73
These measurements conclude the first stage of observations. After that, the positions of the wire and surveyor's levels are changed and the observations are done in the inverse order, i. e. starting from the pit bottom level. The height difference between the bench marks Rsurand Rm is calculated for each series of observations by the formula: hmeas= Nsur-Nm + asur-am -Asur + Am (4.50)
Fig. 4.24 Transferring height mark into mine by means of measuring winch
The weight-staff is then lowered onto the pit bottom level to take similar readings: N m on the counter and scale of the measuring disc; t m on the thermometer in the pit bottom; Amon the scale of the weight-staff by means of the surveyor's level set up in the pit bottom; and am on the staff placed on the bench mark to be controlled by means of the surveyor's level in the underground station point. As on the surface, these measurements are repeated on the check staff.
If the discrepancy between the observations is within permissible value, the arithmetic mean of hmeas is calculated and the following corrections are determined: (a) for wire diameter fj.ll = 0.0017tdl, m, where d is the wire diameter, mm; (b) for standardization of the disc fj.12 = = (k --'-1) I, m, where k is the actual length of the circumference of the measuring disc as given in the certificate; (c) for thermal expansion of wire caused by the temperature difference in the shaft fj.13 = =0.5all(tm-tsur)' m, where al is the temperature coefficient of linear expansion of wire and t surand t m are the temperatures on the surface and in the mine; and (d) for thermal expansion of the measuring disc considering the difference in temperatures during standardization and measurements, fj.14 = a21(tsur-to), m, where a2 is the temperature coefficient of linear expansion of the disc and to is the temperature of disc standardization. The elevation of the bench mark in the mine (Rm) is calculated by the formula: Hm = Hsur + hmeas+ fj.4 + fj.12 + fj.13 + fj.14 (4.51)
Chapter Five Horizontal
Surveys
of
5.1. General on Underground Mining Surveys The mine survey service of mining enterprises has to tackle matters of timely and accurate determination of the spatial position of undergound workings and all other objects essential for the mining production. The spatial coordinates obtained by mine SUfveying are the basis for compiling and supplementing mining work plans and other kinds of graphical documentation, as well as for the solution of various problems of rational and safe exploitation of mineral deposits. The principal objects of mine surveying are: (a) underground workings (opening, preparatory, development, stoping, draining, exploratory, etc.); (b) boreholes (prospecting, operating, unwatering, water-observation, etc.); (c) boundaries of safe mining work, safety and barrier pillars; (d) contours of inundated, gas-laden, and caved workings, centres of underground fires, isolating partitions and other ventilation structures, gas blower sites, areas and contours dangerous in gas or rock outbursts, rock bump, water inrush, floating earth, sources of underground waters, etc.; (e) characteristic points of bedding elements of mineral deposits (dipping angles, capacity, characteristics of quality and structure); (f) points for documentation of geological disturbances and other textural and struc-
Underground
Workings
tural characteristics of deposits and enclosing rocks; (g) points of mineral assaying; and (h) location of surface and underground artificial structures and stationary equipment in underground workings (hoists, ventilating and pumping plants, various chambers, explosive stores, locomotive sheds, medical service, etc.). The mine survey service solves its problems by constructing reference and survey nets at the mining enterprise. Underground survey nets are understood as a combination of geometrically interrelated polygonometric traverst:s and levelling lines which are balanced (adjusted) jointly or separately. Underground reference nets are the principal geometrical basis for making the surveying work and dealing with particular mine survey problems aimed at ensuring rational and safe exploitation of a deposit. The errors permissible in the measurements of horizontal and inclination angles
Table 5.1
20"
0.001
0.00005
0.01
5.2.
Horizontal
Underground
and side lengths in polygonometric traverses can be characterized by the data given in Table 5.1. 5.2. Horizontal Surveys
Underground
The principal kind of horizontal survey in underground workings is theodolite surveying which consists of angular and linear measurements and subsequent calculation of the rectangular coordinates x, y of survey points. The straight lines laid between the mine survey points in underground workings form closed or open polygons, or theodolite traverses. Each theodolite traverse is oriented, i. e. tied to the points of an earlier (initial) survey. Several types of underground theodolite traverses and methods of their connection are employed most often in Soviet mine sur., veying practice, which can be classified by the redundant initial data and the type of (dl
75
Surveys
control. By these features, theodolite traverses may be divided into free and non-free. Free theodolite traverses are referenced to only one point with fixed coordinates and one fixed direction angle; they may be subdivided into open (hanging) and closed. The line of an open theodolite traverse may be stretched (Fig. 5.la) or broken (zig-zag) (Fig. 5.lb). Such traverses are controlled by a repeated theodolite survey. Closed traverses (Fig. 5.1c) are controlled by comparing the sum of the measured angles and the sum of coordinate increases with their analytical values. Non-free theodolite traverses have redundant initial data. They can be run: (a) between the fixed points and fixed direction angles: in that case complete control is ensured in terms of direction angles and coordinates (Fig. 5.1d); (b) between the fixed direction angles with the initial coordinates of one point, i. e. with control in terms of direction angles (Fig. 5.le); (el
(Xn+1 ~I 'L~
cr-
(bl
(f)
Fig. 5.1 Types of theodolite traverses: (a), (b), (c) free traverses; (d), (e), (/), (g) non-free traverses
76
Ch. 5. Horizontal
Surveys
(c) between two points with fixed coordinates and with an initial direction angle, i. e. with control by the coordinates of the fixed points (Fig. 5.1.f);and (d) between two points with fixed coordinates, with the initial direction angle being unknown; in that case, control is possible by the length of the closing line of the traverse (Fig. 5.1g). In cases under (b), (c), and (d), a complete control of whether a theodolite traverse has been run properly is not ensured, because of which a repeated traverse is run or the lines and angles are measured repeatedly. Horizontal surveys in underground workings may involve certain difficulties which increase labour consumption, reduce the accuracy of measurements, and increase the error accumulation. Among the principal factors causing such difficulties are: continuous mobility of the underground objects being surveyed and rock displacement around workings resulting in uncertain spatial position of permanent survey points underground; certain limitations in selecting the most favourable shapes (schemes) of theodolite traverses and the best lengths of traverse sides (some sides may turn out to be too short); constricted conditions for surveying in underground workings; poor illumination of working places; dust-Iaden atmosphere in mines; etc. In order to minimize the influence of the factors indicated on the accuracy of surveys and to avoid unproductive labour expenditures, it is essential to adhere to the following main principles in surveying work: I. Mine surveying should proceed from the more general and more precise procedures to more particular and less accurate work, i. e. it should start from constructing reference nets, after which survey nets are plotted, and finally, the surveys of particular mining objects and other details are performed. 2. In any kind of surveying work, all measurements must be done with the
of Underground
Workings
optimum accuracy sufficient for the purpose. An insufficient accuracy can spoil the survey work and require unjustified expenditures on its amendment; in some cases, inaccurate survey work can have serious consequences endangering the safety of mining workers. On the other hand, an excessive accuracy involves a large loss of labour and time of surveyors on unproductive and uselesswork. That is why the mine surveyor must be able to select pro~rly the suitable method of surveying and the required accuracy. 3. Mine surveying must be carried out under an appropriate and timely control both in the field (in underground workings) and in the office analysis of the results of surveys. First of all, it is essential to make a check, or control, before starting a surveyor continuing a theodolite traverse, i. e. to measure the horizontal angle of an earlier survey in the junction points. The difference between the initial value (known from the earlier survey) and the measured value of a control angle must not exceed I' for the theodolite traverses of a reference net or 2' for the traverses of a survey net. With a larger difference in the measured control angle, it should be supposed that the points of the earlier survey have been displaced and the projected theodolite traverse must be tied to other points which are known to be stable. The elements of a survey (side lengths, angles, height differences) must be checked in the course of survey measurements so that probable errors can be revealed and corrected in situ. For instance, when measuring distances, control can be ensured by measuring forward and back; in angular measurements, a check reading on the circle can be taken, etc. The measured angles of a closed polygon (traverse) can be checked by comparing the sum of angles with their analytical sum. The measured lengths can be checked by the discrepancies in coordinate increases and by other methods of control.
5.3. Underground
Reference Nets of Plan Control
For reliable and efficient performance of mine surveying, it is essential, before starting the work, to study carefully the conditions of the field work, to draft the plan of construction of survey traverses by the results of reconnaissance and consider in it the existing peculiarities, narrow places, etc., to determine the set of surveying instruments and equipment, to test and adjust the instruments, to assign performers for the survey work and acquaint them with the survey work plan, and, when required, to make preliminary calculation of the accuracy of surveys. 5.3. Underground Reference of Plan Control
Nets
Underground reference nets of plan (horizontal) control are the principal geometric basis for all horizontal angle-measuring surveys. They are created in the principal opening and advance workings (adits, inclined shafts, crosscuts, inclines, brake inclines, fringe, group and haulage drifts) by running the theodolite traverses of a particular system. The system of construction of reference nets can be characterized by certain specific features, in particular as regards the shape of polygonometric traverses, provision of additional ties, lengths of sides, and number of fixed direction angles. Depending on the bedding conditions of deposits and methods of opening, there are six principal systems of construction of underground reference nets which are employed in Soviet mine surveying practice (Fig. 5.2). I. The scheme of construction of a reference net for working a single horizontal seam is shown in Fig. 5.2a. This scheme is typical for deposits opened by vertical central doubled shafts and is essentially a system of polygonometric (theodolite) traverses run in the drifts of main directions and other
workings parallel and perpendicular to them. 2. In working of single gently dipping and inclined seams where the deposit is opened by inclined shafts and ventilation shafts are driven at the flanks of the mining field, it can be distinguished between two versions of a reference net depending on the working system employed: (a) with a continuous working system, theodolite traverses are run twice in level drifts (Fig. 5.2b); (b) with the system of longwall retreating on strike, survey traverses form closed polygons adjoining one another (Fig. 5.2c). With advancement of mining work in the systems indicated, theodolite traverses are connected to the initial fixed points on the surface. 3. In mining a suite of gently dipping or inclined seams where the deposit is opened by vertical central doubled shafts with a main crosscut and ventilation shafts are driven at the flanks of the mining field, two versions of a reference net are possible: (a) theodolite traverses form a system with junction points (Fig. 5.2d); and (b) if a longwall mining system is employed, the reference net includes theodolite traverses with junction points and closed traverses (Fig. 5.2e). 4. In mining a suite of steeply dipping seamswhere the deposit is opened by vertical central doubled shafts with a main crosscut, the construction of a net depends on the location of mine workings on the main levels: (a) a system of closed-traverses adjoining one another; such nets can be formed in mining a suite of seams where the fringe or group haulage drifts and auxiliary crosscuts are driven (Fig. 5.2./); (b) a system of polygons with closed traverses and repeated control traverses. This version may appear in mining a suite of thick steep seams liable to self-ignition, which requires that fire pillars be left between the workings (Fig. 5.2g).
78
Ch. 5. Horizontal
Surveys
of Underground
Workings (c)
(b)
(f)
(e)
[~I~ 1-L---
5. In high-capacity ore deposits where vertical shafts are driven both in the centre and at the flanks, theodolite traverses are run in crosscuts and fringe drifts and connected to the points of plummets hung in vertical workings (Fig. 5.2h). 6. In underground mining of salt deposits opened by vertical central doubled shafts, a reference net is Conned as a system of adjoining closed polygons (Fig. 5.21). The considered systems of construction of reference nets have certain essential drawbacks in view of the specifics of mining conditions: (a) redundant fixed direction angles, sides and coordinates may be limited in number or even absent. As a rule, the orientation of reference nets is most often carried out in the
~:=
centre of a mining field; further, some sides of theodolite traverses may turn out to be too short. These factors lead to substantial error accumulation and non-uniform accuracy of a net; (b) if the reference net points are displaced and the number of additional ties (fixed coordinates and fixed direction angles) is insufficient, then a need arises to run an appreciable number of repeated theodolite traverses. In existing systems, and the more so, with ever increasing dimensions of mining fields and mining depths, these drawbacks become especially sensible. This circumstance has led to the appearance of more advanced systems of construction of underground reference nets with autonomous orientation of a net by
5.4.
onstruction
r~-r-r-I I I @---6-L-1--b-L-
Reference
(b)
(a)
1 2 3 -:§)- -;:::)-
of Underground
---C](d)
~
@
'0-
I
~ ---{::J-
5.4. Construction of Underground Reference Nets Underground reference nets are constructed according to an engineering design which should consider the actual positions of the existing mining workings and their expected development and establish the most favourable system of the net, the distances between the sides with reference direction
@):::J
, ..d
r§r ~ Fig. 5.3 Examples of arrangement of sides with reduridant direction angles: l-initial 3- side with redundant direction angle
gyroscopic instruments, i. e. with inclusion of redundant (fixed) direction angles (Fig. 5.3). The mine surveying practice quite often uses free hanging theodolite traverses run twice. In order to avoid the need in running a repeated traverse in autonomous determination of direction angles by a gyrocompass, a polygon is divided into sections (Fig. 5.3a).In a similar manner, additional ties can be included into the theodolite traverses between two fixed sides (Fig. 5.3c). In adjoining. free closed traverses of large extension, the reference direction angles are measured in each closed traverse (Fig. 5.3b). In non-free theodolite traverses controlled by point coordinates, a repeated survey is done by measuring the direction angles of the sides adjoining the points (plummet points) with fixed coordinates or the sides close to them (Fig. 5.3d). A similar construction of a reference net with additional ties is possible in a version when the net is developed from a junction point to points with fixed coordinates (Fig. 5.3e).
79
(cl
I
(e)
-J-
Nets
side; 2-traverse;
angles, points and methods of junction of the constructed net to the reference net on the surface, points for setting up permanent station marks, and the order of net adjustment. The work of construction or reconstruction of a reference net is carried out in the following order: (a) reconnaissance is carried out in underground workings and permanent station marks are revised, located and fixed; (b) the sides of a net are oriented by gyroscopic instruments; (c) angular and linear measurements in theodolite traverses are carried out; (d) the net is centred and the theodolite traverses are connected to the points of the mine survey reference net on the surface; (e) the results of measurements are processed preliminarily and estimated for accuracy; (I) the net is adjusted and the point coordinates are calculated; and (g) the coordinates of permanent station marks are recorded in a list. The object of reconnaissance is to investigate the underground workings in which the reference net has to be constructed, to specify the system of the net, and to choose places for setting up permanent station marks. It is also essential to consider the conditions under which permanent station marks will be preserved longer and will be convenient for survey work. Permanent station points are set up in groups of three or four. The spacings between the points in a group are usually equal to
80
Ch. 5. Horizontal
Surveys
50-100 m and the spacings between the groups must be not more than 500 m. The chosen places for setting up permanent and temporary points are fixed in the underground workin~ and on sketches. The orientation of underground reference nets is carried out by means of small-sized gyrocompasses. These instruments offer the possibility for constructing a reference net as a system with intermediate (redundant) direction angles and a system of local nets, in particular at the mining field flanks. The essenceof the system of a reference net with redundant direction angles consists in that a polygonometric net of a length more than 2 km is divided into sections with fixed (gyroscopic) direction angles. The number of angles in section should be not more than 20. The direction angle of one of the sides is measured by a gyrocompass independently in each section, and the results of angular measurements are combined and adjusted. The direction angles of the sides in the sections determined in this way are taken as fixed angles and their relative weights are considered. Nets with redundant direction angles have an advantage of being more uniform; further, the positions of the remotest points of a net can be determined with a higher accuracy. Calculations have shown that the accuracy of the final point of a theodolite traverse of a length of 5000 m, divided into sections (of a length of 1 km), increases by a factor of seven. Besides, it is possible to control the errors in the positions of the points of a net within wide limits in accordance with the location of the sides having redundant direction angles, which increases the reliability of the net. In mine survey reference nets, gyroscopic sides are located roughly in every 20 traverse sides. In order to check 1hat the locations of gyroscopic sides in a projected reference net are chosen properly, calculation is carried out to determine the error of location of the
of Underground
Workings
remotest point of the net, considering the supposed (planned) development of mining work (usually for 5-7 years). The root-mean square error of location of a point relative to an initial point A of a reference net (Fig. 5.4) can be determined by the formula:
+(Lrf)n
+
(Lrf)k
where I and II are the numbers of sections, k is the number of the last section of a net; ~ and A. are the coefficients of random and systematic influence in side length measurements by a tape; ii is the length of a traverse side, m; L is the distance between the points A and 1; m; mp and m« are the rms errors of a turning angle 13and direction angle a; r i is the distance from a theodolite traverse point to the centre of gravity O of the given section, m; R is the distance from each point of a hanging traverse to the final point 1; m; D are the lengths of intervals connecting the points A and T through the centre of gravity O of the net sections, m; and p" = 20~65". The coordinates of the centre of gravity of a section are calculated as the arithmetic mean of the coordinates x, y of points in the
5.5.
Survey
section. The values of I, L r, R, and D are found on the plan of the projected net. In cases when the mining work is carried out at distances more than 1.5-2 km from the shafts of a mine and the points of a survey reference net are subject to displacements, local reference nets are constructed at the flanks of the mining field and oriented by the gyroscopic method. The horizontal angles in polygonometric traverses of reference nets are measured by theodolites reading with an accuracy not worse than 30". The rms error of angular measurements must not exceed 20". When polygonometric traverses are run in underground workings with dipping angles up to 30°, horizontal angles (forward to the left) must be measured by the method of sets or, in extreme cases, by the reiteration method. In the latter case, the difference between a check value and final value of an angle must not exceed 45". If angles are measured by the method of sets, the discrepancy between the half-sets must be not more than 60". In undergound workings with dipping angles more than 30°, horizontal angles must be measured only by the method of sets (not less than two) under the observance of the following rules: (a) before each set, the instrument is centred once more and the vertical axis is set truly vertical; and (b) before making a second set, the initial reading is shifted by 180°. With measurements in underground workings with dipping angles more than 30°, the discrepancies between the angles measured in individual sets must not exceed the values given in Table 5.2. The side lengths in theodolite traverses can be measured by standardized steel tapes (of a length of 20 m, 30 m or 50 m), linen tapes or light range finders. In length measurements by steel tapes, each side must be measured twice (forward
81
Nets
Table
5.2
Permissible angular discrepancy between half-sets, min at junctions between horizontal and dipping workings 31-45 46-60 61-70
1.3 1.8 2.5
in dipping workings
2 2.5 4
and back) and the discrepancy between the two measurements must not exceed 1/3000 of the side length. The sides of a length more than 50 m are recommended to be measured by light range finders. If the discrepancy between the readings of a measured length in the first and second phase does not exceed 2-3 mm, the measurement can be limited to a single set. The maximum discrepancy between the measurements at different frequencies must be not more than 8 mm. The engineering design for mine surveying should specify that the error in the location of the remotest point of the underground net relative to the initial point of the underground reference net or the closest points of that net on the surface should be not more than 0.8 mm on the map or plan. This requirement is dictated by the specified accuracy of graphical construction of mining work plans. As is known, the permissible error of the position of a contour point of the walls of the main working on a plan relative to the points of a mine survey reference net on the surface is taken to be equal to 0.8 mm, while the positions of the walls are determined by taping directly from the net points with an accuracy to 5 cm. 5.5.
Survey
Nets
Underground survey nets are the basis for surveying of mining workings and solution of
82
Ch. 5. Horizontal
Surveys
Table 5.3 Type of traverse
Theodolite Goniometer
mp
40" 10'
m,
60" 10'
Pernlissible discrepancy between two measurements of side closed 1/1500 open: 1/1000, 1/200
of Underground
Workings
tween the check and final values of an angle must not exceed 1.5'; in the method of sets, the discrepancy between two half-sets must be not more than 2'. The angles in the workings with dip angles more than 300 must be measured in two rounds with resetting of the initial reading roughly by 180° before the second round. In goniometer traverses, angles can be measured by goniometers or theodolites in a single repetition or set. The permissible discrepancy between the check and final values of an angle or the discrepancy of angles in half-sets must be not more than 5'. Before starting a theodolite or goniometer traverse, a check measurement of the last angle of the previous run is made. The discrepancy between the earlier and current measurements of this angle must be not more than 2' in theodolite traverses or 8' in goniometer traverses. The side lengths of theodolite traverses are measured by standardized steel tapes twice, shifting the tape after the first measurement. It is permissible to make both measurements in the same direction. The deviations of intermediate plumb-bob lines from the traverse line must not exceed 1/200 of the length of the smaller interval. Tape readings are taken to a millimetre. In goniometer traverses, side lengths can also be measured by linen tapes or optical range finders with a relative accuracy not worse than 1/300. Tape readings are taken with an accuracy to a centimetre.
problems of mine geometry and are constructed in the form of theodolite and goniometer traverses. Theodolite traverses are run in all preparatory workings except for those in extraction sections and blocks which can be surveyed by goniometers. The permissible root-mean square errors in measurements of horizontal angles mp and inclination angles m" are given in Table 5.3. The points of a theodolite traverse serve as the basis for tackling various problems of mining geometry within the limits of a block or panel and for surveys of indicated workings. Goniometer traverses are developed on the basis of theodolite traverse points and serve as the basis for surveying of preparatory and stoping workings. The fixed points of a theodolite or goniometer traverse in these workings are used only once in surveying of these workings or for connection of preparatory workings within the limits of a face. Theodolite and goniometer traverses in survey nets are usually c.osed or are run twice. When theodolite traverses are run in main workings to supplement the plans for further development of reference nets, it is permissible to run free traverses with mea5.6. Types of Station Points surements of left and right forward angles of Reference and Survey Nets. (except for workings approaching pillars or Their Fixation dangerous zones). The angles in theodolite traverses are Depending on the purpose and existence measured by theodolites. In theodolite tra- term of a survey net, the points of theodolite verses run in the workings with dip angles surveys (station marks) are divided into less than 30°, angles are measured in a single permanent and temporary. repetition or set. If angles are measured by Permanent station marks are the basis for the repetition method, the discrepancy be- the development of reference nets. They are
5.6. Station
Points
of Reference
established in the bottom and robf of underground workings so as to ensure their stability and existence for a long time. In view of this, permanent station marks are established where possible in the areas beyond the zones of influence of support pressure or underworking, weak enclosing rocks and rocks liable to heaving. Some types of permanent station mark for establishing in the footwall of workings are illustrated in Fig. 5.5. A permanent station mark usually consists of a metallic rod 25-30 mm in diameter and 200-700 mm long which is concreted in a drill hole (Fig. 5.5a) or pit (Fig. 5.5b and c). The top face of the rod is marked by drilling a hole or by punching a circular (up to 2 mm) or cross-wise mark. For longer preservation, some types of permanent station mark have a pressed-in copper or lead plug at the top, with a punch mark made in it. Permanent station marks established in the roof of workings should be convenient for plumbing a theodolite under them. For this purpose, they have a drilled hole around 2 mm in diameter for passing the line of a plumb bob (Fig. 5.6). Permanent station marks and special bench marks can also be established in the side walls of underground workings. They are usually fixed by concreting.
and Survey
Nets
83
Temporary station marks are fixed in the roof of underground workings, top beams of support frames or on steel arcs. If a working is driven in a hard rock without supporting, a station mark (centre) can be fixed directly in the roof rock (Fig. 5.7a) or in a wooden plug driven into a cut hole (Fig. 5.7c). Figure 5.7b shows a station mark to be fixed on wooden supports and Fig. 5.7d, a mark for fastening on metal lining.
Fig. 5.6 Pennanent station marks for setting in roof of underground workings: (a) in concrete; (b) in wooden plug; (c) hole for plummet line
84
Ch. 5. Horizontal (a)
Surveys
of Underground
Workings
(c)
(bl
(dl
t++~ ~
Fig. 5.7
Temporary
station
marks
Station marks in underground workings are fixed so that a plumb bob can be hung quickly and conveniently and the plumb line be always in the same position. For quick identification of permanent and temporary station marks, metal plates (markers) with their numbers are fastened on support props or on the opposite side walls of a working. In underground workings without supporting or with concrete lining, the numbers of station marks are marked on the side walls by an oil paint using a template. Upon establishing of permanent and temporary station marks in underground workings, their positions are marked on sketches in the surveyor's field book and in coordinate calculation book. The established permanent station marks are transferred onto the mining working plans. Each kind of permanent station marks is provided with a certificate. All permanent points must be numbered.
5.7.
Theodolites
Theodolites are the principal type of an instrument for making underground angular surveys.
-g~ Mining theodolites differ from those employed for surface survey work in certain design features associated with the specific conditions of surveying in underground workings. The principal parts of a mining theodolite should not corrode under the action of chemically aggressive water. They should have small dimensions and low mass and be provided with illuminating devices. The optical systems should be hermetically sealed to prevent mechanical damage and penetration of dust and moisture inside. The possibility should be provided for automatic centring and for mounting of a theodolite and signals on tripods and console holders. The telescope of a mining theodolite usually has an upper centre (thorn) for centring the instrument under a station point by means of a suspended plumb bob. It should permit focussing onto objects beginning from a distance of lor 2 m. Mining theodolites should allow the measurement of inclination angles up to 90°, because of which some models are provided with an eccentric telescope in addition to the central one. Theodolite, type T2 (USSR), is a precise instrument with a rotating limb and two-
5.7. Theodolites
85
sided optical wedge-type micrometer. The ja) instrument has coaxial sighting devices, an optical centring device, and a detachable tribrach which permits surveying by a three-stand scheme.The telescope is provided with two optical sighting devices for rough aiming at objects. By the consumer's request, the instrument can be supplemented with a box compass, striding level, two-sided optical centring device, eyepiece attachment, range finder attachment, and other auxiliaries. The theodolite is designed for class-3 and class-4 triangulation and polygonometry and can measure horizontal angles with an accuracy to :t: 2-3". Theodolite, type 2T2 (USSR), shown in Fig. 5.8a, is a more advanced model and differs from the former in the following: the system of a vertical axis is non-repeating; the reading device takes readings from two diametrically opposite sides of angle-measuring circles, which eliminates the effect of eccentricity of these circles: for more convenience, the field of view of the reading microscope shows additionally the numbers of tens of minutes; and the telescope gives a better image. The tangent screws are set coaxially with winged-knob clamp screws. Both pairs of screws are arranged at the same side of the instrument for a quicker change from azimuth-sighting to vertical plane-sighting of the telescope. The telescope graticule has two horizontal hairs (stadia hairs); one of the vertical hairs is doubled. The horizontal and vertical circles of the theodolite have 20'-value graduations and 10 numbering. The horizontal circle has double Fig. 5.8 Theodolite, type 2T2: (a) general view; (bifilar) graduation lines and the vertical one, 1 ~objective; 2-optical sighting device; 3 -micrometer head; 4- vertical clamp; 5- vertical tangent single lines. The images of graduation lines and screw; 6- horizontal clamp; 7- horizontal tangent numbers are projected in the field of view of screw; 8-clamp screw of base (support); 9adjusting screw of vertical circle level; IO-level the reading microscope by means of a tube; Il-horizontal circle aperture; (b) field ofvi~w double-channel optical system. Changing of scale micrometer (reads 17o 25' 26.5" on from one optical channel to the other is horizontal circle)
86
Ch. 5. Horizontal
Surveys
performed by means of a handle. With the handle set horizontally, the field of view of the microscope shows the images of the double lines of a horizontal circle and with the vertical position of the handle, it shows the lines of the vertical circle. The field of view of the reading microscope is shown in Fig. 5.8b. The central aperture shows the images of graduation lines of two diametrically opposite sides of a circle, which are separated by a halving line. The upper aperture shows numbered degrees and below them, a scale of six numbers (from O to 5), which indicates tens of minutes. The aperture at the right is the micrometer scale with one division corresponding to one second of the arc. To take a reading, the micrometer head is operated to align carefully the top and bottom images of the lines of a vertical circle or respectively those of the double lines of a horizontal circle. If two numbers of whole degrees are seen in the upper aperture, the true one is that which does not pass beyond the limits of the ten-minute numbered scale. The number on this scale just below the degree number gives tens of minutes. Then, whole minutes and seconds are read off respectively on the left-hand and right-hand part of the micrometer scale. c It should be noted that before aligning the vertical circle graduation lines, it is required to align the ends of the level bubble image by an adjusting screw. Theodolites T5 and T5K (USSR) are precise instruments with a cylindrical repeating system of vertical axes. The horizontal circle can be locked with or unlocked from the alidade by means of a repeater lock. The repeating system of vertical axes allows horizontal-angle measurements by the method of reiteration or the method of sets. These instruments are designed for measuring horizontal and vertical angles in underground workings when constructing reference nets and on the surface in analytical
of Underground
Workings
Fig. 5.9 View field of scale microscope of theodolite, type T5 (reads: 74 o 55.0' on horizontal circle and 12 o 06.0' on vertical circle)
and polygonometric nets of the lst and 2nd order. The theodolite TSK differs from TS by the provision of a compensator whicb automatically eliminates the error in measured vertical angles, caused by the deviation of the vertical axis of the instrument. The working angular range of the compensator is ::t 3'. In view of this, the vertical circle alidade has no spirit level. The compensator also ensures precise levelling of the collimation axis of the theodolite, and therefore, the instrument can also be used as a level. The high-quality telescope of theodolites TS and TSK has a magnification of 27 and the focussing range from 2 m to infinity. Optical sighting devices for rough aiming of the instrument are provided at the top and bottom of the telescope. Precise aiming of the telescope is effected by means of tangent screws. The angle-measuring circles have I-degree graduations. Readings are taken by means of a scale microscope arranged near the telescope eyepiece. The scale microscope shows simultaneously the graduation lines of
87
5.7. Theodolites
the vertical and horizontal circle (Fig. 5.9) and its scale is graduated to single minutes. Angles are measured by reading off the degrees on the limb scale and the minutes on the microscope scale; the seconds are estimated by eye as a fraction of the microscope scale division. The reading accuracy is equal to 0.1 of the scale value of the microscope, i. e. :t 0.1" or :t6". Theodolites 2TS and 2TSK (2TSKP) (USSR) are further modifications of type T5. These instruments are of the non-repeating type. In the theodolite, type 2T5K (Fig. 5.10a), the functioncof the level of the vertical circle alidade is performed by ap optical compensator with a self-adjusting index. Angles are read off at one side of the circles. For easier calculation of vertical angles, the vertical circle is numbered in sectors from 0 to 75° and from 0 to minus 75°. The tangent screws of the telescope and vertical circle alidade are coaxial with the corresponding winged-knob clamp screws; both pairs of screws are arranged at the same side of the theodolite. The telescope is fully reversible, i. e. can be transited at both ends, and focussed by means of a rack-and-pinion gear. The eyepiece can be adapted to the observer's vision by means of a diopter ring which should be rotated until the cross hairs are seen sharp. The two extreme horizontal lines of the cross hairs (above and below the cross) are stadia hairs. The telescope is provided with two collimation sights for rough pointing to objects. When using a sight, the observer's eye should be at a distance of 25-30 cm from it. For aiming at an object, the telescope is rotated on the horizontal axis and the theodolite body, on the vertical axis. Precise aiming is made by operating micrometer tangent screws 5 and 7 when winged-khob clamp screws 4 and 6 are locked. A special handle is provided for changing the sections of horizontal circle (in angular measure-
Fig. 5.10
Theodolite,
type
2T5K:
(a)
general
view; l-objective; 2-optical sighting device; 3 -level tube; 4- vertical clamp; 5- vertical tangent screw; 6- horizontal clamp; 7- horizontal tangent screw; 8-clamp screw of base (support); 9-foot screw of base; IO-horizontal circle aperture; (b) view field of scale microscope (reads 127 o 05.6' on horizontal circle and 0 o 34.0' on vertical circle)
88
Ch. 5. Horizontal
Surveys
of Underground
Workings
ments). To change from one section to measuring the horizontal and vertical angles another, the handle should be turned and at in theodolite and tacheometric traverses, for the same time pressed down along its axis. the construction of plan and elevation survey The setting of the horizontal circle in a nets on the surface and in underground particular section is additionally controlled workings, and for measuring distances (by by indexing in the aperture of horizontal using the stadia hairs of the telescope). circle finder. These theodolites have a repeating system The horizontal and vertical circles have for measuring horizontal angles by the I-degree numbered graduations. The graduareiteration method and are convenient for tion lines and numbers are projected in the assigning directions to mine workings. plane of reading scales of the microscope. The principal parts and units of the instruThe image of the vertical circle is tinted blue ments are protected against dust, dirt and and that of the horizontal circle, yellowishmoisture. The telescope can be plunged green. The illumination of the field of view (transited) at both ends. It is of the internalcan be controlled by a hinged mirror. The focussing type and is focussed by rotating the scales are focussed for distinct vision by eyepiece ring. Optical sighting devices arranrotating the diopter ring of the microscope ged at both sides of the telescope serve for eyepiece. rough aiming at objects. Precise aiming is The field of view of the microscope of done by means of a micrometer screw and theodolite 2T5K is illustrated in Fig. 5.10b. tangent screws when the corresponding The images of the reading scale and the clamp screw is locked. The eyepiece of the vertical and horizontal limb are projected microscope for reading off on the horizontal respectively in the upper and lower apertures and vertical circles is located near the teleof the field of view. Each division of the scope eyepiece. reading scale corresponds to one minute of The vertical axis of the theodolite is set the arc. The fractions of minutes can be truly vertical by means of bubble level which estimated by eye with an accuracy to 0.1 of a is centred by adjusting screws. division. The reading index is the hair of the Theodolites of these types have a hollow limb. Th~ reading error is equal to 0.05-0.1 of vertical axis for centring over a station point a scale division, or 3-6". The readjng scale of by means of telescope. The eyepieces of the the vertical circle has two rows of numbers. telescope and reading microscope are proviThe lower row (with the minus sign) is used ded with zenith attachments which permit for reading off when the vertical limb hair the observations of objects at angles above with the same sign is seenin the reading scale 45° to the horizon and theodolite centring aperture. over a point. A diagonal eyepiece (optional) The certified accuracy of angle measure- can also be used for zenith and nadir sighting ment ( :1:5") is ensured in measurements by and centring over a point. the method of full sets (with the instrument Theodolites, types T30 and 2T30, are positioned 'face left' and 'face right'). In order mainly designed for surface surveying, but to eliminate the division error of the horizonare often employed for surveys in undertal circle, the latter should be reset after each ground workings. full set by 180°: n (where n is the number of Theodolite type T30M (USSR) shown in full sets). Fig. 5.lla is a mining theodolite. It has a Theodolites T30, 2T30, and T30M (USSR) specially designed vertical axis (spindle) and a are angle-measuring instruments of technical reversible bubble level for the operation of precision ( :1:30"). They can be employed for the instrument in both upright and inverted
5.7. Theodolites
"" Fig. 5.11 Theodolite, type T30M: (a) general view; 1- theodolite base; 2- horizontal clamp; 3- horizontal tangent screw; 4- illuminating attachment; 5- diopter ring; 6- microscope eyepiece; 7- telescope focussing ring; 8- optical sighting device; 9-telescope clamp screw; 10-vertical tangent screw; 11 -level tube; 12 -lever for locking of horizontal circle with alidade; 13-1ock; 14-zenith (prism) attachment; 15- diagonal eyepiece;(b) view field of scale microscope (reads 23 o 54' 30" on horizontal circle and 150 12' 30" on vertical circle)
89
positions, which is essential in underground surveys. The sighting devices on the telescope have a centre mark for centring (plumbing) the instrument under a point by means of a plumb bob. For ease of operation in underground workings, the reading scales are provided with an illuminating system which can be switched on by a button either for a short time to take a reading or for continuous illumination. The reading microscope arranged near the telescope eyepiece has the field of view in which the images of the vertical and horizontal circles are projected simultaneously (Fig. 5.llb). The reading scales have 60 oneminute divisions. The graduations of the vertical circle (limb) are projected against the upper reading scale in the field of view and those of the horizontal circle, against the lower scale. A reading can be taken by eye estimation to 0.5 or 0.25 of a division, i. e. with an accuracy to 30" or 15". A version of the former instrument is type T30ME theodolite with an auxiliary eccentric telescope (Fig. 5.l2a); an eccentric telescope with a bracket is also obtainable optionally to the type T30M theodolite (Fig. 5.l2b). Theodolite, type T30ME (with an eccentric telescope) i\ designed for surveys in steep underground workings and for surface surveys connected with sighting of the telescope in the directions close to the vertical. The eccentric telescope has the same optical characteristics as the central telescope and is also provided with optical sights. Theodolite TheoO1O(GDR) is a precision instrument provided with a rotating limb, a lens-and-mirror telescope, and a two-sided optical wedge micrometer. It has a detachable tribrach and an optical plummet. The advanced versions of this instrument, Theo010A (Fig. 5.l3a) and TheoOlOB, have an opticomechanical compensator of the vertical circle and an erect-image telescope. The field of view of the reading microscope of type
Fig. 5.12 Theodolite, type 2T30ME: (a) general view; l-central telescope; 2-eccentric telescope; 3 -level tube; 4- horizontal clamp screw; 5- horizontal tangent screw; 6- base clamp screw; 7- vertical clamp screw; 8-focussing rack-and-pinion; (b) eccentric telescope to theodolite, type 2T30M (b) (a)
.
/1
46""
,10 5
.3 78-
9-
Fig. 5.13 Theodolite, type Theo010A: (a) general view; 1 -objective; 2- optical sighting device; 3- optical centring device; 4 -micrometer; 5 -vertical and horizontal clamps; 6-circle switch; 7, 8-vertical and horizontal tangent screws; 9-foot screw; lO-illuminating mirror; (b) view field of scale micrometer (reads 112o 27' 35.0" on horizontal circle)
5.7. Theodolites
91
lb)
Fig. 5.14 Theodolite, type Theo020A: (a) general view; l-objective; 2-optical sighting device; 3-optical centring device; 4-eyepiece; 5-vertical and horizontal clamps; 6- disconnection of vertical circle; 7-illuminating mirror; 8-vertical tangent screw; 9-horizontal tangent screw; IO-foot screw; (b) view field of scale microscope (reads 235 o 050' on horizontal circle and 256 0 52.0' on vertical circle)
TheoO1O theodolite is shown in Fig. 5.l3b. These instruments are intended for triangulation and polygonometry on the land surface. Theodolite TheoO20 (GDR) is a repeating theodolite of technical precision. It has an optico-mechanical compensator on the vertical circle (instead of a bubble level), an optical centring device, and a detachable tribrach which allows the instrument to be used in surveys by a three-stand scheme. Improved models, TheoO20A (Fig.5.l4a) and TheoO20B, have a new unique system of coaxial tangent and clamp screws for simultaneous locking of the vertical and horizontal
axes and a more perfect reading system (Fig. 5.14b). These instruments are intended for the construction of survey nets in mines and on the surface and of reference nets in underground workings. Theodolite TheoO80 (GDR) is a compact optical repeating theodolite with a detachable base for three-stand scheme surveys; it can also be mounted on console holders. Limb graduations have double numbering: one of them being read off when the instrument is mounted in the common upright position and the other when the theodolite is mounted on a console holder in an inverted Dosition.
92
Ch. 5. Horizontal
Surveys
of Underground
Workings
is swinged slightly and if the image of the object again deviates from the cross hairs, the move of foot screws is made more tight by means of tightening nuts. 2. The bubble level of the horizontal circle alidade is adjusted (when required) so that the bubble level axis can be truly perpendicular to the vertical rotation axis of the theodolite. For checking, the bubble level is arranged amid the line of two foot screws of the tribrach and, by rotating these screws in opposite directions, the bubble is moved into the centre. The alidade is then turned through 180°. If the bubble deviates from the mid position, half of its deviation is taken off by operating the foot screws and the other half, by means of the adjusting screws of the Fig. 5.15 View field of reading-off microscope of bubble level. After that the alidade is rotated theodolite, type Theo080 (reads 359 o 28' on through 90° and the bubble is centred by horizontal circle and 96 o 04' on vertical circle} means of the third foot screw. The check is repeated until the required conditions are The field of view of a reading-off microscope satisfied. is illustrated in Fig. 5.15. The instrument is 3. The position of the telescope cross hairs intended for supplementary surveys in underis tested and adjusted. The horizontal line of eyepiece cross hairs must be perpendicular to ground workings. the vertical axis of rotation of the theodolite. For this test, the theodolite is mounted on 5.8. Tests and Adjustments the tripod, and its vertical axis is arranged of Theodolites truly vertical. Then a convenient point is chosen, and its position relative to the horiBefore starting the survey work, theodolites, tripods, and sighting devices are tested zontal line of the eyepiece cross hairs is in order to avoid the influence of probable observed when rotating the instrument stanerrors on the results of angular measure- dards by the horizontal tangent screw. ffthe image (point) deviates from the horizontal ments. 1. The tripod and tribrach are tested for line, it is required to take off the eyepiececap, stability. To test the tripod for stability, the slacken four fastening screws, and turn the theodolite is mounted on it and the vertical eyepiece so as to horizontalize the horizontal axis of the instrument is set truly vertical. The hair. Upon adjustment, the eyepiece is fastentelescope is then sighted on a distinct object, ed again and the cap is screwed into place. and the tripod table is swinged slightly back 4. The collimation error, which can and forth. If the image of the object is then appear if the collimation axis of the telescope noticed to deviate from the telescope cross is not perpendicular to the axis of rotation of hairs, the wing nuts at the tops of the tripod the telescope, is measured and eliminated. legs must be tightened more firmly. For this, telescope is set roughly horizontally After the tripod has been made rigid, the and aimed at a remote object. Readings are stability of the tribrach is tested. The tribrach taken at two positions of the circle: 'face left'
5.9. Centring
of Theodolites
(FLJ and 'face right' (FRJ. Then the clamp screw of the tribrach is loosened, the theodolite is rotated through 180° and locked again by the clamp screw. The telescope is aimed at the same object and two new readings are taken at two positions of the circle: FL2 and FR2. The collimation error can then be calculated by the formula: (FLl
-FRl
:t 1800) + (FL2 -FR2
c=
:t 180°)
4
For correcting the collimation error, the eyepiececap is taken off to open an accessto the adjusting screws of the cross hairs, and the horizontal circle is set at a reading that is determined by the formula: FR = FR2 -c The graticule (cross hairs) is moved horizontally by means of the adjusting screws until the cross is aligned with the image of the object chosen earlier. The check is repeated until the condition is satisfied. The permissible collimation error should not exceed 30". 5. The zero point (zero offset) is tested and adjusted. The zero point in the reading on the vertical circle when the collimation axis of the telescope is truly horizontal and the bubble of the bubble level of the vertical circle alidade is in the zero point. The zero point of the vertical circle must be known and accounted for in surveys or be excluded. The zero point value is determined by sighting on one and the same point, preferably closer to the horizon, at two different settings of the circle and in the general casecan be calculated by the formula: ZP=
FL + FR + 180° 2
If the reading is less than 90°, add 360°. For the correction of the zero point, the vertical circle is set at the reading FL-ZP and the cross of the graticule is aligned with the image of the selected point on the object
and Signals
93
by moving the graticule vertically by means of the adjusting screws. The test is repeated if required. When testing and adjusting the zero point, it is essential to observe the position of the level bubble on the horizontal circle alidade; if the bubble is moved aside, it must be centralized by means of the foot screws of tribrach. 6. The compensator is tested. This test is carried out to check whether the vertical circle reads the same when the vertical axis of the instrument deviates within ::t:3'. For this test, a distinct point is chosen and the theodolite is mounted on the tripod so thatone of the foot screws is oriented in the direction of that point. The bubble of the adjusted cylindrical bubble level is brought into the central position so that the main axis of the theodolite is truly vertical. The theodolite is then tilted by 2-3 " i. e. by 4-5 level divisions, towards the selected point by operating the foot screw facing that point. After that the theodolite is levelled by the other two foot screws. With a tilted position of the theodolite, the telescope is sighted on the selected point, and the reading is taken on the vertical circle. The procedure should be repeated with the instrument tilted by 2-3' in the reverse direction, i. e. towards the observer. The difference between the readings taken with the instrument tilted in two opposite directions should be not more than 0.1. Otherwise, the theodolite should be sent to the manufacturer for adjustment. 5.9. Centring of Theodolites and Signals When running a theodolite traverse in underground workings, the instrument is set up successively in the traverse points and, before making angular and linear measurements, should be prepared for operation, ioeo it should be centred and levelled. and its
94
Ch. 5. Horizontal
Surveys
telescope should be prepared for observations. The plumb lines are hung or signals (sighting marks, or targets) are established in the "points to be sighted. Centring is essentially the placing of a theodolite or signals into a position in which their vertical axis is brought into coincidence with the vertical line passing through the centre of a survey mark. Suppose that we have to measure a horizontal angle a = BAC (Fig. 5.l6a). If the theodolite is not centred properly, its vertical axis may turn out to pass through a point A l' rather than through A. Then, the measured angle will be a1, but not a. The difference L\a = a -a1 is called the error of angular measurementcaused by inaccurate centring of the theodolite, and the horizontal distance AA1 = I is the linear error of theodolite centring. Suppose now that the signals at sighting points B and C have been centred poorly (Fig. 5.16b). In that case, L\a' = a -a2 is the error of the horizontal angle measurement caused by inaccurate centring of the signals, and the horizontal distances between points BB1 and CC1 are the linear errors of signal centring. If the linear errors of theodolite and signal centring occur simultaneously, the total error (a)
A
Fig. 5.16 Deternlination of measurement error of horizontal angle caused by inaccurate centring of (a) theodolite and (b) signals
of Underground
Workings
of measurement of horizontal quite substantial.
angles may be
The root-mean square error in the measurements of horizontal angles caused by inaccurate centring of the theodolite and signals can be determined by the formula: m.
'.'
.=
J- ~2b 2a
2 [l;(a2
+ b~) + lfh(a2 + b2 -2abcosa)] (5.2)
where a and b are the horizontal projections of the side lengths of the measured angle and I,h and Is are the linear errors of theodolite and signal centring. Taking, for instance, that a = 21 m, b = = 28 m, 11= 175°, Is = 0.001 m, and I,h = = 0.002 m, the error of angle 11will be equal to 24". The analysis of formula (5.2) suggests the following conclusions: I. The effect of the signal centring error is independent of the magnitude of the measured angle. 2. The effect of the theodolite centring error depends on the magnitude of the angle and is the highest for angles close to 180°. 3. The effect of the errors of theodolite and signal centring is inversely proportional to the lengths of the sides making the measured angle and increases with the difference in the side lengths. As may be seen, all these factors, which worsen the accuracy of horizontal angle measurements owing to poor centring of theodolite and signals, are typical for the conditions of surveying in underground workings. In that connection, the matter of theodolite and signal centring is of prime importance in mine surveying. Three main methods of centring are used in the mine surveying practice: with a mechanical plummet, with an optical plummet, and automatic centring. In centring with a mechanical plummet, the theodolite is mounted on a tripod or console holder, its vertical axis is set truly vertically
5.9.
(a)
Fig.
5.17
Centring
(b)
Types
of centring
of
Theodolites
(c)
string
and
Signals
(e)
plummets
and the telescope is set into the horizontal position. The string of plummet is passed through the hole of a survey mark and the height of plummet suspension is controlled so that the plummet point is just to touch the top centre of the theodolite. After that the instrument is moved on the platform of the tripod or console holder until the point of the freely hanging plummet is exactly over the top centre of the instrument. Upon making these operations, the continuation of the vertical axis of the theodolite will pass through the centre of the survey mark if only the top centre of the instrument (with the telescope arranged strictly horizontally) lies in the vertical axis of rotation of the telescope and the plummet point lies in the same vertical line with the plummet string. When plummets are used as signals, the sighting axis of the telescope is aimed at their strings. The following types of mechanical (string) plummets are used in the modern mine surveying practice (Fig. 5.17): (a) a simple centring plummet which has a massive metal body 3 sharpened at the bottom; the sharpened portion ends with a steel point 4; the
plummet is connected with a string 1 by means of a threaded plug 2 at its top; (b) a plummet with a retractable point; (c) and (d) controllable plummets with respectively external or internal pulleys on which the string is wound; and (e) a controllable plummet with an internal reel, which is the most convenient type in operation, since its centring point 6 can be quickly set at the desirable height. On pressing the top portion of a sleeve 1, the plummet string can be freely unwound to the required length. In order to raise or lower the plummet, the operator holds the plummet body 4 by one hand and rotates the sleeve by the other. Depending on the direction of rotation, the string will be either wound onto the reel or unwound from it. To fasten the string to the plummet, the sleeve is taken out upon removing a nut 2, and one end of the string is passed through the slot in the rim of a reel 3 and got made into a knot. The other end of the string should be passed through two side holes and one central hole in the sleeve, after which the plummet can be assembled. At the end of plumbing, the plummet point should be retracted by turning a sleeve 5.
Ch.
5.
Horizontal
Surveys
The surveys in underground workings are carried out with the use of illuminating plummets whose body incorporates, in ad9ition to the string-winding mechanism, also a power source, an electric lamp, and a conical transparent cap. Illuminating plummets are also employed successfully in the orientation of underground workings and check surveys. It is usually warranted by plummet manufacturers that the deviation between the plummet point and the centre of a string hole is not more than 0.5 mm. This can be checked by hanging a plummet and setting up two theodolites at a distance of 5-7 m from it so that the sighting axes of the two instruments, when pointed to the plummet, make an angle of roughly 90°. The telescopesof the two instruments are sighted on the plumb line so that the plumb line and plummet point are within the bisector of cross hairs. If the image of the plummet point in at least one telescope is beyond the bisector, the plummet tested should be repaired or rejected. For more accurate centring, modern theodolites and signals are provided with optical plummets or optical centring devices. The former are built in into an instrument, while the latter are detachable optical plummets and optical centring devices may be either one-sided or two-sided. A one-sided optical plummet permits centring by a vertical collimating ray to be performed either only upwards or only downwards. The scheme of an optical plummet for centring above a surveying mark is shown in Fig. 5.18. By pointing the telescope to the zenith, the theodolite can also be centred under a surveying mark. In the mine surveying practice, when there is no need to fix the intermediate vertexes of theodolite traverses, it is common practice to employ automatic centring of theodolites and signals on tripods or console holders by using a special set of attachments, such as that illustrated in Fig. 5.19.
of
Underground
Workings
3 ~ ~-
Fig. 5.18
Optical
2-mirror;
3-objective;
plummet:
~
I-protective
4-graticule;
glasses;
5-eyepiece
The essenceof the automatic centring of a theodolite and signals consists in that the attachments mentioned make it possible to set up the theodolite in the points where a signal was set up before, and vice versa. This ensures that the vertical axis of the instrument, which passes through the centre of a surveying mark, restores automatically its geometrical position when the theodolite and signal setups are interchanged. This interchanging requires no additional centring. Survey with Automatic Centring of Theodolite and Signals. The sequence of survey with automatic centring of theodolite and signals is as follows. Suppose that a checking theodolite traverse is to be run between two groups of fixed mine survey points: A, R, C and D, E, F (Fig. 5.20). To do this, supports (bases)(see Fig. 5.19) on tripods are set up in points A and C and centred by means of an optical plummet and the theodolite is set up and centred in a point R. Signals c are then mounted on the bases in the points A and C and the checking angle ARC is measured by
5.9.
Centring
of Theodolites
and
97
Signals
b
A d
9
Fig. 5.19
Set of attachments
to theodolite
T30M
the theodolite in the point B. Then the theodolite and forward signal are interchanged on their bases and the rear signal is set up on a tripod (or console holder) in a point 7 The signal in the point 1 is set into the upright position by means of a level tube on a bracket and, then the angle BCl and the length of a side Cl are measured. The theodolite and forward signal are then interchanged on their bases and the rear signal on the tripod is reset onto a next point to run the traverse to the second group of fixed points D, E, and F where, as in the points A, B and C, the bases are set up by means of an optical plummet or a theodolite. This order of survey is characterized by that the theodolite and signals can be interchanged without intermediate centring, the traverse vertexes between the fixed points are not fixed, and the survey is done by using three stands. For that reason this method is also called the survey with lost points, or survey by a three-stand scheme. 7-1270
for surveying
by three-stand
scheme
A similar survey with lost points and automatic centring of theodolite and signals can also be performed by using console holders instead of tripod stands. This method is usually resorted to in steeply dipping workings or where the mine traffic is intensive. The set of attachments for this method 4
Fig. 5.20 Scheme of theodolite two groups of reference points
traverse between
98
Ch. 5. Horizontal
Surveys
of survey (see Fig. 5.19) contains console holders with adapters (e), centring plates with spherical level tube (a), a clamp (b) for fastening a console holder to wooden or metallic mine supports, pin (1), prism attachment (h) for an objective, and a level tube (g). As has been found by experiments, the errors of centring of theodolites and signal~ by various methods are as follows: 1.2-1.5 mm in single centring with string plummets, 0.8-1.0 mm in optical centring, and 0.3-0.8 mm in automatic centring. 5.10.
Measurements of Horizontal
Angles
The operation of measuring a horizontal angle includes centring a theodolite under or over a fixed point in an underground working, sighting on signals, and taking readings on the scales. The sequence of signal sighting and the order of reading on the scales depend on the method of angle measurement employed by a surveyor. In mining workings, left-hand angles along a survey traverse are usually measured by the method of repetitions (reiteration method), method of sets or, less frequently, method of rounds. 5.10.1 .Reiteration
Method
In view of the wide use of repeating theodolites in the mine surveying practice, the method of repetitions (reiteration method) has become very popular in measurements of angles. It consists of the following operations. I. The zero division of the alidade of a horizontal circle is roughly aligned with the zero mark of a limb, after which the latter is unlocked and the hair cross of a telescope is sighted on the rear signal set up in a point B (Table 5.4). The reading 01 is taken on the scale 01 (01 = 0000'.2).
of Underground
Workings
2. The alidade is unlocked and, by rotating the instrument clockwise, the telescope is sighted on the forward signal in a point C to take the reading a2(a2 = 58°23'.5). 3. The telescope is reversed, the limb is unlocked and turned together with the alidade to sight the telescope on the rear signal; no reading is taken. 4. The alidade is unlocked and rotated counter-clockwise to sight the telescope on the forward signal and take the reading a3 (a3 = 116°47'.7). 5. The left-forward angle ~ and its check value ~chare calculated by the formulae: ~ = (a3 -aJ/2 (5.3) ~ch= a2 -al
(5.4)
If the discrepancy between the measured and check angle is more than 1.5 of the instrument accuracy (:!: 1.51),the angle measurement must be repeated. When running theodolite traverses of higher accuracy, the measurements of horizontal angles are repeated more than twice. In that case, in the first position of a circle (say, FL), the limb is moved n times to sight the telescope on the rear signal and the alidade is also moved n times to sight the telescope on the forward signal. Readings are taken only on the first and second sighting, and the check angle is calculated by the formula ~ch= a2 -al. The total value of the angle measured n times will be equal to a3 -al. After that, the telescope is reversed and sighted n times on the rear and forward signal in a different position of the circle. Only one reading, a4' is taken after the last sighting on the forward signal. With n full repetitions, we have: ~ = a4 -a1 + R360°
(5.5)
2n
where R is the number of full revolutions of the alidade around the limb. The number of full revolutions of the
5.10.
Measurements
alidade around the limb can be determined by considering the measured check angle and the number of performed repetitions: R = (2n 13ch + a1 -a4)/360° (5.6) 5.10.2.
Method
of Sets
The measurement of an angle (for instance, CDE, Table 5.5) by the method of sets is carried out in the following sequence. 1. The limb is locked in a position when it roughly reads 00, the telescope is sighted on the rear signal (point C), and the reading a 1 is taken on the horizontal circle and recorded in the field book (01 = 10°07'.5). 2. The alidade is unlocked and the telescope is sighted on the forward signal (point E) to take the reading 02 (02 = 68°31'.0). The measured angle in one position of the circle, i. e. in the first half-set, is 13'= 02 -01 (13'= = 58°23'.5). 3. The limb is turned through 60-90° and locked. The telescope is reversed and sighted again on the rear signal; the reading 03 is recorded in the book (03 = 190°07'.5). 4. The telescope is sighted again on the forward signal to take the reading 04 (04 = = 248°30'.9), and the angle measured in the second position of the circle is calculated: 1311 = 04 -03 (1311 = 58°23'.4). The mean angle calculated by the two half-sets 13m = (13'+ 1311)/2 is taken as the final value (13m= 58°23'.45). In angle measurements by the method of two sets, the sequence of operations is essentially the same, but the limb for the second set is turned initially at a reading close to 90°. 5.10.3.
Angle Measurements Method of Rounds
by
The procedure of angle measurement by the method of rounds consists essentially in the following.
of Horizontal
Angles
99
1. The zero divisions of the limb and alidade are roughly aligned, and the alidade is locked. With the limb unlocked, the telescope is sighted on the initial signal (for instance, point B, Table 5.6) set in the centre of a bench mark, and the reading at is taken and recorded in the book (at = 00003'.0). 2. The alidade is freed (with the limb being fixed) and the telescope is sighted on the signal set in the centre of a bench mark D. In this case,the theodolite is rotated clockwise. The reading a2 is taken and recorded in the book (a2 = 28°08'.1). . 3. The alidade is rota-ted clockwise in the same sequenceand the telescope is sighted on the signal in a point C to take the reading a3 (a3 = 58°26'.7). 4. The observations of the first half-round are finished by sighting the telescope on the signal set in the initial direction B and taking a check reading. This makes it possible to prove that the limb was fixed during the observation of the point (a4 = 00°03'.1). In order to eliminate the instrument error of the theodolite, the same angles between the given directions are then measured at a different setting of the circle (FR). In the second half-round, observations are made in the reverse direction and the alidade is rotated counter-clockwise. The second round is performed in the same sequence, but the limb is initially set at a reading close to 90°. Upon completing the measurements at the second setting of the circle, the collimation error is calculated by the formula: 2c = = FR -FL ::!: 180°; its magnitude is indicative of the accuracy of measurements. After that the mean values of the directions obtained by two measurements are calculated. by the formula: (FL + FR ::!: 180°)/2. The procedure is finished by calculating the corrected directions, i. e. by calculating the mean initial direction from the mean directions found; in our case, the corrected direction is (00°02'..80+ 00°02'.90)/2 = 00~02'.85.
::;Q .: 01 8 = Q ..c ~ .. ~ ." .:, !fJ = 01 8 ~ = "' ~ 01 ~ ..
~ 01 = ~ ~ = ~ ..
~ 00 O ..., ~ E-- 8
>,
1-. ~
...t.s = = ~ ... 8 o ~ ...~ ...> "' = -rnO
8 0 0
~
~ = <
u
I
-
= .~
.
;. 01
~
..."' Q
..~
;..
Q).d 0
o. 8
B
Q Q = ~ ..i::'
Q ~ ~.
~ .~ --~ I£)
01
E--r/JZJ!:.-
3C;~8 ~ ='
00 ~ ... t.s
~
~
. .
.
"5 ~ 00
"' 8';< 000 .J=" ~ 0) " a§ -'" "'.-"' Q.5
., =' ~ I: ~ ~
~.~
~
..1 ~
]
.
~ "E:
1:1. I o
.=: ~
e "'-
1~.5
,"].,-5 '00 ., ~
~ ~ .0 ~
.: O '.: '" ~
= ~ 0
"0
i' ~ = ~ = -= .. Q; e '-'
'tJ = Q; e ~ = "' ~ Q; ~ ..
~ O 00
~ s +"' "' = =
8 0 "' r-I
~ 00 > G) ...+"' =' "'
s ~ e +"' "' = -000
; = ~ = <
";) > .£
= ~
~ Q; = ~ ~
= ~ =
~ .-
..
~ .. -~
~
~ ..Q;
P.8 >.
u ~
.-~ ~ II")
Q; ..: .. ..~ ~ o VJVJ
Q; .-Q; ~
Q; -> .c ~ E-
~
"0 ",,~ ","0 '".~ ~""'",,,
"' = .0 ~
-
~ "'J 0:
~
,
.~.a
" ~
"
"'
~ ~ .
..,
~ 0 ..,
~ .c
I
]
~ O
""'
-o
0 0\ O
Ir) r--v '0 -0 Nr'"\ oN r'"\OO Ir)
1'"10r-.:o 0... 000 O\~ -<""1
o o N
1 0 \Q
0 ""' 0
.
~ ""' N 00 Ir)
Ir\ ..; N Ino r..:...; 0
00 00 o
~ 'r\
00 N on
I
or\ or\ -
~~ ...,...,
~
IDN OOID
~
000 --0
\,)
~
r-ID
~ ...,
'(ij' -= = = e
'Q -g .c ~ ,§, "' .. = .. e .. .. = "' " ..
~ .. ~ = <
'; = = N .~
8"
..
011
~ O M
..
~ -= =
011
o ~
I
e
=
"8
e
-" "' = -VJO
I:: ~
ci)
=
= .,s ;:I 0 ..0
'- "'
"Q)
~ = =
~
u>-o "' ..\r\ 0. I:: ~
-=
~
>-~
>
Ir)
..~~.c ->-~ ...~ " ;:I .-" Eo-(/J~-
-13 .., ~
"g ~ ~ 0 ~ .;;; I: ~ O .!= U"O
;1 N
~ 'X>
+1 .-1 "" I ~ "" II " N
~ ~
i
"' c '5 ~
~.5 o c ~.,g
-1o.r;M OON 00000 ON"'
0"'00 ~~\0~ Nr.:IQN ooNo
000000 ONIr)O
"""'N~ 0000
0000 0000 I I
10 00"' Nr-:IQN OONO 000000 000...'00 -~~-
o-r-'.;00,cj'.; OONO
000000 ONIr)O
~~v~
~
Ir\
I
I
r--
~
102
Ch. 5. Horizontal
Surveys
of Underground
Workings
III
(b) III
,
--
/
"' / /
Fig. 5.21
Measurement
of horizontal
angle by eccentric
The measurements of horizontal angles in underground workings with the angles of dip more than 300 are made only by the method of sets under the provision of the following additional conditions: I. If a repeating theodolite is employed, its limb must be locked for the entire time of measurements. 2. The theodolite for measuring horizontal angles must be provided with a striding level and permit plumbing of its vertical axis of rotation before each set. 3. The alidade of the theodolite should always be rotated in one direction only. 5.10.4.
Measurements of Horizontal Angles by Means of Eccentric- Telescope Theodolites
telescope
is shown in Fig. 5.210 and with the circle at left, in Fig. 5.21b. In order to measure the angle between the directions II-I and 1I-111, for instance, with the circle at right, the telescope is sighted successively on signals I and III. In that case, the horizontal axis of rotation of the telescope moves from position II-I into 1I-2, i.e. its setting is changed by an angle 13" and therefore, the angle 13,will be measured instead of 13.Similarly, with the circle at left, the angle 13! will be measured instead of 13. As may be seen in Fig. 5.21, the exterior angles
(5.7) (5.8)
Hence:
The horizontal angles in steep workings are measured by means of the eccentric telescope of a theodolite. The scheme of measurement of a horizontal angle I-II-III by the eccentric telescope with the circle at right
13= 13,+ '1 -O 13= 131-'1
(5.9)
+ O
Adding these equations, 213= 13,+ 13!
(5.10) we get: (5.11)
5.10.
Measurements
or I:}= (I:}r+ I:},)/2
(5.12)
It follows from formula (5.12) that the central angle is equal to the half-sum of the angles measured in two half-sets. This elirninates the influence of the telescope eccentricity. An eccentric telescope can also be used for angular measurements by the reiteration method. In that case, it should be noted that, in order to determine the check angle, the instrument must be sighted on the signals of measured directions at two different positions of a circle. The accuracy of measurements of horizontal angles by an eccentric-telescope theodolite depends on the difference in the side lengths of the measured directions and on the inclination of the theodolite telescope axis. For that reason, when establishing the points of a theodolite traverse it is desirable that all sides be roughly of the same length. The vertical axis of the telescope must be adjusted by means of a striding level. 5.10.5.
Errors in Measuring Horizontal Angles with Steeply Inclined
Sides
When running theodolite traverses in steep workings, the most critical source of errors is non-verticality of the principal axis of theodolite which causes an additional inclination of the rotation axis of telescope and thus worsens substantially the accuracy of angular measurements. The dependence of the error of a measured horizontal angle on the inclination angle of collimating rays and inclination of an instrument axis can be expressed by the formula: mIl = o[cosutanhf -cos(u -~)tanhr] (5.13) where mp is the root-mean square error of the measured horizontal angle depending on the inclination of the principal axis of theodo-
of Horizontal
Angles
103
lite; O is the inclination angle of the rotation axis of an instrument; u is the angle between the direction of inclination of the principal axis of an instrument and the direction of rotational axis of telescope when sighted on the forward signal; ~ is the horizontal angle being measured; and h f and h r are the angles of inclination of collimating rays when sighted respectively on the forward and rear signal. The analysis of formula (5.13) shows that the error mfJof angular measurement is at a maximum at ~ = 180° and at a change from a horizontal to an inclined workipg or vice versa. In that case, the magnitude of an error increases proportional to the slope and may attain rather high values (3-5' or even more). 5.10.6.
Accuracy of Horizontal Angle Measurements
The accuracy of measurement of horizontal angles is influenced by gross, systematic and random errors. Gross errors may appear owing to the inclusion of improper bench marks into the traverse being run, poor fixation of plummets in the centres of bench marks, instability of tripod (console holder), etc. To avoid gross errors, before sinking into the shaft, the surveyor must prepare all the initial data, write them in the theodolite survey field book, and instruct the workers engaged in the setting and illumination of plummets (signals) and other related jobs. In the shaft, he must check that all the bench marks are reliably fixed and belong to the traverse line to be run. Systematic errors depend on the environmental conditions and inaccuracies in the manufacture and assembly of instruments, for instance, improper mutual arrangement of some elements or non-perpendicularity of the geometrical axes of theodolite. These systematic instrumental errors can be minimized by regular examinations of theodo-
Ch. 5. Horizontal
104
Surveys
lites, signals and other instruments and by using the appropriate methods of angular measurements. Random errors mainly appear owing to instrumental errors, incorrect setting of theodolites and signals, and incorrect sighting and reading. The specific environmental conditions in underground workings, in particular, restricted space, water drip, and dust-laden, atmosphere, and also the specifics of fixation of bench marks (in the ground or roof) set forth additional requirements to the instrument setting and techniques of observation in angular measurements. In view of these specific conditions and difficulties in the performance of survey work, special care should be given to the centring of theodolites and signals (especially when traverse sides are relatively short) and to making the observations strictly accordipg to the adopted method, since these factors can influence substantially the accuracy of measured angles. Accuracy of angle measurements by the reiteration method. As may be seen from the description of the reiteration method, the angle 13 measured by n full repetitions is determined by the readings at and a4. The magnitude of 13is calculated by the formula: B=a4-a1+R.360-o 2n
(5.14)
The error of the measured angle, mp , caused by the limb reading error mi will bJ:
of Underground
Workings
As follows from formulae (5.12) and (5.13), the total error of angular measurement with n repetitions will be: J
m/J =
2
Jm~,
+
2
m~..
I
= v
2
2
m,
-2
mv
n
2 +
-(5.17) n
The limb reading and sighting be calculated by the formulae: t
errors can
mi = 2"J2
"' .0' \J..vJ
mf}= 60"/v
(5.19)
where t is the accuracy of horizontal circle reading and v is the telescope magnification. Accuracy of angular measurements by the method of sets. In this case, the accuracy of measurements depends mainly on the errors of signal sighting and circle reading. Therefore, the error in establishing each direction 1S: mIl = ~
(5.20)
and the error of a horizontal angle measured in a full set is: mIl = 0.5J4(mf
+ m~)
(5.21)
or mIl = ~
(5.22)
If an angle is measured in n sets, the error of the mean arithmetic value of that angle is determined by the formula: J
m
= /In
5.11.
m2
m2
-.!.-+~
n
n
Measurements of Inclination
Angles
In theodolite surveys of underground workings, the inclination angles are measured at the same time with horizontal angles. These are needed for determining the horizontal distances of the sides of theodolite traverses and the elevations between the
5.11.
Fig. 5.22
Measurement
Measurements
of inclination
of Inclination
angle of underground
traverse points. The inclination angle of the side of a theodolite traverse is essentially the angle between the collimating ray {sighting line) and its projection onto the horizontal plane. Suppose that we have to determine the inclination angle of a collimating ray 1-2 passing through a point 2 fixed on a plumb line {Fig. 5.22). To do this, the following operations should be carried out. I. The telescope of theodolite is sighted on a plummet hung at a point 18. The clamp screws of the limb and alidade are locked. Manipulating the tangent screw of the telescope, the hair cross of the telescope is aligned with the point 2 fixed on the plumb line. 2. The level bubble of a vertical circle level is centred by the micrometer screw of the alidade, and the accuracy of sighting is checked. 3. The readings are taken from the microscope.
Angles
working
by central-telescope
105
theodolitl
4. The telescope is reversed, and the same operations are repeated with a different setting of the circle. 5. The magnitude of the measured inclination angle is calculated by one of the formulae: v=
FL -FR
-180° (5.24) 2
v = FL -ZP v = ZP -FR
-180°
(5.25) (5.26)
where v is the inclination angle; ZP is the zero point of a vertical circle; and FL and FR are the readings on a vertical circle with the latter at the left ('face left') or at the right ('face right'). If the readings FR, FL and ZP in calculations of inclination angles are less than 90°, they should be increased by 360°. Upon making angular and linear measurements at a station point 17, the theodolite
Ch. 5. Horizontal
Surveys
is set up under the centre of a mark 18 to make a check measurement oNhe inclination angle in the reverse direction (onto the PQint 17). In measurements of inclination angles, it is also required to measure the instrumental height i and the sighting height v which are then used to determine the height difference between the traverse points and the dipping angle of the working, since the inclination angle of a collimating ray does not always define the dipping angle of a working. Dipping angles larger than 50° can be measured by central-telescope theodolites provided with special attachments on the objective and eyepiece or by eccentric-telescope theodolites. The procedure of angular measurements in this case is similar to that described above. An eccentric position of the telescope (with eccentricity e) results however in that the measured angle v' differs somewhat from the actual inclination angle v (Fig. 5.23). Let us demonstrate how an actual inclination angle v can be found from the measured and known values v', I, and e. The triangles I-11-B and A-11-B in Fig. 5.23 have the common' side lIB, and therefore, it may be written: I sin v = I' sin v'
1 sin v = 1 sin v' or
and I' = ji'=-'ii
(5.27)
e~
sin v = sin vi
v
of Underground
Workings
Fig. 5.23 Measurement of inclination eccentric telescope
angle by
close to 90° or when the lengths of traverse sides are less than 20 m, it is required to introduce corrections for telescope eccentricity. The accuracy of measurement of inclination angles depends mainly on the errors of signal sighting in a vertical plane, mv, errors of limb reading, mi, and errors mt which can
Ti
(5.28)
It is known from the experience that the error of measurement of inclination angles increases with an increase of inclination in the measured direction and a decrease of the length of traverse sides. The corrections (in seconds) to the inclination angles as measured by an eccentric-telescope theodolite of an accuracy of 30" are given in Table 5.7. As may be seen from the table, when measuring the inclination angles
Table
5.7
Inclination
Error for telescope eccentricity with inclined length of traverse side, m
angle
40° 50 60 70 80
214" 307 448 710 1455
96" 137 198 315 650
10
15
20
35"
9"
1"
12
4" 5 8 12 26
2"
49
3
2
5
3
72
18
109
78
234
58
25
8
5
15
9
5.12.
Measurements
of Traverses
appear due to inaccurate centring of the level bubble of the vertical circle alidade (in. theodolites without compensators). Thus, the error of measurement of an inclination angle in one full set can be determined by the expression: m
"
=
I mf
v
+ m;
(5.29)
Measurements of Side Lengths of Theodolite Traverses
Length measurement is one of the most important and labour-consuming operations of theodolite traversing in underground workings, Depending on the specifics of survey work and the reqmred accuracy, length measurements can be carried out by using measuring tapes, light range finders and other instruments. 5.12.1 .Length Tapes
(.)
+ m:
2
where 't is the scale division of the vertical circle level tube; the nns errors mi and mv can be determined by fonnulae (5.18) and (5.19). 5.12.
107
Side Lengths
Measurement
by
Steel tapes 20 m, 30 m and 50 mlong have found wide use for length measurements in theodolite traversing. The most convenient among them are 50-m tapes, since they make it possible to measure in shorter time and with greater accuracy.
Fig.
5.24
Measuring
steel
tapes
The common material for measuring tapes is carbon or stainless steel. Some types of steel tapes are shown in Fig. 5.24. The lengths of sides of theodolite traverses are usually measured by a tape held freely in air (catenary taping). The sides of a traverse are divided into intervals which are somewhat shorter than the length of a measuring tape to be used. Plumb lines along a side are, as a rule, aligned visually. For measuring the lengths of sides in dipping workings, intermediate plumb lines are aligned by means of a theodolite with the collimating ray directed along the measured inclination angle. Marks in the form of movable knots and the like are provided on the strings of plummets. When chaining the intervals, the tape is applied so that it does not touch the plumb bobs. In the extreme interval at the theodolite, the tape is applied to the horizontal axis of rotation of the telescope. The readings on the tape are taken simultaneously at a plumb line and the horizontal axis of rotation
108
Ch. 5. Horizontal
Surveys
of telescope or simultaneously at two plumb lines. Since in most measuring tapes the first decimetre is graduated in millimetres and the remaining length of the tape, in centimetres, the readings with an accuracy to a millimetre are taken only at the initial end of the tape; at the other end, the centimetre mark should be aligned with a plumb line. Readings are taken two or three times, every time shifting the tape along the side being measured. The length of each side in underground theodolite traverses is measured twice, i. e. forward and back. For the back measurement, the intermediate plumb lines are shifted by 2 or 3 m, which ensures the check of measured lengths. The accuracy of length measurements in mines is largely influenced by the errors caused by the sagging of the tape under its own weight, inaccurate standardization of the tape, difference of temperatures during measurements and standardization, poor aligning of plumb lines, and some other factors. To obtain a greater accuracy of measured lengths, which is of essential importance in the construction of reference nets, certain corrections are introduced into the measured results. The correction for tape sagging can be found by the formula:
where q is the mass of I m of tape, kg; Q is the force of tape tension in measurements, N; and 11is the measured length of an interval. The temperature correction is determined by the formula: Alt = 11a (tm -tst) (5.32) where a is the coefficient of linear expansion of steel; tm is the temperature of measurement; tst is the temperature at which the tape is standardized; and 11 is the measured length.
of Underground
Workings
The standardization error L\lst is taken according to the tape certificate. Using these corrections, the corrected inclined length 4" of a measured interval is determined, then the horizontal distance is found by the formula 1 = 4" cos O which includes the inclination angle O measured earlier. When calculating the theodolite traverses of a reference net, the additional corrections must be introduced into the horizontal distances in order to reduce these to the sea level (mean level of the surface) and Gauss projection plane (see Para. 4.8.2). 5.12.2.
