LQS Latin America Avenida Luis Thayer Ojeda 0130 Ofi. 304, Providencia. Santiago, Chile Tel: 562-6573898 Fax: 562-6573897 Toda la información contenida en este manual es de propiedad del Señor Kadri Dagdelen y cualquier reproducción parcial o total de la misma será sancionada legalmente.
Introduction to Mining Practices- Case Studies Open Pit Mining Terminology Pit Geometry and Slope Angles Open Pit Mine Planning Concepts - Circular Analysis Geologic Block Modeling Techniques Assay and Composite Sections and Block Modeling Geostatistical Resource Estimation Techniques Economic Definition of Ore Break-even Cutoff Grades and Stripping Ratio Analysis Economic Block Modeling, Cone and L&G Mining Analysis Final Pit Limits, Nested Pits and Mining Sequence Determination Cutoff Grade Policy, Scheduling and Stockpile Management Mine Sequence, Cutoff Grade, Process Flow Determination
UNIT OPERATIONS AND EQUIPMENT SELECTION Drilling Fundamentals and Drill Selection Blasting Fundamentals Front End Loaders; Hydraulic Shovels and Cable Shovels Excavator Selection Considerations Equipment Cost Calculations Cat Handbook Truck Haulage and Cycle Times Fleet Size Determination
Dispatch Systems In Pit Crushing and conveying systems Mineral Processing
Mining Project Cash Flow Analysis Net Present Value Calculations Mine Sequence, Cutoff grade and Process Flow NPV optimization
Papers by Kadri Dagdelen.
Surface Mine Design
Bingham Canyon Mine Porphyry Copper
Case Study
Surface Mine Design
General Information
2
General Information
Surface Mine Design
•World’s first low grade copper mine. •5 billion tons of material and 13 million tons of copper produced since 1906. •Overall stripping ratio is 0.4:1. •Mine daily production is 111 Kton of ore and 99.2 Kton of waste. (40 and 36 Mton/year respectively). •Reserves are at 1.0 Btons @ 0.5% Cu per ton which results in 25 years mine life. 3
General Information
Surface Mine Design
•210 Kton of copper; 350 oz of gold; 2.5 MM oz of silverand 6350 ton of moly per year. •2.5 miles long; 0.5 miles deep. •Truck haulage – haul road 150 ft wide; also 3 tunnels for ore and waste haulage. •Mine operates three 8-hour shifts per day, 365 days per year.
4
General Information
Surface Mine Design
Layout
5
General Information
Surface Mine Design
Geology
6
General Information
Surface Mine Design
•Block model dimensions 100 x 100 x 50 ft. Each block is assigned a value of Cu, Au, Ag, and Mo using a geostatistical technique known as kriging. •Development drilling on 400 by 600 ft centers. •Density 2.58 t/m3 or equivalent tonnage factor of 12.38 ft3/ton.
7
Mine Plan
Surface Mine Design
•Pushbacks range from 100 ft to 200 ft in width and 50 ft in height. •Five ore shovel production faces to meet average grade and metallurgical blending requirements. •Five waste shovel production faces to meet long range stripping requirements. •Operating interramp pit slope, including bench face angles and catch benches, is 34o; catch benches are 50 ft wide. 8
Mine Plan
Surface Mine Design
Typical Mining Sequence
9
Mine Plan
Surface Mine Design
•Ore is being mined in lower 900 ft of the pit and highest active waste stripping occurs 2000 ft higher elevation. •In extreme cases, mining room must be brought down nearly 40 benches before new ore is exposed; this process can take as long as seven years. •Slope angles for the ultimate pit limits are defined by subdividing the pit surface in 26 sectors.
10
Mine Plan
Surface Mine Design
•Slope angles for each of these sectors range from 29 to 50 degrees. •Slope angles will be achieved by double benching or single benching and control blasting – “digging to hard”. •Slope dewatering using near horizontal drains improves slope angles by 3 to 5 degrees in the ultimate slope. •Mining plans are developed by defining the volume of ore and waste between series of pushbacks. 11
Surface Mine Design
Mine Plan
•The material in pushbacks sequentially mined by a computerized mining simulator algorithm. Highest relative profit margin ore is mined first. •Haulage roads are added to the incremental pits. •Mine plan is a series of annual plans for five-year followed by five year plans to the end of mine life.
12
Drilling •Drills operate 5 days per week and two 8-hour shifts per day.
Surface Mine Design
•8 Bucyrus-Erie 60R track-mounted electric drills. •They can drill 57 to 65 ft in a single pass by exerting 120 Klb thrust. •Rotary tricone bits with carbide inserts are used to drill 12.25 in diameter holes. •One drill can drill 12 holes per 8-hour shift. •Two drilltech D75K track-mounted units; carbide insert bits 9.875 in diameter – 4 35-ft drill rods. 13
Drilling
Surface Mine Design
•D75K drills are used in resilient (hard) formations where closer patterns are necessary for proper fragmentation. •One secondary drill uses 2.5-in and 12-ft drill rods to drill boulders. Also mine has rubber-tired rock breaker. •Drill patterns vary with the rock types but range from 30 x 30 ft to 36 x 36 ft for 12.25-in holes. 25 x 25 ft to 30 x 30 ft for 9.875-in holes. 14
Blasting
Surface Mine Design
•Two ANFO trucks – blending of ammonium nitrate prills and fuel oil occurs when bulk delivery trucks deliver these material to the mine-site storage tanks. •Commercial bulk emulsion-blend explosives are used in wet holes. •Holes are primed with two 0.75-lb boosters placed near the bottom of the explosive column. •A 200-ms delay is inserted into each booster and connected to individual 7.5-grain primaline downlines. 15
Blasting
Surface Mine Design
•25 grain detonating cord is used for trunk lines and cross ties. •Surface delays of 17 ms are used between holes and 100 ms between rows. •A single strand of detonating cord extended from the pattern and initiated by a non-electric cap taped to the cord. •Drill cuttings are used for stemming. Each hole produces 2.4 to 3.7 tons of cuttings. These cuttings are forced into loaded holes. 16
Surface Mine Design
Blasting
•Powder factor varies between 0.13 to 0.25 lbs of explosive per ton depending on rock type; average 0.16 lb per ton. •Ground motion due to blasting is limited to 25 in/sec at the planned final pit slopes.
17
Loading
Surface Mine Design
•2 15-yd3 P&H2100; availability averages 78%; 10 Ktons per shovel shift. •4 27-yd3 P&H2800 Mark II; availability averages 80%; 15 Ktons per shovel shift. •3 30-yd3 P&H 2800 XP; availability averages 80%; 15 Ktons per shovel shift. • 2 34-yd3 P&H 2800 XPA; availability averages 80%; 20 Ktons per shovel shift. •2 8-yd3 International; 1 12-yd3 Clark; 2 12-yd3 Caterpillar rubber tired FEL’s. 18
Surface Mine Design
Loading
•Power is provided by 44-kva substations; radial lines are then fed to smaller substations with voltage reduced to 5500 V ac. •Electric connections between the switch houses and shovels are made through trailing cables up 2000 ft for shovels and 3000 ft for the drills.
19
Haulage
Surface Mine Design
•Mainly trucks and some rail. •Truck haulage utilizes a fleet of 44 trucks composed of 28 190-ton CAT-785 mechanical drive; 8 170-ton Unit Rig diesel electric; 8 170-ton Wabco diesel electric trucks. •In 1990 34 truck-shifts/shift are scheduled with average availability of 94% for the new, larger trucks; 84% for the smaller, older trucks. •All trucks are equipped with two-way radios to assist appropriate dispatching. 20
In-Pit Crusher
Surface Mine Design
•Movable, 60- by 109-in, 1000-hp Allis Chalmers gyratory crusher that has a capacity of 120,000 tons per day on continuous basis. •Two trucks at a time at a dumping rate of one truck per minute. •3 to 4 weeks are required to move the crusher. •-10 in crushed rock is fed directly to a 72-in conveyor. •The belt is 5 mile ling to Copperton concentrator and capable of carrying 10,000 tph at 900 ft/min speed.
21
Road Maintenance •28 miles of haulage roads and 40 miles of service roads. Surface Mine Design
•20 dozers (CAT D9H, D9L, D10L). •11 graders (CAT 16G). •2 scrappers (CAT 631). •4 salt trucks (5.4 or 6 ton capacity). •6 water trucks (converted 65-ton or 59-ton haulage trucks; 10,000 to 30,000 gallons capacity). 22
Open Pit Mining Fundamentals
Surface Mine Design
Dr. Kadri Dagdelen Colorado School of Mines
Terminology • BENCH: Ledge that forms a single level of Surface Mine Design
operation above which mineral or waste materials are mined from the bench face.
2
Terminology (Cont.)
Surface Mine Design
• BENCH HEIGHT: Vertical distance between the highest point on the bench (crest) and the lowest point or the bench (toe). It is influenced by size of the equipment, mining selectivity, government regulations and safety.
3
Terminology (Cont.) • BENCH SLOPE OR BANK ANGLE : Horizontal Surface Mine Design
angle of the line connecting bench toe to the bench crest.
4
Terminology (Cont.)
Surface Mine Design
• BERM: Horizontal shelf or ledge within the ultimate pit wall slope left to enhance the stability of the a slope within the pit and improve the safety. Berm interval, berm width and berm slope angle are determined by the geotechnical investigation.
5
Terminology (Cont.)
Surface Mine Design
•
OVERALL PIT SLOPE ANGLE: The angle measured from the bottom bench toe to the top bench crest. It is the angle at which the wall of an open pit stands and it is determined by: rock strength, geologic structures and water conditions.
6
Terminology (Cont.) • The overall pit slope angle is affected by the width Surface Mine Design
and grade of the haul road.
7
Terminology (Cont.) • HAUL ROADS: During the life of the pit a haul Surface Mine Design
•
road must be maintained for access. HAUL ROAD - SPIRAL SYSTEM: Haul road is arranged spirally along the perimeter walls of the pit.
8
Terminology (Cont.) • HAUL ROAD – SWITCH BACK SYSTEM: Surface Mine Design
•
Zigzag pattern on one side of the pit. HAUL ROAD WIDTH: Function of capacity of the road and the size of the equipment. Haul road width must be considered in the overall pit design.
9
Surface Mine Design
Haul Road Effect on Pit Limits
10
Terminology (Cont.) • ANGLE OF REPOSE: Maximum slope of the Surface Mine Design
broken material.
• SUBCROP OR ORE DEPTH: Depth of waste removed to reach initial ore.
• PRE-PRODUCTION STRIPPING: Stripping done to reach initial ore. 11
Terminology (Cont.)
Surface Mine Design
• ULTIMATE PIT LIMITS: Vertical and lateral extend of the economically mineable pit boundary. Determined on the basis of cost of removing overburden or waste material vs. the mineable value of the ore.
• PIT SCHEDULING: Material may be mined from the pit either in 1) sequential pushbacks 2) conventional pushbacks.
12
Surface Mine Design
Terminology (Cont.) •
STRIPPING RATIO: Expressed in tons of waste to tons of ore in hard rock open pit operations. Critical and important parameter in pit design and scheduling
•
AVERAGE STRIP RATIO: Total waste divided by total ore within the ultimate pit.
•
CUTOFF STRIPPING RATIO: Costs of mining a ton of ore and associated waste equals to net revenue from the ton of ore.
13
Surface Mine Design
Single Working Bench
14
Surface Mine Design
Shovel in Working Bench
15
Surface Mine Design
Two Working Benches
16
Surface Mine Design
Final Pit Limit
17
Surface Mine Design
Cresson Mine – Year 2001
18
Surface Mine Design
Cresson Mine – Year 2007
19
Surface Mine Design
Cresson Mine – Year 2011
20
Surface Mine Design
Pit Sequence (1)
21
Surface Mine Design
Pit Sequence (2)
22
Surface Mine Design
Pit Sequence (3)
23
Surface Mine Design
Pit Sequence (4)
24
Surface Mine Design
Section of Pit Sequence
25
Open Pit Mine Planning and Design: Fundamentals
Surface Mine Design
Dr. Kadri Dagdelen Colorado School of Mines Source: Hustrulid and Kuchta Open Pit Mine Planning and Design
Surface Mine Design
Geometrical Considerations
Parts of a bench
Cumulative frequency distribution of measured bench face angles (Call, 1986).
2
Surface Mine Design
Geometrical Considerations
Functioning of catch benches. Section through a working bench.
3
Surface Mine Design
Geometrical Considerations
Double benches at final pit limits.
Catch bench geometry (Call, 1986).
Typical catch bench design dimensions (Call, 1986). Bench height (m) 15 30 45
Impact zone (m) 3.5 4.5 5
Berm height (m) 1.5 2 3
Berm width Minimum bench width (m) (m) 4 7.5 5.5 10 8 13
4
Surface Mine Design
Geometrical Considerations
Safety berms at bench edge
5
Surface Mine Design
Geometrical Considerations
Height of reach as a function of bucket size. 6
Surface Mine Design
Geometrical Considerations
Example orebody geometry. Ramp access for the example orebody.
Blast design for the ramp excavation. 7
Surface Mine Design
Shovel Working Range
8
Surface Mine Design
Geometrical Considerations
Minimum width drop cut geometry with shovel alternating from side to side.
9
Surface Mine Design
Geometrical Considerations
Minimum width drop cut geometry with shovel alternating from side to side.
10
Surface Mine Design
Geometrical Considerations
Isometric view of the ramp in waste approaching the orebody.
Diagrammatic representation of the expanding mining front. 11
Surface Mine Design
Geometrical Considerations
Dropcut / ramp placement in ore.
Expansion of the mining front.
12
Surface Mine Design
Geometrical Considerations
Plan view of an actual pit bottom Showing drop cut and mining Expansion (McWilliams, 1959).
13
Surface Mine Design
Geometrical Considerations
Extension of the current Ramp close to the pit wall (McWilliams, 1959).
14
Surface Mine Design
Geometrical Considerations
Creating initial access / benches.
Shovel cut sequence when initiating benching in a hilly terrain (Nichols, 1956). Sidehill cut with a shovel.
15
Surface Mine Design
Geometrical Considerations
Detailed steps in the development of a new production level. 16
Surface Mine Design
Geometrical Considerations
Parallel cut with drive by. 17
Surface Mine Design
Geometrical Considerations
Parallel cut with the double spotting of trucks. 18
Surface Mine Design
Geometrical Considerations
Parallel cut with the single spotting of trucks. 19
Surface Mine Design
Geometrical Considerations
Time sequence showing shovel loading with single spotting.
20
Surface Mine Design
Geometrical Considerations
(Continued). 21
Surface Mine Design
Geometrical Considerations
Time sequence showing shovel loading with double spotting.
22
Surface Mine Design
Geometrical Considerations
(Continued). 23
Surface Mine Design
Geometrical Considerations
(Continued). 24
Surface Mine Design
Geometrical Considerations
Section and plan views through a working bench. Simplified presentation of a safety berm.
25
Geometrical Considerations
Surface Mine Design
Initial geometry for the push back example.
Cut mining from bench 1.
Cut mining from bench 2.
26
Surface Mine Design
Geometrical Considerations
Safety bench geometry showing bench face angle.
Overall slope angle.
27
Surface Mine Design
Geometrical Considerations
Overall slope angle with ramp included. Interramp slope angles.
28
Surface Mine Design
Geometrical Considerations
Overall slope angle with Working bench included. Interramp angles associated with the working bench.
29
Surface Mine Design
Geometrical Considerations
Overall slope angle with one working bench an a ramp section. Interramp slope angles for a slope containing a working bench and a ramp.
30
Surface Mine Design
Geometrical Considerations
Overall slope angle for a slope containing two working benches. 31
Surface Mine Design
Geometrical Considerations
Slopes for each working group. 32
Surface Mine Design
Geometrical Considerations
Final overall pit slope. 33
Advances in Pit Slope Management Systems
Dr. Kadri Dagdelen Professor Mining Engineering Department Colorado School of Mines Golden, Colorado 80401
Pit Slope Failure Problems l l
l
Continue to be the source of human and financial losses Recent examples from Wyoming coal mines and Grasberg pit in Indonesia point to additional research needs to be done in the area of pit slope management Pit slope monitoring research is undertaken at the Colorado School of Mines using Lidar Scanners with funding from Kennocott Energy and 3-DP
Plane Failure l
l
l
Failure plane must daylight in the slope face; i.e. its dip must be smaller than slope (S>P) Plane must strike parallel or nearly parallel (within 20o) to the slope face. Less common than other failure modes
Plane Failure in a Limestone Quarry
Wedge Failure
NON-DAYLIGHTING WEDGE
DAYLIGHTING WEDGE
•
Most common mode of failure for rock slopes
•
Line of intersection must daylight into slope face
•
Often, failure is sudden
Circular Failure l l l l l
Soils Stock piles Reclamation piles Waste dumps Highly weathered overburden rocks
Toppling and Step-Path Modes Toppling
Mixed modes (e.g. Toppling & Step-Path)
Overall Slope Design l l l l l
Identify geological sectors; their strength characteristics and possible mode of failures Determine maximum height and angle for interramp design Determine bench geometry Incorporate bench geometry into Inter-ramp design Overall slope design
Failure Modes in Different Sectors
Pit Slope Monitoring - What to look for l l l l l l l l
Overhang rock New geological structures Swell and/or increased rock fall activity on highwall Heavy precipitation Signs of stress Tension cracks Movement (acceleration) Increased water levels
Tension Crack Measurements l l
The formation of cracks behind slope is a sign of instability (Safety Factor ˜ 1) Monitoring changes in crack width and direction can provide information on extent of unstable area
Inclinometers l l
Inclinometers measure horizontal deflections of a borehole They can -
Locate failure surface Determine nature of failure surface (rotational or planar) Measure movement along failure surface and determine if movement is accelerating
Borehole extensometer l
Consists of tensioned rods anchored at different points in a borehole.
l
Measures changes in distance between anchors, as well as collar
l
Provides displacement information across discontinuities.
New and Emerging Technologies l
Automated Total Station Network (robots)
l
Non-reflective Laser scanners (Lidar systems: Cyra, Riegl, I-Site)
l
Radar Technologies
l
GPS (Local sensors with multiple antenna)
l
TDR (Time Domain Reflectometry)
l
Digital photogrammetry
l
Arial photography (Kodak)
Automated Total Station Network in Chuquicamata Mine, Chile • A network of automated total stations for geotechnical monitoring of pit slopes that operate continuously 24 hours a day, 7 days a week and during the 365 days a year. • Provide a reliable and quantitative information in real time that allows to establish with anticipation the behavior of the rock mass and geologic structures on the pit slopes.
Completely Automated Electronic Station Network using Leica TCA2003
Motorized Station, Leica TCA2003
Characteristics • Reach with 1/3 prisms in average atmospheric conditions : 2500/3500 mts. • Precision in distance : 1mm + 1 ppm • Angular precision : 0.3” (0.1 mgon) • Increase of lens : 30 x • Compartment for the insertedable memory card PCMCIA. • Integrated application programs : Reframing, orientation of horizontal circle and drag of levels, reseccion and distance of connection between two points. • Capture of information in modality ATR and DIST.
Wireless Communication Network Bridge Bluebox Switch Energy SHELTER 2
ARTURO ESTE ARTURO OESTE SHELTER 1
SHELTER 4
SHELTER 6
SHELTER 5 SHELTER 3
CONTROL ROOM
ETHERNET NETWORK
Location of Stations and Integration of Information Software of Information Integration •
Have a Computational Software that allows to totally integrate and administer the acquisition of geotechnical data, procesing and analisis of the information in real time originating from the robotic system (TCA) intalled in each of the monitoring stations. SHELTER 2
ARTURO ESTE
ARTURO OESTE SHELTER 1
SHELTER 4
SHELTER 6
SHELTER 5 SHELTER 3
CONTROL CONTROL ROOM ROOM
Total Station and Prism Locations in Chuquicamata Mine, Chile
Caseta Oeste
Caseta Este
GPS Surveyed Control Stations in Chuquicamata Mine, Chile S2
S3 S4
S1
S5
“D” (PR-1) “E1” (PR-2)
PILAR GT-1
Matus (PR-3) GT-1 PR-4 Morgan (PR-5) D1
D2
APS-WEST. D3 D5
ZONA-6
Norte : 2085.491 Este : 3870.863 Cota : 2846.745 Elev
D4
ZONA-5
.
ZONA-7
Coordenadas de la Estación de Monitoreo APS(N;E;Z)
Slope Stability Radar Technology from GroundProbe of Australia
Complete Pit Wall Coverage from Remote Locations
Radar Scan Lines
Location and Time of Wall Movements
Inc r disp easing lace me nt w ith t ime
02:04 9th October 2003
23:22 8th October 2003
20:47 8th October 2003
18:13 8th October 2003
Displacement (mm)
Slip Area
Slope Stability Radar Features • High deformation precision (± 0.2 mm std. dev.) • Broad area coverage (~1000’s pixels/scan) • Continuous operation (~ 1’s min/scan, 24 hrs/day) • 30-850m range • All weather operation (incl. dust, fog) • Rapid Deployment • Remote Operation via radio link and internet • High resolution CCD Camera • Custom software with alarm settings
SSRViewer Images Screen
SSRViewer Figures Screen
10mm movement over 45 hours in Region 1
15mm movement over 45 hours in Region 3
0.0mm movement over 45 hours in Region 2
Laser Scanning Technologies There are Many 3D Laser Scanners Major Companies with Products are: l l l l l
Cyrax (Leica) www.cyra.com (USA) Optech ILRIS (Canada) I-site (Maptek) www.isite3d.com (Australia) LMS 3D Scanning systems (Riegl) www.riegl.co.at (Austria) Z+F Laser Measuring Systems (Zoller+ Fröhlich) www.zofre.de (Germany) Cyrax 2400
Other Application in Laser Technologies Riegl Z 210i Lidar Laser Scanner
Specifications •1200+ ft scan range •2.5cm accuracy @ 900 ft •5 cm accuracy > 900 ft •361 degrees x 80 degree scan •9000 Hz
Riegl LPM 800 HA Specifications •3000 ft scan range 1cm accuracy @ 1250 ft 2 cm accuracy > 1250 ft •0.018 degrees step size •360 degrees of horizontal rotation •180 degrees of vertical rotation •1000 Hz
Riegl Z 420 Lidar Laser Scanner Specifications •2400+ ft scan range •1cm accuracy in topo mode •6 mm accuracy in detail mode •0.01 degree step size •361 degrees x 90 degree scan window •8000 - 12000 Hz
High Wall Scan (Pre Blasting)
Post-Blast Scan
Pre Blast Triangles
Post Blast Triangles
Combined – Pre / Post
Dynamic Cross Section
Complete Pit Scan using Riegl
Pit Wall Scan Using Riegl
Pit Wall Failure Scan - Riegle
Slope Monitoring Systems Technology
Precision
SSR – GROUND PROBE
± 0.2 mm Broad Area
~ mins
850 m Easy (1.4km)
Yes
Laser (Prisms)
~ 1’s cm
Discrete Points
Twice Daily
2 km
Difficult
No
Broad Area
~ secs
900 m
Easy
No
LIDAR ~ 1’s cm SCANNER
Wall Coverage
Update Rate
Range
Deployment
All weather
Extensometers
~ 1’s mm Discrete Points
~ secs
n/a
Difficult
Yes
GPS
~ 1’s cm
Discrete Points
~ secs
n/a
Difficult
Yes
Broad Area
~ hours
< 150 m Moderate
Photogram ~ 1’s cm -metry
No
Slide Management Options l l l l l l l
Reduce slope angle Dewater unstable area Leave unstable areas Continue mining Unload slide Partial clean up Step-out
l l l l l
Reduce slope height by segmenting the slope Support unstable ground Contingency Planning Blasting Erosion control measures (reclamation) - Geotextiles against erosion
and raveling - Vegetating and planting
Leave Unstable Areas untouched Instability can be left alone if it is in – an abandoned area, – an inactive area, – an area that can be
avoided
Continue mining
Displacement (cm)
If the displacement rate is low and predictable, living with the displacement while continuing to mine may be the best action. 150
May continue mining (displacement rate is constant)
100 50
1/4/02
5/4/02
11/4/02
Time
16/4/02
Basic Principles of Drainage l l l l
Prevent surface water from entering to the slope through open tension cracks and fissures Reduce water pressure in the vicinity of the potential failure surface Providing for gravity flow of water is the most common method Pumping is used on a temporary basis depending on the urgency of the problem
Method of Slope Drainage Bench section view
Benches sloped toward toe
Bench face view Slope crest
Inclined bench for gravity flow
Horizontal Drain Network (303 drains/34 miles since 1999) T AN RM DO 55
O DE RO
S EMILY
IND BL
60
60
K EE CR
JB
PATS
1
S CHRISTY
RO DE O
T IGH DN MI
CR EE K
60
EX PLO DIN G
N-00-B 60
60 75
78
ANFO
LAST LA
85
UGH
ST PO
60
FLOWER PATC
25 H
50
UL ERF POW
AMANDA
AN JE
50 BL IND
RO DE O AN TIP OS T
D AN GR
80
CR EE K
RO DE O
CR EE K1
Unload Side l Even
though unloading has been a common response, in general it has been unsuccessful.
l In
fact, there are situations involving high water pressure where unloading actually decreases stability.
Partial clean-up •
Partial cleanup may be the best choice where a slide blocks a haul road or fails onto a working area
•
Only that material necessary to get back into operation need be cleaned up
Step-out l Increased
highwall stability due to shallower slope angle It locks up reserves
l Advantages
of leaving step out should be weighed against cleaning by considering ore lock up and having safer overall slope New Slope Design
Failure Surface Step out
Originally Planned Slope Design
Old Overall Slope Angle New (Flatter) Overall Slope Angle
Reduce slope height by segmenting slope
Support unstable ground
Buttress Rock Bolts
Anchors, Tiebacks, and Shotcrete 1.