Standardization of Measuring Tapes
Tapes for measuring the side lengths of reference and survey nets must be standardized in order that the relative error may be not more than 1:40000. Measuring tapes are usually standardized on a comparator, or check base. If this is non-available at the mining enterprise, standardization can be carried out by comparing the tape with a new standardized tape provided with a certificate. The certificate gives, as a rule, the corrections per metre and for the whole length of a tape and the temperature conditions and tension in standardization. The comparison of measuring tapes can be carried out on a smooth surface where both tapes can be stretched at full length and tensioned by spring balances with a force not less than loo N. The zero marks of the two tapes are aligned by means of a millimetre rule, after which the deviation of the tape being checked relative to the standard one is measured at least twice. If the section being checked is shorter than the standard section, the deviation is thought to have the 'minus' sign, if otherwise, it has the 'plus' sign. The deviations thus measured and the certificate data for the standard tape
5.12.
Measurements
of Traverses
are used to compile the certificate of the checked tape. Two types of comparator, or check base, are employed in the mine surveying practice: stationary check bases for control of metre intervals and the whole length of tapes and field check bases to standardize the whole length of tapes. A stationary check base (Fig. 5.25) is a wooden shelf 3 to 20 m long, which is mounted on steel brackets along the wall of a building, underground working, etc. The place for a check base should be chosen so that the temperature of air can be constant along its entire length. An axial line is drawn on the top surface of the check base and scaleplates with 0.5-mm divisions (Fig. 5.25a) are attached to it symmetrically in l-m intervals. One end of the tape is fastened to the check base, whereas the other end is passed over a pulley and loaded by a weight that develops the required tension. The standardization is done much in the
Side Lengths
109
same way as described earlier, but the deviations for each metre of the tape being checked are determined by means of the scale plates on the check base. Upon completion of the check work, the certificate is filed for the tested tape. A field check base can be arranged on a smooth area of ground. Two bench marks with centre lines are fixed in the ground at a distance of 100 m or 200 m from each other. The distance between the bench mark centres is measured several times by means of invar or steel wires with a relative accuracy not worse than 1 : 50000. Then the comparator base is measured by the tape to be checked and the mean distance is calculated to determine the standardization correction. In practical measurements by the checked tape, the standardization correction is introduced proportional to the measured length, and considering the error of length. A field check base can also be constructed in a mine. In that case, bench marks are
110
Ch. 5. Horizontal
Surveys
usually established in the side wall of an underground working. The procedure of standardization is essentially as described earlier. 5.12.3.
Kinds and Causes of Accumulated Errors in Measurements by Meta!lic Tapes
= I'
mr
In
Workings
or
mL, =m,JL/j/ since n = L/I. Denoting m,/ j/ mL
=
a JL
= a, we get: (5.34)
,
Inaccuracies in the measurements of side lengths in underground traverses can occur due to gross, systematic and random errors. Gross errors mainly appear owing to the carelessness of persons engaged in survey work (for instance, the omission of whole intervals in long sides, etc.). These errors can be revealed by repeated measurements. Systematic errors obey a unique law of accumulation and measurement. They may be either permanent (when both the sign and magnitude of an error are known) or variable, i. e. with the magnitude varying from one measurement to another. An example of permanent systematic errors is, for instance, the error caused by poor standardization of a measuring tape. Random errors may appear irrespective of the instruments and measuring methods employed. The nature of their occurrence in individual measurement is usually unknown. The probable sources of random errors are uneven tension of a tape in various measuremems, poor alignment of intermediate plumb lines, uncertain readings on the tape scale, etc. Let us find the expressions for estimating the random and systematic errors which can appear in length measurements. Let the total effect of a number of random errors be such that the interval 1 is measured with the total root-mean square error ml'. If the length being measured contains n such intervals, then mL
of Underground
(5.33)
As may be seen from this formula, the random error of a measured side length increases proportional to the square root of L. The coefficient a is called the coefficient of random influence; it can be determined experimentally. Depending on the influence of random errors, the relative error of length measurement decreases with an increase in the length of a line: mL,/L= a/JL (5.35) In order to estimate the systematic error, let us suppose that the interval 1 is measured with a systematic error m. .Therefore, the entire length Lof a line, including n intervals, can be measured with a systematic error: mL = m.n . or mL = m.L/I . With m./l = b, mL = bL, i. e the systematic error increasesproportional to the length of a line. Depending on the influence of systematic errors the relative error of length measurement is constant for particular measuring conditions and independent of L: mL. /L= b The total root-mean square error of measurement of a side length depending on m, and m. can be determined by the formula: mL =..ja2L+b2L2
(5.36)
The coefficients of random and systematic influence, a and b, can be found experimentally. To do this, the given length in a mine is
5.14.
Detailed
Survey
of Underground
measured with the common and higher accuracy, and the results of more accurate measurements are considered to be faultless (true). After that, the difference between the common Li and more accurate measurements (LTi) is found: d,=L.-L , ,
T
,.
Using this difference, culate a and b: a=
J
~
and
it is possible
to cal-
b=0
n -[L] where
5.13.
di
=
dj
bLi
Distance by Light
Measurements Range Finders
Light range finders are employed in mine surveying mainly in the case of the centralized construction of reference mine survey nets when the majority of sides of theodolite traverses exceed 50 m in length. The measurement of the length of a theodolite traverse by this method consists essentially in determining the time 't required for a light beam to cover the distance between the two points being measured in the forward and back direction. Light range finders have a light source which emits a narrow light beam onto the reflector placed at the other end of the line to be measured; the reflected light beam enters a light detector. The signals from the light source and light detector are fed into a recording device. Since the light source and light detector are combined and arranged in the same point, the light beam covers twice the distance being measured. Thus: D = v't/2 where v is the velocity of light in air and 't is the time during which the light signal covers twice the distance being measured.
111
Workings
5.14. Detailed Survey of Underground
Workings
Mine survey plans, profiles and sections should represent all the elements and details essential for the geological and mine-engineering characteristic of a deposit: the geometrical form and spatial location of underground workings, geological structure of a section or deposit, mechanisms and structures in a mine, etc. Surveying of these elements, which is called the survey of details, or detailed survey, consists in measuring the lines and angles that determine the location of the characteristic points of these details relative to survey traverse lines. Detailed survey can be carried out either at the same time when the survey traverses are being run or at a different time. The accuracy of location of details depends on the object of surveying and the scale of the survey plan. If the results of survey will be used for analytical calculations, the accuracy of detailed survey must correspond to the accuracy of analytical calculations. Detailed survey for compiling a survey plan should be done with an accuracy at which all details can be shown properly on the scale of the survey plan. For instance, if the scale of a plan is 1/5000, the linear measurements in detailed survey can be made with an accuracy of 0.5 m; for a plan scale 1/1000, the accuracy of linear measurements to 0.1 m is quite sufficient. The angular measurements in detailed surveys do not require an especially high accuracy: angular values can be read off with an accuracy to 5-10'. Detailed surveys can be carried out by the method of ordinates, polar method, method of cross bearings, etc. The first of them is however most popular in surveys of permanent and development workings. When running a theodolite traverse in a working, the clear cross section of the working in each instrument station point is
~
Ch. 5. Horizontal
112
/
x
Surveys
of Underground
Workings
/
,
,~~ O
-.0
Fig. 5.26
Sketch of detailed
survey by method
of ordinates
measured by a tape. The measured distances from the theodolite centre to the right, left, top and bottom are recorded in the field book. The positions of the points of details are determined by measuring the distances from the beginning of a theodolite traverse side to the perpendiculars drawn from these points onto that side and the lengths of the perpendiculars proper (ordinates). The density of measurements depends on the curvature of workings. In detailed surveys by the method of ordinates, it is recommended to choose two intervisible theodolite points so as to measure the distance between them by a tape (such as points 17 and 18 in Fig. 5.26). The zero mark of the tape should be aligned with the projection of one of the final points of the traverse. The distances 01' 02' etc. are measured with an accuracy to 10 cm and recorded in the field book as an increasing total from the starting point. The ordinates h1, h2, etc. are measured with an accuracy to 2-3 cm. The measured values oi, hi, the cross-sectional dimensions of the working along the traverse and other details are written on the sketch (outline) of the working. Using the method of ordinates, detailed survey can be performed quite quickly, and its results can be transferred easily onto the plan of a mine working. Detailed survey should also fix sharp changes of the bedding elements of a deposit,
dipping angles and capacities of seams (veins), probable tectonic disturbances and their main parameters, etc. 5.15.
Office Analysis of Results of Underground Theodolite Survey and Calculation of Point Coordinates
The office analysis of the results of an underground theodolite survey includes the following procedures: (a) control of mine (field) books and preliminary analysis of the measured linear and angular values; (b) calculation of horizontal distances; (c) determination of the closure error of angles (angular discrepancy) and direction angles upon the distribution of this error; (d) calculation of the increase of coordinates, determination of the linear discrepancy, and distribution of this discrepancy proportional to side lengths; and (e) calculation of the corrected increases of coordinates and the coordinates of the points of a theodolite traverse. For successful office analysis, the records in the field book and the book of calculated coordinates should be made accurately arid carefully. It should be noted that these mineengineering documents also have juridical validity. As a rule, as the field books have been controlled and it has been established
5.15.
Office
Analysis
that the results obtained are within the specified allowances, the controller makes corresponding records in them. All erroneous records are struck out and the corrected values are written instead and signed by the controller. The analysis of linear measurements is started from calculating the arithmetic mean of side lengths. The preliminary analysis of angular measurements consists in calculating the mean values of measured angles. The checked mean values of angles and horizontal distances are written in the book of calculated coordinates, and the angular error {discrepancy) is then determined by various formulae, depending on the kind of theodolite traverse. For instance, for an open traverse with measured left forward angles, the formula is as follows: f fJ= l80°n + !:13-{l1f -l1in) -360° R
of Results
13
For hanging traverses run twice, 1;/1perm=2m /1 v ~nl -1-n2 The discrepancy f /1 obtained in this way, provided that it does not exceed the permissible error, is distributed equally for each measured angle, with an opposite sign. After error distribution, the calculated direction angle of the final side in an open traverse and the initial direction angle in a closed traverse will be true. If the angular discrepancy exceeds the specified permissible value f /1 ' the traverse angles must be measured anew. The direction angles of sides of a theodolite traverse with measured left forward angles can be calculated by the formula: an = an-l + /31::t: 180° and with measured right forward angles, by the formula: an = qn-l -/3r ::t: 180° The horizontal distances of sides are calculated by the formula: s = Scosv
where n is the number of measured angles, l1in and 11 I are the direction angles of the initial and final side respectively; and R is an integer or zero. For a closed traverse, the angular error is determined as the difference between the actual and theoretical sums of interior angles of a closed polygon: f fJ= !:13"-!:13th In that case, the discrepancy f fJ must not exceed the permissible angular error:
where S is the inclined length of a side and v is the angle of inclination of that side. With the horizontal distances and direction angles of theodolite traverse sides being known, it is possible to determine the increases of rectangular coordinates by the formulae: dx = scosa = scosr
ffJ
dy = ssina
= 2m perm Jn fJ
= ssinr
}
Table 5.8 Measured parameter
Quadrant II
a, degrees
0-90°
r, degrees ~x
r=a
~y
1270
ill
IV
Table 5.9. Calculation Sheet: Point Coordinates of Theodolite Traverse Nos.
Horizontal
Direction angles a'
angles
of points
measured
Tabulated angles a'
Natural values Horizontal distances s
corrected
cosa'
sin a'
tan (1' or cotan (1'
D 20' 177'
-9" 30'43"
179
-9" 0031
80
-9" 44 43
177° 30'34" 17° 3D' 34"
23.468
0.953667 0.300863 0.315480
16 3056
16 3056
21.508
0.958743 0.284276 0.296509
277 1530
82 44 30
20.809
0.126343
2622926
82 2926
26.367
0;130689 0.991424 0.131820
26021
80 2126
29.489
0.167505 0.985871 0.169905
83 36 44
27.361
0.111257 0.993792 0.111952
17
2
3
00'00"
3034
1790022
80 44 34 0.991987
0.127364
-9"
4
165
1405
1651356
-9"
177
5209
177
5200
26
-9"
6
183
1527
1831518
263 36 44 -9"
94
3147
94
31
38 ~s
1780822
c Lf3m= 1058 0925 Lf3perm =10580822 IIlPnM= 2mp In 111=+1'03"
= 2 x 20" J7 = 1'46"
149.002
Increases
of coordinates,
Coordinates
m
Nos.
of
points
D
+5
+
22.381
+
20.620
+5
+
2.629
+
~/1x
+2.629
20.642
26.141
3.044
2007.061
2
+"20.625
+
2043.011
2013.176
3
2045.645
1992.535
4
2042.205
1966.395
5
2037.271
1937.271
6
2034.233
1910.135
6.115
+
2.634
-3.446
-.20.641
3.440
-26.140
+2
-4.939
29.072
-4.934
-29.070
+1
-3.044
27.191
3.038
-27.190
1:L\y
+.
34.200
89.872
+
34.233
89.865
+
34.233
-89.865
c
fAx = -0.033,
JAy= -0.007
f.=~=0.034,
t=s
8.
2022.386
7.061
+I
3.446
+6
+6.114
6.114
+1
4.940
+ 7.060 + 22.386 +
7.060
+6
+6
2000.000
+I
+5
+
2000.000 +I
~
0.034
= ~
4400
< -,
3000
~=~ ~s
3000
Ch. 5. Horizontal
116
Surveys
The quadrantal bearings r and the signs at Ax and Ay can be found in Table 5.8. Upon the calculation of coordinate increases Ax and Ay. it is recommended to make check calculations by one of the formulae: Ax = Aycotanr or Ay = Ax tan r The calculation of coordinates for an open theodolite traverse run between points C and D (see Fig. 5.20) with the known coordinates Xc, Yc and XD' YD can be done as follows: Xi
= XD +
X2 = Xi
Xc =
+
X7 +
AXD-1
' Y1 = YD +
AyD-1
AX1-2
' Y2 = Y1 +
Ay1-2
Ax7-c
YC = Y7 +
Ay7-C
h = ~1y
+ f1x
Permissible linear discrepancies are specified depending on the purpose of theodolite survey, kind and length of traverse line, and the availability of fixed points. If the linear discrepancy is within the perIilissible value, the errors in coordinate increases are distributed with an opposite sign proportional to the lengths of sides: 0.-. ayi =&" [S] ~i
L\x'. = L\x. + 0. ,
,
-aX.
,
L\ y '.
0. 1= L\y ,.+-ayi
The coordinates of the points of a theodolite traverse are found by the formulae: x. = x. 1
whence LAxcalc = Xc -XD
(5.37)
LAycalc = yc -YD
(5.38)
,
Since the measurements of angular and linear values in theodolite traverses involve certain errors, the left-hand parts in formulae (5.37) and (5.38) are not equal to their righthand parts, and therefore -D
1-
+ -1
L\x'.
Yi=Y~l:!:L\y'i The calculations of coordinates of underground theodolite traverse points are carried out by the formulae given above by one of the following methods: with the use of logarithmic tables; with the use of desktop calculators and tables of trigonometric functions (Table 5.9); or by using electronic computers and special standard programs.
(5.39)
LAycaIc -(yc -YD) (5.40) 1 where f &x and f &yare the linear discrepancies of coordinate increases of an open theodolite traverse along the axes of abscissae and ordinates respectively.
!£\y
The linear discrepancy,h, of a traverse line is found by the formula:
Noting the calculated errors °Ay' and °Ax" , , the corrected increases of coordinates are then determined by the formulae:
xc=xD+LAx Yc = YD + L Ay
LAxcalc -(Xc -XD) 1 D
Workings
.0Axi =&s. [S] ,
Adding the left- and right-hand parts of both columns, we get:
f/1x
of Underground
5.16. Accumulation of Errors in Underground Theodolite Surveys The positions of points in an underground survey are determined with certain errors, so that the calculated coordinates of the points of a theodolite survev do not corresDond to
5.16.
Accumulation
the actual positions of these points in space. As the number of measured angles and the lengths of sides in traverses are increased, these errors are accumulated, i. e. the points which are more distant from the beginning of a traverse are determined with an ever increasing error. The error in the determination of the final point of a traverse depends substantially on the configuration (shape) of a traverse line and mainly on whether the traverse contains the sides of a short length and angles close to 90°. 5.16.1.
Root-Mean Square Errors of the Position of Final Point of Free Theodolite Traverse
Suppose that a free theodolite traverse is run from the initial fixed point I (Fig. 5.27), in which the left forward angles 13iand horizontal projections of sides Si are measured. It is required to determine the errors of the coordinates of the point N of the free traverse relative to a point 1. The traverse is run from a side II-I with fixed values of coordinates and a direction angle (l1I -I. The error of the coordinates of that point is the sum of the errors of measurement of horizontal angles, M /1' and of side lengths, M s.
of
Errors
117
Since angles are measured independently of the side lengths of a traverse, the coordinate errors depending on Mx .My and Mx . My can be determined sepa&tely.fJThen it ;s possible to calculate the total errors of the coordinates of the point N by the following formulae: M x -", -/~. M~p -.: '. "- + M;. My=J~~ The total error of the planimetric position of the point N will depend on the errors of measured angles, M p .and measured side lengths, M s: M2 = M~ + M; = Mi
+ M;
(5.41)
smce M~ = M~p + M;p and M; = M~s + M;s The errors Mx and M y can be determined p p graphically. Let the angle 131be measured with the rms error mp (see Fig. 5.27). In that case the polygon 1-2,1..., N will be turned through an angle mp about a point 1, so that the point N will oc6upy a new position N'. The displacement of the point N can be found from a rectangular triangle 1N N' : NN' = R1 tan mp1 (5.42) Since at small angles it may be taken that m
tan 13= 13"/p", we have: NN'
= -!!..l-R1. The p
displacement of the point N along the axes x and y will then be: N'N" = (mp /p) R1 and N'N" = (mp /p) R1 1 y 1 x where R1 and R1 are the projections of the shortest distance R1 from the polygon vertex 1 to the point N onto the coordinate axes and p" = 206265". If all horizontal angles are measured with the same accuracy mp1 = mp2 = ...= mp; = = mpn= mp, i. e. if any angle 13;is measured Fig. 5.27 Detern1ining free polygon
errors
accumulation
in
with the same error mp;, it can then be written that the displacements of the point N
Ch. 5. Horizontal
118
Surveys
along the axes Ox and Oy are respectively m.. m.. ~ R. and --1:1 R. . p
'y
p
'x
The total displacement of the point N along the axes x and y under the influence of random errors of measurement of all angles will be:
of Underground
Workings
traverse is displaced along a straight line £i connecting that vertex with the initial point 1. Then, the errors along the coordinate axes for the final point N will be: Mx
= s
b£N
and
where
My
=
x
sys LN
s
and
x
LN
are
y
b£N
(5.45) .
sys the
projections
of
closures LN onto the axes of abscissae and ordinates respectively. Using formulae (5.44) and (5.45), we can write: n M2
=
a2
~ L..
Xs
s.cos2a ,
+
b2L2
I
N;
/=1 (5.46)
Let us now find the errors of the coordinates of the final point of a free theodolite traverse, M~ and M; , which are caused by the errors in Sthemeas~rement of side lengths. The errors Mx and My are the sums of the random and systematicSerrors in the measurement of each polygon side. Therefore, we have:
n M2
=a2
""' £..,
y.
s.sin2a.+b2L2 , I
Ny
i=l
The total error of the coordinates of the point N caused by the errors of linear measurements will be:
" M2
=
M2
+
M2
=
.x.
02
~ L..
y.
i=l
M~ = M~ + M~ s sr ssys M2
=
M2
y.
+ y,
where
Y.
and
-sys
-
M y
are
the
errors
of
their
errors
caused
by
the
sXs Influence
sys of
systematic errors in length measurements. The random components M; s and M y2s ,
a2
~ £., ;=1
i=l
cos2a.
+
2 N
(5.47)
b2L2
i.
N
.
(5.48)
"
II
L
S
,
(5.44)
.' r
L
n +
can be found by the formulae: n M; = a2 ~ sj cos2a. s L.. I 1 j=l
M y2 = a 2
b2
Using formulae (5.43) and (5.46), we can obtain expressions for the root-mean square error of the position of the final point N of a free polygon in the coordinate axes:
the
s s , , coordinates of the final point of a free polygon caused by the influence of random errors in length measurements and Mx and M y s s are
+ t
M2
"
Mx
S
S.sm .2 a. I
Under the influence of a systematic error of length measurement, each ith vertex of a
02
~ £...
s.sin2a. I
+ I
b2L2 N
i= 1
m2 " " M2 = --7 L Rf + 02 L Si + b2L~ p i=l i=l
5.16.
5.16.2.
Accumulation
of
19
Errors
where R; , is the projection of the distance between the vertex i and the final point of a polygon onto the direction perpendicular to that for which the error M x' is determined; a; is the angle between the line Si and the direction relative to which M x' is determined; and 4' is the projection of the closing line L onto the axis x', i. e. onto the direction relative to which M x' is determined. The terms Ry' and sicos2a'; can be determined graphically.
Root- Mean Square Error of the Position of Free Traverse Point in the Known and Perpendicular Directions
In practical surveying, it is often required to determine the errors in the positions of points of a free polygon relative to a critical direction. For instance, when a working is being driven towards an abandoned section, it is essential to know the error of the position of the face in the direction of the working being driven; when driving a working from both ends, it is essential to know the connection error in the direction perpendicular to the working axis. Suppose that the axis x' of a rectangular system of coordinates coincides with the direction of driving of a working, CD (Fig. 5.28a) or is perpendicular to the direction AB of a working being driven from both ends (Fig. 5.28b). Let the chosen system of coordinates be denoted x'y'. According to formula (5.48), the rms error of the position of a face relative to the known (specified) direction M x' can be expressed by the following formula: mf32 n n M2, = -~ R~ + a2 ~ s.cos2a' + b2L2, x 2 £... 'y' £... I I x p 1=1 i=l (5.49)
5.16.3.
Root- Mean Square of Direction Angle of Free Theodolite
Error of Side Traverse
The direction angle of the nth side of a theodolite traverse can be calculated by the formula: a" = ao + ~1 + ~2 + ...+ where ao side of a measured Let us errors
~" I
180° x n
is the direction angle of the initial traverse and ~1' ~2' ..., ~" are the angles of the traverse. denote: mIl' m Il ' ..., m Il the rms 1 2 "
of measured
angles;
ma
"
the
rms
error
of the direction angle of the nth traverse side; and ma the rms error of the direction angle of the rnitial side.
(b)
Fig. 5.28 Driving underground working: from both ends in direction A-B.
(a) in direction
of worked-out
sections; (b) in working
driven
120
Ch. 5. Horizontal
Surveys
of Underground
Workings
Then, the fIllS of the direction angle of the nth side of a traverse will be: man= JI-=i
(5.50)
If the angles are measured with the same accuracy, then m. = m(J;;;: Considering theOrms error of the direction angle of the initial traverse side, m~-, the rms
(5.51) man
,
=
V
/ -.2 mao
+ -r
,
nm/i
2 2
Chapter Six Vertical
Surveys
in Underground
Workings
foundations of stationary underground installations and structures. The permanent Vertical survey, or levelling, is a survey station marks or polygonometric and theoprocedure in which the height differences dolite traverses can also serve as height (elevations) of some points over others are control points. The height transfer by geomeasured in a certain sequence,and then the metric levelling should satisfy the following requirements: required heights of points are calculated from (a) the discrepancies of measured heights the heights of initial points and the height of points should not exceed 50 mm Jf differences measured. Vertical surveys are carried out in order to in polygonometric traverses or 80 mm JL determine the height marks of individual in theodolite traverses (where Lis the length points established in underground workings, of a traverse line, km); to assign the specified slope (grade) to wor(b) staff spacings should not exceed 200 m kings, to plot longitudinal and vertical profiin length and differ from one another by les and sections, to determine th~ height more than 10 m; marks of the characteristic points of deposits (c) levelling lines between the initial bench (seams);these measurements are essential for marks should be closed or run forward and the solution of mining geometry and mine back; geometrization problems. (d) the discrepancies of height differences Vertical surveys can be made by two at a station, as read off on the black and red methods: (a) geometric, or direct, levelling face of staffs or at two different settings of the and (b) trigonometric, or indirect, levelling. level instrument, should not exceed 10 mm; The former method is employed in underand ground workings with small inclination ang(e) before starting the levelling procedure, les (up to 5°) and the latter, in steeper the available station points should be workings. checked for stability. Levelling reference nets are extended all The discrepancies between the height diffeover the mining field and are later used as the rence established earlier and the test one basis for vertical surveys in underground should not exceed 10 and 20 mm respectively workings. Additional levelling lines are run in polygonometric and theodolite traverupon advancing the main workings through ses. 500 m (for survey scale 1/2000) or 300 m (for When transferring the height marks in survey scale 1/1000). underground workings. by trigonometric leThe height control in mines is ensured by veiling, the following accuracy requirements bench marks set in the solid rock in the foot should be observed: wall, side walls and roof of workings or in the (a) the permissible discrepancy of a zero 6.1.
General
122
Ch. 6. Vertical
Surveys
in Underground
Workings
offset (horizon point) in the measurements of (.) "-, inclination angles is 1.5' in polygonometric traverses and 3' in theodolite traverses; .. '5 (b) the discrepancy of height differences ~I determined for a line by levelling forward and > back should be not more than 1/2000 of the side length in polygonometric traverses or 1/1000 in theodolite traverses; -11°1150 J (c) the discrepancy of two measured heights .1251. of a theodolite and signals should be not more than 5 mm in polygonometric traverses Fig. 6.1 Special station plugs used in underor 10 mm in theodolite traverses; and ground workings (d) the discrepancy in the height differences of the entire line of levels in polygonometric footwall (Fi"g.6.la) and side walls of workings t~aversing should be not more than (Fig. 6.lb). The bench marks set in the Ah = [s]/4 v'l/n + siwo/3 footwall are preferable, since they are less subject to deformations due to rock displacewhere [s] is the total inclined length of the ment during exploitation of deposit. forward and back traverse, m; n is the total Bench marks should be established at each number of sides in the forward and back level of a mine and preferably in places less traverses; and O is the mean inclination angle probable to be disturbed by stoping. As a of traverse sides; in theodolite traversing, rule, bench marks are established in pit this discrepancy should be not more than bottom and main horizontal workings so as 120 mm JL, where L is the traverse to provide a levelling control net within the length, km. limits of the entire mining field. Side lengths should be measured in accorFor the identification of bench marks, dance with the specifications for linear mea- marker plates are nailed to mine lining surements in polygonometric and theodolite supports, which bear the number of a bench traversing (the discrepancies between two mark and a letter M which indicates that the measurements should not exceed respectively bench mark in question is an elevation point, 1/3000 and 1/1000). Vertical angles are mea- rather than the point of a plan control net. In sured at two different positions of the circle caseswhen marker plates cannot be fastened and in the forward and back direction. The to mine lining, they are replaced by corheights of the instrument and signals are responding inscriptions made in a fast paint measured twice by a metallic tape. The height on the mine lining or side wall rock. difference for each traverse line is determined by levelling forward and back. The heights of the points of the survey net 6.2. Levels are determined by using polygonometric staAll existing levelling instruments, or levels, tion marks as the initial points. can be divided into two main types by the The bench marks to be set in the footwall method of levelling of the sighting axis: or roof of workings may be of the same instruments with a level tube on the telescope design as the station marks of underground (dumpy levels) and those with a tilting angle horizontal referencenets. Special station plugs compensator (automatic-aligning, or simply and marks can also be used for setting in the automatic levels).
6.2.
6.2.1.
Dumpy
Levels
123 9
Levels
Level type N-3 (Fig. 6.2a) is an instrument intended for technical levelling. Its main components are a telescope 13 with a cylindrical level tube attached to it; a telescope support 10 mounted on a vertical axis; a triangular plate (tribrach) 7 with foot screws 6; and a spring plate (trivet stage) 5 having a threaded hole for an attachment screw by means of which the instrument is fastened on a tripod. (a)
.13
2
Fig. 6.3
Fig. 6.2 Level type N-3 (USSR): (a) general view; (b) field of view
Level type N-IOL
(USSR)
The cylindrical level tube with the scale value of 15" is arranged in a box 1 together with an optical prismatic system which brings the images of the ends of level bubble into the field of view of the telescope (Fig. 6.2b). The sighting axis of the telescope can be arranged truly horizontally by manipulating the levelling screw 9 until the images of the bubble halves are perfectly coincident. The cylindrical level tube is provided with four adjusting screws covered with a lid. The instrument has an additional circular level tube 8 with three adjusting screws for rough adjustment of the vertical axis into a truly vertical position. For rough sighting on an object, the telescope can be turned in the horizontal plane manually when the clamp screw 3 is unlocked; precise sighting is done by locking the clamp screw 3 and turning the sighting (azimuth) screw 4. The image of cross hairs in the view field of the telescope is made sharp by rotating the diopter ring of an eyepiece 12. The telescope is focussed onto a staff by means of a focussing wheel 11. Tough sighting of the telescope on a staff is made by using a vane 2. Level type N-I0L (Fig. 6.3) is a small-sized
124
Ch. 6. Vertical
Surveys
instrument for technical levelling and has the following characteristics: telescope magnification 23, scale value of cylindrical level (at 2 mm) 45*, that of circular level 10', stadia factor loo :t 1%, and scale value of the horizontal circle (limb) 10. The instrument has rotatable portion consisting of a telescope 9, cylindrical level with a prismatic system, 8, circular level 3, levelling screw 4 for precise horizontalization of the sighting axis, and a stationary portion with a horizontal circle 7. The prismatic optical system brings the image of the ends of level bubble into the field of view of the telescope; these images must be made coincident by means of the levelling screw before taking a staff reading. The graticule (cross hairs) has a vertical hair and three horizontal hairs of which the two extreme (shorter) ones serve for distance measurements(stadia hairs). A sharp image of the cross hairs is obtained by turning the diopter ring 2 of the eyepiece and a sharp image of a staff, by turning the focussing knob 1. For setting up on a station point, the instrument is mounted on the ball-and-socket head of a tripod 5 so that the bubble of the circular level will be in the centre. For measuring horizontal angles, the tripod is set above the centre of a bench mark by means of a plummet. The limb readings are taken by an index arranged in a window 6. Level type NiO60 manufactured by Carl Zeiss, Jena (GDR) is a small-sized instrument 0.9 kg in mass (Fig. 6.4). It can transfer height marks with a root-mean square error of :t 6 mm per kilometre of a level line. The shortest sighting distance is 1.5 m. The instrument is quite convenient for underground applications. The telescopeis of the internal-focussing type with the field of view wider than 2°. The cylindrical level with the scale value 60" is provided witq a pivotable mirror. Level MOM Ni-Bl is manufactured in Hungary (Fig. 6.5). All sensitive parts of the
in Underground
Fig. 6.4
Workings
Level
2-sphericallevel; callevel
type NiO60 (GDR): 3-pivoting
mirror;
1- telescope; 4-cylindri-
Fig. 6.5 Level type Ni-Bl (Hungary): l-telescope; 2-cylindricallevel tube in casing; 3-scale microscope eyepiece; 4 -levelling screw; 5- endless sighting screw
6.2. Levels
instrument are dust- and moisture-protected. Rough sighting is done manually and precise sighting, by a sighting device. The level has no clamp screw. When measuring height differences by a Ni-BI level, the rms error does not exceed :!: 3-4 mm per kilometre of a level line. The instrument is provided with a levelling screw. The horizonta position of the level tube is controlled by the method of prismatic alignment of the ends of level bubble. The instrument is provided with a horizontal glass limb of 76 mm in diameter and scale value 1°. The readings are taken by means of a scale microscope whose eyepiece is arranged near the telescope eyepiece. With the microscope scale value 10', the accuracy of reading is 1'. 6.2.2.
Test and Adjustments of Dumpy Levels
T he axis of a circular level must be parallel to the rotating axis of an instrument. The bubble of circular level is brought into the centre by means of foot screws (for level type N-IOL, by moving the instrument on the ball-and-socket head of tripod). The upper portion of the instrument is then turned through 180°. If the bubble does not move from the centre, the condition is satisfied. If otherwise, the bubble is moved by adjusting screws towards the zero point through half the deviation arc and then brought into the centre by operating the foot screws (for level type N-IOL, by moving the instrument on the tripod head). The test and adjustment procedure is then repeated. T he vertical hair of the graticule must be parallel to the rotating axis of the instrument and the horizontal hair, perpendicular to that axis. The rotating axis of an instrument is first arranged truly vertical. The vertical hair is sighted on the line of a plummet hung at a distance of 20-25 m from the level instrument. The condition is satisfied if the. vertical hair
125
coincides fully with the plummet line. If otherwise, the eyepiece of telescope should be taken off to allow access to the graticule mount which is fastened by three screws. The top and bottom screws must be slackened by a full turn and the mid one, by a quarter-turn to shift the cross-hair plate if needed. Then the telescope eyepiece is set in place to check the position of the vertical hair. Upon the adjustment of the cross-hairs, the screws of the mount must be tightened (first the mid screw and then the top and bottom screws), after which the telescope eyepiece is fastened in place. T he sighting axis of the telescope must be parallel to the axis of cylindrical bubble level. This is the principal condition to be satisfied by a level. The test is carried out by the method of double levelling forward between points A and B arranged at a distance of 50-75 m from each other and fixed by spikes or pegs. A staff is set up on one of the points, say, B, and a level instrument, on the other (A) (Fig. 6.6a). With the horizontal position of the bubble level axis, the reading ai is taken on the staff in the point B and the height Vi of the level instrument is measured. Then the level and staff are interchanged to take the reading a2 on the staff and measure the height V2 of the instrument in the new position (Fig. 6.6b). If the sighting axis is not parallel to the bubble level axis, but makes an angle i with the latter, i. e. the sighting axis is not horizontal, then the readings taken on the staff will contain an error x and the true readings will be as follows: a'i = ai + x , a2 =
a2 +
x
}
(6.1)
Denoting the height difference of the point B over A as h, we can find from Fig. 6.6 that: h = Vi -a'i = vi -ai + x (6.2) or h = a~ -V2 = a2 + x -v2
(6.3)
Ch. 6. Vertical
126
Surveys
in Underground
Workings
corrected as follows. By operating the levelling screw, the horizontal hair is set on the reading a2 + sjp" (6.6)
(al
on the staff set up in the point A or on the reading at + sjp" (6.7)
~
Fig. 6.6 Check of parallelism of sighting axis and axis of cylindrical bubble level by double levelling forward
2s
on the staff set up in the point B. Then, the images of the ends of the level bubble are aligned by means of adjusting screws. This test can also be made by levelling the same points A and B from the mid forward. The level instrument is set up at equal distance from these points, the staffs are set up in the points A and B, and the readings a and b are taken on them (Fig. 6.7a). If the sighting axis is parallel to the bubble level axis, then h1 = at -b1; if otherwise, h2 = = a2 -b2. If the instrument is set up at equal distances from the staffs, then a2a1 = = b2b1, and therefore, h1 = h2 = h, i. e. the true height difference is obtained irrespective of whether the test condition is satisfied. For better accuracy, the height difference is measured two or three times changing the instrument horizon, and their mean value hm is taken as the final result.
,--,
where p" = 206265" and s is the distance between the points A and B, Inm. The angle i should be measured at least twice, with the discrepancies between the measured values not more than 5". The final value is taken as the arithmetic mean of all measurements. If the angle i has been found to be greater than 10", the non-parallelism of the axes is
Fig. 6.7 Check of parallelism of sighting axis and axis of cylindrical bubble level by double levelling from mid forward
6.2. Levels
Mter that, these points are levelled forward upon setting up the instrument over one of these points, say, A (Fig. 6.7b). In that case, the height difference will be: h2=v-b3
127
(a}
(bl. r' ~
(6.8)
where v is the height of the level instrument and b3 is the reading on the staff set up in the point B. If the discrepancy between the height differences measured by levelling from the mid forward is less than 4 mm (x ~ 4 mm), the sighting axis of the telescope can be regarded to be parallel to the axis of the cylindrical level. Otherwise, it is required to calculate the true reading on the staff set up in B from the true height difference (hm) obtained by the levelling from the mid and the height of the instrument v, by using the formula: b~ = v -hm (6.9)
O -=F:::
Zl
r
E
~' ,
ZI ,
s
=='i=i1£
-£I
~
, z 1
p
Z I
Id)
=40~~ v
~ J~z ~z
(e)
after which the sighting axis of the telescope can be adjusted parallel to the bubble level axis by the method described above. 6.2.3.
Automatic
Levels
Level instruments with cylindrical bubble levels require careful levelling before operation and continuous checking of the bubble position when taking readings. This drawback is eliminated in automatic-aligning (or simply automatic) levels in which the sighting line of telescope is automatically horizontalized by means of a special compensator (stabilizer-compensator) of a mechanical, optical or optico-mechanical type. Let us consider the schemesof stabilization of the sighting line by compensators in modem automatic levels. Suppose that the sighting line of the telescope is in a truly horizontal position zz1 (Fig. 6.8.a). In this position of the axis, the reading on a staff will be correct. Let the sighting axis of the telescope be now non-horizontal and make an angle E with the horizontal plane (Fig. 6.8b). In that case, the centre of cross hairs will be displaced from
Fig.
6.8
Optical
schemes
of level
compensator:
the horizontal line and occupy a position Z'l' Since the cross hairs are usually arranged in the rear focus plane of the objective, the displacement Zlz'l of its centre can be expressed as ZlZ'l = 1 tan £ or, since the angle £ is small, ZlZ'l ~I£, To take a correct reading with an inclined position of the sighting line, the cross-hair centre should be displaced in some or other way from the horizontal line and be in a point z l' This procedure is performed by compensators whose principal schemes will be discussed below, 1, The compensation 1£ can be introduced by displacing the cross hairs from a point Z'l into Zl by turning the level PZ'l on a point P through an angle £' (Fig, 6.8c). 2, The image of a staff (Fig. 6,8d) can be displaced so that the true staff reading is aligned with the centre of cross hairs (comnen-
128
Ch. 6. Vertical (a)
Surveys
in Underground
Workings
-I (b)
~
7
8 \
"
)
9
10 "
--tr
-11
Fig. 6.9
Level type N-I0KL
(USSR): (a) general view; (b) optical
sation with rotation of the sighting ray through an angle EJ. 3. The sighting line is displaced parallel to itself to pass through the centre of cross hairs (Fig. 6.8e). According to the compensation schemes shown in Fig. 6.8c and d, the lever or optical system placed in a point p for the compensation of an inclination angle must satisfy the condition fE = SE'; and for the schemesin Fig. 6.8e, the required condition is f = ks, where E' is the angle of deviation of the ray by a compensator, s is the distance from the compensator to the cross hairs or the length of the path of sighting rays from the point of incidence onto the optical system (prism or mirrors) of the compensator to the cross hairs, and k is the compensation factor (k = E'IE). The compensators of modern automatic levels ensure the compensation of the sighting axis within the angles from:!: 6' to :!:40'. Automatic level type N-1OKL (Fig. 6.9a) is intended for technical levelling with a rootmean square error of 8-10 mm per kilometre of a single run. The direct-image telescope (I, 4) of the instrument is placed in a heat-insulated ca-,
scheme of compensator
sing. The instrument is provided with a horizontal circle 3 having 1° limb divisions. Index readings can be taken with an accuracy to 0.10.The instrument has no azimuth screw and the telescope is sighted onto objects by turning the instrument body by hand. The telescope is focussed by a knob 2. Rough levelling of the instrument is effected by means of a circular bubble level 5 with the scale division 10'. The cross-hair mount is provided with adjustment screws to correct the position of the sighting axis. The deviations of the cross hairs from the true vertical or true horizontal position can be corrected by turning the entire eyepiece unit upon slackening the clamping screws. The prismatic compensator of the instrument ensures the horizontal position of the sighting axis at the inclinations of the instrum...n~support up to::!: 15'. The optical scheme of a level is essentially as follows (Fig. 6.9b). Upon passing through the objective 6, light rays fall onto the reflecting faces of a larger pentaprism 7, change their direction by 90°, and enter the sensitive element (rectangular prism) 11 of the compensator. Upon double reflection in the prism 11, light rays enter a smaller pentaprism 8 where their direction
6.2. Levels
is changed again by 90° and finally get into the lens system 9, 10 of the eyepiece. The pentaprisms are fixed and the rectangular prism is mounted in a tilting frame suspended on two bearings. The axis of suspension of the rectangular prism is chosen so that the distance from the main rear plane of the objective to that prism is equal to the optical distance from that prism to the cross hairs. In that case the coefficient of angular magnification of the compensator is k = 13/a= 2, where a is the inclination angle of the telescope and 13is the deviation angle of the sighting ray of the compensator.
129
The telescope is focussed by means of a focussing knob 2 which moves the rectangular prism 11 vertically in a slide. Level N-3K;Fig. 6.10) is intended for class IV and techJlical levelling. It can transfer heights with a root-mean square error of ::!:3 mm per kilometre of a level line. With the distances between the level and staffs up to 100 mm, height differences can be measured with an rms error within::!: 3 mm. The instrument is provided with an optical (prismatic) compensator having an operating angular range::!: 15'. The collimation line is horizontalized automatically with an accuracy to ::!:0.4". A circular bubble level with 10' scale graduations facilitates rough setting of the instrument axis into the vertical position. The instrument has a horizontal circle with a scale microscope, w,hich makes it possible to employ the horizontal circle for control survey and tacheometric survey on flat terrain. The optical scheme of the instrument is illustrated in Fig. 6.10b. The telescope proper consists of a front lens 1 and focussing lens 3 of the objective, cross hairs 5, and an eyepiece 6. The compensator is arranged between the focussing lens 3 and cross hairs 5 and comprises two prisms 4 and 7, the former being Fig. 6.10 Level type N-3K (USSR): (a) general view; (b) optical scheme of compensator
9-1270
130
Ch. 6. Vertical
Surveys
fastened internally in the telescope tube 2 and the latter suspended on crossed steel wires 8. The oscillations of the compensator suspension are damped by a piston-type air damper 10. The steel wires intersect in the centre of gravity 9. Level NiO25 (GDR) is intended for technical levelling and, if employed under normal conditions, gives a root-mean square error within :t2.5 mm per kilometre of a double run (Fig. 6.1la). The sighting line is horizontalized automatically by a compensator arranged between the focussing lens and eyepiece of the telescope and consisting of two rectangular prisms 1, 3 which are mounted on a pendulum 4 and a fixed roof prism 2 (Fig. 6.llb). If the instrument is inclined by a certain angle E, the pendulum will also deviate by the same angle E under the action of the force of gravity. This arrangement (a)
.3
in Underground
Workings
ensures automatic horizontalization of the sighting line. A double-action air damper 5 brings the pendulum to the state of rest in less than I s. The working angular range of the compensator is::!: 10'. The mean error of the horizontalization of the sighting axis is not more 0.5". The instrument compensator is insensitive to jolting during transportation. Precise aiming of the level at a target is effected by an endless sighting screw. The instrument has a horizontal circle with 10° divisions. Ocular estimation can be made with an accuracy to I '. Level type NiOO7 (GDR) is intended for technical and precise levelling (Fig. 6.12). Precise levelling is carried out by using a parallel-plate micrometer provided on the instrument and precision staffs with invar tape. When used for technical levelling, i. e. without the parallel-plate micrometer and with centimetre-graduated staffs, the instrument gives a mean error of::!: 2 mm per kilometre of a level line; in precise levelling, the accuracy is ::!:0.5 mm. The pendulum-type compensator of the level NiO07 has an air damper and can compensate tilting angles up to::!: 10'. Rough levelling of the instrument is effected by
Fig. 6.11 Level type NiO25 (GDR): (a) general view; 1-endless sighting screw; 2-circular bubble level; 3-rnirror; 4-telescope focussing screw; (b) optical scheme of compensator
6.2.
Levels
131
(a)
Fig. 6.12 Level type NiOO7 (GDR): 1- telescope window; 2-telescope; 3-focussing screw; 4-clamping handle; 5-sighting screw; 6-circular bubble level; 7 -micrometer drum
means of a circular bubble level. The telescope has a large magnification (31.5 X) and can be aimed with a high accuracy. The level is manufactured in two versions: with and without the horizontal circle. The horizontal-circle microscope is located just under the telescope eyepiece. The glass limb of the horizontal circle has a scale value of 10', but ocular estimation can be made with an accuracy to tenths of that value. Level type Ni-B3 (Hungary) can be employed for class III and IV and technical levelling (Fig. 6.13). The root-mean square error of levelling is not more than::!: 2 mm per kilometre of a level line. The instrument has a glass limb with a scale microscope which reads with an accuracy to::!: 1'. The rotation axis of the instrument is set upright by means of a circular bubble level with the bubble image being transferred into the field of view of the telescope. .
Fig. 6.13 Level type Ni-B3 (Hungary): (a) general view (l-telescope eyepiece; 2-optical microscope eyepiece; 3- endless sighting screw; 4- focussing screw; (b) optical scheme of compensator
The compensator of Ni-B3level (Fig. 6.l3b) has three rectangular prisms, two of them (1 and 2) being movable and the third (3) being fiXed. The compensator has the working angular range::!: 8' and the mean error of levelling of the collimation line is not more than::!: 0.4".
132
Ch. 6. Vertical
Surveys
in Underground
Workings
6.2.4. Tests and Adjustments of Automatic Levels
Fig.
6.14
Level
type
TN-6
Levels types TN-6 (Fig. 6.14), TN-7, and TN-9 have been designed specially for underground work. These small-sized instruments (0.7 kg, 1.8 kg, and 2.5 kg in mass respectiveIy) are intended for technical levelling. Level type TN-7 has a wide-range compensator which can stabilize tilting angles up to :t6°. The working angular range of levels types TN-6 and TN-9 is :t30'. Levelling work in constricted underground workings is facilitated by the provision of a diagonal eyepiece on the instruments. The levels of these types are provided with a horizontal angle-measuring circle which makes it possible to assign directions, carry out station fixing, and survey flat areas by the polar method. The optical system of the telescope has a high illumination power and gives an erect image of objects. The tripod has an extendable top portion to quickly change the instrument horizon.
Test of the circular bubble level. The axis of the circular bubble level must be parallel to the vertical axis of rotation of the telescope. The bubble of the circular level is brought into the centre by operating two foot screws. The upper portion of the instrument (telescope) is then turned through 180°. If the bubble deviates from the centre, it is moved back through half the deviation arc by means of its adjusting screws. After that the bubble is brought into the centre by operating the foot screws of the instrument. Mter this procedure, the instrument upper portion is turned through 90° to check that the bubble does not move from the centre. If otherwise, the test and adjustment must be repeated. The horizontal line of cross hairs must be perpendicular to the vertical axis of rotation of the telescope.The test and adjustment in this case is essentially the same as for dumpy levels. The collimation line must remain truly horizontal when the axis of rotation of the instrument is tilted within the range of working angles of the compensator. Pegs are driven into the ground at two points, say A and B (Fig. 6.15a), spaced at a distance of 100:!: 0.2 (a)
x,
K"
~
---~'\
~
a< I
Irb
~
50:!:.0.1 m
D .1.
50.:!:.0.lm
6.3.
Levelling
133
Staffs
5~
0
@ Fig. 6.16
Positions
of bubble
in circular
"\
"-/
level when determining
compensation
error
m from each other, and the level is set up midway between them (in a point D). The height difference between A and E is measured at least three times without changing the horizontal setting (horizon) of the instrument. The mean height difference calculated by these measurements, hl = a -b, is free from all instrument errors, since, with the arms AD and DE equal to each other, x' = x". The instrument is then transferred to a point C (Fig. 6.15b) to make new measurements of the height difference h2 between the points A and E. If the discrepancy between the measured height differences is more than 2 mm, i.e. hl -h2 > 2 mm, it is required to adjust the collimation axis upon determining the corrections by the formulae:
of the distances being levelled, i. e. the difference of arms must be not more than I m. The height differences between the staff points are measured successively, the level axis being perfectly upright and tilted at the maximum working angle of the compensator (v). The latter measurements are made with various positions of the circular level bubble (I, 2, 3, 4 and 5 in Fig. 6.16). At least five measurements are done for each staff distance. The systematic error of the compensator per minute of deviation of the instrument axis is then calculated by the formula:
x= d dl J. f 1 -d2
where h" is the mean height difference measured with the instrument axis tilted at the compensator working angle; ho is the mean height difference obtained with the instrument axis in upright position; s is the length of the collimation line, mm; p" = 206 265"; and v is the angle of inclination of the instrument. If O"c> 0.5", the instrument must be adjusted at the manufacturing works.
v=
d2 dl -d2
Jf
where x is the correction to the reading on the farther staff; y is the correction to the reading on the nearer staff; and dl and d2 are the distances from the instrument to these staffs. To make the adjustment, the level telescope is aimed at the farther staff and the horizontal line of cross hairs is aligned with the true reading on the staff by operating the adjusting screws of cross-hair mount. Determination of the compensation -error. This test is carried out in the field by measuring the height differences with the lengths of instrument arms of 5 m, 25 m, 50 m, and 100 m, i. e. with the distances between the staffs 10 m, 50 m, lOO m, and 200 m. The level must beset up.in the centre
-(hv -ho)p" O'c-2sv
6.3.
Levelling
Staffs
Levelling staffs are made of well-seasoned pine or spruce wood. They may have a different length: 4 m or 3 m for surface work and up to 2 m for underground work. Some types of staff are made of transparent materials, which largely facilitates reading-off in underground workings. Wooden staffs are
134
Ch. 6. Vertical
Surveys
in Underground
initially impregnated with a drying oil and painted white, after which patterned graduations are applied by means of a template or special machine. Staffs for technical levelling have l-cm graduations. For easier reading, centimetre graduations are grouped so as to form clearly seen decimetres. In novel makes of mine survey staffs, graduations are applied on a plastic, reflecting coating or lavsan film. Levelling staffs must be checked periodically to establish their accuracy. A check must determine the mean length of a metre interval, errors of decimetre groups, and prove that graduations are applied correctly. The discrepancy between the actual lengths of decimetre groups must not exceed ::I: 1 mIn. Staffs are checked by means of a standard metre; the use of standardized steel tapes is also possible.
Workings
mainly associated with the fact that the existing bench marks for levelling may be set in the roof and footwall of a working. In either case (with a bench mark set in the roof or footwall), a staff is set up so that its starting end is applied to the bench mark. Let us consider some probable schemes of geometric levelling in underground workings.
(a)
fb
a< ~~
~
I A ,
6.4. Geometric Levelling in Underground Workings Geometric levelling can be employed in underground workings with dipping angles not more than 5-8°. The procedure includes revision and fixation of bench marks, levelling proper, and office analysis of field observations. The principal aim of revision is to check whether the levelling project in question is chosen correctly. The operation consists in studying the state of the workings and existing points of reference nets. Additional bench marks may be set up by the results of revision. Levelling under the conditions of underground workings is recommended to be carried out by the method 'from the mid' (two-staff technique). Staff readings are taken with an accuracy to 1 mm. Geometric levelling in mines does not differ principally from surface levelling, but the schemes of underground levelling are characterized by a greater diversity. This is
Fig. 6.17 underground
Schemes workings
of
geometric
levelling
in
6.4. Geometric Levelling in Underground Workings
1. Levelling is carried out by bench marks set in the footwall of a working (Fig. 6.170). In this case the height difference of a point B over a point A will be determined by the difference of readings on the staffs set on the forward and rear points (bench marks): h=o-b where h is the height difference; a is the reading on the rear staff; and b is the reading on the forward staff. 2. Levelling is carried out by bench marks fixed in the roof of a working (Fig.6.17b). The height difference of the point B over the point A is found as the difference of readings on the staffs suspended from the forward and rear point: h = b -a. 3. Levelling is done by two bench marks, with one of them (rear) fixed in the roof and the other (forward), in the footwall (Fig. 6.l7c).In this scheme, the height difference is the sum of readings on the two staffs, taken with a 'minus' sign: h = -(a + b) 4. Levelling is carried out by two bench marks, the rear one being fixed in the footwall and the forward one, in the roof of a working (Fig. 6.l7d). The height difference of the forward bench mark over the rear one will be determined as the sum of readings on both staffs: h = a + b. The considered particular casesof determination of height differences with various schemes of bench mark arrangement can be covered by a common rule: the height difference between two bench marks in any levelling scheme is equal to the forward staff reading (foresight) minus the rear staff reading (backsight); the staff reading on a bench mark located in the footwall is taken to be positive and that on a bench mark arranged in the roof, to be negative. In geometric levelling in an underground working by the two-staff method, the field work consists essentially in the following.
135
I. If the surveyor's level employed is of the type with the level tube on the telescope, the instrument is set up roughly over the centre of a change (turning) point and prepared for observations. The telescope of the instrument is first sighted on the staff set on the backside point, and the reading is taken on the black face of the staff. The telescope is then pointed to the forward staff, and the reading is taken on the black face of that staff. Mter that, repeated readings are taken on the red faces of both staffs or with a different position of the telescope. At once a check is done whether the readings are taken correctly. For this, the height difference between the change points is calculated for the first and second pair of staff readings. The results of levelling are recorded in a field book of a form like that given in Table 6.1. If the discrepancy between the two height differences thus determined does not exceed the permissible value, the rear staff is taken off from the common turning point and set up successivelyon intermediate points. Upon completing the survey work on the given station, the levelling instrument is transferred onto a next station, and the staff on the point of known elevation is transferred onto the fore-side common point of a next levelling interval, while the forward staff remains in place. The work on the new station is repeated as described above. 2. If the l~vel instrument employed is of the automatic-aligning type, it is set up roughly in the mid between two common (change) points so that one of its foot screws is on the sighting line. The instrument is initially sighted on the rear staff, and the reading is taken on the staff black face. The operation of the compensator is checked by turning slowly the foot screw. The compc:nsator operates properly if the staff reading is not changed on rotation of the screw. The telescope is then reversed and sighted on the forward staff to take the reading on the black face of that staff. The operation of the compensator is
136
Ch. 6. Vertical
Table 6.1. Technical
Levelling
Workil
South
Level N-IOL
entry
P~gs, pOInts
21
22 23
Notes, sketches
1169 5859 1212 5899 1350 6039
242.849 1018 5706 J316 6001 1250 5940
4
in Underground
Book
Work place Performed by
~tations
Surveys
24
26
-1252
-1152
-5948
-5841
-1255
-1606
-5935
-6294
-1556
-1615
-6242
-6299 1314
52
151 153 -104 -102 100 99 2502 2506 354 346 360 364 -2870 -2864
242.697 103 -241.450
242.700 L)U4
240.296 350
239.946 362 239.584
5996 I:R = -22188 21528 Page-to-page control -680
I:F
-22807 21351
1:h
1;h.. = 3368
6736 5940
-1456
-242.451 dh = 398
-2970
796 Checked
checked again. If the compensator operates properly, the staffs are turned by their red faces to the instrument and measurements are repeated, but reading-off on the red faces is now started from the forward staff. Geometric leyelling can be used for vertical survey of haulage tracks in weakly inclined and horizontal workings. Levelling is carried out by change points arranged in intervals of 10 m or 20 m by means of a linen tape. The points are marked by chalk on one of the track rails and fixed by a suitable method on the side walls of the working. Track levelling is done in traverses supported by the points of a levelling reference network. Levelling
242.800
100
by
Date
from a single point is also feasible, provided that it is carried out forward and back. The level instrument is set up roughly in the mid between two change points, and staff readings are taken with an accuracy to a millimetre. In mine track levelling, the initial bench mark may be the last change point of a preceding levelling line, provided that the last height difference is checked and the discrepancy does not exceed 1 cm. The discrepancy of levelling lines must not exceed 30 mm JL, where L is the length of a line in hundreds of metres.
6.6.
Errors in Geometric
At the same time with levelling work, the height of the working at each change point is measured. 6.5. Office Analysis of Results of Geometric Levelling The office analysis of mine measurements in geometric levelling includes the control of the field books, calculation of height differences at stations, page-to-page control, adjustment of calculated height differences, and calculation of the heights of reference net points and change points in track levelling. If levelling is carried out by means of dumpy levels or levels with self-adjusting sighting axes, two height differences are measured on the black and red faces of staffs at each station, after which the mean values of height differences are calculated as the arithmetic mean of two readings. The calculations are checked by page-to-page control which in the case of geometric levelling (see Table 6.1) is made by the formula }:;R -}:;F = }:;hi -}:;h2 = 2hm
137
The corrected height differences are used for calculating the height marks of the points by the formula H., = H,,-
1
where
Hi
is the
point,
Hi-l
point,
and
these
points.
The are
+
the
the
height
hi is the
point. sign
if
this the
working the
of
intermediate
means HB
peg
is
points
the
instrument
is determined where
rear
point
and
the
staff
set
b is taken
with
set
with
between
b,
on
formula,
and
of which
=
of the
reading
In
a preceding
difference
EH
mark
a subsequent on
height
head),
formula
on
mark
marks by
black-face
mark
height
(elevation
by
+
in
the
-a 'minus'
HB
on
that
a 'plus'
footwall
sign
is
b is the
of
a
if it is set
in
roof. The
height
(pegs)
are Hc
=
mark
of
an
reading staff
marks
calculated
head:
EH
the
reading staff
Upon
if
the
staff
is
and
times
as
the
set
up
6.6.
Errors
of
is to
as
in
and
the
height c is
point.
a 'minus'
the
and
a
vertical is usually
horizontal
sign
if
with
a
marks
points, on
the The
roof.
height
in Geometric
elevation
and that
the
scale the
is
footwall
plotted
1/500
vertical
large
on
intermediate
working
The
Hc
with
in
points
the
point
set up
up
it
1/2000
1/50.
using
::!: c, where
calculation
change
scale
intermediate
c is taken
is set
sign
the
of by
intermediate
on
'plus'
to
height
is the
height
horizon
of
h.,
calculated
the
where }:;R is the sum of readings on the staffs set on rear points; }:;F is the sum of readings on the forward staffs; }:;hi is the sum of height differences read off on the black face of a staff; }:;h2is the sum of height differences read off on the red face of a staff; and }:;hmis the sum of mean height differences. The misclosure of a closed line is fh = }:;hi and that of a line run between the bench marks isfh = }:;hi-(HA -HB), where HA and H B are the heights of initial bench marks. The permissible discrepancies are introduced with an opposite sign into the calculated height differences as corrections determined by the formula O = (n/N)fh' where n is the number of stands (tripods) in the line to be corrected and N is the number of stands in the entire levelling line. The sum of corrections should be equal to the actual discrepancy taken with an opposite sign.
Levelling
of
a profile horizontal scale
1/200
taken
20
scale.
Levelling
If the height mark of the initial point is known, -the height mark of the final point of geometric levelling can be found by the formula: H
i
=
H,
+ In
~h. I
where Hin is the height mark of the initial point and ~hi is the sum of the height differences of a levelling line, which are usually obtained by levelling from the mid.
138
Ch. 6. Vertical
Surveys
in Underground
Each height difference is determined as the difference of staff readings, i. e. hi = ai -hi, Let us determine the root-mean square error of the sum of height differences. For this, let the rms errors of height differences be denoted as mi. m2. m3. ., '. mn, Since the distances between the change points of the line of levels are practically equal to one another and the work is done by a single instrument and under roughly identical conditions, the measured height differences can be taken to be equal to one another, i, e. mi = m2 = m3 = , , , = mn = m. Thus, the rms error of the sum of height differences is m; = nm2, The errors of height differences are influenced predominantly by the errors of readings on two staffs and therefore: m2 = m~ + m~ = 2m~ ,:"here mo is the rms error of a staff readmg. The error of a staff reading can be caused by an error of sighting and an error of level tube setting. The reading error caused by a sighting error can be recommended to be found by the formula: 6011 mv = -IMp" where M is the telescope magnification; 1 is the sighting distance (to the stafI), m; and p" = 206000". The accuracy of level tube setting is taken equal to 0.l5t" (here t is the level tube division). Thus, the reading error caused by inaccurate setting of the level tube can be found by the formula: m
t-
-
The mo
-;: -v
0.l5t" --;;--I p.
total mv
2
reading +
mt
error
will
be:
2
By way of an example, let us calculate the root-mean square error of a staff reading if
Workings
the telescope magnification is M = 20, the sighting distance to the staff 1 = 50 ill, and 't= 20": mo=J~=
1.Omm
Hence the rms error of a height difference in levelling from the mid, with the distance between the instrument and the staff 50 m, will be: m=~=1.4mm The formulae given above make it possible to determine in advance the rms error of levelling with an instrument of specified characteristics and under particular conditions or, on the contrary, to choose an appropriate instrument and method of levelling to ensure the required accuracy.
6.7. Trigonometric
Levelling
Trigonometric (indirect) levelling is resorted to in underground workings with a dip angle more than 5-8° where geometric (direct) levelling becomes inefficient. Theodolites employed for indirect levelling should have the accuracy of vertical circle reading not worse than 30". Trigonometric levelling is usually carried out at the same time with establishing the underground horizontal (planimetric) control (polygonometric traversing). Theodolites are mounted on the platforms of console holders. Measurements are made with the use of sighting marks or height compensators; disc-type signals are recommended at dipping angles greater than 30°. If plummets are used, marks should be provided on their strings for easier sighting. Vertical angles are measured in one set luf.'..rd and back. The measurements are checked by observing that the zero point is in a constant position. The permissible difference between zero point positions may be seen in Table 6.1. The instrument height i and the sighting height v are measured twice by a
6.7.
Trigonometric
measuring tape. Tape readings should be taken with an accuracy to I mm. If trigonometric levelling is to be carried out over polygonometric points, the following conditions should be observed: (a) the difference of zero point positions should not exceed 1.5'; (b) the discrepancy of the height differences measured by levelling forward and back for the same side should be not more than 1/2000 of the length of that side; and (c) the difference between two measurements of the height of a theodolite or signals should be not more than 5 mm. If trigonometric levelling is to be carried out over the points of a theodolite traverse line, the following conditions are essential: (a) the difference of zero point positions should not exceed 3'; (b) the discrepancy of the height differences of a side, determined by two independent measurements, should be not more than 1/1000 of the length of that side; (c) the difference between two measurements of the height of a theodolite or signals should be not more than 10 mm; and (d) the height discrepancy of a traverse should be not more than 120 mm JL. where L is the length of a level line, km. The lengths of trigonometric levelling lines are measured according to the specifications for linear measurements in underground polygonometric traverses. Each height difference is measured twice: by sighting forward and back, and the arithmetic mean of the two measurements is then found. Corrections to the calculated mean height differences are determined by distributing the traverse misclosure between the height differences proportional to the lengths of sides or by considering the relative weights of height differences. Let us consider some probable schemes of trigonometric levelling in underground workings. I. Suppose there are two statiQn marks A
139
Levelling
(a) s
~
--
-~--=-
.,
Fig. 6.18 underground
Schemes of trigonometric workings
levelling
in
140
Ch. 6. Vertical
Surveys
in Underground
and B set in the footwall of an underground working (Fig. 6.180). It is required to measure the height difference of B over A. To measure the inclination angle of a side AB, the theodolite can be set up either in the lower point A or in the upper point B; let it be first set up in A. Then a plummet is hung over the point B and a mark (say, the point of string connection or the plummet point) is chosen so as to sight the theodolite telescope on that point. The height difference for the schemeshown in Fig. 6.180 can be calculated by two formulae, one of which includes a horizontal distance s and slope v and the other, the sine of an inclination angle v and inclined length S. Denoting the sighting height by v and the instrument height by i, we obtain for the first case: h+v=stanv+i and therefore h=stanv+i-v For the second case: h+v=S
sinv+i
and therefore h=Ssinv+i-v If the theodolite is set up in the upper point B, the formulae for height differences will be written as follows: h=s
tanv+v-i
h=Ssinv+v-i As may be seen, the structure of the formulae with sin v and tan vis essentially the same and only the trigonometric function is different. Below, we shall use only the formulae with the sine of an inclination angle. 2. If the points A and B are set in the roof of a working and the theodolite is set up under the point A which is at a lower height
Workings
than B, then according to Fig. 6.l8b we have: h=S
sinv+v-i
3. With the point A set in the roof and the point B in the footwall (Fig. 6.l8c), the height difference can be found by the formula: h = -S
sin v + v +i
4. If the points A and B of trigonometric levelling are set in the roof of a working (Fig. 6.18d) and the theodolite stands in the upper point (point B), then the height difference will be found by the formula h=S
6.8.
sinv-v+i
Errors in Trigonometric Levelling
The error of location of the final point in trigonometric levelling is determined by the error of location of the initial point of a traverse and the error in determining the height differences. In this case, the error in determining the location of the initial point will not be considered. We shall only analyse the accumulated errors caused by the errors in determining the height differences. If the root-mean square errors of height differences are denoted as mi' m2' m3, ..., mn,the sum of height differences will be calculated with an error: M
2-
2 -mi
2 +
m2
2 +
m3
2 +
...+
m"
The rms error of a height difference will then be expressed as follows: m2 = m2 sin2v + m2S2/p 2 + m~ + m2
h
.v,
v
where m. is the mean error of measured length of a line, which can be found by the formula m; = ~2S + A2S2 (here ~ is the coefficient of random influence; A is the coefficient of systematic influence in linear measurements; and S is the inclined length of a line); v is the inclination angle of a line; p" = 206
6.8.
Errors
in
Trigonometric
265"; m" is the error of measured vertical angle; mi is the error of measured height of an instrument; and mv is the error of measured sighting height. The last two errors may be taken to be equal to each other, i. e. mi = mv. In view of what has been said above, the preceding formula can be rewritten as follows: S2 m2 h = ,,2Ssin2v + A.2S2sin2v + m2- 2 + 2m?, p Let us calculate the root-mean square error of height difference determined by trigonometric levelling for the following data: sighting length S = 30 m; inclination angle
141
Levelling
v = 25°; ~ = 0.0015; I.. = 0.0001; mv = mi = =2mm: m~ = 0.00152 x 30000 x 0.422622 + 0.00012 x 300002
+ 2 x 22 = 17.6 mm Thus, m" = 4.2 mm. If the height difference is measured when levelling forward and back, then: , r m" = m,j.J2 = 3 mm
Chapter Surveys
of
Preparatory
7.1. General The progress in mining technology is largely due to the introduction of mining systems with a large number of preparatory and stope workings whose position and state can change substantially both in space and time. Deposits of more intricate shape are worked out by more complex mining systems where the problem of accurate and timely coordination of underground workings becomes of crucial importance. As has been found, the surveyors of modern mining enterprises spend the major part of their time on survey work for servicing preparatory and stope workings in extraction sections and stoping blocks. From the standpoint of mine surveying, underground workings can be divided into the following groups: A. Preparatory workings which can be further subdivided by the conditions of surveying into workings with the angles of dip up to 45°; those with the angle of dip more than 45°; and connecting workings and outlet workings (draw holes, funnels, winzes, etc.). B. Stope workings which are subdivided into: faces in gently dipping and inclined seams;faces in steep seams;faces in layerwise worked-out seams; faces with an open stoping area; shrinkage stopes; and chambers (cavities) of large volume. The latter type of workings is again subdivided into three groups: (a) cavities in which the observer with instrument can be present (chambers left in the chamber-and-pillar systems of working, large-sectioll tunnels, etc.);
Seven and
Stope
Workings
(b) cavities into which only instruments (automatic or semiautomatic) can be introduced (usually through vertical holes) that is cavities formed through leaching of salts, underground chambers containing petroleum and gases, deep ore chutes, bins, etc.; and (c) cavities which are accessible neither for observers nor instruments (chambers left in the level-chamber systems of working, caving cones on the surface, voids formed in seams worked out by the caving system, etc.). c. Blasting workings: deep blasting holes, mine chambers, and wells. The list of survey objects includes all preparatory and stope workings, various hoI~s and chambers, fill-in strips, fill-in boundaries, drainage, ventilation and fire-fighting facilities, haulage tracks; elements of the geological structure of deposits, i. e. places of tectonic disturbances, thinning and wash-out of deposits, visible rock-mineral contacts, points of mineral assaying and other elements essential for proper exploitation of deposits; elements of occurrence of rock pressure, i. e. fissures, inrushes, domes, etc. which are important for solving the problems of efficient and safe exploitation of mining workings. The surveys of preparatory and stope workings involve the determination of details of the geological structure of a deposit or. its particular areas (the shape and bedding conditions of deposits, tectonics, distribution of quality of the mineral, etc.); determination of the dimensions and spatial position of mining workings for the construction of mine survey plans and solution of analvtical Droblems
7.2.
Instruments
associated with driving underground workings of the planned dimensions; and ensuring safe conditions of mining. The surveys of underground workings are based on survey nets which can be formed by running theodolite or goniometer traverses. The initial points for theodolite traverses are the points of polygonometric traverses. Angles in theodolite traverses are measured by theodolites of a root-mean square accuracy not worse than 30". If theodolite traverses are run in workings with the angle of dip less than 30°, horizontal angles can be measured in a single repetition or set. The difference between the check and final values of an angle should not exceed 1.5' in measurements by the method of repetitions and 2' in those by the method of sets. The error of centring of the theodolite and signals in theodolite traverses should be not more than 1/2000 of the horizontal length of the smaller side of a measured angle. In underground workings with the angle of dip more than 30°, horizontal angles should be measured by two rounds, with the circle being reset roughly by 180° before the second round. The discrepancy between the angles obtained in individual sets should not exceed 2'. The discrepancy between the angles measured by half-sets should not exceed the values given in Table 7.1. The discrepancy between the two measurements of one and the same side of a theodolite traverse should not exceed 1/1000 of Table 7.1 Angle of dip of wor- Permissible angular discrepancy bekings, degrees tween half-sets, min
31-45 46-60 61-70
at junctions between horizontal and inclined workings
in inclined wor. kings
2 3 4
3 4 5
for Surveys
143
the side length and the linear discrepancy should be not more than 1/2000 in closed traverses with gyroscopic sides or 1/1500 in traverses run between two sides of a polygonometric traverse. The sides of theodolite traverses are measured twice: in inclined workings, in forward and back direction with simultaneous measurement of the inclination angle of the measured line; in horizontal workings, both measurements can be done in the same direction with measuring the length of intervals if the line is longer than the length of a measuring tape. Steel tapes for the measurements must be standardized to have the relative error not more than 1/40000 of their total length; it is permissible in taping to stretch the tape without spring balance. Stope workings can be surveyed by running goniometer traverses with the use of theodolites or instruments of a lower accuracy. Goniometer traverses should be connected at both ends to the points of a theodolite traverse. The accuracy of goniometer traverses can be characterized by the following data: root-mean square error of angular measurements 10'; ultimate length of a traverse 0.3 km; discrepancy between two measured lengths of a line 1/100; and linear discrepancy in traverses run between two sides of a theodolite traverse, not more than 1/200. The points of a survey net should be located at distances not more than 50 m from a face. In places where mining workings approach dangerous zones, this distance should be not more than 20 m. In the latter case, the coordinates of the points of survey control are determined twice. 7.2.
Instruments for Surveys of Preparatory and Stope Workings
The most popular instruments employed in mine surveying practice for the surveys of
144
Ch. 7. Surveys
of Preparatory
and Stope
Workings
formed in the telescope. The magnitude of displacement of the images relative to each other depends on the distance to the stadia pole. The ranging pole (Fig. 7.2a) is made in the form of a rectangular glass plate having four horizontal hairs (to read off tens of metres), two inclined hairs, and a horizontal scale with five square divisions, each of them corresponding to 1 m in distance measurements. Before taking a stadia reading, the telescope is sighted on the mid of the stadia pole (along the height). The telescope tube is then (a)
Fig. 7.1 Goniometer type UTa: l-horizontal circle; 2- vertical circle; 3- telescope; 4 ~ bracket; 5- horizontal axis; 6- index; 7 ~ hinge joint
preparatory and stope workings are engineering theodolites and goniometers; suspension compasses and suspension semicircles are also in use. Since the surveys of stope workings most often are to be carried out in a restricted space, instruments for the purpose should have small dimensions and a low mass and ensure the specified accuracy of measurements of the worked-out area. Goniometer type UTG (Fig. 7.1). The telescope of this instrument has a double-image range finder with the stadia factor K = 500. The goniometer set includes a ranging (stadia) pole. The telescope is of the internalfocussing type with the focussing range from 2 m to infinity. The telescope system has two optical wedges, each of which covers half the objective and deviates the collimation ray by the same angle but in different directions.. Thus, two images of the stadia pole are
(c)
Fig. 7.2 Ranging pole for UTG goniometer (a) and field of view of goniometer UTG (b and c)
7.2.