2. 3. 4. 5. 6.
Reinforced concrete dowel to prevent loosening of slab at crest Tensioned rock anchors to secure sliding failure along crest Tieback wall to prevent sliding failure on fault zone Shotcrete to prevent raveling of zone of fractured rock Drain hole to reduce water pressure within slope Concrete buttress to support rock above cavity
Mesh & Bolts
Buttressing
Buttressing
NE Wall Sept 2002 unwting cut N-00-B 2% ramp & buttress mudslide 4880 buttress 4640
4280
NE Wall Un-weighting Cut
2/1 /0 2/1 2 5/0 2 3/1 /0 3/1 2 5/0 3/2 2 9/0 4/1 2 2/0 4/2 2 6/0 5/1 2 0/0 5/2 2 4/0 2 6/7 /02 6/2 1/0 2 7/5 /0 7/1 2 9/0 2 8/2 /02 8/1 6/0 8/3 2 0/0 9/1 2 3/0 9/2 2 7 10 /02 /11 10 /02 /25 /0 11 2 /8 11 /02 /22 /0 12 2 /6 12 /02 /20 /02 1/3 /0 1/1 3 7/0 1/3 3 1/0 2/1 3 4/0 2/2 3 8/0 3
MOVEMENT IN (INCHES/DAY)
Prism Data Feb 2002 to Feb 2003 PRISM DATA - All In Movement Area
0.20
0.00 TN000084
-1.60 TN000089
-0.20 TN010095
TN010119
-0.40 TN 80
TN 72
-0.60 TN 97
TN 98
-0.80 TN 101
TN 114
-1.00 TN 115
TN 127
-1.20 TN 144
#4
-1.40
#3
-1.80
-2.00
DATE
TN 149
Blasting Line drill holes
Pre-splitting
Production holes Face
Line drilling
Use of less charges next to toe
Slide Management Example PUSHBACK DEVELOPMENT
Displacement rate
Normal
2 a 5 cm/day
Only ore production stripping
5 a 10 cm/day
Stop push-back development
> 10 cm/day DESPLAZAMIENTO (cm)
D5 BENCH
300
250 y = 63.213x - 2E+06 200
150
Catch Berm, ± 40 m. H13 BENCH
SAFETY BERM
y = 16.016x - 597363 y = 8.7432x - 326060
100
Failure
y = 5.6082x - 209126 50
0 1/2/02
6/2/02
11/2/02
16/2/02 TIEMPO
PUSHBACK
Access D5 & H13 closed
21/2/02
Took out shovel
Contingency Planning l l l l l l l
Provide multiple access to production faces Maintain double access to working benches, whenever possible Stockpile ore/rock Design to prevent noses in the plan geometry Provide for failure costs in scheduling and budgeting Add lag times in production scheduling Plan step-outs
Conclusions l
l
New Radar and Lidar based technologies applied to pit slope monitoring appears to be very promising in providing cost effective and accurate real time data . Accurate and reliable slope displacement information coupled with proper pit slope management practices has a potential to prevent unexpected catastrophic pit slope failures.
Haul Road Design
Surface Mine Design
Dr. Kadri Dagdelen Colorado School of Mines
Haul Road Design • HAUL ROADS: During the life of the pit a haul Surface Mine Design
•
road must be maintained for access. HAUL ROAD - SPIRAL SYSTEM: Haul road is arranged spirally along the perimeter walls of the pit.
2
Haul Road Design • HAUL ROAD – SWITCH BACK SYSTEM: Surface Mine Design
•
Zigzag pattern on one side of the pit. HAUL ROAD WIDTH: Function of capacity of the road and the size of the equipment. Haul road width must be considered in the overall pit design.
3
Surface Mine Design
Haul Road Effect on Pit Limits
4
Surface Mine Design
Considerations for Haul Road Design
• Visibility • Stopping distances • Vertical alignment • Horizontal alignment • Cross section • Runaway-vehicle safety provisions 5
Sight Distances and Stopping Distances
Surface Mine Design
• Vertical and horizontal curves designed • •
considering sight distance and stopping distance Sight distance is the extent of peripheral area visible to the vehicle operator Sight distance must be sufficient to enable vehicle traveling at a given speed to stop before reaching a hazard 6
Sight Distances and Stopping Distances
Surface Mine Design
• On vertical curves, road surface limits sight • • •
distance Unsafe conditions remedied by lengthening curve On horizontal curves, sight distance limited by adjacent berm dike, rock cuts, trees, etc; Unsafe conditions remedied by laying back bank or removing obstacles
7
Sight Distance Diagrams
Surface Mine Design
⇒
Sight distance diagrams for horizontal and vertical curves (Kaufman and Ault)
8
Stopping Distances
Surface Mine Design
• Stopping distances depend on truck breaking •
capabilities, road slope and vehicle velocity Stopping distance curves can be derived based on SAE service break maximum stopping distances
9
Surface Mine Design
Stopping Distance Characteristics For example, stopping distance characteristics of vehicles of 200,000 to 400,000 pounds GVW (Kaufman and Ault)
10
Stopping Distances
Surface Mine Design
• Prior to final road layout, manufacturers of vehicles that will use the road should be contacted to verify the service brake performance capabilities
11
Vertical Alignment • Establishment of grades and vertical curves that Surface Mine Design
allow adequate stopping distances on all segments of the haul road
• Maximum sustained grades
• Reduction in grade significantly increases vehicle uphill speed • Reduction in grade decreases cycle time, fuel consumption, stress • •
on mechanical components and operating costs Reduction in grade increases safe descent speeds, increasing cycle time The benefits of low grades offset by construction costs associated with low grades
12
Surface Mine Design
Vehicle Performance Chart
13
Surface Mine Design
Vehicle Retarder Chart
14
Vertical Alignment • Maximum sustained grades Surface Mine Design
• Some states limit maximum grades to 15 to 20% and sustained grades of 10% • Most authorities suggest 10% as the maximum safe sustained grade limitation • Manufacturer studies show 8% grades result in the lowest cycle time exclusive of construction consideration
15
Vertical Alignment • Maximum sustained grades Surface Mine Design
• Property boundaries, geology, topography, climate must be considered on a case by case basis. • Lower operating costs must be balanced against higher capital costs of low grades. • Truck simulators and mine planning studies over the life of mine should be used to make the determination of the appropriate grades
16
Vertical Curves
Surface Mine Design
• Vertical curves smooth transitions from one •
grade to another Minimum vertical curve lengths are based on eye height, object height, and algebraic difference in grade
17
Surface Mine Design
Stopping Distance vs. Vertical Curve For example, vertical curve controls 9 ft eye height (usually minimum height for articulated haulage trucks of 200,000 to 400,000 pound of GVW) 18
Horizontal Alignment
Surface Mine Design
• Deals primarily with design of curves and •
considers previously discussed radius, width, and sight distance in addition to superelevation Cross slopes also should be considered in the design
19
Curves, Superelevation, and Speed Limits
Surface Mine Design
• Superelevation grade recommendations vary • •
but should be limited to 10% or less because of traction limitations Depending on magnitude of the side friction forces at low speed, different values are suggested for small radius curves Kaufman and Ault suggest .04-.06 fpf (basically the normal cross slope) 20
Curves, Superelevation, and Speed Limits
Surface Mine Design
• CAT suggests higher slopes with traction •
cautions and 10% maximum caution Again, where ice, snow, and mud are a problem, there is a practical limit on the degree of superelevation
21
Surface Mine Design
Curve Superelevation
(CAT)
22
Recommended Superelevation Rates
Surface Mine Design
If superelevation is not used, speed limits should be set on curves.
(Kaufman and Ault) 23
Curves, Superelevation, and Speed Limits
Surface Mine Design
• Centrifugal forces of vehicles on curves are • •
counteracted by friction between tire an road and vehicle weight as a result of superelevation Theoretically, with superelevation, side friction factors would be zero and centrifugal force is balanced by the vehicle weight component To reduce tire wear, superelevation or speed limits on curves are required 24
Combinations of Alignments • Avoid sharp horizontal curvature at or near the crest Surface Mine Design
• • • •
of a hill Avoid sharp horizontal curves near the bottom of sustained downgrades Avoid intersections near crest verticals and sharp horizontal curvatures Intersections should be made flat as possible If passing allowed, grades should be constant and long enough 25
Cross Section
Surface Mine Design
• A stable road base is very important • Sufficiently rigid bearing material should be •
used beneath the surface Define the bearing capacity of the material using the California Bearing Ratio (CBR)
26
Surface Mine Design
California Bearing Ratio
27
Surface Mine Design
Subbase Construction
28
Cross Slopes
Surface Mine Design
• Cross slopes provide adequate drainage and •
range from ¼ to ½ inch drop per foot of width (approximately .02 to .04 foot per foot) Lower cross slopes used on smooth surfaces that dissipate water quickly and when ice or mud is a constant problem
29
Cross Slopes
Surface Mine Design
• Higher cross slopes permit rapid drainage,
•
reduce puddles and saturated sub-base, and are used on rough surfaces (gravel and crushed rock) or where mud and snow are not a problem High cross slopes can be particularly problematic with ice or snow on high grades (+5%) 30
Recommended Rate of CrossSlope Change
Surface Mine Design
Slope change should be gradual.
(Kaufman and Ault)
31
Width
• On straight or tangent segments, width Surface Mine Design
depends on
• Vehicle width • Number of lanes • Recommended vehicle clearance, which ranges from 44 to 50% of vehicle width
32
Surface Mine Design
Minimum Road Design Widths for Various Size Dump Trucks
(Couzens, SME Open Pit Planning and Design)
33
Surface Mine Design
Typical Design Haul Road Width Typical design haulroad width for two-way traffic using 77.11-t (85st) trucks
(Couzens, SME Open Pit Planning and Design)
34
Surface Mine Design
Typical Haulageway Sections
(Kaufman and Ault)
35
Width
Surface Mine Design
• Berm height and width as a function of • • • •
vehicle size and material type Ditch(es) added to basic recommendations Runaway provisions may also add to width Road wider on curves because of overhang Minimum turning radius considered on curves (should be exceeded) 36
Haulageway Widths on Curves
Surface Mine Design
⇒
37
Safety Provisions - Berms
• Triangular or trapezoidal made by using local Surface Mine Design
material
• Stands at natural angle of repose of construction material • Redirects vehicle onto roadway • Minimum height at rolling radius of tire
38
Berms
• Larger boulders backed with earthen material Surface Mine Design
• Near vertical face deflects vehicle for slight angles of incidence • Problems with damage and injury and availability of boulders • Minimum height of boulder at height of tire allowing chassis impact
39
Runaway Provisions
Surface Mine Design
• With adverse grades some safety provision should • • •
be integrated to prevent runaway vehicles Primary design consideration is required spacing between protective provisions Driver must reach a safety provision before truck traveling too fast to maneuver Maximum permissible speed depends on truck design conditions and operator 40
Runaway Provisions
Surface Mine Design
• Maximum permissible speed, equivalent •
downgrade, and speed at break failure determine distance between runaway truck safety provisions For example, at an equivalent downgrade of 5% and a maximum speed of 40 mph, Speed at Failure Provision Spacing
10 mph 20 mph 1,000 ft 800 ft
(Kaufman and Ault) 41
Surface Mine Design
Runaway Precautions
(Atkinson SME Handbook)
42
Median Runaway-Vehicle Provision Berms
Surface Mine Design
• Vehicle straddles collision berm and rides • • •
vehicle to stop Made of unconsolidated-screened fines Critical design aspects spacing between berms and height of berm Height governed by height of undercarriage and wheel track governed by largest vehicle 43
Surface Mine Design
Median Runaway-Vehicle Provision Berms
• Requires maintenance in freezing conditions • Agitation to prevent damage to vehicle • May cover berm in high rainfall areas
44
Escape Lanes
Surface Mine Design
• Good tool for stopping runaway but • •
expensive to construct Entrance from road is important; spacing, horizontal, vertical curve and superelevation are all considered in design Deceleration mainly by adverse grade and high rolling resistance material 45
Escape Lanes
Surface Mine Design
• Length a function of grade and speed at •
entrance and rolling resistance Stopping by level section median berm, sand or gravel or mud pits, road bumps or manual steering
46
Surface Mine Design
Escape Lanes
47
Maintenance
Surface Mine Design
• The road surface is •
deformed by the constant pounding of haulage vehicles. A good road maintenance program is necessary for safety and economics. 48
Safety Considerations
Surface Mine Design
• Dust, potholes, ruts, depressions, bumps, and other conditions can impede vehicular control.
49
Economic Considerations • The wear on every component is increased when a Surface Mine Design
•
vehicle travels over a rough surface. If the vehicle brakes constantly, unnecessary lining wear occurs as well.
50
Dust Control
Surface Mine Design
• Dust may infiltrate brakes, air filters, •
hydraulic lifts, and other components of machinery. The abrasive effect of dust will result in costly cleaning or replacement of these items.
51
Deterioration Factors
Surface Mine Design
• Weather • Vehicles follow a •
similar path Spillage
52
Motor Graders
Surface Mine Design
• A motor grader should be used to maintain cross slopes, remove spills, and to fill and smooth surface depressions as they occur. 53
Road Drainage
Surface Mine Design
• To avoid overflow, roadside ditches and •
culverts should be periodically cleaned. Avoid erosion or saturation of subbase materials.
54
Haul Road Design
Surface Mine Design
Open Pit Contour Maps Dr. Kadri Dagdelen
Source: Hustrulid and Kuchta
Surface Mine Design
Example of Mapping Procedure
2
Surface Mine Design
Plan View of a Portion of the Open Pit
Crests denoted by dashed lines and toes by solid lines.
3
Surface Mine Design
Example of Mapping Procedure
4
Surface Mine Design
Midbench Elevation
5
Surface Mine Design
Plan View of Midbench Elevation
6
Surface Mine Design
Map Based on Midbench Contours
7
Surface Mine Design
Procedure to Convert Midbench to Toe and Crest Contours
8
Surface Mine Design
Representation of Crests and Toes
9
Surface Mine Design
Designing a Spiral Ramp Inside the Wall
10
Surface Mine Design
Completing the new crest lines
11
Surface Mine Design
Pit Layout Including Ramp
12
Surface Mine Design
Design of a Spiral Ramp Outside the Wall
13
Surface Mine Design
Pit Layout Including Ramp
14
Surface Mine Design
Design of a Switchback
15
Surface Mine Design
Design of a Switchback
16
Surface Mine Design
Design of a Switchback
17
Surface Mine Design
Pit Layout Including Ramp
18
Surface Mine Design
Example of Two Switchbacks
19
Surface Mine Design
Plan and Section Views of Pit Without Ramp
20
Surface Mine Design
Plan and Section Views of Pit With Ramp
21
Surface Mine Design
Road Volume in the Ramp
22
Surface Mine Design
Block Modeling and Ore Reserves Estimation
Dr. Kadri Dagdelen
1
Surface Mine Design
Basic Block Model Information
• • • •
Topography Data Drill Data Sampling Assays
2
Surface Mine Design
Topography Data
3D Display (Color Coded Elevations)
3
Drill Data
Surface Mine Design
Drill Hole Data Sources
•Collar Coordinates •Geologic Logs •Down Hole Surveys •Lab Tests
4
Samplings
Surface Mine Design
Sampling Data
•Rock Types •Alteration Types •Metal Grades •Attributes
5
Surface Mine Design
Samplings (Cont.)
Data Collections
6
Surface Mine Design
Assays
Assay Data for Cu and Mo Multiple Cutoffs Rock Types Alterations 7
Surface Mine Design
Geological Interpretation
Section View Showing Topography and Alteration Types
8
Surface Mine Design
Geological Interpretation
Boundaries for rock types
9
Surface Mine Design
Geological Interpretation
Color Filled Display for Alteration Types
10
Surface Mine Design
3D Geological View
3D Display of Alteration Type Solids (With Drill Hole Piercing Points) 11
Surface Mine Design
Composites
Composited Grade Data with Corresponding Assay Interval Data
12
Surface Mine Design
3D Block Models
3D View of the Block Models
13
Surface Mine Design
Block Estimation
Kriging - Geological Interpolation Technique for Ore Reserve Estimation
14
Surface Mine Design
Block Values
Block by Block Profit Values in Association with Block Grade Data and Alteration Type Boundaries
15
Surface Mine Design
Block Models
Interpolated Grades from Drill Hole Data
16
Surface Mine Design
Ore Reserve Estimation
Interpolated Grades from Drill Hole Data
17
Surface Mine Design
Economic Pit Limits
Economic Pit Limits for Different Economic Scenarios
18
Surface Mine Design
3D View of Economic Pit Limits
3D View of Economic Pit Limits for Different Economic Scenarios 19
Surface Mine Design
Mine Planning Application (Open Pit Mine)
Yearly Maps for the Open Pit Mine Scheduling
20
Surface Mine Design
Geologic Resource Modeling Techniques
• • • • • •
Exploratory Data Analysis Variogram Analysis Search Strategies Simple Kriging, Ordinary Kriging, Indicator Kriging, Co-Kriging Cross Validation Uncertainty and Risk Evaluation
21
Surface Mine Design
Frequency and Cumulative Frequency Plots
•Classical Statistics •Data Posting and Display •Histograms •Cumulative Histograms •Probability Plots
22
Inverse Distance Technique
• Surface Mine Design
• •
Inverse distance technique is the simplest interpolation method. Give more weight to the closest samples, and less to those that are farthest away. In general, 1 d ip wi = n 1 ∑ p i =1 d i
1 n di p vˆ = ∑ n vi 1 i =1 ∑ p d i =1 i n
vˆ = ∑ wi vi i =1
n
∑ wi = 1 i =1
23
Inverse Distance Technique (pg257)
Surface Mine Design
• •
We can make the weights inversely proportional to any power of the distance. If p=2, it is called Inverse Distance Square.
v4 d3 v1 d 1
vˆ
v2 d2 d4 v3
Inverse Distance Square vˆ =
1 2 d1 4
∑ i =1
1 di2
v1 +
1 2 d2 4
∑ i =1
1 di2
v2 +
1 2 d3 4
∑ i =1
1 di 2
v3 +
1 2 d4 4
∑ i =1
v4
1 di2
24
Inverse Distance Square Example •
Estimate the unknown point Distance Square technique
Surface Mine Design
V3=0.5
d3=4
vˆ
by using the Inverse
v1= 0.2 d1 =1
vˆ
d1=1 V1=0.2
V2=0.3 d2=2
v2= 0.3 d2 =2 v3= 0.5 d3 =4
vˆ = ? 25
Inverse Distance Square Example
•
First of all, calculate the weights w1, w2, w3
Surface Mine Design
w1 = w2 = w3 =
1 12
1 12
1 12
+ + +
1 12 1 22 1 22 1 22 1 42 1 22
+ + +
1 42
1 42
1 42
21 16
16 = 21
=
1 4 21 16
4 = 21
=
1 16 21 16
1 = 21
=
1
Note:
w1 + w2 + w3 = 1 26
Inverse Distance Square Example
Surface Mine Design
•
Then, calculate vˆ vˆ =
16 4 1 × 0.2 + × 0.3 + × 0.5 = 0.233 21 21 21
27
Estimation Error
Surface Mine Design
•
Error estimation between estimation (Exploration data) and true value (Blasthole data). Error = Estimated Grade – True Grade
e.g., Estimation Error for Block 1 = 0.463 – 0.433 = 0.031
28
Surface Mine Design
Histogram of Errors
29
Scatter Graph True grades agai n s t E s t i mated grades 0.90
0.70 E s t i mated (%)
Surface Mine Design
0.80
0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 True (%)
30
Surface Mine Design MNGN312 - MNGN512
Surface Mine Design
Lecture 5 September 14, 2004
Instructor Dr. Kadri Dagdelen
Surface Mine Design
Geologic Block Modeling •
Assume that a geologic model to be created by using 75ft by 75ft blocks from the exploration data set. Estimate the grade of these blocks using the inverse distance square (IDS) technique.
•
Use rectangular search neighborhood of 37.5ft x 37.5ft.
•
Assume that the center of the block represents the block grade.
2
Geologic Block Modeling Estimate the grade of the block (block size 75ft x 75ft) for exploration data set. Estimate the center point
75ft
Surface Mine Design
•
vˆ1
vˆ2
75ft
3
Geologic Block Modeling Rectangular search neighborhood of 37.5ft x 37.5ft.
75ft
Surface Mine Design
•
37.5ft
37.5ft
37.5ft
37.5ft
75ft Use all the exploration holes within a given block (For this block, use 3 exploration samples) 4
Inverse Distance Technique • Surface Mine Design
• •
Inverse distance technique is the simplest interpolation method. Give more weight to the closest samples, and less to those that are farthest away. In general,
Unknown point
1 d ip wi = n 1 ∑ p i =1 d i
1 n di p vˆ = ∑ n vi 1 i =1 ∑ p d i =1 i
Sampling points Weights
n
vˆ = ∑ wi vi i =1
n
∑ wi = 1 i =1
5
Inverse Distance Technique • Surface Mine Design
•
We can make the weights inversely proportional to any power of the distance. If p=2, it is called Inverse Distance Square (IDS).
v4 d3 v1 d 1
vˆ
v2 d2 d4 v3
Inverse Distance Square vˆ =
1 2 d1 4
∑ i =1
1 di2
v1 +
1 2 d2 4
∑ i =1
1 di2
v2 +
1 2 d3 4
∑ i =1
1 di 2
v3 +
1 2 d4 4
∑ i =1
v4
1 di2
6
Inverse Distance Square Example •
Estimate the unknown point Distance Square technique
Surface Mine Design
V3=0.5
d3=4
vˆ
by using the Inverse
v1= 0.2 d1 =1
vˆ
d1=1 V1=0.2
V2=0.3 d2=2
v2= 0.3 d2 =2 v3= 0.5 d3 =4
vˆ = ? 7
Inverse Distance Square Example •
First of all, calculate the weights w1, w2, w3
Surface Mine Design
w1 = w2 = w3 =
•
1 12
1 12
1 12
+ + +
1 12 1 22 1 22 1 22 1 42 1 22
+ + +
1 42
1 42
1 42
=
1 21 16
=
16 21
=
1 4 21 16
4 = 21
=
1 16 21 16
=
Note:
w1 + w2 + w3 =
16 + 4 + 1 =1 21
1 21
Then, calculate vˆ vˆ =
16 4 1 × 0.2 + × 0.3 + × 0.5 = 0.233 21 21 21
8
Surface Mine Design
Geologic Block Modeling
d1
25
g1 25
d1 = 25 2 + 25 2 = 35.36 9
Geologic Block Modeling
Surface Mine Design
0.0008 0.0032
Block1 Centered on (X=37.5, Y=37.5)
X 12.5 62.5 37.5
Y 12.5 12.5 62.5
vi 0.42 0.24 0.41
x dist 25 -25 0
y dist 25 25 -25
di 35.35534 35.35534 25
1/di 2 0.0008 0.0008 0.0016 0.0032
wi wi*vi 0.25 0.105 0.25 0.06 0.5 0.205 1 0.37 (Estimated Grade)
n
1 ∑ 2 i =1 di
10
Geologic Block Modeling
Surface Mine Design
•
Using the estimated block values, one normally determines the overall estimated bench average grade of the copper ore at some cutoff, i.e, 0.7%Cu.
11
Geologic Block Model Reconciliation
Surface Mine Design
•
Determine the average grade of 75ft by 75ft grid blocks for the blasthole data set (blasthole2004.txt) by averaging the grades of 9 blast holes that fall within each block.
Block 1 Grade = (0.42+0.35+0.24+0.33+ … + 0.46) / 9 =0.35
12
Geologic Block Model Reconciliation
Surface Mine Design
•
Error estimation between estimation (Exploration data) and true value (Blasthole data). Error = Estimated Grade – True Grade
e.g., Estimation Error for Block 1 = 0.37 – 0.35 = 0.02
13
Geologic Block Model Reconciliation •
Histogram of Error (Example of 100ft x 100ft estimation) Bin FrequencyCumulative % -0.2 0 0.00% -0.15 0 0.00% -0.1 1 11.11% -0.05 1 22.22% 0 3 55.56% 0.05 3 88.89% 0.1 0 88.89% 0.15 0 88.89% 0.2 1 100.00% 0.25 0 100.00% More 0 100.00%
3.5
100.00% 90.00%
3
80.00% 2.5 Frequency
Surface Mine Design
Histogram of Estimation Errors (Estimation - True)
70.00% 60.00%
2
50.00% 1.5
40.00% 30.00%
1
20.00%
0.5
10.00%
0
0.00% -0.2 -0.15 -0.1 -0.05
0
0.05 0.1 Bin
0.15 0.2
0.25 More
Frequency Cumulative %
14
Geologic Block Model Reconciliation •
Scatter Graph (Example of 100ft x 100ft estimation) True grades agai n s t E s t i mated grades
Draw a diagonal line (y=x) to show perfect estimation line.
0.80 0.70 E s t i mated (%)
Surface Mine Design
0.90
0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 True (%)
15
Univariate Distribution of Errors
Surface Mine Design
• • •
Error = Estimated Value - True Value We also refer to these error as residuals. If error is positive, then we have overestimated the true; if error is negative, then we have underestimated the true. If m=0, then Unbiased Estimates Overestimates and underestimates are balanced. We typically prefer to have a symmetric distribution. 16
Univariate Distribution of Errors
Surface Mine Design
•
We would like to see the error distribution has small spread.
a)
• • •
b)
Both distributions are centered on 0 and are symmetric. The distribution shown in a), however, has error that span a greater range. Therefore, b) is better estimation than a). 17
Surface Mine Design
Over and Under Estimation
a)
b)
•
a) Negative mean: A general tendency towards the underestimation.
•
b) Positive mean: A general tendency towards the overestimation. 18
Scatter Diagrams in Estimation
True
Under Estimation at Low Grade
Estimation
Over Estimation at High Grade
Estimation
Estimation
Surface Mine Design
Good Estimation
True
True
Good Estimation: Falling closer to diagonal on which perfect estimates would plot. 19
Scatter Diagrams in Estimation Under Estimation at Low Grade
Estimation
Estimation
Surface Mine Design
Over Estimation at Low Grade
True
True
20
Surface Mine Design
Floating Cone Algorithm
Dr. Kadri Dagdelen
1
Basic Procedure
Surface Mine Design
Top -1
+1
-1
-1
-1
-1
-1
+3
-1
-1
Bottom Left
Right
-1 -1
-1 -1
-1
-1
Heuristic procedure 2
Floating Cone Steps
Surface Mine Design
• The cone is floated from left to right along the top row of blocks in the section. If there is a positive block it is removed. • Move to the second row. Start from the left and search for the first positive block. If the sum of all blocks falling within the cone is positive, the blocks are removed (mined). • Follow the floating cone process moving from left to right and top to bottom of the section until no more blocks can be removed. Then go back to the top again and repeat the process for a second iteration. If during a given iteration no positive blocks can be mined, stop. • The profitability of the mined area can be found by adding the values of the blocks that are to be removed. • Overall stripping ration can be determined by dividing the number of positive blocks by the total number of negative blocks.
3
Example
Surface Mine Design
-1
-1
-1
-1
-1
+1
-2
-2
+4
-2
-2
+7
+1
-3
-1
Ore
Waste
Initial Block Model
4
Example
Surface Mine Design
-1
-1
-1
-1
-1
+1
-2
-2
+4
-2
-2
+7
+1
-3
-1
Ore Waste Mined
Step 1
5
Example
Surface Mine Design
-1
-1
-1
-1
-1
+1
-2
-2
+4
-2
-2
+7
+1
-3
-1
Ore Waste Mined
Step 2
6
Example
Surface Mine Design
-1
-1
-1
-1
-1
+1
-2
-2
+4
-2
-2
+7
+1
-3
-1
Ore Waste Mined
Step 3
7
Example
Final Pit
Surface Mine Design
-1 -2 +1
-2
-3
8
Shortcomings Missing Combinations of Profitable Blocks
Surface Mine Design
-1
-1
-1
-1
-1
-1
-2
-2
-2
-2
-2
+10
-3
+10
-1
Ore
Waste
Initial Block Model
9
Shortcomings Missing Combinations of Profitable Blocks
Surface Mine Design
-1
-1
-1
-1
-1
-1
-2
-2
-2
-2
-2
+10
-3
+10
-1
Ore Waste Considered but rejected
Step 1
10
Shortcomings Missing Combinations of Profitable Blocks
Surface Mine Design
-1
-1
-1
-1
-1
-1
-2
-2
-2
-2
-2
+10
-3
+10
-1
Ore Waste Considered but rejected
Step 2 There are no blocks to be mined – wrong solution
11
Shortcomings Missing Combinations of Profitable Blocks
Surface Mine Design
-1
-1
-1
-1
-1
-1
-2
-2
-2
-2
-2
+10
-3
+10
-1
Ore Waste Mined (Correct solution)
Final Pit
-3
Correct solution 12
Shortcomings Over-mining
Surface Mine Design
-1
-1
-1
-1
+5
-2
-2
+5
-1
Ore
Waste
Initial Block Model
13
Shortcomings Over-mining
Surface Mine Design
-1
-1
-1
-1
+5
-2
-2
-1
+5
Ore Waste Mined
First block analyzed The search process was started from bottom to top. Everything is mined out. 14
Shortcomings Over-mining
Surface Mine Design
-1
-1
-1
-1
+5
-2
-2
-1
Ore Waste Mined
+5 Final Pit -1 -2
-1
-2
+5
Correct solution 15
Shortcomings Combination of problems
Surface Mine Design
-1
-1
-4
-1
+5
-4
+5
+3
-1
Ore
Waste
Initial Block Model
16
Shortcomings Combination of problems
Surface Mine Design
-1
-1
-4
-1
+5
-4
+5
+3
-1
Ore Waste Considered but rejected
First Step
17
Shortcomings Combination of problems
Surface Mine Design
-1
-1
-4
-1
+5
-4
+5
+3
-1
Ore Waste Considered but rejected
Second Step
18
Shortcomings Combination of problems
Surface Mine Design
-1
-1
-4
-1
+5
-4
+5
-1
+3
Ore Waste Mined
Wrong Solution Everything is mined out.
19
Shortcomings Combination of problems
Surface Mine Design
-1
-1
-4
-1
+5
-4
+5
+3
-1
Ore Waste Mined
Final Pit
-4 +3
Correct Solution 20
Surface Mine Design
Example Initial Data % recovery through mill and smelter Value of recovered copper Stripping and haulage to dump (level 1) Mining and transportation to plant level Haulage cost increase per ton per bench Processing, smelting and refining General overhead, administration, etc. Ultimate Pit Slope
90.00% $1.00 $0.50 $0.80 $0.10 $1.20 $1.20 1:1
per lb per ton per ton per ton/bench per ton per ton
21
Example Geologic Model
Surface Mine Design
0.00
1.15
0.08
0.05
0.00
0.00
0.00
1.25
1.15
1.13
0.00
1.13
1.15
0.50
0.05
Copper Grades (%)
22
Example Block Values
Surface Mine Design
P = Price s = Sales Cost
Ore Block:
c = Processing Cost
BV = ( P − s) * g B * y − c − m
y = Recovery m = Mining Cost gB = Block Grade
Waste Block:
BV = −m
BV = Block Value 23
Example Economic Model
Surface Mine Design
-0.50
17.50
-0.50
-0.50
-0.50
-0.50
-0.60
19.20
17.40
17.04
-0.60
16.94
17.30
-0.70
-0.50
Value per block ($/ton)
24
Example Economic Model
Surface Mine Design
-0.50
17.50
-0.50
-0.50
-0.50
-0.50
-0.60
19.20
17.40
17.04
-0.60
16.94
17.30
-0.70
-0.50
Value per block ($/ton) BV = (1 − 0) *1.15 / 100* 2000* 0.9 − 2.4 − 0.8 = 17.5
25
Example Economic Model
Surface Mine Design
-0.50
17.50
-0.50
-0.50
-0.50
-0.50
-0.60
19.20
17.40
17.04
-0.60
16.94
17.30
-0.70
-0.50
Value per block ($/ton) BV ($ / ton) = (1 − 0) * 0.0 / 100* 2000* 0.9 − 2.4 − 0.8 = −3.2 BV ($ / ton) = −0.6
If mined as ore
If mined as waste
26
Example Economic Model
Surface Mine Design
-1
18
-1
-1
-1
-1
-1
19
17
17
-1
17
17
-1
-1
Value per block ($/ton) Values rounded to the nearest $
27
Example Floating Cone Algorithm
-1
18
-1
-1
-1
-1
19
17
17
-1
17
17
-1
-1
Surface Mine Design
1
-1
1st Increment
28
Example Floating Cone Algorithm
-1
18
-1
Surface Mine Design
1
-1
-1
-1
-1
17
17
-1
17
-1
2
19 17
2
-1
2
2nd Increment
29
Example Floating Cone Algorithm
Surface Mine Design
-1
18 -1
1
-1
2
19
-1 17
2
17
2
-1 17
3
-1
-1
-1
3
17
-1
3rd Increment
30
Example Floating Cone Algorithm
Surface Mine Design
-1
18 -1
1
-1 19 17
2
2
-1
2
17
-1
3
17 3
17
-1
4
-1
-1 4
-1
4th Increment
31
Example Floating Cone Algorithm
-1
18
Surface Mine Design
5
-1 1
-1
5
-1 2
19
2
17
-1 2
17
-1 3
17 3
17
-1 4
-1 4
-1
5
5th Increment
32
Example Floating Cone Algorithm
-1
18
Surface Mine Design
5
-1 1
-1
5
-1 2
19
2
17
-1 2
17
17 3
17 5
-1 3
-1 4
-1 4
-1 6
6th Increment
33
Example Floating Cone Algorithm
Surface Mine Design
-1 -1 -1
Ultimate Pit Limit
34
Example Total Economic Value
Surface Mine Design
-5,000
175,000 -6,000
-5,000
-5,000
-5,000
-5,000
192,000 174,000 170,400 169,400 173,000
Value Per block considering: Tonnage/block = 10,000 tons
35
Example Pit Reserves
Surface Mine Design
Bench
Ore tons
Waste tons
S.R.
$
1 2 3
10,000 30,000 20,000
50,000 10,000 0
5.00 0.33 0.00
150,000 530,400 342,400
Total
60,000
60,000
1.00
1,022,800
36
Surface Mine Design
Manual Pit Design
Dr. Kadri Dagdelen
1
Manual Pit Design Stripping Ratio
Surface Mine Design
S .R.( Breakeven) =
Re cov ered Value ($ / ton) − Total Pr oduction Cost ($ / ton) Stripping Cost ($ / ton)
Surface or Underground Breakeven =
UG Mining Cost ($ / ton ) − Surface Mining Cost ($ / ton) Stripping Cost ($ / ton )
Surface or Underground Breakeven =
$5.04 / ore ton − $0.70 / ore ton = 6.58 : 1 $0.66 / waste ton)
2
Manual Pit Design Example
Surface Mine Design
Ore Grade (%Cu)
0.90
0.85
0.75
0.70
0.65
0.50
0.40
Conc. Recovery (%) Smelt. Recovery (%) Ref. Recovery (%)
0.900 0.980 0.990
0.900 0.980 0.990
0.900 0.980 0.990
0.900 0.980 0.990
0.900 0.980 0.990
0.900 0.980 0.990
0.900 0.980 0.990
Total Recovery (%)
0.873
0.873
0.873
0.873
0.873
0.873
0.873
15.7
14.8
13.1
12.2
11.3
8.7
7.0
Finance Mining Concentration Smelter Refining
0.62 0.70 2.68 1.70 1.80
0.62 0.70 2.68 1.48 1.57
0.62 0.70 2.68 1.38 1.36
0.62 0.70 2.68 1.29 1.27
0.62 0.70 2.68 1.21 1.20
0.62 0.70 2.68 1.19 1.16
0.62 0.70 2.68 1.18 1.12
Total cost ($/ton)
7.50
7.05
6.74
6.56
6.41
6.35
6.30
Stripping cost ($/ton)
0.66
0.66
0.66
0.66
0.66
0.66
0.66
Recovered Quantity (lb/ton) Costs per ton
Breakeven stripping ratio Copper Price ($/lb) 0.90 0.75 0.70 0.65
BESR = 10.07 6.50 5.31 4.12
9.56 6.19 5.06 3.94
15.7 lbs ∗ $0.90 / lb − $7.5 / ton of ore = 10.07 $0.66 / ton of waste 7.65 4.67 3.68 2.69
6.73 3.95 3.03 2.10
5.70 3.13 2.27 1.42
2.29 0.30 -0.36 -1.02
-0.02 -1.61 -2.14 -2.67
3
Manual Pit Design Stripping Ratio – Grade - Price S.R. - Ore Grades - Cu Prices 12.00
8.00 Stripping Ratio
Surface Mine Design
10.00
6.00
0.90 $/lb 0.75 $/lb 0.70 $/lb 0.65 $/lb
4.00 2.00 0.00 0.40 -2.00
0.50
0.60
0.70
0.80
0.90
-4.00 % Cu
4
Manual Pit Design Hypothetical Cross Section
Surface Mine Design
Topo X' X SR =
X' Y' SR = Y'
X Y
Orebody Y
A
B
5
Surface Mine Design
Manual Pit Design S.R. in Section First
First
X’ = 30
X = 10
Y’ = 5
Y=5
S.R. = 6
S.R. = 2
G = 0.67%
G = 0.48%
Second
Second
X’ = 39.6
X = 15
Y’ = 6
Y=3
S.R. = 6.6 (Breakeven)
S.R. = 5
G = 0.70%
G = 0.70%
Current Price = 0.90 $/lb
5 : 1 < 6.6 : 1 OK
6
Surface Mine Design
Manual Pit Design Repeat for All Sections
Pit contour or Final pit
7
Surface Mine Design
Cutoff Grade Optimization
Dr. Kadri Dagdelen
1
Surface Mine Design
Factors Influencing The Cutoff Grades •
As the Cutoff Grade increases in a given operation cash flow also increases
•
The ultimate adjustment of the dial is influenced by the available capacities in the mining system
•
The Cutoff Grade is not only function of economic parameters but also capacities of the mining system with respect to mining, milling and the market (refining)
2
What Is Cutoff Grade 1.
Surface Mine Design
2. 3. 4. 5.
Cutoff Grade is defined as the grade that is normally used to discriminate between ore and waste within a given deposit Cutoff Grade is the dial that is used to adjust the cash flow coming from the mining operations in a given year The Cutoff Grade policy allows a mining company to fine tune their operation with respect to a given financial objective The Cutoff Grade dial also controls how much ore is available to the mill from a given bench and how much of final product to be produced in a given period The overall influence of Cutoff Grade policy on the economics of an operation is profound 3
Surface Mine Design
Economic Objectives And The Cutoff Grade •
The cash costs related to mining, milling and refining along with the commodity price determines the lower limit to cutoff in a given period.
•
If the financial objective of the company is to maximize undiscounted profits, the cutoff grade should be lowered all the way down to process breakeven cutoff grade.
•
Processing every ton of ore that pays for itself will maximize the undiscounted profits for the operation.
4
Surface Mine Design
Economic Objectives And The Cutoff Grade (Cont.) •
If the financial objective of the company is to maximize the discounted profits that is Net Present Value (NPV), the Cutoff Grade in a given period has to be adjusted upwards to pay for the opportunity cost of mining low grade ore now while the higher grades are still available.
•
The mining rate, milling rate, the ultimate rate of production for the commodity being sold, and the production costs determine how far the cutoff grade has to be adjusted upwards to maximize the NPV.
5
Surface Mine Design
Ultimate Pit Cutoff •
Defined as the breakeven grade that equates cost of mining, milling and refining to the value of the block in terms of recovered metal and the selling price.
•
Any administrative overhead expense which would stop if mining were stopped must be included in the cost calculations.
•
Overhead costs should be divided between mining and processing. 6
Surface Mine Design
Ultimate Pit Cutoff
• • • • • •
Price (P) Sales Cost (s) Processing Cost (c) Recovery (y) Mining Cost (m) Overhead (Included in c and m )
$400/oz $5 /oz $ 10/ ton ore 90 % $ 1.20/ ton
7
Surface Mine Design
Ultimate Pit Cutoff Milling Cost + Mining Cost gm = (Pr ice − Sales Cost ) * Re cov ery $10 + $1.2 gm = = 0.0315 oz / ton ($400 − $5) * 0.9 8
Surface Mine Design
Milling Cutoff •
Defined as the breakeven grade that equates cost of milling and refining to the value of the block in terms of recovered metal and the selling price.
•
Any administrative overhead expense which would stop if mining were stopped must be included in the cost calculations.
9
Surface Mine Design
Milling Cutoff Milling Cost gc = (Pr ice − Sales Cost ) * Re cov ery $10 gc = = 0.0281 oz / ton ($400 − $5) * 0.9 10
Surface Mine Design
Block Value Block Grade = gB if gc < gm < gB then Block Value = (P-S)* gB * y – c – m Else if gB Block Value = -m
<
gm
<
gc then
11
Surface Mine Design
Block Value Block Grade = gB if gc < gB < gm then Block contains marginal ore.
•
Marginal ore pays for processing cost but not for mining cost.
12
Block Value Calculation Example
Surface Mine Design
a)
Ore Block Block grade = gB = 0.11 oz/ton gc < gm < gB 0.0281 < 0.0315 < 0.11 Block Value = (P-S)* gB * y – c – m Block Value = (400 - 5)*0.11*0.9 - 10 - 1.20 = $27.9/ton of block 13
Surface Mine Design
Block Value Calculation Example b) Waste Block Block Grade = gB = 0.01 oz/ton gB < gc < gm 0.01 < 0.0281 < 0.0315 therefore Block Value = - $1.20/ton = Mining Cost 14
Surface Mine Design
Mine Design Parameters For The Case Study • • • • • • • • • •
Price (P) Sales Cost (s) Processing Cost (c) Recovery (y) Mining Cost (m) Fixed Costs (fa) Mining Capacity (M) Milling Capacity (C) Capital Costs (CC) Discount Rate (d)
$600/oz $5 /oz $ 19/ ton ore 90 % $ 1.20/ ton 8.35 M/year Unlimited 1.05 M 105 M 15%
15
Surface Mine Design
Calculation of Ultimate Pit Cutoff Grade Milling Cost + Mining Cost gm = (Pr ice − Sales Cost ) * Re cov ery $19 + $1.2 gm = = 0.038 oz / ton ($600 − $5) * 0.9 16
Surface Mine Design
Calculation of Milling Cutoff Grade Milling Cost gc = (Pr ice − Sales Cost ) * Re cov ery $19 gc = = 0.035 oz / ton ($600 − $5) * 0.9 17
Grade Tonnage Distribution
Surface Mine Design
Grade Interval 0.000 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.100
-
0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.100 0.358
KTons 70,000 7,257 6,319 5,591 4,598 4,277 3,465 2,428 2,307 1,747 1,640 1,485 1,227 3,598 9,576
Avg. Interval Grade 0.0100 0.0225 0.0275 0.0325 0.0375 0.0425 0.0475 0.0525 0.0575 0.0625 0.0675 0.0725 0.0775 0.0900 0.2290
KTons
Grade
89,167
Waste Cutoff Grade 0.035 Ore
36,348
0.1023 Oz/ton
18
Constant Cutoff Grades. Yearly Tons and Grade Schedules. Table 3
Surface Mine Design
Year 1 2 3 4 5 6 7 8 9 10 For 11 to 34 35 TOTAL
Cutoff Grade 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035
Avg Grade 0.102 0.102 0.102 0.102 0.102 0.102 0.102 0.102 0.102 0.102 0.102 0.102 0.102
QM
Qc
Qr
3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.4 125.8
1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.00 36.70
96.3 96.3 96.3 96.3 96.3 96.3 96.3 96.3 96.3 96.3 96.3 91.7 3365.9
Profits $M/year 33.0 33.0 33.0 33.0 33.0 33.0 33.0 33.0 33.0 33.0 33.0 31.4 1154.2 NPV $M 218.5 19
Profit
Surface Mine Design
Profits ($M) = (P – s ) x Qr – Qc x c – Qm x m P S Qm Qc Qr c m
– Price – Sales Cost – Total Material Mined – Ore Tonnage Processed By The Mill – Recovered Ounces – Milling Costs ($/ton) – Mining Costs ($/ton) 20
Surface Mine Design
Shortcomings of the traditional cutoff grades •
They are established to satisfy the objective of maximizing the undiscounted profits from a given mining operation.
•
They are constant unless the commodity price and the costs change during the life of mine AND
•
They do not consider grade distribution of the deposit.
21
Traditional
Surface Mine Design
Milling Cost + Depreciati on + Minimum Pr ofit gc = (Pr ice − Sales Cost ) * Re cov ery
$19 + $10 + $3 gc = = 0.060 oz / ton ($600 − $5) * 0.9
22
Surface Mine Design
Nontraditional ???????? Milling Cost + Depreciation gc = (Pr ice − Sales Cost ) * Re cov ery $19 + $10 gc = = 0.054 oz / ton ($600 − $5) * 0.9
23
Constant Cutoff Grades Yearly Tons and Grade Schedules Table 4
Surface Mine Design
Year 1 2 3 4 5 6 7 8 9 10 For 11 to 27 28 TOTAL
Cutoff Grade 0.060 0.060 0.060 0.060 0.060 0.054 0.054 0.054 0.054 0.054 0.035 0.035 0.035
Avg Grade 0.153 0.153 0.153 0.153 0.153 0.141 0.141 0.141 0.141 0.141 0.102 0.102 0.102
Qm
Qc
Qr
6.90 6.90 6.90 6.90 6.90 6.00 6.00 6.00 6.00 6.00 3.60 0.30 125.80
1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 0.09 28.44
144.60 144.60 144.60 144.60 144.60 132.80 132.80 132.80 132.80 132.80 96.30 8.10 3032.10
Profits $M/year 57.8 57.8 57.8 57.8 57.8 51.9 51.9 51.9 51.9 51.9 33.0 2.8 1112.7 NPV $M 355.7
24
Surface Mine Design
Declining Cutoff Grades Milling Cost + Depreciation + Fixed Cost gc = (Pr ice − Sales Cost ) * Re cov ery
$19 + $10 + $7.95 gc = = 0.069 oz / ton ($600 − $5) * 0.9
25
Surface Mine Design
Declining Cutoff Grades Milling Cost + Fixed Cost gc = (Pr ice − Sales Cost ) * Re cov ery $19 + $7.95 gc = = 0.050 oz / ton ($600 − $5) * 0.9
26
Declining Cutoff Grades
Surface Mine Design
Milling Cost + Depreciation + Minimum Pr of . + Fixed Cost gc = (Pr ice − Sales Cost ) * Re cov ery
$19 + $10 + $3 + $7.95 gc = = 0.075 oz / ton ($600 − $5) * 0.9
27
Surface Mine Design
Declining Cutoff Grades
Milling Cost gc = (Pr ice − Sales Cost) * Re cov ery
$19 gc = = 0.035 oz / ton ($600 − $5) * 0.9
28
Surface Mine Design
Declining Cutoff Grades Yearly Tons and Grade Schedules. Table 5 Year
Cutoff Grade
Avg Grade
QM
Qc
Qr
**Profits $M/year
1 2 3 4 5 6 7 8 9 10 For 11 to 17 18
0.075 0.075 0.075 0.075 0.075 0.069 0.069 0.069 0.069 0.069 0.050 0.050
0.182 0.182 0.182 0.182 0.182 0.169 0.169 0.169 0.169 0.169 0.132 0.132
9.2 9.2 9.2 9.2 9.2 8.2 8.2 8.2 8.2 8.2 5.4 1.3
1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 0.26
171.6 171.6 171.6 171.6 171.6 160.0 160.0 160.0 160.0 160.0 124.8 30.5
62.8 62.8 62.8 62.8 62.8 57.1 57.1 57.1 57.1 57.1 39.5 9.6
125.8
18.11
2562.5
885.6 NPV $M 357.7
TOTAL
**Profits ($M)= (P-s) x Qr – Qc x c – Qm x m – f a
29
Surface Mine Design
Cutoff Grade Optimization Determination Of Optimum Cutoff Grades When The Mill Is Bottleneck
30
Surface Mine Design
Formula for Optimum Cutoff Grade c + f + Fi gc (i) = (P − S ) * y
• Where Fi = d x NPVi /C f = fa/C and fa is annual fixed costs 31
Surface Mine Design
Optimum Cutoff Grades Yearly Tons and Grade Schedules Table 6 Year
Cutoff Grade
Avg Grade
QM
Qc
Qr
**Profits $M
NPV $M
1 2 3 4 5 6 7 8 9
0.161 0.152 0.142 0.131 0.120 0.107 0.092 0.079 0.065
0.259 0.255 0.250 0.245 0.239 0.232 0.213 0.188 0.163
18.0 17.2 16.5 15.7 14.9 14.1 12.1 9.8 7.6
1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05
245.2 241.0 236.4 231.3 225.7 219.6 200.9 177.9 153.6
95.9 94.4 92.6 90.5 88.1 85.4 76.7 65.9 53.9
413.8 380.0 342.6 301.4 256.1 206.4 152.0 98.1 46.9
125.8
9.45
1931.4
743.4 NPV $M 413.8
TOTAL
**Profits ($M)= (P-s) x Qr – Qc x c – Qm x m – f a 32
Summary
Surface Mine Design
Avg Grade
Total Amount mined Qm
Total Amount processed Qr
Strip Ratio
Profits
NPV
$M
$M
Life Undiscounted % Reduction INC CUM yrs
NPV % Increase INC CUM
Traditional
0.102
125.8
36.70
2.43
4453.4
218.5
35
n/a
n/a
n/a
n/a
Heuristic (Depr)
0.125
125.8
28.44
3.42
1127.4
355.7
28
3.6
3.6
63.0
63.0
Heuristic (Depr and Fixed Costs)
0.164
125.8
18.11
5.95
885.6
357.1
18
20.4
23.3
0.3
63.4
Lanes's Approach
0.235
125.8
9.45
12.31
743.4
413.8
9
16.0
35.6
15.9
89.0
33
Surface Mine Design
Cutoff Grade Optimization One Constraint Cutoff Grade Optimization Algorithm
34
Surface Mine Design
Steps Of The Algorithm 1.
Start with Grade-Tonnage Curve.
2.
Define: P - Price C - Milling Capacity s - Marketing Costs m - Mining Costs c - Milling Costs fa - Fixed Costs d - Discount Rate 35
Steps Of The Algorithm (Cont.)
Surface Mine Design
3. Determine the cutoff grade gc for year (i).
c + f + Fi gc (i) = (P − S ) * y
• Where Fi = d x NPVi /C f = fa/C and fa is annual fixed costs 36
Surface Mine Design
Steps Of The Algorithm (Cont.)
4.
For Cutoff Grade gmilling (i):
•
Determine Ore Tonnage Tc and Grade gc
•
Determine the Waste Tonnage Tw
•
Stripping Ratio (sr) = T w/Tc 37
Steps Of The Algorithm (Cont.)
Surface Mine Design
5.
Set Qc = C Qc = T c
if Tc > C if Tc < C
And Qm = Qc(1+sr) 38
Steps Of The Algorithm (Cont.)
Surface Mine Design
6. Determine the annual profit (Pi) by using the following equation Pi =(P-s) x Qc x gc x y – Qc x (c + f) – Qm x m P - Price s - Marketing Costs Qm - Total material mined Qc - Ore tonnage processed by the mill c - Milling Costs ($/ton) m - Mining Costs ($/ton) gc - Average Grade (Opt) y - Recovery f - Fixed Cost ($/ton)
39
Surface Mine Design
Steps Of The Algorithm (Cont.) 7. Adjust the Grade-Tonnage Curve of the deposit for Qc and Qw = Qm – Qc . 8. If Qc < C in year (i) go to step 9 otherwise Set i = i+1 and go to Step 3.