Instruments
Fig.7.3 Goniometer type UT-3: I-base; 2limb; 3-vertical circle; 4-clamp screw; 5-sighting screw; 6-telescope; 7-sighting-and-ranging rod
moved by means of the alidade tangent screw until one of the left-hand inclined hairs is made coincident with anyone of the righthand horizontal hairs at which tens of metres are read off. The whole metres and decimetres are then read off on the left-hand portion of the horizontal scale, beginning from the first black square. If the inclined hair coincides with a figure '5', it is required to subtract 5 m from the read-ofT number of tens of metres. Metres and decimetres are read off in a common way; for instance, the reading shown in Fig. 7.2b is: 30 -5 + 3.5 = = 28.5 m. In all other cases, i. e. when the inclined hair does not coincide with '5', the read-ofT number of tens of metres is left unchanged; for instance, the reading in Fig. 7.2c is 10 + 1.6 = 11.6 m. The range finder of the goniometer type UTG can measure distances with a relative accuracy 1/100 to 1/200. Goniometer type UT -3 (Fig. 7.3) is designed for the surveys of preparatory and accessible stope workings, orientation of sublevels via inclined or vertical workings, and height mark transfer to subleve~ workings. 10-1270
for
Surveys
145
This is a repeating-type instrument provided with stadia hairs. The limb of horizontal circle has fivedegrees graduations. The readings on the horizontal and vertical circle are taken by means of a measuring drum with an accuracy to 1'. The stadia hairs permit the measurements of distances from 5 to 30 m with an accuracy of 1/200 and from 30 m to 40 m with an accuracy of I/lOO. The telescope of the instrument carries a sighting-and-ranging rod. Mine surveyor's goniometer-tacheometer (Fig. 7.4) is intended for the surveys of preparatory and stope workings and assigning of directions in driving workings; it can also be used for tacheometric surveys on the surface. The instrument is essentially a repeatingtype goniometer with the telescope having three pairs of stadia hairs. Two of tliem serve for distance measurements by means of a sighting-and-ranging rod and the third pair,
146
Fig.
Ch. 7. Surveys
7.5
Goniometer-tacheometer
type
of Preparatory
UTO-3
by means of a common levelling staff. The range of measured distances is from 2 m to 40 m and a relative accuracy of 1/200 for distances up to 30 m and 1/100 for those above 30 m. The telescope of the instrument is mounted eccentrically and permits the measurements of vertical angles within the limits :t 90°, The goniometer portion of the instrument has worm-and-gear mechanisms instead of reading circles. The readings are taken on measuring drums with estimation by eye to tenths of a division, which corresponds to 1 minute of arc.
and Stope
Workings
Goniometer-tacheometer type UTO-3 (Fig. 7.5) is designed for the surveys of uilderground workings and can also be used for the tacheometric surveys and surveys of quarries in open-cast mining. The instrument has an erect-image broken-type telescope 1 with a diagonal eyepiece 10. A wide-angle finder 2 is provided for quick aiming at objects. The goniometer has an optical reading system in the form of a scale microscope. For convenience of an observer, a reading eyepiece 3 is made rotatable. The vertical and horizontal circles are arranged in the housing 8 of the goniometer. The vertical axis, base 6, and reversible level tube 4 are designed so that the goniometer can be mounted in the upright or inverted position on a console holder 7, as well as in the upright position on a tripod. The goniometer is aimed at an object by means of 'endless' tangent screws 5 and 9 respectively for horizontal and vertical sighting. The instrument can be centred under and over a point by means of a mechanical or optical plummet. The instrument can measure vertical angles between -65° and + 90° and distances in mines between 2 m and 50 m. The reading accuracy of the vertical and horizontal circle is 1-2 minutes and the root-mean square error of angular measurements, not more than 3 min. Distances are measured by means of stadia hairs with a stadia factor loo, which ensures that the relative accuracy of measurements is not more than 1/100. The instrument has vertical and horizontal pairs of stadia hairs. Measurements underground are made by using a special stadia pole with a transparent scale which can be arranged either horizontally or vertically. Suspensioncompassesand suspensionsemicircles can be used for measurements provided that there are no large magnetic masses in the vicinitv.
7.2.
Fig.
7.6
Suspension
Instruments
Surveys
147
compass
A suspension compass(Fig. 7.6) consists of a round housing 1 and a suspension 2 which can be fastened on a cord 3. The housing is hinged in the suspension and can be arranged horizontally. The limb 4 of the compass has one-degree graduations increasing anticlockwise from 0 to 360°. The point axis 5 in the centre of the housing carries a sensitive magnetic needle. In the non-operating state, the magnetic needle is fixed by an arrester. For surveying, the suspension compass is suspended from a cord with the zero mark facing forward; the readings can be taken at both ends of the needle. Before using the compass, the needle is tested for sensitivity. For this, the compass is suspended on a cord and the reading is taken. Then the needle isdisbalanced by a magnetic mass and let to come to rest, after which the second reading is taken. The needle is considered to be sufficiently sensitive if the difference between the two readings does not exceed the read-off accuracy. Otherwise, its sensitivity should be improved. The insufficient sensitivity of the magnetic needle may be caused by some defects of the point axis and needle pivot or by the demagnetization of the needle. The former fault can be eliminated by polishing the point axis and needle pivot or by replacing them and the latter, by applying one pole of a permanent magnet to the needle and drawing it from the needle centre to the opposite pole end of the needle several times (up to 20). 10.
for
A suspension semicircle (Fig. 7.7) is used to measure the vertical angles of the sides of compass traverses and consists of a limb I, plumb bob 2 and two hooks 3 to hang the semicircle on a cord 4. Limb graduations
increase from 0 in the mid of the semicircle to 90° at its ends. Inclination angles can be measured with an accuracy to I 15'. Telescopic rod. The thickness of deposits can be measured by means of a telescopic rod (Fig. 7.8) which has the measuring range from 1.6 m to 4.4 m, root-mean square error Io.01 m, and mass 2.5 kg. The rod consists of three telescopic aluminium tubes 1, 2, 3, a support foot 4, stoppers 5, 6, and an indicator 7 with a clamp screw 8. The lower side of the indicator is covered by a reflecting foil which reflects the light of miner's head lamp and makes the point of rock contact readily visible.
D ~//////////////////////////////// 'l/ ~/;;;;T---
E
F' F --0--
, o o 0 I 0 0 0 0 O
//
~ ,
~.
---o b
9
b.
o
,/
9 a
/
a' ~
--0 ////////////////////////////////~ C C. B Fig. 7.9
Face survey
, .0 ~
0 ~
~
~-(JJ
0---
A
in stepped-face
overhand
stope system
7.3.1 .Surveys of Stope Workings in Steep Seams The positions of stope faces in steeply dipping seams of deposits are mainly determined by linear measurements which are made successivelyalong the entire length of a face. On deposits which are worked out with mineral extraction on the strike, the line of a face is determined by measuring the distances from the face to the survey traverse points located in cross adits or entries of the upper and lower level. With the overhand stope system of work-
ing, the position of a stope face is determined by the tape measurements of bench elements. Referring to Fig. 7.9, a point C is first established along the line of points A and B of a first-order survey traverse in the hauling entry. The distance from the point C to the base of the nearest bench (up dip) is then measured by a tape, which gives a point a. The tape is then stretched along the bench (on the strike) to obtain a point a'. In this way, all benches are measured by the tape up to the ventilation entry. After that, the tape traverse is connected to a point F. The survey of details is then carried out by the method of ordinates, and a sketch is plotted which gives all dimensions and details essential for the compilation of mining work plan and calculation of the voluII1e of the extracted mineral. The orientation of the tape traverse is performed by means of triangles constructed on junction sides FF' and CC'. In steep seams where the mineral is being worked out from the bottom upwards, the
7.3. Surveys of Stope Workings in Coal Fields
149
7.3.2. Surveys of Faces in Gently Dipping
Fig. 7.10 Face survey suspension semicircle
by
means
of cord
and
line of a stope face can be determined by means of a suspension semicircle or special 'bar'. In the former case, a fixed point 19 is chosen on the theodolite traverse in a ventilation entry (Fig. 7.10), and a plumb bob is sunk through the raise to fix the point A at its end. Cords are stretched from this point along the line of the stope face; the lengths of cord sections are measured by a tape and the inclination angles of cords, by a suspension semicircle. The cords should be stretched in a plane parallel to the wall of deposit. For control, the line of a face is closed onto the theodolite traverse via the second raise (onto a point 16). The survey of details is made by the orthogonal method from the cord sections. Survey by using a 'bar' can be carried out in practically vertical seams of a low thickness. The 'bar' is essentially a 2-m wooden rod with decimetre divisions. A plumb bob and semicircle are attached in its centre, which makes it possible to arrange the 'bar' horizontally. Survey is made from a straight line laid out by means of the 'bar' on the side surface of a seam. The ends of a straight line are connected to the points of a control survey established in raises. The discrepancies between the heights of points at the end of a traverse must not exceed 1/200 of the traverse length.
Seams
For the surveys of faces in gently dipping seams, a survey traverse with temporary or lost points is run along the line of a face (Fig. 7.11), after which tape measurements are made from the vertexes (or sides) of the traverse to determine the position of the face and the dimensions of left pillars, filled-in sections, etc. In this survey, the thickness and angle of dip of the seam are also measured, and the peculiarities of seam structure are sketched. The traverse points should be located as close as possible to the face front. Horizontal angles in the survey traverse are measured in one set by engineering theodolites or goniometers (such as types UTG and UT -3). The inclined lengths of
Fig. 7.11 Face survey gently dipping seam
utilizing
survey
net
on
150
Ch. 7. Surveys
of Preparatory
traverse sides are measured by a linen tape or by goniometer stadia hairs. If goniometers with eccentric telescope (types UTG and UT -3) are employed, the inclination angles of survey traverse sides should be measured twice, i. e. forward and back. The actual inclination angle is found as the half-sum of measured values. 7.3.3. Survey Work in Faces with Powered Mining Complexes For the normal exploitation of faces equipped with powered mining complexes, it is essential to ensure survey control of the linearity of a face and the position of a powered complex in it. For controlling the position of the complex, pickets are established at intervals of 10 m or 20 m in the main entry and ventilation entry. The lines connecting like points in both entries should be perpendicular to the axes of entries. The position of the complex is controlled by measuring the distances from its ends to the like pickets in the entries. With horizontal and gently dipping seams, these distances should be equal, i. e. the complex should be located perpendicular to the axes of the entries. For dipping seams (with the angle of dip 15-25°), these distances should not be equal, since in that case the angle between the face conveyer and the axis of hauling (conveyer) entry must be equal to 91-93°. Thus, the hauling (conveyer) face must be advanced to some or other extent depending on the type of complex, length of face, and mining and geological conditions. The linearity of a face with a powered mining complex must be checked at least once a month. The check for the linearity of a face ofa small length (60-100 m) can be done visually or by taping from change points or theodolite traverse points. The faces of a large extension (above loo m) are controlled
and Stope
Workings
for linearity by means of engineering theodolites or goniometers. The junction of a goniometer traverse to a theodolite traverse can be effected by means of a connection triangle. For this, the goniometer is set up in a point 1 in the entry (see Fig. 7.11) to measure the angle 'Y of the connection triangle and angle 13.The length of the first side a of the goniometer traverse is measured. If the first point is chosen so that the connection triangle angle 'Y does not exceed 5°, the junction angle
7.4. Surveys of Underground Chambersand Cavities principles of coordinate determination; and
I
surveys in which coordinates are determined by the conversion of physical quantities into geometrical. 7.4.1 .Tacheometric Surveys of Underground Cavities
II
I Theodolite
Section
~ 2
~-1
,
151
No.2
2
The tacheometric method of surveying is I based on a polar spatial (spherical) system of ~s~!!.o!!.~ -coordinates. The positions of points of an object being surveyed relative to the stand point of the instrument are determined by ~ measuring two angles (horizontal and vertical) and a linear parameter. The volume and contours of a chamber Theodolite No.1 can be determined by the method of intersections by two angle-measuring instruments from two points. Theodolites are set up in two points with known coordinates. Fig. 7.12 Tacheometric survey of chambers by Using a light projector set up in one of the two theodolites two points, light spots are formed on the most characteristic portions of walls of the cavity and fIXed with both instruments by Conned on the chamber wall at the specified making intersections, i. e. by measuring the height. After that, light marks Conned by a vertical and horizontal angles. The results theodolite No.2 are aligned with the light marks a1, a2, etc. produced by the theodolite obtained are then used for the analytical No.1. The readings are taken on the horizonsolution of the problem. The method of angular intersections is tal and vertical circle of the theodolite No.2 (respectively 13'1'13~,etc. and 0'1' o~, etc.). usually employed in cases when special instruments for surveying of inaccessible spaces These measurements make it possible to determine the positions of the points of are non-available. The survey work is started by plotting the specified profiles. This method is rather simple and not very vertical sections of the chamber to be labour-consuming. With the sighting length surveyed, with intervals of 5-6 m. Horizontal angles 131' 132'etc. in the stand point of a up to 50 m, the contours of chambers can be measured with a relative error of 1/200. A theodolite No.1 between the direction I-II drawback of the method of light marks is and the directions onto the points of intersection of profiles with chamber walls (01' that it is impossible to survey the wall in 02' etc.) are measured by a protractor with an which a theodolite is set up. Some makes of tacheometers (such as type accuracy to 10 (Fig. 7.12). For surveying in the chamber, the theodolite is set up in a BRT-006, GDR) are provided with a doublepoint I and oriented onto a point II, and image (coincidence) range finder. The practice horizontal angles 131' 132' etc. are set out of application of type BRT-006 tacheometer successively.With each sighting of the theo- has shown that the instrument can measure dolite.,No.l, light marks 01' 02' etc. are lengths up to 40 m with a satisfactory accura-
Ti
152
Ch. 7. Surveys
of Preparatory
and Stope
Workings
its width is measured by a measuring device (Fig. 7.13). The telescope and projector are focussed synchronously, which facilitates and speeds up observations. With measured distances ranging from 4 m to 100 m, the relative error is 11100 to 11200. Recently, lasers have come into use in mine surveying as sources for making light marks in the measurements of inaccessible distances. This increases the range of measured distances anrl the accuracy of measurements. The essenceof the method of laser ranging in underground chambers consists in that a tacheometer (such as type BRT-006) and a laser are set up in an approach working near a chamber to be measured. The laser together with collimator serves as a laser light-mark projector. Laser marks are projected on the walls of the chamber by a specified programme. The horizontal hair of the tacheometer telescope is sighted on the centre of a laser mark. With an arbitrary position of a mov-.., ' ,
~
, .'"
" ~
~~,"'
11 11
Fig. 7.13 Scheme of projecting (I) and measuring (2) systems of tacheometer type TG-4
-2
II I II 11
cy (1/100). At larger distances, the accuracy worsens substantially, since double images of a light mark cannot be brought to coincidence quite precisely. In recent time, light-projection tacheometers have come into wide use; their range finders operate on the principle of two known directions formed by a telescope and light projector. An example is the type TG-4 tacheometer which has a projection-visual range finder with a variable basis and constant parallactic angle at the instrument. A light mark is formed by the projector, and
1 /
il ll II
11
11'
I
!i I 1111
1I
73 -111' .Iii
~
-IIi /!1
1 1-
i ~
7
// 6
Fig. 7.14 Electro-optical tacheometer type MIFT -2: 1- eyepiece; 2- frequency switch; 3- tan.. gent knobs; 4 -laser switch; 5 -cancel button; 6- scale illumination switch; 7- vertical and horizontal circle readings; 8-distance readings
7.4.
Surveys
of Underground
able pentaprism, two images of the mark are initially seen in the eyepiece.The two images are brought to coincidence, and the readings are taken on the basal scale and vertical and horizontal circles. Experience has shown that this method of surveying with type BRT -006 tacheometer is applicable at distances up to 60 m and gives a relative error around 1/400. An electro-optical tacheometer type MIFT -2 has been developed in this country for tacheometric surveys of inaccessible chambers and cavities (Fig. 7.14). It consists of an angle-measuring instrument and electro-optical laser range finder. Laser beams emitted by the projector are reflected directly from the rock, rather than from special reflectors. A survey is done by the polar method from an approach working. The root-mean square error of measured vertical angles is 0.5' and that of horizontal angles, 1.5'. The rms error of distance measurement in the range from 7 m to 80 m is around 20 cm. 7.4.2. Photogrammetric of Underground
Surveys Cavities
The method of short-base stereophotogrammetric survey of underground cavities was proposed at the beginning of the 1950's. A base-measuring bar 1 (Fig. 7.15) is set up on a tripod in a safe place in the chamber to be measured or in an approach working. At its ends the bar carries two wide-angle shortfocus photographic cameras 2 whose axes are parallel to each other. The base-measuring bar is set by means of a sighting diopter 3 perpendicular to a survey control-net side and the side wall of the working is photographed. The two photographs (stereopair) are viewed through a stereoscope, which makes it possible to observe a stereomodel of the photographed object diminished in a ratio b'/b, whet"e b' = 65 mm is the eye base (interpupillary distance) and b is the base of photographic cameras.
Chambers
and Cavities
153
Fig. 7.15 Scheme of short-base stereophotogram. metric survey of underground workings
This method is principally based on direct intersections, since the two overlapping photographs make a stereopair. Measurements on stereoscopic photographs are made jointly by the principle of stereoscopic viewing. A method of photogrammetric surveying of sections in horizontal workings by means of a light beam is employed with successin the USSR, GDR, CSSR, and other countries. In this method, a photographic camera is set up on a tripod in a working, .the camera shutter is opened and, by moving a light source, the internal contours of the working in the plane perpendicular to the camera axis are gradually illuminated. The principal complications of this method are associated with ensuring that the illuminated plane is strictly perpendicular to the camera axis and also with scaling of photographs. In order to eliminate these difficulties, an instrument set FS-6 has beel;1designed in this country, which makes it possible to obtain the scaling basis together with a photograph of the cross section of a working.
154
Ch. 7. Surveys
of Preparatory
The instrument set includes a photographic camera, power supply unit, light projector, reel with synchronizing cable, and four telescopic scaling rods. The total error in measurements of cross-sectional areas is :t 1.5% . 7.4.3. Sound Ranging of Underground
Cavities
The physical methods of mine surveying of underground cavities are based on the principles of transformation of acoustic, radio and light waves into values which can characterize the direction and length of a measured section. Modern instruments designed on these principles mostly measure the time of passage of acoustic or radio waves from an emitter to an object and back. Sound waves (in particular ultrasonic waves) have turned out to be most suitable for measuring of cavities (sound ranging). They have a relatively low velocity of propagation in air, because of which the time of their propagation can be measured with a rather high accuracy. For instance, ultrasonic ranging can measure relatively short distances with a root-mean square error :!:20 mm. Sound ranging has found wide application for surveys of underground cavities formed through salt leaching and of vertical workings of large cross-sectional area. A borehole sonar 'Luch' has been designed in this country for surveying of brine-filled underground cavities. The apparatus is mounted on a truck and consists of two portions: a borehole tool and instrument stand. The borehole tool is connected with the on-ground equipment by a logging cable which also serves to hold the tool in a borehole. Surveying of brine-filled cavities is a labour-consuming procedure. Before making a survey, it is required to depressurize the underground chamber to be measured, dismount the rig head, extract the brine-lifting pipe string, sink the borehole tool to the bottom of a chamber, and allow time for
and Stope
Workings
natural untwisting of the logging cable (the time of cable untwisting may amount to 1.5 h in boreholes of a depth of 1000 m). After that, surveying proper can be carried out, which consists in measuring the depth to which the borehole tool has been sunk, the velocity of sound propagation at the level of the observation point, and the radii of the horizontal section of a chamber. The velocity of sound propagation at the level of an observation point is determined on brine samples taken beforehand from the borehole. The radii of the chamber are measured by the sonar which automatically turns on the vertical axis in the borehole. Ultrasonic waves emitted by the sonar are reflected from the walls of the chamber and enter the receiver of the acoustic system. The received signals are recorded by the receiver, amplified in an electronic unit, and transmitted as electric pulses through the logging cable to the on-ground station. Large vertical workings and other air-filled cavities can be surveyed by means of a sonar profilograph type ZPR-2 developed in this country. 7.5. Surveys Workings
of
Preparatory
The surveys of preparatory workings are carried out for plotting detailed plans and sections within the limits of a stoping block or extraction section and for determining the coordinates of particular points essential for the solution of various analytical problems. These surveys should include all details large enough to be visible on compiled plans and profiles. When surveying details, linear measurements should be made at the level of the mid section of a working with an accuracy to 5 cm or, in rough surveys, to IO.cm. Angular measurements in the surveys of preparatory workings can be done by using
7.6.
Surveys
theodolites, goniometers, suspension compasses and semicircles. Preparatory workings in seam deposits are, as a rule, surveyed by theodolites. The use of suspension compasses is possible for surveying preparatory workings in seam and ore deposits, provided that there are no magnetic masses which might induce magnetic disturbance. Preparatory workings must be surveyed twice: the first time during driving a working (additional survey) and the second time at the end of driving a complex of workings. All details obtained by a survey are sketched in a special field book or on margins of the books of angular and linear measurements of survey net traverses. Surveying of steep preparatory workings involves certain difficulties compared to that of gently dipping workings: it is more difficult to transport and set up instruments; the angle of inclination of the vertical axis of an instrument can influence substantially the accuracy of horizontal angle measurements. Central-telescope theodolites can be used for survey work in workings with the dipping angle up to 55°. Hanging theodolites are more expedient in workings with the dipping angle up to 65°. Workings with the angle of dip more than 65° are surveyed by eccentrictelescope theodolites. When surveying connecting workings and outlet workings (outlets), it is essential to determine the position of their side walls relative to the initial directions or points. The surveys of day holes and ore chutes of a small extension can be carried out by simpler methods, for instance, by the method of non-free plummet, which is essentially as follows. For surveying a connection working (Fig. 7.16), a polyamide line (or cord) is hung freely between the survey point A at the lower end of the connection working and the point B where it is connected to a vertical shaft. Plumb bobs (1,2) are suspended from
of
Blast
155
Holes
Fig. 7.16 Survey of connection non-free plummet method
working
by
the line in several points so as to form a broken line A-I-2-B lying in a vertical plane. Then, the horizontal angle at the point A between the junction side of the earlier theodolite traverse and the side A-l is measured, which makes it possible to calculate the direction angle of the side A -1. The same direction angle is taken for sides 1-2 and 2-B. The lengths of the lines A-l, 1-2 and 2-B are measured by a tape and the inclination angles of these lines, by a suspension semicircle. The results of measurements are used for calculating the coordinates of points 1, 2, and B. 7.6. Surveys
of
Blast
Holes
The efficiency of drilling and blasting operations depends substantially on the correct position of blasting workings in the rock massif, especially when these wbrkings have an appreciable length and are intended for primary (mass) blasting. The correct position of the centres and
156
Ch. 7. Surveys
of Preparatory
axes of blast holes in accordance with the blasting work plan is closely linked with the quality of survey and layout work performed by mine surveyors. Surveying of deep blast holes consists in connecting the hole mouth to the points of the survey net (goniometer traverses) and determining the depth of the holes and the directions and inclination angles of their axes. The error in determining the depth of blast holes must not exceed 0.2 m and that of their direction in plan and inclination angles, 30'. The techniques of surveying of deep blast holes depend on the drilling direction (horizontal, inclined or vertical), arrangement of blast holes (parallel or fan-like), and the drilling equipment employed. With a fan-like arrangement of l?last holes (Fig. 7.17), they are drilled from chambers constructed so that the point of arrangement of the drilling rig ( C) is at the intersection of block boundaries (in plan). Upon driving a chamber, survey work is carried out to determine the chamber contours and the direction AB and to calculate the coordinates of the point c. These results serve for de-
and Stope
Worki ngs
termining the horizontal angle ARC and distance RC to set out the point C in the ground. The point C is then established in the chamber roof and an angle-measuring instrument is set up under it and oriented relative to the direction CR in order to assign directions to future blast holes. The oriented directions are fixed by means of wooden bars fastened under the chamber roof. Before drilling, plumb bobs are hung from the bars to orient the blast holes in plan. In cases when directions should be assigned to inclined blast holes, an angle-measuring instrument is set up in the point C in the chamber at the same height with the rotation axis of the drilling rig. Upon hanging a plumb bob from the wooden bar, and thus fixing the direction in the horizontal plane, the required inclination angle is set on the vertical circle of the instrument and points m and n are marked on the chamber wall and plumb bob line (Fig. 7.18); these points determine the inclination of the blast hole to be drilled. After drilling a fan of blast holes, a control survey is carried out. When assigning directions to parallel blast holes (Fig. 7.19), points I, 2, 3, etc. are set out along the line between points A and R in the working. An angle-measuring instrument is
Fig. 7.18 Assigning vertical plane
direction
to
blast
hole
in
7.7.
Orientation
of Sublevel
number of levels are to be oriented succe'ssively, this discrepancy must not exceed m = = 14'IJ~, where n is the number of levels. At least three station points should be established at the oriented level. Orientation can be effected through two vertical workings connected on the oriented level; through one vertical working; through one inclined working; or by the gyroscopic method.
hori
7.7.1. Orientation of Sublevels Through Two Vertical Workings (Raises)
c \
I
~~-~;;;"--o::j ,
15.41
0' "',
15.0
0, "'I 0,1 (0)'
'J~~ B Fig. 7.19 Assigning zontal blast holes
directions
to parallel
set up successively on these points to layoff angles 131'132'133'etc. Looking through the telescope, the centre and number of a blast hole are marked on the wall of the working (most often with chalk). After drilling, a check survey of blast holes is done. The depths of vertical blast holes are measured by a tape or wire cable with numbered I-metre marks. The depths of horizontal and inclined blast holes are measured by a steel wire 3-4 mm in diameter, which is pushed up to the hole bottom and then withdrawn, and the length of the immersed portion of wire is measured by.a tape. It is also possible to make these measurements by means of self-straightening elastic steel tapes 50 m long or light-metal bars 1-1.5 m long which can be joined with one another to form a measuring bar up to 40 m in length. 7.7. Orientation of Sublevel
157
"...
/
~~~1( ~
Workings
Workings
The orientation of survey nets in sublevel workings should be carried .out so that the maximum error of orientation in a block of a size not exceeding 120 m relative to the theodolite traverse points of the main level will be not more than 10'. Orientation should be made twice, and the discrepancy between two measurements must not exceed 14'. If a
Orientation through two vertical workings (raises} is made essentially in the same way as orientation via two vertical shafts: two plumb bobs are hung in the vertical workings; the coordinates of plumb lines on the initial (upper} level are determined by connecting to polygonometric or theodolite traverse points; a theodolite traverse is run on the oriented level between the plumb lines; the horizontal angles in this traverse are measured with a root-mean square error of 40" and the lengths of sides, with a relative error of 1/1000. The relative discrepancy between the lengths of a plumb-connection line calculated on the oriented and initial level should not exceed 1/1000. In caseswhen sublevel workings are opened by two vertical workings with one of them being stepped (Fig. 7.20}, orientation can be done by the indirect solution of a triangle 010203. Connecting polygons 01-1-2-02 and O2-3-4-5-03 are run on the levels to be oriented and a connecting polygon 01-A-BC-D-03 on the main level. The coordinates of plumb lines 01 and 03 are determined by connecting them to the theodolite traverse on the main level. The connecting traverses on the oriented levels are constructed in a conditional coordinate system, and the lengths of the triangle sides 0102 and 0203 are calculated. The side 0103 and direction angle
~
Ch. 7. Surveys
158
Vertical
of Preparatory
0-- --
~ Ll! 0-8
o.c
0
Fig. 7.20 Orientation via two vertical with one of them being stepped
~ D
workings,
no o are calculated by the results of survey on1tfie main level. Having found the triangle sides 0102 = a, 0203 = b, and 0103 = c, the angles of the triangles are calculated by the formulae: b2 + C2-a2
Workings
7.7.2. Orientation of Sublevels Through One Vertical Working (Raise)
projection
~-IcF;:-:::::.:::.:::: llrI. I =--!I~-.~- ,
b-A
and Stope
a2 + C2-b2
Orientation through one vertical working has to solve essentially the same problems as orientation through one vertical shaft, i. e. the problem of projection and that of junction (connection). Since the depth of a vertical working (raise) is usually not large, the projection problem can be solved by using for plumbing a brass wi,re or polyamide resin line 0.5-0.6 mm in diameter. Plumb bobs should have a relatively low mass, up to 4-5 kg. The distance between the plumb lines must be not less than 0.5 m. The discrepancy in the measured distances between the plumb lines on the oriented and initial level must be not more than 3 mm. The mean positions of plumb bobs are determined by observing the oscillations of plumb lines on the reading scale of a theodolite telescope. To solve the junction problem, the bisector of cross hairs must be set symmetrically relative to the extreme positions of a plumb line. The problem of junction in the orientation of sublevel workings is usually solved by means of connection triangles or by the method of plumb-connecting lines. The angles of triangles are calculated by the same formulae as in orientation through a vertical shaft (see Ch. 4). A check of the side lengths of connection triangles can be done by calculating the distance between the plumb bobs, for triangles with the angle 'Y not more than 5° by the formula: c = (b -a)
+
ah(l
-cosy) h-a
and for those with the angle greater than 5°, by the forrnula: . C2= a2 + b2 -2abcosy The difference between the measured and
7.7.
Orientation p
of Sublevel
Workings
159
tripod table until coincidence is attained. The procedure is repeated until the vertical axis of the instrument is precisely on the plumbconnecting line, after which the point, is fixed. Then the angle !3 between the plumbconnecting line and the first side CD of a traverse is measured by a theodolite. The distance from the point C to the closer plumb line is measured as well. By the results of measurements on the main level, it is now possible to calculate the direction angle of a plumb-connecting line and the coordinates x, y of one of the plumb lines. Now that we know the direction angle of a plumb-connecting line, and therefore, that of a line PQ, and the distance QA, we Fig. 7.21 Orientation via vertical working by can calculate the coordinates of a point A on means of two plumb bobs the oriented level. Gyroscopic orientation of survey nets in calculated lengths of sides must not exceed sublevel workings is carried out by the 4mm. techniques disclosed in Ch. 4. Connection by the method of plumb-conThe orientation of sublevel workings via necting lines can be used effectively on the inclined raises can be carried out by several lower level when the depth of the sublevel is methods, in particular, by the popular method not large; this method is generally applicable of nonlree plumb line which is resorted to in provided that the distance between the cases when the workings on the main and plumb lines on the upper level is sufficiently oriented level and the inclined working have the same direction. The essence of the large. Connection to the plumb lines of an oriented method (Fig. 7.22) consists in that a polyamilevel can also be performed without using de resin line or soft wire is attached by one angle-measuring instruments. For this, plumb end in a point B on the upper level and a bobs are suspended from a wire drawn weight P is fastened to its lower end on the between the points P and Q tFig. 7.21). In main level. The line or wire is 'broken' in that case, the direction angle of a plumbpoints C and D by two guys AC and DE connecting line is equal to the direction angle attached to it at the upper and lower level. of a line PQ. To transfer the coordinates onto Both guys should lie in the same vertical the level being oriented, it suffices to measure plane. distances QA and BP. For the connection of Theodolites or goniometers are set up the plumb lines, a theodolite is set up on the under the points A and E on the upper and main level in a point C (roughly at the lower level respectively. When sighting in the plumb-connecting line). The telescope is telescope, the plumb-fastening point B is sighted on the rear (farther) plumb line and is displaced until the direction AB coincides focussed on the closer plumb line, the limb with the vertical hair in the telescope. After and alidade being locked. If the cross hair the plumb line and guys are arranged in the bisector does not coincide with the closer same vertical plane, the directi()n angle can plumb line, the theodolite is shifted on the be transferred from one level onto the other Q
160
Ch. 7. Surveys
of Preparatory
and Stope
Workings
the upper level (Fig. 7.23). The second theodolite is set at the lower level and centred under a point C, and a special staff is attached to its objective part. The telescope of the upper theodolite is pointed to the top centre mark of the telescope of the lower instrument, and the reading is taken on the vertical circle. The theodolite set up in the point Cis first sighted on a point D to take the reading on the horizontal circle, after which the instrument telescope together with the staff attached to it is set horizontally. By rotating the upper instrument on the vertical axis, the horizontal hair line of its cross hairs is roughly aligned with the axis of the staff on the lower instrument. By operating the tangent screw of the horizontal-circle alidade of the upper instrument, the horizontal hair A
by measuring junction angles ~ and ~l by instruments set up in points A and E in a single full repetition. The distances dl, d2, CD and the distances from the points A and E to the horizontal rotation axes of the instruments are measured twice by a tape. The inclination angle v of the section CD of a non-free plumb line is measured by asuspension semicircle with an accuracy to 15'. The direction angle of the oriented side is calculated by the formula aAI = a37E+ ~l -~ :t 2 x 180° and the coordinates x, y of a point A, by the formulae: xA = XE + (dl + CDcosv -d2)cosaED YA = YE + (dl + CDcosv -dJsinaED The method of mutual orientation is also widely used. It employs two goniometers or two eccentric-telescope theodolites. In the latter case, one of the theodolites is set up at
B
7.8.
Measurements
D
(..8
.."
~ ~
SUblevel!!
~.
Y//////////;////////////~
" ////////;~'
A Main level
~,
F~
~//////////////////////////////////////;/~ Fig. 7.24 Orientation via inclined od of plumb-line points
raise by meth-
line is aimed 4-5 times precisely on the staff, and each time the readings are taken on the horizontal circle, after which the mean of these readings is calculated. Upon the completion of the described cycle of observations, the telescopes of both instruments are reversed and a second cycle of observations is made. After sighting the lower theodolite on the upper one, it is horizontalized and the upper theodolite is aimed 4-5 times at the staff axis. Mter that, the observations of points D and A are made by the upper and lower theodolites respectively. If an inclined raise has an intricate configuration, it may be recommended to use the method of plumb-line points. A theodolite is set up on the main level under the point C of a survey net (Fig. 7.24), and, using the instrument, two plumb-lines are suspended in points B and K in line with the point C. A point E on the plumb line KB is fixed on the sublevel to be oriented, after which a point D is fixed on the plumb line EB. Since lines DE and CK lie in the same vertical plane, their direction angles are equal to each other. Having measured the horizontal angles ACK and KED and using the direction angle of a line AC, it is now possible to calculate the 11-1270
of
Mining
Workings
161
direction angle aEDof a line ED, which is the initial angle for the orientation of the survey net on the sublevel. Then the inclined distances and inclination angles of line sections are measured to transfer the coordinates x, y and z from the point C to the point E. 7.8. Measurements of Mining Workings and Reserves of Mineral in Stocks Stope faces are measured to plot a sketch of the stoping area (Fig. 7.25), and the points are fixed from which the surveys of details are carried out (position and dimensions of left pillars of the mineral, fill-in strips, angles of dip, thickness and structure of a seam, position and bedding elements of tectonic disturbances, seam pinches, etc.). By the results of survey, the position of the stoping area is plotted on a large-scale plan of mining workings on which the mean length of a face line can be determined from the expression: Lm = SlAm where Am is the mean advance of a face for a specified period, m and S is the working area determined by the formula S = Spllcos v where Spl is the working area measured planimetrically on the plan and v is the angle of dip of a seam. With coal seamsof an intricate structure, it is essential to determine by measurements the total thickness of a seam (from the footwall to the roof) with all interlayers and the total useful thickness, i. e. the sum of the thicknesses of all coal bands in the seam. The thickness of mineral seams is measured by a linen tape or telescopic measuring rod perpendicular to the bedding plane. The results of measurements are recorded and sketched in the field book. The data of field books of working measurements are used as the basis
162
Ch. 7. Surveys
of Preparatory
for calculating the volume of mineral extracted from a stope face. The quantity of mineral mined in stope faces in a specified period can be determined by the formula: Q = Vy -Lm where V is the volume of the worked-out space, m3; y is the density of the mineral in the rock massif, t/m3; and Lm is the loss of the mined mineral. The quantity of useful commercial mineral mined in the specified period, Qc, can be determined by the formula: Qc = Vy -Lm + Q' or Qc = (V'Y -Lm)kckm where Q' is the quantity of barren rock present in the mined mineral, t; kc is the coefficient of contamination of the useful mineral with barren rock; and km is the moisture coefficient of the useful mineral. The coefficient of contamination of coals in coal deposits is usually determined by the
and Stope
Workings
formula k = A r.b -A c.b c Ar.b -Ac where Ar.b' Ac.band Ac is respectively the ash content of barren rock bands, coal bands and commercial coal. The moisture coefficient can be found by the formula: 100 -Wo k m= loo -W where Wo is the moisture content of useful mineral in the massif and W is that of mined commercial mineral. Under particular mining conditions, the determination of the quantity of mined coal by measurements of mining workings is carried out with insufficient accuracy or sometimes is not done at all. In such cases,a reliable check is to measure the amount of mineral in stocks at the end of a month. The quantity of mineral mined during the month elapsed is then found by the formula: Q = Ql + Q3 -Q2
7.8.
Measurements
where Ql is the quantity of mineral shipped to consumers or spent at the mining enterprise,t; Q2' Q3 is the remainder of useful mineral at the beginning and end of the period considered in stores, bins, and railway cars, t. The quantity Ql is determined by weighing at shipping of the mineral or is taken according to accounts, whereas Q2 and Q3 are found directly by the results of the survey measurements of the mineral contained in stores, bins and other storage places. Since the amount of mineral in stocks at the beginning or end of a month is usually much less than the monthly output by the enterprise, the errors of measurements in stocks have practically no effect on the montWy output of the mineral by a mine. The remaining mass of mineral in stocks (Q, t) is found by multiplying the volume Vof dumps (or of the filled-in portion of bins) by the density y of the mineral in dumps (bins). The accuracy of determination of the mass of mineral in stocks depends on the accuracy of the volume and density determination, which in turn depends on the difficulties of measurements in stocks. In this respect, it is possible to distinguish between three categories of dumps. Category I includes dumps having an essentially regular geometrical shape: cone-shaped, pyramidal, prismatic with trapezoida,l cross section (of the type of road embankments) and some other shapes typical of stockyards with trestles. Category II includes dumps whose shape is a combination of cone-shaped, prismatic, pyramidal, etc. bodies. Category III includes dumps with a complicated shape of the surface typical of binscraper and scraper stores. The volumes of dumps related to the first and second category (except for second-category dump~ of a height more than 5 m) can be recommended to be determined by tape measurements, with approximation of these
of
Mining
163
Workings
dumps to regular geometric bodies when needed. In order to determine the volume of a dump or pile, its height, width, length, base diameter, etc. are measured by a tape. Substituting the measured values into suitable geometrical formulae (Fig. 7.26), the volume of a dump is calculated with an accqracy to 10% depending on. the shape complexity and dimensions of the dump. The volumes of dumps (piles) of category III and partially of category II (with the height more than 5 m) are determined on the basis of tacheometric, plane-table or profile survey. In such cases, the terrain area allotted for mineral storage is surveyed topographically to plot a large-scale plan of the area with horizontals. The method of profiles is employed mostly for surveying of elongated dumps. In that case, profile lines are assigned perpendicular to the longitudinal axis of a dump. The profile lines are plumbed, and the most characteristic points are fixed by pickets. The spacing between the profile lines is taken equal to 5-10 m depending on the shape complexity of the dump. Surveying by profile lines consists in measuring the distances between the picket (change) points (starting from the initial points) and the height differences between them. Distances are measured by tapes (twice), and the tape readings are rounded off to decimetres. The height difference is determined by technical levelling. Theodolite-tacheometers can also be used for profile line surveying. The measured results are recorded in a field book. Using the height difference of the base isolines and the points (pickets) on the dump surface, the cross sections of the dump are plotted (Fig. 7.27) and their areas are measured by a planimeter (with double contouring). The volume of a dump is found by the formula: S1+S2 V=-/
2
S2+S3 1 +-/
,
8.+8.+1 2 +..0+
,
/.
Ch. 7. Surveys
164
of Preparatory
and Stope
Workings
(b)
$,
/ v=*
(SI + S b + 1{S;""";f;:)
(cJ
(e)
(f)
-v=~[(
20-::~)bb
+(
2ot
+ °b)bt]
it
(9)
7
v=
hb b 6(2Ib+I,)
Fig. 7.26 Shapesof dumps suitable for tape measuring: (a) trapezoidal profile pile; (b) truncated pyramid; (c) circular cone; (d) truncated circular cone; (e) truncated elliptical cone; (f) spherical segment; (g) truncated trihedral prism; (h) wedge
~
7.8.
Measurements
of
Mining
Workings
165
points are established in all characteristic places of the dump surface, with spacings between them not more than 6 m. 60The results of survey are plotted on the plan of the dump (store) on a scale 11200(or a larger scale),and isolines of the dump surface are drawn with height intervals 0.25-0.50 m 50--for dumps less than 5 m in height and 1.0 m for those with the mean height more than 5 m. 40The volume of a dump can be calculated by the method of vertical sections or that of horizontal sections. In the latter case, the 30dump is cut into layers by horizontal planes, and the areas of the sections are measured twice by a planimeter, the mean value of the two measurements being taken as the final 20result. The volume of the dump is the sum of th~ volumes of the layers confined between the horizontal planes drawn in intervals of ~, 1~ 0.25 m, 0.5 m or 1.0 m. The error of volume 3 measurement by tacheometric survey is not 2 more than 4% . 3. The measurements of preparatory workII ings are essentially simplified surveys with the Fig. 7.27 Scheme of measuring volume of dump use of simpler instruments (steel and linen by method of profiles: l-contour of dump; 2-cross-sectional profile of dump; 3-fixed points tapes, suspension semicircle, inclinatorium, of profile lines and longitudinal axis etc.). The measurements of preparatory workings include the following operations: sketching the working and face in the field book; where Sl' S2' ..., Sn are the areas of profile measuring the length of a working and the sections of the dump and I; are the spacings amount of advance during the specified pebetween two adjacent profiles. This method riod; measuring the cross section of the can determine the volume of dumps with an working, its area within the boundaries of accuracy to ::t 3.5% . prospected mineral, seam thickness, and If the tacheometric or plane-table method bedding elements of the seam. is employed for measuring the volume of The amount of advance in workings is dumps, the tacheometric or respectively pla- measured by tapes from fixed survey points ne-table survey is started from the points of a or other reference points located near the survey net. The coordinates x, y of surveying face. points are determined by theodolite traverses, Sketches in the field book should show: the chains of triangles or other figures or of their positions of the initial points and distances intersections. The z coordinate is found by from them to the faces according to the technical or trigonometric levelling, The dis- previous and current measurements; the ditances from the instrument to staff (picket) mensions of workings for calculating the points should be not more than 60 m. Staff worked-out area and volume of extracted 9"
~:
a
166
Ch. 7. Surveys
of Preparatory
and Stope
Workings
1-
a -I
Im aav a1
~-I~!
~/////////////~, 02
mineral and rock; thicknesses of the seam in measured points .md outlines of structural elements of the seam (deposit); location and measurements of bedding elements of the seam; location of geological disturbances and their bedding elements; and some other data that should be reflected in mine survey plan. An advance of a working may be determined as the advance in coal (Ic)' that in gangue (barren rock), 19' or that in support (lining), Is (Fig. 7.28a). The amoUnt of advance is found as the difference between the corresponding distances from the initial point at the beginning and end of the specified period. Hence, the amount of advance of a working during the specified period will be: in coal Ic = Ic2-Ic1; in gangue 19= 192-/91' and in support Is = Is2-Is1. Upon determining the advances of a working, the working cross section is measured. If the working is driven partially in the mineral and
partially in barren rock, it is required to measure the total cross-sectional area and the area in mineral (Fig. 7.28b) as the product of the seam thickness by the mean width of the cross section in the seam: 8 = amm,where am is the mean length of the face line of the working in mineral and m is the seam thickness. The mean cross-sectional area in mineral by the results of several (n) measurements will then be: 8 m=
81 + 82 + ...+
8n
n
The quantity of mineral extracted from the working during the specified period can be calculated by the formula: Q = IcSmY where Y is the density of coal, tlm3.
Chapter
Special
Surveys
Eight
in Underground
8.1. Assigning Directions to Underground Workings One of the most important tasks of mine surveying service in the construction and exploitation of mining enterprises is to transfer correctly the designed location of underground workings into nature. In that connection, the mine surveyor has to deterrnine the places of location (intersections) of workings in accordance with the design or calendar plan of mining work development, to assign, fix and transfer the directions, and to control the driving of workings along the assigned direction with due observance of the designed profile and the chart of supports. The most common job of a mine surveyor is to check the driving- of workings along a specified direction in the horizontal and vertical plane. The method by which directions are assigned depends on the mining conditions and the kind of working, elements of seam bedding, and some other factors. In many cases,the work of direction assignment is facilitated by the availability of a natural landmark or element (for instance, the bedding plane of the foot or roof of a seam). In practice, such elements are called 'conductors'. For workings to be driven on dip of an inclined or steeply deeping seam, where the line of dip is a good landmark, directions are assigned only in the horizontal plane. For workings to be driven on the strike of an inclined or steeply dipping seam, only the directions in the vertical plane are assigned. For crosscuts or lateral drifts which have no
Workings
'conductors', directions are assigned both in the horizontal and vertical plane. For assigning the direction to a working in these planes, the mine surveyor should know the spatial coordinates (x, Y, z) of the points to be used in calculations and be capable of solving such problems as the determination of direction angles of the projected direction, angle between directions, inclination angles of lines, inclined length (distance) and its projections onto the horizontal or vertical plane, etc. The solution of some most typical problems encountered in practice will be demonstrated below. I. Figure 8.la gives the coordinates of a point A (x A' YA' zA) and a point B (XB' YB' ZB). It is required to determine: the direction angle of the direction from a point A to a point B; the horizontal projection of the line that connects points A and B; the inclination angle of a line A-B; and the length (distance) of a line A-B. The direction angle of the line AB is found by the formula: tan aAB= YB -Y A XB -xA
or SAB =
J(YB
-y
Af
+
(XB -XA)2
~
168
Ch. 8. Special Surveys in Underground Workings (a)
(bJ
(cl
x
x
YO-YA
~
y
(AB)y PL
(BC) ~C8) ~rC)
~..:
7
A
4:
'~ B
(CG) ~
B
..r
B
8~
G/ ',E " Fig. 8.1 Schematic diagrams: (a) for solving the inverse problem; (b) for measuring the angle between directions; (c) for determining the coordinates of intersection point of two straight lines
The inclination angle of the line AB is found by the formula: rany=
ZB -ZA
where s is the horizontal projection of the length S between the points A and B (horizontal distance). The inclined length of the line AB can also be determined from the expression S = s/cos v or, for checking, from the expresslon: s = J(YB -YA)2 + (XB-XA)2 + (ZB-ZA)2
The coordinates of the point of intersection (a point D) of these lines can be found by solving the triangle BCD: XD = xB + BDcosaAB' YD = YB + BDsin aAB where BD=-
CB
sin
a
siny
First, we find the direction
angle !lCB
tan !lCB = YB -Yc XBand the length
2. Figure 8.lb shows two intersecting line sections AB and BC with known direction angles; it is required to find the forward left and forward right angle of crossing. Tfese angles can be found by the formulae: 13,= aBc -aBA 13,= aBA -aBc 3. In practice, the mine surveyor often has to determine the coordinates of intersection point of two directions, say, of a point D where lines AE and CG intersect (Fig. 8.lc). The line AE is specified by the coordinates of a point B (XBand YB)and the direction angle a AB. Similarly, the line CG is given by the coordinates of a point C (Xc, Yc) and the direction angle aCG.
CB = YB -Yc
XB -Xc
sin aBc
COSaBC
The angles O and y can be found as the differences of the corresponding direction angles. The coordinates of the intersection point D can also be determined by the combined solution of the equations of intersecting lines: xD=
xB tan(1AB-Xctan
(1CG-YB + Yc
tan (1AB-tan (1CG YBcotan(1AB
-Yccotan(1CG
-'- xB + Xc
YD=
cotan(1AB-cotan(1CG The directions to mining workings are assigned by surveying instruments. The
8.1. Assigning Directions to Underground Workings
choice of a particular type of instrument depends on the kind of problem to be solved, type of working, and required accuracy. 8.1.1. Assigning Direction
the Horizontal to a Working
The horizontal direction to the straight section of a preparatory working can be assigned by means of a theodolite, compass or gyroscopic instrument by laying out in nature the design or calculated angle or by ranging the direction directly according to the known direction angle by means of a gyrotheodolite or gyrocompass. An assigned direction is fixed by survey marks (clamps) in at least three points at a distance of 1-3 m from one another. Plumb bobs hung above these points form a ranging line to be used by drivers for the orientation of a face. As the face is being advanced, the direction is continued, and the required check measurements are made. If a working is designed so that its direction varies, a new direction must be assigned in each turning point. In caseswhen a working is to be driven from two ends, it is required that the geometrical axis of one of its sections be perfectly coincident with the continued geometrical axis of the other section. The direction to a working in the horizontal plane can be assigned by means of a theodolite by one of two methods depending
169
on whether the accuracy of angle assignment is lower or higher than the accuracy of the instrument. In both cases, the working is marked out and the theodolite is set up and centred in the initial point B (Fig. 8.2a). Since the distance from the initial point to the wells of the working is smaller than the sighting limit of the telescope, a provisional direction is assigned through the telescope of the instrument according to the calculated angle ~. This direction i~ fixed by at least two points (Bl, B2); noting the station point of the instrument, the provisional direction will thus be fixed by three points (B, Bl, and B2). Upon driving the working by 5-10 m in the provisional direction, the permanent direction is assigned and fixed by three points. If the required accuracy of laying off a horizontal angle is lower than the instrument accuracy, the permanent direction is assigned in the following order. The theodolite is set up again in the point B, and two points P 1 and P2 are marked in the range of the directions obtained by constructing the angle ~ at two different positions of the theodolite tube. The distance Pl-P2 is then halved and a survey mark is fixed in the mid point (P). The angle ABP will correspond to the calculated angle ~. Upon the fixation of the point P, the angle ABP should be measured again. The discrepancy between the measured and calculated values of the angle ~ must be within CI C r---, 611 ~S'I .rs"1
(b)
I 6~1
~
.'I ~«'
A
B
Fig. 8.2 Schemefor assigning a direction: (a) with an accuracy less than the instrument accuracy; (b) with a higher accuracy
Ch. 8. Special
170
Surveys
in Underground
Workings
r--Fig.
8.3
Assigning
a direction
by
compass
horizontal plane can be assigned by means of a suspension compass. For this purpose, the plan of a working is oriented along the magnetic meridian, and a straight line is drawn on the plan from a survey point B at the beginning of the working in the direction of the projected axis. The miner's compass is then laid on the plan to measure the magnetic azimuth of a line. A cord is fixed at the point Bin the mine and tensioned roughly in the specified direction (Fig. 8.3). A suspension compass is hung from the cord and the free end of the latter is moved laterally until the compass needle points at the specified magnetic azimuth. The cord is fixed in this position, and two or three plumb bobs are hung from it. The method is, however, employed only rarely. Points for assigning the direction to a working in the horizontal plane can be located more conveniently at a certain distance (20-30 cm) from the walls of the 111 = -111~" working, rather than along the central axis. p" In that case, plumb bobs hung from the fixed points will not obstruct the motion of mining or workers and will be preserved better. Drivers, L\l = 1sin L\j3 however, must know the distance from these The point C 1 is then displaced by this points to the face walls, which is called a correction (to a point C), which gives the 'bracket' and can be found in the following sought-for angle ARC. The theodolite is way. Suppose that a working must be driven sighted on the point C, and two new points, B' and B", at a distance of 1-3 ill from each from a point A (Fig. 8.4) in the direction of a other, are set up and fixed. Thus, the specified line AC which is its axis. Points At and A2 near the walls of the working fix a direction direction will be given by the line RR"B' . The directions of auxiliary workings in the that is parallel to the axis. The width of
the permissible limit. If so, two other points, P' and P", are set up by a theodolite along the collimating ray RP, at a distance of 1-3 m from each other. Thus, the "line passing through the points P, P', and P" will be the beginning of the permanent direction. In caseswhen the angle must be constructed with a higher accuracy (for instance, for driving a working from two ends), the procedure is as follows. A point Cl is set up in one position of the,elescope (Fig. 8.2b), and the angle ARCl thus obtained is measured with the required accuracy. The measured angle ~m= ARC 1 is compared with the specified value ~sP' and the difference 11~= = ~m-~sP is compared with the required accuracy of angle laying. If 11~is higher than the required accuracy, angle ARCl must be corrected. To do this, the distance RC 1 = I is measured and a linear correction is calculated by the formulae:
8
Fig. 8.4
Assigning Directions to Underground Workings
Scheme for calculating
'brackets'
when axial direction
'brackets' Cl and C2 can be determined from triangles AA1D1 and A1A2D2. First, we have to calculate the distances dl and d2 by the formulae: dl = AA1 sin 11 and d2 = A1A2 sin 12 or, since the angles 11 and 12 are small, by the formulae: dl = AA1- 1~ and d2 = A1A2- 1;
p" where
11
=
p" aAA
-a 1
AB'
12
=
aA
B 1
-aA
A 1
, 2
and p" = 206265". As may be seenfrom Fig. 8.4, Cl = 0.51- dl and C2= 1- (Cl + d2), where I is the clear width of a working. Drivers are usually provided with a sketch of the working which gives the positions of plumb bobs and the size of a 'bracket'. Points assigning the direction to a working are usually fixed in support beams or roof. In permanent workings, range points are fixed more reliably by drilling holes 20 cm in depth in the roof and driving survey markers with hooks for plumb bobs into them. As the working is advanced, the plumb bobs are transferred closer to the face. With the transfer distance up to 15-20 m, new points can be marked visually (by sighting along the line of the earlier plumb bobs) and with distances up to 50 m, by means of a theodolite. Directions to workings can also be assigned by using light plummets (Fig. 8.5). A light
is transferred
171
closer to working
sides
plummet has a cylindrical housing 2 with a cover 1, which contains a dry cell. An electric lamp 3 at the bottom end of the housing is covered with a red or green transparent cap 4. At the top of the housing, there are a switching knob 6 and eyelet 5 for hanging the plummet from a cord. Light plummets are hung along the specified direction so that the line formed by the lamps is the direction axis in the vertical and horizontal plane. Light plummets are visible at a distance of 60- 70 m on the average.
Fig. 8.5 Light plummet: 1- cap; 2- metal housing; 3-electric lamp; 4-coloured acrylic plastic cap; 5 -eyelet; 6 -light-switching screw
172
Ch. 8. Special
Fig. 8.6 Laser indicator: 1 -projector; casing; 3- separate power supply unit
Surveys
in Underground
2- base in
Laser instruments are also coming into wide use for direction assignment in underground workings. An explosion-proof laser indicator is illustrated in Fig. 8.6. It is essentially a light projector with a laser source, which forms a narrow directed beam of red light to be used for assigning the directions to underground workings. The principal element of the instrument is the projector consisting of a light source (laser tube) placed together with a collimating system into an explosion-proof housing. For operation with a laser indicator, a survey point (initial point), above which the instrument will be set up, is fixed at a distance not more than 40 cm from the wall of a working. A theodolite is set up above this point to layoff the calculated direction angle, and the direction thus determined is fixed by two temporary marks located at a distance of 10-20 m from the initial point. The bracket of the laser indicator set is fastened below the initial point to the supports of the working wall. The laser indicator is mounted on the bracket and connected to the power supply source. The laser beam is directed' roughly ('by hand') onto a plummet that has been hung in advance. Upon fastening the
Workings
instrument, the sighting micrometer screw of the laser is turned so as to make coincide the light beam with the plummet and fix up the specifi~d direction. For better visibility, a bright screen may be placed behind the plummet. It is recommended to use the focussing ring of the instrument for more accurate sighting. For assigning the direction along the height, it is required to turn the optical wedges at the exit of the collimating system relative to each other. The design inclination (slope) of the working is set up on the scale connected .with the optical wedges. The light beam directed onto the face or tunnel shield forms a bright red spot up to 80 mm in diameter, which is easily seen from a distance up to 500 m. 8.1.2. Assigning Directions to Curvilinear Sections of Workings Directions to curvilinear sections of underground workings can be assigned by the method of perpendiculars or the method of radii. Method of perpendiculars. A circular curve of the curvilinear section of a working on a large-scale plan (1/20, 1/50) is replaced by inscribed chords according to the precalculated turning angles and lengths. Then the lengths of perpendiculars from a chord to the wall of the working in intervals of 1-2 m are measured on the drawing (Fig. 8.7). The numerical values of perpendiculars are written on the drawing. Method of radii. In this method, a largescale (1/20, 1/50) drawing (Fig. 8.8) of the curvilinear section of a working is used for the graphical determination of radial distances from a chord to the wall of the working, after which it is possible to calculate the distances between the axes of adjacent supports by the external (dJ and internal (dl) side of the working. These distances can be
8.
~
"
Assigning Directions to Underground Workings
.!) ~
'l
... .~ O
0:) C?
"' .~, .~~ t?~\:o \:;...,;.~
'X((
8-' ~.O~~ ' ;
1 :!0
0
"'
,-,
,- ?,
0 .~ .6] a
173
.."
"
0 ~
.~ o
'-i0.6~0
~
40"15"
3.00~i2.55~
11.05 -1.8
R=17.5m
1.80
~O 1.65~
....;
1.35 ~li
Q95
(X=93.30.
~1.'J5 R=18.5m . 7 Fig. 8.7 Scheme of direction assigning by method of perpendiculars
found by the formulae: dl = d + d(s/2R) and dl = d-
d(s/2R)
where d is the distance between the support frames in the straight section of a working (according to the chart of supports); s is the average width of a working; and R is the radius of curvature of the curvilinear section. All dimensions essential for checking are indicated on the drawing of the curvilinear section. The method of radii is more convenient and expedient than that of perpendiculars. In this method, it is easier to check the dimensions of a working at both sides of a chord and to control a correct placing of support frames along curvature radii. 8.1.3. Assigning the Vertical to a Working
Direction
The direction to a working in the vertical plane is assigned according to the design slope which is given as the difference of the elevation marks of the extreme points related to the distance between these points. It is marked by axial or side bench marks which
Fig. 8.8 of radii
Scheme of direction
assigning by method
are established as the working is being advanced. With inclination angles of workings up to 5-6° (i = :J:0.1), the directions in vertical planes can be assigned by means of level instruments, templates with levels, water level with light instruments, inclinometer, etc. If a level instrument is used for the purpose, side bench marks are fixed in the wall at a height of 1-1.5 m above the design position of the working foot or rail head, i. e. in a plane parallel to the design. slope. For instance (Fig. 8.9), a bench mark Rl is fixed in the wall of the working at a height d above the rail head. A point A is then marked on the wall at a distance of 5-6 m from the bench mark, which is the projection of the collimating ray of the level instrument. A staff is set up on the bench mark R1, and the reading a is taken. Upon measuring the distance i between the levelling staff and the point A, the height difference h = ii corresponding to the given slope i is calculated. The position of the second bench mark, R2, is found by laying off vertically the height a + h. The line connecting the bench marks Rl and R2 gives in nature the specified slope. If required, similar
174
Ch. 8. Special
Surveys
in Underground
A
--a
Workings
,
R1
Fig. 8.9
Scheme of vertical
direction
assigning
to working
bench marks may be fixed in the opposite wall of the working. Directions to workings can also be assigned by using laser indicators whose optical system includes a wedge compensator with the working range :t 2°. The desired slope is set up by means of a special ring arranged before the collimator and graduated in thousandths of gradient. A laser sight (Fig. 8.10) has many applicalions, in particular, for direction assignment and control of cutting of heading machines and tunnel shields in workings with inclinalion angles up to 10°. Laser sights of this type can operate properly at temperatures from + 30° to -40° and air humidity up to 80% . Their working range is above 200 m and the
by a level and wall marks
diameter of light beam varies depending on distances and reaches 200 mm. A level-inclinometer (Fig. 8.11) consisting of a level 1 and wedge-type inclinometer attachment 2 can be employed for assignment and checking of slopes of horizontal workings and for laying rail tracks in mines and on the surface. It has the following operating characteristics: Range
of slopes
main Ditto,
with
the
Division wedges,rad value Accuracy Mass
assigned
optical-wedge
by
system,
the rad
::t:0.008
.
use of additional of slope
of slope
of inclinometer
I
scale, rad ..
assignment,
rad
.
0.048
I
0.0001
I
0.0005
attachments,
0.33
kg.
4 /
5
Fie. 8.10 Laser sight
\ 2
Fig. 8.11 Level-inclinometer assembled: l-level; 2-wedge-type inclinometer attachment; 3~micrometer screw of inclination scale; 4- inclinationmeasuring microscope; 5 -clamp screw of inclinometer attachment
150
Ch. 7. Surveys
of Preparatory
traverse sides are measured by a linen tape or by goniometer stadia hairs. If goniometers with eccentric telescope (types UTG and UT -3) are employed, the inclination angles of survey traverse sides should be measured twice, i. e. forward and back. The actual inclination angle is found as the half-sum of measured values. 7.3.3. Survey Work in Faces with Powered Mining Complexes For the normal exploitation of faces equipped with powered mining complexes, it is essential to ensure survey control of the linearity of a face and the position of a powered complex in it. For controlling the position of the complex, pickets are established at intervals of 10 m or 20 m in the main entry and ventilation entry. The lines connecting like points in both entries should be perpendicular to the axes of entries. The position of the complex is controlled by measuring the distances from its ends to the like pickets in the entries. With horizontal and gently dipping seams, these distances should be equal, i. e. the complex should be located perpendicular to the axes of the entries. For dipping seams (with the angle of dip 15-25°), these distances should not be equal, since in that case the angle between the face conveyer and the axis of hauling (conveyer) entry must be equal to 91-93°. Thus, the hauling (conveyer) face must be advanced to some or other extent depending on the type of complex, length of face, and mining and geological conditions. The linearity of a face with a powered mining complex must be checked at least once a month. The check for the linearity of a face ofa small length (60-100 m) can be done visually or by taping from change points or theodolite traverse points. The faces of a large extension (above loo m) are controlled
and Stope
Workings
for linearity by means of engineering theodolites or goniometers. The junction of a goniometer traverse to a theodolite traverse can be effected by means of a connection triangle. For this, the goniometer is set up in a point 1 in the entry (see Fig. 7.11) to measure the angle 'Y of the connection triangle and angle 13.The length of the first side a of the goniometer traverse is measured. If the first point is chosen so that the connection triangle angle 'Y does not exceed 5°, the junction angle
176
Ch. 8. Special
Surveys
in Underground
Workings
coincide with a mark 5 when the longer bar is perfectly horizontal; and wooden blocks 4 and 6 of different height (H I and H 2) which define the specified slope. The slope is determined by the ratio (HI -H2)!1 which is constant for a given instrument. For instance, with H I = 0.04 m, H 2 = 0.02 m, and 1 = 2 m, the slope is: Fig. 8.13 Water level with plumb bob
direction of the working in the vertical plane. With the known vertical distance from the top of a plumb bob to the head of a rail (which is equal to Ht -ht for the initial point), it is then possible to check the gradient of the rail track. It should be noted that the plumb bobs described can be used for assigning the direction to a working in the horizontal plane. The specified slope during driving of a working can also be checked by means of a water level with plumb bob (Fig. 8.13). The instrument consists of two mutually perpendicular wooden bars: a long bar 1 (up to 2 m) and a short one 2, which are fastened together; a plumb bob 3 whose point must
Fig.
8.14
Mining
track
gauge
.HI 1=
-H2 1
0.02 = -= 2.0
0.01
When checking the profile of a working, the instrument is set onto a rail or a board placed on the smoothened foot surface of the working so that the smaller block is 'on the rise'. If the plumb bob is against the mark 5, the slope is correct. If otherwise, the foot soil must be cut off or respectively more ground must be added. A more convenient and perfect instrument for laying railway tracks of a specified gradient and for assigning directions to workings is a mining track gauge (Fig. 8.14). It consists of a tubular rod 3, two fixed blocks 6 and 8, a movable block 5 with an extendable stop 4, spring clamp 7, two hinged sighting stands 9, a transporting handle 2, quadrant 10 graduated in degrees, and a spirit level 1. For operation, the gauge is placed with
8.1. Assigning Directions to Underground Workings
blocks 8 and 5 on a rail so that the block 5 is on the rise, and fastened by the spring clamps 7. The required slope of the track is set up on the spirit level. Mter that the forward end of the rail is moved vertically until the level bubble is in the centre, and the rail is fixed in that position. A check of the specified gradient of a working is done by means of geometrical levelling along the rail track laid in the working in accordance with the recommendations on vertical surveying of rail tracks as given in Ch. 5. Automatic levelling of haulage tracks can be carried out by using a track-measuring complex, such as shown in Fig. 8.15. It measures and records on a chart strip three main parameters of a surveyed rail track: a longitudinal profile 2 (Fig. 8.16), elevation 3 of one rail above the other, and discrepancy 1 of the track gauge against the specified value. The complex consists of a carriage 1 with a standard track gauge (900 mm or 1520 mm), an explosion-proof casing 2, power supply unit 3, and a box for spare parts 4. The casing contains sensors for measuring the specified parameters and a recorder and has a window 6 where the measured parameters are displayed. The main operating characteristics of the complex are as follows: Error of recorded longitudinal slope at a travel length of 500 m, rad ..
up
to
:t 0.0005 Root-mean
square
Root-mean relative
rail square elevation,
Relative trackgauge,mm
Limits length.
Travelling Temperature gradient,
of
error
of
error
of
measured
error
of mm
measured
recorded
measurement
speed, rad limits,
degrees
.5
travel
of
m/s
2.5
rail
'200
track
.
:f:0.05 0.9-1.2 -10°
to
+ 40°C
Mass of set, kg. ... Number of operators 12-1270
55 2
177
Fig. 8.15 Track-measuring complex
Before using the complex for measurements, the zero points of all its sensors are adjusted, the chart paper is charged into the recorder, and the dimensions of picket distances are set up on the scheme, which will be fixed on the chart by a lever 5. The complex is placed at a distance of 5-7 m from the initial picket point and is started by switching on the power supply. The speed of the complex is increased gradually so as to attain the optimum speed (roughly 3-4 km/h) beginning from the first picket. The operator passes on the lever 5 at all specified pickets and track switches, and the measured track parameters are thus recorded on the chart strip. As a rule, a track section is measured twice (when travelling forward and back). At the end of a measuring run, the chart strip is taken off from the recorder and processed. The day of survey, number of run, track section, and record scale are written at the top of the chart. All picket and other characteristic points are numbered on the chart. Then the elevations of all pickets are determined in a conventional system of coordinates relative to the elevation of the first picket, and the gradients of the track are calculated. For instance, the gradient of the track section between the picket points Nos. 15 and 25 (see curve 2 in Fig. 8.16) is determined in the following way. The height difference is found by subtraction: 55.2 -
178
Ch. 8. Special Surveys in Underground Workings
ooooooo ' :
~
100 -ii'". 2mmt
000 -
F-.'.'i'Y
5mm
'II
t==M.:
01
11mrr 0) "0 la
:1@
80
I~
60 !!!!!i
~2
40
3
20
-of
I~ ~ \~.r= ...C) "Q;:E =-
~ ...~ ~Q) ...0: .0:"' ".~:c
0
,CI:
o
alo
Picket15
O O O O O O O O O O O O O O
Picket25
Fig.8.16 Chart strip with recorded data: }-curve of track gauge variation (::t2mrn); 2-curve recorded longitudinal profile; 3 -curve of recorded discrepancies between the heights of rails
-52.8 = 2.4 mm on the chart and, considering that the chart scale is 1/50, the actual height difference will be 120 mm. Dividing this height difference by the distance between the chosen picket points, we obtain the gradient 120/103, or 12. The elevation of one rail above the other, say, in a point H (see curve 3 in Fig. 8.16) is found by multiplying the distance from the point H to the zero line by the scale base, i. e. 2x3x5=30mm. The deviation of the track gauge from the standard size, say in a point p (curve 1 in Fig. 8.16) is determined by multiplying the
of
number of divisions by the width of one division on a scale 1/1, i. e. 5.5 x 2 = II mm. By the results of these measurements, it is possible to judge on the condition of the rail track and the necessity of repairs. In mining practice, it is essentiar to control that underground workings are cut to the design cross-sectional area. This is especially important for opening and development workings, air ways, and haulage ways. With reduced cross sections of workings, the clearance for the rolling stock or conveyer trains will decrease below the permissible limits and may be the cause of accidents and
8.1. Assigning
Directions
injuries. Further, reduced cross sections can worsen the conditions of ventilation of stopes and be the restricting factor in the extraction of the mineral. Surveying practice employs several methods for checking the cross section of workings, depending on the cross-sectional shape: the method of measurement by common staffs and plumb bobs moved on a cord along the walls; the polar method; the method of linear intersections; method of direct measurements of the width and height of workings; etc. The method of direct measurementsis one of the simplest and is resorted to when workings have a trapezoidal or rectangular cross section. By this method, one can determine the total cross-sectional area of a working (as formed in the rock) and the clear crosssectional area. For this, it is required to measure the total height ho of the working between the roof and foot and the clear height hi (between the top beam and rail head); the total width A and clear width a at the level of the top beam; the total width C and clear width c at the level of the top of a carriage; and the total width B and clear width b at the foot of the working (Fig. 8.17). It is also essential to measure the clearances between the supports and the top of the carriage, between the rail head level and the contact wire, etc. The measured parameters are oriented correspondingly relative to the assigned direction of the working. The results of measurements and a sketch of the working are written in a standard field book. The method of measurement of cross sections by means of two staffs (Fig. 8.18) is mainly employed in workings with temporary railway tracks. Picket points are arranged in a working at intervals of 1-5 m, and the axis of the working at the foot level is marked at these points. Then the distances from this axis to the rail heaQs,a and b, are measured. Staffs with decimetre divisions are set up vertically on the rail heads, and a rod with centimetre
to Underground
1---
179
Workings A
.v/
~ .P..
I-~.-, Fig. 8.17 working
B
Measuring cross section of trapezoidal
divisions is applied transversely to them at intervals of 0.3-0.5 m to measure distances /1 and /2 from the left and right rail to the respective walls of the working. The results of measurements are marked on the sketches of cross sections in the field book, after which
Fig. 8.18 Measuring working cross section by two staffs
180
Ch. 8. Special
Fig. 8.19 Measuring working method of linear intersections
cross
Surveys
section
in Underground
by
Workings
template placed onto the head of rails. The procedure consists in measuring the distances from the protractor centre to the contour points of a working and the angles of these distances which are read on the protractor. The cross sections of workings 2-4 m high can be measured by telescopic (sliding) staffs such as those illustrated in Fig. 8.21. The staff shown in Fig. 8.210 consists of a metallic (light alloy) tube 1 3-5 cm in diameter and 2110 cm long in which a wooden rod 2 of the same length can slide freely. Two pins 3 are screwed into the wooden rod at the bottom end and roughly in the mid of its length. The heads of pins move in a 5-mm wide slot made longitudinally in the tube. The tube length at the slot is graduated in (b) 2
.2
~
~
3.5
Fig. 8.20 protractor
Measuring and rule
working
cross
section
by
these cross sections are drawn on a suitable scale. The working cross sections having a curvilinear or irregular shape are measured by means of templates, by the method of linear intersections or by the polar method. The method of linear intersections consists in measuring distances 11 and 12 from bench marks R1 and R2 to the typical points of the contour of a working (Fig. 8.19). In the polar method, measurements are done by means of a protractor arranged on an extendable stand (Fig. 8.20) or on a
3.0.
3
0
" 3
3 I
2.5
m..
2.0
2.0
..
jfJ:4
, 30
Fig. 8.21 Measuring rods: (a) tubular (l-tube; 2- extractable rod; 3- pins; 4- bar with hole for plummet); (b) staff-type (l-graduated staff; 2extractable rod; 3- pins; 4- guide cleats)
8.2.
Surveying
of Workings
Driven
from Two
Ends
8.2. Surveying of Workings from Two Ends
Fig. 8.22 Measuring working cross section up to 4 m high by means of telescopic staff, tape and plummet
decimetres with numbering in every 0.5 m. A different length of the staff can be chosen when needed. The staff illustrated in Fig. 8.21b consists of a wooden rod 1 with guide cleats 4 for retaining a sliding rod 2 with pins 3. The stationary rod has decimetre divisions numbered in 0.5-m intervals. The cleats and sliding rod are bevelled longitudinally at an angle of 75°. The cross sections of workings are measured with a sliding staff in the following way (Fig. 8.22). A plumb bob is hung in the desired cross section onto the direction line given by a surveyor. A linen tape is stretched and fixed perpendicular to that line; it also serves to fix the position of the plumb bob. The sliding staff is applied to the tape at definite intervals to measure the heights of the working contour. Before every measurement, the staff is checked for verticality by a plumb bob attached to it. The intervals at which staff measurements are done depend on the complexity of the working contour shape. The results of measurements are indicated at sketches in the field book.
181
Driven
For successfulconnection of faces in workings driven from two ends, it is essential to solve properly and correctly the whole complex of surveying tasks, the principal ones among them being: examination of the engineering purpose of a working and of its design data (cross section, slope, method of driving, etc.); determination of the place (point) of connection of faces; determination of the permissible deviation of faces in the connection point; compilation of the scheme of mining workings which connect the approaching faces; compilation of the project of mine surveying work and selection of suitable methods and instruments; preliminary calculation of the ultimate error of connection of approaching faces; determination of the expected ultimate error which is found by preliminary calculation for the established ultimate deviation of the faces; survey work and calculations for determining the connection parameters (angles, direction of connection axis, axis length, elevation marks, gradients, inclination angles, etc.); assignment and fixation of the connection axis in nature; and systematic survey control of the driving of a working in the assigned direction and determination of the actual connection error of approaching faces by making horizontal and vertical connection surveys for comparing the actual discrepancies with the permissible and precalculated ones. In the preliminary calculations, it is essential to consider three principal directions: along the connection axis, y'; perpendicular to that axis, x'; and in the vertical plane, z. Depending on the availability of a 'conductor', it is distinguished between critical and less critical (free) directions. The former are those whose errors can ,influence the technology of mining work. The choice of surveying methods and their accuracy for developing the planimetric and
Ch. 8. Special Surveys in Underground Workings
182
height control of workings driven from two ends depend on the particular mining production conditions and requirements. The principal factor that determines the accuracy of connection of mining workings is the kind of mining transport. For instance, for electric haulage trains, the permissible deviation of faces is up to 0.5 m in plan and 0.3 m vertically. In every particular case, mine surveyors must be informed on the permissible connection error by the engineering management of the mine. Main kinds of face connection. For workings driven simultaneously from two ends, it may be distinguished between the following kinds of connection: (a) a working is driven from two ends by two approaching faces; (b) faces in a working are advanced in the same direction and follow each other; and (c) a working is driven from one end (face) towards another face in which no mining work is being done. All these cases of face connection may be divided into three principal types: (a) connections carried out within the limits of a single mine, (b) connections between different mines, and (c) connections of vertical workings. Accordingly, let us consider three examples of face connection. 8.2.1.