40
Steps Of The Algorithm (Cont.)
Surface Mine Design
9.
Calculate incremental NPV for each year (i) N
NPVi = ∑ j =i
Pj (1 + d )
j −i +1
41
Surface Mine Design
Steps Of The Algorithm (Cont.) 10. If NPV1 for this iteration is not within some tolerance (say plus-minus $500K ) on the NPV1 of the previous iteration go to Step 1 otherwise Stop the cutoff grade gc (i) for years i = 1, 1 N is Optimum Policy.
42
Surface Mine Design
Open Pit Sequencing and Production Scheduling
Dr. Kadri Dagdelen
Surface Mine Design
Open pit production scheduling • It is a timed sequence of extraction of the ore and waste within the ultimate pit limits from the initial condition of the deposit up to a predetermined stage that mat be referred to as an intermediate of final pit limit.
• It sets the relationship between quantity and quality of the material to be mined, time, geometry of the orebody, and the available resources.
2
Declining Stripping Ratio Method 1
Surface Mine Design
2
1
2 3
2
3 4
3
4 5
4
5 6 7
6 7
5
Stripping Volume
1
6 7
Time
Orebody Waste
3
Surface Mine Design
Increasing Stripping Ratio Method
Orebody Waste
4
Surface Mine Design
Constant Stripping Ratio Method
Orebody Waste
5
Surface Mine Design
Long Term Production Scheduling •Long term production scheduling is usually carried out from the initial condition of the deposit (i.e. initial topography) to the ultimate pit limit, in periods of at least one year. •Its purpose is to determine ore reserves, stripping ratios, future investments, and to conserve and develop owned resources. •Long term production scheduling takes into account capital availability, geometry and grade distribution of the orebody, metallurgical and physical properties of the material, as well as environmental and legal constraints. 6
Short Term Production Scheduling
Surface Mine Design
•Short term production scheduling is concerned with schedules on a daily, weekly or monthly basis. •Its main objective is to furnish the requirements of the processing plant with ore of uniform quality to ensure operating efficiency. •To accomplish this objective, short term production scheduling has to comply with restrictions imposed by the long term plan, equipment availability, blending of different materials from different sites within the mine, and the availability of exposed ore. 7
Surface Mine Design
Objectives in Open Pit Mine Planning • To ensure the tonnage required by the processing plant in order to operate efficiently and to produce the expected amount of concentrate per mining period. • To meet the grade specifications at the processing plant within a given range for each ore parameter that has an effect on the operating costs or the quality of the final product.
8
Surface Mine Design
Objectives in Open Pit Mine Planning (cont.) • To minimize the pre-production stripping volume required to expose enough ore at the beginning of the mine life in order to ensure a continuous operation.
• To defer waste stripping as long as possible to maximize cash flow in the early years of the operation.
9
Surface Mine Design
Objectives in Open Pit Mine Planning (cont.) • To ensure a feasible schedule in terms of mining practice. This implies mining exposed material sequentially, keeping appropriate mining widths, maintaining access to the mining areas, and maintaining stable pit walls.
• To ensure the schedule is compatible with the remaining periods. In other words, the present schedule must ensure the feasibility of the future extraction.
10
Objectives in Open Pit Mine Planning (cont.)
Surface Mine Design
• To mine the orebody in such a way that for each year the cost to produce a given kilogram of metal is at minimum. • To develop an achievable start-up schedule with respect to manpower training, equipment deployment, infrastructure and logistical support in order to ensure positive cash flow as planned. • To have enough exposed ore at the beginning of each scheduling period to offset any problem that could arise in the case of underestimation of ore tonnages and grades in the reserves model. 11
Surface Mine Design
Objectives in Open Pit Mine Planning (Cont.) • To maximize design pit slope angles in response to adequate geotechnical investigations, and yet through careful planning minimize the adverse impacts of any slope instability, should it occur. • To properly examine the economic merits of alternative ore production rate and cutoff grade scenarios. • To thoroughly subject the proposed mining strategy, equipment selection, and mine development plan to “what if” contingency planning, before a commitment to proceed is made. 12
Pit Sequence Planning
Surface Mine Design
• Orebodies are normally mined in stages, so as to defer waste stripping and maximize the net present value of the surface mining venture. • These stages are commonly called sequences, expansions, phases, working pits, slices, or pushbacks. • They are the basic building block on which more detailed time period planning is subsequently made. • Phase planning should commence with mining that portion of the orebody which will yield the maximum cash flow and then proceed to mine other stages of lessening cash flow. 13
Procedure to obtain the pushbacks • Generate nested pits by increasing and/or decreasing Surface Mine Design
the product price. • According to the size of the deposit, pick a number of phases that allow enough operating room for the equipment.
14
Surface Mine Design
Example of how to obtain the pushbacks •% Recovery through mill and smelter
90%
•Value of recovered copper
$1.10/lb
•Stripping and haulage to dump (level 1)
$0.50/ton
•Mining and transportation to plant level
$0.80/ton
•Haulage costs increase per bench
$0.10/ton
•Processing, smelting and refining
$1.20/ton
•General overhead, administration, etc. (ore blocks only)
$1.20/ton
•Ultimate pit slope
1:1
15
Example of how to obtain the pushbacks (Cont.)
Surface Mine Design
Block Model showing copper grades in % Level 1 0.00 2 0.00 3 0.05 4 0.04 5 0.05 6 0.08
0.10 0.22 0.05 0.15 0.08 0.10
0.15 0.08 0.12 0.12 0.15 0.08
0.08 0.25 0.13 0.45 0.12 0.01
0.05 0.15 0.02 0.08 0.30 0.05
0.00 0.13 0.14 0.09 0.21 0.34
0.00 0.10 0.11 0.25 0.09 0.45
0.05 0.13 0.08 0.20 0.79 0.02
0.03 0.45 0.22 0.29 0.10 0.01
0.00 0.20 0.09 0.14 0.45 0.04
0.05 0.20 0.08 0.15 0.32 0.38
0.05 0.32 0.15 0.04 0.23 0.00
0.05 0.10 0.22 0.24 0.01 0.00
0.05 0.15 0.20 0.05 0.01 0.00
0.05 0.24 0.14 0.02 0.01 0.01
0.05 0.21 0.05 0.04 0.01 0.15
16
Example of how to obtain the pushbacks (Cont.) Economic Model showing block values in $/ton
Surface Mine Design
Original copper price of $1.10/lb 1 2 3 4 5 6
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 1.06 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 1.65 -0.70 5.41 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 2.34 -1.00
-0.50 -0.60 -0.70 -0.80 0.56 3.03
-0.50 -0.50 -0.50 -0.60 -0.60 5.61 -0.70 -0.70 0.96 1.45 0.46 2.24 -0.90 12.04 -0.90 5.21 -1.00 -1.00
-0.50 0.66 -0.70 -0.80 5.31 -1.00
-0.50 0.66 -0.70 -0.80 2.74 3.82
-0.50 3.04 -0.70 -0.80 0.95 -1.00
-0.50 -0.60 0.96 1.25 -0.90 -1.00
-0.50 -0.60 0.56 -0.80 -0.90 -1.00
-0.50 1.45 -0.70 -0.80 -0.90 -1.00
-0.50 0.86 -0.70 -0.80 -0.90 -1.00
For ore blocks: BV = ( P − s ) * g B * y − c − m
For waste blocks: BV = − m
17
Example of how to obtain the pushbacks (Cont.)
Surface Mine Design
The floating cone algorithm was used to find the ultimate pit limit 1 2 3 4 5 6
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 1.06 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 1.65 -0.70 5.41 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 2.34 -1.00
-0.50 -0.60 -0.70 -0.80 0.56 3.03
-0.50 -0.60 -0.70 1.45 -0.90 5.21
-0.50 -0.50 -0.50 -0.50 -0.50 -0.60 5.61 0.66 0.66 3.04 -0.70 0.96 -0.70 -0.70 -0.70 0.46 2.24 -0.80 -0.80 -0.80 12.04 -0.90 5.31 2.74 0.95 -1.00 -1.00 -1.00 3.82 -1.00
-0.50 -0.60 0.96 1.25 -0.90 -1.00
-0.50 -0.60 0.56 -0.80 -0.90 -1.00
-0.50 1.45 -0.70 -0.80 -0.90 -1.00
Pit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-0.50 0.86 -0.70 -0.80 -0.90 -1.00
The ore block left at the right cannot be mined due to slope constraints. All ore blocks are mined in the first iteration. 1 2 3 4 5 6
18
Example of how to obtain the pushbacks (Cont.)
Surface Mine Design
To find a smaller pit reduce the copper price to 0.60/lb Economic block model 1 2 3 4 5 6
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 1.36 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 1.16
-0.50 -0.60 -0.70 -0.80 4.93 -1.00
-0.50 1.56 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 1.26 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 0.40
-0.50 0.16 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
For ore blocks: BV = ( P − s ) * g B * y − c − m
For waste blocks: BV = − m
19
Example of how to obtain the pushbacks (Cont.)
Surface Mine Design
The floating cone algorithm was used to find the limit of the pit at $0.60/lb 1 2 3 4 5 6
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 1.36 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 1.16
-0.50 -0.60 -0.70 -0.80 4.93 -1.00
-0.50 1.56 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 1.26 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 0.40
-0.50 0.16 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
1 2 3 4 5 6
20
Example of how to obtain the pushbacks (Cont.)
Surface Mine Design
To find an intermediate pit reduce the copper price to $0.86/lb Economic Block Model 1 2 3 4 5 6
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 0.11 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 0.57 -0.70 3.47 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 1.04 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 1.56
-0.50 -0.60 -0.70 0.37 -0.90 3.27
-0.50 -0.60 -0.70 -0.80 8.63 -1.00
-0.50 3.67 -0.70 0.99 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 3.37 -1.00
-0.50 -0.60 -0.70 -0.80 1.35 2.18
-0.50 1.65 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 0.22 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 0.42 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
21
Example of how to obtain the pushbacks (Cont.)
Surface Mine Design
To find an intermediate pit reduce the copper price to $0.86/lb Economic Block Model 1 2 3 4 5 6
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 0.11 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 0.57 -0.70 3.47 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 1.04 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 1.56
-0.50 -0.60 -0.70 0.37 -0.90 3.27
-0.50 -0.60 -0.70 -0.80 8.63 -1.00
-0.50 3.67 -0.70 0.99 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 3.37 -1.00
-0.50 -0.60 -0.70 -0.80 1.35 2.18
-0.50 1.65 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 0.22 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
-0.50 0.42 -0.70 -0.80 -0.90 -1.00
-0.50 -0.60 -0.70 -0.80 -0.90 -1.00
Pit 1 2 3
The ore block left at the right cannot be mined due to slope constraints. All ore blocks are mined in the first iteration. 1 2 3 4 5 6
22
Example of how to obtain the pushbacks (Cont.)
Surface Mine Design
The three pits shown in together 1 2 3 4 5 6
$0.60/lb $0.86/lb $1.10/lb
23
Hypothetical Deposit and Pit Development Sequence Ultimate Pit
Surface Mine Design
Design Phase Limits
Rock Type I
Rock Type II
F
C
B
A
D E
Ore
24
Tonnage Inventory by Phase Thousands of tonnes
Surface Mine Design
Bench 5100 5050 5000 4950 4900 4850 4800 4750 4700 4650 4600 4550 Total
Phase "A" Waste Ore 15,000 32,000 50,000 38,000 15,000 4,000 10,000 3,000 9,000 2,000 8,000
159,000
27,000
Phase "B" Waste Ore
2,000 18,000 20,000 15,000 4,000 3,000 2,000 1,000
9,000 9,000 7,000 6,000
65,000
31,000
Phase "C" Waste Ore
4,000 15,000 18,000 22,000 16,000 3,000 5,000 8,000 3,000 1,000 95,000
10,000 20,000 22,000 17,000 7,000 76,000 25
Summary by Phase
Surface Mine Design
Thousands of tonnes Waste above Waste on Phase first ore ore Ore bench benches A 150,000 9,000 27,000 B 55,000 10,000 31,000 C 75,000 20,000 76,000 D 128,000 38,000 125,000 E 182,000 49,000 151,000 F 220,000 45,000 130,000 Total 810,000 171,000 540,000 *Assuming an annual milling rate 0f 25,000 tonnes
Ore Cumulative Life* ore life (years) (years) 1.08 1.08 1.24 2.32 3.04 5.36 5.00 10.36 6.04 16.40 5.20 21.60 21.60
26
Time (Years) -10 250
-5
0
5
10
15
Phase "D" ore = 125 M tonnes Phase "D" life = 5 years It requires 128 M tonnes stripping
25
Earlier ore development due to the proposed stripping schedule
Hypothetical Deposit and Pit Development Sequence
200
D
100
150
E
C
F
D
50
100
B C
31
0 -10
A
-5
0
3.04
27
B
1.08
50
76
A
1.24
Developed Ore (Millions of tonnes)
20
5
0
Cumulative Stripping (Millions of tonnes)
Surface Mine Design
1000 500
- Production period 50 M tonnes / year
F
A proposed stripping schedule - Pre-production period 4 yrs. Yr 1 25 M 2-3 50 M 4 75 M 200 M
750 E
500 D C
250
0
75 A
50
Minimum waste stripping required to sustain ore deliveries
Pre-production Period
5 10 Time (Years)
15
C
B
200
50 25
0 -5
1 50
250
B A
0 -10
A proposed stripping schedule - Pre-production period 4 yrs. Yr 1 25 M 2-3 50 M 4 75 M 200 M - Production period 50 M tonnes / year
D
20
25
-10
-5
1
2 3
4 0
5
Pre-production Period
27
-10
Time (Years) 0
-5
5
10
Earlier ore development due to the proposed stripping schedule
Phase "D" ore = 125 M tonnes Phase "D" life = 5 years It requires 128 M tonnes stripping
E
150
Developed Ore (Millions of tonnes)
D Cushion = 0.34 years
100
C
Cushion = 0.80 years
125
Cushion = 0.66 years
50
B
76
A 31
27
0 3.04 1.24
5.00
750 E
Cumulative Stripping (Millions of tonnes)
Surface Mine Design
1.08
500
- Production period 50 M tonnes / year D
250
- Pre-production period 4 yrs. Yr 1 25 M 2-3 50 M 4 75 M 200 M
C B
75
A
50 50
0 -10
Minimum waste stripping required to sustain ore deliveries
25
-5
1 2 3 40 Pre-production Period
5 10 Time (Years)
28
Period 2 $72M
Period 1 $81M
Period 1 $50M Period 8 $9M
Period 3 $63M Period 4 $61M Period 7 $43M
Period 5 $37M
Period 6 $32M
Period 2 $37M Period 7 $52M Period 8 $19M
($398M)
Period 4 $50M
Period 3 $60M Period 5 $49M
Period 6 $50M
($366M) Period 4 $65M
Period 1 $46M
Period 2 $32M
Period 2 $42M Period 3 $63M Period 5 $51M
($374M)
Period 3 $71M Period 7 $43M Period 8 $16M Period 6 $48M
Period 1 $42M Period 7 $57M Period 8 $11M
Period 4 $51M Period 5 $57M Period 6 $52M
($372M)
Long Term Planning and Sequencing
Surface Mine Design
Dr. Kadri Dagdelen Colorado School of Mines
Long Term Planning and Sequencing
Surface Mine Design
• • • •
Objective is to determine the suitability of the limestone resource for the subsequent processing by the cement plant Life of mining and reclamation plans Equipment Selection Facility layout and Permitting
2
Long Term Planning and Sequencing
Surface Mine Design
• Create a geologic model
• Define structural domains and stratigraphy • Chemistry • Long and short term variability
• Long term reserves and average chemistry • Estimate the block chemical values • Estimate possible raw mix requirements
• Quarry layout and operational plan yearly mine plans 3
Surface Mine Design
Long Term Planning and Sequencing
• Determine mineable resource boundaries • Haul road layout • Define long term reclamation needs
4
Surface Mine Design
Midlothian Cement Quarry: Case Study • Current production 1.8 million tons of limestone • One 50ft to 60ft bench operation • In pit crushing - 1000 ton/per hour capacity • Expand the capacity to 3.6 million tons by bringing • •
the second bench into production 50 percent of the production from first 50ft bench and another 50 percent from the second bench. %SO 3 is not very good for the limestone coming from the second bench. Blending of these two benches are necessary. 5
Midlothian Cement Quarry: Case Study
Surface Mine Design
• Quarry currently operates 10 hours per shift, • • •
5 days per week 1000 ton per hour Krubb In Pit Crusher 2000 ft long main movable belt conveyor with 500 ft long extension belt Komatsu 14 and 10 cubic yard loaders
6
Midlothian Cement Quarry: Case Study
Surface Mine Design
• Determine next 50 years life of mine plans • Sequencing plan to come up with the right •
blend limestone that meets the minimum of %1.3 SO3 requirements Determine equipment and capital investment needs for the next 10 years
7
Surface Mine Design
Quarry Development and Sequencing
8
Surface Mine Design
Holnam Quarry Mining Sequence: First Bench Development
9
Surface Mine Design
Holnam Quarry Mining Sequence: Second Bench Development During the First Three Years
10
Surface Mine Design
Holnam Quarry Mining Sequence: First and Second Bench Development
11
Surface Mine Design
Holnam Quarry Mining Sequence: First and Second Bench Development
12
Surface Mine Design
Holnam Quarry Mining Sequence: First and Second Bench Development
13
Surface Mine Design
Midlothian North Area Quarry Progress Contours Year1
14
Surface Mine Design
Midlothian North Area Quarry Progress Contours Year 2
15
Surface Mine Design
Midlothian North Area Quarry Progress Contours Year 3
16
Surface Mine Design
Midlothian North Area Quarry Progress Contours Year 4
17
Surface Mine Design
Midlothian Quarry Block Model Definition
18
Surface Mine Design
Midlothian Quarry Block Model Definition
19
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 790
20
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 780
21
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 770
22
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 760
23
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 750
24
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 750
25
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 730
26
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 720
27
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 700
28
Surface Mine Design
Midlothian Quarry Sequence: One Year Increments on Elevation 690
29
Equipment Selection Three Different Options were Evaluated: Surface Mine Design
• One 15 yd3 Caterpillar 992G model loader working • •
with a 70 ton CAT 775D truck fleet. One 15 yd3 Caterpillar 992G model loader working with a 98 ton CAT 777D truck fleet. One 11 yd3 Caterpillar 990series II model loader working with a 70 ton CAT 775D truck fleet
30
Surface Mine Design
Loader - Truck Fleet Evaluation and Cost Analysis Year 1
31
Surface Mine Design
Loader - Truck Fleet Evaluation and Cost Analysis Year 2
32
Surface Mine Design
Loader - Truck Fleet Evaluation and Cost Analysis Year 3
33
Surface Mine Design
Loader - Truck Fleet Evaluation & Cost Analysis Haul Road Profile
34
Loader - Truck Productivity Calculations Assumptions Surface Mine Design
• 90 % Loader and truck availability resulting • • • •
in 81 % fleet availability 92 % Operator efficiency 75 % bucket fill factor 2400 scheduled hrs 0.55 min. loader cycle time 35
Loader - Truck Productivity Calculations
Surface Mine Design
Assumptions (Cont.)
• 0.1 min. first bucket dump time • 0.7 min. hauler exchange time • 2492 lbs/yd3 density • 14 ton/pass; 5 passes per truck • 2400 hours per year 36
Surface Mine Design
Equipment Productivity & Cost Estimation
• For CAT 992G Loader - 775D Trucks
37
Option 1: Cat 992G Loader 775D Trucks
Surface Mine Design
The truck cycle time for four different conditions:
• Year 1: 9.67 minutes • Year 2: 11.05 minutes • Year 3: 10.86 minutes • Year 7: 11.04 minutes 38
Surface Mine Design
Option 1: Cat 992G Loader - 775D Trucks Fleet Productivity in Tons # of 775D's 1 2 3 4
Year 1 Year 2 Year 3 Year 7 825,332 808,107 801,532 808,669 1,540,565 1,524,899 1,504,316 1,525,959 2,111,530 2,108,190 2,070,839 2,109,657 2,586,695 2,644,575 2,580,165 2,644,575
39
Option 2: Cat 992G Loader 777D Trucks
Surface Mine Design
The truck cycle time for four different conditions
• Year 1: 12.16 minutes • Year 2: 12.63 minutes • Year 3: 12.42 minutes • Year 7: 12.27 minutes 40
Surface Mine Design
Option 2: Cat 992G Loader 777D Trucks # of 777's 1 2 3 4
Year 1 945,127 1,731,661 2,285,652 2,737,983
Year 2 903,286 1,667,466 2,234,289 2,714,476
Year 3 920,644 1,695,274 2,254,834 2,724,550
Year 7 934,223 1,715,981 2,275,379 2,731,266
41
Surface Mine Design
Operating Cost for the Loader and Trucks Model Operating Cost CAT 992G $125/hr CAT 775 D $63/hr CAT 777 $82/hr
42
Surface Mine Design
Operating Cost for the Loader and Trucks Model Operating Cost CAT 992G $125/hr CAT 775 D $63/hr CAT 777 $82/hr
43
Surface Mine Design
Loader - Truck Capital Requirements Model Purchase Price CAT 992G $1,270,000 CAT 775 D $740,000 CAT 777 $1,060,000 44
Loader - Truck Capital Requirements
Surface Mine Design
• At the start of the production from bench • •
two, $2.1 M is needed to purchase 1 Cat 992G Loader and 775D truck. In year 2, additional $1.5M is needed to purchase 2 more Cat 775D trucks. For the Cat 992G loader, Cat 777D truck combination, $2.35M and $2.12M would be needed at the start and beginning of year 2. 45
Loaders and Shovels
Surface Mine Design
Comparative Analysis Dr. Kadri Dagdelen Colorado School of Mines Source: J. Wiebmer, Caterpillar Incorporated
Surface Mine Design
Hydraulic Shovel Applications
• Hard Digging • Poorly shoot material • Selective loading • Wet, jagged floor • Pitching floor • Single face operation 2
Hydraulic Shovel Selection Considerations
Surface Mine Design
• Multiple loading fronts • Fast cycle time (25 to 30 • • •
seconds) Low capital costs Moderate mobility Highly productive
3
Surface Mine Design
Hydraulic Shovel Favorable Site Conditions
• Single loading face • Tight digging materials • Face height equals to stick • •
length Some will dig below and above Soft floors 4
Surface Mine Design
Hydraulic Shovel Unfavorable Site Conditions
• Requires clean-up support • Excessive tramming • High benches
5
Surface Mine Design
Wheel Loader Applications
• Mobility and versatility • Well blasted material • Low pile profile • Smooth, level floor • No clean-up support equipment • Short mine life 6
Surface Mine Design
Wheel Loader Selection Considerations
• Highly mobile/versatile • High bucket fill factors • Low capital costs • No clean-up support
7
Surface Mine Design
Wheel Loader Favorable Site Conditions
• Good loading materials • Lower face profile • Multi-face loading
8
Surface Mine Design
Wheel Loader Unfavorable Site Conditions • Poor underfooting (tire cost) • Soft floor • Tight load area
9
Comparison Shovels vs. Loaders
Surface Mine Design
Hydraulic Shovel Wheel Loader % Operating Weight as bucket payload
8-11%
18-21%
Cost/CY of capacity ($1000)
100-120
60-80
Economic life (1000 hours)
30-60
30-60
Operating Cost/ton
0.07 - 0.12
0.07 - 0.12
Market Share (1980)
15%
85%
Market Share (1990)
30%
70% 10
Mobility
Surface Mine Design
Wheel Loader
Hydraulic Shovel
0
200
400
600
800
1000
1200
1400
Feet Traveled in One Minute
11
Breakout Force • Surface Mine Design
• •
For similar bucket capacities, a hydraulic shovel and a wheel loader will show approximately the same breakout force. However, because the difference in bucket shapes, the shovel can apply twice as much force. The shovel can apply the force over its reach of the face.
12
Bucket Fill Factors
Surface Mine Design
Hydraulic Front Shovels Hydraulic backhoes Caterpillar wheel loaders Other wheel loaders
80-85% 100% 100-115% 85-95%
13
Power and Fuel
• Hydraulic shovels burn less fuel per hour Surface Mine Design
than wheel loaders.
• But considering tons moved per gallon burned, wheel loaders and hydraulic shovel compare very favorable to each other.
14
Two-to-Three Minute Rule
Surface Mine Design
• A truck does not make money when its tires • •
are not running. Truck load times should be in the two to three minute range. Loading times are reduced by the use of the right loading tool, better rock fragmentation, operator training, and face supervision. 15
Loading Tool Preferences
Surface Mine Design
Region
North & South America
85%
15%
Europe, Africa, Middle East
60%
40%
Australia, Far East
50%
50%
16
Surface Mine Design
Hydraulic Shovel Production Range Operating Weight (Tons)
Production Range (tons/hour)
140
800 - 1,100
230
1,100 - 1,800
340
1,600 - 2,400
620
3,000 - 4,000
17
Surface Mine Design
Wheel Loader Production Range Model
Production Range (tons/hour)
Cat 994
2,700 - 3,100
Cat 992D
1,300 - 1,700
Cat 988B
700 - 900
Cat 980F
500 - 700
Cat 966F
300 - 500
18
Conclusions
Surface Mine Design
• No two pits are the same. • There is a wide array of loading tools to meet operational needs.