Connection Within
of a Working the
Limits
of
Driven a
Single
Mine
This case may be exemplified by driving a crosscut AB simultaneously from points A and B (Fig. 8.23). In the crosscut No.2, which has been driven in the rock between the entries of seams 14 and 15' there are three fixed permanent bench marks I, II, and III. We draw on the plan the axis of the projected crosscut No.3 and de'termine the coordinates of the. points A and B (XA' YA' XB' and YB). The matter consists in transferring the
(a)
Fig. 8.23 Scheme of assigning direction to crosscut driven from two ends: (a) plan view; (b) section along the axis of projected crosscut
points A and B, which are the initial ones for assigning the direction to a crosscut AB, into the seams 14 and 15. For this purpose, approach points 1 and 2 are established in the entries by running theodolite traverses from permanent bench marks I, II, III to the points A and B. The measured angles and side lengths are used for calculating direction angles al-l and aIlI-2 and the coordinates of points 1 and 2 (XI' YI; X2' Y2). To establish the points A and B in nature, it is required to calculate angles !31 and !32 and side lengths S2Aand SIB. Besides, for assigning the direction to the crosscut, it is essential to know angles !3A and !3Band a side length sAB. For this, the direction angles and horizontal distances SIB and S2A are calculated by the formulae of inverse geodetic problem. Mter that, it is possible to calculate the angles:
8.2.
Surveying
~l = alB -all, ~l = alA -alIIl, -aAl' and ~B = aBA-aBl.
of Workings
Driven
from
Two
Ends
183
~A = aAB-
Theodolites are then set up under the fixed points A and B, and the horizontal direction
to the crosscut is assigned by setting the angles ~A and ~B on the limb. In order to determine the direction of the crosscut in the vertical plane, a line of levels is run through the workings between the points A and B, and the height differense of the point A above the point B is measured (L\z). As may be seen in the vertical section in Fig. 8.23b, the crosscut must be driven in the direction from B to A with a gradient i = tan v (v is the angle of inclination of the crosscut foot), which can be found by the formula: L\z sAB -(a
+ b)
where sAB is the horizontal distance between the points A and B, which can be calculated by the foimula: sAB = YB.=-Y A smaAB
XB -xA
Fig. 8.24 Scheme of (a) elevation and (b) planimetric control for driving crosscut between two shafts
cosaAB
the collars of both shafts, R3 in the pit bottom of a mine No. I, and R4 in the wall of a shaft No.2 (near the face). Then a closed geometric levelling run is laid off between the bench marks Rl and R2 in order to deter8.2.2. Connection of Workings in mine the coordinate z of these bench marks Non-Communicating Mines and to transfer this coordinate to bench As an example of this type of connection, marks R3 and R4. After that the design let us consider the complex of surveying elevation of the pit bottom of the mine No.2 operations for driving a crosscut between two is determined, for which purpose the elevavertical shafts by approaching faces. One of tion of the bench mark R3 (z;) is transferred the shafts is sunk to the projected level and onto the pit bottom, and the design length of has a pit bottom, while the other is in the a crosscut, L, is then determined. Now that stage of driving (Fig. 8.24). we know the elevation of the pit bottom in The survey work in the case considered the mine No. I, the design length of the may be performed in the following sequence. crosscut, and the design gradient, it is posFirst, it is required to determine the design sible to determine the elevation of the pit elevations of the inset of pit bottom and the bottom in the mine No.2 by the formula: required deepening of the shaft of a mine z'5 = z; + iL. The difference between the eleNo.2. For this, four bench marks are estab- vation of the bench mark R4 and the design lished: Rl and R2 on the ground surface at elevation of the pit bottom of the mine No.2 where a and b are the distances from the points A and B to the corresponding sides of entries, which can be measured by a tape.
Ch. 8. Special
Surveys
in Underground
Workings
(z~) permits us to find the required deepening
~ , -Z4 -ZS. Upon deepening the shaft of the mine No.2 to the design level z's and making the inset in the pit bottom, both mines are oriented, and the elevation mark is transferred onto the bench mark Rs. For this purpose, two approach points are established on the surface near each shaft and three permanent points, in the pit bottom of each mine. A closed theodolite traverse is run between the approach points, I, II of the mine No. 1 and III, IV of the mine No.2, which is given, where possible, a shape stretched in the direction of a connection axis. The angles and side lengths of the traverse are measured. For proper checking, the orientation is done at least twice for each shaft. The results of orientation are used for determining the coordinates x, y of points V, VI, and VII in the mine No. 1 and of points VIII, IX and X in the mine No.2. The coordinates of the points VII and X are used to calculate the direction angle of the connection axis avIl- x. The direction angles 131 and 132 are determined by the difference of the direction angles of initial sides VI-VII and IX-X and the connection axis, i. e. 131= aVII-X -aVII-VI' 132= = ax -VII -ax -IX . The calculated gngles 131and 132are laid off in nature in the points VII and X, and three points are fixed at each angle side, which define the direction of the axis of approaching faces in the crosscut. h
8.2.3.
Connection Workings
of Vertical
Let the shaft of the mine No. 1 (Fig. 8.25) open the levels + 150 ill and + 50 ill and the shaft No.2 be sunk to the working level + 150 ill. At the level +50 ill, mining operations are advanced under the shaft of the mine No.2, which should be deepened froill the bottoill upwards.
Level +50 m Fig. 8.25 Scheme of connection shafts (axonometric projection)
of vertical
mine
Surveying work required for this connection consists in finding a point at the level + 50 m, which lies on the same vertical line with the centre of the shaft No.2 at the level + 150 m. For this, it is required (a) to determine the coordinates of the centre and the direction angle of the axis of the shaft No.2 at the level + 150 m; (b) to run a theodolite traverse from the shaft No.2 to the shaft No. 1 at the level + 150 m; (c) to perform the orientation of mine surveying at the level +50 m from the level + 150 m through the shaft No. I; (d) to run a theodolite traverse at the level + 50 m from the shaft No. 1 beneath the shaft No.2; and (e) to determine the centre of the shaft No.2 at the level + 50 m and arrange the axes. The coordinates of the centre and the direction angle of the shaft axis are determined by a special technique or according to the recommendations of specifications on mine surveying. The theodolite traverse from the shaft No.2 to the shaft No. 1 at the level + 150 m is run from the points for which the coordinates of the centre and the direction angle of the shaft No.2 are determined. The orientation of surveying work at the level
8.3.
Preliminary
Estimation
of Face Connection
Accuracy
185
+ 50 m from the level + 150 m should be done at least twice. When the coordinates of the shaft centre at the level + 150 m, the coordinates of a point 61, and the direction angle of a side 60-61 at the level + 50 m are found, the centre of the shaft is transferred onto the lower level. For this, it is needed to calculate the angle 13of the direction from the point 61 onto the point 62 (shaft centre) and the distance d from the point 61 to the point 62. 8.3.
Preliminary Estimation of Accuracy of Face Connection
For driving a working from two ends, it is essential to estimate preliminarily the expected accuracy of face connection in each critical direction. For this purpose, a project of surveying work with explanatory notes is compiled, which specifies the proposed method of surveying and the list of instruments to be used. When compiling the project, the surveyor must consult with the management of the mining enterprise on the permissible discrepancies of workings in the critical directions. Upon compiling the project, it is required to calculate the expected error in the determination of the point of connection of approaching faces (M exp). If the calculated expected error is greater than the permissible value, it is required to find out which of the measurements associated with the determination of the connection point is most responsible for the error Mexp.This measurement should then be done by a more perfect method or more accurate instruments. For higher accuracy of face connection, it is recommended to make additional measurements of direction angles by gyroscopic instruments. In the final result, the expected error must be smaller than or, in exceptional cases,equal to the permissible error (M exD~ M D).
Fig. 8.26 Scheme for preliminal'Y calculation of error of face connection
186
Ch. 8. Special
Surveys
in Underground
the angles and sides in the polygon A-EIII-II-D-C-B in Fig. 8.26. Let a point k be the expected point of face connection. We can draw two axes through this point: y' along the axis of a working and x' perpendicular to that axis. We are interested in the deviation of the axes of faces in the direction perpendicular to the axis x' and in the direction of the axis z' (vertically). The mean error of face connection due to the errors of angular measurements in hanging polygonometric traverses run twice can be determined by the formula: m
Xp
=
-.!!!!!-~ p"j2v
I~R;.
.
(8.1)
where mIl is the mean square error of angular measurements, s; Ry. are the projections of the distances from the connection point to the corners of a polygon onto the y'-axis, m (the values of Ry are found graphically on the plan, see Ch. 4); and p" = 206265". The mean error of face connection depending on the accuracy of measurement of side lengths in polygonometric traverses run twice can be determined by the formula: mx = ,
JI.12~SiCOS2 a, + A.L2 cas ~~2 "'I 2
(8.2)
where 1.1 is a coefficient which accounts for the influence of random errors per unit of measured length; I.. is a coefficient of the influence of systematic errors per unit length; Si is the length of the side of a theodolite traverse, m; L is the projection of the closing side of a traverse onto the x'-axis (the distance between the initial poirits of a polygonometric traverse in a mine); ai is the angle between the side of a polygonometric traverse and the critical direction (to be found graphically on the plan); y is the angle between the closing side of a traverse and the critical direction (to be found graphically on the plan); the term SiCOS2 ai can be found graphically by double projection on the plan (see Ch. 4).
Workings
The total mean error of face connection in the horizontal plane in the critical direction x' is found from the formula: Mx
=
Jm~.
+
m~
p
(8.3) ,
The mean error of face connection along the height can be calculated by the formula: Mz = Jm;l + mll
(8.4)
where mgl is the root-mean square error of geometric levelling in the mine and mtl is the mean error of trigonometric levelling in the nune. In caseswhen it is needed to determine the mean error of connection of approaching faces along the height considering the error of height transfer through the mine shafts, it is essential to take into account the following probable sources of errors: (a) error of geometric levelling on the surface mz; (b) erro~ of geometric levelling in the mine, mgl; ~(c) error of trigonometric levelling in the mine, mtl; and (d) error of height mark transfer through a vertical shaft, mz (see Ch. 4). The expected total error of face connection along the height can be found by the formula: M z = ~;
, + m;, + mfl + 2m;'
(8.5)
In preliminary calculation of the error of face connection in vertical shafts (see Fig. 8.24) the following errors must be deterrnined: (I) errors of angular measurements in theodolite traverses run at the upper and lower levels of a mine: m" M = --.!!. rr:iii {1 "V~~i p where m{1is the root-mean square error of angular measurement and Ri is the distance from the centre of connected shafts to the corners of a theodolite traverse;
8.3.
Preliminary
Estimation
(2) errors of measurements of side lengths in theodolite traverses run at the upper ( + 150 m) and lower ( + 50 m) levels: M s = ft;;;:; where ms is the mean error of length measurement~; and (3) errors of the orientation of surveys at
of Face Connection
Accuracy
the lower level being connected
187 ( + 50 m):
mar Mar = -Ro
p where mar is the mean error of orientation and Ro is the distance between the centres of shafts.
Chapter
Surveying
9.1.
Nine
in Mine
General
Survey work in mine construction is an important part of mine surveying. It consists specifically in that the angular and linear measurements which determine the design dimensions of underground workings and mine head-gears are transferred into nature and fixed properly. Further, modern mines are characterized by intricate underground complexes with hoisting vessels a few tens cubic metres in capacity and high lifting speeds, which sets forth especially rigorous requirements to the accuracy of their assembly. These circumstances make the survey work in mine construction the most complicated and critical part of mine surveying servIce. The principal problems to be solved by mine surveying in mine construction are as follows: (a) construction of reference nets on the surface for making the layout work; (b) determination of the scope of the earthmoving work; (c) instrumental layout of the axes of a mine hoist on the surface and transferring the geometrical elements of buildings, structures, etc. into nature; (d) special measurements and surveys during sinking and equipment of mine shafts; (e) control of the relation between the geometrical elements of mine hoists during construction; (I) assigning directions to underground workings and surveying control of the di-
Construction
rections, gradients and cross-sectional dimensions of driven workings; (g) measurements for determining the deformations of buildings and structures; and (h) revision surveys of construction objects and driven workings for depicting them in maps, plans, sections, etc. The layout of buildings and structures and assignment of directions to underground workings are carried out according to the design drawings. For the construction of mine objects, the following technical and design documentation should be available: an engineering report on the topographic and survey work on the site; the general layout which is of prime importance, since it gives horizontal distances of all permanent and temporary structures, etc. from the axes of a shaft and their elevations; the design plan of arrangement of heading equipment on the mine surface; the design plans and vertical layout of earth-moving work with distribution of soil masses; the general plan of permanent and temporary underground service lines; the topographic plan Qf the territory allotted for construction; drawings of foundations; and design documentation relating to mine shafts and other mine objects. The instrumental layout of construction objects is carried out from the points of a mine survey reference net, points located on the axial lines of mine shafts, and the points of a layout net. The layout work underground is done from the points of underground polygonometric nets and survey nets 'of the first or second order.
9.1. General
The layout control work is understood as the work of transferring the project of a structure into nature. The principal layout control operations consist in the construction on the terrain of the main axes of a constructed site (mine camp), such as the axes of mine shafts or the sides of a layout control net. The axes of a vertical mine shaft are essentially two horizontal lines one of them being parallel and the other, perpendicular to the main buntons (dividers) of that shaft. The point of their intersection is called the centre of the shaft. Detailed layout control is performed by mine surveyors and consists in the construction of the main axes of buildings, structures, machine foundations, and hoist axes. 9.1.1.
Layout Camp
Control
Net of Mine
Detailed layout work at the construction site of a mine head-gear (mine camp) is facilitated by constructing a layout control net of reference points. Its construction is based on the results of topographic and mine surveys carried out on the territory of mine construction. In cases when the objects of a surface complex are distributed all over the mine camp, layout control can be reduced to the construction of a layout net consisting of points located on the axes of the main and auxiliary shaft. At large mines, all main buildings of the surface complex are Jlsually combined into three blocks: main shaft block, auxiliary shaft block, and office and accommodation block. In such cases,the points on the axes of shafts do not form a common net and thus cannot always ensure the required accuracy of layout work. Besides, if the objects of a large extension are to be built in the central portion of a mine camp, most points on the shaft axes will be inevitably lost. In such caSes,it is required to construct preliminarily (before construction) a special
CIj'I I
il Bf II
189 E ~
D
v'
r-:::
---y -I
I ~
i E3J! n +-~--I"---tl-~ II I ,Main shaft :11 IAu~iliaryr:
,.,
~
FI ~ II
.
I
~--I II A0..:
[]
+-I. --~~h.:~- + I t!
2:
O ~
O H
--1
J
, O G
Fig. 9.1 Layout control net layout control net covering all the territory of the mine camp. In modem mine construction, a layout control net is formed as a system of rectangles with vertexes in spaces between the surface structures and with sides oriented parallel to the axes of a shaft (Fig. 9:I ). A layout control net should be formed along the following recommendations: (a) the main points of a net should be arranged at the vertexes of rectangles and the auxiliary ones, on lines connecting the main points; (b) the sides of rectangles between the main points should be 80-350 m long; (c) the main points should be established in places where their long preservance can be guaranteed; and (d) the coordinates of points should be determined analytically in a conventional system of coordinates whose axes are directed along the axes of a shaft. The construction of a layout control net is carried out in the following order: (a) the main points of a net are transferred into nature and fixed by permanent bench marks; (b) a polygonometric traverse is run through these points; (c) the results of measurements are processed for the reduction of the system of polygonometric traverses; (d) the points are reduced, and check measurements are carried out;
190
Ch. 9. Surveying
in Mine
Consl
(e) auxiliary points are established on lines between the main points; and (1) the elevations of these points are determined by levelling. The accuracy of construction of a layout control net must satisfy the following requirements: (a) an error in the position of the first established point of a layout net relative to )f horizontal angle into nature the points of a reference net (national geo- Fig. 9.2 Transfe detic net or densification net) must not exceed 0.1 m; FL) do not coincide, i. e. there is a collima(b) the direction angle of the first side of a tion error, the section between these points is layout net must differ from the design value halved, and the point C is found in the mid, by not more than 20"; which determines an angle 13.For checking, (c) the non-perpendicularity of the sides of the angle 13is measured and compared with a layout net must not exceed 20"; the design value. If the difference between the (d) the root-mean square errors of angular specified and measured angles is greater than measurements must be not more than 10"; the permissible error of angle measurement, and this difference is used to calculate the linear (e) linear measurements must be done with correction by which the second side of the a relative error not worse than 1/15000. angle should be transferred (a point Cl in The axes of mine shafts are established Fig. 9.2b). This correction can be calculated from the points of a layout control net and by the formula: each semi-axis is fixed by at least two points; AI = IA13"/p" in that case, the errors of angular measurements must be not more than 40" and those where 1is the horizontal distance between the of linear measurements, not more than theodolite and the point C; A13is the difference between the specified and measured 1/3000. angles; and p" = 206265". Transfer of a specified horizontal distance 9.1 .2. The Concept of Layouts into nature. The method of transferring the specified horizontal distances into nature is Layout control is carried out in horizontal and verti'tal planes and contains a number of chosen depending on the terrain relief, regeodetic operations, such as transferring a quired accuracy, length of lines, etc. The point, design distance, design horizontal an- following main cases may be encountered in gle, elevation mark, axes, etc. into nature. mine surveying practice. If the terrain is flat, the inclination angle Transfer of a horizontal angle into nature. This operation reduces to finding the second does not exceed 3°, and the length of a line is not more than 50 m, the design distance is side of that angle on the terrain. For this purpose, the theodolite is set up at the vertex laid off on the terrain by taping along the specified direction and is fixed by a point. If of the angle (a point B in Fig. 9.2a). The the terrain is an even slope and the line specified angle is laid off from the initial direction at two positions of the telescope length does not exceed 50 m, the inclination (FR and FL). If points C' and c" determined angle of the specified direction is first measat the two positions of the telescope (FR and ured by a theodolite, after which the design
9.1.
General
On a rough terrain and with a large design distance, the layout work is started by setting up a theodolite in a point A (Fig. 9.4). The point Bo near the future point B is established on the specified direction by means of a range finder. Then, the line AB is ranged in that direction and the points where the slope is measured are fixed by stakes. The lengths and angles in each inclined section Si are measured. After calculating the horizontal Fig. 9.3 Transferof specifiedhorizontal distance distances Si' their sum (~sJ is found and compared with the design horizontal disinto nature on terrain of intricate relief tance. This gives the length of a line section horizontal distance is laid off. With the angle L\s = ~s., -s v being known. the inclined length S is calculated by the formula: for determining the position of the design point B. S = s/cos v Transfer of design points into nature. The This length is laid off by a tape along the transfer of design points during layout can be specified direction. On the terrain of an performed by several methods. intricate relief. an auxiliary point Eo is first I. Polar method. It is essential to have two established on the specified direction near the points with known coordinates on the terrain sought-for point E (Fig. 9.3). The inclination (A and B in Fig. 9.5a). The design angle ~ and angle v is measured by a theodolite and the length s are laid off from the direction AB, inclined length AHo. by a tape. The horiwhich gives the position of a point C. The zontal distance is calculated by the formula: polar method is the most popular one for Sf = AEocosv transferring points into nature. The rootmean square error of the position of a point Then the difference between s' and the can be found by the formula: design horizontal distance s is determined As=S-Sf
~ mp=
which is laid off from the point Eo. and at last the point E is fixed.
Fig. 9.4
Transfer
of specified horizontal
(smpf ms
+~
p
where
distance into nature
ms and
on rough
mp are the
terrain
rrns errors
of
Ch. 9. Surveying in Mine Construction
192
point C (xc, Yc) are known, they can be found by solving the inverse geodetic problem. The direction angle of a line EC can be determined by the formula: tan IlBC= Yc -YB
c
A
Xc -XB With the known direction angle of a line EA and the calculated direction EC, we can find the angle 13= IlBC-IlBA. The length of the section EC will then be found from the expression: EC = .~= Yc -YB J'l ~ -!..!!.
8 An
(c)
'c -!
(d)
-, Oc
RI =AC / / / o A
, R =BC ,2 ,
//
,
O B
--sin aBC
O
-O
B
Fig. 9.5 Layout of points: (a) polar method; (b) method of angular intersection; (c) method of linear intersection; (d) method of rectangular coordinates
measurement of lengths and angles respectively and s is the distance from the known point to that to be established. Assuming that the accuracy in detailed layout work is up to 1/3000 for linear measurements and up to I' for angular measurements and the error in the determination of the positions of corner and axial points of building foundations is not more than 0.01 m, the maximum distance from a point of the net to the contour being laid out should be not more than: Imax
=
I~-
0.012
Jr., moo~ ,
-~22m (~)2
Thus, the points of layout control and reference nets in the layout work should be located at distances not more than 25 m from the contour being laid out. If the angle 13and length s (Fig. 9.5a) are not specified, but only the coordinates of a
COSaBC
2. Method of angular intersection. The position of a point C can be detennined by the point of intersection of two directions drawn at angles ~A and ~B from points A and B of a known side (Fig. 9.5b). If the angles ~A and ~B are not specified, they can be calculated from the known coordinates of points A, B, and C by the fonnulae: ~A=aAB-aAC' ~B=aBC -a ' .
BA
tan
aAC
=
Yc -y A ,
Xc -XA
tan
aBC
=
Yc
-YB
Xc -XB
The method of angular intersection is used in caseswhen the points A and B are at large distances from the point C and linear measurements would involye difficulties. 3. M ethod of linear intersection. In this method, the arcs of radii AC and BC are drawn on the ground from the centres in known points A and B (Fig. 9.5c), and their intersection gives the sought-for point C. 4. M ethod of rectangular coordinates. This is employed in cases when the points to be laid out on the ground are essentially close to a reference (layout) net. The coordinates x and y of a point C relative to a reference net are determined on the plan and then laid off and fixed on the ground (Fig. 9.5d). The layout work is checked by measuring the distances between the points established on
9.2.
Surveying
the ground. In mine construction, a version of this method is popular with one of the rectangular (layout) axes being fixed by means of a stretched wire. A plumb bob is suspended from the wire, and the required distance is laid off from it perpendicularly. Instead of plumb bobs, other means can also be used for the fixation of points on the wire. 5. M ethod of ranging measurements.In order to transfer into nature design points, say, A and B, which lie on the line between points 1 and 2 of a layout net, the theodolite is set up, say, in the point 2. The instrument is sighted at the point I, and the design distances S2Aand S2Bare laid off by means of a tape from the point2; the points A and B found in this way are t~en fixed. In the construction of structures and other construction jobs it is often needed to transfer points with design elevations into nature. Such points can be transferred by geometric levelling with two staffs or by means of an instrument horizon. For this purpose, the level instrument is set up midway between the bench mark A with the known elevation H A and the point B to be established, whose elevation HB is specified in the project (Fig. 9.6). The staff is set up onto the bench mark A, the reading a is taken on it, and the instrument horizon is calculated by the formula: IH=HA+a Mter that, the reading of the staff set up in the point B, at which the staff foot will be at the design elevation, is calculated by the 13-1270
at
Mine
193
Camp
fomlula: b=IH-HB If the design elevation is transferred onto the well of a working or another object above the ground, the staff set up in the respective point should be lowered or lifted until the reading on it is equal to the design value. A line drawn at the staff foot will then give the design elevation mark. If the design elevation mark is to be transferred onto the top of a peg, the latter should be hammered down until the reading on the staff set up onto it will be equal to b. 9.2.
Surveying
at Mine
,Camp
The main axes of all buildings and structures should be laid out in nature and fIXed at a mine camp before starting the earth-moving work. The distances from the net being laid out to the points determining the axes of structures should not exceed 25 m. The directions onto the points to be established should be assigned with an accuracy not worse than I' and the distances to these points, with an accuracy not worse than 10mm. The main axes of buildings and foundations should be laid out so as to be preserved fully for the entire period of construction. Linear measurements of distances between the layout axes of buildings, structures, foundations and machinery, between the axes of columns, and between the layout axes and the axes of support structures, embedded parts, anchor bolts, axes of precast
Ch.
9.
Surveying
in
reinforced concrete and steel structures, and mounting axes of process equipment and mechanisms are made by standardized tapes. All measurements are fixed in a layout book together with the date of the layout work, coordinates of initial points, numbers of design drawings, distances and measurements used for layout, and the orientation of objects relative to the axes of the site. The layout work at a mine camp is started from the centre and axes of a shaft. The axes are laid out and fixed according to the coordinates x, y of the shaft centre and the direction angles of the shaft axes, proceeding from survey net points located at a distance not more than 300 m from the shaft. The centre of the shaft is established independently twice; the discrepancy between the two measurements should not exceed 0.5 m. The angular error of the layout of the main axis of the shaft relative to points of the survey reference net should not exceed 31. If the centre and main axes are established for a shaft associated with an operating mining complex, the errors should not exceed respectively 0.1 m and 1'30". The error of the layout of a perpendicular axis relative to the main one should be not more than 45". At least six points should be established and fixed at each axial line of a shaft. These points should be arranged so that they can be used for the construction of buildings and structures at the site. At least two points shQl.11d be established beyond the limits of the mine camp. The distances between adjacent points must be not less than 50 m. The layout of the centre of a shaft can be done by the method of perpendiculars or polar method. Upon finishing the layout work, a secondorder polygonometric traverse is run through the shaft centre, axial points and points of the survey reference net, and the coordinates of the axial points are calculated. Before starting the earth-moving work, the main axes of buildings and structures should be transferred into nature and fixed at the
Mine
Construction
mine camp. The plan position of each structure is determined by the distances from its characteristic points to the axial points of the mine shaft or points of the layout net. When laying out the foundation of a building, its characteristic points (A and B in Fig. 9.7) are established by the predetermined angular and linear elements, and the axes 1-1, 11-11and 111-111of the building are marked in nature. Using these axes, it is then possible to layout the axes of the walls (mostly by the method of perpendiculars or polar method). The main axes of the building are fixed by axial points and the axes of the foundation are transferred onto and fixed on batter boards fastened on poles- (Fig. 9.7). The batter boards should be arranged at a certain distance (not less than 3 m) from the exterior walls of the building. Wires stretched
9.3. Surveying in Construction of Mine Hoists
between the axial points of opposite batter boards determine the directions of the building axes, and their intersections define corner points. In the construction of large blocks of industrial buildings (of a length more than 80 m), batter boards and wires are also used for the fixation of the axes of exterior walls; plumb bobs 1,2,3,4 are suspended from the points of wire intersection (Fig. 9.8). The vertical layout of foundations is carried out by means of a level instrument and staff, starting fr.om bench marks usually fixed on the piles of batter boards. .. Buildings and structures in mine construction may have cast in-situ, strip, pile foundations, etc. The layout work for strip foundations consists in checking that the foundation pit has been dug properly, arrangement of a shuttering (formwork), and transferring the design elevation marks of the foundation top onto the formwork. The position of the formwork in plan is checked by means of plumb bobs suspended from the points of foundation axes marked on batter boards. The deviations of the foundation axes from the design values should be not more than 2 cm and the deviations of the axes of wells, columns, beams and girders, not more than 1 cm. A decrease of the cross-sectional size of a foundation against the design value is inadmissible; an increase by not more than
195
5 mm is allowed. The vertical position of a formwock is checked by a plumb bob; the permissible error is 2 mm per metre of the foundation height. After concreting a foundation, it is controlled by planimetric and height surveying. The discrepancy, between the actual and design elevation marks of the foundation top must be not more than 20 mm. The mine survey servicing of precast foundations means the fixation of their exterior and interior faces by cords or wires stretched between batter boards. The design position of a foundation is marked initially, after which the foundation is laid in place. For this purpose, the foundation guide blocks are first laid in place in every 20-25 m, cords are stretched between them, and intermediate blocks are then laid. In the construction of deep foundations, the axes of the exterior rows of piles or the axes of pits are first marked in the foundation pit, and the contour of the cutting shoe of a caisson ring is established. After pile driving, levelling is carried out to check that all pile heads are in the same horizontal plane. Plane foundations are the most popular type of foundation for reinforced-concrete columns. In laying, the foundation plates are checked by a theodolite or level instrument. The deviations of the axes of a foundation from the design values should not exceed 5 mm and those of the support surfaces from the design elevation marks, 3 mm. Anchor bolts for fastening metal columns must not be displaced from the design position by more than 5 mm in the horizontal plane and by more than 20 mm, vertically. 9.3. 9.3.1.
Surveying of Mine
in Construction Hoists
Brief Data on Hoisting Complexes of Vertical Shafts
Modern hoisting complexes employed in mining can be characterized by ever increas-
196
Ch. 9. Surveying in Mine Construction
ing hoisting depths, increased speeds of hoisting vessels, and larger mass of cargoes. In addition, the construction of mine complexes is often oriented at industrial methods. These circumstances set forth new complicated problems before mine surveyors. In particular, they must ensure the proper accuracy of mounting the process equipment and safe operation of mine hoists. The mine surveyor has to take part in all stages of the construction and operation of mine hoists. He is directly engaged in the construction and installation work, plays an essential role in the acceptance of a mine hoist, and performs control during the hoist operation. A mine hoist has the following main components: (I) hoisting plant, (2) shaft equipment, and ,(3) auxiliary hoisting equipment. The hoisting plant of a mine includes a hoisting machine, head-gear (head-frame), hoisting (driving) pulleys, hoisting ropes, and hoisting vessels. According to the kind of hoisting vessel, hoisting plants can be divided into skip hoists, cage hoists, skip-cage hoists, and bucket hoists. They may be of the single- or multi-rope type depending on the number of hoisting ropes. Further, by the method of rope winding, it is distinguished between hoisting plants with a constant winding radius and those with a variable radius. Depending on the kind of guides, the equipment of a shaft may be either rigid or consist of ropes. Combined equipment is also employed, in which rigid conductors are used for hoisting vessels and rope guides, for counter-weights. The auxiliary equipment of a mine hoist includes load-handling facilities and landing stages. Hoisting machines, which are the principal part of mine hoists, may be provided with either rope-winding drums or friction type pulleys (Koepe sheaves).Druni-type hoisting machines may be with a constant or variable winding radius. Those with Koepe sheaves
may be of the single- or multi-rope type. Hoisting plants of vertical shafts are equipped with medium-sized or large-sized drumtype machines. The former have a winding drum 2.5 m. 3 m or 3.5 m in diameter and ensure a hoisting speed of 7-10 m/s. Largesized hoisting machines have drums 4-9 m in diameter and up to 1560 m in coiling length. The hoisting speed of these machines attains 16 m/s. Multi-rope hoisting machines have several ropes which are driven from a hoisting pulley owing to the friction between the pulley lining and ropes. Each of the ropes is fastened to both hoisting vessels. Multi-rope hoisting machines are mainly employed in tower-type head-gears. Multi-rope machines manufactured in this country have four. six or eight ropes. a load-carrying capacity from 3 t to 50 t and driving pulleys 2.1-5 m in diameter. A head-frame is a structure above a shaft which carries guide pulleys. conductors. cage rests. unloading curves. etc. There are two main types of head-frame: jib head-frames and tower head-frames. A jib-type head1rame (Fig. 9.9) consists of a vertical frame 1. a jib 2 which serves as a strut for the vertical frame and absorbs the tilting force developed by a hoisting rope. and a pulley (landing) stage 3 for guide pulleys. Jib-type head-frames are mostly made of metal and much rarely of wood and may be classified as A-shaped. four-standtype and tent-type. A tower-type head1rame carries the entire hoisting complex. including the hoisting machine. Tower-type head-frames may have a metal framework or reinforced-concrete (cast-in-situ or precast) carrying walls (Fig. 9.10). The walls of a head-frame form an interior shell of a rectangular cross section which serves as a support. and an exterior shell of a circular or rectangular cross section. Hoisting pulleys are mounted on the pulley stage of a head-frame. They hold the ropes
9.3. Surveying in Construction of Mine Hoists
197
(b)
Fig. 9.9 Steeljib-type head-frames:(a) A-shaped;(III) with four stands;(c) tent type; 1-vertical frame; 2-jib; 3 -pu1ley (landing) stage and direct them from the hoisting machine into the mine shaft. Hoisting pulleys may be without lining or with a lining made of soft metals, wood, rubber, etc. The diameter of a pulley depends on the diameter (thickness) of a hoisting rope. For tight contact of a rope on a pulley, the diameter of the latter must be not less than 80 rope diameters. Non-lined pulleys are made of high-strength cast iron (with the diameter up to 3 m) or stamped of steel (with the diameter more than 3 m). Hoisting ropes. Only steel-wire ropes are employed in hoisting plants. Round-strand right- or left-hand twisted ropes and flattenedstrand ropes are used in hoists of a small or moderate hoisting height. With a large hoisting height, use is preferably made of crosstwisted round-strand ropes and self-tightening sheathed ropes, as well as of self-tightening multi-layer ropes. Hoisting machines with Koepe sheaves are equipped with flattenedstrand and sheathed ropes. Hoisting vessels.Buckets, cages, skips and combined types (such as skip-cage) are employed as hoisting vessels. Cages may be of the non-tilting (common) or tilting type and are divided by the type of load into man-cargo and man (passenger) cages. Single- and double-stage non-tilting cages are the most popular types. Skips 7-15 m3 in capacity are employed in single-rope hoists
and those 9.5-35 m3 in capacity, in multirope hoists. Suspensionsof hoisting vessels.Suspensions (bails) are devices by which hoisting vessels are connected to ropes. According to safety regulations, cage bails have a double independent suspension with l3-fold safety margin and skip bails, a single suspension with lO-fold safety margin. Loading-unloading devices (stations). Loading and unloading of hoisting vesselsare the most critical operations of hoisting. Skips are loaded in a shaft by means of a loading device which includes an underground bunker, chutes, and gates with drive mechanisms. Skips and tilting cages are unloaded on the surface by means of unloading curves mounted in the head-frame. A cage hoist has landing stagesin the shaft and on the surface, which are provided with landing chairs to support the cages during loading and unloading; they also have arrangements for moving carriages into and from cages and safety devices. Landing dogs are the most popular type of landing chairs. Equipment of vertical shafts. The equipment of shafts is understood as a complex of elements which ensure the directed motion of hoisting vesselsunder the specified operating conditions of a hoist. The shaft equipment may be either rigid or of the rope type. A rigid equipment consists of conductors
198
Ch. 9. Surveying in Mine Construction
Fig. 9.10 Reinforced-concrete tower-type headframe: 1 -machine rooms; 2 -level of guide pulleys; 3- metal stand; 4- floors; 5- foundation
and buntons (dividers) which carry the former. The conductors serve to direct the moving hoisting vessels. They are made of rectangular wooden bars, steel rails or rolled U-shaped steel sections in the form of continuous cage structures which are arranged vertically in a shaft. The conductors are fastened to buntons (dividers) which are essentially horizontal beams built in by one or both ends in the shaft lining. The buntons are made of wood or various rolled steel sections. A rope equipment can be employed in shafts where one or two hoists are arranged in parallel and the path of hoisting vesselsis not curved. A rope equipment (Fig. 9.11) includes rope guides 1, balance ropes 2, rope clips 3, rope-tensionirig weights 4, a tensioning frame 5, guides for hoisting vessels6, and devices for the fixation of hoisting vessels at the loading and unloading stages, 7 and 8. The rope guides are usually made from sheathed ropes. Four rope guides are usually provided for a hoisting vessel, which are arranged either at the corners or pairwise along the larger side of a cage. In shafts with two hoists, the balance ropes are stretched between the vesselsin order to prevent their collisions. The ropes are tensioned by means of weights arranged in a sump or by means of a hydraulic device mounted on a headframe. The equipment of a shaft can be mounted either after driving the shaft or at the same time. In the former case,all operations can be carried out by a consecutive, parallel or combined scheme.With the consecutive scheme, buntons are mounted from a suspended stage, beginning from the top of a shaft, and after that, conductors are fastened to them from a cradle, beginning from the bottom. With the parallel scheme, conductors are mounted at the same time with buntons, but the latter are mounted from a sinking platform and the former, from a cradle that moves behind the platform. With the combined scheme of arrangement of the shaft
9.3. Surveying in Construction of Mine Hoists
199
arrangement of metal structures, to make the profile survey of the head-frame structure, and to transfer the layout axes of a pulley stage, guide pulleys, and unloading curves. For mounting a jib-type head-frame, a supporting frame is made around the collar of the shaft and foundations for a jib are built. The correct position of the supporting frame is checked relative to the axial points fixed in the permanent lining of the shaft collar. The errors in the position of the supporting frame should be not more than 5 mm in the horizontal plane and 30 mm in the vertical plane, and the difference between the elevation marks of the frame corners should be not more than 5 mm. The layout of the foundations of a jib is done according to a working drawing and the plan of arrangement of foundations relative to the shaft axes. Upon the construction of the foundation, the mine surveyor checks the depth of the foundation pit, the horizontality of the foundation pad, and the correct mounting of a shuttering. Since the faces of the foundation are represented in the working drawing with distortions of their dimensions, it is essential to determine their actual dimensions for the manufacture of shuttering panels. For the arrangement of the shuttering equipment, buntons and conductors are along the axes of a head-frame foot (Fig. 9.12), these axes are first transferred mounted simultaneously. In cases when the shaft equipment is onto side piles, and cords are stretched mounted simultaneously with shaft driving, a between the piles. After that, corner points A, section of shaft lining is first fastened in the B, C and D are marked on the foundation shaft, after which buntons and conductors pad by means of plumb bobs sunk from the cords. The correct arrangement of the shutare mounted on it from a sinking platform. tering is checked at its top, by using points a, b, c, and d. A shuttered foundation foot is 9.3.2. Survey Control During concreted partially, anchor bolts are set up, Mounting of Metallic and concreting is finished. Jib-Type Head-Frames Metallic jib-type head-framescan be mountDuring mounting a jib-type steel head-fra- ed by two methods: (a) the head-frame is me, the mine surveyor has to layout the axes preassembled on an assembling stage and of the supporting frame and foundations for then lifted and mounted on a supporting the head-frame jib, to check the correct frame or (b) the sectiQfis of a head-frame are
200
Ch. 9. Surveying in Mine Construction
\,
~"~
,0/.
\ \
"
1!11
~1\\ I .I~i'!'Y
\I \ I \ 1\1 , I
A
l\
\
D Fig. 9.12
Arrangement
of shuttering
of head-frame
jib foundation
mounted successively on a supporting frame. the conductors (the permissible deviation is Before lifting an assembled head-frame, the not more than 10 mm); the corresponding design positions of the shaft axes should be points of external and internal curves should not deviate from the same level by more than marked on the pulley stage and the horizontal ties of the jib. The axes are fixed finally 10mm. A check of the correct arrangement of after they have been transferred onto the pulley stage of the erected head-frame. In that guide pulleys is done after the final fixation of case, the deviations of the axes of the pulley the jib and head-frame foundation. For this stage from the design positions must be not purpose, the layout axes of the shaft and hoist are transferred onto the landing stage. more than 25 mm in directions perpendicular to the hoisting axis and not more than The distance from the pulley rim to the 50 mm in the direction parallel to the layout axis (hoisting axis) should not differ from the design value by more than 10 mm hoisting axis. In cases when a head-frame is erected by for pulleys up to 6 m in diameter and by mounting individual sections one on top the more than 15 mm for those above 6 m in other, the survey work consists essentially in diameter. If it turns out that these distances exceed the specified values, the pulley must checking that each section has been mounted be readjusted. A check should then be made correctly. For mounting unloading curves, it is re- that the axis of the pulley is perfectly horiquired to transfer their layout axes. An error zontal (the permissible discrepancy between of arrangement of unloading curves in plan the elevations of the shaft ends is 1 mm). A check of the arrangement of a pulley on relative to conductors should not exceed 10 mm; the planes of the plates to which the a landing stage is done by the mine surveyor unloading curves are fastened should be in the following sequence. A cord is stretched along the hoisting axis perpendicular to the plane passing through
9.3. Surveying in Construction of Mine Hoists
(Fig. 9.13), from which horizontal distances to the pulley rim are measured (/1' /1,4 and /2). These measurements are then repeated after turning the pulley through 180°. The final results are found as their mean values, i. e.: a1=-
11+/1
a2=-
2
12+/2
2
If the distances a1 and a2 are not equal to each other, it is then required to calculate the angle'Y = a 1--a 2 n thrO1lgh whicJ, thp n1111p\T r
0--
,
.,'~
t'.."~J
Dp
must be turned (here D p is the diameter of the pulley). The position of the axis of the pulley shaft is determined by measuring the distances Si and S2from the shaft axis to the plumb bobs hung from wires which fix the shaft axis on the landing stage.
201
The horizontality of the shaft of a headframe pulley can be controlled by a frame level with a division value not worse than 20", hydrostatic level, or level with a compensator, which permit the measurements of the elevations of shaft ends with an accuracy up to 1 mm. The permissible deviations of the pulley axis from the horizontal are established by specifications on assembling particular hoists.
9.3.3.
Survey Control In Construction of Tower Head-Frames
The layout work for the construction of steel tower head-frames consists mainly in laying out the axes of columns of the first and upper stages of the frame structure. Before mounting steel structures on the
202
Ch. 9. Surveying in Mine Construction
foundation, a mounting network is marked whose points should be principally coincident with the centres of columns. For convenience, however, the reference points are shifted somewhat aside, which makes it possible to use them during the entire period of mounting work. The spacings between adjacent sides of the network should not differ from the design values by more than 5 rnrn. The upright position of columns is checked by the method of vertical plane with the use of two theodolites which are set up on two mutually perpendicular axes of columns or on axes of the mounting network. At each theodolite station and with two different positions of a telescope, the upper axial marks of a column are projected onto the column base. The displacement of the upper centre relative to the lower one is measured by a millimetre-graded staff; the permissible deviation is up to 15 rnrn for columns up to 15 m high and 0.001 of the column height (but not more than 35 mm) for higher columns. Mter mounting each stage of the frame structure, the schemes of column rows are drawn in the vertical projection in planes parallel to the two axes of the shaft (Fig. 9.14). As the frame structure is being erected, the shaft axes are laid out on each platform; upon the construction of reinforced concrete stage floors and arrangement of wall panels, these axes are transferred onto brackets. In the construction of cast-in-situ concrete tower head-frames in slip forms, the survey work consists in the following. The mine surveyor checks the dimensions, shape and position of the slip form which is assembled on the head-frame foundation. In the first place, he makes a check by measuring the distances from the shaft axes transferred onto the slip form to the plane of each panel that divides the slip form into sections; he also makes the levelling of the working floor in the corners of sections.
Upon erecting the walls to a height of 2 m, the shaft axes are fixed by brackets from the external and internal side of the head-frame. Later in the course of the erection of the head-frame, the position of the slip form is controlled by means of a vertical sighting device, preferably by an automatic zenithtelescope (Fig. 9.15). The instrument is intended for vertical projection of a point from the bottom upwards; it gives an error not .more than I mm per 100 m of vertical distance. The zenith-telescope or another similar instrument is sighted at sighting marks (Fig. 9.16) which are fastened on slip forms. Each sighting mark is essentially a square network drawn or printed on a transparent material (such as triacetate film). Sighting marks are fastened to wooden bars that support the working floor of the slip forms.
9.3. Surveying in Construction of Mine Hoists
Fig. 9.15 Zenith-telescope tective glass; 2- housing;
PZL (GDR): I-pro3 ~ telescope eyepiece;
4- focussing screw; 5- reading-olT microscope; 6- pivoting mirror; 7- clamp screw; 8- sighting screw; 9-base;
JO-tripod
203
The zenith-telescope is set up successively under each sighting mark, which makes it possible to control the verticality of the tower, hoisting compartments, and exterior walls. The arrangement of sighting marks depends on the shape of slip forms. The principal diagram of the arrangement of sighting marks for the construction of a tower head-frame of rectangular cross section is shown in Fig. 9.17. In order to determine the height of the working floor of the slip forms, control staffs are fastened at the corners of the shaft portion and external portion of a tower head-frame. These staffs are extended periodically as the slip forms are lifted. In addition, as the slip forms are advanced through every 20 m, the mine surveyor measures the height of the working floor relative to a bench mark concreted in the bottom portion of the headframe. If the heights of the working floor determined by the check measurements differ from the readings of the staffs on the slip forms by more than 20 mm, the staff readings are corrected. The results of control of the position of slip forms are presented as a scheme of matched
L
l
Fig. 9.16 Sighting mark: 5, 10, 15, 20, 25-num. bering of smaller scale; 55, 60; 65, 70, 75-num. bering of larger scale
Fig. 9.17 Principal diagram of arrangement of sighting marks for construction of head-frames of rectangular cross section: I-sighting mark; Land S -increasing numbers of larger and smaller scale; x. y-coordinate axes
~
204
Ch. 9. Surveying in Mine Construction
sections of the headframe constructed in intervals of 2-4 ill, which makes it possible to check the positions of the headframe walls and thus to take measures for preventing further deformations and deviations of the slip forms.
9.3.4.
Geometrical Elements of a Mine Hoist
For efficient and safe operation of a mine hoist, its individual elements should have the specified geometrical relationships. Geometrical elements of a single-rope hoist. The principal geometrical elements of a single-rope hoist are as follows.
5000 ---
The total hoisting height H is the vertical distance from the lowermost point of a hoisting vessel when this is in the lowermost position to the same point of the vessel in the uppermost position at the end of unloading (Fig. 9.18): H = h + ht + hb, where h is the depth of the shaft; ht is the distance from the zero stage to the lowermost point of the hoisting vessel at the moment of unloading; and hb is the maximum sinking of the hoisting vessel below the pit-bottom level during loading. The height of a head-frame Hhf is the vertical distance between the axis of rotation of the guide pulley and the zero stage: Hhf = ht + hv + hp + hz + O.75Rp
dia
5000
dia
/
"/'~
ii ;,,; ~~
~
,
'~ Level
, of discharae
--~
:" ,
~ " "
~. "',
> ~
~Receiving
stage
curves
'. "
,,,
"
,
level
5000 dia ~r~or
level
\,
~
~ ~ + ~
30000 Fig. 9.18
Geometrical
elements of single-rope
17500
mine hoist
205
9.3. Surveying in Construction of Mine Hoists
by the formulae:
Rp 11'-" ,
where
,
"
" ~
!.0.0
r
Lu ~'a, L~ ," R 17' Rdr
L
p
~~/&'/~~~
"'-' ~
./ ~
~
Fig. 9.19 Inclination angles of hoisting ropes
drum and pulley;
d..
L where hv is the height of a hoisting vessel; hi is the height of overlifting; hp is the elevation of the top pulley axis over the bottom pulley axis; and Rp is the pulley radius. The hoisting axis of a vertical shaft is the straight line that passes through the point midway between the two vertical hoisting ropes perpendicular to the axis of the main shaft of a hoisting machine. The hoisting centre of a single-rope hoist is the point that <;:oincideswith the projection of the rope axis onto the horizontal plane; for a double-rope hoist, this is the point of intersection of the hoisting axis with the straight line passing through the axes of the two vertical hoisting ropes. The centre of the shaft of a hoisting machine is a point on the axis of the main shaft midway between the internal edges of the rims of a drum (for single-drum machines) or midway between the internal edges of the rims of drums (for two-drum machines). The axial plane of a guide pulley is the straight line that passesperpendicular to the axis of a pulley shaft midway between the internal faces of pulley rims. The inclination angles of hoisting ropes are the angles
where H p is the height of the pulley axis above the zero stage; Hdr is the height of the drum axis above that stage; and L is the horizontal projection of the line connecting the axes of the pulley and drum. The terms A
A(D - Rdr -Rp 'I Loc
where Rdr and Rp are respectively the radii of the drum and pulley of the hoisting machine and Loc is the distance between the centres of the drum and pulley (0 and C). The length of a rope string is the distance between the point of run-off of the rope from the drum and the point of run-on of the rope on the guide pulley. It is distinguished between the string of an upper rope, Lu, and that of a lower one, L (see Fig. 9.19). Among various types of hoisting machines, those with cylindrical drums are the most popular, that is why the characteristics of rope coiling will be discussed for this type of machine. The distance between the internal faces of the rims of a drum is called the construction width and denoted Ldr. Various portions of the construction width of a drum serve different purposes and accordingly the following zones are distinguished (Fig. 9.20).
206
Ch. 9. Surveying
in Mine
Construction
cated: hemp =
Ldr
( H+ ~
30 +
n
)
(d
e)
The zone of working coils of a width hw which depends on the total hoisting height and can be determined by the formula:
h=cw
H
(d + e) 1tDdr
where H is the total hoisting height; d is the rope diameter; D dr is the drum diameter; and e is the spacing between the adjacent coils of a rope. The zone of reserve coils, br, which is needed to take on the additional length of a rope. Its width can be found by the formula: 30 b. = -=--(d + e) 1tl}dr where 30 is the additional length of a rope, ill, required for strength tests. The zone of friction coils, hfr , which is provided for stronger holding of the rope on the drum. This width is usually determined by three or five rope coils, i. e. hfr = n(d + e) where n = 3-5. The empty portion of a drum, hemp,is the difference between the construction width of a drum Ldr and the SUm of the zones indi-
where a is the distance from the hoisting axis to the pulley plane at the pulley axis; bl and b2 are the distances from the hoisting axis respectively to the farther and closer end of the working portion of a drum; and L is the vertical distance between the centre lines of the drum and pulley of the hoisting machine. In order to make the fleet angles on a pulley equal to each other (131 = 13u)'the axial plane of the pulley is oriented onto the centre of the working portion of the hoist drum. In cases when the axial plane of a pulley is arranged parallel to the axis of a mine shaft, the fleet angles of the rope on a pulley and drum ar~ equal to each other (al = 131, au = 13u).If the axial plane of a pulley is not parallel to the hoisting axis, the fleet angles
208
Ch. 9. Surveying in Mine Construction takes place when a,-au 1'=
2 cos q>
Substituting the expressions for a, and au into this formula, we obtain the condition that makes it possible to find in each particular case the magnitude a2 -al , i. e. the magnitude by which a pulley should be turned so that its axial plane will be oriented onto the centre of the working portion of a drum: +b2
- 2a
2Lcos
D,
Geometrical elements of a multi-rope hoist. The scheme of the most popular four-rope hoist with pulleys which deflect one system of ropes is shown in Fig. 9.22. The main geometrical elements of this hoist are as follows: the axes of hoisting ropes of a non-deflected rope system (2); the axes of intermediate rope strings between the drive pulleys and guide pulleys (9); the axes of hoisting ropes of a deflected rope system (6); the mean points of suspension devices (4, 5); the mean point of rope run-off from guide pulleys (3); the mean point of rope run-off from drive pulleys (1); the axis of the non-deflected rope system (8) which is a straight line connecting the mean run-off point and the mean point of a suspended balancing device; the axis of the on the pulley can be found by the formulae: deflected rope system (7) -a straight line connecting the mean run-off points and the 13,= a, -ycos , 13u= au + ycos mean point of a suspended non-balanced where y = [(at -a2)/Dp] p' is the horizontal device; the hoisting axis v-v which is a angle of the turn of a pulley relative to the horizontal line passing perpendicular to the hoisting axis; at and a2 are the distances from main shaft axis through the mean run-off the hoisting axis to the pulley plane at the point on drive pulleys; the vertical axes of the ends of the horizontal diameter of a pulley; hoisting compartments of a tower head-frais the angle of inclination of a hoisting rope; me; and the angles of bending of hoisting and D p is the pulley diameter. ropes by guide pulleys. For normal operation of pulleys, which In multi-rope hoisting machines, it is disprevents one-sided wear, the fleet angles on a tinguished between the following fleet angles: pulley must be equal to each other, which (a) the fleet angles of descending ropes on
(c)
10
3
\
9
I~-
L.u
~-
-
J1~
-/10 ~ 11 Fig. 9.23 Geometrical elements and parameters of multi-rope hoisting plant: (a) and (6) vertical projections; (c) plan view; 1-drum of drive pulleys; 2, 3-mean run-off points of ropes on drive and guide pulleys; 4- guide pulleys; 5 -level of guide pulleys; 6- numbers of ropes; 7- bunton; 8- hoisting vesselclip; 9-conductor; 10-mean point of suspension device (clip); 11- hoisting vessel; l-length of intermediate rope string; h-elevation of main shaft axis above guide pulley shaft axis; hi, hl -elevation of main shaft axis and guide pulley shaft axis above guide pulley stage level; h3' h4 -elevation of main shaft axis and guide pulley shaft axis above mean points of suspension devices; R"p. Rgp- radii of drive and guide pulleys 14-1270
j
210
Ch. 9. Surveying in Mine Construction
drive pulleys, ai, Fig. 9.23 (an angle formed by the axis of a rope with the plane of a drive pulley); (b) the fleet angles of descending ropes on guide pulleys, Pi (an angle between the axis of a descending rope and the plane of a guide pulley); and (c) the fleet angles of intermediate rope strings on drive pulleys (~J and guide pulleys ('1'J. In addition to fleet angles, of essential importance are also the angles of deviation from the vertical axis of symmetry of the system of ropes and the angle of contact (wrapping angle) of a rope on a guide pulley, 11 (see Fig. 9.23). The elevated fleet angles of ropes are the main cause of quick wear of a pulley lining, while the deviation of a rope system from the vertical may cause increased horizontal loads exerted by hoisting vesselson the shaft equipment. The fleet angles of ropes on drive and guide pulleys of multi-rope hoisting machines must not exceed 30-40'. The control of the relation between the main geometrical elements of hoisting machines of this type consists essentially in observing the following requirements: (a) the axes of the main shaft and guide pulley shaft should be horizontal and parallel to one' another; (b) the axes of main hoisting ropes should be perfectly vertical; (c) the drive and guide pulleys of a rope string should lie in the same vertical plane; (d) the straight line connecting the mean run-off point of a rope and the mean point of a suspension device should lie on the vertical axis of a hoisting compartment; (e) drive and guide pulleys should have the same diameters corresponding to the design specifications; and (1) the angles of deflection of ropes by guide pulleys should be within the limits of 8-15°. The experience of operation of multi-rope hoists has demonstrated that the design dimensions of these machines should be observed with a high degree of accuracy, since their deviations may influence substantially the operating conditions of a hoisting ma-
chine, lead to uneven wear of a pulley lining, and cause uneven loads on ropes and elevated forces acting .on conductors. The main causes which may lead to the distortions in the relation between the geometrical elements and deviations of main ropes from the vertical are as follows: (a) inaccurate assembly of a hoisting machine and equipment; (b) wear of a pulley lining, and (c) displacement of a hoisting machine or equipment due to underworking a tower head-frame or mine shaft. 9.3.5.
Survey Work During of Hoisting Plants
Mounting
Survey work for mounting a hoisting plant consists in transferring the hoisting axis and the main shaft axis into the hoisting plant building and laying out the foundation for the hoisting machine and its elements. The layout work is started by transferring into nature the point of intersection of the axis of the main shaft and the axis of the hoist shaft. Upon erecting the walls of the hoisting machine room to a height of 1-1.5 m above the ground, the axis of the main shaft and the axis of the hoisting machine shaft are transferred by means of a theodolite inside the building and fixed by brackets on the inner walls. Mter erecting the building walls to the full height, a second row of brackets (mounting brackets) is built in at a height somewhat below the ceiling floor level. The axial points are transferred onto these brackets from the lower ones by a theodolite or plumb bobs. The hoisting axis and the machine shaft axis are laid out twice. The mean direction angle of the main shaft should differ from the design value by not more than 2', and the angle between the two fixed perpendicular axes should differ from a right angle by not more than 1'. The distance from the centre of the mine shaft to the machine shaft should differ from the design value by not more than 100 mm, and the side displacement of the
9.3. Surveying in Construction of Mine Hoists
point of intersection of the hoisting axis and machine shaft axis, by not more than 50 mill. The permissible deviation of the machine shaft axis from the horizontal position is established by the specifications for hoisting machine assembly. Mter laying the supporting frame of a hoist into its place, it is checked for horizontality and correct position relative to the hoisting axis and the main shaft axis of the machine. The position of the frame along the height is checked by levelling the corner points of the frame in plan relative to the axes by means of plumb bobs. The deviation of the frame from its design position should not exceed 10 mill in plan and 100 mill vertically. The highest difference of elevations of the corner points of the frame should be not more than 15 mm. The arrangement of the main shaft bearings is checked along the height by levelling the lower points of their internal surface and in the horizontal plane, by means of plumb bobs hung from a cord stretched between the axial brackets of the main shaft of the hoisting machine. The deviations of bearings in plan and vertically should not exceed 1-2 mill. The actual position of the shaft of the hoisting machine is checked by the same method as the position of bearings. Mter the completion of the machine assembly, the position of the drum relative to the hoisting axis is checked by hanging two plumb bobs and measuring the distances from the plumb bob lines to the drum rims. 9.3.6.
14.
traverse A-I-2-3 (Fig. 9.24) is run from the layout axis of the main shaft which is taken as the initial direction. The point 4 of a traverse is fixed approximately on the hoisting axis near the zero stage. The angle 2-3-1 is laid up at a point 3 (from the side 3-2), which is calculated so that the direction 3-1 is perpendicular to the axis of the machine shaft. This direction is transferred onto the pulley stage and fixed by a wire I-II. At the pulley stage, the distances a1, a'1' a2 and a~ from the wire I-II to the external edges of pulley rims at the ends of a horizontal diameter are then measured. The distance 1 between the external faces of the pulley rims is also measured. In the machine room building, there are measured the distance between the internal faces of drum rims ho, the width of empty portion of the drum h and h', the width of the working portion hw and h;., the +x
I
'~~ ""\ ~ ~,
~
SItB ~~
Survey Work for Checking the Geometrical Elements of a Single- Rope Hoisting Plant
After the assembly of a hoisting plant, it is required to check the horizontality of the axes of machine shafts and drive pulleys, the positions of the axes of hoisting ropes relative to conductors at the level of the zero stage, and the fleet angles of hoisting ropes on drums and pulleys. For this purpose, a theodolite
211
/.
2
/
Fig. 9.24 Theodolite traverse for checking of relation between geometrical elements of hoisting plant
212
Ch. 9. Surveying in Mine Construction
total width of the zone of friction coils and reserve coils (bfr + br) and (bfr + b~)for twodrum machines; for single-drum and bicylindrical machines, it is required to measure the total width of the empty portion and of the zones of friction coils and reserve coils (b + bfr + br) and (b' + bfr + b~)and the total width of the drum, B. Taking the system of coordinates with the axis of machine shaft being the y-axis and the axis of symmetry of the machine, the x-axis, it is now possible to calculate the coordinates of theodolite traverse points and of the axes of ropes and conductors. For each rope, there are determined the maximum exterior (a.x) and interior (ain) fleet angles on the drum of the hoisting machine: (a) for a hoisting plant with two cylindrical drums and pulleys: b.x -a, a -bin , a.x= p, ain=-p L L (b) for a hoist with one cylindrical or bicylindrical drum: b.x -a, bin + a , Uin = u"x = .p -:--p 1 L
The distances a and a' for hoisting machines of the first and second type are found by the formulae: a = 0.5(a1 + a2) + 0.5/ :t c a' = 0.5(a'1+ a~) + 0.5/ :t c where c is the distance between the transferred I-II direction and Ox axis, which is equal to the ordinate of point I. For hoisting machines of the third type, the distances a and a' are determined by the formulae: a =10.5(a1+a2)+0.5/-cl a' = 10.5(d1+ a~) + 0.5/-
cI
The inclined distance L (of a rope string) can be found from the expression
L=~ where Lo = x.. -D J2 (here x.. is the abscissa of a rope in the adopted system of coordinates and D p is the pulley diameter); Ah is the height difference of the pulley axis above that of the machine shaft. Since the axis of a pulley may turn out to be unparallel to the machine shaft axis, the fleet angles on the pulley may respectively differ from those on the drum. For pulleys, where p' = 3440'; hexand hin are the distances we determine the two maximum fleet angles from the axis Ox to the rope on the drum in of ropes: an exterior angle ~ex and interior its extreme (exterior or interior) positions; a is the distance from the axis Ox to the axial angle ~in' by the formulae: plane of the pulley; and L is the inclined ~ex= a ex -'Y cos
olstlng
axis
tan
for single-drum and cylindrical machines (see Fig. 9.21h and c) hex= O.5B -hfr h,- = 0.5B -(h'
+ h: + h'..-)
,
y
=
~
p
an
.
lS
t h
e
9.3. Surveying in Construction of Mine Hoists
9.3.7.
Survey Work for Checking the Relation Between the Geometrical Elements of a Multi-Rope Hoisting Plant
Surveying a multi-rope hoisting plant is carried out in order to determine the angles of deviation of the axes of rope systems from the vertical in projections onto the axes x and y (ex, ey, mx' and my),fleet angles of the main and intermediate ropes on drive and guide pulleys (a, ~,
Fig.
9.25
Determining
radii
of drive
pulleys
213
One of the probable methods for determining the radii of drive pulleys consists in the following. A line parallel to the main shaft axis is fixed in the machine room, after which the distances from that line to hoisting ropes are measured. The point A is fixed on the floor of the machine room (Fig. 9.25). A theodolite is set up on that point and sighted roughly along the rope line (direction AaIl). The readings aI and all are taken on two staffs set up in points I and II horizontally and tangentially to the machine shaft. The distances SI and SII from the point A to staffs I and II are then measured. The shaft is measured circumferentially in the points I and II (CI and CII) and its radii are calculated by the formulae rI = cJ21t and rIl = cIJ21t These radii and the measured values aI and all make it possible to take readings on the staffs with the theodolite telescope sighted parallel to the main shaft axis: sIlaI -sI(aIl + rIl -rJ bI=
SII-SI
Ch. 9. Surveying in Mine Construction
214
SIl(aI + rI -rIJ
-sIall
bll=
SII- SI The vertical hair of the telescope is sighted at the reading bll of a staff, provided that the sighting line passesthrough the reading bI.1f it turns out that (bll + rll) -(bI + rJ is less than 0.5 mm, the direction parallel to the main shaft axis is fixed on a bracket or plate (point B) concreted in the wall of the machine room. Mter that, the telescope is sighted at the point B and the readings 15,16,17,and 18 are taken, with an accuracy to 1 mm, on a horizontal staff set successively to ropes 5, 6, 7, and 8 in points of their run-off from pulleys. The radii of drive pulleys are calculated by the formulae: R5 = bll + rll -(b5 + rr) R6 = bll + rll -(b6 + rr) R7 = bll + rll -(b7 + r r) R8 = bll + rll -(b8 + rr) where r r is the radius of the rope. Fixation of auxiliary axes on the measuring level and determination of coordinates of reference points. The points which fix auxiliary axes are called referencepoints. They are laid off on a cross-piece below the machine room where the ropes descending into the mine shaft are easily accessible. The hoisting vessel is sunk into the lowermost position, and a staff is laid on the m~asuring level to the non-deflected ropes (5, 6, 7, 8, see Fig. 9.26). The shortest distances from the staff to plumb bobs 5 and 8 are then measured. Then, using the calculated radii of drive pulleys, the distances from the main shaft axis to the staff axis are calculated. The staff is then placed in a position so that its axis can be parallel to the main shaft axis, and this direction is fixed by points C and D. Using the method of corner sections, points A and B are marked from these points. They determine the direction parallel to the line of deflected ropes (I, 2, 3 4). Non-parallelity
between AB and CD should be not more than 10'. The coordinates of points A, B, C, and D are determined by ordinate surveying of non-deflected ropes, with the hoisting vessel in the lowermost position, and by measuring the sides and diagonals of rectangle ABCD. The distances from the rope axes to the staff axis and the staff readings corresponding to the projections of the rope axes onto the staff are determined in the following manner. The staff is fixed on points C and D. After an extreme rope, say 5, has dampened, an angle is placed to it (Fig. 9.27a), and an ordinatometer is placed to the staff and moved to the angle. The reading /51is taken by means of a rule against the edge of the angle and the reading! 51is taken on the staff against the ordinatometer edge. The angle is turned into another position (Fig. 9.27b) and new readings 15II and !5II are taken. Similarly, the readings 151II,15IV'!51II'and!5lV are taken in a third and fourth position of the angle (Fig. 9.27c and d). The positions of other ropes are determined in a similar way. The readings are reduced to the staff axis
9.3. Surveying in Construction of Mine Hoists
If aCD::!:90° < 10', then Xc = Xr5 and YC= = v -f 5' where v is the staff reading corresponding to the centre of a hole for the fixation of the staff in the point C (see Fig. 9.27). The angles of rectangle ABCD are found
and rope axes by the formulae: liI +
lill
+
2d -lillI
-liIv
'=k+ 4
1; =
J;I
+ J;II
+J;III
+ J;IV
4
215
where i is the number of a rope; k is the distance from the staff axis to the beginning of the ordinatometer scale; and d is the length of the ordinatometer scale. The values of abscissaeon the staff can be found from the expressions: x r5 = -R 5 + 15' x r6 = -R 6 + 16 --R + 1 --R + 1 Xr7 -7 7' Xr8 -8 8
by solving the triangles into which the rectangle is divided by diagonals AD and CB. Taking the coordinates of the point C as the initial ones and knowing the direction angle aCD' it is possible to determine the coordinates of points A, B, and D. Determination of the angle of turning of guide pulley shaft axis relative to the main .. shaft axis. In order to determIne the angle &,a staff is fixed on points A and B laid up
where R is the radius of a drive pulley. The direction angle ofa side CD (staff axis) can be found by the formula: (x -x) r5 r8 p' aCD = 90° + .
parallel to the line of deflected ropes (Fig. 9.28). Two plumb bobs 01 and O2 are hung at one end of the shaft in a point IV, and a metal rule is laid below them perpendicular to a staff AB. A series of readings n1, n2' n3'
f8 -f5 The
coordinates
calculated
x,
Xc = Xr5 + (V -f5)tan(aCD Yc = v -f5
y
of
a point
by the formulae:
+ 15tan(acD
-90°) -90°)
C
are
n4' etc., and m1, m2, m3, m4, etc. are taken under the centres of plumb bobs, and their mean values are found (n and m). The distance CIVfrom the metal rule to the axis of the staff AB is measured, after which the distance from the shaft axis to the staff axis AB is
216
Ch. 9. Surveying
in Mine
Construction
Staff
Fig. 9.28
Determining
angle of turning
of guide pulley
shaft axis relative
AHI-II
to main shaft axis
+ Arl-ll
°II-
p' SI
where Arl-Il is the difference of radii of the shaft in the measured sections (in points I and II) and SI-II is the distance between points I and II. The angle of inclination of the axis of guide pulley shaft, OIV-III is determined by a similar formula. Determination of the coordinates of rope axes on the measuring level. The coordinates of ropes in two extreme (upper- and lowermost) positions of hoisting vesselsare needed (dIv + d;v) -(dIll + d;lI)0' + (a.D -900) E= for determining the angles of their deviation. 2s The coordinates of plumb bobs are deterwhere s is the distance between points III and mined from reference points CD and AB on IV. the measuring level (see Fig. 9,26) by means Determination of the angles of inclination of of a staff-type coordinatometer. the axes of the main shaft and guide puUey With the hoisting vessel in the lowermost shaft. These angles can be determined with position, we determine the coordinates of the the aid of hydrostatic levels by measuring the axes of non-deflected ropes (Xi' Y;) and those height difference L1Hbetween the end points of of deflected ropes (xr, Yr). Similar measurethe axis of a shaft. The inclination angle of the ments are made with the hoisting vessel in main shaft axis is calculated by the formula: the uppermost position (respectively x;, Y;
The rule is displaced through several centimetres, and a new distance d;v is determined, which should differ from the fornler by not more than 2 mill. Similarly, two distances from the end III of the shaft of guide pulleys to the staff axis AB are determined (dIll and d{lI). The turning angle E is calculated by the formula:
9.3. Surveying in Construction of Mine Hoists
217
measurements; Yr and Y~are the ordinates of the axes of deflected ropes respectively in the lowermost and uppermost positions of a hoisting vessel; Xr and X~are the abscissaeof the axes of these ropes; h2 is the elevation of the axis of the guide pulley shaft above the measuring level; h4 is the elevation of the axis of the guide pulley shaft above the adjacent point of a suspension device; and R9,dand Rg is the design radius and actual radius of guide pulleys at measurements. Thefleet angles ofmain ropes can be found by the formulae: on drive pulleys: a = ey + 8 + A., on guide pulleys: ~ = my + 8' + Ar where 8 and 8' are the inclination angles of the main shaft axis and guide pulley axis and Ai and Ar are the corrections for the position of balancing devices, which can be determined by the formula:
where n is the number of ropes in a system; Yi and Y; are the ordinates of the axes of non-deflected ropes respectively in the lowermost and uppermost positions of a hoisting vessel; hi is the elevation of the main shaft axis above the measuring level; xi and x; are the abscissae of the axes of these ropes; h3 is the elevation of the main shaft axis above the mid point of a suspension device; Rdr,dis the design radius of a drive pulley; Rdr is the actual radius of a drive pulley at
s -s. A=---2 h where s is the distance from the system axis to the axis of a rope at the level of balancing devices; Si is the distance from the system axis to the axis of a rope in a run-off point; and h is taken equal to h3 for determining Ai and equal to h4 for determining Ar. Thefleet angles of intermediate rope strings can be found by the formulae: on drive pulleys: t1.y" .
218
Ch. 9. Surveying in Mine Construction
11is the wrapping angle of a rope on a guide pulley; E is the angle of turning of the axis of the guide pulley shaft relative to the main shaft axis; ° and 0' are the angles of inclination of the axes of the main shaft and guide pulley shaft; and 1 is the length of an intermediate rope string: 1 = [h -(Rg + xr) tan 11] where h is the height difference between the axis of the main shaft and that of the guide pulley shaft and Xr is the abscissa of the axis of a deflected rope. The permissible values for the indicated angles are as follows: Ox,Oy,rox and roy not more than 0°15'; angle of inclination of the main shaft axis, 0, not more than 0°05'; angle of inclination of the axis of the guide pulley shaft relative to the direction of the main shaft axis, not more than 0°45'; fleet angles a and ~, not more than 1030' and those for intermediate strings (
dimensions of the shaft, the arrangement of equipment and hoisting vessels, the line of vertical section along which records are being made, and conventional symbols of rocks and lining materials. The second page contains data on the course of shaft sinking. On the third and subsequent pages, a vertical section of the shaft on a scale 1/100 and sketches of shaft elements are drawn. Mine surveying work during the sinking of a shaft can be divided into two periods: (I) initial period during which the shaft is provided with mining (heading) equipment and the shaft collar is constructed and (2) shaft sinking proper. 9.4.1 .Survey Work During the Initial Period of Shaft Sinking
The survey work at this stage consists in transferring the axes of temporary buildings and structures into nature, which is required for arranging a layout network and marking 9.4. Survey Work During Sinking the axes of a shaft according to the dimenof Vertical Shafts sions indicated on the general layout and on The construction of mine shafts include.s the drawings of the arrangement of mining sinking a shaft and the arrangement of a equipment. During the mounting of hoisting lining and equipment. The main object of machines, special attention should be given mine surveying service in the construction of to checking the arrangement of the hoist mine shafts is to ensure the design position of frame relative to the predetermined hoisting the shaft and its elements. To achieve this, the axis and machine shaft (drum) axis, as wen as mine surveyor has to perform the following to correct arrangement of the shaft of the procedures: to transfer the axes of hoisting mine hoist. The deviation of the hoist frame plants into the driven shaft; to assign the from the hoisting axis should not exceed design direction to shaft sinking; to transfer 50 mm; the deviation of the elevation marks and mark the layout net for the assembly of of frame corners from the design level should hoisting machines; to make check measure- be not more than 300 mm, and the elevation ments in the shaft; and to layout shaft marks of corners should differ from one workings and chambers. another by not more than 15 mm. The deAll mine surveying measurements are re- viation of the hoist shaft axis from the axis of corded in a register which is the main docu- a layout network should be not more than 2', ment reflecting the actual state of the const- the height difference on one end of the shaft ruction of a shaft (Fig. 9.29). The first page of above the other being not more than 0.001 of the register gives the design section of the the shaft length. shaft on a scale 1/50 and the principal The sinking frame should be mounted
9.4. Survey
Work
During
properly relative to the shaft axis; the displacement of the pulley stage in the horizontal plane from the design position should be not more than 60 mm. The layout of the pit for the shaft collar, construction of a cap, and the arrangement of
Sinking
of Vertical
Shafts
Intermediate shoe at -25.5 m
219
a zero frame are carried out relative to the axial lines of the shaft. The displacement of the zero frame axes relative to the design position should not exceed 5 mm, the deviation of the elevation marks of the frame from the design position should not exceed 50 mm,
220
Ch. 9. Surveying in Mine Construction
and the difference of elevation marks of the support points of the unloading bedframe should not exceed 5 mm. Since the zero frame defines in nature the contour of the shaft cross section, its dimensions and shape should correspond strictly to the design cross section of the shaft. The centre of the shaft is fixed on the zero frame, and the directions of the shaft axes are indicated by marks. The positions of the shaft centre and axial marks are determined twice by independent measurements; the discrepancy between the measurements should be not more than 5mm. The directions of the shaft axes are then transferred from the zero frame into the shaft mouth and fIXed by marks on brackets built in at a distance of 50-100 mm from the walls of the shaft lining. Elevation marks are transferred onto the axial brackets. The displacement of the marks from the axial line should not exceed 2 mm. If upon sinking the shaft mouth to the design level it turns out tpat the actual geological section corresponds well to that designed, permission is given to make the first circular cut for a foundation CUl;b. Otherwise, the problem should be coordinated with the designer. Upon sinking the shaft to the first foundation curb, the position of the shaft along the depth and in the horizontal plane is checked by taping the vertical distances and the distances from the zero frame to the cut floor. The position of the shuttering for the foundation curb is checked in the vertical and horizontal plane by measuring the radii from a temporary central plumb bob to the exterior surface of the shuttering, and the distances from the frame to curve pieces. Upon the construction of the shaft lining, the zero frame is replaced by the main heading frame which is placed .onto the permanent lining of the shaft mouth and oriented properly relative to the centre and axes of the shaft (Fig. 9.30). Deviations above 20 mm
Fig. 9.30 Main heading frame: l-opening for bucket; 2- rescue ladder; 3- ventilation column; 4- concrete pipeline passage; 5- compressed air column; 6-central plumb bob
are not allowed. The centre of the shaft is transferred instrumentally from the axial points onto the heading frame, and the guide pulley of the central plumb bob is fixed so that the plumb bob line is not displaced from the shaft centre by more than 5 mm. The survey control of shaft sinking is performed from the central plumb bob and side plumb bobs suspended from the main heading frame. 9.4.2.
Survey Work During Sinking a M ine Shaft
In shaft sinking by the conventional drilling-and-blasting method, the survey work consists in checking the positions of vertical directions, determining the scope of the mining work performed, locating the places and dimensions of rock inrush and backfilling behind the lining, and checking the position of travelling forms and the dimensions of the shaft section and vertical walls of a lining. For the horizontal and vertical control of shaft sinking, there is formed a geometrical basis as a system of plumb bobs, light
5. Survey
Work
for Arranging
indicators or projection meters. Plumb bobs are mostly employed for the purpose. Their number and arrangement depend on the cross-sectional shape of the shaft and the arrangement of mining and hoisting equipment in it. For instance, a single central plumb bob is employed in shafts of a circular cross section, four plumb bobs hung at a distane of 20-30 cm from the shaft walls, in shafts of a rectangular cross section. In shafts of an oval cross section, two plumb bobs are suspended near the walls at each axis of an ellipse. The positions of plumb bobs during sinking a shaft should be checked at least once a month. The deviations of vertical directions from the design values are checked by making measurements from the axial points fixed in the shaft mouth or on the main heading frame. These measurements can be made by using plumb bobs, light indicators or projection meters. In order to minimize errors, the cables of projection meters should be fixed in every 300 or 400 m. The error in the position of fixation points of light indicators relative to the previous level should not exceed 15 mill. The state of shaft walls is controlled by measuring the radii from the central plumb bob to walls in vertical intervals of 3-4 m. The measured results are used to calculate the actual cross-sectional area of the shaft which should not differ from the design value by more than 4-10% for shafts up to 20 m2 in cross-sectional area, by 3-8% for those 20-40 m2 in area, and by 2-5% for those above 40 m2 in area. The permanent lining of vertical shafts is constructed by means of travelling forms which are placed into the working positions relative to the central plumb bob. The position of the travelling forms and shaft walls should be checked by the mine surveyor at least after every three or four travel cycles. The correct position of the travelling forms relative to the central plumb bob is checked
of Shaft
Equipment
221
at least in eight points around the periphery of the forms. The vertical axis of the forms should not deviate from the mean position of the plumb bob by more than 20 mm. The vertical position of the forms is checked by hydrostatic level with an accuracy not worse than 10 mm. The errors of measurement of distances from the central plumb bob to the forms of a shaft lining should not exceed 10 mm. For cast-in-situ concrete and reinforced-concrete linings, the deviations of radial distances from the centre should be not more than 50 mm. A concrete-tubbing lining is built from the top downwards, support tubbings (crib seats) being placed after every 20-24 m. They are placed in the presence of the mine surveyor who checks that the distances from the central plumb bob to the internal faces of tubbings differ by not more than 10 mm from the design value. All placed tubbing crib seats and each tenth ordinary tubbing should be controlled by mine surveying. The plan position of a tubbing ring is controlled by measuring the distances from the central plumb bob to selected points at tubbing joirits. Vertical control is effected upon mounting 6-8 rings. If it turns out that the deviation of a tubbing column from the vertical is more tban 30 mm, the lining should be corrected. 9.5.
Survey Work for of Shaft Equipment
Arranging
The main task of the mine surveyor during the arrangement of shaft equipment is to control that buntons and conductors are mounted strictly in their design positions. The equipment of a mine shaft is a complex of structures and elements which ensure correct motion of hoisting vessels.The main elements of equipment are conductors and buntons; the latter are divided into the main and auxiliary ones depending on their position in the shaft. The main buntons are
222
Ch. 9. Surveying in Mine Construction
built in into the shaft lining at both ends, whereas the auxiliary ones are either fastened between the main buntons or attached at one end to a main bunton and built in at the other end into the lining. The main bunton arranged in the centre of a shaft or near it is called the central bunton. The combination of main and auxiliary buntons located in the same horizontal plane is called a bunton stage. The distance between adjacent bunton stages is called the pitch of equipment. Conductors (of the rigid or rope type) are fastened to buntons. The arrangement of equipment in a shaft may be done by a consecutive or combined scheme. In the former case, first all buntons are mounted to the entire depth of the shaft, after which conductors are fastened to them. In the latter case, conductors are suspended upon mounting three or four bunton stages.
(a)
(b)
The survey work during the arrangement of the equipment of a vertical shaft includes three stages: (I) the control of preparatory work and the arrangement of hoisting and mining equipment; (2) the control of the arrangement of buntons and suspension of conductors; and (3) the final control of the accuracy of mounting the equipment by making the profile survey of conductors and buntons. At the first stage, the profiles of the shaft and drawings of cross sections at various levels are prepared, and it is checked that the dimensions of buntons, points of connection of buntons, etc. correspond to the design specifications. Upon sinking the shaft, the profiling of the shaft walls (control survey) is carried out in order to determine the minimal gaps between the shaft lining and the most protruding portions of hoisting vessels. The
from Geological section ~DeptliMouth level +193.5 m Soil
Sections
surface, m
through
II
O
shaft
walls
III
IV
0
5
+30
10
+10
15
-10
20
+10
25
+20
0
Sand
30
+10
0
35
+10
-10
Floating earth
40
0
0
Clay shale
45
0
0
Sandstone
50
0
55
0
60
-10
65
-10
mm
Clay
~,
~ --
~ ~
Shale Coal
Fig. 9.31 Profiling of walls of vertical mine shaft: (a) arrangement of plumb bobs; (b) profiles of walls
~
;[;1 Sandstone
70 ,i~\;~(i~
-40
~
9.5.
Survey
Work
for Arranging
results of profiling are used for revealing the lining defects and making decisions on changing the scheme of equipment or eliminating the detected curvatures of the shaft. The profiling survey is done by measuring the distances from plumb bobs to shaft walls. The number and arrangement of plumb bobs are determined by the cross-sectional shape of the shaft and the arrangement of hoisting vessels in it (Fig. 9.31a). The measuring interval is usually taken equal to the pitch of equipment. The results of profiling are used for plotting the vertical profile of the shaft wall. The profile is drawn on a vertical scale (along the plumb bob line) of 1/100-1/200 and horizontal scale 1/10-1/20 (Fig. 9.31b). At the preparatory stage, the mine surveyor should also compile the scheme of arrangement and fastening of plumb bobs in the shaft, work out templates for the arrangement of buntons, and control the correct positioning of winches, pulleys, buckets and other mining and hoisting devices. At the second stage, the mine surveyor controls the design dimensions of the first bunton stage and then checks with especial care that the first bunton stage is mounted properly in its place, since plumb bobs will be later hung from it to control the positions of subsequent bunton stages. The correct mounting of the first bunton stage is controlled by measuring the distances from the shaft axes to the ends of each bunton, sleepers, and the points of connection of buntons and by levelling the ends of each bunton by a striding level. The displacement of the axes of buntons in the horizontal plane should not exceed 3 mm and the difference of the elevation marks of bunton ends, 5 mm. The number and arrangement of plumb bobs in a shaft depend on the scheme of equipment and arrangement of buntons. With the consecutive scheme of arrangement of equipment, plumb bobs are arranged against sleepers;with the combined scheme, they are arranged so as not to obstruct the placing
of Shaft
Equipment
223
Fig. 9.32 Schemes of plumb bobs for arrangement of shaft equipment
of conductors. The distances from the suspension points of plumb bobs tobuntons and side faces of conductors should not exceed 200 mm. A scheme of suspension of plumb bobs 1-6 for arranging the rigid equipment of a shaft of a unified cross section is shown in Fig. 9.32. The survey work for controlling the placing of buntons and suspension of conductors consists in checking the vertical distances between bunton stages, the positions of conductors and buntons relative to the horizontal axes of a shaft, the points of junction of buntons in a stage, and the positions of
~
224
Ch. 9. Surveying in Mine Construction 3~
p:C9
51
2F
D
lA 6
A-A
~
'r==' ~
88:z.tzA
Fig.9.33 Templates for arrangement of shaft equipment: I. 2. 3-spacing templates; 4. 5-vertical templates for marking holes for buntons; 6. 7- horizontal templates; 8- templates for correct placing of buntons relative to plumb bobs
plumb bobs proper. Since the positions of the characteristic points of the shaft equipment are repeated from one bunton stage to another, it is possible to employ templates for the control of mounting operations. The number and design of templates are chosen depending on the arrangement of buntons and plumb bobs and the technology of arrangement of the equipment. The templates are
usually made from steel sheets, angles or tubes. According to their application, templates can be divided into the following groups: (1) templates for marking the lengths of buntons and places of location of sleepers or mounting holes; (2) templates for placing the buntons at specified vertical distances from one another (spacing templates); (3) templates for
9.5.
Survey
Work
for Arranging
marking holes for buntons; (4) templates for coordinated arrangement of buntons in a stage (horizontal templates); and (5) templates for correct placing of buntons relative to plumb bobs. Some types of templates for these purposes are illustrated in Fig. 9.33. After mounting the equipment of a vertical shaft, the surveying of conductors is carried out in order to compile the profiles of conductors, buntons, and shaft walls. In this country, vertical shafts are surveyed by means of a complex for automatic control of the parameters of the equipment and lining. The complex comprises stations for the profile surveying of conductors, apparatus for the surveying of shaft walls, an instrument for measuring the safe spacings in mine shafts, apparatus for measuring the wear of conductors, and straightening instruments for the control of conductors. The stations are provided with instruments for measuring the angles of deviation of conductors from the vertical and distances between conductors and for checking the mutual arrangement of conductors in the shaft. Two instruments for measuring the vertical deviation angles are arranged at an angle of 90° to each other and mounted on carriages (Fig. 9.34) which are run along conductors. In this way, the angles of deviation of conductors in two mutually perpendicular planes are recorded. Records are made on 35-mm perforated photographic film together with the base line and elevations of buntons. The accuracy of measurements is 30" and the measuring range, :t20'. The instrument for measuring the distances between conductors is essentially a mechanical recorder fastened on one of the sections of the carriage. Records are made on a paraffin-impregnated tape on which one stylus draws the curve of deviations of the actual distances between conductors from the rated measure, whereas another stylus draws the base line. The elevations of buntons are also marked on the tape. The horizontal scale of 15~1270
of Shaft
Equipment
225
Fig. 9.34 Carriage: 1- box frame; 2 -detachable covers; 3- springs; 4- telescopic rod; 5- clamp; 6- supports; 7- auxiliary safety rollers; 8- manual winding mechanism; 9-axles; 10-shackles
records of distances is 1I 1 and the vertical scale, 1/500; the measuring accuracy is :to.5 mm, the range of deviations of conductor spacings from the rated value is :t40 mm, and the range of measured distances, 350-3000 mm. The speed of motion of the carriage on conductors is up to 0.8 mls and the largest depth of shafts which can be profiled by this complex is 1700 m. The survey of conductors of a single compartment of a shaft 500-800 m deep requires only 0.5-1 hour. The photograms of deviation angles obtained in this way are processed in the office to construct the profiles of conductors. This is done by means of a semiautomatic integra-
Ch. 9. Surveying in Mine Construction
Fig. 9.35 Integrator
Fig. 9.36
Aligning
inclinometer
9.5.
Survey
Work
for Arranging
",1
of Shaft
Equipment
227
partment, etc. The measuring range is from 0 to 500 mill and the accuracy of measurements is I5 mill. The apparatus illustrated in Fig. 9.38 is designed for continuous measurements of the wear of conductors and spacings between conductors. It contains two mechanical recorders which simultaneously register the degree of wear of two conductors separately at each side of each of them and the spacings between the conductors. The apparatus can be used for measurements of conductors in combination with a station. In that case, the apparatus is connected to a carriage on which the instruments of the station are mounted.
Fig. 9.37 Profiling instrument: I-photographic camera cap; 2-measuring drum; 3-lock screw; 4- wide-angle objective; 5- handle; 6- illuminator
marked on 35-mm photographic film. The distance range of the instrument is from 0 to 3000 mm; the scale of recorded distances to the shaft walls is 1/25 or 1/50; and the root-mean square error of measured distances is I 5 mm in the range from 0 to 500 mm and I 10 mm in the range from 500 mm to 3000 mm. The instrument for measuring the gaps between the protruding portions of hoisting vessels and elements of shaft equipment is based on the same principle as the instrument for profile surveying, but has substantially smaller dimensions and mass. It is mounted on the top of a hoisting vessel or in a cage. The instrument can be set up for measuring the gaps between the guide paws of a hoisting vessel and equipment elements; the distances to the lining, tube stand, cables, ladder com15.
Fig. 9.38 Apparatus for continuous measurements of wear of conductors and spacings between conductors
Ch. 9. Surveying in Mine Construction
When used individually, the apparatus is fastened to a hoisting vesselor to the hoisting cable of a mine hoist. The measuring accuracy is:!: 1 mm, the scale of recording 1/1, and the working speed of lifting or lowering in a shaft, 1-2 m/s. The survey work during mounting of a rope equipment consists in transferring the layout axes onto the mounting levels; checking the tensioning frame; control of arrangement of suspension clips, guide and tensioning devices;control measurements during mounting of auxiliary conductors; checking the track gauge of guides for hoisting vessels; and final surveying of shaft portions with hoisting and mining equipment. The layout axes of tower head-frames are transferred onto the mounting levels (headframe ceilings) by using the layout axes of a multi-rope hoisting machine. For jib-type head-frames, the axes are transferred onto the mounting level from the axial points by means of a theodolite and plumb bobs hung from a pulley stage. The axes of a shaft are transferred onto the fixation levels of guide ropes by means of plumb bobs at an earlier stage (during sinking a shaft). The discrepancies between the positions of axial marks obtained in two measurements should not exceed 20 mm on a suspension level and 50 mm on a fixation level. The arrangement of a tensioning frame and auxiliary conductors at loading levels is controlle.d relative to the layout axes of the fixation level of rope conductors and the axial points set up in the lining near the shaft bottom. The displacements of axes of buntons on a particular level should be not more than 3 mm in the horizontal plane, and the difference of elevations of the ends of buntons should not exceed 5 mm. The mounting of hoist clips and jacks on a suspension level is controlled relative to the axes of a shaft or multi-rope hoisting machine which are fixed on that level. The axes of these devices are laid out by the method of
ordinates. The design positions of hoist clips and jacks are denoted by axial marks op supporting surfaces. Rope conductors are fixed in the vertical position by using a projection meter; for this purpose, the vertical sensor of the projection meter is fastened on a rope conductor above the tensioning frame. The final surveying of rope conductors is carried out after mounting the hoist clips and fastening the guide sleeves and consists in measuring the linear distances from the layout axes. The results of measurements are processed to compile a scheme of fastening of rope conductors on a head-frame ceiling and tensioning frame. The actual distances between the axes of ropes (devices) and layout axes should differ from the design values by not more than 7 mm. 9.6.
Survey Work During of Shaft Workings
Driving
The survey work during driving of underground workings near a shaft may involve certain difficulties, since such workings often have a rather intricate configuration with many joints, curvatures and with variable cross sections, combinations of straight and curvilinear sections, an intricate profile of haulage tracks, and contain large-sized stationary equipment units. Before constructing the shaft bottom, a design polygon on a scale of 1/200 or 1/500 is drawn (Fig. 9.39) which serves for checking whether the dimensions of underground workings are correct and for obtaining the initial data for the instrumental transfer of the axes of designed workings into nature. The drawing of such a polygon contains numerical data on the dimensions of straight and curved sections of workings, angles of turn of circular curves, elevations of particular pqints, etc. The axes of curved sections are replaced by chords whose number is chosen so that the
9.7.
Survey
Work
by Special
Methods
229
assigned from two side plumb bobs sunk into the shaft. The mining work for insetting a working is permitted at a distance not more than 40 m from a plumb bob sunk into the shaft. The working can then be driven further only after the points and bench marks of an ~ underground survey reference net have been fixed on its level. As the face is advanced in a working, the mine surveyor checks all parameters of the working being driven, marks the actual diFig. 9.39 Design polygon of shaft workings mensions of the working on a survey plate chords do not touch the lines of the walls of and compares them with the design dimensions, and determines the actual discrepanworkings. Check calculations determine the design cies. The discrepancies of the cross-sectional angles of a closed polygon and the coordinate area of a roughly driven working should be increases at all its vertexes. The check calcu- not more than 5-12% for a cross-sectional area up to 8 m2, 5-10% for an area up to lations are done by the formulae: 15 m2, and 3-7% for an area above 15 m2. ~13-180° (n -2) = 0, ~Ax = ~Ay = ° All cases of rock inrush and caving that where n is the number of vertexes of a took place during driving of a working are recorded in the mine surveyor's documents polygon. If the conditions described by these for- where their locations and main dimensions mulae are not fulfilled, the polygon should be are indicated. The voids left in the rock redesigned. Mter the plan adjustment of the massif due to inrushes and cavings should be polygon, a design profile is drawn, whose supported reliably and backfilled with noncharacteristic points are those where the combustible rocks in order to prevent further workings intersect one another or the angles rock displacement and the possible harmful of their inclination change. effects on the shaft lining. The insets of conjunctions of workings and Directions are assigned to workings by vertical shafts are determined after transfer- means of a theodolite and fixed by at least ring the elevation mark from the ground three plumb bobs hung at a distance not less surface onto the bench marks concreted in than 3-5 m from one another. Miners engaged the walls of the shaft. These bench marks are in the driving work can use the direction line usually set up somewhat above a conjunction defined by the plumb bobs on advancing to a so as to enable a convenient transfer of the distance not more than 40 m from the last elevation mark onto the roof (bottom) of an plumb bob. With a larger distance, instruadjacent working or onto the head of a track mental surveying is needed to set up new rail. Conjunction axes are usually transferred plumb bobs in the face. from two plumb bobs sunk from the surface, ' which define the axis of the shaft. This axis is 9.7. Survey Work During Driving fixed by means of two or three brackets of Vertical Shafts driven into the shaft walls somewhat above by Special Methods the level of the projected conjunction. The direction of inset for a conjunction Geological and hydrogeological conditions between the mine shaft and a working is of mineral deposits are not always quite
Ch. 9. Surveying in Mine Construction
230
suitable for the construction of vertical shafts by conventional methods. In such cases, special methods are resorted to, in which measures are taken for strengthening the rock massif, ground water lowering, plugging and soil freezing, which can facilitate the driving of mine shafts. Under complicated conditions, vertical shafts can also be driven by drilling. In mine shafts driven by these special methods, the mine surv~yor has to solve certain specific survey problems. 9.7.1
Survey Work During Driving of Vertical Shafts with Artificial Rock Freezing
During driving of a mine shaft with artificial freezing of the rock, the mine surveyors perform the following operations: the layout of the centre of a shaft and the mouths of freezing and monitor holes; checking the construction of a drilling site, assembly and
position of drilling equipment, and the verticality of surface casings; surveying drill holes during drilling; and the compilation of level plans of ice-rock enclosure. The centre and axes of a shaft are transferred into nature by the method described in Sec. 9.2. The most popular method of layout of holes in the terrain consists in the following. A theodolite is set up at the centre of the shaft and oriented along one of the shaft axes, after which the required angle is laid off and distances to each drill hole are measured by a tape according to the design data. The accuracy of laying out of holes should be not worse than :J:50 mm. The mouth of each hole is marked by pegs. Before drilling the holes, a geometrical check is made (for verticality, centring above the hole mouth, linearity of the kelly, etc.) in accordance with the direction assigned by the mine surveyor, and the hole mouth is drilled for the surface casing. The length of the latter ,Jf
~
5'
Fig. 9.40
lnclinometric
level; 5- counterweight
station: 1- automobile block
3
with logging hoist; 2- inclinometer;
3- tripod; 4- striding
9.7.
Survey
Work
by Special
Methods
231
depends on the thickness of alluvium and upper caving rock and is usually of an order of 20 m. Before mounting a drilling rig, the rings of a drilling site are checked for horizontality by geometrical levelling at the top edge of the rings with an interval of 1 m. The. difference of height marks should not exceed 10 mm. A drilling rig is regarded to be ready for operation provided that the difference of elevations of the corner points of a platform does not exceed 5 mm; the error of centring of a rotary table above the hole mouth is not more than 10 mm; the difference between the height marks of the axial points of a rotary table is not more than 2 mm; and the deviation of the kelly in a rotary table from the vertical is not more than 0.001 of the kelly length. Deep vertical freezing and monitor holes can be surveyed by means of gyroscopic inclinometers which measure zenith angles in the range from 0° to 4-6° with an accuracy of 1.5-2' and direction angles, with an accuracy of 3-6°, The interval for measuring zenith and direction angles is not more than 30 m. Figure 9.40 shows an inclinometric station for measuring drill holes up to 1000 m in depth with a casing string and drill string of 96-127 mm in diameter. The station is mounted on a truck chassis, The main instrument of the station is an inclinometer (Fig. 9.41) with a gyroscopic direction stabilizer and zenith attachment for the orientation of the inclinometer from the surface. The measuring portion of the inclinometer consists of an azimuthal gyrostabilizer unit and zenith angle measuring unit. The latter has two penduli which make it possible to determine the zenith angle of the axis of a drill hole. The measured values of zenith angles are transmitted onto the surface. Fig. 9.41 stabilizer
Inclinometer
with gyroscopic
direction
~
232
Ch. 9. Surveying in Mine Construction
The inclinometer consists of a housing 2, measuring portion 8, and guide rollers 1. The measuring portion includes the unit of azimuthal gyrostabilizer and unit for determining the zenith angle. The gyrostabilizer has a sensitive element 5, semiconductor amplifier 4, actuating motor with a reducer 3, and a m9tor with a rocker 7. When the inclinometer moves in a hole, there appears an external moment which rotates the housing 2 on the longitudinal axis of the instrument. This moment is transferred onto the measuring portion 8 and tends to turn the latter. Under this action, a gyromotor together with an angle sensor frame 6 deviates from the neutral position, and the sensor pulse is transmitted to the actuating motor 3. The motor develops (through the reducer) a compensating moment which retains the measuring portion of the instrument
~
Field sheet No.5 Shaft No.1
Hole No.3
JuneI5,'83900 M 110 01
g2S0r.1
HI
~ 1230 Or.2 02
"I 1
0;1
Fig.
9.42
Plate
with
inclinometer
in the given direction, so that its orientation is not changed. The unit for zenith angle measurements has two measuring elements which determine the zenith angles in two mutually pocpendicular planes. Each element has a flat pendulum 9 contained in a h()rmetically closed cylinder which is filled with a viscous liquid. Each pendulum carries the frame of an induction sensor; Surveying a drill hole is started from centring the inclinometer on a tripod above the hole mouth, after which the first orientation is carried out by means of an orientation attachment fastened on the inclinometer housing. For this purpose, a distinct object is chosen on the terrain at a distance not less than 30 m from the inclinometer, and the direction angle of this object relative to a line OlHl is measured (Fig. 9.42). The incli-
records
~
9.7.
Survey
Work
by Special
N
,
.--J e
5
26,
3
24/
~
23/ /
)~
,1
~ -;,~,
/'
,
3 \ \
(21( I ,201 --r19\
" ~, "
~
18
4 \ \
I--,
, 6'r
"
17
,
, 18'
\
'-14
the lines HlOl and 02H2. The angular correction is then introduced into the two orientation directions obtained during sinking and lifting of the inclinometer. The corrected directions are brought to coincidence in the points of the hole mouth, which gives two positions of the inclinogram. The results of surveying of freezing holes are used for plotting the level plans of an ice-rock enclosure (Fig. 9.43), which make it possible to estimate the thickness of the enclosure and determine the boundaries of frozen rock (to the centre and to the rock massif). The radii of ice-rock cylinders can be calculated by the formula: r = J(I/2
~ 16
~
..
,If ,f~ I
/
s Fig. 9.43 Level plan of ice-rock enclosure
nometer is then unclamped and sunk into the drill hole. As the instrument is being sunk, the planigraph records an inclinogram with elevation marks of depth intervals. Upon reaching the face of the drill hole, the orientation (inclination) of the inclinometer axis 0191 is recorded, and the gyrostabilizer is turned through 180° to record a new orientation of the inclinometer axis, 0292. Mter that, the inclinometer is lifted in the hole to make measurements from the bottom upwards. As the inclinometer appears on the surface, it is again oriented, and the direction angle of a line H2O2 is measured. The lines 0 1H 1 and H 20 2 are shifted parallel to themselves until points 0 1 and H 2 coincide. The angle 'Y formed by these lines (and called the angular correction) is determined graphically. A similar procedure is done for
233
Methods
+ af + k
where 1 is the spacing between freezing holes; a is the deviation of a hole from the vertical; k is a coefficient depending on the thickness of an ice-rock enclosure; it is taken equal to 0.6L for the inner boundary and 0.4L for the outer one (L is the thickness of the ice-rock enclosure as specified in the project). The permissible deviation of freezing holes from the vertical is 0.5 + 0.002 H, where H is the depth of a shaft, m; in all cases, the maximum deviation of freezing holes from the vertical to the shaft centre should not exceed 0.6 m. 9.7.2.
Survey Work During of Vertical Shafts
Drilling
The drilling method is used widely for driving of mine shafts. It allows one to mechanize completely the operations of rock disintegration and rock lifting onto the surface and eliminates the dangerous and hard work of underground miners. The method is mainly employed for shaft driving in soft water-bearing rocks (drift sand, water-bearing sands, chalk, clays, etc.); in coarse-grained sands, the method is not quite efficient in view of large losses of a clay drilling mud. Mine shafts are drilled by drilling rigs
234
Ch. 9. Surveying
in Mine
permitting the drilling out of the rock allover the face. Drilling a shaft is started from drilling a pilot hole of a depth exceeding by 5-10 m the design depth of the shaft and of a diameter of 0.5-1.2 m. The pilot hole serves for guiding the drilling tool in subsequent widening of the shaft. Upon drilling, the shaft lining is constructed by the float-on or sectional method. With the float-on method, a number of lining rings are mounted on one another on a reinforced concrete bottom plate. The cylinder thus formed is sunk into the fore shaft filled with washing fluid and floats, as it were, in the latter. New ring sections 4-6 m high are then put on top of the floating cylinder. After placing a ring section on the cylinder, ballast fluid is pumped in to ensure sinking the cylinder to a certain depth. After building the lining to the entire height of the shaft, the space between the lining and rock is plugged with a cement mortar. With the sectional method, a fixing section of the lining is first sunk onto a concrete pad prepared on the shaft bottom. Upon checking whether the section is placed correctly, it is fixed by a cement mortar poured into the space behind the lining. Mter that, the lining sections 15-20 m high are placed successively onto the fixing section and secured by pluggmg. Mine survey servicing during drilling of min shafts consists in checking the verticality of the shaft axis and observing that the lining is errected properly. The deviations of the shaft axis from the design (vertical) position should not exceed the spacing between the outer surface of the lining and the surface of the rock, which is taken equal to 200350 mm. The control of verticality of a shaft axis is complicated by the fact that the shaft is filled by clay drilling liquid during drilling. In shaft drilling without lifting the drilling tool onto the surface, the verticality is controlled by the position of the centre of the
Construction
drilling tool, which is done by the optical or geometrical method. With the optical method, the surveyor observes a light signal projected through a drill string; with the geometrical method, a cable is stretched through the drill string from the shaft mouth to the drilling tool, and its deviation is measured. In the former method, which is applicable at depths up to 200-250 m, use is made of instruments of the type of direction projectors. In the latter method, the deviations of the cable from the vertical can be measured at any desired depth with an accuracy to 20" by means of a projection meter. The error in the position of the cable relative to the drill string axis does not exceed 20 mm. Shaft walls are surveyed during drilling by means of ultrasonic locators which make it possible to take measurements in mud-filled shafts with an error up to 2% along the radius and 3%, in the orientation of a measured radius. 9.8.
Survey Work During Deepening of Vertical
Shafts
Deepening vertical shafts can be performed from the top downwards or vice versa. In the former case,the survey work is essentially the same as that during sinking of a shaft from the surface, though some specifics relate to the restoration and fixation of the centre and axes of the shaft in the deepened portion. Deepening a shaft from the top downwards can be done by one of three probable schemes: (I) under a platform constructed below the floor level of the working connected to the shaft bottom; (2) by means of a special passageway driven in the shaft portion to be deepened;and (3) through auxiliary workings driven sideways of the shaft. In deepening by the first scheme, the survey work consists in determining the centre and axes of the shaft in its section adjacent to the conjunction between the shaft
9.8.
Survey
Work
During
Deepening
/
0
l..v
I"
I:o'~
A-A -r--
b~ ~n
AL -=
11A
2l
t.k~~
W//////& Fig. 9.44 Restoration of centre and axes in deepenedportion of shaft through sinking passagewayby meansof plumb bobs and theodolite and pit bottom, after which the restored axes are fixed by brackets below the future platform. In that case, the centre of the shaft is determined by the point of intersection of wires stretched between the brackets that fix the shaft axes. With the second scheme of shaft deepening (Fig. 9.44), the survey work is started from determining the centre and axes of the shaft in the bottom portion, by using the points of an underground survey reference net. The centre and axes are transferred under a pillar by means of plumb bobs 01 and O2
of Vertical
Shafts
235
(see Fig. 9.44) whose coordinates are determined from the points of the reference net of the workings near the shaft bottom. Mter cutting a chamber under the pillar, the centre and axes of the shaft are laid out by means of plumb bobs 01 and O2. For this pu~ose, the theodolite is set up in a point A which is chosen so that the shape of a connection triangle A01O2 can be convenient for solving the junction problem. The theodolite is sighted at points 01 and O2, and points a and b are marked on the shaft walls. Solving the connection triangle A01O2, it is then possible to determine the coordinates of the point A and the direction angles of lines A01 (Aa) and A02 (Ab). The coordinates of the shaft centre determined at the level of shaft workings and the coordinates of the point A just found are used for solving the inverse geodetic problem of determining the layout angle aAC and the distance AC. By constructing the angle aAC and distance AC in nature, we then determine the position of a point C, the centre of the shaft, which is then transferred and fixed in the safety pillar. With the known direction angles of the shaft axis and of direction CA, we can now calculate an angle ~ and lay it off from the direction CA by means of a theodolite set up in the shaft centre point. The direction of the shaft axis determined in this way is fixed by brackets on the shaft walls. The transfer of the centre and axes of the shaft under the safety pillar is performed twice. The discrepancies between the two results should be not more than 5' in axial directions and not more than 20 mm for the position of the shaft centre. If a shaft is to be deepened through auxiliary workings driven beyond its limits (winzes, blind pits, inclined workings, etc.), the coordinates of the shaft centre and the direction angle of one of the shaft axes are determined on the desired level from the points of an underground reference net (H and D in Fig. 9.45). A polygonometric
236
Ch. 9. Surveying in Mine Construction
A-A
p Fig. 9.45 Transferring centre and axes in deepened portion of shaft through winze
traverse is then run from these points to the auxiliary working. In the case illustrated in Fig. 9.45, the auxiliary working is oriented by means of plumb bobs 01 and O2. This orientation makes it possible to find the direction angle of a certain direction fixed by points A and B on the level to which deepening should be done. The coordinates x, y of these points are also determined. With the known coordinates of the shaft centre and the coordinates of the point B of the polygonometric traverse on the lower
level, it is possible to solve an inverse geodetic problem and calculate the layout angle ARC = 13and layout length RC = I, which are laid off in nature and determine the position of the shaft centre. Then, as in the previous case,the direction of one of the shaft axes is assigned and fixed by points F and G. For a shaft to be deepened from the bottom upwards, the coordinates of the shaft centre and the direction angle of the shaft axis are determined before starting the layout work. The survey work in the workings on
9.8.
Survey
Work
During
Deepening
the level of deepening is also carried out. All measurements essential for laying out the centre and axes of the shaft on the level of deepening are carried out. The centre of a shaft on the lower level is usually fixed in the foot of a working, and the shaft axes are fiXed by brackets in the walls or roof of the working. The verticality and cross-sectional area of the shaft are checked by means of plumb bobs hung under the sinking platform from brackets in the temporary lining. The
of Vertical
Shafts
237
positions of the plumb bobs are checked by measuring the distance between them and the centre of the shaft. The centre of the shaft in the face is found by means of templates or measurements from temporary plumb bobs which are centred above the permanent plumb bobs. The shaft should be checked for verticality in every 3 m of face advance, and the shaft axes should be transferred onto the brackets of permanent plumb bobs after every 10 m of shaft advancement.
Chapter
Surveying
10.1.
General
The principal aims of the mine-surveying service in open-cast mining are as follows: the provision of the geometric basis for the surveying work in the form of a reference net; surveying of mining workings and land surface; compilation of graphical documents for the normal operation of a mining enterprise; participation in the planning of drilling and blasting; control of the specified parameters of working systems and the dimensions of structures; calculation of the output of a mineral, volume of burden rock, dynamics of losses and the dilution of a mineral; observations on the motions of quarry flanks and development of measures for their prevention. The results of mine surveying are used for compiling calendar plans of mining work development, investigations of the geological structure of deposits, solution of various problems associated with the activity of production sections, etc. The objects of surveying in quarries include the following main groups: (a) exploratory, draining and drillingblasting workings, crests, accesstracks, working trenches, catchwater ditches, etc.; (b) tectonic disturbances, contacts of the lying and hanging wall with the mineral, boundaries of sections with different grades of ore or different ash content of coal, assaying points, boundaries of landslides, etc.; (c) haulage lines in a quarry, pay-ore area
Ten
in Quarries
structures, hoists, trestles, power transmission lines, pulp pipelines, etc.; (d) flooded workings, cavities left after underground mining work, fire zones, etc. 10.2.
Reference and
10.2.1
and
Surveying
Mine-Surveying Nets
Survey
Nets
Work
Reference
Mine-surveying reference nets on deposits extracted by open-cast methods are developed in accordance with the requirements set forth to reference nets on the land surface for the territories of economic interest of mining enterprises. They may include triangulation points, trilateration points, and polygonometric points. Levelling bench marks can be used as the reference basis for surveying nets in quarries. Modem organization of mine surveying in open-cast mining of deposits is characterized by that the work proceeds successively 'from the general to particular', with measurements at each stage of the work being made with the specified accuracy. On the land surface of a mining enterprise, a reference net beyond the limit of the design contour of a quarry is formed initially. After that, as the mining work is developed on the quarry flanks, and sometimes inside a quarry, reference points are set up in these places, which are called approach points and serve for the formation of a surveying net.
~
10.2.
Reference
and Survey
Nets and Surveying
239
Work
,"
A
,I
2
3 '>f'
/-~
~2'
"1' ~.J 6
\
B
Fig. 10.3 Construction of reference net by poly. gonometry --
~ c
Fig. 10.1 Insertion of point into development of reference net
rigid
angle for
Depending on the configuration of a quarry, local conditiQns, methods of stripping and provision of technical facilities, the approach points can be determined by the methods of triangulation or polygonometry. The method of triangulation is employed in cases when approach points are readily visible from reference points. In such cases,use is most often made of the insertion of one (Fig. 10.1)or several points into a rigid angle, construction of a chain pf triangles between two fixed points (Fig. 10.2) or the construction of a geodetic quadrangle. In triangle chains, the number of figures should be not more than five. The angles of triangles should JA
'/134
6
.~B
-, ,
1 /"7
)
~
\
I
13\
2 """
fi5y I 1'10
M
R 1"12
~L~
N
4
3 Fig. 10.2 Construction of chain of triangles between two reference points
be not less than 30° in chains or 20° in geodetic quadrangles. The method of polygonometry is resorted to in cases when there is no visibility between the reference points and the points to be determined (approach points), but the land surface is quite convenient for linear measurements to determine the approach points. The polygonometry can also be used with successon a rough terrain if it is possible to employ light or radio range finders. Polygonometric traverses are commonly run between the points of a mine-surveying reference net (for instance, points A, B, and C in Fig. 10.3). 10.2.2.
Surveying
Nets
Surveying nets are constructed on the basis of points of a reference net. In surveying the land surface, waste dumps and quarries, surveying nets are constructed according to the following requirements: the main points of a surveying net should cover evenly the survey surface area; their density is determined so as to have four points per km2 in surveyings on a scale 1/5000, 10 points per km2 on a scale 1/2000, or 16 points per km2 on a scale 1/1000; each surveying plate made on a scale 1/5000 should have at least three main points fixed by permanent centres; two such points are sufficient on plates on a scale
240
Ch. 10. Surveying in Quarries
of 1/2000 and one such point, on those on a scale 1/1000. Depending on the terrain relief, shape of a quarry in plan, mining technology and some other factors, surveying nets can be constructed by the following methods: method of geodetic intersections; method of analytical nets; method of theodolite traverses; method of range lines; polar method; and method of a rectangular network. Since a survey control net has to exist only for a relatively short time, it can be fixed by permanent or temporary points in the form of wooden page or metal rods driven into the soil. In hard rocks, temporary points are usually fixed by cross marks made on the protruding portions of the rock. Survey points are usually located on the lower platform of each working bench at distances not more than 400 m from one another. Method of geodetic intersections is em-' ployed in cases when the points of a surveying net are located at appreciable distances from those of a reference net. Right and side intersections and reverse intersections (resections) are usually employed. Right and side intersections are drawn from at least three initial points. A resection is drawn from four points, provided that the point to be determined lies near the circle passing through three of the four initial points. The coordinates of the points determined by r.ight or side intersections are calculated from two triangles; in the method of resections, they are found from two versions. In all cases,the final coordinates are taken as the arithmetic means from two measurements. The maximum discrepancy should not exceed 0.8 m. Method of analytical nets is employed in quarries where both flanks are working (moving). Analytical nets are constructed as chains of triangles or other figures (geodetic quadrangles, a central system, etc.) which are supported by sides and points of a reference
net. Triangle chains and central figures are used most often. The latter are employed for constructing a surveying net on the lower levels of quarries of a small area or of some portions of a quarry, whereas triangle chains are preferred in the quarries of an elongated shape and appreciable depth. The number of points detennined by an individual triangle chain or figure should be not more than seven. Triangles should have a shape close to equilateral. The angles at the points being determined should be not larger than 120° or smaller than 30° and the side lengths, not smaller than 300 m or greater than 1000 m. Angular measurements are commonly made by means of theodolites. The permissible angular discrepancy in triangles with the side length up to 1000 m is l' and in those with the side length more than 1000 m, 40". Method of theodolite traverses is employed in quarries having a large extention of the front of mining and stripping work and benches of a form convenient for linear measurements. Theodolite traverses are run between two known points A and B (points of a reference net) or between closed polygons. At junctions of theodolite traverses to the initial points, there are measured the angles between the junction side of a theodolite traverse and two directions onto the points of a reference net (Fig. 10.4). The distances between the points of theodolite trayerses should not exceed 400 m and, as a rule, should be less than loo m. The length of a traverse should be not more than 2.5 km. The angles in theodolite traverses are measured by theodolites. An angular discrepancy should not exceed f fJ= 30"J~ , where n is the number of measured angles. The three-stand scheme can be recommended for angular measurements. The theodolites should be centred with an accuracy not worse than 2-3 mm. The length measurements in theodolite
10.2.
Reference
and
Survey
Nets
and
Surveying
Work
241
Fig. 10.4 Providing survey control by means of theodolite traverses
traverses can be made by means of steel or cloth tapes or range finders. In some cases, the lengths of traverse sides can be determined by indirect methods, but in all casesall measurements should be done in the forward and reverse direction, and the relative difference between two independent measurements should be not more than 1/1000. The linear discrepancies in theodolite traverses should be not more than 1/3000 of the traverse length. The corrections for temperature, tape standardization, and horizontalization of lines should be introduced into the measured lengths. A temperature correction is introduced in cases when the temperature at measurements differs by more than 5 deg. C from that at which the tapes have been standardized. A correction for horizontalization is introduced when the inclination angle is larger than 10. Linear measurements can also be carried out by the optical method with the use of optical range finders and range finder attachments and a base-measuring (subtense) bar. In some cases when the form of benches is inconvenient for length measurements on the ground and optical range finders are not 16-1270
available, it is possible to measure the lines of a theodolite traverse by the indirect method of geodetic intersections which is essentially as follows. A theodolite traverse is run on the working platform of a bench and connected at the ends to the points of a reference net (I, II, Fig. 10.5).Auxiliary points A, B, and C are chosen at certain distances away from the theodolite traverse line. Angles ~1' ~2' ~3' ..., ~17 are measured from the points of the theodolite traverse line and lines I-I and 6-1I, which are the refere~ bases, are measured by a tape. The side l-A of a triangle IAl is calculated by the sine theorem:
A-l
1-2=
sin P4
sma2
In a similar way, the side 2-3 is calculated, which is the connecting side for solving the triangles constructed from the point B. The calculations of the next series of triangles give
242
Ch. 10. Surveying
in Quarries
~ I B
C
A
I'~ \
/~,
\\
~,
l~n
~ (15
i
6
\
"
a-,'l:
! ):
I
~17 ~
8m
\
\
{,
I ,
I Pel
"
Fig. 10.5
Indirect
measuring
of sides of theodolite
a side 4-5 which is the basis for solving the last series of triangles constructed from the point C. A check is done in this method by comparing the calculated length of the last line of a theodolite traverse, 6-11, with its length measured in the field. Method of range lines is employed in quarries where the working front is advanced in one direction only, so that the reference points fixed on the non-mining flank can be easily observed from the working benches. This method is especially convenient in cases when the platforms of working benches have a certain elevation above the ground surface of the opposite flank of a quarry (Fig. 10.6). For laying out a range line, a secondorder .polygonometric traverse is first run (A, B, C, ..., G). With the known direction angles of range lines, it is possible to calculate the angles 'I' and
traverse
nates of the point p 1 are found, In order to have an optimal shape of triangles, it is essential that the angles a and 13 be not smaller than 30°, If however these angles are smaller than 30°, it is possible to sight the instrument at reference points located on adjacent range lines (for instance, a point p 2 and sighting at points B and F). Polar method of providing survey control has become popular with the appearance of 123 y III I A ~~~
456 ~ I B
~ 111 I C
~ IV I D
7 I v
~ VI I F
~ VII I G
~
-7 Oj:l=.:
JJI.::.--I~
-:::.
1--
~ P2
Fig. 10.6 Providing range lines
survey control
;:J by method of
~
10.2.
Reference
and
Survey
Nets
and
Surveying
A<
243
Work
,
(
e
I
oB
[3
4
Aa< \{5 l5 \
.2 I
b\
I
~
~
~
2
DO
~
.
j Fig. 10.8 Providing rectangular network
geodetic light range finders. For successful application of this method, a greater portion of a quarry must be readily visible from a few number of points ofa reference net. For the construction of a surveying net, a light range finder i.s set up on a point (A) of the reference net, and light reflectors are set (Fig. 10.7) up on surveying net points 1, 2, 3, ...which are to be determined. Upon measuring the distances, the light range finder is replaced by a theodolite to measure polar angles ~l' ~2' ~3' etc. Method of a rectangular network for the construction of surveying nets is applicable in quarries of a shallow depth and with a flat relief of the surrounding land. A network of rectangles is laid out on the territory of deposit, and survey points are fixed in their corners (Fig. 10.8).It is a common practice to layout two systems of rectangles: the main network with the side length d equal to 50 m, loo m or 200 m and the densifying network of rectangles with the side length dl equal to 5-40 m, which is used directly for surveying. The orientation of the sides of a network is
survey control
~c by method
of
chosen parallel (perpendicular) to the main mining front or coincident with the orientation of a coordinate network. For laying out a rectangular network, a plan of the surface is compiled, which gives the technical boundary of a quarry and a number of reference net points (1, 2,3,4, 5) near it. Then the directions of the axes of a rectangular survey net are chosen, the rectangular network is laid out, and the coordinates of its corners are calculated on the plan. After that, a project of the densification of the reference net is designed so that its points can be as close as possible to the corners of the rectangular network; the densification network is transferred into nature and fixed on the ground. The corners of the network can be fixed by laying off the distance and direction angle from the closest reference point or by the method of angular intersections with the use of one or two theodolites (see Fig. 10.8). For the transfer of surveying net points onto the lower levels of a quarry or the restoration of annihilated points, use is most
244
Ch. 10. Surveying (a)
in Quarries
(b)
L--L. r--r-
:J=' --r-! .+-~ , ~
'
.(, ~-+ L Fig. 10.9 Transfer angular intersection
(restoration)
of surveying
net points: (a) by method
often made of the method of range lines in which two theodolites are set up on two closest existing points (Fig. 10.9a),and a new point is fixed at the intersection of their collimation lines. It is also possible to use the method of direct angular intersection. In that case the position of a point of the reference net is determined on the ground by laying off two horizontal angles ~1 and ~2 by means of two theodolites (Fig. 10.9b); the sought-for point is then found at the intersection of the collimation lines of the two instruments. 10.2.3.
Elevation
Control
of Quarries
Elevation control is required for determining the heights of the points in a quarry. The heights of the points of a surveying net are measured by geometric or trigonometric technical levelling. Geometric levelling is usually employed in quarries with railway transport. Technical levels and levelling staffs of any type are suitable for the purpose. Technical levelling between the points of a reference net may be done in one direction only; hanging lines are permitted, provided that they are run in the forward and reverse direction. The readings in levelling are taken only relative to a single line. The difference of elevations determined on the black and red face of staffs should not exceed 10 mm. The permissible discrepancy of level lines is
1
, --1 !
of range lines; (b) by method
of
50JL mm, where Lis the length of the level line, km. Trigonometric levelling has found use in quarries with railless transport and in cases when a surveying net is formed by the method of geodetic intersections. When det.ermining the elevations of points by trigonometric levelling, vertical angles are measured by means of theodolites at the same time with measuring the horizontal angles; the accuracy of reading-off devices of the vertical circle of the instruments should be not worse than 30". The heights of an instrument and sighting target should be measured with an accuracy to 1 cm. The measurements of vertical angles can be controlled by the constant place of the zero point of the vertical circle. The deviations of the zero point should be not greater than thrice the reading-off error on the vertical circle. Trigonometric levelling lines should be connected to the points whose elevations have been determined by geometric levelling. Their length should not exceed 2.5 km. The permissible discrepancy between a forward and reverse elevation is not more than 0.041cm where I is the length of a line, m. The discrepancy of a levelling line, cm, should be not more than mh = 0.04[1]/J~ where [I] is the length of the levelling line, m, and n is the number of levelling lines.
10.2.
Reference
and
Survey
If the points of a surveying net are determined by the polar method or method of geodetic intersections, the elevations between the points are found by trigonometric levelling in the forward and back direction or in a single direction only, but from at least two points. In such cases,elevation discrepancies (in centimetres) should be not more than 0.031for distances up to 1 km or 0.021for distances above 1 km (where 1 is the length of the lines, m). If a side in one-sided levelling exceeds 700 m, a correction for the Earth curvature and refraction should be introduced into the measured elevation. 10.2.4.
Surveying
in Quarries
The surveys of quarries and complementary surveys of benches can be carried out by the following methods: tacheometry, method of perpendiculars, plane-table survey, stereophotogrammetry, and their combinations. For the compilation and complementation of mining working plans, it is advisable, where possible, to perform aerial and ground stereophotogrammetric surveys. Tacheometric survey is employed for: (a) surveying of quarries where the mining technology is such that the volume of extracted burden rock and that of the mineral in the pillar can be determined directly from the results of bench surveying; (b) for surveying of quarries of a relatively low capacity; (c) for surveying of'dead' spaces obtained in ground stereophotogrammetry; and (d) for check surveying of mining workings in the selective control of their plan positions and for surveys in cases where stereophotogrammetric methods are inefficient or inapplicable. Plane-table survey has found no wide application. It is mainly used for single surveys of small quarries or their portions when a general plan of mining workings is to be compiled.
Nets
and
Surveying
Work
245
The periodicity and sequence of surveys in quarries are as follows: surveys of contours of bench crests and blast holes are made only in places where blasting work is to be performed. All other objects except for mineral stores are surveyed only when a need arises. Mineral stores are surveyed every ten days or once a month depending on the method adopted for calculating the amount of the extracted mineral. Surveys in quarries are made from the points of a survey net. The distances between these points on a bench should not exceed 300 m for a scale 1/1000 or 400 m for a scale 1/2000. It is permissible when needed to determine the additional points of a surveying net by running a single-sided hanging theodolite traverse. The length of sides should be not more than 300 m in surveys on a scale 1/1000 or 400 m on a scale 1/2000. The staff is set up on all characteristic points of the contours and surfaces being surveyed. In surveys on a scale 1/1000, the distances between the staff points should not exceed 20 m for the bench crests of intricate shape or 30 m for the extended crests. In surveys on a scale 1/2000 the respective distances are 30 m and 40 m. In the surveys of the surface of blasted rock the distances between the staff points should not exceed 10 m for a scale 1/1000 or 20 m, for a scale 1/2000. A sketch of bench contours is drawn at each survey station (Fig. 10.10a). A sma[[-sized geo[ogica[ a[timeter (Fig. 10.11) has been developed in this country for the geological documentation of quarry benches. The instrument is intended for the remote measurements of vertical thickness and dip angles of visible seams. It can also determine the relative elevations of the position of geological elements and other objects. The altimeter is essentially an opticomechanical goniometer provided with a direct-image telescope and self-adjusting verti-
246
Ch. 10. Surveying
(a)
in Quarries (b)
~ ~~-,I.:Lg--~
-13
o-~~
: 10--:~--
:~
("I
"' ("I.
cpi ("II
~ ~ c.; c-.
LO (I)
v.:.-~
39.71-
-~
;15
0: ~
-:.~,;~5~~
~
3
\
~I--
--'0
ir::::njt1r~ Fig.
10.10
Sketch of bench contours:
(a) by tacheometric
cal circle with scales of elevations and vertical angles. The working portions of measuring scales are visible directly in the telescope. The range of measured elevations is :t 10 m for a sighting length up to 10 m or :t 20 m for a sighting length of 20-40 m. The range of measured visible dip angles is :t 90°. The error in the measurements of the vertical thickness of seamsis not more than 5 cm and that of the visible dip angles of seams, 1°. The mass of the instrument is 1.5 kg. Method of perpendiculars can be employed efficiently for the surveys of bench crests with simple contours when the required number of staff points is not large (Fig. 10.10b). The surveying net for the method of perpendiculars is constructed in the form of theodolite traverses or as a rectangular network. The length of ordinates, as a rule, should not exceed 30 m. For a length more than 15 m, they should be set up by means of a right-angle mirror. Lengths are measured by tapes and rounded off to decimetres. The distances between the staff points are chosen according to the recommendations given for tacheometric surveys. Stereophotogrammetric surveying of quarries. In recent time, stereophotogrammetry has come into use in many quarries in place of tacheometric surveying, which offers the following advantages: (a) increases the labour productivity of the field work;
method;
(b) by method
of perpendiculars
(b) eliminates the need in staffmen and thus increases the safety of work; (c) provides a large choice of points in compiling plans by photographs and thus better characterizes the section surveyed; and (d) involves all visible objects including those which are inaccessible for tacheometry.
Fig. 10.11 Geological altimeter: l-eye-piece; 2-housing; 3-adjusting level; 4-reading-otT magnifying glass; 5- horizontal circle; 6- base; 7-levelling wedges;8-handle; 9-horizontal sighting screw; 10-vertical sighting screw; ll-telescope; 12-focussing device
10.2.
Reference
and
Survey
Ground and aerial stereophotogrammetry can be employed. Ground stereophotogrammetry can be used either independently or in combination with tacheometric surveying. Stereophotogrammetry can determine and represent graphically the shape, dimensions, and spatial positions of objects and relief of the Earth's surface. It is especially efficient in large quarries. To compile a plan of a quarry section, this section is photographed stereoscopically from two points at the ends of a base S1S2 (Fig. 10.12). The two photographs of the same portion of land, when viewed through a stereoscopic device, produce a three-dimensional effect. When made from two ends of a base line they represent a stereoscopic pair whose principal elements are as follows: (1) the left-pand (PJ and right-hand photograph (P 2); t2) the centres of projection of the left-hand and right-hand photograph, SI and S2' or the rear optical centres of the two objectives of stereophotogrammetric camera; (3) the photographic base Bph = S1S2 which is also equal to the distance between the centres of projection of the photographs; (4) beam bundles alSlA, ~ISIC, a2S2A, C2S2C,etc., i. e. the combination of projecting beams which form images on the photographs; (5) the main beams S101 and S202 which are perpendicular to the planes of photographs; (6) the main points 01 and O2, i. e. the points of intersection of the main beams with the planes of photographs; (7) identical points a1 and a2' c1 and C2' etc.; (8) the images of the same point on the land on the photographs of a stereoscopic paIr; (9) corresponding beams Slal' S2a2' etc.; and
Nets
and
Surveying
247
Work
A
c
I 'I
s -1J / 'y-
f!i!f: 1
/
~
10.12
~S ,11\ 2
~
a C1
Fig.
~
B~h
J I
Elements
of stereoscopic
a., C2
pair
(10) the focal distances of photographs !1 = 8101 and!2 = 8202. In stereophotogrammetry, the'position of a point on the land is determined by a direct spatial intersection which is formed by the projecting beams passing through tq~ leftand right-hand point of the base. For instance, the position of a point C (see Fig. 10.12)can be determined if the directions of projecting beams c181C and c282C are known. The surface formed by the plurality of the points of intersection of corresponding projecting beams is called the geometrical model, or simply model. Photographic cameras for making stereophotographs are provided with devices which ensure their definite and fixed position during exposure. A photographic camera can also be combined with a theodolite, and the combination is called a photo theodolite. The stereophotogrammetry of quarries can be performed from a fixed base on the
248
Ch. 10. Surveying
ground or from a flying object (aeroplane). It is distinguished between two principal cases of ground photogrammetry: with a horizontal position of the optical axis of a photographic camera (horizontal stereophotogrammetry) and with the optical axis inclined substantially relative to the horizontal (oblique, or perspective, stereophotogrammetry). Horizontal stereophotogrammetry is easier to make and has an essential advantage over the oblique method, since the latter requires more intricate techniques of photoreading. Horizontal stereophotogrammetry is usually done as a combination of three cases: with the optical axis of a photographic camera directed perpendicular to the base and deviated by 30-35° to the left and right from this position (Fig. 10.13). The coordinates of points on photographs are determined in a rectangular system of coordinates (x'x' and z'z' in Fig. 10.14).The point of intersection of coordinate axes, 0', is the origin of coordinates. The coordinates of a parti<;ular point a, as measured on a photograph, are commonly called the photocoordinates (xa, Za). Coordinate marks are fixed so that the point 0' which is the origin of coordinates, and the main point 0 of a photograph, are perfectly coincident. In that case, the coor-
Fig. 10.13 Horizontal survey
stereopho togrammetri c
in auarries
dinates of the main point, Xo and Zo, are equal to zero. The coordinates of points on the land are determined in the coordinate system adopted for a quarry. In contradistinction to photocoordinates, they are designated by capital letters xYZ. The coordinates of points on the land are determined on photographs according to the positions of the bundles of projecting beams at the instant of exposure. The characteristics that determine the positions of beam bundles are called the elements of the orientation of a photograph (which are subdivided into external and internal). The elements of internal orientation include the focal distance (focal length) of a camera and the coordinates of the main point Xo, Zo. Among the elements of external orientation (Fig. 10.15)are the coordinates of the left-hand end of a photographic base, Xs , ys and Zs ; the angle of inclination of thelmaih beam 6f the left-hand photograph, (J)1;the angle of turn of the left-hand photograph in its plane, "1; the oblique angle of the left-hand photograph
Fig. 10.14 Coordinate system of photograph
10.2.
Reference
and
Survey
Nets
and
Surveying
249
Work xph
Yph
/
ZPh
//
/ /~
:..'
/ //
/
1112
(111
~
/
HoLta,
/
x ~
x
,.../
01 ys
z
190 8 ~ ,
S1 i
xI I X
,.ls, I
---1
/
,I
B
./ Xph
I':/ / / Xs1
/ ff 2
Base
,
~
c --\-"'
/
z x
/
/
2 /
02
/
Horizontal.11
X
X2
1
Fig. 10.15 Element of external orientation of stereoscopic pair
base QB; the projection of the photographic base onto a horizontal plane; the height difference of the right-hand- end of the photographic base above the left-hand end, Az; the angle 'of inclination of the main beam on the right-hand photograph, m2; the angle of the turn of the right-hand photograph in its plane, "2; and the angle made by the main beam projections of the photographs onto a horizontal plane, y (Figc 10.16). With a positive angle y, the main beams are convergent, and the angle y formed by them is caned the angle of convergence; with a negative y, the main beams are divergent, and y is called the angle of divergence. The coordinates Xs , ys , and Zs , the photographic base Bp~, arid its dirbction angle QBare determined by geodetic methods. The oblique angles of photographs are set up by the orientation device of a phototheodolite. The inclinatio~ angles of the main beams of photographs, m, and the angles of the turn of photographs, ", are reduced to
nearly zero values by means of spirit levels mounted on the camera. The mine-surveying plans of land surface and mining workings art: usually constructed in a left-hand system of coordinates, whereas stereophotogrammetry employs a right-hand coordinate system. In both cases, however, the z-axis is arranged vertically. Let us analyse a case of normal stereophotogrammetric survey (see Fig. 10.16) in which the optical axes of the photographic cameras set up in points SI and S2 are parallel to each other and perpendicular to the photographic base Bph. It is assumed in this example that: (a) axis Xphcoincides with the direction of the photographic base; (b).axis yph coincides with the direction of the optical axis of the photographic camera set up in the point SI (the left-hand end point of the base); and (c) axis Zphhas a direction perpendicular to the plane formed by the two other axes.
250
Ch. 10. Surveying
in Quarries
-:4
<
"-
~
Fig. 10.16 Normal stereophotogrammetric survey
We have to determine the photogrammetric coordinates of a point K on the land. Let the image of the point K on the left-hand photograph be denoted by k, and that on the right-hand one, kr (see Figs. 10.16 and 10.17). The designations adopted in the figures are as follows: Yph'Xph'and Zphare the photogrammetric coordinates of the point K on the land (Yphis also called the distance to the point K); XI is the abscissa of the point k, on the left-hand photograph; Xr is the abscissa of the point kr on the right-hand photograph; ZI is the ordinate of the point k, on the left-hand photograph; Bph is the photograI'hic base; and fc is the focal length of the photographic camera of a phototheodolite. Noting the similarity of triangles KK'Sl and k,k~Sl (see Fig. 10.17), we can write: Yphlfc= Bphl(XI -Xr) Denoting X, -Xr = p (which is called the horizontal parallax, or x-parallax), we can write the formula in the form: BpJc Yph=-=-
xi -Xr
Bp,jc
p
(10.1)
..A'
From the similarity of triangles SlOK and Slojkj, it may be written: Xph/Yph= Xj/!c
or
Xph= (Xj/!c)Yph
Substituting for Yph' we get: Xph= BphX,/P
(10;2)
Similarly: Zph= BphZj/P
(10.3)
As follows from these formulae, in order to determine the photogrammetric coordinates Yph' Xph' Zphof points, one has to know the photographic base in nature and the focal length of the photographic camera of a phototheodolite and to find on the photographs the values of X" Z" and p. The length of a photographic base, the distance from the photo theodolite to the objects being photographed, and the focal length of a photographic camera are considered the principal parameters of a stereophotogrammetric survey. All objects of a stereophotogrammetric survey should always lie within a range between the minimum permissible distance Yph .and the maximum permissible distance mln
10.2.
Fig. 10.17 Y ph
Determining
from
the
Reference
and Survey
photogrammetric
pho-tographic
base.
coordinates The
for-
max mer IS needed "lor the appearance of a stereoscopic effect and the latter ensures the specified accuracy of measurements. The minimum permissible distance depends on the technical characteristics of stereoscopic devices and the specifics of the stereoscopic vision of an observer. It can be determined by the formula:
Yph
.= mln
(3-4)Bph
(10.4)
The maximum permissible distance is found by the formula: Mfc ~ Yph
= max
1.25-tmin loo
Nets and Surveying
(10.5)
where fc is the focal length of a phototheodolite; M is the denominator of the scale of the plan to be compiled; tmin = COS~ = = (x2/fc)sin~ (here ~ is the oblique angle of a photograph and X2 is t~e largest coordinate x on the right-hand photograph within the limits of the stereoscopic pair working stage).
of point
Work
251
on terrain
Depending on the length of the photographic base, accuracy requirements, and possibilities of photoreading, the length of the photographic base can be determined by one of the following methods: (I) if a quarry or land portion is surveyed for mapping, the base can be calculated by the formula: 2 B=Q~ (10.6) Mfctmin where y f is the distance to the farther boundary of the working portion of a given stereoscopic pair and Q is a coefficient which is taken equal to 15 for a single survey of a quarry and to 20 for mapping of the land surface; (2) in monthly complementary surveys for calculating the volumes of excavator cuts, the base length is found by the formula: y} . Bph
=
1.8 Mfcdmvtmin
( 10.7)
252
Fig.
Ch. 10. Surveying
10.18
Determining
useful
area of stereogram
where d is the width of a cut, m; mv is the specified root-mean square error of the volume measurement, %; and YI'fc, tmin and M as in formulae (10.5) and (10.6). It is also essential to know the overlapping area in a stereoscopic pair taken from a particular photographic base. Consider, for example, the photographic base SlS2 (Fig. 10.18). We construct the horizontal vision angles (working angles) a of a phototheodolite on the land from the ends of the base. The useful area F us' confined by points abcd, is depicted on each photograph of the stereo pair and later processed in a stereocomparator. It can be written by reference to Fig. 10.17: Fus= (D/t)(Lmin + Lmax) (10.8) where D is the depth of a survey; Lmin is the closer base of a trapezium; and Lmax is the farther base of a trapezium. The trapezium bases can be found by the formulae:
(
a Bph Lmin = 2tan 2 3.5Bph-Tcotan
Lmax = 2tan-
a 2
(Yph max
Bph --cotan2
a
2 a
) )
(10.9)
(10.10)
2
Noting these expressions, the formula for the useful survey area will be as follows:
in Quarries
(10.11) Ground stereophotogrammetric surveying includes reconnaissance, geodetic measurements, and land photography. Reconnaissance is done for selecting the locations of the points of a referenee net, photographic bases, and fiducial (correcting) points. Since the length, number and dire:c!tion of photographic bases can influence substantially the productivity of the survey work, it is advisable to have a minimum number of bases that is sufficient to cover the entire survey area without leaving 'dead' spaces (Fig. 10.19). In order to obtain the required accuracy in the determinations of the coordinates of points on the photographs of stereoscopic pairs and the horizontal parallax at each station, it is essential to establish a number of fiducial (correcting) points whose coordinates are determined by the photogrammetric or geodetic method. Thus, it is possible to compare the coordinates obtained by two independent methods and to check the ste~eophotogrammetric survey. Three correcting points are usually established for each photographed stereoscopic pair at each station. One of these points should be located in the closer plan and the other two, in the farther plan of the area being photographed. In order to decreasethe number of correcting points, some of them are usually made common for adjacent stereoscopic pairs. Places for establishing the photographic bases are chosen so that the bases can be ~llel to the working front and at the same level with the objects to be photographed (or somewhat above them). It is also essential that the height difference of the ends of the photographic basesbe as small as possible. In stereoscopic photographs of a quarry taken from an inclined base, the like points will be displaced relative to each other (vertical f)a-
10.2.
Reference
and Survey
Base3 (200 m) Base3a (BOm) ~
Nets and Surveying
Work
253
photographic bases can be located on the flanks of a quarry if the quarry depth is not large; in deep quarries, photographic bases Base2 (170m) ./1 \ are arranged on bench berms; Base2a (60 m) ./ .I;:-, ~ i 1/ .';Z:A'.-~ (2) in working systems with internal waste I ~, 'x::i .\',. \dumps and in those with conveyer bridges, I .1 ~' I ~// \ , .i" <." zee""7-:7'\ -.) photographic bases are located directly on ~ --' ,~ / /-r. \ ( \~ / the dumps; \ ---"t;..~:7 .\ (3) in combined working systems where Basel(80m) ...\ Base4(100m: \ rocks are transported to external and \ internal waste dumps, the upper and lower t;') \ I I H8 ~ benches are photographed separately. The 1 Base 5 (100 m) upper benches are photographed from the ~I "'1 ,.\ baseslocated on a non-working flank and the \ , .. lower ones, from the bases on internal waste \ Fiducial' ) points I dumps. To take photographs, tripods are set up at ~ the ends of a base. A theodolite is arranged on the left-hand end of a base (relative to the direction onto the objects to be photographed) in order to measure the length of the base line. After that, the photographic 100 0 100 200m camera is oriented relative to the base, and photographs are taken from the left-hand Fig. 10.19 Example ,of stereophotogrammetric and right-hand end of the base. The optical survey of quarry axis of the camera is arranged normally to rallax). This effect can be fully avoided or at the direction of the base line. least minimized to a tolerable level in a Geodetic work in ground stereophotostereocomparator only in cases when the grammetry includes the following operations: height difference between the ends of the I. Determination of the planimetric cophotographic base is not more than O.3Bph. ordinates of the left-hand points of basesand Besides,base points should be established in measurements of base lengths. The length of places where they can be preserved for a long a photographic base can be measured by a time. Adjacent bases should be chosen so as tape, wire or other instruments, provided that to ensure the specified overlap in adjacent the discrepancy between the forward and stereoscopic pairs. Places for the location of back measurements is not more than photographic bases should be chosen so that 1/5000-1/2000 of the base length. The plaa porti~~ of quarry or land can be photonimetric coordinates of the left-hand base graphed With the least possible number of points can be determined by triangulation, method of analytic network, by intersections stereoscopic pairs. Depending on the size of quarries, working and resections, polygonometric or theodolite systems, and the orientation of the mining traverses, polar method, and photogramfront, the following versions of the arrange- metry. ment of bases in quarries are possible: 2. Determination of a direction angle. The (1) in working systems with overburden direction angle (aB) of a photographic base is transportation to external waste dumps, found by measuring in the left-hand base
J
254
Ch. 10. Surveying
point of horizontal angles between the direction from that point onto the righthand point of the base and the direction formed by two certain points of a geodetic reference net. These angles are measured with an accuracy not worse than 5". The error in the measured direction angle of a base should be not more than: ma =
me
(101?) , ,
D
2yphmax
where p" = 206265" and meis the permissible root-mean square error in determining the positions of contour points. 3. Determination of the elevation marks of bases and correcting points by technical geometric levelling. The correcting points are fixed by placing marks on them, which are made as screensof plywood or another material. The vertical and horizontal sizes (b and a) of screens are calculated by the formulae: b = O.12yp h /j~, max
a = O.O6yPh
max
/fc
(10.13) Photography proper is a critical procedure in stereophotogrammetric surveys of quarries, since the quality of negatives produced is decisive for the accuracy with which the point coordinates and parallax will be detemlined. The best results are obtained on sunny cloudless days. During exposure, the Sun should be behind or sideways of a surveyor. On cloudy days, it should be observed that the objects being photographed are not shaded by clouds at the instant of exposure. Photographs are made on high-contrast repro-c duction films or plates. ~\ When making the photographic field work, the phototheodolite is set up on one of the base points so that two of its foot screws are arranged along the direction of a base line. A lifting apparatus with a sighting mark is established on the other base point; the foot screws of this apparatus should also be
in Quarries
oriented along the direction of a base line. Photographs are taken by the techniques including the following procedures: (I) tripods with lifting devices are set up on both points of a base line, and the elevation of the left-hand base point is measured; (2) the phototheodolite is then arranged on the left-hand point, and the sighting mark, on the right-hand point; (3) the phototheodolite is oriented onto the right-hand point of the base, and it is checked that the camera lens is closed; (4) a plate-holder (film-holder) is set in place, and its shutter is withdrawn; (5) the plate-holder is pressed against the focal frame of the camera by means of a screw on the back cover; the serial number of the photograph to be taken and the number of a station are set up on the numerator, and the kind of photograph (normal or with right- or left-hand deviation) is recorded; (6) the positions of spirit levels and the orientation of the phototheodolite are checked; (7) the correct exposure time is determined; (B) the plate is exposed, and the positions of spirit bubbles and phototheodolite orientation are checked again; (9) the holder shutter is closed, and the plate-holder is taken off from the camera; (10) new photographs are taken irl this way, with the camera axis shifted first to the left and then to the right; (II) the phototheodolite is taken off, and a sighting mark is set up in its place; and (12) the photo theodolite is set up on the right-hand base point to take new photographs as described. Stereophotogrammetric office work includes the processing of exposed plates (films) in a laboratory, preparatory work, and the compilation of the plans of mining workings. The preparatory work includes the following procedures: (a) calculation of the geodetic coordinates
10.2.
Reference
and
Survey
and elevations of base points and reference points; (b) preparation of the processing apparatus; and (c) preparation to the correction of a model. The results of the planimetric and elevation surveying of bases and correcting points are processed in the office by common geodetic methods. The most popular one is the graphometric method with the use of stereoautographs and other devices operating by the principle of photogrammetric intersections. These devices can solve mechanically the formulae for the normal and equi-deviated cases of photogrammetric survey. The coordinates of the points of a terrain are determined on stereophotographs by means of stereocomparators. The operating principle of a stereocomparator reduces to the reconstruction of the land portion photographed at a particular instant by constructing a geometrical model. Each point of the model is obtained by making intersections from the ends of the projection base. The planimetric coordinates of points, x and y, are found graphically in the stereoautograph and fixed by counters, in millimetres, on the scale of a model. The elevations of points are read off, in metres, from the altitude counter of the stereoautograph. By combining the stereoautograph with a plotting table (coordinatograph), it is possible to construct plans and profiles and deliver the planimetric and height coordinates of points onto a perforated tape or printer. Plotting a plan is started from drawing the elements of hydrography. After that, horizontals are plotted. In the plans of mountainous regions, plotting horizontals is started from the highest points. The results of the stereophotogrammetric survey of a quarry can be used for calculating the volume of mined rock. This can be done by using the measured photogrammetric co-
Nets
and
Surveying
Work
Zphi
al,
rph
ordinates of points of bench crests. Volumes are calculated by means of digital models or tables of positions of benches with their characteristic cross-sectional areas. If vertical sections are used (Fig. 10.20), the areas are calculated by the following formulae: a -" , a -" , ;,u-Yph;,u-Yph;.u' ;,I-Yph;,I-Yphi,1 a; = 0.5 (a;,u + ai,,) h 'i = Zi,u, -Z;,I' , h "; = Zi,u" -Z;,I " h=0.5
(h~+h'~ ,
,
),
S.=a.h. ,
,
,
256
Ch. 10. Surveying
oblique stereophotogrammetry, the optical axis of a camera is held at a specified angle to the vertical. The planimetric aerial stereophotogrammetry of quarries is carried out from specially equipped aeroplanes and helicopters controlled by an on-board electronic computer. This ensures automatically that the aircraft will follow very accurately the given survey route at the specified altitude. The computer also calculates the paths of turns and takes into account descending and ascending air currents and the velocity and direction of wind. The equipment of an air-survey aircraft can control automatically the frequency of exposures. The brightness of the land surface is measured continuously by exposure meters, and the variations of the terrain relief are traced by locators. Since aerial photographs are taken from an appreciable altitude, aerophotogrammetric cameras are of the fixed-focus type, i. e. focussed at the infinity. Photographs are made mostly on a photographic film. A large number of photographs (up to 200-300) can be taken without recharging the camera. The size of photographs can be 18 cm x 18 cm or 30 cm x 30 cm. As may be seen from Fig. 10.21 which shows the scheme of taking an aerial photograph of a terrain, an aerial photograph is the central projection of the terrain with the projection centre in a point S. The distance fc along the perpendicular drawn from the projection centre S onto the plane of an aerial photograph is ,called the main focal distance (length) of an ~rial photographic camera. The point of intersection of that perpendicular with the plane of a photograph (point 0) is the main point of an aerial photograph. The vertical line SN is called the photographic altitude (or clearance) (H), and the point where this line intersects the plane of a photograph is called the photographic nadir. The angle OSN (a) is conventionally called the angle of inclination
in 01
Fig.
10.21
Taking
aerial
photograph
of terrain
of a photograph. If this angle is equal to zero, a photograph is called horizontal. A horizontal photograph of a flat horizontal terrain is virtually the plan of that terrain. The scale of a horizontal photograph is equal to the main scale, i. e. 1 : m = fc : H. Aerial photographs with the angle of inclination to the horizontal up to 3° are termed planimetric. With the inclination angles more than 3°, oblique, or perspective, aerial photographs are obtained. Before making an aerial photogrammetric survey, it is required to make calculations for selecting the survey parameters. For quarries with the rate of face advancement not more than 30 m, the recommended scale of an aerial photogrammetric survey is l/Ms = 1/10000; if the rate of face advancement exceeds 30 m, it is advisable to use the scale l/Ms = 1/15000. The selected values of l/Ms are then compared with its value calculated by the formula: ---
1.4m~
(10.14)
D Ms-(~). where
m~ =
0.02 mm
is the
root-mean
10.2.