• Analysis, not luck, will yield the winner for your operation 19
Types of Mobile Surface Mining Equipment •Dozers •Scrapers •Trucks •Front-end Loaders •Hydraulic Excavators •Electric Shovels •Draglines •Bucket Wheel Excavators •Blast Hole Drills
Other Bulk Material Handling Systems
Surface and Underground Mining •Belt Conveyors •Rail Haulage
Types of Underground Mining Equipment •Blast Hole Drills •Roofbolters •Slushers •Overshot Loaders •Load-Haul-Dump Units (LHDs) •Trucks •Belt Conveyors •Rail Transportation •Hoisting Systems
Loading & Hauling Equipment Loading Rubber Wheel
Front End Loader
SURFACE UNDERGROUND Hauling Combination Loading Hauling Combination Trucks
Back Hoe
Crawler
Loader Scrapers Bulldozers Graders
Track Loader Hydraulic Shovel Cable Shovel Drag Line
Bulldozers Bucket Wheel Excavator
Front End Loader
Trucks
Load Haul Dump
Over Shot Loaders Track Loaders Hydraulic Shovel s Over Shot Loaders
Back Hoe Conventional Rail Cars
Rail Other
Over Shot Mine Cars/ Loaders Locomotives
Walking Drag Line
Pneumatic/ Hydraulic
Pneumatic/ Hydraulic
Dredge
Conveyer
Conveyers Skips
Slusher
Comparative Equipment Size
Transport Distances
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Dozers The dozer, or bulldozer is a crawler or wheel driven tractor with a front mounted blade for digging and pushing material. It is used to both excavate and transport material over short distances.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Dozer Powered Functions
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Typical Dozer Production Cycle
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications Land clearance: The dozer can be sized to provide sufficient power, and with proper operating techniques can move most obstacles in its path, including boulders, trees, etc. This makes it the primary tool in clearing land prior to mining. Special blades are available for this application. Stripping overburden: Some mine plans utilize scrapers and dozers for overburden removal. The dozer, in these operations, moves a portion of the overburden by pushing it over the highwall. Grading and leveling mining benches: Draglines, electric shovels and wheel excavators require a flat work surface free of boulders; dozers are commonly used in this clean-up operation. (Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications Feeding a belt conveyor: The dozer can be effectively employed to push material into a "belt loader" which in turn feeds a belt conveyor. Trapping for loaders: The efficiency of small to medium sized loading equipment can be improved by using a dozer to rip and position material to be loaded. Reclamation: Dozers are a basic tool for leveling and recontouring mined out land. Special blades and special wheel models are available for this type of work.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Fait-Allis 41B with single shank ripper leveling dragline spoil piles.
CAT D11, Black Thunder Mine, Wyoming, Spring 2002
CAT D11, Black Thunder Mine, Wyoming, Spring 2002
CAT D11, Black Thunder Mine, Wyoming, Spring 2002
Scrapers The scraper is a rather unique machine because of its ability to excavate material in thin horizontal layers, transport the material a considerable distance, and then discharge it in a spreading action.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Scrapers
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Scraper Powered Functions
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Scrapers
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications Topsoil removal: The scraper is broadly used in those activities which involve selective removal of horizontal horizons and transport to storage. General reclamation: The scraper is applied in the rough leveling and contouring phase and for replacement of the upper horizons prior to revegetation. Ore/Coal removal (with or without ripping): Scrapers are employed in cases where the seams are thin and other types of excavating equipment are inefficient.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications Overburden removal (with or without prior ripping): These can be either initial cuts or prebenching operations for other excavating equipment, or complete overburden removal. The latter case requires a well planned circular operational layout to minimize travel distances and utilize downgrade loading and dumping. Typically, operations of this type use dozers for preshaping, supplementary material transport and push-pull scraper loading techniques.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
x
Terex S-24B tandem scraper self loading overburden. (Source: Surface Mining Equipment, Martin, et. al., 1982)
Trucks A truck is simply a mobile piece of equipment for hauling material. It is often an integral part of the material handeling activities in the mine for either transport of ore from the face to processing or stockpile, or for transport of overburden to spoil.
Trucks
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Truck Powered Functions
(Source: Surface Mining Equipment, Martin, et. al., 1982)
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications These trucks are used exclusively for material transport. The material can be just about anything but, in mining, the broad classifications are: •Overburden •Ore/Coal When trucks are used to haul overburden, the mine normally has an open pit or area mine plan with dumping off of spoil benches. Trucks can be used to haul ore/coal to a hopper or stockpile, in virtually any surface mine plan. Dumping to stockpile is generally done in shallow lifts. (Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications Bottom dump units, driving over a grizzly, are used to feed a hopper. A back-in hopper station is utilized with rear dumps. In some cases the trucks carrying coal directly to a nearby power plant will on the return trip transport ash back into the pit for burial.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Large Haul Trucks, Cripple Creek –Victor, Colorado, Fall 2002
Large Haul Truck, Cripple Creek –Victor, Colorado, Fall 2002
Wabco 3200B, 250 ton, three axel rear dump. (Source: Surface Mining Equipment, Martin, et. al., 1982)
Rimpull three axel bottom dump coal hauler. (Source: Surface Mining Equipment, Martin, et. al., 1982)
(World Mining Equipment, September 2002)
(World Mining Equipment, March 2003)
Front-End Loaders (FEL) The front-end loader is a wheel or crawler mounted tractor with a front mounted bucket and is utilized in excavating, loading, and transporting material. Because of its versatility, the front end loader is found in a wide variety of mining applications.
FEL Powered Functions
(Source: Surface Mining Equipment, Martin, et. al., 1982)
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications The wheel loader is a competitive excavator, loader and transporter. It competes with shovels, dozers and, over short transport distances, with scrapers and trucks. Being quite fast, mobile, and versatile, it can be used in a number of mine applications. Because the FEL has generally not been considered to have the digging ability of a shovel in consolidated digging faces, it finds many of its applications in softer formations, coal/ore and stockpile work. The larger sizes are more rugged and powerful, and are proving themselves in difficult digging. (Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications The primary mine applications are the following: •Loading and/ or transporting topsoil •Loading and/ or transporting coal/ ore from the digging face •Loading and/or transporting coal/ore from stockpile •Loading and/or transporting overburden and waste In all of the above loading can be into trucks, hoppers, railroad cars, or belt loaders. Transport can be for distances up to 1000 feet on the level or grades up to 12%. (Source: Surface Mining Equipment, Martin, et. al., 1982)
CAT 994D loading a haul truck
Heavy Equipment, John Tipler, 2000
Hydraulic Excavators Hydraulic shovels, primarily a European development, have proven themselves on construction projects.
The have now reached a level of reliability and have increased in size to the point where units are common in surface mining applications.
Digging Profile
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Hydraulic Excavator Powered Functions
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Hydraulic machines are employed in overburden removal, coal/ore loading or, in the smaller sizes, for utility work generally related to mine drainage systems. The hydraulic shovel is primarily an excavating and loading device. While it can swing and/or propel to transport material short distances, it is used almost exclusively to load trucks or, in some cases, hoppers/crushers. Hoes have similar uses to shovels. However, their below grade digging capability makes them particularly suited to tasks such as trenching or excavating under water. Hoes are utilized in mining when floor conditions warrant keeping machines off the bottom of the pit.
Typical Hydraulic Shovel Production Cycle
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Typical Hydraulic Hoe Production Cycle
(Source: Surface Mining Equipment, Martin, et. al., 1982)
CAT 5230 hydraulic excavator loading a haul truck
Heavy Equipment, John Tipler, 2000
Electric Shovels The shovel is one of the oldest types of excavating equipment. With time, the machines grew in capacity , steam power was replaced by gas, then diesel fuel and finally, in the larger units used in mining today, by electricity. In recent years, smaller shovels below 5 cubic yards in capacity are being replaced by front-end loaders and hydraulic machines.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Steam Shovel Mining Virginia Minnesota, circa 1910
Electric Shovels
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Electric Shovel Powered Functions
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications Electric shovels generally have the same applications as hydraulic shovels although the electric units are considered to be particularly suited to more severe digging conditions. They are available in larger sizes and have a proven service record in multi-shift mining operations. Electric shovels also tend to have longer range capabilities. These shovels are applied in benching operations in either overburden or coal/ore. Discharge is commonly into trucks but can also be into mobile hoppers. The larger models and/or those equipped with long range front ends may be applied in direct spoiling overburden removal operations. (Source: Surface Mining Equipment, Martin, et. al., 1982)
Loading Plans
(Source: Surface Mining Equipment, Martin, et. al., 1982)
The Bucyrus-Erie 1850-B Brutus with 90-yard dipper at Pittsburg and Midway Coal Mining Company in 1961. This shovel is currently maintained by a preservation group.
Extreme Mining Machines, Keith Haddock, 2001
The last stripping shovel produced was this 105-yard Marion 5900, sold in 1971 to Amax Coal Company’s Leahy Mine in Illinois.
Extreme Mining Machines, Keith Haddock, 2001
Draglines
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Draglines Through the years, the dragline has remained a unique excavating tool and has experienced a dramatic growth in maximum size. With its long reach and ability to dig to substantial depths below itself, it has had broad applications on many irrigation projects and, in more recent years, in surface mining. The hydraulic hoe has, to some extent, replaced the smaller sized diesel draglines but the larger diesel and/ or electric machines retain their popularity. Draglines, along with the bucket wheel excavators, are the largest pieces of mobile equipment currently manufactured.
Draglines
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Dragline Powered Functions
(Source: Surface Mining Equipment, Martin, et. al., 1982)
The world’s largest operating dragline (one of two), the Bucyrus 2570-WS with 160 yard bucket at the Black Thunder Mine, WY.
Extreme Mining Machines, Keith Haddock, 2001
The 100 yard Marion 8800 loading in Kentucky
Extreme Mining Machines, Keith Haddock, 2001
Bucyrus International’s Big Muskie’s 220-yard bucket easily accommodates a high school band. Photo taken in 1969.
Extreme Mining Machines, Keith Haddock, 2001
Bucket Wheel Excavators Wheel excavators dig with a rotating bucket wheel that discharges the material onto a belt conveyor. The material is transported on this conveyor or a series of belt conveyors until it is discharged from the machine.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Bucket Wheel Excavators Wheel excavators have been used, in limited numbers, for continuous excavation of unconsolidated materials starting back in the mid 1920's. Interest in the machines has been much greater overseas with the Germans, in particular, performing extensive application studies and machine development. Overall use within the United States has been very limited.
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Bucket Wheel Excavator Powered Functions
(Source: Surface Mining Equipment, Martin, et. al., 1982)
Applications There are currently very few bucket wheel excavators in service in the US. They have been used for: •Overburden excavation with direct spoiling •Overburden excavation with conveyor or truck loading, prestripping for a large dragline or stripping shovel •Large earthmoving projects (medium size or small fixed wheels) •Coal excavation with conveyor or truck loading (medium size or small fixed wheels) •Topsoil removal and Reclamation leveling (small fixed wheels) (Source: Surface Mining Equipment, Martin, et. al., 1982)
Rhineland Lignite Mine, Germany www.mining- technology.com
Förderanlagen Magdenburg (FAM) bucket wheel excavator.
World Mining Equipment, September 2002
Loading Equipment
Surface Mine Design
Dr. Kadri Dagdelen Colorado School of Mines
Surface Mine Design
Excavators
2
Surface Mine Design
Hydraulic Shovels Specifications
3
Surface Mine Design
Excavator Specifications
4
Surface Mine Design
Digging Envelopes Front Shovels
5
Surface Mine Design
Curl and Crowd Forces Front Shovels
6
Surface Mine Design
Digging Envelopes Excavators
7
Surface Mine Design
Excavators Bucket
8
Surface Mine Design
Loaders
9
Surface Mine Design
Breakout Force Loaders
10
Surface Mine Design
Breakout Force from Rackback Loaders
11
Surface Mine Design
Carry Position Loaders
12
Surface Mine Design
900 Series II – Dimensions Loaders
13
Surface Mine Design
900 Series II – Dimensions Loaders
14
Surface Mine Design
Specifications Loaders
15
Surface Mine Design
Specifications Loaders
16
Surface Mine Design
Travel Time – Loaded Loaders
17
Surface Mine Design
Travel Time – Empty Loaders
18
Surface Mine Design
Excavator Production Calculations A standard formula for cyclic excavators can be employed: O = B x BF x D x HS x J x A x 3,600 seconds (1+S) C hour Bucket Load Buckets/Period
19
Surface Mine Design
Bucket Load B x BF x D/(1 + S) < Recommended Operating Capacity • With wheel loaders: 50% of full turn static tipping load for a specific bucket type • With front shovels: Maximum load 20
Bucket Load
Surface Mine Design
• Bucket
weight depends on size, duty and ground engaging tools Bucket size depends on reach Bucket size (B) based on 2:1 heap
• • • Bucket fill (BF) decreases with increasing material consolidation
21
Surface Mine Design
Wheel Loader Bucket Fill Factors
(CAT) 22
Surface Mine Design
Weight of Materials
(CAT)
23
Bucket Load
Surface Mine Design
• % Swell increases and load factor decreases •
with degree of consolidation In place density (D) important and should be a measured number
• Loose density (D/(1 + S)) important and should be a measures number
24
Buckets/Period
• Average Surface Mine Design
cycle time (C) based on standard cycle time adjusted for:
• Material • Material fragmentation • Material size distribution • Pile configuration
25
Buckets/Period
• Average Surface Mine Design
cycle time (C) based on standard cycle time adjusted for:
• Consistency of operation • Swing angle (Shovels) • Travel distance (Loaders) • Operator ability 26
Wheel Loader Cycle Time
Surface Mine Design
Average cycle time for truck loading increases with machine size Loader Size (cy) 1.7-4.5 5.0-7.5 7.5-11 15-21
Cycle time (min) .45-.50 .50-.55 .55-.60 .60-.70 27
Cycle Time
Surface Mine Design
• Hours scheduled (HS) usually a given, based •
on management preferences and required output Longer shifts appear to be trend to minimize start-up, shut-down impact
28
Cycle Time
Surface Mine Design
• Job factor (J) depends on: • Truck assignment • Management issues • Job layout (Blending, etc.)
29
Cycle Time
Surface Mine Design
• Mechanical availability (A) depends on: • Material • Management/suppliers • Age of machine • Schedule
30
Loading Methods
Surface Mine Design
• Loading method impacts cycle time and job factor • Wheel loaders • Y pattern used with machine digging point left to right • Truck spotting location important • With a limited truck fleet and excess loader capacity, staggered and chain loading can be utilized
31
Surface Mine Design
Loading Methods
32
Surface Mine Design
Loading Methods
(Mining Magazine)
33
Surface Mine Design
Shovels: Double Back-Up Options include • Double back-up • Single back-up • Drive-by • Modified drive-by
34
Surface Mine Design
Shovels: Double Back-Up
• Trucks loaded on both sides • Average swing angle reduces • Clean-up allowed on one side while loading •
continues Moves required as shovel penetrates bank
35
Surface Mine Design
Shovels: Double Back-Up
36
Surface Mine Design
Shovels: Double Back-Up Requires balance of move time versus cycle time
(Oslund and Russell)
37
Surface Mine Design
Shovels: Single Back-Up
• Truck loaded on one side • Larger swing angle • Potential clean-up delays • Potential spotting delays
depending on
excavator first cycle
38
Surface Mine Design
Shovels: Single Back-Up
39
Surface Mine Design
Shovels: Drive-By
• Used with tractor trailers • Large swing angles • Potential clean-up delays • Minimal amount of shovel moves • Blending problems
40
Surface Mine Design
Shovels: Drive-By
41
Surface Mine Design
Shovels: Modified Drive-By
• Truck backs in to reduce swing angle • Potential clean-up delays • Minimal amount of shovel moves • Blending problems • Depth of cut effects cycle time and
move
time
42
Surface Mine Design
Shovels: Modified Drive-By
43
Surface Mine Design
Modified Drive-By: Optimum Width
44
Production Estimating of Material Movement With Earth Moving Equipment There are five factors which need to be considered in preparing a production estimate of earthmoving equipment for any particular job.
These factors include: 1. Earthmoving Cycle Components 2. Job Efficiency Factors 3. Material Weights & Swell Factors 4. Vehicle Payloads 5. Selection of Equipment
1. Earthmoving Cycle Components The productivity cycle of any earthmoving job may be separated into six components: 1. load, 2. haul or push, 3. dump, 4. return, 5. spot, 6. and delay. Each of these components is responsible for a certain percentage of the total cycle time. The factors affecting these components will determine the time each component will require.
Load Factors • • • •
Size and type of loading machine Type & condition of material to be loaded Capacity of unit Skill of the loading operator
Haul/Push Factors • • • • •
Performance ability of unit Hauling distance Haul road condition Grades Miscellaneous factors affecting haul speed
Dump Factors • • • •
Destination of material -Hopper, Over Bank, Fill, Stockpile, etc. Condition of dump area Type & maneuverability of hauling unit Type & condition of material
Return Factors • • • • •
Performance ability of unit Return distance Haul road condition Grades Miscellaneous factors affecting return speed
Spot Factors • • • •
Maneuverability of unit Maneuver area available Type of loading machine Location of loading equipment
Delay Factors • •
Time spent waiting on loading unit or pusher Time spent waiting to dump –at crusher
2. Job Efficiency Factors An estimate must indicate sustained, or average earthmoving production over a long period of time. Overly optimistic hourly production estimates will result in failure to maintain forecasted production, and an insufficient number of units assigned to the job. It is necessary to allow for the unavoidable delays encountered on all operations such as night operating, shovel moving, blasting, weather, traffic, shutdowns, or for factors such as management and supervision efficiency, operator experience, proper balance of auxiliary equipment such as tamping roller, pusher or spreader bulldozers, proper crusher capacity, etc.
2. Job Efficiency Factors The maximum productivity of an earthmover should be derated to meet actual conditions. Typical deration factors are found in the following table:
3. Material Weights & Swell Factors The weight of material is most often expressed in pounds per cubic yard. Undisturbed or “in place” material is called a bank cubic yard (BCY). Material in a loose, broken, or blasted state is called a loose cubic yard (LCY).
3. Material Weights & Swell Factors The relationship between bank and loose cubic yards is established by the swell factor or percent swell. For example, the percent swell of shale is 33% indicating that one bank cubic yard of shale will swell to 1.33 cubic yards in the loose state. Shale weighs 2800 pounds per bank cubic yard. At a swell factor of 0.75 (inverse of 1.33) the weight of one loose cubic yard of shale is 2100 pounds (2800 pounds * 0.75).
Note: Earthfill projects employ mechanical means such as rolling, tamping and adding water to compress the deposited loose cubic yard back to the state it was in the bank. This compaction may reduce the volume of the bank cubic yard by as much as 15%.
4. Vehicle Payloads The rated payload of hauling units is given on the specification sheets in pounds, struck (water level) capacities and SAE capacities. For haulers the SAE heaped capacity is for a load at a 2: 1 slope. For scrapers the SAE heaped capacity is for a load at a 1: 1 slope. For estimating purposes, the payload in pounds should not be exceeded.
Vehicle Payloads Should Not Be Exceeded
4. Vehicle Payloads Loaders, scrapers and haulers all carry material in the loose condition. To assure adequate volumetric capacity, the pounds payload should be divided by the weight per loose cubic yard and compared to the heaped capacity as shown below:
5. Selection of Equipment After the estimator has examined the job requirements and operating conditions and decided to investigate earthmoving equipment, a tentative equipment selection will be made. The final decision will, of course, depend on which method offers the lowest cost per yard or ton. In some cases, methods such as draglines, belt conveyors, etc. will also be considered.
Example Rock density: 11 cubic feet per short ton Swell factor: 1.6 Shovel Bucket capacity: 18.8 cubic yards Digging cycle time: 30 seconds per pass Bucket fill factor: 0.92 Truck Load capacity:
62 cubic yards struck 88 cubic yards at 2:1 SAE 140 tons payload capacity
a) Calculate the number of passes to load the truck. b) Calculate the total time required to load a truck.
Surface Mine Design
Loading and Hauling Fleet Productivity
Dr. Kadri Dagdelen Source : Hrebar – Lafarge 2000 Presentation
Truck Selection
Surface Mine Design
• Number and type of trucks selected should •
be based on overall system economics Lowest cost fleet selected considering operating and capital coats
2
Truck Selection
Surface Mine Design
• Production requirement and operating •
schedule Material characteristics
• Density in place and loose, swell • General size distribution, particularly maximum and minimum sizes and percentage of total • Hardness and texture • Ease of handling 3
Truck Selection • Physical and climatic conditions Surface Mine Design
• Effect of altitude on engine efficiency • Effect of ambient temperature on engine cooling, tire •
performance, and use of lubricants Effect of rainfall, frost, snow, fog, etc. on road conditions and travel
• Haul road characteristics
• Length, grade, and surface
condition of
segment
4
Truck Selection
Surface Mine Design
• Loading
• Space and ground conditions at loading point • Type and size of loading equipment • Total availability of loading equipment
• Dumping
• Dumping arrangements: rear dump into hopper, drive over hopper, edge of spoil, windrow, etc. • Space and ground condition at dump point • Total availability of down stream equipment
5
Truck Selection: Rear Dump
Surface Mine Design
• High horsepower to weight ratio • Deep pits, high grades, maneuverability required • • •
high impact and rough in pit conditions. Can be used with any type of material ( e.g., blocky, free flowing, etc. ) Used for dumping into hoppers or over bank or fill Economic distance limited
6
Surface Mine Design
Truck Selection: Bottom Dump
• Low HP/weight ratio • Free flowing material • Dumping over hopper or in windrow • Operational advantages: Dump on the move, •
More favorable tire and axle loading, high speed hauling on level hauls Moderate grade and long distance hauls 7
Production Calculations
Surface Mine Design
• The prime mover delivers a force that • •
propels the haulage vehicle plus the load The force the drive wheels deliver to the ground is referred to as rimpull This force is a function of: the torque developed by the engine, the ratio of the gears, and the size of the wheels 8
Production Calculations
Surface Mine Design
• Maximum velocity is reached when rimpull is equal to resisting forces of gravity, rolling resistance. etc. Horsepower x 375 x Efficiency Available Rimpull = Speed in MPH
9
Surface Mine Design
Rimpull vs. Velocity
10
Rolling Resistance
Surface Mine Design
• Measure of the force required to overcome internal • •
bearing friction and the retarding effect between the tires and the ground (i.e., tire penetration and tire flexing). Expressed in terms of lb/ton vehicle weight or % vehicle weight Haul Road Resistance can be estimated by: RR = 2%+1.5% per inch of tire penetration
11
Surface Mine Design
Rolling Resistance Factors TYPICAL ROLLING RESISTANCE FACTORS Various tire sizes and inflation pressures will greatly reduce or increase the rolling resistance. The values in this table are approximate, particularly for the track and track+ tire machines. These values can be used for estimating purposes when specific performance information on particular equipment and given soil conditions is not available See Mining and Earthmoving Section for more detail: ROLLING RESISTANCE, PERCENT` Tires Track Track UNDERFOOTING Bias Radial ** +Tires A very hard, smooth roadway, concrete, cold asphalt or dirt surface, no penetration or flexing 1.5%* 1.2% 0% 1.0% A hard; smooth, stabilized surfaced roadway without penetration under load; watered; maintained 2.0% 1.7% 0% 1.2% A firm, smooth, rolling roadway with dirt or light surfacing, flexing slightly under load or undulating, maintained fairly regularly, watered 3.0% 2.5% 0% 1.8% A dirt roadway, rutted or flexing under load; little maintenance, no water, 25 mm (1”) tire penetration or flexing 4.0% 4.0% 0% 2.4% A dirt roadway; rutted or flexing under load; little maintenance, no water, 50 mm (2”) tire penetration or flexing 5.0% 5.0% 0% 3.0% Rutted dirt roadway, soft under travel, no maintenance, no stabilization 100 mm (4”) tire penetration or flexing 8.0% 8.0% 0% 4.8% Loose sand or gravel 10.0% 10:0% 2% 7.0% Rutted dirt roadway, soft under travel, no maintenance, no stabilization, 200 mm (8”) tire penetration and flexing 14.0% 14.0% 5% 10:0% Very soft, muddy, rutted roadway, 300 mm (12”) tire penetration, no flexing 20.0% 20.0% 8% 15% *Percent of combined machine weight. **Assumes drag load has been subtracted. to give Drawbar Pull for good to moderate conditions. Some resistance added for soft conditions. (CAT)
12
Grade Resistance • Force required to overcome gravity when moving Surface Mine Design
vehicle uphill. Expressed in % vehicle weight (adds power to vehicle downhill).
•
Percent Grade = Vertical rise or drop (ft) x 100 Horizontal Distance (ft) e.g., 60 ft rise in 1,000 ft, Grade = 60/ 1,000 x 100 = 6% Horizontal Distance = (Horizontal distance2 + vertical distance2)1/2 e.g., (1,0002 +602)1/2 = 1,001.8 ft
13
Weights and Traction • Weights: determines the force required to propel vehicle. Surface Mine Design
• Function of vehicle weight, rated capacity (CY), and density of material hauled, number of passes of excavator
• Traction: force deliverable can be limited by traction conditions
• Usable rimpull is a function of road surface and weight on the drive wheels Usable Rimpull = Coefficient of Traction x Weight on Drive Wheels 14
Surface Mine Design
Coefficient of Traction Factors
(CAT)
15
Surface Mine Design
Altitude Deration
(CAT) 16
Speed Limits
• Speed Limits: limits on curves, in pit, and on Surface Mine Design
main haul roads
• Curves based on radius and super elevation • In pit, ramp, and main haul roads, the speed limit depends on haul road width and conditions
17
Acceleration, Deceleration, Operator
Surface Mine Design
• Speeds obtained from performance curves indicate •
maximum velocity under optimum conditions on a given profile. These speeds must be corrected for acceleration, deceleration, and operator performance to yield reasonable haul and return times.