Reference
and
Survey
Nets
and
Surveying
Maximum depth of quarry, m
fc, rnrn
up to 300 up to 200 200-300 300-500
100 100 140 200
'M,
'10000
Maximum depth of quarry, m
J;. mm
up to 300 100 300-400 140 400-500 200
square displacement of contour in plan expressed on the scale of a photograph; mv/v = 2.5% is the specified accuracy in determining the volume of extracted rock; and D is the width of a face. If it turns out that the survey scale calculated by formula (10.14) is larger than that adopted initially, the aerial survey should be carried out on a larger scale. The focal length fc of the aerial photographic camera for quarry surveying is chosen depending on the selected scale M. and the depth of the quarry by reference to Table 10.1 The photographic altitude H ph above the medium plane of the quarry is calculated by the formula: Hph = fcM. The photographed materials are processed in stereophotogrammetric apparatus with projector cameras similar to those used for taking photographs. The projector cameras and negatives are arranged mutually in the same positions they had at the instant of exposure. In this way there is formed a spatial model of the surveyed terrain on a reduced scale, which is analysed by means of a binocular microscope and spatial marks. For aerial surveys of quarries, a flight course for a photoairC!:alt should be plotted. For most quarries, a single course is usually sufficient. For those of an intricate configuration and large dimensions, a number of courses are plotted (Fig. 10.22). Aerial photographs taken along a course 17-1?70
257
""'
Table 10.1
15000 18000
Work
.x
v
Fig. 10.22 Making two courses of flight for aerial photography of quarry of intricate configuration
should have a longitudinal (forward) lap (Fig. 10.23)which is denoted by p and expressedas percentage of the side I of a photograph. The longitudinal lap can be calculated by the formula: h p = 62 + 50 ~
(10.15)
2Hph If parallel courses are plotted, the photographs of adjacent courses should have a lateral (side} lap q which is e~pressed as percentage of the photograph side length and calculated by the formula:
where 1 is the size of a photograph and m is its scale. An inclination angle of a photograph causes the displacements of points on it. For planimetric aerial photographs, it can be
Ch. 10. Surveying
Fig.
10.23
Longitudinal
and lateral
~ laps of photographs
taken approximately that the displacements take place in the direction of a line connecting a particular point with the main point of the photograph. Depending on the location of a point and the inclination angle of the photograph, this displacement can be directed towards the main point or away from it. The maximum displacement of a point in planimetric photographs under the effect of the inclination angle can be determined by the approximate formula (see Fig. 10.21): 8" = (r2/fc) (a/p) (10.18)
in Quarries
in courses
displacements on aerial photographs (Fig. 10.24). Introducing the designations: AAo = h is the height difference of a point A above a point N; SN = H is the photographic altitude; aO = r is the distance on an aerial photograph from a point a to the main point of a photograph 0; and aao = L\r is the displacement of a point on a photograph due -q-Qo
Q
~s
where r is the distance from the given point to the main point of a photograph; a is the inclination angle of a photograph; and p = 57.3!1. For instance, the maximum displacement of a point on a photograph withfc = 200 mm, r = 50 mm, and a = 2° will be: 8" = (502/200) (2/57.3) = 0.4 mm ~
It then follows that the displacements of points on aerial photographs under the effect of the inclination angle are mostly insignificant and in some cases can be neglected. Since the points of the physical surface of the Earth are located at different heights relative to a level surface, this oauses their different
AO
, Fig. 10.24?Determining on aerial photographs relief
" N displacements of points owing to the effect of land
10.2.
Reference
and
Survey
Nets
and
Surveying
259
Work
S1S2Ml' we have: H1 = Bphfc/P1
(10.20)
This expression can also be written for any other point on the terrain, say, M 2: H2 = Bp/c/P2 (10.21) Since the elevation difference of two points can be regarded as the difference of their distances, then: h=H2-H1
Fig. 10.25 to distance base
MO Longitudinal parallax and its relation from point on land to photographic
Noting expressions (10.20) and (10.21), we obtain: h= ~
-~
P2
= Bp/c(P1 -P2) P1
PtP2
Denoting (Pi -Pi+ J by Lip. we can finally write: to the terrain relief, it may be written that: Ar = rh/H (10.19)
h=~
Experience shows that the distortions in aerial photographs increase with increasing distance of points from the main point of a photograph. Thus, in operation with aerial photographs, it is advisable to utilize only the central portion of photographs, which is called the useful (working) area, rather than the entire area. Practically, the useful area of a photograph is limited by the lines drawn in the mid of the longitudinal and lateral lap. Photographs obtained by aerial stereophotogrammetry have a longitudinal lap more than 50%. Thus, each portion of a terrain is depicted on two photographs. Let the point M I of the terrain (Fig. 10.25) be represented by a point mI on the left-hand photograph and by a point m~ on the right-hand photograph. The distances from the photographic centres to these points are mI OI = xi on the left-hand photograph and m~O2 = -x.. on the right-hand on~)The difference xI -x.. = = PI is called the lon-gitudinal parallax. Considering similar triangles m~m~S2 and
On aerial photographs with an inclination angle or non-horizontal base, Pi and ~P turn out to be distorted. For that reason, before calculating the elevation differences, the values of Pi and ~P are corrected for the effect of the inclination angle and inclined base line. This problem can be solved analytically or with the use of photogrammetric devices. The observations and measurements on aerial photographs are made by a stereoscopic method. The simplest stereoscopic device is a stereoscope in which a left-hand photograph is mounted at the left and viewed by the left eye and the right-hand one is mounted at the right and viewed by the right eye. In this method, a direct stereoscopic effect is produced, i. e. points which are closer to an observer in nature will be seen closer in a stereomodel. Before the aerial surveys of a quarry, it is required to carry out field preparations. In particular, each stereoscopic pair should be provided with four points of planimetric and
17.
(10.22) Pi+
~p
260
Ch. 10. Surveying
elevation control (control points, or beacons), which are usually arranged in places where they can be preserved for a long time and used in subsequent aerial surveys. The planimetric coordinates of the control points should be determined with an accuracy specified for the coordinates of survey net points. The elevation marks of control points are determined with the accuracy of technical levelling. Aerial photographs are processed for the purpose of compilation and complementation of mining work plans. This is done in all-purpose stereophotogrammetric devices. Irrespective of the type of device, processing includes the preparatory work, mutual orientation of aerial photographs in the device, and geodetic orientation. The preparatory work includes the preparation of plates (application of kilometre network and control points), manufacture of transparencies, preparation of aerial photographs, checking of the device, calculation of model scale, focal lengths of cameras, etc. The mutual orientation of aerial photographs is essentially the determination of the position of one photograph in a stereo pair relative to the other. This procedure can be performed by various motions depending on the design of a particular device. For instance, one of the cameras may be considered to be fixed and forms a stationary basis relative to which the position of the other camera is measured. The mutual orientation in a stereophotogrammetric device is carried out by observing successively a number of points on photographs and eliminating their lateral parallax. Though the problem is solved by the method of successive approximations, the resulting solution is quite accurate (to the accuracy offered by the apparatus for the elimination of lateral parallax). The geodetic orientation of a geometrical model includes its scaling and horizontalization. The scaling consists in determining
in Quarries
the ratio of like line sections s and S taken respectively on the restored and photographed surfaces, i. e. l/m = s/S. In order to determine the scale of a model, at least two control points should be available. The horizontalization of the model reduces to determining the angles of turn of the model on the corresponding axes x and y of the geodetic system of coordinates. Thus, for solving the problem of geodetic orientation of the model, it is required to have at least three control points, all the coordinates being known for two of them and the elevation mark, for the third point. In geodetic orientation, the plate is also oriented. For this purpose, the measuring mark of the device is matched with one of reference points, and the centre of a focussing microscope is set up above the corresponding point on the plate. The microscope is then sighted onto another reference point, and the plate is turned until the centre of the microscope will be on the line connecting these points. 10.3.
Mine-Surveying of Drilling and Blasting
Coverage Work
Mine-surveying servicing (coverage) of drilling and blasting work consists in the following: (a) preparation of the initial materials for making a plan of blasting operations; (b) transfer of the blasting plan into nature; (c) determination of the actual positions of blasting holes after drilling; and (d) determination of the volume of blasted rock and the location of worked-out area after rock excavation. A plan of blasting operations is compiled on a scale of 1/1000 or 1/500. Surveys are carried out for the purpose, which have to determine the following characteristics: the position of the upper bench crest; boundaries of the slope fully cleared up by excavation;
10.3.
Mine-Surveying
boundaries of the muck pile left after earlier blasting work; elevations of the characteristic points of the upper and lower berms of a bench (in intervals not more than 20 m); positions of contact-line supports and railway tracks (in quarries with railway transport); boundaries of rocks in the massif with different characteristics of drillability and explosibility; positions of tectonic disturbances and characteristics of cleavage cracks; boundaries of a dangerous zone as determined by the rules of blasting work and positions of buildings and structures near that zone. According to the plan of blasting operations, the design positions of the mouths of blasting holes are transferred into nature and fixed by pegs with marks indicating the number of a hole, the number of a drilling rig, the design depth of a hole, and the soil resistance. In laying out the hole mouths, the mine surveyor, as a rule, transfers instrumentally into nature only the boundaries of the block to be blasted and marks them on the upper crest of a bench. The mouths of blasting holes in a block are marked by a blaster foreman. The instrumental layout of the mouths of blasting holes is carried out only in cases when the portions to be blasted are located at the design boundary of a quarry and per" manent access roads are being built. The main methods for transferring blasting holes into nature are the polar method and method of perpendiculars with the use of points of a surveying net. Angles are laid off with an accuracy not worse than 5'. Distances up to 50 m can be measured by means of range finders. In the method of perpendiculars, measured distances are rounded off to a decimetre. If a quarry has high benches of an irregular shape, these should be surveyed properly. Since, according to safety regulations, staffmen are prohibited to stand on the slopes of benches, such slopes should be surveyed by
Coverage
of
Work
261
(a\
/
II " " "
/ / QJ 0.
~
/ 4 /
..,i~, " , ~
/
~I
I
~ (b)
't-:
Fig. 10.26 Surveying means of inclinometer; rod
of bench profile: (a) by (b) by means of telescopic
instruments which can determine the positions of staff points without the presence of men on them, for instance, tacheometers, inclinometers (or theodolites) with an attachment for measuring inclined distances, a telescopic rod with a tape, etc. For making a profile survey by an inclinometer (Fig. lO.26a), the instrument is set up on the upper crest of a bench to measure the inclination angle onto a characteristic point, after which the distance to the sighting point
262
Ch. 10. Surveying
is measured by a special tape. In order to measure a length, a cord with a weight is tied to the end of the tape and is let to slide along the slope of the bench. One of the workers stands on the upper crest and lowers the tape end with the weight, whereas another worker, standing on the bench foot in a safe place, stretches the cord and the tape so that the tape beginning is matched with the point to be measured. Measurements with a telescopic rod are made in the following manner (Fig. 10.26b). The telescopic rod with a roller at its end is applied horizontally to the crest and a measuring tape with a weight is passed over the roller to the point of interest on the slope. Two coordinates are measured: the horizontal distance from the upper crest to the rod end and (on the tape), the vertical distance from the rod end to the surface of the slope. After drilling the blasting holes, the block to be blasted should be surveyed. The positions of the holes at the flanks of the block are fixed from the points of a surveying. The positions of intermediate holes are determined by measuring the distances between the holes. Besides, it is required to measure the distances from the holes to the upper crest and the soil resistance. If the excavator work or clear-up work is carried out on the bench after compiling the plan of blasting operations, an additional survey of the bench should be carried out. The height marks of the mouths of blasting holes are determined by geometrical levelling. Having surveyed a prepared blasting block, the mine survey6r compiles cross sections through blasting holes on a scale of 1/500, 1/1000 or 1/2000, which are needed for making a corrected plan of blasting work. These sections should show the profile of the bench slope, blasting holes, the design and actual level of the bench foot, contacts of various rocks and mineral, and drillability and explosibility characteristics of the rocks. It is also required to draw a plan of the
in Quarries
blasting block which should give the block boundaries, blasting holes, the positions of the upper and lower bench crests, rock contacts, and the situation on the bench berms. Mter blasting, the blasted rock is surveyed in order to determine the boundaries of the muck pile, the break line, and several characteristic points along the profile lines on the surface of the muck pile. 10.4.
Survey Work Servicing
for
Transport
This work, which occupies an essential place in the daily activity of mine surveyors in quarries with railway transport, includes the laying out of routes of face railway tracks, periodic profiling of tracks, etc. In order to obtain initial data for laying out railway tracks, a levelling survey of the bench surface is done after the removal of the first strip of the rock from the muck pile. This survey determines the recessed places which should be filled with soil and the protruding ones which should be cut off for evening the berm. After that, the railway track axis is transferred onto the working berm of the bench. Two circumstances should be considered in this case: the axis should be laid out so that two bands of an excavator cut can be charged into cars without relaying the railway track, and the tracks should not occupy the zone of the muck pile of a next blast. As the design axis of the railway track is transferred into nature, picket points are established along it, and geometric or trigonometric levelling is carried out. By the results of levelling, it is decided to correct the track profile in accordance with the permissible ruling gradient. The surveys of permanent railway tracks in a quarry and beyond its boundaries are made by the method of perpendiculars or polar method from the sides of a theodolite traverse run along the track axis. These surveys have to determine: the axis of a track; centres
10.5.
Survey
Work
of switches; the top gauge width; the width of filling and grooves at the top and bottom; places for kilometre poles; etc. Track curves are surveyed by the method of perpendiculars: chords are drawn between the ends of a curve and distances to the axis of the curve are measured along perpendiculars to these chords. The layout work for the construction of automobile roads is carried out by mine surveyors according to the design materials which give the gradients, curvature radii, width of roadbed, etc. At the end of road construction, instrumental survey should be carried out in order to check that the actual characteristics of the road correspond properly to the design values. 10.5.
Survey
Work
in Trenching
This work is carried out on the basis of design materials which should include: the plan of a trench with the coordinates of junction points, direction angles of junctions, angles of turn, distances between the vertexes of turning angles and radii of connecting curves; longitudinal and transverse sections of a trench which should show the profiles of the Earth's surface and the design profile of the trench bottom, the sequence, cross sections and axes of cuts, and railway and drainage ditches; the plan of blasting holes with the coordinates of their mouths, direction angles of hole axes, and hole cross sections. For laying out a trench on the ground, a theodolite traverse is run. The positions of upper crests (for trenches to be cut in loose rocks) or the positions of blasting holes (for those to be made in hard rocks) are transferred into nature from the sides of that traverse. In making trenches by power shovels without blasting work, the following cases of mine-surveying servicing are possible: 1. A trench is dug in a slope and the extracted rock is dumped downhill
in
263
Trenching
30
-3~=--3'{,1-
!':-
cT
1~~
64
~o
93
"
O
4'
.
J~
~ ~
O 40
~/'lc
1?0 ~2 I,
~2 .-A
~ "
..A
" 8 8
Fig. 10.27 Trench digging in slope (Fig. 10.27). The main task of the mine surveyor in this caseis to observe that the trench axis has a specified gradient. Initially, the junction point 1 of the trench axis is transferred onto the ground according to the design coordinates. A theodolite traverse is then run according to the preliminary direction of the trench axis. This direction is fixed by temporary picket points in intervals of 50-100 m. With the known points of the trench bottom, points 10' 20, 30, 40 are determined in nature; these points form the line along which the plane of the trench bottom intersects the slope. After that, the corrected trench axis is laid out (points 1, 2, 3, 4) by using the intersection line and the design width of the trench. Finally, the lines of the upper crest (points 1", 2",3", 4") and of the lower crest (points 2' and 3') are marked
264
Ch. 10. Surveying in Quarries c-c
1°°° i 0 0
0
1 00°°'0
1000 C -.1-0
072
'/\I'fi~~r# \ I III
0001 I
I'
-0-0-
~-0-o-0-'--
I...
I/
\JrLI-~1
c
...1
1...t..~1 1...t...1 B : ... -+
! ...I
IB
~.~-81A-A
y
>---r ~
A
Fig.
Fig. 10.28 Trench cutting with continuous and rock loading into railway cars
iJ7
10.29
Trenching
by excavating
explosions
face
on the ground by measuring from the trench axls. 2. A trench is cut in a continuous face and the extracted rock is loaded into transport vehicles on the trench flank (Fig. 10.28)or the rock is extracted by drag line and discharged onto the trench sides. A theodolite traverse is run as described in the previous example. The trench axis AB is transferred and fixed in straight portions at distances up to 50 m and in curved portions at intervals up to 10 m. At the same time, the axis of the railway track is laid out on the trench flank (or the axis of the waste rock dump if the trench is dug by a drag line). During the cutting of the trench, bench marks are established in intervals of 20-30 m (R1,R2, R3, etc.) which give the elevations of the trench foot. The bench marks should be displaced from the trench axis so as to be on the line of one of excavator tracks.
3. A trench is made by excavating explosions (Fig. 10.29). In this case, the design positions 2 of the blasting holes are transferred into nature by means of theodolite traverses or geodetic intersections. After drilling 'the blasting holes 1, they are surveyed for the correction of the plan of explosions. Mter blasting, another survey is done to determine the volume of blasted rock: then the axis and side crests of the trench are transferred into nature, and bench marks are established to control the trench foot gradient. 10.6.
Survey Work in Open-Cast with Conveyer
Mining Bridges
The specifics of survey work in this case are associated with the fact that conveyer bridges have a rather intricate design and a very larg~ mass (sometimes more than 7000 t) (Fig. 10.30), that is why high dynamic loads that may cause overstressing the bridge el-
10.6.
Survey
Fig. 10.30 Conveyer bridge: I-facing support; 5- dumping console truss
Work
console
in Open-Cast
truss; 2-facing
ements are inadmissible. This necessitates additional survey observations on the trusses and other e,lements of conveyer bridges in order to preserve their strength. The minesurvey servicing of conveyer bridges consists in checking the plan position and gradients of the railway tracks of bridges and controlling the horizontal, vertical and angular mobility of a bridge. The plan position of tracks is controlled by theodolite surveying with measuring the spacings between the rail lines by a steel tape; the track gradient is controlled by geometric levelling. The control of horizontal mobility is carried out in view of the fact that the distance between the facing and dumping supports of a conveyer bridge can be increased or decreased depending on the varying geometry of faces.An increase or decrease of this spacing beyond the specified limits is however inadmissible. The mine surveyor has to control periodically the spacings between the axes of the facing and dumping supports. For this purpose, theodolite traverses are run along or near the track axes on the working berms of benches on which the bridge supports are moving. The theodolite traverses should always be connected to the points of a reference net. A series of profile lines roughly perpendicular to the mining front are also laid out in a quarry. In each profile, the distances from the sides of the theodolite traverse to
Mining
support;
265
3-middle
truss; 4-dumping
the nearest rail are measured by the method of perpendiculars and recalculated into the distances to the support axes. By the results of field measurements, the positions of support axes are marked on the mine-surveying plan which serves as the basis for correcting the positions of tracks and supports of a conveyer bridge. The control of vertical mobility of conveyer bridges is done to check that the height difference between the supports of a bridge does not exceed the specified safety licnit. The detailed surveys of coQveyer bridges are carried out for determining their deformations in order to prevent the appearance of dangerous deformation. This work requires the stoppage of a bridge for a long time. In these surveys, points are marked at the intersections of beam axes in each unit of the metal structure of a bridge. The axial line bb' (Fig. 10.31) is fixed at the upper and lower horizontal belts of the bridge. A theodolite is then set up at the edge of the upper belt above a point 19-b', and the directions onto a point lI-b (longitudinal axis of the belt) and points 19-a' and 19-c' are determined. In order to determine the lateral deformations of the bridge truss, the ordinates from the axial lines to the centres of units of metal structures are measured by a millimetregraduated rule or ordinatometer arranged perpendicular to the collimation axis of the
266
Ch. 10. Surveying
in Ouarries
Top cho
~
a' ***~~1918171615141312
A
1110
9
876
54
3210111a
Axis b'
--c -b
c'
Bottom a,19181716151413
12All
10
chord 9876543210111111
.
~.
~
~~~=a ---b
.c c
Fig.
10.31
Fixation
of axial lines of conveyer
bridge for detailed
theodolite. The distances between the points along the collimation axis of the theodolite are measured by a controlled-tension steel tape. Similarly, the distances in cross sections to the extreme points of the belt are determined. The results thus obtained are used for plotting the actual state of the bridge on the design plan and listing the deformations of all units of the upper belt of the main truss. The horizontal surveying of the lower belt of the main truss is carried out by the method of ordinates from the sides of a theodolite traverse run on side ladders along the truss. Measurements are made by controlled-tension steel tapes with an accuracy to a millimetre. A plan of the lower belt is plotted by the results of a survey, and the actual positions of structures are marked on it.
10.7. Calculations of Volumes of Extracted Overburden Rock and Mineral in Quarries In mine surveying, the volumes of extracted mineral and overburden rock are calculated by the main plans of mining work levels. The choice of the best calculation method depends on the mining technology and the surveying method employed. I. In open-cast mining of loose rocks by conveyer bridges, excavators, etc. the work-
surveys
ed-out area has a more or less regular shape, and the required accuracy in calculations of the volumes of excavator cuts can be ensured by any method of surveying, including tacheometry. 2. On some kinds of loose deposits, the worked-out area has an irregular shape, so that tacheometry cannot ensure the specified accuracy. In such casesit is recommended to employ the ground stereophotogrammetric surveymg. 3. In the extraction of igneous and hard ro9ks with preliminary loosening to the width of one excavator cut, the calculations of volumes should be carried out by the results of ground stereophotogrammetric surveys or by weighing the mined rock and considering its density. 4. If rocks are loosened by multirow blasting and the loosened rock is later loaded by several excavators, the calculations of volumes can only be done by the results of weighing of the mined rock (of the known density), since other methods are insufficiently accurate. The determination of volumes by the results of weighing of the mined rock (operative accounting) has a number of essential advantages: (a) the method offers the highest accuracy and can be used with all technological schemes of mining;
10.7.
Calculations
of Volumes
(b) it provides timely information on the volumes of mining and stripping work even for individual mining teams and for any time interval; and (c) it is possible to control efficiently how fully the transport vehicles are loaded. The volumes of extracted and blasted overburden rock and mineral can be calculated by the method of arithmetic mean, horizontal and vertical sections, volumetric measuring grid, etc., provided that the 'errors in their determination do not exceed the following permissible values. 1. If the volume of the extracted overburden (mineral) is found directly by surveying of benches, the permissible error cry, %, can be calculated by the formula: p cry
=
1500/JV
(10.23)
p
where V is the volume of the extracted rock (recalculated to the undisturbed rock), m3. Formula (10.23) is applicable for volumes from 20000 m3 to 2000000 m3. For larger volumes, it may be taken that cry = 1%; for smaller volumes, the method of surveying and calculatiO;n of volumes is established by an instruction so that the error cry is not p greater than 10%. 2. If the volumes of the extracted (blasted) overburden rock and mineral are determined in the loosened state and recalculated to the volume of the undisturbed rock (using the loosening factor), the permissible error cry, p %,
can
cry
=
be
found
2200/JV
by
the
formula:
(10.24)
p
where V is the volume of the extracted (blasted) rock recalculated to that of the undisturbed rock, m3. Formula (10.24) is applicable for volumes ranging from 45000 m3 to 2200000 m3. For greater volumes, it is taken that cry = 1.5% p and for volumes smaller than 45000 m3, the method of surveying and volume calculation and the determination of the loosening factor
of Rock and Mineral
267
are established by an instruction so that the error ay is not greater than IO%. The ~thod of arithmetic mean is recommended for cases when the mining technology permits the determination of the volumes of the mined rock (recalculated to the undisturbed rock) directly by the results of bench surveying. The volume of a block is calculated in that case by the formula: v= Shm where S is the area of the base of a figure or section, m2, and hm is the mean depth of a cut, m, or by the formula: V=~S!h2
m
where Su and SI are the cross-sectional areas at the upper and lower bench crests, m2, and hm is the mean depth of a cut, m. The mean depth of a cut can be found by the formula: hm= 1: 2u/nu-1: 2l/nl where 1: 2uand 1: 21are the sums of elevations respectively at the upper and lower bench crests and nu and nl are the numbers of staff points on these crests. The method of horizontal sections is advisable in cases when bench crests and intermediate sections are indicated on the plan of mining workings. This is usually done by stereophotogrammetric surveying. In this method, the total volume is calculated as the sum of volumes of individual horizontal layers. The areas of horizontal sections are measured by a planimeter or measuring grid or determined analytically. Planimetry is carried out twice, following the contours of sections clockwise and counterclockwise. The discrepancy between the two measurements should not exceed 3% for areas up to 15 cm2 or 2% for larger ones. The final result is taken as the arithmetic mean of the two measurements. Large areas and sections of a regular shape
268
Ch. 10. Surveying 2 ..!:.Q.
~\
~: s
-/\\\1:,\
. n
'\. \
can be divided into simple geometrical figures whose elements are measured by a rnillimetre-graduated rule. Analytical determination of areas is also possible. The method of vertical sections (Fig. 10.32) is usually employed for calculating the volumes of blasted rock surveyed by tacheometric methods. The following formulae are used in calculations: (I) in cases when spacings between the section planes are different: SI + S2l
S2 + S3 2
l2
S.-1
-..on +Sn. ~ln-l
I +
+
tlU.L:»
where s 1 and S. are the cross-sectional areas at the boundaries of an extracted cut (block), m2; S2' S3' ..., S.-1 are the areas of intermediate sections, m2; and 11,12, 13' ...,1.-1 are the spacings between the sections, m; (2) "in case of equal spacings between the
) \
.I.
volumes of blasted rock if this is shown on a plan in projections with numerical marks or in cases when a cut has intricate contours and surface. The volume of the rock in this method is found by the formula: n
v
Fig. 10.32 Determining mineral reserves by vertical sections
v- -2
in Quarries
2
where I is the spacing between the sections, m; S are the areas of intermediate sections, m2; and n is the number of sections. The spacings between the sections should be not greater than the distances between the staff points. The method of volumetric measuring grid is recommended for the calculations of the
sLh, 1
where S is the area of the grid base, m 2; n is the number of baseswithin the boundaries of the contour being measured; and h is the thickness of the layer of extracted (blasted) rock in the centre of each grid base. The choice of a method for volume calculation depends on the shape of the worked-out area and muck pile, as well as on the method of surveying. In surveying of undisturbed rock, various methods can be used for the calculations of volumes. With a tacheometric survey which determines the positions of bench crests, the method of horizontal sections is preferable. With tacheometric surveys carried out once a month, area measurements should be done plans plotted on a scale not smaller than .1/1000. If calculations are done once a quarter of a year, plans on a scale 1/2000 can be used. If surveying is done by ground stereophotogrammetry, rock volumes can be calculated by the method of horizontal or that of vertical sections. In the former case, areas are measured by a planimeter. In the method of vertical sections, areas can be determined by analytical or graphoanalytical methods. surveys of mined rock a muck pile byIna the tacheometric method, theinvolumes can be calculated by the method of vertical sections; if the muck pile is surveyed by stereophotogrammetry, the method of vertical and that of horizontal sections are applicable. Recalculation from the volume of loosened rock to that of undisturbed rock is done by dividing the measured volume by a loosening factor.
10.8.
Reclamation
The calculations of the volume of a muck pile produced by multirow blasting can involve certain difficulties, since the loosening factor of rock may vary within rather wide limits (its average variation may attain 8% or even more). In such cases,the calculations of blasted rock and the determination of a loosening factor should be carried out separately for each block before and after blasting. for blocks exploded onto a cleared-up slope, the mean loosening factor can be found by the formula: k, = ~/V.n where ~ is the volume of a block in the loosened state and ~n is the volume of undisturbed rock in a block. If blasting is done onto an uncleared slope, the volume of undisturbed rock in the blasted block should be summed with the volume of the blasted rock left on the slope from the previous blasting; the loosening factor of this rock is taken such as adopted for the calculations of the volumes of the last extracted cuts. Thus, the mean loosening factor is calculated by the formula: k. = ~/V' where J-;is the volume of the loosened rock; V~. = v.. + V~, (here v.. is the volume of the undisturbed rock in the block and V~l is the volume of the blasted rock remained from the previous blasting, recalculated to the volume of the undisturbed rock). By the resl,llts of surveying before and after the extraction of the first excavator cut, it is possible to calculate the volume of that cut and the mass of rock in it and in the remaining portion of the blasted rock. The volume of the undisturbed rock in the first cut can be found by the formula: V~. = V;/k; where V; is the volume of rock of the first cut in the loosened state and k; is the mean
of
269
Land
loosening factor for the first cut, which should be determined experimentally. In the calculation of the volume of the first cut of a block, a correction (with a plus sign) for the generalization of the slope shape is introduced: AV= (O.O3h3+ O.7h)L where h is the mean height of a slope and L is the length of a block. The volumes of subsequent cuts are calculated without this correction. The loosening factors for the subsequent cuts are determined by considering the factor for the first cut, the mean loosening factor of the block, and the areas of corresponding vertical sections of the first cut and the remaining portion of the block: V"
= V"
un
,
/
k" 1
k'1 -kl (P' + pI') + k;P' , -11 p where k7 is the loosening factor of the second and subsequent cuts in a block; k, is the mean loosening factor of the rock; k; is the loosening factor of the rock in the fJ.fstcut, and p' and p" are the weights of the loosening factors, which are taken equal numerically to the mean areas of vertical sections in the first and subsequent cuts. 10.8.
Reclamation
of Land
The problem of the restoration of land areas spoiled by opell-cast mining of mineral deposits is of crucial importance. A complex of measures aimed at the restoration of land on the territories abandoned on opell-cast mining is called land reclamalion. Land reclamation can be carried out by engineering, biological and construction techmques. A mining enterprise should carry ellgin" eering reclamation which consists in the preparation of land territories. freed after
270
Ch. 10. Surveying
in Quarries
The design position of workings on the terrain is usually determined by the polar method from control points or by tape measurements from the nearest exploring workings whose mouths are shown on the plans of mining workings. The elements of layout work are determined graphically on plans plotted on a scale 1/1000 or 1/2000. The positions of workings relative to the surveying net points should be determined on the plan with an accuracy not worse than 1.6 m. Elevation marks should be determined with an accuracy to 0.3 m in valleys with a weakly expressed thalweg (valley floor) or to 0.5 of the vertical contour interval in those with a pronounced thalweg. The main objects of mine-survey servicing in open-cast mining of placer deposits are as follows: the determination of the volumes of 10.9. Survey Work in Open-Cast the mining work performed, control of the Mining of Placer Deposits mining work and of the completeness of sand Placer deposits with the bedding depth up extraction. For these purposes, mine surveyto 15 m are worked out, as a rule, by ors fix on the ground the design contours of open-cast mining. Open-cast workings for- polygons, hydraulic sections, waste dumps, med by mechanization means (bulldozer- berms, access roads, and working platforms scraper complexes or excavators) are called for excavating machines; make the surveys of polygons if their depth is substantially smaller pqlygons or pits and determine the volumes than the width; deep and narrow workings of stripped turfs and washed sands and mined are called pits. Valley placers are often mined rock; control the thickness of stripped and undisturbed turfs and the depth of mining; by dredges. In open-cast mining of placer deposits, complement mine-surveying plans and secreference nets are usually developed at the tions; determine the reserves,losses and diluperiod of detailed prospecting so as to pro- tion of sands; and compile the documents on vide basis for surveys on a scale 1/2000. In the volumes of stripped and transferred sands regions not covered by a national reference and of mined and washed sands. net, individual reference nets can be estabThe following methods of surveying are lished by triangulation or trigonometry. Sur- mainly employed in open-cast mining of veying nets are developed according to the placer deposits: surface levelling by a rectanrequirements for land surveys. The points of gular network, ground stereophotogrammea surveying net should be established beyond try, tacheometry, and surveys by profile lines. the contours of a placer deposit. At least Surface levelling by a rectangular network three or four permanent points should be is used for surveying of polygons on perprovided per kilometre of the length of a mafrost placers which are worked out layerdeposit, and these points should lie at distan:- wise with an average thickness of layers 0.5ces not more than 150-200 m from exploring 1.5 m. The surface of polygons is levelled and mining workings. before the beginning of the mining work and open-castmining, for biological or construction cultivation. Engineering reclamation includes the following operations: preservation of the upper (vegetable) soil layer, levelling of dumps, construction of drainage networks, chemical melioration of the soil composition, for instance, chalking of acid soils (when required), and covering the levelled surface with a layer of fertile soil. The minesurveying service of a mining enterprise participates in the engineering reclamation of land. Mine surveyors have to observe that the upper soil layer is removed properly from the territory of future quarries and dumps, to control the levelling of worked-out areas and dumps and the covering of prepared areas with fertile soil.
10.9.
Survey
Work
in Open-Cast
Mining
of Placer
Deposits
271
at the end of each planned period. The by the points of the upper unflooded crests of contours of polygons and sections at the slopes in a polygon with a smooth surface upper and lower crest are usually surveyed by relief where there is the required number of the polar method from the points of survey surveying net points and control points. The control. distances between the surveyed points and Ground stereophotogrammetry is employ- pickets or control points are measured by ed for surveying of large polygons when an tapes. area of at least 25 000 m2 can be photoTacheometric surveying has found appligraphed from a single photographic base. cation in all main regions of dredging work. Tacheometry and method of profile lines In this method, the line of a lower crest is have found use for surveying of pits and also fixed upon determining the combination of of polygons which are deepened by more points of the largest depths at the foot of a than 1.5 m monthly, i. e. when a placer de- facing slope. With depths more than 2 m, the posit is being mined by excavators or hyd- positions of the crests of the facing slope is, as raulic machines actually to the entire depth a rule, determined by the position of the of bedding of loose deposits. The techniques centre of the lower bucket drum as it moves of tacheometric surveying on placer deposits over the facing platform. are the same as elsewhere. Range lines which On some placer deposits, tacheometric are parallel to one another are laid out across surveying is used only for determining the the strike of a pit. position of the upper crest of a facing slope. In the method of profile lines, the upper The position of the lower crest is drawn on and lower crests of the side slopes of a pit are the plans of the mining work relative to that first surveyed and plotted on the plan of the of the upper crest considering the specified mining work, after which transverse vertical slope angle, which is determined experimensections are marked with intervals of tally for different depths and lithologic cha20-25 m, the depths in the equidistant points racteristics of loose placer deposits. This of each section are measured, and a sketch of method is applicable only in rare caseswhen measurements .is drawn. the flanks of a dredge pit are composed of The survey work in dredging consists es- rocks quite resistant to caving, so that the sentially in surveying of dredge faces and pits, face retains its initial configuration during the determination of the volume of mined rock entire period between measurements. The mean depth of a dredge face is found and losses, and the dilution of the mineral. The periodicity of face surveying is determi- by averaging the measured face depths (depth ned by the accuracy of measurement of the of digging plus the height of freeboard) or by geometric parameters of dredge pits (poly- averaging the differences of elevation marks gons). For instance, for dredges of moderate of the polygon surface in the upper crest capacity, each third or fifth face should be contour and the bottom of the dredge pit. surveyed, i. e. roughly after every 10 m of The depth of digging can be measured by a dredge advancement. lead-and-line, mechanical depth gauge, echo Surveying of dredge pits can be performed sounder or asdic (sonar). The error in depth by one of the following methods. measurements should not exceed 0.1 m. With the linear method, surveying is done
Chapter Rock
11.1.
Introductory
Disturbance of Surface
Notes
Underground voids and cavities left on mineral extraction can impair the stability of enclosing rock and result in the disturbance (displacements) of the rock massif and the subsidence of the Earth's surface. Examples of destruction of underground and surface structures under the effect of rock disturbance are quite numerous. Rock displacements attracted miners' attention from the earliest times. In Liege (Belgium), already in the lSth century, colliery owners were obliged by the local law to mine coal at depths not less than 100 m in order to minimize the harmful effect of rock disturbance on municipal buildings. The scientific studies of the process of rock disturbance under the effect of underground workings were started in the first half of the 19th century when hypotheses were proposed to explain the laws of rock displacement. In 1838, Toilliez expressed an idea that rock layers above a stopiIig space destroyed along the planes perpendicular to the bedding plane. This idea was utilized by Gonot of Belgium for explaining the destruction of buildings in Liege. Later, these ideas were generalized into a hypothesis which was called the 'rule of normals' and reduced to the following. The mass of a portion C 1 of the roof above the worked-out space (Fig. 11.1), denoted by Q, has two pressure components: N which is normal to the bedding plane and T which is directed along that plane. Assuming that the
Eleven and Protection Structures
force T is counterbalanced by the reaction of the rock under the worked-out space, the motion of the same portion (layer) C 1 above the worked-out space (i. e. displacement of the roof) will take place only under the effect of the normal component. The same reasoning is true of the overlying layers C2' C3' etc. It then follows that the fracture of the roof rock layers above the worked-out space should occur at the upper and lower boundary of the stoping working and propagate along the normals to the bedding plane. Thus, the displacement angles in this case are 13= 90° -a and y = 90° + a, where a is the angle of dip of a seam. In 1867, J. von Sparre developed further the hypothesis of normals, but he supposed that displacement took place due to the fracture in dangerous sections where the
Fig.
11.1
Scheme
explaining
the 'rule
nonnal
11.1.
Introductory
bending moment was at the maximum. Considering rock layers as beams built in into the rock massif at both ends, Sparre derived the formula for the length of a span along which the displacement (fracture) of a rock layer should occur: 1= J2kd/D cos a where 1 is the length of a span; k is the bending strength of rock; d is the thickness of the rock layer; D is the mass of the rock layer; and a is the angle of dip of a seam. Sparre supposed also that rock displacement should occur not along the normals to a seam, but along the lines somewhere between the normals and verticals. Thus, the dangerous section in the lower portion of the roof should protrude, as it were, from the rock and that in the upper section should pass through the roof rock (Fig. 11.2). In 1882, F. Rziha suggested the hypothesis of rock displacement according to which the caving surface of a roof could be likened to a paraboloid (Fig. 11.3). As caving proceeds, the volume of the rock involved into displacement increases. Caving (displacement) comes to an end when the angle a of the lines 18-1270
273
Notes
confining the subsidence zone relative to the horizontal becomes equal to the angle of repose of 1he rock. In 1885, H. Fayol published a work which confirmed Rziha's hypothesis. According to Fayol, rock displacement occurs by the caving mode and involves a zone having the shape of a cupola (dome). By Fayol's assumption, the dome retains its stability even when its end supports have collapsed; this is due to filling of the dome space by caved-in rock. By Fayol's reckoning, the loosening factor of the caved-in rock is equal to 1/200. Thus, with the depth of the mining work equal to 200 m (where m is the thickness of a seam) the extraction of a seam should have no effect on the surface. In 1864, J. Goodwin, a British scientist, carried out instrumental observations of SUfface subsidence on coal fields and determined the displacement angles ~ depending on the angle of dip a: Angle of dip a, 0
10 15 20
Displacement angle13,° ..73
24 27 31 40
71 70.5 70 68 67 64
In his experiments, the displacement angle 'Y was always equal to 83-85°. In 1895-97, R. Hausse proposed another hypothesis of rock displacement according to which the mechanical properties of rocks and their alternation played an essential part in the process. He also emphasized the effect of
Fig.
11.3
Scheme
to
Rziha's
hypothesis
274
Ch
a Fig.
11.4
Scheme
Rock Disturbance
and Protection
of Structures
b depicting
Hausse's
hypothesis
working systems on the pattern of rock displacement. According to Hausse, the process of rock displacement can be represented as follows (Fig. 11.4). A zone abdc forms immediately above the worked-out space,in which rock is displaced by caving and bending. Above that zone, there is another zone, dcef, where only the bending of rock layers is observed. The thickness of the cave-in zone was found to be equal to (30-60) m, where m is the thickness of the mined seam. A large contribution to the advancement of the theory of rock displacement was made by A. Goldreich in 1913 when he published a monograph based on his instrumental observations of rock subsidence. He came to a conclusion that the fault fissures in rocks of the coal age should have directions governed by the bisector rule (Fig. 11.5), i. e. the displacement boundary is a line coincident with the bisector of an angle between the normal to a seam and the vertical. For tertiary rocks, it was proposed to determine the angles of displacement by considering the angle of repose e = 45° + p/2 where p is the angle of repose. Further, Goldreich was one of the first to refer to the horizontal displacements of rocks. In recent time, the studies of rock sub-
Fig.
11.5
Scheme
of bisector
rule
sidence have been carried out extensively and on a wider scope and have included the problems of the pressure of rocks and filling materials, specific effects of rock pressure in mines with powered supports, laws of rock pressure in ore deposits. Recent investigations of the mechanism of such dangerous effects as rock, coal and gas bursts carried out in a number of countries have provided the basis for developing effective measures to prevent the dynamic effects of rock pressure. 11.2.
General on Rock
Data Disturbance
The stressed state that appears after the formation of a cavity in the rock massif (say, upon driving a working) is determined by initial stress fields. The magnitude and distribution of stressesdepend substantially on the shape of workings. At the initial period when a stope working still has not been advanced far from the rock massif, the roof of a deposit is in a relatively stable state, and its bending is insignificant. As however the worked-out space is widened, the amount and rate of roof bending increase, the continuity of rock layers is disturbed, they are stratified, fissures form in the rock, and finally, roof layers cave in into the worked-out space. With an increase of the dimensions of the
11.3.
(a)
Rock
Displacement
Parameters
275
According to natural observations, the thickness of the cave-in zone along the normal to a seam in most coal basins does not exceed three- or four-fold thickness of the seam. The bend zone II which can be observed both in the overlying roof and underlying bedrock. Rock deformations in this zone occur by the separation of the bent layer into strata, though the bonds between the individual blocks remain undisturbed. Two portions are distinguished in the bend zone: a fissured portion just above the zone of complete caving and the portion above it where (b) Fall.through bending takes place without fissuring of the rock. The zone of bearing pressure III which can --~~-~1-~=~7 , ., \ form in the rock massif near the boundaries , , , of a stope working. Bearing pressure appears in places near a driven working where the ~(', overlying rock massif becomes unsupported, hangs up, and its weight is redistributed onto the enclosing rock of the working. The size Fig. 11.6 Pattern of rock displacement around and pattern of the bearing pressure zone in stope working: (a) with gently dipping bedding; (b) with steep dipping of seam the overburden rock depend on the extent of rock hanging at the boundaries of workings, the depth of the mining work, and rock worked-out space, the zone of rock defor- properties. mations, or displacement zone, becomes larThe zone of total displacementIV which can ger. At a certain ratio of the dimensions of form both at the surface and in the rock the worked-out space and the depth of the mass. It is assumed conventionally that the mining work, the displacement zone reaches stressed state in this zone is close to the the Earth's surface. gravitational state. In the general case, the following zones of In working of thick steeply dipping coal rock deformation around a stope working seams, the rock at the )ying wall often slides can be distinguished (Fig. 11.6): down and forms fall-throughs on the surface The cave-in zone I which is formed im- above seam outcrops. mediately at the worked-out space. Here, rock layers separate from the massif, disin11.3. Rock Displacement tegrate into blocks, and fall into the workedParameters out space. The thickness of the cave-in zone depends mainly on the ratio of thicknesses of An area of the ground surface affected by rock layers in the roof and seam of extracted the displacement from the mining work is mineral, the strength of the roof rock, the called a displacement trough, or basin. It working system employed, and the angle of usually appears as a plate- or trough-like dip of the seam. (seldom cup-shaped) depression of the IS.
Ch. 11. Rock
Disturbance
Earth's surface. Of particular interest are the vertical sections through a displacement trough in which the trough ends are at the farthest distance from the boundaries of a working. These sections usually pass through the centre of a trough on and across the strike and are called the main sections of a displacement trough. The displacements and deformations of the Earth's surface within a trough are distributed non-uniformly. A portion of the displa;, cement trough where the deformations of the ground are such that can cause damage to surface structures is called the hazardous displacement zone. Hazardous displacement zones are defined on the Earth's surface by using displacement angles which are meant as the exterior angles relative to the worked-out space,formed in the main vertical sections of the displacement trough on and across the strike by horizontal lines and by lines connecting the boundaries of the worked-out space with the boundaries of critical surface deformations. Displacement angles are determined from the conditions of complete underworking. This is understood as the state of the trough bottom in which further expansion of the area being worked out does not increase the displacement in this portion of the trough. Not all deformations appearing on surface subsidence are dangerous for the objects being underworked. The highest deformations of the Earth's surface which still cause no damage to surface structures are called the critical, or ultimate safe, deformations of surface. Though the critical deformations for various structures are different, experience shows however that for the majority of structures the following levels of critical deformations can be taken: 4 x 10-3 for inclination, 0.2 x 10-3 for curvature, and 2 x 10-3 for expansion. It is distinguished between the displacement angles in bedrocks and sedimentary rocks. For bedrocks, in sections across the strike, the displacement
and Protection
of Structures
(a)
Fig. 11.7 Displacement angles in section across strike: (a) with gently dipping bedding; (b) with steeply dipping seam
angles in the hanging wall at the lower boundary of the worked-out space are denoted by ~ and at the upper boundary, by y (Fig. 11.7a).For steeply dipping bedding, the dangerous zone is determined from the lower boundary of the worked-out space by the displacement angle ~ in the hanging wall and by the angle ~1 in the lying wall (Fig. 11.7b). In sections on the strike, the displacement angles are taken to be the same at both sides of the worked-out space and denoted by O (Fig. 11.8).For sedimentary rocks, the displacement angles are the same in all three ~irections and denoted by
Fig. 11.8 strike
Displacement
angles
in
section
on
11.3.
Rock
Displacement
(a)
Parameters
277
ibt
Fig. 11.9 Boundary angles for seams: (a) gently dipping ((J-angle of maximum subsidence); (b) steep
boundary points, i. e. the points on the Earth's surface in which subsidence does not exceedthe mean error of levelling. In practice, the boundaries of a displacement trough are defined by points with a subsidence of 15 mm or relative horizontal tensile deformations 0.5 x 10-3. It is distinguished between the boundary angles in sections across the strike ([30' [301' and y ° in Fig. 11.9) and those in sections on the strike (00). Boundary angles depend substantially on the depth of the mining work, dipping angle of seams, and, rock density. Boundary angles are used in preliminary calculations of displacements and deformations of the Earth's surface. With the horizontal bedding of a seam, the centre of a displacement trough lies above the middle of the worked-out space. With dipping seams,it is shifted from the middle by an angle e (Fig. 11.9a) which is called the angle of maximum subsidence. This angle is measured at the dipping end of a seam in the vertical main section of the displacement trough across the strike and is formed by a horizontal line and the line connecting the middle of the working with the point on the surface having the maximum subsidence or with the middle of a plate-shaped displacement trough. If the dimensions of the worked-out space are large relative to the bedding depth, the
Earth's surface may subside to the same depth (maximum for the given conditions) over a large area. Further expansion of the working will not increase the subsidence area, and the latter is then considered to be under the conditions of complete underworking. Otherwise, underworking is incomplete. The area of complete underworking is determined by means of angles of total displacement, i. e. the interior angles relative to the worked-out space, which are formed in the vertical main sections of a displacement trough by the seam lines and the lines connecting the boundaries of the worked-out space with the boundaries of the flat bottom of the trough. It is distinguished between the angles of complete underworking in sections across the strike: "' 1 at the dipping end and", 2 at the rising end of the worked-out space (Fig. 11.10) and those in sections on the strike; "' 3 at both sides of the worked-out space.
.1. ~I
0/1
\1
~I
Fig. 11.10 Complete underworking angles
278
Ch. 11. Rock
Disturbance
The process of rock displacement is often characterized by the coefficient of underworking which is understood as the ratio of the length of a stope working to the minimal length required for complete underworking of the Earth's surface in the given direction. The coefficients of underworking can be determined along the dipping line and on the strike of a seam. Denoting, respectively, the actual dimensions of a working on the dip and on the strike by Dl and D2 and the minimal dimensions for complete underworking by DOl and Do2, the coefficient of underworking on the dip will be nl = Dl/Dol and that on the strike, n2 = D2/Do2. An important characteristic of underworking is the ratio of the length of a longwall D to the depth of a mine H at which complete underworking occurs. It is taken that complete underworking takes place at nl :;:?;1 and n2:;:?;I. In many cases, rock displacement causes fissures in the trough. The portion of the displacement trough in which fissures are observed is delineated by rupture angles (caving angles), i. e. the exterior angles relative to the worked-out space, that are formed in the vertical main sections of the displacement trough by a horizontal line and the lines connecting the boundaries of the worked-out space with the nearest surface fissures at the trough edges (Fig.ll.ll). It is distinguished between the rupture angles in sections across
Fig. 11.11 Rupture angles
and Protection
of Structures
(a)
1 Ib)
\=::7 A
AI jc)
A
"\\
8
82
~
' \ \
--~C 81
8 \
c
~~
"
A
81 Fig. 11.12 Deformations: (c) r~spectively compressive deformations
(a) vertical; (b) and and tensile horizontal
the strike (13"and y") and those in sections on the strike (0"). Surface subsidence (11), i. e. the vertical component of the displacement vector, has been studied much more thoroughly than other parameters. It is distinguished between the maximum subsidence in complete underworking, 110' and that in incomplete underworking, 11m. Vertical deformations may arise due to non-uniform subsidence and are characterized by inclination, curvature, and radius of curvature. Referring to Fig. 11.12a, points I, 2, 3 are bench marks on the surface before under-
11.3.
Rock
Displacement
working and J', 2', 3' are the same points after underworking; 111'112'113are the subsidencesof respective bench marks; 11-2' 12-3 are the distances between the points before underworking; and ~1' ~2' ~3 are the horizontal displacements of respective bench marks. The inclination of an interval on the surface is determined relative to the initial position of that interval. For instance, the inclination of a section 2-3 after underworking is expressed by an angle i2-3. In practice, inclination is measured as the difference of subsidences of extreme points of a section related to the initial length of the section: '2-3 = 113-112 4-3 The inclinations of adjacent sections in a displacement trough are in most cases different. This non-uniform subsidence gives rise to another kind of vertical deformation, curvature. Non-uniform subsidence of the surface can be characterized by the difference of inclination angles of two adjacent sections: k2 = i2-3 -il-2 11-2/2 + 12-3/2 i. e. curvature is the ratio of the difference of inclinations of two adjacent sections to the half-sum of the lengths of these sections. The radius of curvature is the inverse of curvature: R = l/k Horizontal deformation is one of the most important characteristics of surface subsidence. Let us analyse the combined motion of two surface points, A and B (Fig. ll.12b). As a result of displacement, the point A will be shifted to A1 and the point B, to B1. In the case of the compression of a section AB, vectors AA 1 and BB 1 will be directed as in Fig. 11.12b and in the case of tension, as in Fig. 11.12c. Let a line parallel and equal to the vector
279
Parameters
AA 1 be drawn through the point B. It is also clear that AlBl is the length of the section AB after surface deformation. The relative horizontal deformation will be: E --AB-AB
AB-
AlBl
CB2 -AB
Thus, horizontal deformation (tensile or compressive) is the elongation or contraction of the initial length of a section related to this length. The duration of the displacement process may be of interest mainly when deciding on the possibilities of the construction of buildings on an underworked area. It is agreed to distinguish three stages of surface subsidence: the initial, active, and attenuating. The initial stage, i. e. that during which deformation initiates, usually continues to the moment when a mine is advanced under a particular observation point and can be characterized by the subsidence rate from tenths of a millimetre to 1-1.5 mm per day. The active stage is the period in which the rate of subsidence exceeds 50 mm/month on gently dipping seams or 30 mm/month on steep ones. The displacement process is considered to be finished at that day of observations after which the total subsidence during six months does not exceed 30 mm. The duration of the subsidence process mainly depends on the depth of the mining work, thickness of seams, and the physicomechanical properties of rocks. The path of the motion of surface points and the distribution of displacements and deformations within a displacement trough obey definite regularities. As a mine face approaches, the paths of points deviate from the vertical towards the face. After the face has passed beneath the points, their paths deviate towards the advancing face. Finally, as the face has been moved sufficiently far, the paths of points become perfectly vertical. When solving problems associatedwith the protection of surface structures, it is essential
280
Ch. 11. Rock Disturbance
and Protection
~
Fig. 11.13 Distribution of surface displacements and deformations: 1-vertical displacements; 2horizontal displacements; 3- horizontal deformations
to know the distribution of displacements and deformations within a displacement trough. It is usually sufficient to analyse the distribution of the following elements in a trough: the maximum values of the horizontal and vertical components of motion; maximum deformations in the main sections of the trough on and across the strike; maximum inclination; maximum curvature; and maxifuum elongation and contraction. The curves of the distribution of surface deformations on a gently dipping seam in a section across the strike are illustrated in Fig. 11.13a. With horizontal and gently dipping seams, the curves of inclinations usually follow the pattern of the curves of horizontal displacements. The curves of curvature are similar to the curves of horizontal deformations. With horizontal (flat) seams, the points of essential importance, in addition to boundary points A and B, are also points E, £1, and 0.
of Structures
The last point is the point of the maximum subsidence, minimum horizontal displacement, and maximum contraction. The points E and El are the inflection points of a subsidence curve. They are the points to which the maximum inclination, maximum displacement, and zero horizontal deformation are confined. The maximum tension is observed roughly amid between the inflection points and trough boundary. With an inclined bedding of seams (Fig. ll.13b), the patterns of these curves are different. With an increase in the angle of dip of seams,a curve 1 becomes more asymmetrical on the rise: the point of zero horizontal displacement does not coincide with the maximum subsidence point, whereas the points E and El become asymmetrical relative to O and O 1. The asymmetry of curves increases further with an increasing angle of dip of seams. 11.4.
Factors Responsible for Rock Displacement
Physico-mechanical properties of rocks and bedding conditions. The state of rocks is largely responsible for the pattern of displacement. For instance, with loose-grained rocks having a low cohesion, subsidence proceeds rapidly, appears sharply on the surface, and often leads to the formation of ledge-shaped fissures. A typical example is the Moscow district coal basin where, with the mining work carried out at a depth of 40-50 m, the roof subsidence becomes noticeable on the surface already in 2 or 3 hours. Plastic rocks, such as clay shales, promote plastic deformations, so that rock displacement occurs uniformly and smoothly following the advancement of a mine face; the surface subsides slowly and does not cause large damage to surface structures. The structure of a deposit can influence substantially the pattern of displacement. With alternating hard and soft rock strata in
11.4.
Factors
Responsible
a bed, secondary subsidence can appear in the mine roof, especially when quickly caving soft rocks lie immediately on the roof, whereas the layers (bands) of hard rock are overlying and hang up periodically over a large area. Poorly predictable cavings of these bands can develop an elevated rock pressure in stope workings and adjacent preparatory workings and sometimes are the cause of emergencies and rock bursts in mmes. Quicksands can complicate substantially the process of rock displacement. Cases have been recorded when quicksands occurring in the rock massif being underworked caused sharp flattening of displacement angles. Underworking of quicksands can involve large water losses, which can result in surface subsidence far ahead of the working face. The angle of dip of a deposit is among the critical factors governing the rock displacement process qualitatively and quantitatively. The pattern of displacement of the overlying rock is closely associated with the angle of dip. With steep angles of dip, substantial shear deformations in displaced rock are quite typical. With horizontal or gently dipping seams, the main kind of deformation is bending of rock strata. With steep bedding, the horizontal component of a displacement vector is predominant, whereas the vertical component prevails in the rock displacement on flat seams. It is found by observations that, under similar conditions, structures above workings in seams with steeper angles of dip suffer from greater deformations. For instance, in the Donetsk coal basin, mining in gently dipping seams at a depth of 200-250 m causes no fissuring on the surface, whereas the mining work in steep seams, even at a depth of 600 m, can lead to the appearance of large rupture cracks on the surface. An increase in the angle of dip of a deposit involves a change in the position of a displacement trough relative to the worked-out space, i. e. the trough is shifted towards the
for Rock
Displacement
281
strike. The distribution of hazardous zones in a trough is also associated with the angle of dip. A steeply dipping structure of a deposit, sharp changes in the angle of dip, folded bedding, and the presence of moderate and large tectonic disturbances can lead to the appearance of concentrated deformations, fissures and ledges in the surface. Depending on the thickness of seams and bedding depth, these deformations may vary from a few millimetres to tens of centimetres and are quite dangerous for surface structures, since structures located on ledges then suffer from substantial deformations or even break down if these deformations exceed 20-30 cm. The sites for the construction of new objects should, as a rule, be located on non-underworked territories or on those with favourable geological conditions. If a need arises to erect new objects in underworked zones which can cause the appearance of large deformations and ledges, protective measures should be taken to increase the strength and spatial rigidity of buildings and structures (reinforced-concrete, belts in the underground portions of buildings, cast-insitu concrete foundations, reinforced joints, continuous horizontal reinforced-concrete belts at the level of floor ceilings and partitions, division of buildings into sections, provision of horizontal sliding joints, etc.). The construction of new objects on areas above old stope workings at depths of 20-80 m can only be started after preliminary geological examination to reveal empty cavities in the worked-out space. The construction of residential buildings above the zones of preparatory mining workings at depths less than 10 m (where m is the height of a working) is possible only after geological examination for determining the non-caved portions of workings (voids). In all cases, detected voids should be filled in. The depth of the mining work can influence substantially the magnitude of rock displa-
282
Ch. 11. Rock
Disturbance
and Protection
of Structures
cement and the time and rate of its ma- cohesion), which in turn leads to a loss of nifestation. With an increase in the mining stability of slopes and landslide phenomena. The disturbance of the rock massif by old depth, the amount of displacement decreases and the process becomes smoother and less stope workings. Numerous field observations dangerous for surface structures, though this have demonstrated that the mining work in a is true only to a certain depth. An increase in disturbed rock massif can activate rock disthe depth of the mining work always in- placement by increasing deformations, rates, creases the time of the displacement process. and non-uniformity of surface subsidence. The thickness of an extracted seam. Com- The activization of rock displacement may be pared with the depth of the mining work, the due to the following factors: (I) voids formed due to hanging up of thickness of a seam has an inverse effect on overlying rock layers during primary unthe rock displacement: with a larger thickness, the process of displacement is more derworking. Repeated underworking can largely eliminate hang-ups and produce better pronounced and involves higher horizontal and vertical deformations. With an appre- compaction of the disturbed rock massif; (2) primary underworking decreases the ciable thickness of a seam, the zone of smooth sagging can disappear fully, and the strength of a rock massif by opening old and rock then subsides by caving and with the forming new fissures. For that reason, rock displacement on repeated underworking proformation of terraces. On seams of a small thickness, the rock ceedsat a high rate, since it takes place in the displacement occurs mostly by bending of rock massif with impaired strength properstrata. The cave-in zone develops only weak- ties. ly and only in the direct vicinity of the Working systems.The principal parameters of working systems which can influence rock worked-out space. The presence and thickness of sedimentary displacement are the height of levels, length rocks and the surface relief In bed rocks, the of a mining field, method of roof control, rate .rock displacement occurs so that points , of face advance, and the completeness of move almost along the normals to the bedding mineral extraction. The height of a mining level and the length plane. In sedimentary rocks of an appreciable capacity, the rock displacement occurs in of a mining field are equally important, since directions from the edges to the centre of a they determine the shape of a displacement displacement trough. In the contacts on the trough. With small dimensions of the workrise of a seam, sedimentary rocks and bed ed-out space, a cup-shaped trough usually rocKs are displaced in opposite directions, forms. With an increase in the space di. which often causes the separation of sedi- mensions, a cup-shaped trough changes to a mentary layers from the bed rock and the plate-like form. The best method of roof control to prevent destruction of underground objects. The effect of the surface relief on rock the surface subsidence is backfilling of the displacement is appreciable only in moun- worked-out space. The filling decreases the tainous regions where underworking of steep size of voids, supports the overlying rock, and slopes often triggers landslides. Rock stability decelerates and decreasesto a certain extent depends substantially on the angle of internal the process of rock displacement. The effect of filling depends on the filling friction and the cohesion at slip planes. The rock displacement then results in loosening of material used. Continuous dry filling decreasthe rock massif and associated reduction of es the volume of voids only insufficiently the strength properties of rock (mainly of (sometimes only by 40 per cent). Hydraulic
11.5. Monitoring
Rock Displacement. Observation Stations
filling and hardening filling produce the most favourable effect on surface subsidence. With carefully packed hardening filling, the surface subsidence may be as low as only 3 per cent of the seam thickness. In this case, surface displacements are uniform and smooth, so that even large structures settle down slowly and without large damage. With continuous working systems, especially with a large-Iength longwall and complete roof caving, surface displacement occurs smoothly and uniformly. With pillar and room-pillar working systems having roof caving where safety pillars are left at short intervals in the worked-out space,the overlying rock massif may be broken by the pillars into individual blocks, with fissures propagating up to the surface and causing largely uneven subsidence. 11.5.
Monitoring Rock Displacement. Observation Stations
An observation station on the surface is a system of fixed points (bench marks) placed in the ground or surface structures (Fig. 11.14). Bench marks are usually set up along the profile lines on and across the strike of a deposit. In mountainous, wooded and densely built-up areas, broken profile lines are permissible. When examining the underworking conditions for railroads, pipelines and other stretched objects, the profile lines may be arranged diagonally to the strike. In some cases, say, for monitoring underground gas pipelines, stations may be established as a network. An observation station is set up according to the design plan which includes an explanatory note and graphical appendices. The graphical material of the design plan should contain: (a) a joint plan of the land surface and underground workings with profile lines of an observation station (on a scale
283
1/500, 1/1000 or 1/2000); it should give the boundaries of the mining field, the current state of the mining work and its further development, the supposed position of the displacement zone, tectonic disturbances, and the scheme of junction of control points; (b) geological cross sections along the profile lines with indication of the workings; and (c) the designs of control and working bench marks. The place for establishing the observation station is chosen by considering the positions of mining workings and according to the particular object of observations. An area on a flat country with few structures and away from haulage tracks and roads is a convenient place for an observation station. Usually, two profile lines across the strike and one on the strike are laid out. When working deposits with varying geological and mining conditions, the profile lines are laid out separately on the sections which differ from one another in the bedding elements, thickness of a seam, working system, etc. The profile line across the strike which is the closest to undisturbed (intact) rock is located at a distance not less than 0.85 Hm from a breakthrough or the point where the face is stopped (Hm is the mean depth of a working). If the longwall face has already moved from the breakthrough, the distance from the latter to the profile line is found by the formula: d = Hm cotalloo :;::?; 0.85Hm The next profile line is laid out at a distance of 50 m from the previous one. The length of profile lines drawn across the strike (Fig. ll.l5a) is determined on vertical sections by the boundary displacement angles. Two control bench marks are established on the continuations of the profile lines beyond the expected displacement zone. The distance from the first control bench mark to the end of the working portion of the profile line should be not less than 50 m, and
Ch. 11. Rock
Disturbance
and Protection
the spacing between the control bench marks, 50-100 m depending on local conditions. The profile line on the strike passes through the point of the maximum subsidence of a displacement trough. To find this point on the vertical section across the strike, a line is drawn at an angle 9 from the middle of the worked-out space up to its intersection with the surface. The length of the profile line on the strike is found in the following way (Fig. ll.15b). The point where the face will be supposedly stopped is projected onto the surface (point k). A distance B = Hmcotan 00 is the~ laid off
of Structures
towards the undisturbed rock massif, and a distance 1.75Hm, towards the worked-out space. Control bench marks are established by the same rules as for the profile lines across the strike. Working bench marks are set up along the profile lines at intervals decided by the depth of the mining work. Bench marks should be designed so as to ensure their stability and preservation for a long period; in addition, they should be inexpensive and convenient for establishing and observations. Bench marks for long-term
11.5.
Monitoring
Rock
Displacement.
Observation
Stations
285
(b)
Fig. 11.15 strike
Determination
of length of profile
lines: (a) in section across the strike; (b) in section on the
and ordinary stations are made from metal tube sections, studs or rail pieces which are set up below the freezing line and concreted. For temporary stations, they can be made from wooden stakes or pegs driven into the soil. For better preservation, bench marks are often buried in the ground to a depth of 30-40 cm. Observations. Observations at stations on the surface include tying (connecting) control bench marks to an existing reference net, primary observations on the bench marks in horizontal and vertical planes, and secondary observations. The horizontal connection of control bench marks is carried out by triangulation or by closed theodolite traverses. It is permissible to run a hanging theodolite traverse, provided that the angles and sides are measured in the forward and back direction. The permissible relative discrepancy of a theodolite traverse should not exceed 1/2000. The vertical connection of control bench marks is done from the points and bench marks of a levelling net by means of geometric levelling with a discrepancy not more than
15 JL, mm (where L is the length of a level line, m). Upon connecting a station, it is possible to start primary and secondary observations. A complete set of instrumental observations contains: the levelling of all bench marks; the measurements of bench spacings along profile lines; determination of the deviations of working bench marks from a profile line; surveys of surface fissures with records of the time of their appearance; and the measurements of the deformations of structures. The first observation at a station is recommended to be carried out in 7-10 days after setting up of bench marks (if these have been concreted) or in 2-3 days for bench marks driven into the ground. Primary observations are carried out twice, and the final result is obtained as the arithmetic mean of the two observations. The time intervals between the observations depend on their task. If it is essential to obtain detailed information on rock displacement, at least four intermediate observations between the initial and final observa-
286
Ch. 11.
Rock
Disturbance
and Protection
tion should be made, in time intervals determined by the formula: t = H/6c where H is the depth of the mining work at the lower boundary of a working and c is the rate of the face advance, m/day. During the initial and active stage of rock displacement, observations are carried out at least three times a month and during the attenuation stage, at least once a month. After checking field measurements, the displacements and deformations are calculated, and curves are plotted. Calculations are made by the formulae: subsidence: 11= Hn -Hn-l (11.1) inclination: i = (11n-11n- J/I
(11.2)
curvature: k = (in -in- J/lm
(11.3)
horizontal displacement: ~ = D2 -Dl
(11.4)
and horizontal deformation: E=(ln-In-J/I
(11.5)
where 11is the subsidence of a bench mark; Hn- 1 is the absolute elevation of the bench mark in the previous observation; Hn is the absolute elevation of the bench mark in the current"observation; i is the inclination of a subsidence curve; k is the curvature of that curve; in and in -1 are the inclinations of the current and previous interval; ~ is the horizontal displacement; Dl, D2 are the distances from a control bench mark to the given bench mark in the previous and current observation; E is the horizontal deformation; In' In- 1 are the length of intervals in the current and previous observation; and Im is the half-sum of the lengths of intervals in the previous and current observation. The calculated deformations and displace-
... .. :E .~
of Structures
11.6.
Calculations
of Rock
ments of the Earth's surface are tabulated as given in Tables 11.1 and 11.2. 11.6.
Calculations of Rock Displacement
An increase in the depth of the mining work leads to an increase of the zones of harmful effects on the surface, and therefore, more objects on the surface will be subjected to these effects and require protection. On the other hand, with an increase in the mining depth, surface deformations decrease,so that it becomes possible to underwork even critical structures which could not be underworked when mining was done at higher mining levels. In densely inhabited areas with multistorey residential and public buildings and extended networks of gas and water supply and seweragesystems,underworking requires complicated engineering calculations for determining the expected deformations and degree of damage to structures. It is also needed to carry out observations on the surface subsidence and the state of structures and control the protective measures and the repairs of damilged buildings. The existing methods of calculation of rock subsidence can be divided into the following groups: (a) empirical methods; (b) methods based on distribution function; and (c) methods based on theoretical models. Empirical methods are the most preferable since they use the results of direct observations on subsidence. Among the empirical methods, the method developed in this country is quite accurate. It is used in cases when the roof control is effectedby complete caving of the back-filling of the worked-out space and is applicable when the underworking ratio is Him > 20 for the angles of dip between 0° and 55° or Him > 15 for the angles larger than 55°. The underworking ratio is here the ratio of the mean mining depth H to the extracted or effective thickness of a seam, m.
Displacement
287
Depending on the completeness of initial data, it is possible to detennine the expected or probable displacements and defonnations of the Earth's surface. The expected displacements and defonnations can be calculated when the calendar plans of the mining work development are available and the probable ones, when there are no such plans. In the calculations of the expected displacements and defonnations of the Earth's surface, the following characteristics are detennined: subsidence 11,horizontal displacements ~, inclinations i, curvature k and curvature radius R, horizontal defonnations E, and displacements and defonnations caused by rock motion along the bedding. If the angle of dip a is smaller than the limiting value a" the expected displacements and defonnations are detennined by the calculation method for the conditions when there is no rock motion at the lying wall. If the angle of dip is equal to or greater than the limiting value, the calculation method considers rock motion at the lying wall. The limiting angle of dip of a seam, a" is the angle at displacements thewhich lying dangerous wall can appear. , of rock at The calculation of displacements and defonnations is started from constructing the geological sections on and across the strike, in which sedimentary and bed rocks should be indicated. These sections should also show the driven and projected workings (with the dates of driving), the depth of the mining work, and the dimensions of workings and pillars. The extracted thickness m of a seam is detennined as the total sum of the thicknesses of layers of coal and enclosing rock extracted from the stope workings. With back-filling of the worked-out space, the calculation of displacements and defonnations is carried out by considering the effective thickness of the seam: mer=(hc+hin)(I-BJ+Blm (11.6) where hc is the convergence of the roof and
Ch. 11. Rock
288
Disturbance
and Protection
of Structures
Table 11.2 Bench
mark
Interval
length,
m
No.
Subsidence Inclination Inclination Curvature difference of i difference k, l/m interval ends, mm
2 3 4 5 6 7 8 9 10
156.262 9.893 10.031 10.002 10.134 10.062 9.951 9.943 9.972 10.051
0 +1 O +1 +1 +2 +2 +2 +5 +1
Radius of Subsidence Inclination curvature difference of i R. m interval ends, mm O
°
+ 0.1 + 0.1 °
+ 0.1 + 0.1 + 0.2 + 0.2 + 0.2 + 0.5 + 0.1
floor before back-filling (if there are no observation data and the face is advanced by 8-20 m ahead of the filling, hc is taken equal to 0.15 m); hin is the incompleteness of filling (mean distance from the top of a filling massif to the roof of a seam), which is determined experimentally; m is the extracted thickness of a seam; and B 1 is the shrinkage factor of filling whose values are given below: Hydraulic filling: B1 sand. 0.05-0.15 crushed rock. .0.15-0.30 Pneumaticfilling 0.25-0.40 Gravity-f1owfilling: crushed rock. .0.25-0.45 ordinary rock. .0.35-0.50 In the calculations of displacements and deformations, it is essential to consider the influence of all projected stope workings and of those driven earlier, which can activate the displacement process in the given section. The maximum subsidence of the Earth's surface is found by the formula: llm = qomcosaNllN2 (11.7)
0.03 -0.01 +0.01 0.00 +0.01 0.00 0.00 +0.03 -0.04
+0.1 -0.1 +0.1 0.0 +0.1 0.0 0.0 +0.3 -0.4
0
+33.3 -100 +100
+100
+33.3 -25.0
+3 +4 +8 +8 +4 +23 +45 +73 +136
+ 0.3 + 0.4 + 0.8 + 0.8 + 0.4 + 2.3 + 4.5 + 0.73 +1 3.5
where qo is the relative maximum subsidence; m is the extracted thickness of a seam; a is the angle of dip of a seam; and N 1 and N 2 are the factors depending on the ratio of the design length of a longwall Dd to the mean mining depth H, T he subsidenceof the Earth's surface in the pdints of the main sections of a displacement trough is determined by the formula: Tl(x,y) = TlmS(z) (11,8) where S(Z)is the function of a typical subsidence curve, which depends on coefficient N 1 and N 2' The inclinations in the main sections of a displacement trough are determined by the following formulae: for a half-trough on the strike: F(
~
1 zx,
L3 for
a half-trough
on the dip:
11.6.