• F=Ma Simulation utilized to account for acceleration and •
deceleration Time studies indicate that simulated haul times are less than actual haul times 18
Tires
Surface Mine Design
• Limit capability of machine to perform by •
limiting load and speed Ton-mile-per-hour ratings should not be exceeded and depend on:
• Weight (Flex/revolution) • Speed (Flexes/period) • Ambient Temperature • Road Surface Temperature 19
Tires TMPH = Average Tire Load x Average Speed for Shift
Surface Mine Design
Average Tire Load = Empty Tire Load + Loaded Tire Load (tons) 2 Average Speed = Round Trip (mi) x Trips/Shift Total Hours (hr) Limits by tire type and limits may also include maximum speed 20
Surface Mine Design
Ton-MPH Data
(CAT) 21
Estimating Cycle Time
Surface Mine Design
• Limiting factors are considered in developing an estimate of the cycle time. The cycle time consists of variable or travel time (haul and return time) plus the fixed time (load, dump, and spot times).
• Travel time (haul and return times) is a function of payload, vehicle weight, HP/weight ratio, haul road segment lengths, rolling and grade resistance, speed limits, etc.
22
Estimating Cycle Time
Surface Mine Design
• Loading time is a function bucket size, fill factor, •
excavator cycle time, loose material density, and truck capacity Other fixed times depend on loading method and dump configuration
• Spot and maneuver in loading area (typically .6-.8 min) • Dumping (typically 1-1.2 min)
• Unit production calculated considering truck payload, truck cycle time, hours per shift, and operating efficiency 23
Unit Production • Unit Production (Tons/shift) Surface Mine Design
• Truck payload / Truck cycle time x Operating •
efficiency x Hours/shift Units required are a function of total shift tonnage requirements and unit production and mechanical availability
• Units Required Operating • Tons required/shift / Unit truck production/shift (Usually rounded up) 24
Unit Production
• Units Required Purchased Surface Mine Design
• Units Required Operating (Not rounded) / Mechanical availability
25
Match Factor and System
Surface Mine Design
• Production of the excavator truck system dependent on the number of trucks assigned to the excavator
26
Match Factor and System Allocations based on at least two approaches:
• Number of trucks = Truck cycle time / Load time Surface Mine Design
(excluding first pass) This calculation approach reduces excavator delays
• Number of trucks = Truck cycle time Load time (excluding first pass) + Truck exchange time
27
Match Factor Approach • Match factor approach reduces truck delays Surface Mine Design
compared to first method. For example: Loader cycle tim e N o . of passes Effective loading tim e (7-1)x.5 Truck spot tim e (exchange tim e) H aul, dump and return Truck cycle tim e N o . T ru c k s ( 1 7 . 0 1 / 3 . 0 0 ) N o . T ru c k s ( 1 7 . 0 1 / ( 3 . 0 0 + 1 . 3 0 ) )
3 1 12 17
. 5 m in 7 .0 0 m i n .3 0 m i n .7 1 m in .0 1 m in 5.67 3.96
28
System Production
Surface Mine Design
• System production must consider number of trucks, •
unit production and excavator availability. System production
• Number of truck/shift x Unit production (Tons/shift) x Excavator availability
• Complexity of calculations and variability of times leads to use of fleet production simulators such as FPC and TALPAC 29
Surface Mine Design
The End
30
Surface Mine Design
TRUCK SELECTION AND PRODUCTION CALCULATIONS
Dr. Kadri Dagdelen
Wheel Loader Production Calculations
Surface Mine Design
• Example: Calculate the output in tons/hr of a 990 Wheel Loader with a 11cy bucket with .55 min. cycle time and 95% bucket fill factor loading material with 3100 lbs. per LCY. Assume 85% mechanical availability and 83.3% job factor.
2
Wheel Loader Production Calculations (Cont.)
Surface Mine Design
•
Equation to estimate the production per hour:
O = BC*BF*D*MA*JF*3,600sec (1+SF)*CT Where,
hour
O =Production, tons/hr BC =Bucket Size, CY (Usually heaped at 2:1) BF =Bucket Fill Factor, % D =In Place Density, tons/CY MA=Mechanical Availability, % JF =Job Factor, % SF =Material Swell, %100 CT =Average cycle time, seconds 3
Wheel Loader Production Calculations (Cont.)
Surface Mine Design
• Solution: O = 11*0.95*1.55*0.85*0.833*3,600sec 33sec = 1252 tons/hr
4
Loader-Truck Production Calculations
Surface Mine Design
•
Example: CAT775 truck (65ton) is loaded with a 11.0CY 990 loader with 0.55min cycle time with 95% fill factor. For truck cycle time, use the following table. Determine the number of trucks needed for the loader and the total production per hour. Truck cycle time Haul
3.8min
Dump
1.0min
Return
1.8min
Spot
0.6min 5
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
Tons / cycle = 11CY/cycle * 0.95*3100lb/cy / 2000lb = 16.2T/cycle # of cycles/truck = 65T / truck / 1 cycle/16.2T = 4 cycles Loading time = (4-1) cycles * 0.55min / cycle = 1.65 min
6
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
Cycle time Load
1.7min
Haul
3.8min
Dump
1.0min
Return
1.8min
Spot
0.6min
Total Cycle time
8.9min 7
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
• Number of Trucks/ Loader No. of Trucks = Truck cycle time / Load time = 8.9 min / 1.65 min = 5.4 trucks (Assume 6 trucks)
8
Loader-Truck Production Calculations (Cont.)
• Total Production Surface Mine Design
Assume – 50 min / hour, and 85% availability 65T/cycle*1cycle/8.9min*50min/hr*0.85/unit = 312T/hr Total Production = No. of trucks * tons/hr – unit = 5.4 trucks * 312T/hr per truck = 1685 tons/ hr
9
Loader-Truck Production Calculations
Surface Mine Design
•
Example: A quarry works with CAT769D flat floor trucks (Max payload 41T, Engine+-450hp) that is loaded by 8cy loader. The material density is 2800lb/LCY and the quarry is located at the sea level, sending material at 260tons/ hour to the crusher. Calculate truck loading time, productivity, and number or trucks required.
10
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
• Example (Cont.): Loader data: Capacity: 8cy Fill factor: 80% Cycle time: 0.5 min/pass Mechanical availability: 88%
11
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
• Example (Cont.): Truck cycle time data: Spot time: 0.8 min Dump time:1.5min Truck mechanical availability: 85%
12
Loader-Truck Production Calculations (Cont.) •
Example (Cont.):
Surface Mine Design
Road profile: Segment
Length (m)
Speed limit (km/hr)
Grade (%)
Rolling resistance (%)
1
122
45
0
4
2
762
20
8
2
3
152
45
0
4
Road condition: Firm 13
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
Tons / cycle = 8CY/cycle * 0.8*2800lb/cy / 2000lb = 9T/cycle # of cycles/truck = 41T / truck / 1 cycle / 9T = 4.6 cycles (5 cycles) Loading time = (5-1) cycles * 0.5min / cycle = 2.0 min
14
Loader-Truck Production Calculations (Cont.) Haul Speed: Surface Mine Design
Segment1 Total Resistance = 4% Max speed = 42km/h < Speed limit (45km/hr)
42
15
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
Conversion of Max Speed to Average Speed
Weights to HP ratio: 75050kg = 165456lb 165456lb / 450hp = 368lb/hp Haul load length: 122m = 401ft Conversion factor = 0.51
Avg speed = 42km/hr*0.51=21.4km/hr 16
Loader-Truck Production Calculations (Cont.) Haul Speed :
Surface Mine Design
Segment2 Total Resistance = 10% Max speed = 16km/h < Speed limit (20km/hr)
Conversion factor = 1 Avg speed = 16km/hr 16
17
Loader-Truck Production Calculations (Cont.) Haul Speed :
Surface Mine Design
Segment3 Total Resistance = 4% Max speed = 42km/h < Speed limit (45km/hr)
Conversion factor = 0.68 Avg speed = 42km/hr*0.68=28.6km/hr 42
18
Loader-Truck Production Calculations (Cont.) Haul Time:
Surface Mine Design
Segment1: 0.122km / 21.4km/hr * 60min = 0.34 min Segment2: 0.762km / 16km/hr * 60min = 2.86 min Segment3: 0.152km / 28.6km/hr * 60min = 0.32 min Total Haul Time: 0.34+2.86+0.32 = 3.52 min 19
Loader-Truck Production Calculations (Cont.) Return Speed:
Surface Mine Design
Segment1 Total Resistance = 4% Max speed = 73km/h > Speed limit (45km/hr) So, choose 45km/hr
Avg speed = 45km/hr*0.68=30.6km/hr 73
20
Loader-Truck Production Calculations (Cont.) Return Speed :
Surface Mine Design
Segment2 Total Resistance = -8%+2% = -6% Max speed = 69km/h > Speed limit (20km/h) 6%
Choose 20km/hr
Avg speed = 20*0.95 = 19km/h
69
21
Loader-Truck Production Calculations (Cont.) Return Speed :
Surface Mine Design
Segment3 Total Resistance = 4% Max speed = 73km/h > Speed limit (45km/hr) So, choose 45km/hr
Avg speed = 45km/hr*0.54=24.3km/hr 73
22
Loader-Truck Production Calculations (Cont.) Return Time:
Surface Mine Design
Segment1: 0.122km / 30.6km/hr * 60min = 0.24 min Segment2: 0.762km / 19km/hr * 60min = 2.41 min Segment3: 0.152km / 24.3km/hr * 60min = 0.38 min Total Return Time: 0.24+2.41+0.38 = 3.02 min 23
Loader-Truck Production Calculations (Cont.) Haul and Return Time Summary:
Surface Mine Design
Haul Segment
Length (m)
Grade(%)
RR (%)
Total Resistance (%)
Speed (km/hr)
Limit (km/hr)
Conversion
Avg. Speed (km/hr)
time (min)
1
122
0
4
4
42
45
0.51
21.42
0.34
2
762
8
2
10
16
20
1
16
2.86
3
152
0
4
4
42
45
0.68
28.56
0.32
Segment
Length (m)
Grade(%)
RR (%)
Total Resistance (%)
Speed (km/hr)
Limit (km/hr)
Conversion
Avg. Speed (km/hr)
time (min)
1
122
0
4
4
73
45
0.68
30.6
0.24
2
762
-8
2
-6
69
20
0.95
19
2.41
3
152
0
4
4
73
45
0.54
24.3
0.38
Return
Total time = 3.52min(haul)+3.02(return)=6.54 min 24
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
Truck cycle time (min)
Load
2.0 min
Haul
3.5min
Dump
1.5min
Return
3.0min
Spot
0.8min
Total
10.8min 25
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
• Slip condition check (Segment2): Available Rimpull =(Grade resistance + Rolling resistance) * Gross Vehicle Weight = (8% + 2%) * (34050kg + 41000kg) = 10%*75050kg = 7505kg 26
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
Usable Rimpull: Function of road surface and weight on the drive wheels Usable Rimpull = Coefficient of Traction * Weight on Wheel
27
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
Typical Coefficient of Traction
28
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
Weight of Wheel: 769D: Rear 66.7%, Front 33.3% Distribution (by CAT Performance Book) Weight on Rear Tire is 75050kg * 0.667 = 50058kg
Then, Usable Rimpull is 0.6*50058kg*Cos(8%) = 29939kg
29
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
• CONDITION CHECK Usable Rimpull > Available Rimpull There is no slip condition.
30
Loader-Truck Production Calculations (Cont.)
• Unit Production Surface Mine Design
Assuming 50min / hour Productivity: 41T/cycle*1cycle/10.8min*50min/hr*0.85 = 161T/hr
31
Loader-Truck Production Calculations (Cont.)
Surface Mine Design
• Number of Trucks/ Loader For maximum productivity: 10.8min / 2.0min = 5.4 (6trucks) To achieve 260T/hr: 260 / 161 = 1.61 (2 trucks)
32
Fleet Size Determination Using Binomial Distribution
Surface Mine Design
by
Dr. Kadri Dagdelen
Example
Surface Mine Design
Consider the following fleet: One loader, 80% mechanical availability and an estimated productivity of 9,000 tons per operating shift. Three haul trucks, 70 percent mechanical availability and an estimated productivity 0f 4,000 tons per operating shift. 2
Surface Mine Design
Example Assume that the fleet is scheduled 100% of the time and will only be inoperative if either the loader or all the trucks are down for repairs.
3
Surface Mine Design
Wrong Assumption One could incorrectly assume that the average loader production would be 80% of 9,000 tons per shift, or 7,200 tons per shift. However, since the loader production is dependent on available haul trucks, the truck downtime distribution must be considered.
4
Surface Mine Design
Binomial Distribution n! ⋅ p x (1 − p) n− x x! (n − x)! This formula gives the fraction of time x units are available out of a fleet of n units with a given availability of p.
5
Binomial Distribution for Trucks
Surface Mine Design
Availability = 70% Fleet Size (n)
Number of Units Available (x) 0
1
1
0.30
0.70
2
0.09
0.42
0.49
3
0.03
0.19
0.44
0.34
4
0.01
0.08
0.26
0.41
0.24
5
0.00
0.03
0.13
0.31
0.36
0.17
6
0.00
0.01
0.06
0.19
0.32
0.30
2
2! ⋅ 0.71 (1 − 0.7)2−1 = 0.42 1! (2 − 1)!
3
4
5
6
0.12
Fraction of the time that 1 truck out of a fleet of 2 will be operating 6
Fleet Capacity
Surface Mine Design
The fleet capacity can be stated as follows: The loader operates 80% of the time and during this time, 34% will be at 9,000 tons per shift, 44% will be at 8,000 tons per shift, and 19% will be at only 4,000 tons per shift. 0.80 x 0.34 x 9,000 = 2,448 tons 0.80 x 0.44 x 8,000 = 2,816 tons 0.80 x 0.19 x 4,000 =
608 tons
TOTAL = 5,872 tons
7
Surface Mine Design
Fleet Capacity From this example, it can be seen that production from the loader would be 18% short of the initial estimate of 7,200 tons per shift that was determined without consideration of the haul fleet.
8
Surface Mine Design
Haul Truck Requirement Determination Annual target objective
1,800,000 tons
Shifts scheduled
250 shifts
Tonnage requirements per shift
7,200 tons
Average truck productivity
4,000 tons per shift
Need 1.80 operating trucks per shift 3 trucks at 70% availability will average 2.1 shifts
9
Haul Truck Requirement Determination
Surface Mine Design
It could be incorrectly assumed that 3 trucks would be sufficient. However, if the loading fleet contains only 1 loader , then 20% of the time the haul fleet would be idle waiting for the loader to be repaired. It is also known that the loader could not keep up with three trucks and production would be limited to 9,000 tons per shift, not the 12,000 tons indicated by the haulage capacity.
10
Surface Mine Design
Haul Truck Requirement Determination 250 shifts x 0.80 x 0.34 x 9,000 tons =
612,000 tons
250 shifts x 0.80 x 0.44 x 8,000 tons =
704,000 tons
250 shifts x 0.80 x 0.19 x 4,000 tons =
152,000 tons
TOTAL = 1,468,000 tons per year
The solution in this case would be to purchase another loader or work more shifts.
11
Estimating Owning and Operating Costs
Surface Mine Design
by
Dr. Kadri Dagdelen
Hourly owning and operating cost estimate
Surface Mine Design
Analyst Date
Machine Designation Estimated Ownership Period (Years) Estimated Usage (Hours/Year) Ownership Usage (Total Hours)
Antonio Peralta 11/7/2005 1 Track-type Tractor 7 1200 8400
2 Wheel Loader 5 1500 7500
Owning Costs 1. a. Delivered Price (including attachments) b. Less Tire Replacement Cost if Desired c. Delivered Price Less Tires 2. a. Residual Value - % of original deliverd price b. Less Residual Value at replacement 3. a. Value to be recovered through work b. Cost per hour 4. a. Interest rate b. Interest costs 5. a. Insurance rate b. Insurance Costs 6. a. Tax rate b. Property tax 7. Total hourly owning cost
135,000 135,000 35% 47,250 87,750 10.45 16% 10.29 1% 0.64 1% 0.64 22.02
1,200,000 4,000 1,196,000 48% 574,080 621,920 82.92 16% 76.54 1% 4.78 1% 4.78 169.03
2
Hourly owning and operating cost estimate
Surface Mine Design
Operating Costs 8. a. Fuel unit price b. Fuel consumption c. Fuel cost 9. Lube oils, filters, grease 10. a. Life of tires (Hours) b. Tires replacement cost c. Impact factor d. Abrasiveness factor e. Z factor f. Basic factor g. Under carriage 11. a. Extended use multiplier for repair reserve b. Basic repair factor for repair service c. Repair reserve 12. a. Special wear items
2.20 5 11.00 0.46
2.20 4 8.80 0.43 3,500 1.14
0.20 0.20 0.30 6.20 4.34 1.00 4.50 4.50 1.32
1.00 4.00 4.00 0.60
13. Total hourly operating cost
21.62
14.97
14. Maching Owning plus operating
43.64
184.01
15. Operator's hourly wage (include fringes)
30.00
30.00
16. TOTAL OWNING AND OPERATING COST
73.64
214.01
3
9A. Lube Oils, Filters, Grease
Surface Mine Design
Track-type tractor Wheel Loader Unit Price Consumption Cost/Hour Unit Price Consumption Cost/Hour Engine Transmission Final Drives Hydraulics Grease Filters Total
0
Total
0
4
12A. Special Wear Items
Surface Mine Design
# 1 2 3 4 5 6
Track-type tractor Cost Life $/Hour 105 150 0.70 165 450 0.37 125 500 0.25
Total
1.32
Wheel Loader Cost Life 50 165 80 450 70 600
$/Hour 0.30 0.18 0.12
Total
0.60
5
Surface Mine Design
Drilling
Dr. Kadri Dagdelen
Drilling Methods • Top hammer drilling Hydraulic self-contained drills
Surface Mine Design
Pneumatic drills with portable air compressors
• Down-the-hole (DTH) drilling Pneumatically operated carriers with portable air compressors Hydraulically operated self-contained carriers
• Rotary drilling Drills for rotary crushing Drills for rotary cutting 2
Surface Mine Design
Surface Drilling Methods and Applications
3
Surface Mine Design
Components of Surface Drilling Methods
4
Top Hammer Drilling • Soft to hard rock
Surface Mine Design
• Diameter from 7/8” to 10” • Top hammer drills can be classified according to their size and principle of operation: Hydraulic or pneumatic handheld drills Light hydraulic drills mounted on feeds for mechanized drilling in different types of boom applications Pneumatic crawler drills operated by a separate portable air compressor Hydraulic crawler or wheel-based drills operated by a powerpack onboard 5
Principle of Top Hammer Drilling • It can be hydraulic or pneumatic • It combines four functions Surface Mine Design
Percussion Feed Rotation Flushing
• Parameters that affect the penetration rate: Impact energy, impact frequency, rotation speed, feed force, and flushing of the hole 6
Surface Mine Design
Relative Penetration Rate as a Function of Percussion Pressure
7
Surface Mine Design
The Optimal Adjustment of Drilling Parameters Means Maximum Penetration
8
Surface Mine Design
Flushing
9
Surface Mine Design
Flushing
10
Surface Mine Design
Penetration Rates Between Pneumatic and Hydraulic Top Hammer Drilling
11
Surface Mine Design
Bench Drilling Rig
12
Bench Drilling Rig
Surface Mine Design
A modern surface crawler drill should fulfill the following requirements, to make the operation economical: • High penetration rate • Short cycle times • High quality holes • High availability • Low operating cost 13
Surface Mine Design
Choice of Bit Type
14
Surface Mine Design
Application Range of Tube Drill Steels
15
DTH Drilling • It is more efficient than top hammer drilling • A DTH hammer follows immediately behind the bit Surface Mine Design
• Good drilling accuracy • DTH drills are used in bench drilling of 3½” to 6½” holes on benches up to 150 feet • DTH hammer life is dependent on: Hammer size, operating pressure, rock abrasiveness, and rock drillability
16
Surface Mine Design
Principle of DTH Drilling
17
Surface Mine Design
A Typical DTH Hammer
18
Surface Mine Design
Features of DTH Hammer
19
Surface Mine Design
Truck Mounted DTH Drill
20
Surface Mine Design
DTH Bit Designs
21
Rotary Drilling • It is used in most major open pit mining operations • Diameter from 4” to 17½”, depth up to 150 feet Surface Mine Design
• The key elements in rotary drilling are: Sufficient torque to turn the bit in any strata encountered Sufficiently high bit loading capability (pulldown force) for optimum penetration Sufficient flushing air volume to remove the cuttings during penetration, as well as to provide cool air to the drill bit bearings Selection of the proper type of bit for the material being drilled
22
Surface Mine Design
Principle Rotary Drilling
23
Surface Mine Design
Rotary Drills
24
Surface Mine Design
Rotary Drills
25
Surface Mine Design
Principles of Rotation
26
Surface Mine Design
Rotary Power versus Hole Diameter
27
Surface Mine Design
Pull Down versus Hole Diameter
28
Surface Mine Design
Principles of Feed Systems
29
Surface Mine Design
Thrust and Pulldown Force
30
Surface Mine Design
Flushing Air Compressor Size
31
Surface Mine Design
Carrousel Type Pipe Changer
32
Rotary Drilling Accessories
• Drill bits Surface Mine Design
• Drill pipes • Shock subs • Stabilizers • Saver subs • Bit subs
33
Surface Mine Design
Rotary Drill Bit Components
34
Rotary Bit Selection Parameters
Surface Mine Design
Type of ground Tooth or insert spacing Tooth depth Soft formations with low Large: Inserts compressive strengths and High extended chisel high drillability: shales, unconsolitaded sands, shaped calcites
Cutting action Mostly gouging and scraping by skew cone action, with little chipping and crushing
Medium: Inserts short or blunt chisel shaped
Partly by gouging and scraping but with significant chipping and crushing action especially at harder end of type
Hard formations: siliceous limestones, hard Close with low intermesh sandstones, porphyry copper ores
Low: Inserts spherical or conical
Mostly by chipping and crushing by cutter rolling action
Very hard formations: taconites, quartzites
Very low: Insert hemispherical conical or ovoid
Nearly all excavation by true rolling action of cutters
Medium Formations: harder shales, limestone, sandstones, dolomites
Medium, close
Very close with low intermesh
35
Surface Mine Design
Bit Selection for Rotary Drilling
36
Surface Mine Design
Insert Shapes for Tricone Bits
37
Surface Mine Design
Penetration Rate versus Bit Load
38
Surface Mine Design
Principles of Rotary Cutting
39
Surface Mine Design
Drilling
Dr. Kadri Dagdelen
Penetration Rate
Surface Mine Design
W rpm P = (61 − 28 log10 Sc) ⋅ ⋅ φ 300 Where: P = penetration rate (ft/hr) Sc = uniaxial compressive strength, in thousands of psi W/F = Weight per inch of bit diameter, in thousands of pounds rpm = revolutions of drill pipe per minute Bauer and Calder, 1967 (Surface Mining Handbook) 2
Horse Power
hp = K ⋅ rpm ⋅ D
2.5
⋅W
1.5
Surface Mine Design
Where: D = bit diameter (in.) W = weight on the bit in thousands of pounds K = constant that varies with rock type. As material strength decreases, the value of K increases. This caters for the greater teeth penetration experienced in soft rocks. Values vary from 14 x 10-5 for soft rocks down to 4 x 10-5 for high-strength materials. Surface Mining Handbook 3
Balancing Air Velocity
Um = 264 p
1/ 2
⋅d
1/ 2
Surface Mine Design
Where: Um = 2420 fpm for 13 mm (1/2 in.) diameter platelets with a density of 2.7 g/cc d = diameter of the chip in inches p = density of the chip in lb/ft 3
Surface Mining Handbook 4
Surface Mine Design
Bailing Velocities
5
Surface Mine Design
Bailing Velocities
6
Surface Mine Design
Air Requirements Chart
7
Optimal Bit Load C×D OptimumBitLoad = 5 Surface Mine Design
Where: C = Rock compressive strength D = bit diameter in inches
Source: R. Baker, Tamrock 8
Total Work Total Work (WT ) = W × R × 2π × N × T Surface Mine Design
Where: W = bit load (lbs) R = penetration rate (feet/min) N = bit rotation speed T = torque (foot lbs)
Source: R. Baker, Tamrock 9
Rotary Horsepower 4.95 × D × R × (W / 1000)1.6 Horse Power (hp) = C Surface Mine Design
Where: hp = rotary horsepower R = bit rotational speed D = bit diameter (inches) W = optimum bit load (lbs) C = rock compressive strength Source: R. Baker, Tamrock 10
Maximum Bit RPM Maximum Bit RPM ( R ) =
hp × C 4.95 × D × (W / 1000)1.6
Surface Mine Design
Where: hp = rotary horsepower R = bit rotational speed D = bit diameter (inches) W = optimum bit load (lbs) C = rock compressive strength Source: R. Baker, Tamrock 11
Volume CFM 0.25πD 2 0.25πD 2 × SF + P × Volume CFM = P × 144 144 Surface Mine Design
Where: P = penetration rate D = bit diameter (inches) SF = swell factor (0.6 sedimentary or 0.4 Igneous/metamorphic)
Source: R. Baker, Tamrock 12
Air Velocity 183× CFM Air Velocity = D2 − d 2 Surface Mine Design
Where: d = pipe diameter (inches) D = bit diameter (inches) CFM = effective compressor volume (CFM)
Source: R. Baker, Tamrock 13
Compressive Strength Compressive Strength (C ) =
2.18 × W × R 0.2 × (1 / 10000) × P × D 0.9
Surface Mine Design
Where: P = average pure penetration rate (feet/hour) W = average bit load (lbs) R = average bit rotation D = bit diameter (inches)
Source: R. Baker, Tamrock 14
Pure Penetration Pure Penetratio n ( P ) =
2.18 × W × R 0.2 × C × D 0.9 × (C / 10000)
Surface Mine Design
Where: P = average pure penetration rate (feet/hour) W = optimum bit load (lbs) R = optimum bit rotation speed D = bit diameter (inches) C = average compressive strength Source: R. Baker, Tamrock 15
Explosives Definitions Explosive -A chemical mixture that releases gasses and heat at high velocity, causing very high pressures. Explosion –Thermochemical process in which mixtures of gasses, solids, or liquids react with almost instantaneous formation of gaseous pressures and heat release. Detonation – Supersonic explosive reaction which creates a high pressure shock wave, heat, and gasses.
Theory of Blasting The rock is affected by a detonating explosive in three principal stages. In the first stage, starting from the initiation point, the blasthole expands by crushing the blasthole walls. This is due to the high pressure upon detonation. In the second stage, compressive stress waves emanate in all directions from the blasthole with a velocity equal to the sonic wave velocity in the rock. When these compressive stress waves reflect against a free rock face, they cause tensile stresses in the rock mass between the blasthole and the free face. If the tensile strength of the rock is exceeded, the rock breaks in the burden area, which is the case in a correctly designed blast.
Mechanics of Detonation Tensile Shock Waves
Compressiv e Shock Waves
Mechanics of Detonation In the third stage, the released gas volume "enters" the crack formation under high pressure, expanding the cracks. If the distance between the blasthole and the free face is correctly calculated, the rock mass between the blasthole and the free face will yield and be thrown forward.
Bench Blast
(Atlas Copco)
History of Explosives Development 1000 -Black Powder •Discovered in China around 1000 A.D. •Mixture of potassium nitrate (saltpeter), sulfur and charcoal. •The combustion of charcoal (C) and sulfur (S) is the fuel, and oxygen is contained within the nitrate ion (NO3). •Marco Polo brought it to Europe where it was originally used for military purposes. •The first blasting application was in Hungary in 1627 and by the end of the 17th century most of the European miners used black powder to loosen rock. •The first black powder mills were established in America around the year 1775.
History of Explosives Development 1831-Safety Fuse •William Bickford, an Englishman, patented the “Miners Safety Fuse”, in 1831. •Safety fuse gave blasters a safe and reliable means of initiating black powder. 1846 -Nitroglycerin •In 1846, Ascanio Sobrero, an Italian, discovered nitroglycerin (C3H5N3O9), but he considered it too unpredictable and hazardous for anyone to use.
History of Explosives Development 1867 -Blasting Caps •The main problem with nitroglycerin was to get it to shoot consistently. •Alfred Nobel, a Swede, solved this problem with the invention of the fulminate of mercury blasting cap in 1867. •Use together with safety fuse, the blasting cap provided an excellent initiating system for nitroglycerin.
History of Explosives Development 1866 –Dynamite •In his efforts to make nitroglycerin safer to handle, Alfred Nobel in 1866 discovered that Kieselguhr (a diatomaceous earth) not only absorbed three times its own weight of nitroglycerin, but also rendered it less sensitive to shock. •After kneading and shaping it into a cartridge, it was wrapped in paper and the Dynamite was invented.
History of Explosives Development 1894-PETN •The explosive PETN (C5H8N4O12) was discovered in 1894. •It was not widely used until the 1940’s and today it is the primary explosive compound in modern initiators and boosters. 1922-Electric Blasting Caps •In the beginning of the 20th century the electric initiation was introduced, and by 1922 the first electric delay detonator (with 1 sec. delay) came into practical use. •The introduction of the short delay detonator 10-100 milliseconds) in the late 1940's has had the greatest importance in the development of modern blasting techniques.
History of Explosives Development 1956 –ANFO •In 1956, ANFO (Ammonium Nitrate and Fuel Oil) was introduced to the U.S. market. •The success of the ANFO in U.S.A. is indisputable, from a consumption rate of almost nil in 1956, the consumption had increased to over 1,000,000 tons by 1975, the consumption of dynamites has, during the same time, declined from 340,000 tons to 135,000 tons.
History of Explosives Development 1960’s -Water gels and slurries •In the 1960's, we have seen the development of water gels, also called slurries. •A slurry explosive is a high density aqueous explosive containing ammonium nitrate which is an oxidizer. •Water gels contain 10 to 30 percent water and are sensitized by carbonaceous fuels, TNT, aluminum, or certain organic compounds like methylamin nitrate. •Both cap sensitive and non-cap sensitive water gel explosives are available
History of Explosives Development 1970’s-Nonel •In the late 1970's we saw new non-electrical initiating systems like Nonel being developed. 1970’s -Emulsions •1970's the development of emulsion explosives. •Emulsion explosives are composed of separate, very small drops of ammonium nitrate solution and other oxidizers, densely dispersed in a continuous phase, which is composed of oil and wax. •The oil/wax mixture, which is the fuel, is in this way given a very large contact surface to the oxidizer, the ammonium nitrate solution .
Properties of Explosives In the ideal conditions of dry blastholes a simple explosive can be used, while under wet conditions, more sophisticated products are called for . The most important characteristics of an explosive are: •velocity of detonation (VOD) •strength •detonation stability •sensitiveness (propagation ability) •density •water resistance •sensitivity •safety in handling •resistance to freezing •oxygen balance •shelf life
Classification of Explosives The explosives used in civil engineering and mining can nowadays be classified as: •High explosives •Blasting agents High explosives are characterized by high velocity of detonation (VOD), high pressure shock wave, high density and by being cap sensitive. Blasting agents are mixtures consisting of a fuel and oxidizer system, where none of the ingredients are classified as an explosive and when unconfined cannot be detonated by means of a #8 test blasting cap (1.0 grams of high explosives). Blasting agents have to be initiated by a primer. ANFO is a typical blasting agent.
Firing Devices Firing methods can be divided into two main groups: Non-electric •Safety Fuse and Blasting Cap •Detonating Cord •Nonel system Electric •Electronic Blasting Caps
Safety Fuse and Blasting Cap The safety fuse consists of a black powder core that is tightly wrapped with coverings of textile and waterproofing materials. Safety fuse has a steady well controlled burning speed, usually around 40 seconds per foot.
Safety Fuse and Blasting Cap To initiate the explosive, a plain detonator has to be attached to the safety fuse. Detonators of different strengths expressed as a number are available, currently #6 or #8 caps. The #8 detonator contains approximately 1.0 grams of high explosives, and the #6 about 0.8 grams.
Detonating Cord Detonating cord consists of a PETN core which is wrapped in coverings of textiles and waterproofing materials. Detonating cord may be initiated with a #6 detonator and detonates along its entire length at about 7000 meters/second. It initiates most explosives. Does not work well with ANFO in small to medium sized blastholes, (incomplete detonation).
Firing pattern for detonating cord blast.
Electric Blasting Caps Electric detonators can be divided into three different classes according to their timing properties: •instantaneous •millisecond delays •half second delays The millisecond delay detonator has a built-in millisecond delay element. Delays are usually available in 25 ms delay intervals.
Electric Blasting Caps Electric detonators may be connected in series or parallel depending on the number of detonators in the round, and the current available in the blasting machine.
Parallel series circuit.
Electric Blasting Caps
The testing instruments for blasting circuits have to be specially designed for their purpose and be approved by the authorities concerned. An Ohm-meter is used to control the resistance of single electric detonators, detonators in series and in parallelseries and for the final check before firing.
Electric Blasting Caps The series are connected in parallel and subsequently measured. The resistance of the parallel connection is in accordance with Kirckhoffs law: 1 1 1 1 = + + ... + R R1 R 2 Rn
As the difference in resistance between the series must not exceed ± 5 percent, the resistance of the parallel connection will be: Resistance/series R= Number of series
Example Assume a blast of 250 V A-detonators with a resistance of 3.6 Ohms each. (The resistance is always 3.6 Ohms independent of legwire length.) The firing cable has a resistance of 5 Ohms and a CID 330 V A blasting machine is used. In accordance with the instructions on the blasting machine, the round may be connected in 5 parallel series. Number of detonators in each series: 50. Resistance per series: 50x3.6=180 Ohms. Resistance after parallel connection :
Resistance/series 180 R= = = 36 Ohms Number of series 5 Resistance at the firing point is the resistance of the parallel-series connection plus the resistance of the firing cable. 36 + 5 = 41 Ohms.
Possible errors during measuring: Resistance too high: * Larger number of detonators than calculated. * Sub-division into series wrongly carried out. * Poor contact ill some connection or detonator . Resistance too low: * All detonators are not connected into the circuit. * Sub-division into series wrongly carried out. * Some part of the round not connected into the circuit. Infinite resistance: * Interruption in series through incomplete connection. * Faulty detonator (usually torn off legwire).
Electric Blasting Caps Blasting machines of various types are used to fire the rounds. Shown is the model CI 50 which is designed for firing a maximum of 50 conventional detonators.
Nonel system The NONEL detonator functions as an electric delay detonator, but the legwires and the fuse head have been replaced by a plastic tube through which a shock wave is transmitted. The endsplit of of the shockwave from the plastic tube initiates the delay element in the detonator. The 3mm diameter plastic tube is coated on the inside with a thin layer of reactive material which transmits the shockwave with a velocity of about 2000 meters per second.
Non-Electric vs. Electric Tubing
Shell
Closure
Air Space
Non Electric Cap
Fuse Element
Crimps Ignition Plug Charge Fuse Powder
Bridge Wire
Priming Charge
Electric Cap
Base Charge
Nonel system A connector with a strength of 1/3 a #8 cap is used to connect and initiate the detonators.
Nonel system
NONEL connected for bench blasting.
Nonel system NONEL detonators may also be connected to a detonating cord using a specially designed clip if noise is not a problem.
Nonel system A NONEL round may be fired using a plain detonator and safety fuse, or by using a specially designed NONEL system blasting machine.
Bench Blasting Bench blasting is the most common kind of blasting work. It can be defined as blasting of vertical or nearly vertical blastholes in one or more rows towards a free surface. The blastholes can have free breakage of fixed bottom.
Fixed bottom Free breakage
Bench Blasting The tensile, compressive and shearing strengths of a rock mass vary with different kinds of rock and may vary within the same blast. As the rock's tensile strength has to be exceeded in order to break the rock, its geological properties will affect its blastability. Faults and dirt-seams may change the effect of the explosive in the blast. Faulty rock containing voids, where the gases penetrate without giving full effect, may be difficult to blast even though the rock may have a relatively low tensile strength.
Bench Blasting The requisite specific charge, (kg/m3 ) provides a first-rate measure of the blastability of the rock. By using the specific charge as a basis for the calculation, it is possible to calculate the charge which is suitable for the rock concerned. The distribution of the explosives in the rock is of the utmost importance. A closely spaced round with small diameter blastholes gives much better fragmentation of the rock than a round of widely spaced large diameter blastholes, provided that the same specific charge is used.
Basic Definitions Burden -the distance between the drill hole and the nearest parallel free face.
Spacing - the distance between holes along rows that are parallel to the face.
Stemming -non-explosive material that is placed in the bore hole to confine the explosives (usually placed near the collar of the hole).
Sub-drilling is the amount of hole that is drilled below the intended new bench level.
After Blasting
Partial Reflected Wave
Before Blasting
Blasting Theory Leaves Unfractured Toe
Un-reflected Compression Wave
When hole depth equals the bench height masses of rock are often left at the toe of the bench because of lack of reflected tension energy from the free face. The solution for this is either sub-drilling or inclined holes.
Blasting Theory
Inclined holes cause total reflective tensile waves at the toe of the bench. This causes a flat lower bench and is a more efficient use of explosives.
Total Reflected Tensile Waves
Vertical Holes vs. Inclined Holes
Vertical Holes
Inclined Holes
• Easier to drill • Avoids difficulties in fractured rock
• Commonly drilled between 10 & 15 degrees • Causes more productive reflected shock wave in toe of bench
Bench Height Factors Bench Height is a function of both hole diameter and burden distance. Zone of optimal fragmentation
Research indicates that bore hole length should be approximately 3 times the burden distance. -Ash & Smith, Society of Explosives Engineers, 1976
Burden Spacing Equations
Burden Spacing Equations Anderson B = K(d*L)**2
Pearse B = K*d*(P/T)**2
Ash B = K*d/12
Fraenkel (meters & mm) ((R*L)**0.3)*(l**0.3)*(d**0.8) B= 50
B burden distance (inches) d hole diameter (inches) L hole length (feet) T ultimate tensile strength of rock (pounds per square inch) P stability pressure of explosive (pounds per square inch) K constants (empirically determined)
Rock characteristics are difficulty to mathematically model since rock is never really homogeneous.
Burden Spacing Equations Langefors/Kihlström Bmax
Bmax d p s c c f S/B
d p*s = 33 c * f * S/B
= maximum burden (m) = diameter in the bottom of the blasthole (mm) = packing degree (loading density) (kg/liter or g/c3 ) = weight strength of the explosive (ANFO = 1) = rock constant, 0.3 to 0.5 = c + 0.05 for Bmax between 1.4 and 15.0 meters = degree of fixation, 1.0 for vertical holes and 0:95 for holes with inclination 3:1 = ratio of spacing to burden
Terminology
Charge Calculations The maximum burden in the bottom of the blasthole depends on: •weight strength of the actual explosive (s) •charge concentration (lb) •rock constant (c) •constriction of the blasthole (R1)
Table 1a.
RECENT DEVELOPMENTS IN VEHICLE PROXIMITY WARNING AND COLLISION AVOIDANCE SYSTEMS USING GPS AND WIRELESS NETWORKS
Kadri Dagdelen Fuat Bilgin Mining Engineering Department Colorado Shool of MInes
OUTLINE INTRODUCTION PREVIOS WORK CURRENT WORK
MAIN
FUTURE WORK CONCLUSIONS
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2 COLORADO SCHOOL OF MINES
INTRODUCTION
Surface Mining Safety Research Program
• Safety Issues • Truck Proximity Warning • Collision Avoidance
• Global Positioning System (GPS) • Wireless Network Technology
10/29/2006
3 COLORADO SCHOOL OF MINES
The Problem We Face E-Mail Requesting Help Jim: You may or may not be aware that at couple of weeks ago El Abra suffered a fatal accident when a truck driver backed through the berm. Shortly after that happened, I was asked by Dennis Barlett and Hunter White to lead a team of representatives from North American operations to make sure that this was the last accident of this type that we had to suffer. …. ………….. Thanks, Ferol
10/29/2006
4 COLORADO SCHOOL OF MINES
CONCEPTUALIZED SYSTEM • Software for dump edge recognition • Trimble GPS • Trimble 900 MHz radios • Introduction to 802.11b
10/29/2006
5 COLORADO SCHOOL OF MINES
MORENCI TEST
PREVIOUS WORK
Field Tests at the Morenci Copper Mine - Arizona
10/29/2006
6 COLORADO SCHOOL OF MINES
CURRENT WORK • LAFARGE QUARRY IMPLEMENTATION OptiTrack • Real Time • Design of the System • Hardware Development • Software Development • Robustness of the System
10/29/2006
7 COLORADO SCHOOL OF MINES
OptiTrack SYSTEM
10/29/2006
CURRENT WORK
8 COLORADO SCHOOL OF MINES
Description of the System (Infrastructure) OptiTrack Network at Lafarge Quarry GPS Differential Correction Service
GPS Wireless Communication Transmitting Truck Position
Data, DTM
Wireless Communication Between Lafarge Quarry and CSM
GPS data GPS Differential
DTM Control Base 10/29/2006
9 COLORADO SCHOOL OF MINES
OptiTrack (Lafarge)
CURRENT WORK
• Mobile Clients • Haul Trucks • Manager Trucks • PDAs
• Central Points • Repeaters • Trailer
10/29/2006
10 COLORADO SCHOOL OF MINES
OptiTrack Mobile Clients
10/29/2006
CURRENT WORK
11 COLORADO SCHOOL OF MINES
OptiTrack Haul Trucks
CURRENT WORK
Omni Antenna
Lighting Arrestor WRLA-1.2/1.8 N-Female N -Female
Barrel Adapter N-Male N -Male
Wireless PCMCI Card Cisco LMC 352 Jumper Cable
LMR600
N-Male RPTNC-Female
N-Male N-Male
DC Injector N-Female N-Female
GPS Device & Antenna
Amplifier 1wt WAF2400-1000 N-Female N -Female
GPS Satellites
RS 232
10/29/2006
12 COLORADO SCHOOL OF MINES
OptiTrack Central Points
CURRENT WORK
• Repeater at Mechanic House
• Repeater on the Trailer 10/29/2006
13 COLORADO SCHOOL OF MINES
OptiTrack Repeater
10/29/2006
CURRENT WORK
14 COLORADO SCHOOL OF MINES
OptiTrack Trailer
CURRENT WORK
10/29/2006
15 COLORADO SCHOOL OF MINES
OptiTrack Trailer
CURRENT WORK
10/29/2006
16 COLORADO SCHOOL OF MINES
Schematic Representation of OptiTrack Trailer CURRENT WORK Point to Point Antenna WR2400-24M H Pol N-Female Coax Cable LMR600 Directional Antennas N-Male N-Male WRPA2400 11-AM V Pol N-Male
Coax Cable LMR600 N-Male N-Male
Coax Cable LMR600 N-Male N-Male
Lighting Arrestor WRLA-1.2/1.8 N-Female N-Female Power Supplies Solar Panels
Barrel Adapter N-Male N-Male
Jumper Cable
LMR600
N-Male RPTNC-Female
N-Male N-Male
Cisco AP 350
DC Injector N-Female N-Female
Amplifier 1wt WAF2400-1000 N-Female N-Female
RPTNC-male
10/29/2006
17 COLORADO SCHOOL OF MINES
OptiTrack (CSM)
CURRENT WORK
OptiTrack at CSM GPS Laboratory
Server
10/29/2006
18 COLORADO SCHOOL OF MINES
OptiTrack Antenna
CURRENT WORK
Point to Point Antenna (Brown Building)
10/29/2006
19 COLORADO SCHOOL OF MINES
Schematic Representation of OptiTrack (CSM) CURRENT WORK
Amplifier 1wt WAF2400-1000 N-Female N-Female
Antenna on the roof of Brown Building RF Coax Cable N-Male N-Male
Jumper Cable N-Male RPTNC -Female LMR600 N-Male N-Male
Lighting Arrestor WRLA-1.2/1.8 N-Female N-Female
Cisco AP 350 RPTNC-male DC Injector N-Female N-Female
Barrel Adapter N-Male N-Male
10/29/2006
20 COLORADO SCHOOL OF MINES
OptiTrack Software
10/29/2006
CURRENT WORK
21 COLORADO SCHOOL OF MINES
Future Work • New Mobile Clients • PDAs • Sensors
• Radar Implementation
• Mobile Adhoc Network (MANET) 10/29/2006
22 COLORADO SCHOOL OF MINES
Description of the System (Ad Hoc) OptiTrack Network at Lafarge Quarry GPS Differential Correction Service
GPS Data, DTM Wireless Communication Between Lafarge Quarry and CSM
GPS data
Wireless Communication Transmitting Truck Position
GPS Differential
DTM Control Base 10/29/2006
23 COLORADO SCHOOL OF MINES
Broadcast Protocols
Future Work
Existing Protocols • Flooding • Adaptive-SBA • AHBP-EX
OptiTrack Protocols • Naive Bayes • Adaptive Boosting (AdaBoost) 10/29/2006
24 COLORADO SCHOOL OF MINES
Existing Protocols
10/29/2006
Future Work
25 COLORADO SCHOOL OF MINES
Machine Learning Approach
Future Work
Classification
Rebroadcast Incoming Packet Discard
10/29/2006
26 COLORADO SCHOOL OF MINES
OptiTrack Protocols
10/29/2006
Future Work
27 COLORADO SCHOOL OF MINES
Simulation Comparison Simulation Parameter
Value
Simulator
NS-2 (1b7a)
Network Area
350 x 350 meter
Node Tx Distance
100 meter
Data Packet Size
64 bytes payload
Node Max. IFQ Length
50
Simulation Time
100 seconds
Number of Trials
10
Confidence Interval
95 %
Trial
1
2
3
4
5
Number of Nodes
40
50
60
70
90
Average Speed (m/sec)
1
5
10
15
20
Pkt. Src. Rate (pkts/sec)
10
20
40
60
80
10/29/2006
Future Work
28 COLORADO SCHOOL OF MINES
Delivery Ratio of the Protocols Future Work Delivery Ratio
100
95
90
Delivery Ratio
85 Adaptive SBA AHBP-EX 80
Flooding AdaBoost Naive Bayes
75
70
65
60 1
2
3
4
5
Trial
10/29/2006
29 COLORADO SCHOOL OF MINES
Number of Retransmitting Nodes Future Work Number of Retransmitting Nodes
60
NumberofRetransmittingNodes
50
40
Adaptive SBA AHBP-EX 30
Flooding AdaBoost Naive Bayes
20
10
0 1
2
3
4
5
Trial
10/29/2006
30 COLORADO SCHOOL OF MINES
End-to-End Delay
Future Work
End-to-End Delay
3
2,5
End-to-EndDelay
2
Adaptive SBA AHBP-EX 1,5
Flooding AdaBoost Naive Bayes
1
0,5
0 1
2
3
4
5
Trial
10/29/2006
31 COLORADO SCHOOL OF MINES
ADHOC & INFRASTRUCTURE
Future Work
Infrastructure ADHOC
10/29/2006
32 COLORADO SCHOOL OF MINES
Conclusions 1. The tests that are being carried out at CSM as well as in Lafarge Quarry indicate that “OptiTrack” soft ware system can be used as a proximity warning d evice to avoid collisions between off highway truck s and the other vehicles as well as to monitor truck positions with respect to dump edge on a 3-D topo graphy map. 2. Integration of the developed GPS based system wit h other systems based on concepts such as RFID, r adar, and video cameras need to be pursued to hav e a complete and reliable collision avoidance syste m. 10/29/2006
33 COLORADO SCHOOL OF MINES
Sustainability Issues in Mining by Antonio Peralta
Source: Rozgonyi and Ramirez, January 2003
Surface Mine Design – MNGN312/512
What is Sustainable Development? Sustainable development is:
ECONOMICAL
• A concept of needs; • Idea of limitations; • Future oriented paradigm, and; • A process of change.
SUSTAINABLE DEVELOPMENT SOCIAL
ECOLOGICAL
This concept reflects a compromise between the world’s tripartite aspirations: •
ECONOMICAL: Promoting economic betterment but preserving of options for future generations.
•
ECOLOGICAL: Protecting, maintaining and restoring of environmental quality.
•
SOCIAL: Promoting and improving social and community stability and values.
Surface Mine Design – MNGN312/512
Sustainable Development in Mining §
Applying the concepts of sustainable development and sustainable natural resource management to energy and mineral resources is not an oxymoron.
§
Energy and mineral resources are mostly not renewable; sustaining any given deposit or mine is not possible. However, SD involves designing, developing and managing resources in a way that is conducive to long-term wealth creation. Minerals are a form of natural capital and thus of endowed wealth.
§
Therefore, mining projects can serve sustainability objectives if they are designed and implemented in ways that build viable long-term capacities, strengthen communities and rehabilitate damaged ecosystems.
Surface Mine Design – MNGN312/512
Global Mining and Mineral Industry Trends •
International mergers, and globalization,
•
Shifts in supply availability and recycling,
•
Consumer demand (responsibility for the whole life cycle of the minerals, metals),
•
Political restructuring,
•
Economic transformations,
•
Social and cultural developments,
•
Public attitudes about mining and minerals,
•
The new paradigm of “sustainable development”,
•
An era of increasing regulations affecting all phases of activity from exploration and extraction to processing and products.
Surface Mine Design – MNGN312/512
Principal Mining and Environmental Actions During Each Phase of Mine Development PHASE IN MINE PROJECT DEVELOPMENT
PRINCIPAL MINE PLANNING ACTION
PRINCIPAL ENVIRONMENTAL MANAGEMENT ACTION
Exploration road construction Exploration
Pre-feasibility study
Rock core drilling Geochemical analysis Geostatistical analysis Orebody evaluation Initial mine and minerals process planning Facilities siting Scheduling Econometric analysis Initial technology selection Plan of operations Technology selection
Feasibility study
Conceptual to final designs Costing and cost benefit analysis Investment brokerage
Environmental assessment Rehabilitation plan Exploration permit application
Environmental baseline study Environmental assessment “Fatal Flaw” analysis Initiation of permitting process Comprehensive EIA and review Mitigation planning Reclamation and closure planning Conceptual design for closure Reclamation and closure costing Closure fund design
Surface Mine Design – MNGN312/512
Principal Mining and Environmental Actions During Each Phase of Mine Development (cont.) PHASE IN MINE PROJECT DEVELOPMENT
PRINCIPAL MINE PLANNING ACTION
PRINCIPAL ENVIRONMENTAL MANAGEMENT ACTION
Construction
Access and haul road development Site clearing and grubbing Earth moving and surface water management Mine dewatering Utilities installation Building and infrastructure construction
Installation of pollution control facilities General environmental management (air, water, land) Construction phase reclamation and closure
Production
Ore extraction Size reduction Minerals processing Smelting and refining Maintenance and upgrade
General environmental management Performance assessment/audit Monitoring Concurrent reclamation Final closure design Partial closure Partial bond release
Closure
Facilities decommissioning Dismantling Decontamination Burial Removal Asset recovery Recycling
Implementation of closure plan Site cleanup Final reclamation Final impact assessment Post closure planning
Post closure
Treatment Maintenance Monitoring Final bond release
Surface Mine Design – MNGN312/512
Elements of Environmental Planning
A). INITIAL PROJECT EVALUATION B). THE STRATEGIC PLAN C). THE ENVIRONMENTAL PLANNING TEAM
Surface Mine Design – MNGN312/512
Environmental Planning Procedures (EPP) A). INITIAL PROJECT EVALUATION: 1.
Prepare a detailed outline of the proposed action.
2.
Identify permit requirements.
3.
Identify major environmental concerns.