Calculations
of Rock
289
Displacement
lst-4th observations Inclination difference
Curvature k. Radius of curSubsidence I/m vature R. difference of m interval ends, mm 0
+0.3 +0.1 +0.4 0.0 -0.4 +1.9 +2.1 +2.8 +5.2
+0.01 +0.01 +0.04 0.0 -0.04 +0.19 +0.21 +0.28 +0.52
Inclination i
+25.0 -25.0 +52.5 +47.5 +35.7 +19.2
+6 +9 +10 +9 +13 +27 +57 +79 +163
Curvature k, I/m
+0.6 +0.3 +0.1 -0.1 +0.4 +1.5 +2.6 +2.5 +3.5
+0.02 +0.03 +0.01 -0.01 +0.04 +0.15 +0.28 +9.25 +0.85
Radius curvature m
of R,
0
+ 100.0 + 100.0
Inclination difference
+0.6 +0.9 +1.0 +0.9 +1.3 +2.8 +5.4 +7.9 +16.4
+I -I + + + + +
50.0 33.3 00.0 00.0 25.0 67.5 38.5 40.0 11.8
T he horizontal displacements of the points in the main sections of a displacement trough are found as follows: for a half-trough on the strike: fox = O.5ao1lmF'(zx) for a half-trough
(11.15) on the dip:
f,yl = O.5aoTlmF'(zyJ
and for a half-trough ~y2 = O.5aoTlmF'(Zy2)
(11.16) on the rise:
(11.17)
where the factor ao is the relative maximum horizontal displacement and functions F'(zx), F'(zyJ, and F'(zyJ are the same as in formulae (11.12)-(11.14). The horizontal deformations (tensile and compressive) in the main sections of a displacement trough are determined by the formulae: for a half-trough on the strike:
"x = O.5ao -L1lmF'(zx) 3 19-1270
(11.18)
290 for a half-trough
Ch.1
Rock
Disturbance
on the dip:
Eyl = O.5ao ~ F'(zyJ Ll and for a half-trough
E = 0.5a ~ F'(z ) y2 O L2 y2
on the rise
of Structures
of surface structures will be discussed below. I. Mining measures may consist in (a) the (11.19) protection of structures by back-filling of the worked-out space and (b) the application of special methods of mineral extraction, which ensure proper safety of surface structures. (11.20) Among these methods, it is worth to mention the following: (a) extraction sections are plan-
where functions F'(zx), F'(Zyl)' and F'(Zy2) are the same as in formulae (11.12)-(11.17). 11.7. sMe;sure;t ur ace
and Protection
for tProtectIng .quickly ruc ures
ned so that the surface structures turn out to be on the portions of a displacement trough where earth subsidence is the most uniform; (b) a stope face is advanced continuously and as toworking minimizeonthe time structures; of influence of theso stope surface and (c) mineral is extracted at both sides of a
The problems of the protection of buil- breakthrough which is located under the dings and structures against harmful effects centre of a surface structure, etc. of underground mining have become crucial One of the most efficient methods of in recent time, especially in large coal fields structure protection is the provision of strip where underworking of buildings leads either pillars having a large strength margin and to a substantial increase of the cost of mining spaced at intervals which ensure proper sta(owing to expensive additional measures for bility of the roof. The essenceof the method the protection of buildings) or to large losses consists in the following: ~s the intermediate of coal in safety pillars. chamber pillars, which are left between the The conditions of safe mining are determi- barrier pillars, are destroyed, the caving proned by using the concepts of permissible cessis localized in the space confined between deformations and ultimate deformations. the. barrier pillars. In that case, the overlying Permissible deformations are taken as the rock will cave in only within the equilibrium deformations of the Earth's surface which dome, whereas the rock massif above it cause only repairable damage to surface remains undisturbed. structure. Ultimate deformations of the Earth's 2. Construction measuresdecreasethe stressurface are understood as the ultimate limit ses and deformations in structures and builfor deformations; any deformations above dings and increase the load-carrying capacity, this limit"Will be dangerous for the stability of but do not exclude the appearance of fine buildings and structures and the life of people. fissures in walls, foundations, and floors. The For determining the conditions of safe principal construction measures for minimiunderworking of objects above a single seam zing the deformations of structure are as or the first seam of a suite, it has been follows: proposed to use the concept of safe mining (a) settlement joints by which long buildepth which is understood as the depth dings are divided into sections of a suitable below which mining operations cannot cause size and closed contour. Settlement joints are in structures the deformations exceeding the arranged near internal partition walls. Their permissible ones. At mining levels below the thickness should be such that the building safe depth, the mining work can be carried sections can settle down independently under out without taking protective measures. the effect of underworking. It is recommenThe principal measures for the protection ded to divide a building by settlement joints
11.8.
Construction
to its entire height (except for the foundation); (b) yieldable foundations which absorb the horizontal stressesin buildings. This is achieved by providing a horizontal joint to separate the underground portion of a building from the foundation; the joint is filled with a material having a low coefficient of friction; (c) foundation plates. The idea consists in that a reinforced-concrete plate is laid onto the levelled and compacted soil surface. The plate is cut through by diagonal joints filled with an elastic material. A layer of wet sand up to 5 cm thick is laid on the plate and above it another plate (without joints) is placed on which the building will be erected. Effective protection of buildings against the effect of underworking is provided by compensating ditches dug in the ground along a building; they diminish horizontal deformations by 33-50 per cent. The bottom of a ditch is made somewhat lower (around 50 cm) than the foundation foot. Compensation ditches are filled with corrugated steel, fine coke or a mixture of soil and sawdust. 3. Safety (protective) pillars are left in the worked-out area of mines. This method is resorted to when other protective measures are inefficient or too expensive.
11 .8.
Construction of Safety
Pillars
Safety pillars can be constructed by the method of vertical sections or method of perpendiculars.
11.8.1.
Method
of Vertical
Sections
Let us consider two examples of the application of this method: construction of safety pillars for a building and for an extended object. Example 1. It is required to construct a safety pillar for a four-storey brickwork 19.
of
Safety
Pillars
291
building of a rectangular form 28 x 45 m in plan (Fig. 11.16) and arranged diagonally (at 45°) to the strike of a seam. Another seam, 11, of a thickness m = 0.9 m and an angle of dip a = 30°, lies under the seam mentioned. The thickness of sedimentary rock is 25 m. The displacement angles are:
292
Ch. 11. Rock
Disturbance
and Protection
of Structures
2004080m I I I I I I I
a Fig. 11.16 Construction of safety pillar for building by method of vertical sections
tions of the pillar, the plan contours of the the bed rock on the dip. The two latter angles can be found from the formulae: pillar are determined (abcd). The reserve of coal in the pillar is calcula- cotanf3' = Jcotan2f3 cos2e + cotan2o sin2e ted by multiplying the seam thickness by the cotany' = Jcotan2y cos2e + cotan2o sin2e total area of the pillar. Example 2. It is required to construct a safety pillar for a railway bed in a brown coal where 13,y, and O are the displacement angles field (Fig. 11.17).The railway bed is arranged in the main sections of a displacement trough diagonally to the seam strike. The seam for the given seam and e is the acute angle thickness is 1.3 m and the angle of dip, 25°. between the strike line of the seam and the The overlying bed rock is represented by clay contour of the object to be protected. The boundaries of the safety pillar are shales, argillites, and aleurolites. The thickness of sediments is 20 m. The displacement determined by plotting a number of vertical angles are: ~ = 47°, y = 65°, O = 65°, and sections perpendicular to the railway line in
~
11.8.
Construction
of Safety
Pillars
293 7-8
9-10 10
/ --8
?
400 -375 -~
--
~o
9
~
47~
/ ~o--
~5° 5-6
~
45O
-I
0°
---
3-4
4
° 5
,
--~~~.6
4
50 I I
45°
~6O I
-45°
-,-I
I,
65°I I
I
350 --
1-2
2
325 -
45° -45" .rI
300
W
225
3
/
~~
!1 SectionNo.1 6113'11'1 1-2 '~1561651
3-4
Fig. 11.17 Construction of safety pillar for extended object by method of vertical sections
rock at displacement angles J3iand yi. The bedding deptb of the seam under the railway bed is determined as the difference of elevations between the Earth's surface and the seam foot. This depth is laid off in the sections, and the line of the seam is drawn at an angle ai through the points thus obtained.
The angle of dip of the seam ,in the section plane is determined graphically. The points obtained by the intersection of seam traces with protection planes are transferred onto the plan where straight lines or smooth curves are drawn to determine the contours of the pillar. Seam outcropto overburden
<)6
278~ 200 -
/
" ,---
2 "~--~'2'
280~ 150-
" .',
1~
250~
-""
100
Fig. 11.18 Construction of safety pillar by method of perpendiculars
Ch. 11. Rock
11.8.2.
Method
Disturbance
of Perpendiculars
In this method, the boundaries of a pillar are obtained directly on a plan, i. e. without plotting vertical sections. The lengths of perpendiculars are determined by the formulae: (H -M) q=
1 + cotan [3' tan 11cos e (H -M)
I=
cotan [3'
1 -cotan
cotan y' y' tan 11cos e
where q is the length of perpendiculars to the rise; I is the length of perpendiculars to the dip; H is the depth from the Earth's surface to
and Protection
of Structures
the seam foot; a is the angle of dip "of the seam; M is the thickness of the sedimentary rock; and 13' and y' are the displacement angles. Consider, as an example, the construction of a safety pillar for a railway bed passing diagonally to the strike (Fig. 11.18). Points are chosen in the characteristic places of the protected area and perpendiculars are drawn in these points to the contour of a safety berm. The corresponding lengths q and 1 are laid off along the perpendiculars. Points 1, 2, 3, J', 2', and 3' are connected by lines which define the boundaries of the safety pillar. The coal reserve in the pillar is then calculated.
Chapter
Stability
12.1 Principal
Twelve
of Quarry
Flanks
in quarry flanks can be divided into five principal kinds: taluses, downfalls, landslides, subsidences, and mud-streams {mud-flows). Rock displacements in open-cast mining of A talus takes place when small volumes of minerals determine to a large extent the loose rock roll gradually from the top of a mining economics and labour safety. slope to its bottom. This can occur when the The loss of stability (displacement) of angle of a slope is steeper than the angle of flanks and benches in quarries is mainly internal friction of loose rock, and the latter associated with changes in the stressed state has practically no internal cohesion. of the undisturbed rock massif, which can be A downfall is essentially quick movement caused by open-cast mining. of rock masses along slip surfaces, such as In this process, the destruction of rock surfaces weakened by geological disturbances mainly occurs under the action of tangential or fissures. These surfaces may be plane or stresses which under particular conditions curved, in the latter case, mostly circular-cycan induce irreversible shear deformations in lindrical. the rock massif along the surfaces called slip In order to prevent downfalls, .quarry flanks and benches are designed by consideplanes. The studies of the patterns of stressed state ring the specific characteristics of the rock in quarry flanks demonstrate that in the massif or by providing artificial measures for general case the distribution of shear stresses increasing the rock stability. in a rock massif weakened by a side cut (such Landslides are characterized by that the as a flank) may be represented by stress motion of rocks occurs slowly, the process diagrams like those shown in Fig. 12.1 (lines may continue for a long time and entrains 1-1, 11-11, and 111-111).The points of the large massesof rock. The moving rock massif maximum shear stresses,which are located at in a landslide is subjected to plastic deformadifferent heights of the flank, form the direc- tions. Both bed rocks and rocks of waste tion of the weakest plane abcde.In the case of dumps may be involved into the process. ultimate stresses, this plane becomes a slip A subsidenceis essentially a vertical sinking plane. A slip plane of this kind mainly of loose rock masses at the edges of flanks, corresponds to a homogeneous (isotropic) which occurs without forming a continuous rock massif. If the massif has anisotropic slip surface. Landslides can occur on compacplanes (bedding planes, jointing systems, tion of loose rocks in waste dumps, which are tectonic disturbances, etc.), the position of a strengthened on wetting; on saturation of slip plane changes and in some casesmay be high-porous sediments with water; or in cases coincident with the planes of anisotropy. when there are soft plastic layers in the base The whole diversity of rock deformations of waste dumps.
Causes and Kinds of Rock Deformation
296
Ch. 12. Stability
Mud-streams (mud-flows) can occur in some rocks whose state changes from solid to fluid on water saturation. Mud-streams are observed most often upon saturation of loose and high-porous sedimentary rocks (loesses, loess-like loams, etc.) or when sands are carried off from sediments by filtering water flows. Mud-streams can be prevented by drainage. 12.2.
Factors Affecting Flank Stability
The stability of quarry flanks depends on the correlation between the forces that tend to retain a slope and those which displace it. These forGes can be influenced by many factors. The determination of the stable angles of inclination of quarry flanks (slopes) is essentially a problem of the theory of ultimate equilibrium according to which the strength of a rock can be characterized by a certain curve plotted in coordinates t, O"n(shear and normal stress),see Fig. l2.2a. A curve ARC in the figure determines the ultimate state of the rock in a specimen. A section OB' cut off by the curve on the t axis determines the cohesion. The angle of inclination of a
of Ouarry
Flanks
straight section mn to the an axis is called the angle of internal friction and the tangent of that angle is the coefficient of internal friction. A section OA describes the ultimate tensile strength of the rock, at' and a section OD is numerically equal to the ultimate compressive strength ac. In the general form the equation of the curve of ultimate equilibrium is 't = f(an) and can be described by a parabola, cycloid or a straight line depending on the kind of rock. A linear equation of equilibrium (Fig. 12.2b)has the form: 't = an tanp + k (12.1) where 't is the tangential stress in a shear plane, MPa; an is the normal stress in that plane, MPa; p is the angle of internal friction of the rock, degrees;and k is the coefficient of cohesion of the rock, MPa. The curves of ultimate equilibrium are plotted by the results of shear tests of rock specimens. A real rock is essentially a complex medium possessing a certain non-uniformity (anisotropy) of properties. The main factor responsible for anisotropy is the structure of a rock massif, in particular, various planes of weakness (bedding and stratification planes, fissures, etc.). Because of anisotropy, the laws
12.2. Factors Affecting
Flank Stability
297
Fig. 12.2 Strength certificate: (a) with curvilinear envelope of Mohr's circles; (b) with straight envelope
of geometrical similarity which are true for isotropic solids (metals, plastics, etc.) are inapplicable to rock massifs. For that reason, the mechanical properties of a rock massif may differ from those obtained by testing rock specimens. The properties of rocks in a massif are determined by special tests of rock prisms delineated in their natural bedding and oriented in a definite way relative to the planes of anisotropy. Forces p applied to a prism are developed by ,powerful jacks (Fig. 12.3). A prism usually breaks along a certain surface ab. The knowledge of the position of this plane makes it possible to determine the strength characteristics of a rock massif. Experiments have shown that among the two parameters characterizing the shear strength (cohesion and angle of internal friction), cohesion is subject to larger variations. Therefore, taking a particular value of friction by the results of laboratory tests of rock specimens, it is possible to determine the cohesion in the rock massif by considering that the resultant force of external pressure p can be resolved into a normal component N and a tangential component 1: If slip surfaces do not coincide with the planes of contact between rock layers in a massif, the angle of internal friction can be taken equal to the angle determined in shear
tests of rock specimens. The angles of internal friction for selected rocks are given in Table 12.1. The angles of internal friction at contacts of layers are taken equal to the angle of friction obtained by the results of laboratory tests for friction on these surfaces.The angles of friction obtained in tests at contacts of layers and fissures are given in Table 12.2. The mechanical properties of rocks in a massif (especially cohesion) not only differ from those in specimens,but are variable and depend substantially on the size ratio of the object being deformed, dimensions of structural blocks, and the strength of rock in specImens. During their formation and especially after the formation, rock massifs were subjected to
T
Fig.
12.3
Diagram
of natural
shear tests of priSJ
298
Ch. 12. Stability
Table 12.1 Rock
Sandstones Aleurolites Argillites Limestones Metamorphic schists Quartz-porphyries and granodiorite porphyries Syenites and porphyries
Angle of inter- Angle of renal friction in pose, degrees lumps, degrees 36 33 27-30 34 29
34-36 34-36 34-36 33-35 33-35
36
33-35
35
35
various changes and transformations which were associated with the appearance of rupture cracks, cleavages, stratification planes, etc. These surfaces divide rock massifs into individual polyhedrons or structural blocks which are essentially the elementary structural particles from which a rock massif is composed. In deformations of large rock massifs, structural blocks can be likened to mineral grains in small specimens subjected to deformations. Thus, for the estimation of the strength properties of rock massifs, it is essential to
of Quarry
Flanks
proceed from considering individual structural blocks. Plastic deformations of rocks are characterized by the appearance of two conjugate systems of fissures which, in the case of an isotropic medium, make an angle
Table 12.2
Porphyries, hornfelses, jaspilites, strong sandstones
28-31
Secondary quartzites, granodiorites, quartz-porphyries, granodiorite porphyries, skarnated rocks, syenites, diorites, aleurolites
25-28
Limestones, metamorphic schists, magnetites
24-27
Clay shales, argillites
23-26
Phyllites, talcochlorite and sericitic schists
23-25
24-28
22-27
20-26
20-23
17-20
23-25
20-22
16-19
21-23
18-20
15-18
20-22
13-15
9-12
12.2.
Table 12.3 (after
Factors
Affecting
Flank
299
Stability
G. Fisenko)
Rock group
Rocks and type of jointing
Cohesion in lumps, MPa
III
Weakly compacted and weakly fissured sand-clay sediments; strongly weathered, fully kaolinized igneous rocks; compacted sand-clay sediments with normal jointing
0.4-0.9
Strongly kaolinized igneous sand-clay rocks; compacted sandclay rocks with developed diagonal jointing; moderatestrength laminated rocks mostly with normal jointing Hard rocks mostly with normal jointing Hard igneous rocks with developed diagonal jointing
following fornlula suggested by G. Fisenko:
3.0-8.0
Coefficient a
0.5
10,0-15.0 15.0-17.0 17.0-20.0
3 3 4 5
20.0-30.0 30.0 20.0
6 7 10
entire complex of rocks and all structural elements of a deposit is involved into examiksp k = ( 12.2 m 1 + a In(H//) ) nation. In rock massifs divided into blocks by geological disturbances, each block should have one or two measuring sections. where km and ksp are the coefficients of With a simple structure of a deposit or cohesion of the rock in a massif and a quarry field, measuring sections can be spaspecimen, MPa; a is coefficient which can be ced at distances of 150-200 m from one found in Table 12.3; and H/l is the ratio of another. In each measuring section, there are the flank height to the mean size of structural determined the bedding elements of all joinblocks delinea~ed by fissures. ting systems, elements of stratification and Thus, for estimating the mechanical pro- foliation, linear dimensions of individual fisperties of rocks in massifs, it is essential to sures, distances between the fissures in each know the specific features of their jointing, in jointing system, pattern of fissure surface, and particular, the primary and secondary system the shape and size of structural blocks. of joints Uoint sets), contribution of each The bedding elements of fissures are measystem to the total quantity of fissures, sured by an inclinatorium. The total number spatial angles between the systems of joints, of measurements of bedding elements on an intensity of jointing, patterns of distribution area depends on the number of jointing of fissures in the quarry field, and the signifi- systems and the pattern of surface of fissures. cance of each jointing system in the structure As a general rule, 15-20 measurements of of a deposit and the stability of slopes. bedding elements should be made for each The field observations of jointing are car- jointing system. With a large discrepancy ried out on natural and artificial rock out- between the measured results, the number of crops and in exploring and drainage wor- measurements should be increased up to 30. kings. The density of sections for the measOffice work consists in determining the urements of jointing and their mutual ar- typical orientations of fissures and the intenrangement are deternlined by the geological sity {density) of jointing. The elements of structure of a deposit or quarry field. Mea- fissure orientation in space can be measured suring sections should be located so that the most conveniently by means of stereographic
300
Ch. 12. Stability
grids. Statistical processing of stereographic grids makes it possible to divide the entire totality of fissures in the rock massif into particular systems. The number of fissures, i. e. the density of jointing, can be determined by two methods: I. ~sually. i .e. by recording all detected fissures in each system; the results are then corrected by the data of statistical processing of a small number of selective measurements in systems. 2. By statistical processing of a fairly large number of measurements of bedding elements of fissures. The density of jointing can be characterized by several coefficients: (I) a linear coefficient which gives the ratio of a unit length to the mean spacing between the fissures. In some cases, the unit length may be taken as the length of the object being studied, for instance, the height of a quarry flank, etc.; (2) an area coefficient. or the ratio of a unit area to the area confined between two pairs of fissures forming a structural block; and (3) a volume coefficient, i. e. the ratio of a unit volume to the volume of an averaged block. An important factor affecting rock stability is weathering, i. e. degradation of rocks on the Earth's surface caused by natural agents (temperature, water, oxygen, carbon dioxide, living organisms, etc.). Weathering effect is especially noticeable in the flanks of old quarries. Rock stability can be influenced substantially by hydrogeological factors: inflow of ground waters, hydrostatic and hydrodynamic pressure, suffosion, leaching, sudden water outbursts, and mud-flows. Acting separately or in combination, these factors can decrease substantially the strength characteristics of rock, in particular the shear strength. When estimating the stability of quarry flanks, it is also essential to take into consider-
of Quarry
Flanks
ation the climatic factors: atmospheric precipitation, local temperature conditions, microrelief, and wind velocity. Without proper drainage, atmospheric precipitation can cause the inundation of sand-clay rocks to a state when capillary water changes to gravitational water, thus reducing sharply the shear strength, and therefore, the stability of slopes. Temperature changes and winds often accelerate weathering and thus diminish rock stability. Some kinds of microrelief can be the cause of swamping. Rock stability can depend substantially on engineering factors, especially on the method of blasting work. After blasting, the strength of rock in some portions of the massif can drop to 20-25 per cent of the initial (natural) strength. In order to prevent landslides and downfalls, it is then required to change properly the elements of working systems (width of berms and platforms, heights and angles of slopes and benches, etc.), though sometimes at the expense of the mining productivity. It is also essential to consider other engineering factors which can influence the stability of, flanks, such as the width of stoping and transport berms, profile of working, platforms, underworking of flanks, etc. 12.3.
Mine-Surveying Observations on Rock Mining Deformations in Open-Cast Mining
Observations on rock disturbance in open-cast mining and processing of the results of observations are an important object of mine-surveying service in quarries. Observations on landslides include two stages: (a) exploration and detection of seats of landslides and (b) observations on landslide seats and development of particular measures to prevent landslide phenomena. In view of the continuous technological mobility of slopes in quarries, the organi-
12.3.
Mine-Surveying
zation of observations has certain specific features. Observation points established in slopes cannot be preserved for a long time (especially those on the benches of working flanks). In that connection, it is essential to organize observations so as to complete them in relatively short terms. There are two principal kinds of observations: (1) observations on visible deformations of flanks and benches in order to predict the shape of a landslide and the pattern of its development in space and time and (2) observations on sections where deformations are invisible but can appear and cause serious damage to the mining plant. The results of observations should establish the displacements of particular points of a rock massif in space and time; dimensions of a sliding massif, slip surfaces, stages of the displacement process (initial, active, and attenuating), and the degree of hazard of rock displacements for mining operations and for surface structures. For observations on rock displacements, observation stations are established on the flank of a quarry, and instrumental observations are made at them in specified time intervals. An observation station is essentially a system of bench marks set up along the lines perpendicular to the length of a quarry flank. In order to take into consideration the effects of various factors on flank stability, the profile lines of an observation station are usually located in sections of rocks having different geological conditions. The length of profile lines should be such that one or both ends of the line is beyond the zone of expected displacements. In quarries of a small depth, profile lines can be drawn through the entire quarry. Spacings between the bench marks of a profile line depend on the quarry depth and dimensions of benches.At least two bench marks should be established on each bench: one near the bench crest and the other at the foot of the overlying bench. Bench marks should be
Observations
301
located on benches so as to ensure safety for an observer. Control bench marks are provided at the ends of profile lines. During the construction of an observation station, at least three initial bench marks are established so as to guarantee their preservation. Control bench marks of all lines are connected to the initial bench marks. Mine-surveying observations at stations include the following procedures: levelling of all bench marks, including control bench marks; measurements of spacings between the bench marks by controlled tension steel tapes (with recording the temperature during measurements); instrumental surveying of particular benches, muck piles, bedding elements, jointing, existing displacements, etc. All measurements should be made with checking. The accuracy of measurements should satisfy the following conditions: (I) in geometric levelling, the difference of two measured elevations should be not more than 3 mm; (2) in measuring the spacings between the bench marks, the discrepancy of two measurements should be not more t:han 2 mm; (3) in trigonometric levelling, the difference between two measurements of the same elevation should be not more than 5 mm for lengths up to 10 m or 8 mm for lengths above 10 m. The results of measurements are presented in the following graphical documents: the plan of an observation station (Fig. 12.4)on a scale 1/500, 1/1000 or 1/2000 which should show profile lines, mining workings, the situation and relief of the land surface; vertical sections for each profile with the positions of a flank at the moment of laying out a profile line and during a given series of observations; vector diagrams of bench mark displacements in the vertical plane on a scale 1/1, 1/5, I/lO or 1/20; and the diagrams of the rates of bench mark movement in the directions of these vectors. In observations on landslides, it is also
302
Fig.
Ch. 12. Stability
12.4
Plan
of observation
station
of Quarry
Flanks
required to determine the position of a slip surface in the body of a slope and establish the cause of its appearance. When the results of observations are analysed on profile lines, it is assumed that all displacement vectors of individual points on the slip surface coincide with the movements of the points of the slope surface which are located on normals to the slip surface. Then, having determined the displacement vectors from the results of mine-surveying observations, it is possible to determine the position of a slip line. The position of a slip surface is found in the following manner (Fig. 12.5): (I) the profile of a slope is constructed by the results of observations on the movement of a landslide, and all bench marks and fissures that appeared during the landslide are marked on it; fissures in the top portion and at the foot of the slope should be documented especially carefully; (2) the displacement vectors of bench marks are plotted on a profile, and a perpendicular from the mid of each vector is drawn towards the rock massif; (3) line sections parallel to the displacement vectors of bench marks are laid off on corresponding perpendiculars from the upper
Fig. 12.5 Determining position of slip line by results of observations on displacements of bench marks
~
12.4.
Stability
of Benches
and Flanks of Quarries
12.4. 1TT1nI -J.-J.-+-+--~~
I
I
I
I...
,
t...'
I"
, ,
/
,l".,j"I
,'.
/i
\ v ,
\
II'
)
~
Fig. 12.6 Determinationof angleof internal friction and cohesion by results of surveying of landslide
Stability Benches Quarries
of Working and Flanks
of
In the design, construction and operation of quarries, it is essential to choose a suitable method for calculating the inclination angles of quarry flanks so as to ensure proper stability of flanks and benches, provide place for berms and roads, and achieve a high economic efficiency of mining. There are a number of methods for calculating the flank stability which is estimated in terms qf a stability coefficient. This is understood as the ratio of the sum of all retaining forces to the sum of thrust forces acting on a landslide wedge:
and lower boundary of a landslide (from the break fissure at the top and from the support n = ~F fr + ~F c + A (12.4) line at the bottom). The broken line thus ~Fthr + B constructed is essentially the slip line of the landslide. where ~F fr = j"i:.N i is the sum of friction The results of observations on landslides forces; ~F c = kL is the sum of cohesion can be used for determining the angle of forces; ~F thr = ~ ~ is the sum of thrust forces; internal friction p and the coefficient of f is the coefficient of internal friction of the cohesion k of the rock by the method of rock; k is the coefficient of cohesion deterinverse calculation. mined by the force acting on a unit surface A rock massif at the moment when it loses area; and A and B are some additional balance is assumed to be under the action of retaining and thrust forces. the system of thrust forces ~ and retaining Tensile forces acting in the top portion of a forces: the force of friction tan p1;Ni and the slope produce vertical rupture cracks, beforce of cohesion kL (Fig. 12.6): cause of which the length of the slip surface 1;~ = tan p1;Ni + kL (12.3) decreases.The length of such a crack is found by the formula: where L is the length of the landslide surface 2k cotan (45° -p/2) in the section considered. If-= I"'C\ ~1~.JJ After a certain displacement, the moving y mass of rock stops in a new state of equiliwhere k is the coefficient of cohesion; p is the brium in which the thrust forces are counterangle of internal friction; and y is the mean balanced by the forces of friction. density of the rock. Solving the above equation for this state of In the calculations of the stable position of equilibrium under the action of friction for- d quarry flank on a circular-cylindrical slip ces, we find the angle of internal fric~ion of surface, it is rather difficult to find the centre the rock massif. Substituting the value of p of the most dangerous arc of slip. The into Eq. (12.3),it is then possible to determine analysis of equilibrium of a landslide wedge the coefficient of cohesion k of rock in the gives us only one equation, so that the massif. problem cannot be solved uniquely. Because
Ch. 12. Stability
of this, the centre of this arc is found by the trial-and-error method which involves laborious calculations. It is however possible to use a method which immediately determines the position of the slip surface when the landslide wedge has the least reserve of stability. The method is essentially as follows (Fig. 12.7): (I) a horizontal line BD at a distance H9o from the slope surface and a vertical line AB are drawn on the vertical section of a slope; (2) an arbitrary point D is taken on a line BD and a line at an angle 45° + p/2 to the line BD is drawn from that point (a line DC); a line BC is drawn from a point B at the same angle; (3) a line M K is constructed from the lowermost point of a slope (a point M) at an angle 45~ -p/2; (4) equal sections MP, PP', and P'P" are laid off on the line MK from the point M and equal sections CC', C'C", and C"Co, on a line DC from a point C; (5) lines parallel to the slope line MA are drawn from points P, P', and P" and lines parallel to BC, from points C', C", and Co; the intersections of these lines are points E , E l' E 2' and E 3; a straight line EO is drawn through these points up to the intersection with the line MK; (6) a straight line parallel to DC is drawn
of Quarry
Flanks
from a point a up to the intersection with the line ED (a point E); (7) two perpendiculars are raised to the lines aE and MK respectively in points N and M (Rl and R2 in Fig. 12.7); the intersection of these perpendiculars determines the centre of the circle passing through the points M and E. After these geometrical constructions, a check of the slope stability is made. For this purpose, the landslide wedge is plotted on a larger scale and divided by vertical lines into a number of prisms (Fig. 12.8). The area of each block Si is measured, and the mass of the rock in each prism per metre of the quarry front is calculated by the formula Qi = sir. The vertical lines, which are the boundaries of prisms, are continued downwards to a distance corresponding to the mass of a prism on the given scale. Perpendiculars are raised from the points of the intersection of these lines with the slip surface. After that, N i and 1; are found by the formulae: N i = Qi cos 9; and 1; = Qi sin 9; (values of N i and 1; are given in Table 12.4), and the angle 9; between Qi and N i is measured.
Fig.
12.8
Scheme of landslide
ing slope stability
wedge for calculat
12.5.
Table 12.4
Measures
for Controlling
Landslides
305
popular: flattening out the inclination angles of benches and flanks; leaving safety pillars of Block No. Qi.MN 1;, MN e" deg. N;.MN overburden rock or mineral it.l zones where landslide centres are probable to appear; I 2.33 45 1.65 1.65 decreasing the load on a slope in order to II 2.91 39 2.26 1.83 diminish the forces developed by the active III 2.72 27 1.24 2.43 pressure prism; removing the rock from proIV 1.97 20 0.67 1.85 bable centres of landslides; and strengthening V 0.75 7 0.74 0.09 artificially the rocks in the massif. 8.93 5.48 In undertaking measures for the prevention of landslides, it should be distinguished The length L of the slip surface is then between the cases when the slip surface is found, after which the stability coefficient is distinctly pronounced in nature (along cleacalculated by the formula: vage planes, layer contacts, etc.) and when it tan pI:N i + kL (12.6) is a merely imaginary line. In the former case, n= the slip surface can be represented by weak 1:1;; contacts in a rock bed dipping towards a where p is the angle of internal friction, working. Slip surfaces can also pass along the degrees;k is the coefficient of cohesion of the interlayers of clays and loams in a homogerock; and L is the length of the slip surface. neous bed of rock in a slope or along the The forces A and B (see Eq. 12.4) are not contacts of inundated rocks. considered here. In the latter case, the position of the slip If the calculated stability coefficient is surface cannot be detected visually and is greater than or equal to the specified value, determined only by survey observations on the flank is considered to be stable, if otherslope deformations or analytically. Such a wise, it is unstable, and it is then required to surface cannot be determined precisely, but flatten out the slope or employ artificial even an approximate determination of its measures for increasing the rock stability. position makes it possible to predict the kind of expected landslide and take suitable protective measures. With a known position of 12.5. Measures for Controlling the slip surface, landslides can be prevented Landslides by one of the methods described below. Landslides in quarries cause enormous Flattening out the slope angle. This method damage to mining plants, disturb the normal consists essentially in diminishing the angle course of mining operations, often lead to of inclination of a slope or bench to a certain large losses of stripped and prepared reserves safe value at which the landslide is imposof minerals, and necessitate multiple transfer sible. The calculation is carried out succesor even haulage of sliding rock masses. sively for a number of different values of an If the working flanks and benches of a inclination angle (Fig. 12.9). The results of quarry are designed correctly, their total stability calculations for these angles are stability will be guaranteed. It is not exclu- represented graphically as a curve 11= .f(a) on ded, however, that local landslide centres will which the angle a corresponding to the appear in certain sections. It is economically specified stability coefficient is found. In the efficient to prevent these local events by example shown in Fig. 12.9,with 11= 1.5, the taking appropriate anti-landslide measures inclination angle of the flank should be 41°. among which the following ones are more Mter that, the mine surveyor calculates the 20-1270
Ch.
306
12.
Stability
of
Quarry
Flanks
less than 18-20°. Underworking of the strata inevitably leads to rock sliding along bedding planes. To preclude a landslide, it is good plan to remove part of the rock mass in advance and thus to increase stability. I 1/
/
'ix
y
~~\~'.4 \:\~k,.. ,,~~
' Q.
> T2
12.6. Artificial Strengthening of Rock Massif Artificial strengthening of slopes in quarries is principally effective in cases when the specified inclination angle a = arctan
AI:h.'
(12.7)
I:a., + I:h.cotano. , I
turns out to be flatter than the angle found from the conditions of slope stability. (In the formula above: hi is the height of a bench; ai is the. width of a berm; and Oi is the incli35 40 45 a. degrees nation angle of a bench slope). Fig. 12.9 Flattening out of slope angle The existing methods of slope strengthening can be divided into the following groups: position of the point corresponding to 11= (1) those based on mechanical principles; = 410 on the top platform of the flank. This (2) those which increase the mechanical point is marked on the ground by a peg and characteristics of rock by the injection of determines the line to which the slope must stren,gthening materials; and (3) those employing durable coatings of slope sections be flattened. Unloading the active pressure prism. When (mainly for rocks liable to quick degradathe mining work is being carried out in zones tion). The first group includes methods in which where deep landslides occur or are probable to occur, the stability of slopes can be slopes are strengthened by bolting, cables, controlled efficiently by unloading the active retaining walls, etc. In the second group, the most popular pressure prism or, on the contrary, by increamethod is the injection of cement slurry. sing the mass of the support prism at the foot of the waste dump. The efficiency of this The injections of liquid polymer resins are method can be explained by the circumstance efficient in some cases. In the third group, gunned-concrete, bithat landslides on flank slopes with low inclination angles develop only slowly, so tumen and epoxy-resin coatings are used that there is enough time to transfer a large more often. An artificial coating is often mass of rock from the active prism into the applied onto a metal net or bolting. Each of these methods may be preferable zone of a passive prism (support prism). Removing the centre (locus) of a landslide. over others under particular conditions. For This method gives good results in caseswhen instance, slopes with distinct cleavage planes: tectonic fissures, laminations, disturbance the bed strata are dipping towards the worked-out space and the inclination angle is not zones, etc. can be strengthened reliably by
~
12.6. Artificial Strengthening of Rock Massif
307
as a variety of bolting. Casesare known when flexible cables were arranged in boreholes up to 30 m long. Flexible cables are especially efficient under the conditions when strengthening elements are subjected to bending as well as to tensile stresses. For slopes composed of sand and sand-clay rocks, strengthening methods based on the use of direct-current electric fields are promising. As a d. c. electric field is applied to a rock massif, it causes certain phenomena of electric transfer (movement of electrically charged particles between the field poles). The associated electrokinetic and electrochernical processesgive rise to coagulation and crystallization phenomena which decrease the moisture content of the rock and increase its density, and therefore, strength. It is advantageous to form electric fields in which the lines of force are thickened towards the cathode. This is achieved by arranging the anodes around the cathode. In that case, the strengthened zone in a rock massif acquires the shape of a cylinder with the radius equal to the distance between the unlike poles. In practice, the method of rock strengthening by d. c. electric field is realized as follows. The clusters of holes are drilled in the slope to be strengthened, with the anode holes being arranged around a single cathode hole. The depth of holes should be 10-15 per cent (b)
y
k,V,&/~/~//i
ii,/ J.( j --" (
,
,
¥"
~ Fig. l2.11 Slope strengthening: (b) by flexible cables
(a) by
bolting;
308
Ch. 12. Stability
of Quarry
Flanks
Fig. 12.12 Slope strengthening in quarry flank by do c. electric field
greater than the thickness of the zone of unstable rock. Spacings between the hole clusters are chosen so as to ensure the stability of the entire slope. The scheme of slope strengthening by this method is illustrated in Fig. 12.12. In clays with disturbed or undisturbed structure and a high concentration of finedispersed particles and rather low coefficient of filtration, strengthening rock piles can be formed efficiently by using composition binders. A hole is drilled in the rock massif and filled with a composition binder consisting of cement, quicklime, and clay (for
instance, 40 per cent of Portland cement grade 300 or 350, 10 per cerit of quicklime with an activity 85-92 per cent, and 50-55 per cent of Neogene clay). The composition binder interacts with the rock, so that clays in a certain volume around the hole are dried due to the hydration of the binder, and the associated chemital and adsorption processes lead to the formation of water-resistant and strong calcium hydrosilicates which bind disperse clay particles. With the hole diameter 23 cm, the stre~gthened zone has a diameter up to 50 cm.
Chapter Mine-Surveying
Control
Thirteen of
Mining
Safety
ent seams, and (3) foffi1ation of unprotected zones and zones of elevated rock pressure in seams liable to outbursts. Hazardous zones associated with flooded Modem mining can be characterized by ever increasing depths of mines and accor- workings can in turn be divided into the dingly, more complicated geological and hyd- following types: (a) zones near flooded or rogeological conditions. With an increase in gassy workings in a single seam; (b) those the mining depth, rock pressure increases near flooded or gassy workings in adjacent intensively. Moreover, the cases of sudden seams;(c) zones near flooded workings driven rock, coal, gas and water outbursts, self-igni- in the overburden; (d) those near unplugged tion of coal, etc. are more probable to occur or poorly plugged boreholes; and (e) zones in deeply bedded seams. Under such con- near tectonic disturbances (dislocations). In mine-surveying practice, dangerous conditions, special methods and means are required for carrying out the stoping and prepara- ditions are encountered most often in wortory mining operations, which should be kings approaching flooded or gassy old worstrictly observed and controlled properly to kings. Methods for the construction of safe boundaries and special safety measures of the ensure the safety and efficiency of mining. Under the conditions of elevated hazard of mining work have been developed for each mining, mine-surveying service plays an espe- type of hazardous zone. cially important part and has certain specitics. In many aspects of mining safety, minesurveying service takes the prime role and is 13.2. Control of Mining Work responsible for making decisions which are near Old Workings obligatory for all other mining specialists and When the mining work is carried out near workers. To effect safety control, mine surveyors determine the boundaries of hazard- flooded or gassy abandoned old workings, ous zones and represent them on the plans of special engineering measures should be taken the mining work; inform mine managers and to prevent sudden outbursts of water or gas foremen beforehand when mining workings into the existing workings. In that case, are approaching hazardous zones, participate mine-surveying service has to determine how in the development of safety measures, and reliable are the contours of old workings on survey plans, to calculate the width of barrier observe that these measures are fulfilled pillars (boundaries of safe mining), and plot properly. There are three principal groups of hazard- the pillars on a survey plan. The contour of an old working is conous zones which may be associated with (I) flooded mining workings; (2) formation of sidered reliable if there are the results of mine zones of elevated rock pressure between adjac- surveying obtained upon complete stopping 13.1.
Role of Mine-Surveying Service in Mining Safety
310
Ch. 13. Mine-Surveying
of mining in the working. As a rule, a contour is considered reliable if the old plan of the mining work and field books with the coordinates of theodolite surveys and measurements of workings carried out after the working has been abandoned are on hand. In caseswhen the contour of an old working is not confirmed by mine-surveying documents, it is regardcd as unreliable. Mine-sur\cying service is responsible for the reliability of the contours of flooded workings. With a reliable contour, the boundary of a barrier pillar is established. If the contour is unreliable, the mine surveyor determines the boundary of safe mining work. In coal fields; the width of a barrier pillar, d for seams up to 3.5 m thick and angles of dip up to 30° can be found by the formula: d = 5 m + 0.05 H + 0.002 L (13.1) where m is the extracted thickness of a seam, m; H is the mining depth, m; and L is the length of underground theodolite traverses run from the initial survey points to the contour of flooded workings and the boundary of a barrier pillar, m. The width of a barrier pillar should however be not less than 20 m. In seams more than 3.5 m thick and with angles of dip more than 30°, barrier pillars are not usually left. Instead, as a working approaches an old working, water from the latter is pumped off in due time. For flooded workings driven in the overburden rok, the width of a barrier pillar is determined by the formula: d = 0.05 H + 0.002 L+ Lln (13.2) where H and L are as in formula (13.1); Lln is equal to zero for barrier pillars extended on the strike with the angles of dip of the rock between 0 and 30°; with the angles of dip between 45° and 90°, Lln = 10 m; and with the angles of dip between 30° and 45°, Lln is found by interpolation. For barrier pillars extended to the dip, Lln = 0. The width of barrier pillars near flooded
Control
of Mining
Safety
vertical shafts, pits, and large-diameter boreholes is taken not less than 20 m in all directions and can be determined by the formula: d = 0.05 H + 0.002 L+ 5 (13.3) where H is the depth of a shaft to the mining level on which the barrier pillar will be left, m; and Lis the same as in formula (13.1). The boundaries of safe mining work should be determined by considering the materials of the geological structure of the flooded portion of a mine field, stored in the mine-surveying department of a mining plant, geological parties, archives, etc., the calculations and graphical documentation of the period when the working was in operation, and other information. Depending on the available materials, it is possible to determine approximately the error of the contours of flooded workings and to establish the boundary of the zone safemining work. As a rule, the dimensions of that zone may vary from the width of two barrier pillars up to 200 m or sometimes 300 m. Measures for ensuring safe mining work in hazardous zones should solve the principal problems of organization and give engineering solutions and terms for effecting of these measures and their control. A typical example of such measures is an optimal scheme of the arrangement of unwatering and advancing boreholes. The number, length and direction of advancing boreholes should be such as to preclude the breakthrough of a new working into an old one. The calculation of the expected water inflow for an unwatering borehole can be done by the formula:
(13.4)
where Q is the expected water inflow to the hole, m3/h; b is the hole diameter, m; His the height of a water column above the hole
13.3.
Calculation
and Construction
mouth, m; 9 = 9.8 m/s2 is the acceleration due to gravity; and 1is the length of a hole, m. The mouths of unwatering and advancing boreholes should be packed hermetically. By the most popular method of packing, a guide tube is inserted into a hole drilled to a depth of 10-15 m and fixed in place by a cement slurry. A gate valve is mounted on the tube, and the whole system is tested for strength and tightness by pumping in water into the hole at a pressure exce~ding 1.5 times that in flooded workings.
of Dangerous
Zones
311
contour of flooded workings is 1800 ill on the airway level 350 ill and 3200 ill on the haulage level 450 ill. In accordance with formula (13.1), the width of a barrier pillar on the airway level is: dl = 5 x 1.5 + 0.05 x 350 + 0.002 x 1800 = 28.6 ill and that on the haulage level is: dl = 5 x 1.5 + 0.05 x 450 + 0.002 x 3200 = 36.4 ill
On the horizontal projection (Fig. 13.1), the sections of length dl = 28.6 ill are laid off 13.3. Examples of Calculation from points 1 and 2; the points l' and 2' thus and Construction obtained define the boundaries of a barrier of Dangerous Zones pillar on the strike on the airway level. At the Calculation and construction of a barrier level 450 ill, the sections of length dl = pillar in a seam with flooded workings. Sup- = 36.4 ill are laid off from points 3 and 4; the pose that a worked-out field in a seam 16 resulting points 3' and 4' give the boundary 1.5 m thick and an angle of dip of 20° is of a barrier pillar on the strike on the haulage flooded at a depth of 350-450 m from the level. Earth's surface (Fig. 13.1).The contour of the To find the pillar boundaries on the dip of mining work (1-2-3-4) is reliable. The length a seam, the horizontal projection of dl, i. e. dl of mine survey lines for determining the cos v = 36.4 cos 20° = 34.2 ill is laid off from the points 3 and 4. The resulting points 311 and 4" determine the boundaiy of a barrier Vertical section across the strike pillar on the dip. The contour of the barrier Level 350 m pillar at flooded workings in the inclined I. tI\.,\.~11' £,e"311' 6 seam field 16passes through points 1'-2'-5-6. \v=20' It is depicted on the plan of the mining work. Calculation and construction of a safety Level 450 m pillar under flooded workings. Let a seam 14 Plan 2 ill thick be bedded along a normal at a 6 ~dl=2B.6 m distance of 25 ill under a seam 16(Fig. 13.2). 4li~ E- Id2=36.4m The seam 14is expected to be worked out in ~ "'1" one or two years. Since it is bedded along the "' " normal under the seam 16 in which the workings are flooded, in order to prevent water inrush from the seam 16into 14,a safety 3. 'to i,,- 3" pillar is constructed at a distance not less =28.6m than 40 times the seam thickness. The proI Jd2=36.4m 5 2 tected area is represented by a contour 1'-2'3' 5-6 which confines the flooded workings of Fig. 13.1 Graphical construction of barrier pillar the inclined field together with a barrier at flooded workings pillar. The construction of the safety pillar is
l
312
Ch. 13. Mine-Surveying
Control
of Mining
Safety
Fig. 13.2 Graphical construction of safety pillar under flooded workings of overlying seam
carried out by using rupture angles. For the conditions considered, the rupture angles are: ~' = 64°, y' = 70°, and 0' = 70°. The points I' (2') and 5 (6) are projected from the plan onto the vertical section across the strike, which gives points 11 (21) and 51 (6J and onto that on the strike, which gives points 1',2.: on the level 350 ill and points 51, 61 on the level 450 ill. In the section across the strike, lines are drawn from the points 11 (21) and 51 (6J at angles ~' = 64° and y' = 70° respectively up to the intersection with the seam 14.Points 71 (8J and 91 (IOJ found in this way determine the boundaries 9f a safety pillar on the rise and on the dip. Mter that angles 0' = 70° are laid off from the points 1',2', 61, and 51 on the levels 350 ill and 450 ill on the vertical section on the strike. The resulting points 11, 81,91, and 101 in the seam 14define the pillar
boundary in that section. The points 71, 81, 91 and 101 are projected from the sections across and on the strike onto the plan. This gives the general contour of the safety pillar (hazardous zone) in the seam 14' which is confined in the plan by the contour with corner points 7-8-9-10. Calculation and construction of a barrier pillar near an unplugged prospecting borehole. A prospecting borehole is drilled through a seam [6 at a depth of 320 m and stopped in 7 m after passing out from the seam (Fig. 13.3). The position of the borehole in the seam [6 is determined by the measurements of the hole curvature. A seam [4 is bedded at 40 mbelow the normal, The seam thickness is: [6 = 1 m and [4 = 0.9 m. The total extension of mine-surveying theodolite traverses is 4 km in the seam [6 and 5.5 km in the seam 14.
13.3. Vertical
section
Calculation
and Construction
~/""')Y
/~/AW/~
d16=29m
/ ~
/~
~ 7m
'1'*'---
:..: 6
sea((\\&
seali\14
w '
iI-J
I 1 ~' "5' O ,
B
~
~
5
¥
.. II arrlerplar
in seamJ6
I dt4=31.5m I Barrierpillar
I
, I
I
Inseam [4 -from
-the '1B' +
~ ~
I ~
4
Zones
313
deteffilines in plan the contour of the barrier pillar in the seam 16. Since the borehole has been stopped in the underlying rock at a depth of 7 m below the seam foot, the actual distance from the seam 14 is 33 m. Since, however, the safe distance between the seamsis 40 times the thickness of the seam 14, i. e. 40 x 0.9 = 36 m, and the
across the strike
Hole No.100 //$/
of Dangerous
B
Fig. 13.3 Construction of barrier pillar near unpluggedcurved borehole By fofl1lula (13.1), the width of a barfler pillar will be: for the seam 16: dl = 5 x 1.0 + 0.05 x 320 + 0.002 6 x 4000 = 29 ill and for the seam 14: dl = 5 x 0.9 + 0.05 x 360 + 0.002 4 x 5500 = 31.5 ill In the vertical section across the strike, llne sections equal to half the pillar width, i. e 14.5 ill are laid off from a point 01 in the seam 16 on the rise and on the dip. The resulting points 1 and 2 fix the barrier pillar boundary. These points are then projected onto the plan (points I' and 2'). The sections of the half-width of a barrier pillar are again laid off from the point 01 along the strike line passing through the intersection of a borehole with the seam 16,which gives points 3 and 4. These points define the pillar boundary on the strike. After that, points I', 3, 2', and 4 are connected by a smooth curve which
actual distance between the borehole bottom d h 1 . II ...
an t e seam 4 lS sma er, it lS reqwre d to leave a barrier pillar in the seam 14. For constructing this pillar, a noffilal is drawn
... the hole bottom to the mtersectlon with seam, which gives a point O2. The sections of a length dl /2 = 15.75 m are then laid off from that point on the rise and on the dip, which gives points 5 and 6. Similarly, the points 5 and 6 are projected onto the plan to obtain points 5' and 6'. Mter that, the sections of length dl/2 = 15.75 m are laid off from the point o24in the direction perpendicular to a line 5'-6', which gives points 7 and 8. Finally, the points 5', 7, 6', and 8 are connected by a smooth curve which defines the contour of the barrier pillar in the seam 14. Arrangement of advancing boreholes when approaching flooded old workings. When a working is approaching flooded old workings, the mine surveyor develops the scheme of the arrangement of advancing (unwatering) boreholes and determines the number of holes from the following considerations: the probability of the breakthrough of a new working into the old working should be completely precluded; the distance from advancing boreholes to the flooded old working in the section considered should not exceed the width of the crushed edge zone of a barrier pillar in stope workings, i. e. 5 m; the pitch of the advancement of the working should be chosen so as to ensure a constant (not reducing) advance of the prospected portion of the boundary of safe mining work, but not less than the width of the barrier pillar.
314
Ch. 13.
rI...
Mine-Surveying
Control
~
iui!
,..
~1 Reserve
ventilating
B
F:==:=-
.,{'
~
=3 entry
in seam
m4
Safety
2=5m -~ij~~~r~~~d
11=2m ~rr'-
d= 20m
~T "~j',of Mining
I' 87.1
1"'"-
~O\e
---Hole ~!
le
--
~0.'3
-
I
\",.0--
u
1=50m d= 20 m
"
E o "' II ...
Seam m4 iL
d=20~ ~
m=l.omTIO° -.,---
4 Fig. 13.4 Arrangement of advancing boreholes across barrier pillar
When driving a single working in the hazardous zone in a seam with flooded workings, a fan of diverging advancing boreholes is drilled. Consider a case of the arrangement of advancing boreholes when driving a single working in the hazardous zone with the width d of a barrier pillar 20 ill (Fig. 13.4). The planned ventilation adit in a seam m4' boundary of the hazardous zone (I-II), and the boundary of a pillar (1-2-3-4), where water inrush is probable and which should be proved by advancing holes, are plotted on the plan of the mining work. Lines 1-2 and 3-4 are drawn at a distance d = 20 ill frOm the axis 9f the projected working. The first borehole (No. 1) is directed along the axis of the projected working (ventilation adit in a seam m4)' and its optimal length is 50 ill. The second borehole (No.2) is directed into a point which ensures the control of a band of width 12= 5 ill. For this, the shortest possible distance to the flooded working (11= 2 ill) is laid ofTfrom a point 1, which gives a point A. The zone of the crushed edge portion of a barrier pillar 5 ill wide is constructed from the point A. An arc of radius 5 ill is drawn by compasses from the point A, and the bore-
2 .,
-;d"ge
Jl
-1~
hole is directed along ;1 tangent to this arc. Considering the distance between the bottoms of boreholes No.1 and No.2, the number of additional advancing holes is determined, noting that a distance of 5 m at both sides is controlled by each borehole and that the entire zone controlled by a borehole should be not wider than 12 m. In the example considered, it is required to drill an additional borehole (No.3). In a similar way, the directions and number of boreholes for controlling the hazardous zone on the dip are determined. Thus, five holes are drilled from the point of the first setting of a drilling rig (a point Bl). The place for drilling another group of boreholes is determined from the condition that the working face should be stopped in a point B2 which is spaced from the point Bl at a distance d = 20 m. The number of advancing boreholes in the second and subsequent groups diminishes by one both on the rise and on the dip of a seam. Arrangement of advancing boreholes at distortions intersecting flooded workings. When mining workings are approaching the distortions which intersect flooded old workings, exploratory drilling should be
1 3.4.
Construction
of Zones
made. This is done for determining the degree of inundation of a dislodger zone and for preventing the probable water inrush, since the disturbed rocks in the distortion zone are considered to be flooded and, when establishing the boundaries of a hazardous zone, are equated to flooded old workings. The width of the hazardous zone at a discontinuous geological disturbance (distortion) is determined in each particular case depending on the accuracy with which the disturbance is represented on the plans of rocks, gypsometric plans, and geological sections. In all cases,however, the boundary of the hazardous zone should be at a distance not less than 30 m along a normal to a dislodger. If the dislodger of a discontinuous geological disturbance has been opened and intersected by preparatory workings and it has been established that the inundation of the rock in the disturbed zone is insignificant, the width of the hazardous zone can b~ calculated by formula (13.1), but it should be not less than 20 m. If the intersection of distortion and flooded workings gets into the zone of rock displacement by the future stope working, the width of the hazardous zone is increased so that the distance along a normal from the seam to the dislodger is not less than 40 m, where m is the seam thickness. The width of the hazardous zone in this case can be determined by the formula: 40 m cos v (cotan d=
v cotan
O + cos ro) sin A
cotan v cos (I) -cotan O
where d is the distance in a plan along a normal from the line of the intersection of a seam and dislodger to the boundary of a hazardous zone; v is the angle of dip of a seam; O is the angle of dip of a dislodger; (I) is the plan angle between the lines of dip of a dislodger and seam; and A is the plan angle between the line of dip of a seam and the intersection line. With a working approaching a discontinuous distortion which intersects a flooded working 1 (Fig. 13.5), two
of
Elevated
Rock
Pressure
315
Fig. 13.5 Arrangement of advancing boreholes for a working approaching geological distortion
advancing boreholes 2 are usually drilled. One of them is arranged normally to the plane of a dislodger and the other is drilled horizontally along the axis of a working. Places for the arrangement of advancing boreholes are determined by the boundary of a hazardous zone. Barrier pillars in mines in an upper seam being worked or in underlying seams located at a distance along a normal not less than 40 m from overlying seams (where m is the extracted thickness of an underlying seam) can be calculated by formula (13.1). In such cases, L is found by considering the total extension of theodolite traverses from the adjacent shafts to the barrier pillar. If the distance along a normal between the adjacent working seams is less than 40 m, the barrier pillar in the underlying seam is constructed as a safety pillar under flooded workings. The protected area is taken as the boundary of the barrier pillar in the overlying seam. 13.4.
Construction of Elevated
of Zones Rock Pressure
Operations in stope workings can cause the deformations and displacements of rocks. The displacement process can influence the state of the rock massif and coal seams.The seam being extracted is bedded in a suite in which one or more seams have already been worked out earlier and coal pillars have been
~
316
Ch. 13. Mine-Surveying
left, so that the projections of these pillars get into the displacement zone on the seam being worked out. This gives rise to an additional effect which is called the bearing pressure and forms a zone of elevated rock pressure. It is distinguished between three types of zones of dangerous effect of pillars and edge portions of adjacent seams. The zone of elevated hazard is characterized by a sharp loss of stability of rocks in the roof, in the first place, immediately above a working. Dynamic effects of rock pressure can be observed, such as instantaneous destruction of the rock massif around a stoping face. These effects can raise catastrophically the load on the supports and often lead to rock bursts in stoping faces. Strong swelling of ground and squeezing of coal can often occur in the zones of elevated hazard. The dangerouszone can be characterized by a reduced stability of the lower layers of a roof in the worked-out seam owing to increased fissuring and stratification. This usually leads to roof rock inrush and sometimes to rock bursts in stoping faces. The prediction zone has no noticeabe effect on the lining of stoping faces, but the local changes of the stability of the lower roof layer and phenomena of secondary subsidence of the main roof are possible. The dimensions of influence zones under various conditions of seam underworking (or overworking) are determined by the distance of influen~ of pillars and edge portions and by the influence angles. The boundaries of zones of elevated rock pressure are constructed graphically on vertical geological sections perpendicular to the boundaries of pillars or edge portions of a seam. Pillars and edge portions of seams may be in a different position relative to the line of a stoping face. In this case, pillars are understood as non-extracted portions in adjacent coal seams,which have a width up to 2 1,whereas the portions of a width more than 2 1 are regarded as the edge portions of a seam (here
Control
of Mining
Safety
la)
-4
3
'1
I
~ 1
.. 'I~...
1..fJ
~ ~
~I (b)
O
0.4
08
1.2
04
08
12
1,6
all
t6
all
NILr 5
3
0
Fig. 13.6 Nomograms to determine distance of influence of zones of elevated rock pressure in faces: (a) under pillars or edge portions; (b) above pillars or edge portions; 1 -zone of elevated hazard; 2- dangerous zone; 3- prediction zone (solid lines for perpendicular pillars and dotted lines for parallel ones)
I is the width of the zone of bearing pressure). For the pillars of a width less than 2 I. the boundaries of dangerous zones are not constructed. The dimensions of zones of elevated rock pressure in stoping faces driven under pillars (edge portions) can be determined in the nomogram 2 in Fig. l3.6a and of those driven above pillars, in the nomogram 3 (Fig. l3.6b). For constructing the boundaries of the zone of elevated rock pressure, the following characteristics should be known: the bedding depth H of the seam in which a pil)ar or edge portion is left; the extracted thickness m of that seam; the thickness h of the interlayer between the worked-out seam and the seam in which a pillar or edge portion is left; the width a of a pillar; the width I of the zone of bearing pressure in the seam with the left
~
13.4.
Construction
of Zones
of Elevated
Rock
Pressure
317
N Ii is found in the nomogram (here N is the distance of influence, m). In the nomograms of Fig. 13.6, curves 1 correspond to the boundary of influence of zones of elevated hazard, curves 2 to the distance of influence of dangerous zones, and curves 3 to prediction zones. To change from the dimensionless ratio N Ii to dimensional N, this ratio should be multiplied by I, the width of the bearing pressure zone. Mter that, a vertical section through the given pillar is plotted (Fig. 13.8) on which the seam of influence and the worked-out seam, the pillar (or the edge portion of a seam), and the position or a stoping face in the worked-out seam are shown. The calculated distances of influence of the zones of elevated hazard, dangerous zones and prediction zones are laid off in the roof and foot of the seam of the pillar perpendicular to the bedding plane. Then, lines parallel to the influence seam are drawn through the points obtained (3-4, 5-6, 7-8, 3'-4', 5'-6', and 7'-8').
50 40 30 20 10
40
80
120
160 200
7
240 Hm
8
Fig. 13.7 Norn.ograms to determine width 1 of bearing pressure zone: (a) for depths 200-1200 m; (b) for depths 20-280 m
pillar or edge portion. The last characteristic can be found in the nomograms of Fig. 13.7. The zones of elevated rock pressure are constructed in the following way. For the known mining depth H and seam thickness m, the width I of the zone of bearing pressure is found in the nomogram of Fig. 13.7. For instance, with H = 750 m and m = 2 m, the width of the bearing pressure zone is I = 65 m. On the nomogram of Fig. 13.6, the distance of influence of the zones of elevated rock pressure is then determined. For this purpose, the width of a pillar, a, is divided by the width of the bearing pressure zone, I, which gives the dimensionless ratio all according to which the dimensionless ratio
DZ
~ Seam
'8
Seam
I
Seam
I
"
!I
E HZ \
A
,1
\
p oll I
ar
I
~
B 10
!
10'1
Fig. 13.8 Construction pressure from pillar
'~
of zones of elevated rock
318
Ch. 13. Mine-Surveying
As an example, let us determine the zones of influence of elevated rock pressure in the roof and foot if the width of the zone of bearing pressure is 1 = 65 m and the width of the pillar is a = 50 m. The ratio of the pillar width to the width of the bearing pressure zone is a/[= 0.77. Using this ratio, we find N /I for faces passipg under pillars (N 1// = 2, N fl = 3.4, and N 3/[ = 5) and for those passing above pillars (N'1/1= 3.5, N~/l = 4.9 and N~/l = 5.9). The distance of influence of a pillar for underlying faces will be as follows: for the zone of elevated hazard: N = 1 = 65 x 2 = 130 m; for the dangerous zone: N 2 = 65 x 3.4 = 221 m, and for the prediction zone: N 3 = 65 x 5 = 325 m. For overlying faces we have: for the zone of elevated hazard: N'l = 65 x 3.5 = 227.5 m, for the dangerous zone: N~ = 65 x 4.9 = 318.5 m, and for the prediction zone: N~ = = 65 x 5.9 = 383.5 m. For the construction of zones of elevated rock pressure from a pillar (see Fig. 13.8), lines are drawn from points 1 and 2 at an angle of 60 o to the bedding plane up to the intersection with the line of distance of influence of elevated hazard zone in points 3 and 4 (3' and 4'). Perpendiculars to the bedding plane are then drawn from these points up to the intersection with the lines of distance of influence of dangerous zone and prediction zone in points 5 and 6 (5' and 6') and 7 and 8 (7' and 8'). To determine the side boundaries of the elevated hazard zone, sections 1-9 (1'-9') and 2-10 (2'-10'), each 20 m long, are laid off in the bedding plane from points 1 and 2 (I' and 2'). Points 9 (9') and 10 (10') are connected with points 3 and 4 (3' and 4') by lines which define the side boundaries of the elevated hazard zone. For a seam [8' the width of the elevated hazard zone is equal to (AB) and for a seam [4' to (CD). The construction of the boundaries of the zones of elevated rock pressure from the edge portions at the side of the worked-out space is done in the same way as for the pillar, but at the side
Control of Mining Safety
of the rock massif. The boundary of the zone of elevated rock pressure is a straight line drawn perpendicular to the bedding plane at a distance corresponding to the width of the zone of bearing pressure. If a number of coal seams are being mined under (above) pillars, the boundaries of the zones of elevated rock pressure are constructed for each seam. If pillars have been left in a number of seams under (above) the seam, being mined, the boundaries of the zones of elevated rock pressure are constructed for each pillar. If the zones of elevated rock pressure from a number of adjacent seams overlap on the seam being mined, they are considered in the first place by the degree of hazard. 13.5.
Construction of Dangerous Zones for Mining Work in Seams Liable to Coal, Gas and Rock Bursts
The mining work in deeply bedded coal seams increases the risk of harmful and dangerous effects of rock and gas pressure which, may be associated with dynamic phenomena: sudden bursts of coal, gas and rock. Soviet scientists have studied the nature of the principal engineering and geological factors causing gas-dynamic phenomena and rock bursts, established the relationships between the effects of gas and rock pressure, determined the parameters for the construction of dangerous zones, and developed the measures for preventing outbursts. One of the main methods for preventing sudden outbursts is working out of protective seams. A protective seam is a seam (or interlayer, or rock layer) which, when being worked out, ensures complete safety from outbursts in another seam of a suite that is to be protected, or relieves partially the rock pressure. In mining of a suite of seams which are dangerous in outbursts, a non-dangerous protective seam is extracted in the first place.
13.5.
Dangerous
Zones
in Seams
Liable
to Bursts
319
Upon the extraction of this seam, the rock pressure in the massif decreases due to the displacement of underworked rock volumes. Protective seams should be worked out without leaving coal pillars. The duty of mine-surveying service in this case is to construct the protected zones and zones of elevated rock pressure, depict them on the plans of the mining work, and inform miners and foremen when workings approach to dangerous zones by 20 m. For seams liable to coal and gas outbursts, the protected zones and zones of elevated rock pressure are constructed on the basis of the following initial data: mining depth H in the protective seam; extracted thickness m of the protected seam; angle of dip v of the Ream; concentration 11, per cent, of sand
(cl
I' I
[i 'Q1
r 2 I~
~
Fig. 13.9 Construction of protected zone in working of protective seam on dip: (a) section on strike with b < 2~; (b) section on strike with b > 2~; (c) section across strike; l-protective seam;2 and 3- seams to be protected; 4- protected zone; 5- zone of dangerous loads
~
Ch. 13. Mine-Surveying
320
Control
of Mining
Safety
Table 13.1 Depth
of work m
Values
H,
Values of S~, m
of S:' m
Smallest dimension, a or b, of working in plan, m (refer to Figs. 13.9 and 13.10)
300 400 500 600 800 1000 1200
Smallest dimension, a or b, of working in plan, m (refer to Figs. 13.9 and 13.10)
50
75
100
125
150
175
200
250
50
75
100
125
150
200
250
70 58 50 45 33 27 24
100 85 75 67 54 41 37
125 112 100 90 80 57 50
148 134 120 109 90 71 63
172 170 154 138 117 100 92
190 155 142 126 103 88 80
205 182 164 146 127 114 104
220 194 174 155 135 122 113
56 40 29 24 21 18 16
67 50 39 34 29 25 23
76 58 49 43 36 32 30
83 66 56 50 41 36 32
87 71 62 55 45 41 37
90 74 66 59 49 44 40
92 76 68 61 50 45 41
on the strike. It is required to take into consideration only pillars whose dimensions exceed the following values: 4 m for the seam thickness up to 1 m; 3 m for the seam thickness from 1 m to 2.7 m, and 8 m for the seam thickness above 2.7 m. The dimensions of the protected zone in the roof, SI' and in the foot, S2 (Fig. 13.9)can be determined by the formulae: SI = ~1~2S'1and S2 = ~1~2S~ (13.6) where ~I is a coefficient depending on the method of roof control:
this is done by using protection angles O and pressure angles
=
[31L;
(13.7)
where L; is to be found on a nomogram (Fig. 13.11b). ma The permissible maximum and minimum but should not be less than unity; mo is the values of advancement of the stoping face in critical thickness of a protective seam which the protective seam relative to the mining can be found in the nomogram of work in the seam being protected (Figs 13.9 Fig. 13.11a; ~2 is a coefficient considering the and 13.10) are given in Table 13.3. Construction of protected zone. The protecconcentration 11, per cent, of sandstones in tive seam is worked out at a depth of 1000 m, the interlayer: the extracted thickness is m = 0.7 m, and the ~2 = 1 -0.4(11/100) angle of dip v = 50°. The inclined height of a level is 150 m and the size of the worked-out and S'I and S~ are taken from Table 13.1. If hI < SI in underworking or h2 < S2 in space on the strike is 650 m. A pillar 15 m overworking, it is required to separate sec- wide is left on the airway level. The roof is tions where dangerous loads can appear again; controlled by complete pneumatic back-fil~1
=
mef
13.5.
Dangerous
Zones
in Seams
Liable
to Bursts
321
(a)
(b)
"'"
., L3
b,
.1
--if
4
?
H , 1
"{45~: "'
2
/i
;.:,
~\
t
~ b2~!~ Fig. 13.10 Construction of protected zone in working of protective seam on strike: (a) section across strike with a < 4 + ~; (b) section across strike with a >4 + ~; (c) section on strike; I-protective seam; 2 and 3- seams to be protected; 4- protected zone; 5- zone of restoration of dangerous loads
ling. A seam dangerous in rock bursts is bedded in the ground at a distance h2 = = 10 m. The interlayer contains 50 per cent of sandstones. Since the size of the pillar between the levels is greater than 4 m, then a is taken as the inclined height of a level, i. e. a = 150 m. The size of the protected zone towards the foot of a protective seam is: S2 = f31f32S~ 21-1270
According to the nomogram (Fig. 13.11a), with a = 150 m and H = 1000 m, the critical thickness is mo = 0.68 m. For the roof control by pneumatic back-filling, k = 0.3, and therefore: me! = km = 0.3 x 0.7 = 0.21 m ~1 = me!lmo = 0.21/0.62 = 0.31 ~2 = 1 -0.4(11/lOO) From
Table
= 1 -0.4(50/lOO)
13.1, we find:
= 0.80
S~ = 45 m,
Ch. 13. Mine-Surveying
322
Control of Mining Safety
Table 13.2
whence the size of the protected zone along a normal to the bedding plane is:
Angle of Protection angles 0, deg Pressure angles
S 2 = 0.31 x 0.80 x 45 = 11 m
0 10 20 30 40 50 60 70 80 90
63
From find ~ v = 50°; and 230
61
Ll = L'l13l = 180 x 0.31 = 56 m
01
B,
03
04
!P2
<1>3
80 77 73 69 65 74 72 74 70 75
80 83 87 90 90 90 90 90 90 80
75 75 75 77 80 80 80 80 78 75
75 75 75 70 70 70 70 72 75 80
64
64 63 60 59 56 54 52 48 46 43
64
62 60 59 58 56 54 54 54 54
59 57
£2 = £~J32= 230 x 0.8 = 184 m
55 53 52 50 48
N ole: If the direction of stoping work coincides with neither the line of strike nor the line of dip, angle v is taken as the angle of inclination of the seam in a section perpendicular
the nomogram of Fig. 13.11b, we and 1; for jhe inclination angle they are equal respectively to 180 m m. Thus, we have:
to the face direction.
Since a < 4 + ~, the zone of the restoration of dangerous loads cannot form and, according to Table 13.3, the permissible advancement b2 is not limited, and the minimal advancement b~ can be taken equal to 20 m. We find from Table 13.2 that 01 = 70° and 03 = 80°. The construction of zones of elevated rock pressure is illustrated in Fig. 13.12. For the zone of elevated rock
Table 13.3 Pernlissible advancement to prevent rock bursts, m
Mining conditions
Minimal advancement: b; in underworking b; in oveI;;Working Maximal advancement** b1 in underworking b2 in overworking: if a < Ll + L2 if a > Ll + L2
Permissible prevent
advancement outbursts, m
khl h2
h1, but not less than 20 m* h2, but not less than 20 m
Not limited
Not limited
b1 < L3 + h1 cotan b2 < L3 -0.3
~3
Not limited
h2
* Coefficient k depends on the rate of advance of a stoping face in the protected seam: v, m/day k
up to 2 I
2 to 5 1.2
over 5 1.4
** Permissible advancements are given for the stoping work on the strike. If the stoping work is carried out on the dip, LJ and
13.5.
Dangerous
Zones
in Seams
Liable
to Bursts
323
(a) ron
200
/.I\
0.8 1150
III
IIII
100
\ \
0.4
=50m
0
400
800
\
\
H,m
(b)
I~~
t(J&, II
300
, La
250
L~ 200
~
\0
30
60
IXo
y
.,,\
y Fig. 13.12 Zones of influence , of seam edge portion: I -protected zone; 11- unprotected zone; 111- zone of elevated rock pressure
21.
Chapter M ine-Surveying of Geological
Fourteen Control Exploration
the geological structure of the region in view of the collected geophysical and geochemical data and (2) to use the established regularities Geological exploration is essentially a of mineral location in order to find out the cycle of investigations which are carried out most perspective geological structures, evaluin a definite sequence and can be character- ate their prognostic resources, and determine ized by the following stages: further directions of geophysical and geo1. The stage of regional geological recon- logical survey and search. naissance which is aimed at determining the 2. The stage of geological survey and genprincipal bedding characteristics of various eral search is the main stage when large-scale minerals in a particular region so as to make investigations of geological structures are prognostic valuations of the perspectives of carried out in order to distinguish local areas their extraction and outline areas for more and structures which are promising for the detailed geological prospecting. This stage detection of mineral deposits. Geological surcan be divided into two substages: (a) re- veys at this stage should be made primarily gional geological and geophysical reconnais- within the limits of mining areas. The results sance and (b) regional geophysical and geo- of surveys and prospecting at this stage are logical surveys and hydrogeological and represented in the form of geological maps, engineering-geological work. register maps of minerals, and prognostic Geological and geophysical reconnaissance maps of mineral location. (the Ist substage) is effected for the formation 3. The stage of geological search is carried of a new or renovation of the existing geo- out in order to detect mineral deposits within logical and geophysical basis which is needed the limits of known and potential ore fields for establishing the principal characteristics and basins of sedimentary minerals where the of the geological structure of large regions previous exploration work has revealed the and the regularities of the location of probability of the detection of deposits. The minerals within their boundaries. search work at this. stage takes place in The results of geological and geophysical boreholes and pits with the use of georeconnaissance are used for plotting geo- physical and geochemical methods, rock logical, prognostic and other general and sampling, panning, etc. sheet maps, geological and geophysical key Investigated areas are represented on geosections, and schemesof the geological struc- logical maps which show the regularities of ture of deep levels. the localization of mineral bodies. The main purpose of prospecting opera4. The search-valuation stage is an intertions at the second substage is (I) to analyse mediate stage between the reconnaissance 14.1.
Brief Data Exploration
on
Geological
14.2.
Mine-Surveying
Control
and the exploration of mineral deposits. The main object of this stage is to evaluate the commercial significance of detected deposits, reject. those which are of no interest for the mining industry, and select objects for preliminary prospecting. The results of the search-valuation work are represented in the form of preliminary geological maps and geological sections of a detected deposit. 5. The stage of preliminary prospecting is done in order to obtain trustworthy information for reliable geological, technological and economic evaluation of commercial significance of deposits. Most deposits are explored by prospecting boreholes. The results of preliminary prospecting are represented in the form of approved temporary specifications and technico-economical report on the expediency of the detailed exploration of a deposit. 6. The stage of detailed prospecting (exploration) is carried out only for deposits which are evaluated positively by preliminary prospecting and recommended for commercial exploitation. 7. The stage of complementary prospecting can be fulfilled both on explored deposits which are not still mined commercially and on those which are being mined. 8. The stage of exploitation prospecting is continued during the whole period of mining of a deposit and is carried out for collecting systematic reliable information required for current (annual) and operative (quarterly, monthly, and daily) planning of mineral extraction and the control of the completeness and quality of extraction. The main objects of exploitation prospecting consist in determining more accurately the contours of mineral bodies and their internal structure and bedding conditions, quantity and quality of mineral resources, geometrization of technological types and grades of a mineral, etc. All stages of geological reconnaissance and prospecting are associated with geodetic, to-
of Geological
Work
325
pographic and mine-surveying operations which are done to attain the following objectives: I. The formation of the geodetic basis for the layout, connection and geological survey work required for geological prospecting; provision of a control network for topographic surveys when these are needed; and the solution of various engineering problems when driving mining and exploring workings or making the geophysical and drilling work. 2. The formation of the topographic basis for geological prospecting; this is meant as a topographic plan or map with the points of field observations, which is plotted in a simpler form, i. e. without showing some elements of the topographic situation and relief that are inessential for the construction of geological boundaries. The topographic and geodetic materials collected at the stage of geological prospecting are latt;r used in the design and exploitation of mining plants. 14.2.
Mine-Surveying of Geological
Control Work
The mine-surveying control of geological work includes the following procedures: the transfer of the design positions of objects of geological observation (boreholes, mining workings, etc.) into nature; determination of the planimetric and height coordinates of these objects; and the formation of the topographic basis for geological and other special maps. The geodetic control for the mine-surveying work can be provided by: (a) geodetic nets; (b) elements of survey control, such as planimetric, elevation and combined planimetric-elevation surveying nets and individual points, and geodetic reference nets; (c) distinct contour points of deposits whose coordinates can be found on topo-
Ch. 14. Mine-Surveying
326
Control of Geological Exploration
Table 14.1 Root-mean square errors of positions of geological observation objects relative to initial points, m
Stages of geological prospecting
plan
in elevation
90(100) 40(50) 20 (25)
10(20) 5 (10) 2(3)
in
I. Regional geological investigations, geological survey work, and geperal search with compilation of maps on a scale: 1/100000 and smaller 1/50000 1/25000 2. Search work, search-valuation work and preliminary prospecting with compilation of maps on a scale 1/10000 3. Search-valuation work, preliminary and detailed prospecting with compilation of maps on a scale 1/5000 and larger N ole: Numbers desertous,
woody,
in brackets
are rms errors
and mountainous
regions.
for determining
(2) 0.5
the positions
of geological
observation
objects
the accuracy recommended in Table 14.1. The elevations of these objects should be determined with errors not exceeding the following data: (a) in hydrogeological surveys, 0.5 of the adopted interval of hydroisohypses on hydrogeological maps, but not more than twice the error given in Table 14.1; (b) for individual hydro geological surveys for determining the gradients of underground flows, inundations of sections and mining workings (mines, shafts, etc.), within t!!e accuracy for technical levelling, i. e. 50 J L, mm, where L is the length of a geometric level line, km. The coordinates of the mouths of stationary hydraulic boreholes should be determined from the closest bench marks and points of a national levelling net with an rms accuracy not worse than I 10 cm. In geological work, deep geological mapping and general search with the compilation deposits. For the objects of hydrogeological obser- of maps on a scale 1125000 and smaller, the vations, the survey work for determining the objects of geological observations are transplanimetric coordinates should be done with ferred into nature and connected, as a rule,
graphic maps (plans) or aerophotogrammetric plans with the required accuracy; and (d) objects of geological observations whose coordinates are determined with the required accuracy. The mine-surveying control for transferring the design positions of objects of geological observations into nature includes the following steps: (a) the preparation of initial data and the compilation of schemesand the plan of work; (b) measurements for determining the positions of observation objects on the ground; and (c) the fixation of the positions of transferred objects. The accuracy of the determination of planimetric and height coordinates of geological observation objects can be taken by reference to Table 14.1 for deposits of solid minerals and to Table 14.2, for oil and gas
14.3. Topographic
327
Basis of Geological Exploration
Table 14.2 Kind
(category)
of
Ultimate
borehole
transfer into nature
Single reference and parametric boreholes Structural and search boreholes Exploratory boreholes Boreholes on exploited areas Boreholes in water areas
150
errors, m
preliminary determination of elevations of borehole mouths
determination of planimetric position of borehole mouths
detennination of elevations of borehole mouths
150
100
5.0
10
30
1.0
5
12
0.5
4
0.3
10
0.5
50 25 10 20
5
Notes: I. Errors are given relative to the points of a national geodetic net and geodetic densification nets. 2. As initial points of connection, it is possible to use any points including those by which the structural maps are plotted, provided that this ensures the accuracy indicated in the table.
according to the topographic maps and materials of aerophotogrammetric surveys, Instrumental field measurements at these stages of geological work are only possible in exceptional caseswhen topographic maps are unavailable or cannot ensure the specified accuracy of the connecting work. The points of a geodetic net or surveying nets fixed on the ground by permanent bench marks can be used for the layout, connection and geological survey work, planimetric and elevation control of topographic surveys, and for solving certain engineering-geological problems. The points of geodetic survey control fixed by temporary bench marks, points of geodetic reference nets, and distinct contour points on the terrain whose coordinates are taken from a topographic map can be used only for the layout, connection and geological survey work. The coordinates of geological observation objects can be used: for marking the positions of these points on maps and sections with an accuracy that can ensure reliable representation of the results of observations and accurate calculation of mineral resources;for deter-
mining the boundaries of mineral deposits, revealing geophysical anomalies, etc; and for compiling special maps, sections, prospecting profiles, and other graphical documentation. 14.3.
Topographic of Geological
Basis Exploration
The topographic basis for the geological exploration work can be provided by: (a) topographic maps (plans); (b) large-scale plans; or (c) special topographic plans. . In the geological, search and exploration work, the scale of the topographic basis should correspond to that of the map to be plotted. The recommended scales of the topographic basis for preliminary and detailed geological prospecting are given in Table 14.3. In the maps and plans of the topographi(; basis on a scale 1/10000 and smaller, the errors in the positions of contours, orientation marks and horizontals should be not more than 2.5 times the errors permissible in national topographic maps. In special topographic plans used as the
328
Ch. 14. Mine-Surveying
Control of Geological Exploration
Table 14.3 Stage of geological prospec- Scale for topographic sur. ting veying
Preliminary prospecting 1/10000 to 1/5000 Exploration of: (a) metal ores 1/10000 to 1/1000 (b) carbonate rocks, phosphorites, sands, and gravels 1/25000 to 1/5000 (c) salts 1/25000 to 1/10000 (d) coals and oil shales 1/1000 to 1/2000 (e) underground water 1/1000 to 1/5000 (I) other non-metallic minerals 1/10000 to 1/5000
topographic basis, the errors in the positions of land contours and objects relative to the nearest points of a surveying net should. not exceedthe pef111issible errors of corresponding topographic maps by more than 1.5 times for a scale 1/5000 or 2 times for larger scales. The errors of relief surveys relative to the nearest points of elevation control on the topographic basis should not exceed 0.5 m for contour intervals of 1 m or 1/3 of the contour interval in other cases. For better clarity, the amount of topographic details on geological maps on a scale 1/10000 and larger is diminished. Coordinate grids are shown as ticks of kilometre lines in intervals of 10 cm. The points on geodetic nets and on the schemesof geological observations are.taken selectively, i.e. only those points which are essential for the compilation of geological and geophysical maps are used. The points of a national geodetic basis are shown only in caseswhen this is specified by the design. Land relief is indicated by horizontals and numerical marks of individual heights. For the topographic basis on a scale 1/10000, land relief is shown in the same vertical contour intervals as on national topographic maps. For larger scales, the following contour intervals may be recommended: 2.0 m for a scale 1/5000; 2.0 m or
1.0 m for a scale 1/2000, and 1.0 m for a scale 1/1000. For mountainous regions and foothills, the recommended contour intervals are respectively 5.0 m, 5.0-2.0 m, and 1.0 m. Hydrographic objects are indicated on the topographic basis only as the coastal lines of seas,lakes, rivers, etc. without detailed characteristics. Vegetation is not shown. Woods are marked by contours. Swamps and marshes are shown by conventional symbols without detailed characteristics. Other typical features of the terrain and ground are not indicated on the topographic basis. The topographic basis of geophysical maps should give only the situation associated with the text of the report; land relief is shown only in rare cases. 14.4.
Transfer of Plan of Exploratory Workings into Nature
Exploratory workings are transferred into nature according to the plan of the minesurveying work. Depending on local conditions and the specifics of geological prospectiDg, this plan may involve various kinds and volumes of the topographic and minesurveying work. For instance, Fig. 14.1 shows the plan of the topographic and mine-surveying work for detailed prospecting of a deposit by drilling exploratory boreholes along profile lines. The plan envisages triangulation surveys (points I, II, III and IV); running of base lines (main theodolite traverses) for the layout of profile lines; the connection of base lines (by closed theodolite traverses) to triangulation points III and IV; plane;.table surveying of the territory of a deposit on 10 plates; and the transfer and connection of points for borehole drilling. Exploratory workings and objects of geological observations are transferred into nature and connected relative to the points of reference nets which can include main theodolite traverses (base lines), profile lines. and
14.4.
Transfer
of Exploratory
the points of a surveying net and national geodetic net. The layout work is carried out with an accuracy which can ensure the required accuracy of connection. If an object is transferred into nature with an accuracy insufficient for connection, additional connection to the closest control points should be carried out. Networks for detailed geological prospecting usually have a relatively regular geomet-
Workings
Plan into
Nature
329
ric shape and consist of a system of parallel base lines intersected by a system of parallel profiles (Fig. l4.2a). In many cases, some base lines can be matched conveniently with extended objects on the terrain (roads, river banks, open watersheds, etc.). In such cases, base lines may have a curvilinear shape (Fig. l4.2b). As a rule, the plans of exploration nets are transferred into nature by instrumental methods.
Ch. 14. Mine-Surveying
330
Control of Geological Exploration (b)
(a)
.-~::. ...Profile Fig.
14.2
Construction
Main traverse with observation points
of base lines and prospecting
In laying out geological exploration nets, the mine-surveying and geodetic work is practically organized on the following principles: (a) the initial points and directions are transferred into nature, and the survey area is delineated by laying out base lines, which provides a 'framework' for subsequent layout operations; (b) the. base lines delineating the survey area are connected to the points of a geodetic net, i. e. the 'framework' is connected to the existing system of coordinates; and (c) profiles are laid out and picked points are established. For transferring the initial points into nature and assigning direction to the initial portions of base lines, the following methods can be employed: (a) one of the base lines passes through a point of the geodetic reference net existing in the region being explored. In that case, the
profiles
angle between the direction of the base line and the direction onto another point of the reference net (for instance, angle 13,Fig. l4.3a) is measured on a topographic map. This angle is then laid off on the ground by an angle-measuring instrument set up in the initial point; (b) base lines pass far from the points of a geodetic reference net. Then a point of the reference net near the base lines is selected, from which two or three adjacent reference points are visible, and a theodolite traverse is run between the selected reference point and the base line (Fig. l4.3b). By means of this traverse, the base lines can be connected to the existing local system of coordinates; (c) the region of geological prospecting is located in an inhabited area, so that the points of a geodetic reference net are invisible from it. In that case, the directions of base lines can be assigned by means of a magnetic azimuth. If the prospected region is located in
14.4.
Transfer
of Exploratory
Workings
Plan into
Nature
331
(a)
.,A /
~
--c.
(32
(b)
==
-
~ B.
Fig.
14.3
Scheme
of base
"""6
lines
a closed area with poor visibility (woods, etc.) and where there is a magnetic anomaly, base lines can be' connected by a geographic azimuth. The intervals between the pickets (observation points) on profile lines are measured in one direction by means of range finders or tapes. Inclination angles wider than 5° are measured by theodolites or inclinometers; in such cases a length laid off between the pickets is corrected for the inclination angle. The coordinates of the final pickets of profiles are determined by running theodolite traverses between the ends of profiles. For observation points and exploratory workings not coincident with the points of a reference net, connection can be done by tacheometric or plane-table surveys, length measurements or intersections.
14.4.1.
Connection and Transfer of Geological Observation Objects from Topographic Map into Nature
In the geological survey and search work made on a scale 1/25000 or smaller, geological observation objects are transferred into nature and connected by reading off their positions on topographic maps or aerophotographic maps and plans. For regions with a small quantity of contours and for which renovated maps are not available, the plane coordinates and elevations of geological observation objects are transferred into nature and connected according to the materials of the aerophotogrammetric surveys of the latest years. Objects can be transferred from aerophotographs onto a topographic map by visual, graphical or instrumental methods.
Ch. 14. Mine-Surveying
Control
of Geological
Exploration
map; the directions connecting the central points on the transparent paper sheets are matched with the corresponding line of the topographic map. The intersections of like directions determine the positions of the 2' point being transferred on the map. The accuracy of the position of points Fig. 14.4 Transfer of points from aerial photo. transferred by the method of intersections graphs onto topographic map by intersections can be estimated by reference to Table 14.4. The method of resections consists in that at In the visual method, a point is transferred least four reference points are chosen on an by linear intersections from two or three aerial photograph and a topographic map reference points on a map. In that case, the (for instance, points a, b, c, and d on an aerial lengths of corresponding sections on the photograph and points A, B, C, and D on a aerophotographs and map are compared map). A sheet of transparent paper is laid on the aerial photograph, and directions are visually. The visual method is employed in cases drawn from the point to be transferred (say, when the terrain has distinct contours and x) onto the selected reference points a, b, c, only slightly dissected relief. Experience has and d. The transparent paper sheet is then shown that, for transferring of points with the laid on the map so that the drawn directions root-mean square error of I mill, the distance x-a, x-b, x-c, and x-d pass through the points from reference points to the given object on A, B, C, and D on the map. After that, the maps should be not more than 5 mill for flat point x is punched from the transparent land, 3 mm for foothills, and I mm for moun- paper onto the map. The instrumental method of point transfer tainous regions. The graphical methods of transfer most is the most accurate and least labour-consuoften employ direct intersections from the ming. central points of aerophotographs and resecGeological observation objects can be tions. connected or transferred into nature from a In the method of direct intersections, the topographic map (aerial photograph) by one central points of aerophotographs are first of the following methods. transferred onto the map by the method of photo triangulation. The points to be transferred onto the topographic basis are read off Table 14.4 and punched on two adjacent aerial photo~ graphs. The central points (431 and 432 in Map scale Accuracy of positions of points, mm, for mean difference of elevations between Fig. 14.4) and points to be transferred (say, points, m points I, 2, 1', and 2' in Fig. 14.4) are punched from each aerial photograph onto 50 150 200 500 transparent paper. Then, the directions onto 15000 1.4 2.0 2.7 5.4 the central points and points to be transfer110000 0.6 1.0 1.4 2.7 6.7 red are drawn on the sheets. Mter that, the 125000 0.3 0.4 0.5 1.8 2J sheets of transparent paper are laid onto the 150000 0.3 0.3 0.3 0.5 1.4 topographic basis and oriented so that the 1100000 0.3 0.3 0.3 0.3 0.7 central point of each sheet is coincident with 1200 000 0.3 0.3 0.3 0.3 0.3 the corresponding point on the topographic ~ I 430
431
' 432
14.4.
Transfer
of Exploratory
1. By reading off a point if this point coincides with a contour point on the map. 2. If the given point is located between two contour points on the map, by measurements on the range line of these points from one of the points to the point to be connected (or transferred). 3. If the point to be determined is visible from contour points, its position can be found by direct intersections. 4. If three typical points are visible from the point to be determined and these points are indicated on the map, the position of that point can be found by resection. The determination of the planimetric coordinates and elevations of geological observation objects on topographic maps (aerial photographs) includes the following steps: (a) contours and orientation marks depicTable 14.5 Pattern of terrain and relief
Workings
Plan into
Nature
333
ted on a topographic map are found on the terrain; measurements are carried out, when needed, on the terrain between the objects being determined and the orientation marks; and the objects are indicated on the map; (b) observation objects are transferred from aerial photographs onto a map; and (c) the planimetric coordinates and elevations of observation objects are read off on a map. Measurements on maps and terrain should be carried out by methods which can determine the plan positions of objects relative to a known contour with a root-mean square error not exceeding 0.2 mm on the map being used. The measurements of planimetric coordinates and elevations on maps are made twice. The errors in elevations of observation
Root-mean square errors (m) of elevations determined by interpolation between marked points (numerators) and between horizontals (denominators) map scale
Flat terrain (inclination angles up to 2°) Flat woody terrain (inclination angles up to 2-4°) Flat densely inhabited terrain (inclination angles up to 2°) Hilly rugged (open) terrain with prevailing inclination angles up to 6° Hilly rugged (closed) terrain with prevailing inclination angles up to 6° Foothill and mountainous terrain with prevailing inclination angles up to 15° High-mountainous terrain
0.4-0.8
0.8-1.6
1.2
2.5
5.0
11.0
0.5-0.8
0.8-1.6
1.5
3.0
6.0
12.0
0.4-0.8
0.9-1.6
1.5
3.5
7.0
14.0
0.6-1.0
1.2-2.0
2.5
5.0
10.0
20.0
1.0
1.8-2.2 4.0 8.5 17.0 Error not more than 1.5 of contour interval
33.0
10.0 20.0 Error not more than 2.0-2.5 of contour interval
40.0
334
Ch. 14. Mine-Surveying
Control of Geological Exploration
objects on topographic maps should correspond to the data given in Table 14.5. The determination of the planimetric coordinates and elevations of geological objects on topographic maps should be made with a check of at least 20 per cent of the points being measured.
of the oriented directions from the rotor centre in order to establish deviations and (b) the layout and fixation on the ground of the design direction of boreholes and the determination of the plan position of faces.
14.4.2.
The layout of open exploratory workings (ditches, trenches, etc.) consists in transferring the design position of an axis and side crests of a working into nature. The layout procedure is started by transferring the ends of the axis onto the ground, which can be done by various methods or their combinations depending on the conditions of measurements and the provision of a geodetic basis. These methods have been discussed earlier. On a closed (woody or hilly) terrain it is however more preferable to use the method of a design theodolite traverse. In the plan shown in Fig. 14.5, points K and N are the ends of the design axis of a ditch and A and B are the points of a geodetic basis. In order to transfer the points K and N onto the ground by the method of a design theodolite traverse, it is essential to know angles /3B and /3K and horizontal distances BK = SBK and KN = SKN which can be obtained by solving inverse geodetic problems by the formulae:
Transfer of Geological Observation Objects from Reference Net into Nature
In the geological search and exploration work made on a scale 1/10000 or larger, exploratory workings and geological observation objects are transferred into nature and connected by instrumental methods to the points of a national geodetic net, densification nets, surveying nets, or reference nets. If workings are located at distances not more than 300 m from a reference net, their positions can be determined by a polar method (by a theodolite 01 a plane table), the distances being measured by a range finder. The positions of points near profile lines can be determined by the method of perpendiculars with the distances measured by measuring tapes or range finders. The positions of fixed boreholes and mining workings can be determined by analytical methods relative to the points of a national geodetic net, densification nets, surveying nets or base lines. The work for the connection of geological observation objects includes: (a) the compilation of a connection scheme; (b) measurements for determining the planimetric coordinates and elevations of geological observation objects; and (c) the compilation of the list of planimetric coordinates and elevations of geological observation objects. With directional drilling of boreholes, the following additional operations are made: (a) the layout and fixation on the ground
14.5.
tanaBK
Layout Ditches
=
of
YK -YB
Exploratory
,
XK -xB SBK
---
YK-YB sin
XK-XB IlBK YN
COS IlBK -YK
tanaKN XN
SKN=
YN-YK .= smaKN
13B= aBA -aBK'
XK
XN-XK cosaKN 13K = aKB -aKN
where x K' Y K' X N' and Y N are the coordinates of the points K and N determined graphically
14.5. Layout of Exploratory Ditches
335
(a)
v ~ ~o ~o
0
..inewood
0( 7 PK
v
14.5
Layout
of exploratory
6
v
0
Fig.
. :
v
VI
ditch
on the plan; x B' y B are the coordinates of the point E taken from the list of calculated coordinates of the points of a geodetic net; and aBA is the initial direction angle taken from the list of the calculated coordinates of the points of a geodetic net. A theodolite is set up in the point E and the junction angle 13Bis constructed from a direction EA at two different positions of a circle, after which the length of a line SBK is
laid off in that direction, and the point K thus obtained is fixed. The angle ~K is constructed in the point K relative to a direction KN, the design length SKN of a ditch is laid off, and the point N is fixed. The upper crests of a ditch are laid out by using a number of profiles which are plotted on millimetre-squared paper on a large scale (say, 11200).The width 1 of the ditch bottom
Ch. 14. Mine-Surveying
Control of Geological Exploration
(Fig. 14.5,where it is shown by a dotted line), the depth h, and the inclination angle of ditch sides are taken from the design and the elevations of the points of the Earth's surface, from the plan. In the case considered, three profiles are plotted: a longitudinal profile along the axis KN (Fig. 14.5b) and two transverse profiles through the points K and N (Fig. 14.5c). The construction of profiles gives the points of intersection of ditch crests with the Earth's surface (1, 2, 3, 4, 5, and 6). Inclined distances K-l, K-2, N-3, and N-4 are then found on transverse profiles and K-6 and N-5, on a longitudinal profile. These distances are laid off on the ground from the points K and N; the former four perpendicularly to the ditch axis and the latter two, along the axis. The points 1, 2, 3, 4, 5, and 6 are fixed on the ground. The angles of the upper crests of the ditch (points 7, 8, 9 and 10 in Fig. 14.5) are obtained at the intersections to the continued lines 1-4 and 2-3 and perpendiculars raised to the ditch axis in the points 5 and 6. If the terrain is flat, cross-sectional profiles are not constructed, and the distance from the ditch axis to its crest is determined by the formula: N-4 = N-3 = 112+ d where d is calculated by the formula: d = hltan..
Geodetic Control of Geophysical Prospecting Methods
14.6.1 .General Data on Geophysical Prospecting Methods Geophysical prospecting includes the methods of the investigation of the Earth's crust, search and prospecting for minerals, and engineering geological studies which are based on the analysis of various physical
fields, either existing in nature or formed artificially. Any kind of these fields can be characterized by its specific parameters. For instance, a gravitational field can be represented by the acceleration due to gravity or second derivatives of the gravity force potential; a magnetic field is characterized by the total intensity vector and its components (vertical, horizontal, etc); an electromagnetic field is characterized by the vectors of magnetic and electric components; an elastic field is described by the time of the propagation of various elastic waves; etc. The principal possibility of geophysical methods of prospecting with the use of various physical fields is based on the fact that the distribution of field parameters on the Earth's surface, underground, in air, outer space, and in the Ocean is determined by the general structure of the Earth and the near space, variations in the physical properties of rocks, and the dimensions and bedding depths of geological objects. Geophysics has to solve two types of problems: a direct problem and an inverse one. Since the parameters of physical fields depend uniquely on the properties and dimensions of the geological objects being prospected, the parameters of a field can be uniquely determined when one knows the properties and dimensions of geological objects. This is the direct problem to be solved in geophysics. The inverse problem consists in determining the dimensions, bedding depth and other characteristics of geological objects by the measured parameters of a physical field, which, as a rule, cannot be determined uniquely. The inverse problem can be solved uniquely by studying a complex of fields. Geophysical prospecting methods can be employed in outer space, on the Earth's surface, in seas,and underground. According to the problems and objects of investigation, geophysical prospecting can be divided into regional, structural, prospecting for ores,
14.6. Geodetic Control of Geophysical Prospecting
petroleum and gas, and engineering geophysics. Among the various methods used for geophysical prospecting, the gravitational, magnetometric, electric, seismic, nuclear and geothermal methods are more popular. 14.6.2.
Principles of Gravitational Prospecting
Gravitational prospecting is based on measuring the acceleration due to gravity and its variations (gradients) in different directions. The parameters of the field of gravity force depend, on the one hand; on some factors associated with the shape and rotation of the Earth (normal field) and, on the other, on the density variations of rocks in the lithosphere (anomalous field). The gravitational (normal) field of the Earth is the field of the gravity force which is the resultant of two forces: the force of attraction of the Earth and the centrifugal force caused by the rotation of the Earth on its axis. The force of gravity can be measured in terms of the acceleration 9 acquired by a freely falling body. In gravitational prospecting, the unit of acceleration is 1 cm s- 2 which is called the gal. Gravitational prospecting is based on measuring the anomalies of the gravity force, i. e. its deviations from normal values. The normal field of the gravity force can be analysed by the formula: Yo =Ye(l-
~sinB-
where ~ = (Yp-Ye)/Y,
~lsin22B)
~1 = (1/8)a2 + (1/4)a~
a is the contraction of the Earth's ellipsoid; B is the geodetic latitude; Yp is the normal gravity field at a pole; and Ye is the normal gravity field at the equator. Thus, the anomaly of the gravity force is essentially the difference between the gravity force observed and its theoretical value which can be calculated by one of the formulae for 22-1270
337
the normal gravity force with the introduction of corrections (reductions). In gravitational prospecting, the most popular formula for describing the inhomogeneous density of the Earth's crust is based on Bouguer's anomaly (Bouguer's effect): AgB = gm -'Yo + Agl + Ag2 + Ag3 where gm is the measured gravity force; Agl is the correction for altitude which reduces the measured value to the sea level (Faye's correction), A 9 1 = 0.308 H (H is the altitude above sea level, m; Ag2 is the correction for the attraction of an intermediate layer, which is equal to the attraction of the masses located between the sea level and a real surface, Ag2 = 0.0419 o-H (0- is the mean density of rocks in that layer and H is the altitude of an observation point); and A g3 is the correction for relief. The relief correction takes into account the deviations of the physical surface of the Earth from the horizontal plane passing through the given point. For calculating the relief correction, the portion of the Earth's surface around the point of observation is divided in a particular manner into a number of areas so as to approximate the relief by simple geometric bodies whose gravitational effects can be determined analytically. The correction for the surrounding relief is calculated for particular annular zones arranged concentrically around a gravimetric point. Since the shape of the relief in each zone may be variable, these zones are divided further into curvilinear prisms. The actual (physical) surface of the Earth within each prism is replaced by a horizontal plane whose altitude is equal to the mean altitude of the prism relative to the observation point. The effect of the terrain on the topographic correction decreases proportionally with an increase in the distance from the observation point, because of which the entire region for which the correction is taken into account is divided into three zones: the closer (up to
338
Ch. 14. Mine-Surveying
Control of Geological Exploration
200 m), the mid (from 200 m to 2000 m), and the farther (from 2000 to 13000 m). The highest effect is produced by the relief elements in the closer zone. In some cases,a central zone of a radius of 10-50 m is separated in the closer zone. In high-precision gravimetric surveys, the relief corrections in the mid and closer zone are determined by instrumental methods.
sections composed of horizontally bedded or gently dipping structures; and (3) underground electric prospecting used for the detection of geoelectric inhomogeneities between the boreholes or underground workings and the Earth's surface. Electric prospecting deals with the following kinds of field: I. Local natural electric fields, including those of electrochemical and electrokinetic origin. Electrochemical fields can be caused 14.6.3. Electric Prospecting by oxidation-reduction reactions at boundaThe electric methods of geological prospec- ries between the electronic conductors (ore or ting are based on studying natural and mineral bodies) and ionic ones (underground artificial electromagnetic fields in the Earth's water surrounding an ore body). Electrocrust. Natural fields may be either permanent kinetic fields exist due to the filtration of or variable in time. The former are conven- underground waters through porous rocks and the associated processesof diffusion and tionally called electric fields and the latter, adsorption of ions on solid particles. electromagnetic. In electric prospecting, both normal and 2. Regional natural electromagnetic fields anomalous fields are studied. Normal fields (called magneto-telluric fields) which appear are those which exist above a semispace in the Earth's crust in the regions of an appreciable area. Their origin is attributed to having homogeneous electromagnetic properties. An anomalous field may appear due the influence of flows of charged particles to an inhomogeneous structure of the geo- emitted by the Sun on the ionosphere of the electric section of an area being prospected, Earth, and therefore, they depend on the i. e. of the combination of geological bodies solar activity. and seams, each of which has particular 3: Artificial permanent electric fields prodimensions and specific electromagnetic duced in the Earth by means of earthed cables connected to a d. c. voltage source. parameters. In electric prospecting, the measured field 4. Artificial variable harmonic electromagparameters are the amplitudes and phase netic fields formed by various electric genshifts of the intensities of electric and mag- erators producing a voltage that varies harnetic fiel~. The principal electric properties monically in time. (parameters) of rocks are the specific electric With the use of an alternating current, a resistance, dielectric constant, magnetic per- field can be excited by an inductive (contactmeability, electrochemical activity, and po- less) method. For this, a loop of a number of wire coils, usually of a square shape with the larizability. Depending on the problems to be solved, size from 10 m to 1000 m, is laid on the all methods of electric prospecting can be Earth's surface and connected to an a. c. divided into three groups: (I) profiling, which generator. 5. Transient electric and electromagnetic is used for the examination of inhomogeneous geoelectric sections represented by fields excited by quick switching of rectanclosely folded strata and electromagnetically gular d. c. pulses into the feed line. In any method of electric prospecting, the inhomogeneous inclusions; (2) probing, which is employed for the investigation of set of instruments contains electric generators
14.6.
Geodetic
Control
of Geophysical
and other supply sources, measuring and recording instruments, earthing electrodes or non-earthed contours for the galvanic or inductive field excitation, earthing electrodes and antenna rods for measuring the electric field components or frames and loops for measuring the magnetic components, and auxiliary equipment. 14.6.4. Seismic Prospecting Seismic prospecting for minerals is a geophysical method based on studying the propagation of elastic waves excited by explosions or other sources. Since rocks have different density and are characterized by different velocities of the propagation of elastic waves in them, reflected and refracted waves can appear at the boundaries between the rock strata and, besides, elastic waves of a different kind can form in inhomogeneous media. The records of these waves provide information on the structure of the region being studied. Seismic prospecting is based on the analysis of the kinematics and dynamics of waves. The seismic.methods of prospecting consist essentially in the excitation of elastic waves and detection of the induced soil oscillations which are transformed into electric pulses; these pulses are amplified and recorded on seismograms and magnetograms. These are processed in order to separate various kinds of seismic waves and determine the time of their propagation to a point with the known coordinates. Quantitative interpretation of the results of seismic prospecting gives the velocities of wave propagation, variations of their propagation along the depth and over an area, bedding depths of seismogeological boundaries, their dipping, extension, etc. Using additional geological characteristics, it is often possible to establish the geological nature of detected boundaries of geological bodies, i. e. to construct a seismogeological section. 22.
Prospecting
339
The principal methods of seismic prospecting are as follows: reflected wave method; refracted wave method, sometimes called refracted wave correlation method; transmitted wave method; method of common reflection point; method of vertical seismic profiling; etc. In practice, the reflected wave method is used most often, in particular for the dissection of sedimentary beds. It is the leading method for structural investigations and prospecting for petroleum, gas, and other minerals. The refracted wave method can provide information on the elastic wave velocities and the depth of beds composed of rocks with high elastic moduli and on the bedding depths of these rocks. The transmitted wave method is employed for detecting various inhomogeneities in rock beds. 14.6.5.
Magnetic
Prospecting
Magnetic prospecting is a geophysical method based on studying the spatial distribution of variations of the geomagnetic field which can appear due to different magnetization of rocks. The principal methods of magnetic prospecting are the aeromagnetic, hydromagnetic and ground magnetic surveys, underground and borehole observations, and the measurements of the magnetic properties of rock specimens. In any point on the Earth's surface, there exists a magnetic field which can be described by the total magnetic intensity vector T or its vertical (2) and horizontal (H) components. As a first approximation, the magnetic field of the Earth can be likened to the field of a uniformly magnetized sphere or dipole (To). In addition to this unifQrm field of the magnetized sphere, however, the magnetic field of the Earth also has the components of anomalous geomagnetic fields which are associated with continental (TJ, regional (T2), and local (T3) anomalies. In the practice of
340
Ch. 14. Mine-Surveying
Control of Geological Exploration
magnetic prospecting, the normal magnetic field is usually taken as the field of a uniformly magnetized sphere (To) plus the continental anomaly (TJ. The normal geomagnetic field can be characterized by a normal gradient, i. e. a change in field intensity per kilometre. The deviations of the observed values of magnetic vectors from the normal field are regional or local anomalies depending on the area of their appearance. In magnetic prospecting, the measurements of the magnetic field may be either absolute or relative. In ground magnetic prospecting, however, relative vertical components of the geomagnetic field, A Z, are measured most often and, less frequently, relative values of the total vector, A 1;' i. e. increments of these characteristics relative to an initial (reference) point. Ground magnetic surveys can be done on scales from 1/50000 to 1/2000 and larger. With scales 1/50000, 1/25000 and 1/10000, geological magnetic surveys are carried out for mapping the territory being studied, as well as directly for searching iron-containing ores. Magnetic surveys on scales 1/10000, 1/5000 and 1/2000 are fulfilled for more detailed analysis of magnetic anomalies, detection of ore bodies and tectonic distortions, and for the estimation of the dimensions, shape and location of ore bodies. Ground magnetic surveys are carried out, as a rule,. on areas which are recognized prospective by the results of aeromagnetic surveys. Observation profiles are assigned across the strike of anomalies on aeromagnetic maps. Spacings between the profiles depend on the scale of surveys and can range from 500 m (1/50000) to 50 m (1/5000). Distances between the observation points on profiles should be 50-60 per cent smaller than the profile spacings. The connection of observation points can be done by instrumental (in prospecting work) or semi-instrumental methods. In the
latter case, however, the starts and ends of profiles and the centres of anomalies are connected instrumentally. 14.7.
Mine-Surveying in Geophysical
Work Prospecting
The principal object of the mine-surveying work in geophysical prospecting is to layout the set-up points for instruments and to determine their planimetric and height coordinates. A particular method of geodetic control in geophysical surveys is chosen mainly depending on the scale of geophysical work, provision of the geodetic basis, and physico-geographic conditions in the prospected region. The elevations and plan coordinates of points for geophysical measurements can be determined easily and efficiently by reference to topographic maps. If reliable maps are unavailable, the plan positions of points in regional geophysical surveys can be determined on aerial photographs. The elevations of these points are usually determined by barometric levelling. In geophysical field surveys on scales 1/50000 to 1/10000, point coordinates are most often determined by running main traverses (base lines) and laying out profiles between them. Theodolite traverses and level lines are then run along base lines and sometimes along profile lines. The topographic and geodetic control of geophysical prospecting includes the following steps: (a) the design positions of prospecting profiles or individual observation points are transferred into nature and fixed on the ground; in gravimetric and magnetometric prospecting, all observation points should be transferred into nature, and in seismic and electric prospecting, this involves all centres of excitation and reception of signals; the positions of profiles and individual points should be transferred onto the ground with
14.7. Mine-Surveying
Work in Geophysical Prospecting
the accuracy of planimetric connection; (b) observation points located on profiles and beyond them are connected, i. e. their plan coordinates and elevations are determined; this should be done for all points of geodetic observations; (c) the topographic basis for geophysical maps is formed; and (d) height differences around the gravimetric points are determined in order to take into account the effect of a terrain relief on the measured values of a gravity force. In aerogeophysical prospecting, the plan connection of aerogeophysical routes is usually done by aerial photogrammetry. 14.7.1.
Mine-Surveying in Gravitational
Work Prospecting
The mine-surveying work in gravitational prospecting consists of the following operations: (a) the transfer of the design position of reference and ordinary gravimetric points into nature (laying-out of base lines, profiles, etc.); (b) fixation of the points by suitable marks;
341
(c) determination of the plan and elevation coordinates of observation points; (d) determination of relative height differencesaround observation points in order to take into account the effect of a terrain relief; (e) provision of the geodetic basis for gravimetric maps; and (f) the technical control and estimation of the accuracy of the work performed. The planimetric connection of gravimetric prospecting points can be carried out by using topographic maps on scales corresponding to or larger than the scale of a gravimetric survey, aerophotogrammetric materials, instrumental geodetic methods, autometric topoconnectors, etc. For determining the elevations of gravimetric points, it is possible to use topographic maps on scales which ensure the required accuracy; geometric and trigonometric levelling; barometric levelling; materials of stereophotogrammetric surveys; and hydrostatic levelling. The permissible errors for determining the positions of the points of gravimetric observations are given in Table 14.6. In cases when the surface of observations
Table 14.6 Scale of gravimetric map
Interval, milligal
Root-mean square erros (m) of point position relal initial points
in elevation
in plan flat terrain
'1000000 '200000 '100000 150000
0.5 0.25
1/25000
0.25 0.20 0.20 0.10 0.05
mountainous terrain
1.0 0.50 0.50 0.25 0.50 0.20 0.10
flat terrain
::t200 ::t100 ::t80 ::t40 ::t40 ::t20 ::t20 ::t4 ::t4 ::t2
mountainous terrain
flat
terrain
mountainous terrain
:!: 5.0 :t 100
:!: 2.5
:t 100
:!: 1.2
:t 50
:!: 0.70
:t 50
:!: 0.35
:t 25
:!: 0.35
:t 25
:!: 0.25
:t5
:!: 0.20
:t5
:!: 0.10
:t2
:!: 0.05
:I: 3.0 :I: 1.8 :I: 1.6 :I: 0.9 :I: 0.9 :I: 0.45 :I: 0.25
:to.1
~
Ch. 14. Mine-Surveying
Control of Geological Exploration
cartographic materials of an appropriate accuracy, which are not always available, especially for what is called the closer zone, i. e. the portion of the Earth's surface in the direct vicinity of a gravimetric point. In such cases, levelling of the surrounding terrain is carried out along radial rays (eight or sixteen). The radial distances from a gravimetric point to staffing points are usually taken equal to 1.2 m, 2 m, 6 m, 15 m, 35 m, 75 m or 150 m. 14.7.2. ~
"Z
Mine-Surveying Work in Electric Prospecting
The mine-surveying work in all kinds of electric prospecting is carried out mainly for the preparation and connection of obser~ vation points and detected anomalies on the Fig. 14.6 Terrain relief representedas combinaterrain and for laying-out and surveying of tion of elementaryseparations base lines and profiles. The principal requirements to the accudiffers substantially from a planar one deterracy of the mine-surveying work in electric mining the relief corrections which are introduced into the observed values of the gravity prospecting are given in Table 14.7. The mine-surveying work in various kinds force has certain specifics. With either positive or negative relief, the gravity force of electric prospecting has certain specifics. decreases, because of which the relief correction is always introduced with a positive sign. Corrections for the surrounding relief are calculated for individual annular concentric zones around a gravimetric point. Since the terrain relief in an annular zone may be variable, these zones are further subdivided into curvilinear prisms which are called elementary separations (Fig. 14.6). The real surface of each elementary separation is replaced by a horizontal plane whose elevation is equal to the mean elevation of the elementary separation relative to an observation point. The correction for the surrounding relief can be determined directly on a topographic map or by instrumental measurements. B For determining the relief corrections with the required accuracy, it is essential to have Fig. 14.7 Electric prospecting by probing --(
14.7. Mine-Surveying
Work in Geophysical Prospecting
343
Table 14.7 Method of electric prospecting
Map scale
Root-mean square errors of point position relative to initial points in
flat terrain
Natural field, induced polarization, transient, electroprofiling, isolines, etc.
Telluric currents, magnetotelluric profiling, and magnetotelluric probing Vertical electroprobing; dipole probing, partial electromagnetic probing Formation of electromagnetic field
in elevation
plan
mountainous terrain
1/5000
4
5
1/10000
8
10
5
1/25000
20
25
10
1/50000
40
50
1/50000
40
50
1/50
of reference
1/200000
160
200
level
depth,
more
than
5
10 but
not
15 m
Ditto
Ditto
Ditto
Specified
Ditto
Ditto
Ditto
1/50 of reference level depth
For instance, in the method of isolines, linear electrodes are laid on the ground at distances of 500-1500 m from one another and connected by insulated wires to the poles of a current source. The points of the same potential are found on the terrain by means of what is called a search circuit. The minesurveyor's task in this caseis to determine the positions of these points. In regional prospecting, the coordinates of these points are mainly determined by the materials of aerophotogrammetry and in detailed work, by instrumental methods. In induction, natural direct current and the like methods, the points for setting up instruments in regional prospecting are determined by reference to aerophotogrammetric materials and topographic maps and in detailed work, by measurements on a preliminarily laid-out square or rectangular network. In electric prospecting by probing methods, the object of mine-surveying is to determine the plan and elevation coordinates of a record point Q, which is required for the construction of a geoelectric section, the length of a feeding dipole AB, the area of a
receiving loop q, an active distance 001 and an angle 6 (Fig. 14.7). The length of the feeding dipole can be calculated by the coordinates of the feeding dipole AB centre 0 and the centre of a receiving circuit 01. The connection of points A, B, 0, and 01 is usually done by means of topographic maps or aerophotogrammetric materials. 14.7.3.
Mine-Surveying Work in Seismic Prospecting
In seismic prospecting by the reflected wave method, seismic profiles are laid out on the ground and connected in plan and vertically by instrumental methods. In the refracted wave correlation method, seismic profiles are connected instrumentally, and the explosion points located beyond the profiles are connected in plan. In seismic logging, it is required to determine the distances between the logged and explosion boreholes, height differences between them, and the direction angle from the logged boreholes onto explosion points. In spatial mass probing, the plan and elevation positions of probes and explo-
344
Ch. 14. Mine-Surveying
Control of Geological Exploration
Table 14.8
Table 14.9
in
plan
in elevation
Scale of magnetic Root-mean square Relative error of surveying error of connection measured distance of initial point of between profile profile or base line points relative to initial points
1/50000 1/25000 1/10000 1/5000 1/2000 1/1000
sion points are determined, and the figure for the arrangement of seismographs is constructed. The accuracy requirements for the minesurveying work in seismic prospecting are given in Table 14.8. In seismic prospecting in seas at a small distance from the coast, observation points can be connected by means of a reflecting circle (index) by the method of resections onto the initial points on the coast. In such cases, profiles are ranged out by poles or buoys set up at intervals not more than 2-3 km in detailed surveys or 5-6 km in regional surveys. In cases when the seismic work is being carried out far from the coastal line, observation points are connected mainly by radiogeodetic methods. 14.7.4.
Mine-Surveying Work in Magnetic Prospecting
In ground magnetic surveys, the minesurveying work includes the transfer of the contours of a survey area, layout, connection and fixation of observation points, and the connection and fixation of detected anomalous zones, structures, etc. In ground magnetic prospecting, the methods of the preparation of observation points can be divided into three main types:
15 15 8
1/100 of interval between points on profile
8
(a) profile methods with a preliminarily laid-out observation network; (b) profile methods with the simultaneous semi-instrumental layout of an observation network; and (c) route methods with the observation points being read off from a topographic map or aerophotogram. In magnetic prospecting with a preliminarily laid-out observation network, the accuracy of the mine-surveying work should be as given in Table 14.9. Profile methods with the simultaneous semi-instrumental layout of an observation network are usually employed in the search work on a scale of 1/50000, 1/25000 or 1/10000 in woody territories; in that case, survey profiles can be ranged out by a magnetic azimuth, and distances along a profile can be measured by striding. Magnetic surveys are carried out, as a rule, along roads, forest cuttings, footpaths, rivers, etc., and the surveying net is connected visually to the orientation marks which are present both on the ground and on the map. The errors of the planimetric positions of points on a survey line should not exceed 1/4 of the spacing between the points, but not more than 250 m in any case.
14.8.
14.8.
Barometric
Levelling
Barometric Levelling of Geological Observation Objects
Table 14.10
:I: 0.35 :I: 0.5 :I: 1.0 :I: 2.5 :I: 5.0
Objects
345
Table 14.11
Barometric levelling has found rather wide use for the elevation control of geological surveys. It is mainly resorted to in caseswhen other levelling methods are insufficiently accurate or less efficient economically. The method is especially popular in gravitational prospecting. An essential advantage of barometric levelling is that it is applicable even when the points to be levelled are mutually invisible. The accuracy of barometric levelling depends on the instruments employed, kind of a terrain relief, and the techniques of levelling. Barometric levelling is based on a certain correlation between the elevation of a terrain and atmospheric pressure. As has been demonstrated by the practice of levelling, with properly organized work it is possible to measure elevations with an error less than 0.5 m. Depending on the accuracy of measurement of the elevations of geological observation points, the recommended accuracy in the measurements of atmospheric pressure is given in Table 14.10. Barometric levelling in geophysical surveys can be carried out by various methods, the choice of a particular method being dependent on the scope of work, available instruments, number of observations, and required
Root-mean square error of measured heights, m
of Observation
Time intervals between measurements of pressure and temperature of atmospheric air at barometric stations, min
Root-mean square error of measured heights, m
in flatland regions 0.35
10
0.5
10
1.0
15
2.5
20
5.0
30
at barometric
::!: 0.015
:t 0.010
::!: 0.020
:t 0.015
::!:0.05 ::!: 0.15
:t 0.03 :t 0.05
::!: 0.30
:t 0.10
mountain-
ous
regions
10 10 10 15 20
accuracy. In all methods, however, the measurements of air temperature at particular points and initial barometric stations are done at the same time with measuring the atmospheric pressure. Barometric stations should be located on open places with smooth shapes of the relief. It is not advisable to locate stations on sharp summits, in deep and narrow valleys, on the crests of cliffs, and (in summer time) near large water basins. Instruments for atmospheric pressure measurements should be placed at baromet-
Table 14.12 Root-mean Mean distance square error of observed of height dif- points from ference, m TBS *, kIn
Mean height difference of observed points relative to TBS *, m
without cor- with correction for sys- rection tematic error of air temperature measurement
Root-mean square error of measured atmospheric pressure, mb
at observation -~:-,.
in
0.4:> 0.70 0.90 2.0 .TBS
L.-() 2-9 2-13 10-25
-temporary
barometric
)U-IU 80-20 110-10 210-30 station.
14U-4j 245-55 320-45 680-180
346
Ch. 14. Mine-Surveying
Control of Geological Exploration
Table 14.13 Time of traverse run, h
Root-mean square error of height difference, m
0.25
Mean length of tra. verse, km
1.0 2.0 4.0 1.0 2.0 4.0 1.0 2.0 4.0 1.0 2.0 4.0 6.0 8.0 2.0 4.0 6.0 8.0
0.45
0.70
0.90
2.0
Mean height difference of observed points relative to TBS, m without correction for systematic error of air temperature measurement
with correction
2.7
20-5
70-25
2.6
20-5
70-10
2-4
20-5
60-5
5-15
50-10
140-25
5-14
40-10
130-20
5-9
40-5
120-10
5-40
85-35
240-70
5-25
85-35
240-90
5-15 5-50
75-10 110-50
235-65 320-130
5-40
110-10
320-40
5-20
100-25
310-40
5-13
100-10
290-50
5-12
95-5
10-50
240-200
700-550
10-30
240-200
700-540
10-15
230-210
700-590
10-15
220-200
700-570
280-5
Table 14.14
Table 14.15
Root-mean Mean distMean height difference of square error ance between points relative to RBS * in of height dif- RBS *, km calculation, m ference, m
Root-mean square error of measured heights of points,
up to I
Permissible fInS error of comparison of mercury barometers at reference stations, mb
0.03
without cor- with correcrection for systion tematic error of air temperature measurement 1.2 2.0 3.5
50 50-130 150
* RBS -reference
barometric
180-50 250
station.
90 500-135 700
up 2.5
above 2.5
0.07
0.10
to
14.8.
Barometric
Levelling
of Observation
B
A
347
Objects
><
~
~
~
~
~
~
~
00 ,..; ;0 -
""' ai Ir) -
.,; O N
00 ~ +
V) ~ ""'
~ r-i -0 +
"' r-
11-
:=:
~
N tO -
<=!
N ...;
"' -
b
Fig. 14.8 Calculation of elevation of observed point by method with severalbarometricreference stations ric stations permanently for the entire period of station operation. Air temperatures are measured at barometric stations and measuring points by means of aspiration (sling) thermometers set up at a height roughly 2 m above the Earth's surface, with an accuracy to 0.5 degree C. Time intervals between the measurements at barometric stations and points depend on the error in elevation measurements at the points and can be determined according to Table 14.11. Barometric levelling can be carried out by one of the following methods. Barometric levelling by the methods of level lines can be performed with reference to one initial point.(closed level lines) or to two points (open lines). A temporary barometric station is arranged at the initial point of a closed level line. With an open level line, one temporary station is placed at the initial point and another, in any point of the line. In the method of closed level lines, it is possible to work with one or two barometers. Barometric levelling by the method of closed level lines should"be done according to the requirements given in Table 14.12. Barometric levelling by the method of open level lines is carried out with the use of two sets of barometers. In this method, the deviations of observed points from the range
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348
Ch. 14. Mine-Surveying
Control of Geological Exploration
line of initial points should be not more than 0.2 of the distance between these points. The principal requirements to the field work by this method are given in Table 14.13. In barometric levelling by the method with several barometric reference stations, these stations are located so that all points of observation can be inside the figure formed by the stations (in most casesa triangle). In a particular case, barometric reference stations can be located on the range line. The permissible distances between the barometric reference stations should be as recommended in Table 14.14. In this method, it is possible to use meteorological stations or special temporary reference stations. All barometers used at the stations are standardized by determining their corrections relative to one of them which is taken as the standard instrument. The standardization of barometers should be carried out with an accuracy as specified in Table 14.15. The elevations of observed points are determined by the results of the measurements of air temperature and pressure at these points, which are done at the same time with air temperature and pressure measurements at the stations. The point elevations are calculated as weighted mean values, by considering the following circumstances. Let an observed point O be inside a reference .triangle ARC (Fig. 14.8). The elevation of the point O can be calculated by the formula: H = H~k1 + H~k2 + H~k3
where H~, H~, and H~ are the preliminary elevations of the point observed and k1, k2, and k3 are the weight coefficients which depend on the position of the point and can be found by the formulae: k1 = 11/Ll, k2 = 12/L2, k3 = 13/L3 where 11= Oa, 12= Ob, 13= Oc, L1 = Aa, L2 = Bb, and L3 = Cc. The elevation of the observed point is calculated by a scheme given in Table 14.16. The elevations, H, of reference stations are recorded in column 4. The distances, I, from the observed point to the side connecting two other barometric stations are written as numerators in column 5 and the distances, L, from a barometric station to the same side through the point being observed, as denominators in the same column. Columns 7, 8, 9, and 10 contain data from the field books. The difference in atmospheric pressure, l\P , between the barometric station and the point observed is calculated in column 11. Column 12 contains the values of barometric stages. The values given in columns 11 and 12 are then multiplied to give the height difference between the barometric station and the point observed (column 13). The preliminary values of elevations found by algebraic summation of the elevations of barometric stations and elevation differences are written in column 14. Finally, column 15 gives the elevation of the 'point observed, which is obtained by summing the products of preliminary elevations and the c9rresponding coefficients.
Chapter
Mine-Surveying in Water
15.1.
Fifteen
Work for Mineral Extraction Areas of Seas and Oceans
General
One of the novel trends in mining industry is the exploitation of mineral resources of the Ocean bottom. Our knowledge of the Ocean is still insufficient for large-scale mining of its minerals, but it can be already stated quite definitely that the mineral reserves in the shelf and deep-sea zones of the Ocean are enormous and can be estimated approximately by the following figures: 4 x 1015t of aluminium, 100 x 109t of cobalt, 300 x 109t of nickel, 350 x 109t of copper, 42 x 109t of manganese,120 x 106t of zirconium, 80 x 106t of molybdenum, etc. In addition, almost all elements of the Periodic Table are present in the Ocean in the dissolved state. The sea medium has certain specific features which can influence the organization and accuracy of the mine-surveying work. The principal among them is the dynamics of water masses.The level surface of the Ocean is subject to periodic, non-periodic and secular variations. Periodic variations mainly include tidal oscillations. Non-periodic variations may be of geodyllamic or geothermal origin, i. e. they may be caused by earthquakes, underwater volcanic eruptions, tectonic disturbances in the Earth's crust, water surges, occasional sharp changes of atmospheric precipitation, changes of atmospheric pressure, etc. For estimating the dynamic conditions of the level surface of the Ocean, of prime importance are the tidal phenomena which may depend substantially on the geographic latitude, depth of sea, and the shape of a coastal line. The highest water level at
tides is called high water, the lowest level at ebbs is low water, and the medium level is what is called mean water. In open sea, the tidal variations of the water level are equal to roughly 1 m; near coasts, especially at the head of narrow bays, the difference between high and low water may attain a few tens of metres. The surface of seas and oceans to a depth up to 60 m can be disturbed substantially by winds which often create waves up to 12-13 m high. The effect of wind disturbance is especially detrimental for the accuracy of minesurveying observations, since prospecting and mining work in seasare carried out now and will be done in the nearest future only in the shelf zone where the effect of wind waves is quite strong. Water waves can be characterized by the length, height, velocity, period, front, and steepness. The length A of waves is the horizontal distance between the crests (or troughs) of adjacent waves; height h is the vertical distance from the trough to the crest of a wave; velocity v is the distance covered by a wave crest in unit time; wave period Tis the time interval during which two wave crests pass successivelythrough a given point; wave front is a line perpendicular to the direction of wave motion; and steepnessis the height-to-length ratio of a wave. As a wave approaches the coastal line, its profile changes substantially. The top portion of the wave slope facing the coast becomes steeper, i. e. the wave profile becomes asymmetrical. The asymmetry of waves is notice-
350
Ch. 15. Mine-Surveying
Work
able at depths roughly twice the wave height. At the coast, wave crests tip over and form feathers, or breakers. As the wind velocity decreases,water waves attenuate slowly, the rate of attenuation being proportional to the wave length. The waviness of the sea surface that remains after winds have ceased to blow is called swell, or aftertossing. 15.2. Brief Data on Geomorphology of Ocean Bottom Relief By modern concepts, the ocean bottom has four structural zones (Fig. 15.1). I. The first is the submerged margin I, which includes the shelf la, continental slope Ib, and continental base Ic. The submerged margin is regarded geologically as the flooded portion of the continental plateau which is characterized by relatively calm tectonic conditions and markedly prevailing slow vertical deformations of the surface. The shelf is essentially a shallow-water portion of the submerged margin, which extends from the coastal line to a sharp bend of the bottom surface, usually at a depth of 130-140 m. The part of a shelf to a depth of 30-50 m is called shoal. The continental slope is a relatively steep
in Water
Areas of Oceans
portion of the bottom at the external edge of the shelf. Its width is rather small and usually measures from 15 km to 30 km. Inclination angles are equal to 3-6° on the average, ranging from lO to around 45°. The surface of the continental slope is often furrowed by U-shaped valleys called submarine canyons. Submarine canyons may have a length from a few tens to a few hundreds of kilometres and penetrate to depths of 3-4 km. The continental slope changes to what is called the continental base, a slightly inclined undulating plain at depths of 2-4 km. 2. The transition zone II is an intermediate zone between the submerged margin I of the continent and the ocean bottom (floor) III. This zone has the basin of marginal sea at the side of the continental base and island arcs lIb and deep-sea troughs IIc, at the side of the ocean. The deep-sea troughs form the boundary between the continent and ocean, so that one of their slopes is represented by the continental crust and the other by the oceanic crust. 3. The ocean floor III is represented by the oceanic type of the Earth's crust and lies at depths of 2500-6000 m. It mostly has a hilly relief of the accumulative type with large oceanic troughs and uplifts.
Fig. 15.1 Profile of ocean bottom: l-submerged margin; la-shelf; lb-continental slope; lc-contin~ntal base; ll-transition zone; lla-pits of marginal seas; llb-island arcs; IIc-deep-sea troughs; III -ocean bottolD; lV -mid-ocean ridges
15.4.
Geological
Prospecting
4. Mid-ocean ridges are essentially mountainous formations of a width of 500-2000 kID. A depression, or rift valley, usually runs along the axial line of a ridge. At both sides of the rift valley, there are rift crests with individual summits 7000-8000 m high above the foot of a mid-ocean ridge. Earthquake centres (foci) are confined to rift crests. 15.3.
Characteristics of Some Solid
Minerals
and
Mining
351
of sands and a high concentration of useful components in them (up to 90% of non-native ones). As a rule, band-shaped shelf placers have discontinuities at capes and in river estuaries. Placers in the continental slope are usually located at distances from 500 m to 15 km from the coastal line and have a length of a few tens of kilometres and width, .a few hundreds of metres. The mechanism of transfer of heavier minerals forming a submarine placer is determined by the same processes as the transfer of the mass of sediments forming the bottom topography.
At present, over loo countries are carrying out geological prospecting in the water area of seasand oceans, and enormous reserves of minerals have already been discovered (Fig. 15.2). 15.4. Mine-Surveying Service Submarine deposits of minerals are conof Geological Prospecting ventionally classified by the following groups: and Mining in Water Areas metal-bearing concretions and red clays; primary deposits; and submarine sedimentaIn prospecting for submarine deposits, the ry deposits, mainly shelf placers and mine-surveying service has the following metal-bearing silts. objects: (a) the collection and examination of geoAt present, shelf deposits attract the main detic, hydrographic and meteorological interest, in particular, placer deposits formed due to the dynamic activity of seas and the documents available for a given water area; (b) the provision of the planimetric and chemical processes occurring in sea water. By the time of origin, submarine placers elevation survey control for the coastal part can be classed into buried (concealed), con- of land and alloted water area; (c) the complementary surveys of the bottinental, and young (present-day). Buried placers formed on overlapping of ancient tom relief and prospecting workings; (d) the control of the positions of prosplacer deposits by younger sediments at changes of the sea level and displacement of pecting and mining workings in the water the coastal line. Continental buried deposits area upon their transfer into nature; (e) the compilation of the graphical are formed due to sinking of the coastal documentation of the alloted water area, surface of land below the sea level. All buried submarine placers, as a rule, are not subject which should reflect the bottom relief of a basin, the shape, dimensions and geological to hydrodynamic actions and lithodynamic changes. Present-day placers are more easily characteristics of a deposit, and the characaccessible for exploitation than other types, teristics of enclosing rocks; (f) surveying of underwater workings; since they are not covered by sediments. (g) the calculation of the mineral reserves; Present-day placers mostly have the shape of and bands extended along the coastal line. (h) the analysis of the lithodynamic chanDelta placers have an irregular shape in ges of the bottom relief. plan and variable characteristics. Shelf plaIn the construction of underwater worcers can be characterized by a very thin bed
352 Ch. 15. Mine-Surveying
Work
in Water
Areas of Oceans
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15.5.
Marine
Mine-Surveying
kings and the exploitation of deposits, the tasks of the mine-surveying service are as follows: (a) survey work for the construction of engineering structures in the water area (wharfs, pulp pipelines, hydro-engineering objects, etc.); (b) the development of measures for the protection of structures and environment against harmful effects of underwater workings; (c) the transfer of the geometrical elements of designed structures and objects into nature., (d) the control of assembling of plants, hydro-engineering objects, etc.; (e) the assignment of directions to stripping and preparatory mining workings; (1) servicing and control of the dynamics of stripping and mining work; (g) the complementation of mine-surveying plans, sections and graphical documentation with the results of the surveys of mining workings and waste dumps; (h) the compilation of mining-geometricaf graphs for more accurate determination of the shape of a deposit, quality of a mineral, properties of enclosing rocks, and the distribution of useful components; (i) the control of the variations in lithodynamic processesduring the exploitation of deposits and the prediction of changes in the depth and contours of underwater workings; and 0) the calculation of the dynamics of mineral reserves, output, losses and dilution of minerals. Mine-surveying measurements in the water area should provide data on the dimensions, shape and structure of submarine deposits, which are then represented in graphical documents. The mine-surveying work in water areas consists mainly in profiling of the sea bottom and underwate:r workings.
23-1270
15.5.
Reference
Nets
353
Marine Mine-Surveying Reference Nets
Marine mine-surveying reference nets are developed for making various surveys associated with prospecting and mining of the bottom of seas and oceans (Fig. 15.3). Depending on the distance from the coast, they can be divided into off-shore nets which are formed in the zone of geometric visibility from the coastal line and open-sea nets, i. e. those beyond the geometric visibility. Off-shore surveying nets are developed from geodetic nets on the shore land and
354
Ch. 15. Mine-Surveying
Work
in Water
(c)
Ibl
1a)
Areas of Oceans
12
(d)
(e)
Fig. 15.4 Benchmarks for marine mine-surveyingnets:(a) pole-type;(b) pile-type;(c) wooden frame; (d) metallicframe;(e)buoyant; 1- bottom of seaor basin;2 ~ water line; 3 ~ earth embankment;4- tube or rod; 5- benchmark centre;6- end fastening(plug);7~ concretefilling; 8- instrumentalplatform enclosure; 9-navigation signal; 10-bench mark platform or pontoon; 11-boundary of compacted layer; 12-concrete filling; 13-concrete base; 14-counterweights; 15-buoy rope; 16-anchors; 17-bottom centre those in the open sea, from the points of a polygonometric method is mostly employed marine mine-surveying net, in particular for deposits extended along the coastal line. from a local net connected to the geodetic The root-mean square error of determireference net on the land. nation of the direction angles of sides in Marine mine-surveying nets can be const- marine mine-surveying nets should not exructed by the methods of triangulation, trilaceed I'. For the plan positions of the points of teration and polygonometry. Reference nets a net, the rms error should be not more than for deposits located near the shore can be 0.2 mm on the scale of a plan. constructed by the methods of intersections, The elevation control for the surveying combined intersections or resections. The work in the near-shore water area is provided
15.6.
Special
Mine-Surveying
by levelling points. The absolute elevation marks of survey points on the shore are determined by geometric or trigonometric levelling and of those in the water area, mostly by trigonometric levelling. The rms error in the determination of heights of the points of marine (off-shore) nets relative to initial (control) bench marks should not exceed 0.02 m and the rms error of height difference between two adjacent points, should be not more than 0.05 m. When the water area is covered by firm ice, it is more preferable to use geometric levelling. The points of marine reference nets are fixed by means of special bench marks (beacons) which may be of the pole-type (Fig. l5.4a), pile-type (Fig. l5.4b), with a wooden or metallic frame (Fig. l5.4c and d), or buoyant (Fig. 15.4e) with automatic correction or recording of their deviations from the centre. Marine bench marks should be set up before the beginning of stormy seasons, and each should be provided with a navigation signal. If a marine mine-surveying net is developed on ice, its points can be marked by metal rods qr wooden poles frozen into the ice. Polygonometric traverses should be run so that the mean arithmetic error of the final point of a traverse line of any shape is not higher than the value calculated by the formula:
Work
in Water
Areas
355
nometric traverse; L is the length of the closing line of a traverse; mp is the rms error of angle measurement; n is the number of sides in a traverse; and D is the distance from the centre of gravity of a traverse to each turning point. The best time for observations and measurements is when the temperature of water surface is close to that of air, since this minimizes the effect of refraction on measured results. 15.6.
Special Mine-Surveying Work in Water Areas
In the general case, all kinds of the minesurveying work carried out on submarine deposits can be divided into special and routine. In special mine-surveying work, mine surVeyors together with geologists determine the geological and hydrogeological characteristics of deposits, geomorphological and lithodynamic specifics, hydraulic conditions in the water area, etc. The main object of special work is, however, to analyse the lithodynamic processes responsible for the variability of a given relief and to determine the principal parameters of the deposit and underwater workings. Surveys for mapping of a deposit should be carried out both in the period of detailed prospecting and during exploitation. It is principally important to decide on the frequency of repeated observations which should be such that the variations of relief that may occur between the surveys can be commensurable with the accuracy of surveying. The frequency of observations is usually determined experimentally. Special mine-surveying work also includes the formation and development of planimetric and elevation control (for off-shore and open-sea mine-surveying nets), establishment of level-gauging stations, navigation marks, etc.
356
15.7.
Ch. 15. Mine-Surveying
Work
in Water
Areas of Oceans
Routine Mine-Surveying Work in Water Areas
The main objects of the routine mine-surveying work are to provide the basis and control for geological prospecting and the basis for the mining work. The basis for geological prospecting in water areas is done by preliminary investigations which consist in observations on the hydrologic conditions of the sea and the lithodynamic processesin loose sediments on the bottom. These observations include large-scale surveys of the bottom relief and the determination of the planimetric and height coordinates of prospecting boreholes, contours of ditches and trenches, points of geological sampling, and the corner (final) points of traverses in mine-surveying and geophysical profiling. In the period of underwater mining work, mine-surveying service makes the surveys of underwater workings and represents them on the plans of the mining work and compiles profiles and sections. The results of surveys make it possible to calculate the volumes of extracted rock and determine the places of mineral losses and sources of mineral dilution. The set of mining graphical documentation includes the plans of the submarine mining work on scales 1/1000 or 1/2000, lithological sections along prospecting lines, and the profiles of ~arlier exploring and mining workings in the most typical directions. The contours of a deposit and design boundaries of underwater workings are transferred into nature and marked by means of stakes, beacons or buoys (Fig. 15.5) set up in the sea at intervals of 100-200 m. During prospecting and mining of a deposit, surveys are carried out in order to obtain the plan coordinates and depths of the points of the bottom relief and underwater workings. In practice, these measurements are usually made simultaneously. In the general case, the surveys of planimetric coor-
dinates and depth measurements are planned so as to attain the required accuracy and minimize the number of traverses which may have different directions depending on the pattern of the bottom relief and the purpose of surveying (Fig. 15.6). The survey method with parallel traverses is used most often (Fig. 15.6a). Traverses should be directed in the sense of the highest ruggedness of the bottom relief; for workings, they should be oriented perpendicular to their axis. Depth measurements can be made by zig-zag (Fig. 15.6b and c) or radial traverses (Fig. 15.6d). Zig-zag traverses are used when it is essential to reveal sharp bends of the relief, such as in hollows, valleys, ranges, etc. Radial traverses are run in cases when they can represent a relief without noticeable distortions (which is possible since radial traverses diverge from the coast or control points, i. e. distances between them increase with moving farther into the sea). Radial traverses are used, for instance, for surveying of capes, off-shore bars, islands, and extended and weakly dissected surfaces of the bottom relief. The root-mean square error of locating the bottom relief points in mine surveys should be not more than 1.5 mm on the scale of a
15.7.
Routine
Mine-Surveying
Work
in Water
Areas
(a:
(c)
Id)
,~~ -I
,
\--
~
~ Fig. 15.6 Typical schemes of traversing in bottom relief surveying: (a) with parallel traverses; (b) with zig-zag extension traverses; (c) zig-zag traversing with control extension traverses; (d) radial traversing with additional transverse extension traverses
358
Ch. 15. Mine-Surveying
Work
in Water
Areas of Oceans
base line and the line of sight on a vessel);Dl and D2 are the distances from the base points to a vessel; and mp is the instrumental rms error of angle measurement. The plan position of a moving target is determined by the method of linear intersection with the use of optical or radio range finders and with reference to two or three initial points. Optical range finders are employed in cases when linear intersections are made to relatively shortJ distances (up to 2 km and less frequently, up to 4-5 km). When the objects of marine surveys are removed from the coast to distances more than 3 km, use is made of high-precision radiogeodetic and radionavigation systems which can determine the positions of points in the sea with the rms error around 1 m. 15.9.
where v is the vessel velocity, m/s; D is the distance from an observer to the measured point, m;
mmt =
[
b2
2 .4 p Sill
(
.2 mIl Sill
A + Sill .2 1'1
)
A 1'2
'1
+~)J D~ where b is the length of a base; 'Y is the angle at the measured point; 1:11and 1:12are the angles at the base points (angles between the
Depth
Measurements
The measurements of the depths of bottom points relative to the sea level can be made by sounding poles, sounding leads,echo sounders, photometric and stereophotogrammetric methods. At present, echo sweeps and bottom-scanning sonars (asdics) are being employed widely. A sounding pole is a metal or wooden round pole up to 5 cm in diameter and up to 8 m long, which has 5-cm or 10-cm graduations. Depths can be measured by sounding poles with an accuracy to 2-3 cm. A hand sounding lead consists of a hemp or metal rope with a lead or cast-iron weight around 5 kg in mass tied to its end. The rope is graduated in metres and decimetres by the marks of different colour. Hand leads can measure depths up to 50 m with a relative accuracy of I/lOO to 1/200. A mechanical lead (sounding machine) has a winch with a counting mechanism, rope, and weight up to loo kg in mass. The accuracy of depth measurements by sounding machines depends on the degree of rope sagging which is determined by the size and shape of the weight,
15.9.
Depth
Measurements
359
Fig. 15.7 Operation oflaser-acousticsystemin bottom profiling: Ah3-height of lasersight abovebench mark; R,,-elevation of point (benchmark) in adopteld system;h -depth of measuredpoint on echogram; ho-reading of nth stageof photodetector;hi -readil Ig of laser beam on vertical staff water flow velocity, variations of water velocity along the depth, and the length of a rope. At present, depth measurements are most often made by using echo sounders whose operating principle is based on the propagation of ultrasonic pulses emitted by an ultrasonic source and reception of pulses reflected from the sea bottom. The oscillations of floating vesselsin rough sea reduce substantially the accuracy of depth measurements by echo sounders. This effect is largely eliminated in laser-acoustic systems which have come into use in recent time. A laser-acoustic system (Fig. 15.7) is a combination of a laser and echo sounder and consists of a laser sight 1 with a scanning attachment 2, vertical staff 3 with a photodetector, acoustic system 4, electric pulse generator, amplifier, and a recorder. The laser sight sends a beam 0-01 which defines a reference plane and enters the photo-detector on the staff. The received
pulse is transmitted to a pulse delay generator which fonns a delayed pulse and then sends a starting pulse to the generator. The latter produces an electric pulse to excite the acoustic system which transfonns electric pulses into acoustic signals. Upon reflection from the sea bottom, acoustic signals are transfonned back into electric pulses. These are sent to the recorder which makes a record of the sea bottom depths and the elevation marks of the sea level. The measured values of depths are reduced to a particular level of sea surface which is called the hydrographic datum, or datum level. For seaswith small amplitudes of level oscillations (height of tide up to 0.5 m), the mean water level of many-years observations is taken as the datum level. For seas with substantial level oscillations, the lowest level surface of the sea is taken as the datum level. In surveys in water areas, depths are measured relative to a conventional (phantom) horizon which is called the datum and is
360
Ch. 15. Mine-Surveying
Work
somewhat lower than the horizon of the lowest level. This is done in order that calculated levels may be always positive. A level-gauge station, or simply gauge, is made in the form of a level-measuring pole which is fastened to a pile, wharf or another stationary structure. Level-gauge poles are mostly made of cast iron and have inserted porcelain pieces forming 2-cm graduations. Enamel-painted metal poles are also in use. Depth measurements are also carried out for studying the lithodynamic processes, in particular, the intensity and amount of wash-out (erosion) or, on the contrary, the accumulation of drifted sediments on the bottom and in underwater workings. The thickness of an active layer of sediments is established by measuring the maximum depth in fixed points in the periods of rough sea, which can be done by the method of a 'movable disc' or by successive measurements between the periods of rough sea. The former method is employed at depths up to 3 m and consists essentially in that the disc is let to slide down a metal rod fixed in the bottom, after which the depth of disc sinking is determined on the staff that is connected with the disc and protrudes from water. If the bottom ground is washed out, the disc sinks deeper and this is detected by the changed position of the staff. Staff readings can be done instrumentally from the on-shore or off-shore points of a reference net. . The method of successivemeasurements is not as accurate as the former, but is less laborious. Measurements are carried out strictly on the same profiles, and the thickness of an active layer is determined by differences between successivemeasurements. 15.10.
Calculation of Extracted
of
Volumes Rock
The volumes of rock extracted in subma. rine mining can be calculated by the follow.
in Water
Areas of Oceans
ing methods: (I) by the results of surveying; (2) by measuring the volumes of extracted rock shipped in ore carriers or contained in on-shore stores; (3) by the readings of flow meters and consistometers mounted on pulp pipelines. Volume calculation by results of surveys. This method can be recommended for cases when the contours of mining workings are not changed substantially during the period of measurements. The calculation of the volume of the extracted mineral on the basis of the results of surveys can be made most easily by the method of horizontal sections. The volume of a working is determined by the formula: v = hm8m where hm is the mean depth of a working, m and 8m is the mean area of a working, m2. The mean area is found as the half-sum of the upper and lower areas: 8m = (8u + 8,)/2 and the mean depth: hm = ~h.I/ n where ~hi is the sum of measured depths within the boundaries of a working floor, m and n is the number of measurements. In practice, the mean extractive capacity of a mineral is usually determined as the difference of the mean elevation marks of the surface of a submarine deposit (within the boundaries of the upper crests of slopes) and of the bottom or as the difference of the mean depths of a working floor and the mean depths of the initial surface of the sea bottom. Calculation of volumes in vessels and onshore stores. In this method, the mine surveyor has to make the following operations: (a) measuring the geometrical parameters of a vessel or store; (b) determining the coefficient of filling of a capacity with loose rock mass; (c) calculating the volumes of loose rock in
15.10.
Calculation
of Volumes
of Extracted
Rock
361
(I) making an additional survey of submarine workings in order to determine the Rock Rock Loosening Loosening mineral reserves left in the ground and the factor factor amount of losses and dilution. -The most difficult step is the determination Sand 1.01-1.02 Loam 1.15-1.30 River gravel 1.03-1.04 Clays 1.30-1.45 of a loosening factor, but this can be taken Gravel 1.07-1.18 Shingle 1.40-1.60 from Table 15.2. Coarse- and Hard rocks 1.45-1.65 Determination of volumes of rock mass mediumtransported through pulp pipelines. In this grain sand I. 14-1.28 Frozen flood case, the volumes of rock mass are determiplain dePebbles, ned in terms of the flow rates of pulp crushed posits in transported through pipelines and measured stone I. 23-1.30 river valby means of flow-meters and consistometers. Sandv ]nam 1.1 07-1.18 leys and Hydraulic-type flow-meters are used to estuaries 1;20-1.17 - measure the flow rate of hydraulic mixture a waste dump or vesselby the formula for the (pulp) sucked in by a dredge. The density of a volumes of regular geometrical bodies (a pulp is determined by the pressure gradient appearing in the pulp in a vertical pipeline cone, pyramid, cylinder, cube, etc.); (d) determining the loosening factor of the owing to the settlement of heavier fractions. extracted rock by considering the physical Automatic recorders have been developed state and quality (moisture content, granu- which record instantaneous and summarized lometric composition, etc.), time of storage, data on the throughput capacity of a pumand the amount of settling; ping station and dredge, pulp density, and (e) recalculating the volume of loose rock actual time of operation. The error of volume to that of rock in the rock massif, using the measurements by flow-meters is not more than 3 per cent. loosening factor; Table 15.2