4.
Evaluate the opportunity for and likelihood of public participation in the decision making process.
5.
Consider the amount and effect of delay possibly resulting from public participation during each stage of the project.
6.
Evaluate the organization and effectiveness of local citizens groups.
7.
Determine the attitudes and experiences of governmental agencies.
8.
Consider previous industry experience in the area.
9.
Consider recent experience of other companies.
10.
Identify possible local consultants and evaluate their ability and experience.
11.
Consider having a local consultant check the conclusions of the initial evaluation.
Surface Mine Design – MNGN312/512
Environmental Planning Procedures (EPP) (cont.) B). THE STRATEGIC PLAN: 1.
Outline of technical information needed to obtain permits and to address legitimate environmental, land use and socio-economic concerns. Permitting process is quite long and complex.
2.
Categorically assign responsibilities for the acquisition of the technical information and hire necessary consultants.
3.
Prepare a schedule for obtaining information and data and for submitting permit applications to the appropriate agencies.
4.
Select local legal, technical and public relations consultants.
5.
Avoid hostile confrontations with environmental groups.
6.
Develop a consistent program for the generation of credible factual information.
7.
Perform risk assessment.
8.
Perform cost analysis.
9.
Prepare mine reclamation plan.
Surface Mine Design – MNGN312/512
Environmental Planning Procedures (EPP) (cont.) C). THE ENVIRONMENTAL PLANNING TEAM The team shall be multidisciplinary: Ø Mining engineers Ø Metallurgical engineers Ø Biologists Ø Environmentalists Ø Toxicologists Ø etc.
Surface Mine Design – MNGN312/512
Risk Assessment 1.
Data collection and hazard evaluation.
2.
Toxicity assessment.
3.
Exposure assessment.
4.
Risk characterization. a). Non carcinogenic risks. b). Carcinogenic risks.
5.
Risk assessment / management by considering: a). What types of problems or failures could occur, and what is the probability that each one will occur? b). What types of environmental impacts could result? c). What types of compliance-related retrofits or remediation methods could be required? d). What are the possible fines or remediation costs?
Surface Mine Design – MNGN312/512
Cost Analysis By considering: Ø
Capital costs
Ø
Operating costs
Ø
Closure costs
Ø
Potential costs for retrofits associated with regulatory compliance
Ø
Potential cost for remediation
Ø
Life-cycle environmental costs
Surface Mine Design – MNGN312/512
Mine Reclamation i.
Surface and groundwater management
ii.
Mine waste management
iii.
Tailings management
iv.
Cyanide heap and vat leach systems
v.
Acid Mine Drainage Control
vi.
Landform reclamation
vii.
Revegetation
viii. Site stability ix.
Subsurface stabilization
x.
Erosion prevention
Surface Mine Design – MNGN312/512
Mine Reclamation i.
Surface and groundwater management
ii.
Mine waste management
iii.
Tailings management
iv.
Cyanide heap and vat leach systems
v.
Acid Mine Drainage Control
vi.
Landform reclamation
vii.
Revegetation
viii. Site stability ix.
Subsurface stabilization
x.
Erosion prevention
Surface Mine Design – MNGN312/512
Location of the McLaughlin Mine in California
Surface Mine Design – MNGN312/512
Facilities map of the McLaughlin Mine
Surface Mine Design – MNGN312/512
Mine waste management M
1)
2)
c L a u g h
Early stage for waste disposal & AMD control facilities
3)
Advance of the waste disposal works
4)
l i n
Final limit of the waste dump
Erosion control by revegetating is started
Surface Mine Design – MNGN312/512
Mine waste management (cont.) M
5)
05/04/ 92
6)
05/04/ 93
c L a u g Advance on the erosion control & and pit backfilling
h
7) 05/10/ 93
East waste dump is completely covered
8) 06/14/ 98
l i n
South pit is backfilled & west dump is almost covered
Waste dumps encapsulation is finished
Surface Mine Design – MNGN312/512
Acid Mine Drainage Control
AMD control facilities at the west waste dump
Surface Mine Design – MNGN312/512
Revegetation
Supervising the revegetation works on the west waste dump (notice the AMD control facilities on the right side)
Surface Mine Design – MNGN312/512
Minimizing AMD in open pit mining through mine planning by
Antonio Peralta
Surface Mine Design – MNGN312/512
q It encompasses all issues associated with
the environmental effects of sulphide oxidation resulting from mining activities.
q Its significant potential for long-term environmental degradation makes it one of the biggest environmental issues facing the mining industry.
Acid Mine Drainage (AMD)
Acid Mine Drainage Examples
q Primary factors are directly involved in the
generation of sulphide oxidation products. q Secondary factors consume or alter those products. q Tertiary factors are the physical conditions that influence the process.
Contributing Factors
q Impact on mine water quality. q Impact on aquatic ecosystems. q Impact on riparian communities. q Impact on groundwater quality. q Impairment of the use of waterways. q Revegetating and stabilizing mine wastes. q Long term liability.
Problems for Mine Operators
q There is a number of well established
principles for minimizing AMD. q Mine planning to minimize AMD is the most cost effective and desirable solution to the problem. q Treatment is less desirable due to the long term nature of AMD and associated high treatment costs.
Acid Mine Drainage Control
q Exclusion of oxygen from wastes.
q Control of water flux within wastes. q Minimize transport of oxidation products. q Neutralization of AMD with alkaline materials. q Monitoring to determine the effectiveness of remediation measures.
Principles to Prevent Acid Mine Drainage
q Geological assessment.
q Geochemical tests, classified as static and kinetic tests. q Static testing evaluates the acid generating and acid neutralizing processes. q Kinetic testing evaluates the rate of sulphide oxidation, AMD characteristics, and assess potential management techniques.
1st Step – Characterization of Rock Types
q Acid generation characteristics of similar ore
bodies and host rocks. q Relevant information should be logged and recorded from drill core during the exploration stage. q Core samples must be retained for further testing.
Geological Assessment – Information Sources
q Sampling should be representative, based on
accepted statistical procedures. q Representative profiles of all geological units should be sampled. q The number of samples will depend on geological variability, complexity of rock types, and level of confidence required.
Geological Assessment – Sampling
q Samples should be stored in a cool, dry
environment to minimize sulphide oxidation prior to testing. q Static tests may require as little as 2 grams of sample. q Kinetic tests require a minimum of 500 grams of sample.
Geological Assessment – Handling of Samples
q Topography and drillholes
Geological Assessment – Interpretation
q Cross section of the drillholes
Geological Assessment – Interpretation
q Interpretation of rock types
Geological Assessment – Interpretation
q 3D view of two interpreted sections
Geological Assessment – Interpretation
q 3D view of two interpreted sections
Geological Assessment – Interpretation
q Acid base accounting or net acid producing
potential (NAPP) test. q Net acid generation (NAG) test. q Saturated paste pH and conductivity (EC). q Total and soluble metal analysis
Geochemical Tests – Static Tests
q NAPP is determined by subtracting the
estimated acid neutralizing capacity of a sample from the estimated potential acidity of the sample. q It has three components: Maximum potential acidity (MPA) Acid neutralizing capacity (ANC) Sample classification.
Net Acid Producing Potential
q NAG comprises the addition of a strong
oxidizing agent such hydrogen peroxide to a prepared sample and the measurement of the solution pH and acidity after the oxidation reaction is complete. q This test can provide and indication of sulphide reactivity and available neutralizing potential within 24 hours.
Net Acid Generation Test
q The test gives a preliminary indication of the in situ
pH and the reactivity of the materials present in the sample. q A crushed sample (<1 mm) is saturated to create a paste and the pH and EC is determined after a period of equilibration.
Saturated paste pH and conductivity
q Initial screening should compare metal
concentration in the solids with that of the background soils and country rocks in the area. q Statistical methods are available to determine whether any enrichment is significant.
Total and soluble metal analysis
q They simulate weathering and oxidation of rock
over time under exposure to moisture and air. q They provide an indication of the oxidation rate and time periods for onset of acid generation (lag time). q Columns and humidity cells are the most used kinetic test techniques.
Geochemical Tests – Kinetic Tests
Classification for regulatory and permitting purposes.
q Acid Generating (AG)
q Potentially acid generating (PAG) q Potentially acid consuming (PAC) q Potentially neutral (PN)
Rock Classification
q AMD waste materials includes overburden, waste
rock, pit walls, pit floor and tailings. q A database of the AMD parameters determined in the tests is required. q A predictive AMD block model should be created using the information available in the database.
2nd Step – Quantifying the Materials to be disposed
q A block model is a three-dimensional spatial
representation of an ore body. q It is used to quantify the geology an economics of the deposit. q It is developed by dividing the ore body and the host rock into regularly shaped blocks representing the smallest mineable unit.
Block Modeling
q Ore grades.
q Contaminants. q Metallurgical recoveries. q Physical parameters of the ore. q Economic parameters. q Environmental parameters.
Information in the Block Model
q Produce a detailed geologic interpretation.
q Create drill hole composites per material type. q Perform statistical analysis. q Perform spatial analysis if sufficient data exist. q Interpolate a value into each block, for each of the required variables.
Steps to create a block model
q Block model includes waste and ore blocks.
Complete Block Model
q Block model includes only ore blocks.
Constrained Block Model
q Blocks inside and outside the final pit limit.
Block Model and Mine Design
q Site potential and reserves éExpected pit development q Development phasing éPeriod of development éAreas of extraction by phase
3rd Step - Mining Development
2005
2020
2035
2050
Maps for different time periods
q Clearing / Vegetation removal q Topsoil management q Overburden / Waste rock management q Grading principles q Erosion control q Revegetation
Coordination with Reclamation
q The objective is to isolate reactive wastes for
selective disposal either separately or within nonreactive materials. q In some cases, it may be preferable to segregate highly reactive wastes within a separate facility to permit intensive treatment and control strategies.
Isolation Strategy
q AMD waste is selectively handled and surrounded
with non-acid producing materials to limit flow of air and water into waste and AMD flow out. q A cell structure is formed. The surface is covered with compacted benign material, usually clay.
Waste Encapsulation
q Similar in concept to encapsulation. Method is
useful where a mined out pit of sufficient size is available. q With effective mine planning an early closure of one of a series of mined pits allows for in-pit disposal of AMD wastes.
In -Pit Disposal
q Involves the blending/mixing and co-disposal of
AMD wastes with benign non-acid producing materials or even acid neutralizing materials. q Small cells within a waste dump are rapidly filled and covered to reduce AMD generation and water ingress.
Co-disposal and Blending of Waste
q A low permeability cover is constructed over an
existing waste dump, mainly using locally available borrow or benign waste, to reduce the infiltration of surface water and infusion of air into the dump.
Covers
q Option for marginal acid producing wastes where
subsequent acid drainage is recovered and treated downstream. q Collection/recovery systems can include catchment ponds, drains, trenches and groundwater bores.
Recovery and Treatment
q Mine planning can be a cost effective method to
control AMD in open pit mines. q There are three basic steps to achieve AMD control: characterize the rock types, quantify the amount and content of the rocks, and develop a mine plan according to the previous steps. q The mine plan should include waste management strategies to minimize AMD: isolation, encapsulation, in-pit disposal, co-disposal, blending, covers, and treatment. q A combination of these strategies could be highly effective to control AMD.
Conclusions
Questions and comments???????
Summitville, Colorado
According to the United States Environmental Protection Agency (US EPA), mining generates twice as much waste as all other American industries put together. So-called "hard rock" mining wastes are acidic and contaminated with toxic heavy metals which have poisoned more than 12,000 miles of streams and rivers and 180,000 acres of lakes. EPA estimates the public cost to clean up the more than 550,000 abandoned mines in America at between $32-72 billion. The very scale of today's massive open-pit mining operations means that sometimes cleanup costs will outstrip the value of the metals pulled out of the ground, as happened with the $232 million cleanup of the Summitville mine in southern Colorado.
Summitville, Colorado
At Eagle mine, a zinc, copper and silver operation, ten million tons of mine waste and mine tailings were left along the banks of the Eagle River in Gilman Colorado. Cleanup costs exceeded $55 million which totaled more than $5.50 per ton of mine waste. A zinc, lead and silver mine at Smuggler Mountain in Pitkin Colorado. The estimated cost for environmental recovery is $7.2 million. This equals $2.40 per ton of waste.
Examples, Colorado
Feasibility Studies The formal feasibility study includes an economic analysis of the rate of return that can be expected from the mine at a certain rate of production. Some of the factors considered during such an economic analysis are: Tons in the deposit Grade of the mine product Mill recovery Sale price of the metal or mineral Cost of mining per ton Cost of milling per ton Royalties Capital cost of the mine
Capital Cost of the mill Exploration and development cost Mining rate, tons per day Depreciation method used Depletion allowance Working capital necessary Miscellaneous costs of operation Tax rate
Risk Mining is a very risky business. The most serious risks in any mining project are those associated with: •Geology: the actual size and grade of the minable portion of the deposit, •metallurgical factors: how much of the orebody can be recovered, and •Economics: metal markets, interest rates, mining, processing, ect.
Return on Investment In order to compensate for risk, a mining organization will require a minimum acceptable rate of return on investment. The cost of borrowing capital for the mine or of generating the needed capital internally within the company must be considered. If a company has a number of attractive investment opportunities, the rate of return from the proposed mine venture may be compared with the rate expected on a different mining venture elsewhere, or with some other business opportunity unrelated to mining. Management has an obligation to its stockholders or investors to select projects with the best rate of return.
As a general rule of thumb, a project must have better than a 15percent rate of return to be considered by a major company. An individual commonly expects a 30- to 50 percent rate of return to consider investing in a mining venture. Among other uses of the cash flow generated by the mine, these funds must finance: •continuing exploration elsewhere, •pay for past failures, and •contribute to the mine's portion of main office and general overhead.
Time Value of Money Money has a time value. The future value of an investment can be calculated by:
F = P(1 + i) N where: P = Present value of investment F = Future value of investment i = interest rate N = number of years For example $100 invested at 10% interest for 1, 2, and 3 years would yield: F = 100(1 + .10) 1 = $110.00 F = 100(1 + .10) 2 = $121.00 F = 100(1 + .10) 3 = $133.10
Time Value of Money Conversely money received in the future is not as valuable as money received today. If money is received in the future:
P = F / (1 + i) N Using the same example: P = 110.00/(1 + .10) 1 = $100.00 P = 121.00/(1 + .10) 2 = $100.00 P = 133.10/(1 + .10) 3 = $100.00
DCF-ROR The criterion most commonly employed in the minerals industry when evaluating the rate of return on an investment proposal is called the discounted cash flow rate of return (DCF-ROR). The term is a special version of the more generic term, internal rate of return (IRR). The internal rate of return is defined a that interest rate which equates the sum of the present value in cash inflows with the sum of the present value of cash outflows for a project: ΣPV cash inflows = ΣPV cash outflows
(3)
DCF-ROR The DCF-ROR can be calculated by: N
where:
CFn =0 ∑ n n = 0 (1 + i)
(4)
CFn = Amount of cash in or out in a given year n = Year N = Project life i = DCF-ROR Once the cash flows for a project have been determined, the interest rate i can be solved for using an iterative process, i.e. guess at an initial value for i and then solve Equation 4 until a result of 0 is obtained.
Steps Involved in Cash Flow Analysis The evaluation of a mining project is usually an iterative process using the following steps: 1. 2. 3. 4. 5.
Select a mining method Select a production rate Calculate Capital and Operating Costs Select cutoff grade and tonnage Calculate cash flow and return
Change steps 4, 2, and 1 and select the alternative that gives the highest return.
Steps Involved in Cash Flow Analysis In a feasibility study, attempt to quantify all geologic, technical, marketing, environmental, political, etc. factors. Many of these variables are dependent on each other. A feasibility study are usually divided into the pre-production, production, and postproduction phases: 1. Preproduction Period Exploration Water and land acquisition Mine and mill capital Working capital, etc 2. Production Period Revenue less costs Calculation Of Annual Cash Flow 3. Postproduction Period Equipment salvage Working capital liquidation
Steps Involved in Cash Flow Analysis
Depletion One of the features that distinguish a mining enterprise from many other businesses is that during production, the company’s assets, i.e. the ore, is consumed. The percentage depletion allowance is based on the idea that as minerals are extracted, the mine is worth less. The percentage depletion allowance permits mining companies to deduct a certain percentage from their gross income to reflect the mine's reduced value over time.
Depreciation Depreciation is an allowable deduction when computing taxable income that represents the exhaustion, wear, and tear of property used in a trade or business, or of property held for the production of income. The purpose of the depreciation deduction is to provide a means by which a business or trade can recapture the capital needed to keep itself in business. Therefore depreciation allowances for capital assets are deducted from taxable income in an orderly manner such that the property owner has deducted the initial investment in the asset by the time it wears out or becomes exhausted. Having recaptured the initial asset cost from the annual tax deductions, the owner can, in theory, replace the worn-out piece of equipment with a new one and keep himself in business.
Case Study The calculation of the cash flow and DCF-ROR is illustrated using a bedded zinc deposit, producing 6000 tons per day, with total reserves of 22.5 MM Tons @ 14% zinc. Simplifying and other assumptions: 1. No royalty 2. No investment tax credits 3. Straight line depreciation and depreciation life equal to life of property 4. Federal, state, and local taxes equal to 40% net after depletion 5. No replacement or additional equipment requirements 6. No start-up costs or learning curve 7. Uniform grade mined over mine life 8. Uniform production rate over mine life 9. Operating costs constant over mine life 10. Mine would be division of large profitable corporation with 100% of exploration and development expensed 11. No consideration of cost depletion 12. Price/cost differential constant over life of mine with no consideration of escalation and inflation
Cash Flow Calculations Cash Flow Calculations ($1,000) Pre-Production Period Year 1 Exploration *1 2,000 Development *2 0 Mine/Mill 0 Working Capital 0 Total Investment (2,000) Tax Savings *3 800 Net Cash Flow (1,200)
2 4000 0 0 0 (4,000) 1600 (2,400)
3 4000 0 0 0 (4,000) 1600 (2,400)
4 0 4000 15000 0 (19,000) 1600 (17,400)
5 0 8000 36000 0 (44,000) 3200 (40,800)
6 0 8000 36000 2600 (46,600) 3200 (43,400)
*1 Expensed under Section 617 of IRS Code *2 Expensed *3 Assume federal, state, and local tax rate = 40% of net after depletion
7 0 0 0 9,300 (9,300) 0 (9,300)
Total 10,000 20,000 87,000 11,900 (128,900) 12,000 (116,900)
Zinc Smelter Schedule Payments Silver: Deduct 2 Troy oz., pay for 80% of remainder at Handy & Harman quotation for refined silver in Metals Week, averaged for the calendar month following delivery, less $.055 per oz. Lead: No payment. zinc:
Pay for 85% of zinc content at delivery price for prime western zinc published in Metals Week, averaged for the calendar month following delivery, less $.015 per pound.
Zinc Smelter Schedule Deductions Smelter Charge: $170/dry ton Price Adjustment: Increase by $3.00 per ton for each $.01 that the zinc quotation exceeds $.40 per pound. Fractions in proportion. Decrease by $2.00 per ton for each $.01 that the zinc quotation decreases below $.40 per pound. Fractions in proportion.
Smelter Schedule Calculations Concentrate Grade = 55% zinc Price = $0.47/lb Payments: 2,000 lb/ton * 0.55 * 0.85 * $(0.47- 0.015)/lb = Deductions: Base Charge Price Adjustment (47- 40)c * $3.00/c Total Deductions: Freight: Truck Rail Total Freight:
$425.43/ton
170.00 = 21.00 (191.00)
5.00 15.00
Net Smelter Return/Ton Concentrate (NSR/T)
(20.00) $214.43/ton
Revenue and Operating Calculations Revenue/year = Tons/year Concentrate * NSR/ton Tons/year Concentrate = (Tons/year Ore * Grade * Mill Recovery)/(Conc. Grade) Mine Schedule = 250 Days/year Mill Recovery = 90% Tons/year Concentrate = 6,000 T/D * 250 D/Y * 0.14 * 0.9/0.55 = 343,636 Tons/year Concentrate . Revenue/year ($1,000) = 343,636 T/Y * $214.43/1,000 = $73,684/Year Direct Operating cost/Year = Tons/year Ore * Operating Costs/Ton Ore Direct Operating Costs Mining $15.00 /Ton Ore Milling 5.00 Overhead 3.00 Total 23.00 /Ton Ore Operating Cost/Year ($1,000) = 6,000 T/D * 250 D/Y * $23.00/T/1,000 = $34,500/Year
Production Period Year Revenues Operating Costs Net Before D & D Depreciation Net After Depr. Depletion Taxable Income Tax @ 40% Net After Tax Depreciation Depletion Cash Flow Working Capital Net Cash Flow Depletion Calculation: Initial Recapture 22% Revenue 50% Net After Depr. Depletion Earned Depletion Recaptured Recapture Balance Depletion Claimed
7 73,684 (34,500) 39,184 (5,800) 33,384 (6,211) 27,173 (10,869) 16,304 5,800 6,211 28,315 (9,300) 19,015
8 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
9 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
10 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
11 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
12-21 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
7 10,000 16,211 16,692 16,211 10,000 0 6,211
8
9
10
11
12-21
16,211 16,692 16,211 0 0 16,211
16,211 16,692 16,211 0 0 16,211
16,211 16,692 16,211 0 0 16,211
16,211 16,692 16,211 0 0 16,211
16,211 16,692 16,211 0 0 16,211
Depreciation and Depletion Depreciation/Year = (Mine & Mill capital)/Mine Life Mine Life = Reserves/Annual Production = 22,500,000 Tons/(6,000 T/D * 250 D/Y) = 15 years Depreciation/Year ($1,000) = $87,000,000/15 Yr/1,000 = $5,800/Year Depletion ($1,000): Statutory % * Revenue or 50% Net after Depreciation, Select Smaller zinc Depletion Rate = 22% 22% * $73,684 = $16,211 <=== Select Smaller OR 50% * $33,384 = $16,692
Production Period Year Revenues Operating Costs Net Before D & D Depreciation Net After Depr. Depletion Taxable Income Tax @ 40% Net After Tax Depreciation Depletion Cash Flow Working Capital Net Cash Flow Depletion Calculation: Initial Recapture 22% Revenue 50% Net After Depr. Depletion Earned Depletion Recaptured Recapture Balance Depletion Claimed
7 73,684 (34,500) 39,184 (5,800) 33,384 (6,211) 27,173 (10,869) 16,304 5,800 6,211 28,315 (9,300) 19,015
8 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
9 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
10 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
11 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
12-21 73,684 (34,500) 39,184 (5,800) 33,384 (16,211) 17,173 (6,869) 10,304 5,800 16,211 32,315 0 32,315
7 10,000 16,211 16,692 16,211 10,000 0 6,211
8
9
10
11
12-21
16,211 16,692 16,211 0 0 16,211
16,211 16,692 16,211 0 0 16,211
16,211 16,692 16,211 0 0 16,211
16,211 16,692 16,211 0 0 16,211
16,211 16,692 16,211 0 0 16,211
Post-Production Period Year 22 Working Capital 11,900 After-Tax Reclam. -8,000 Net Cash Flow 3,900
DCF-ROR or Internal Rate of Return Year (j) Net CF 1 (1,200) 2 (2,400) 3 (2,400) 4 (17,400) 5 (40,800) 6 (43,400) 7 19,015 8 32,315 9 32,315 10 32,315 11 32,315 12 32,315 13 32,315 14 32,315 15 32,315 16 32,315 17 32,315 18 32,315 19 32,315 20 32,315 21 32,315 22 3,900 367,726
1/(1+.20)^j 0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162 0.135 0.112 0.093 0.078 0.065 0.054 0.045 0.038 0.031 0.026 0.022 0.018
Present Value CF @ 20% (1,000) (1,667) (1,389) (8,391) (16,397) (14,535) 5,307 7,515 6,263 5,219 4,349 3,624 3,020 2,517 2,097 1,748 1,457 1,214 1,011 843 702 71 3,580
1/(1+.25)^j 0.800 0.640 0.512 0.410 0.328 0.262 0.210 0.168 0.134 0.107 0.086 0.069 0.055 0.044 0.035 0.028 0.023 0.018 0.014 0.012 0.009 0.007
Present Value CF @ 25% (960) (1,536) (1,229) (7,127) (13,369) (11,377) 3,988 5,422 4,337 3,470 2,776 2,221 1,777 1,421 1,137 910 728 582 466 373 298 29 (5,666)
By Linear Interpolation DCF-ROR = 20% + 3580/(3580+5666)*(25-20)% = 21.9% Exact Solution
21.5090%
0.21509 0.823 0.677 0.557 0.459 0.378 0.311 0.256 0.210 0.173 0.143 0.117 0.097 0.079 0.065 0.054 0.044 0.036 0.030 0.025 0.020 0.017 0.014
Present Value CF @ 21.509% (988) (1,626) (1,338) (7,982) (15,403) (13,485) 4,862 6,800 5,597 4,606 3,791 3,120 2,567 2,113 1,739 1,431 1,178 969 798 657 540 54 0
Projected Cash Flows For Bedded Zinc Deposit
17
19
21
17
19
21
15
13
11
9
7
5
3
10000 0 -10000 -20000
1
$ *1000
40000 30000 20000
-30000 -40000 -50000 Year
Present Value of Cash Flows at 21.5% Discount Rate 10,000
(10,000) (15,000) (20,000) Year
15
13
9
7
5
11
(5,000)
3
0 1
$ *1000
5,000
Definitions of troy ounce on the Web: ounce: a unit of apothecary weight equal to 480 grains or one twelfth of a pound
he traditional unit of weight for gold is the troy ounce, named, it is thought, after a weight used at the annual fair at Troyes in France in the Middle Ages. Although the metric system is used increasingly in mining and the gold business, the troy ounce remains the basic unit in which the price of 995 gold is quoted. One troy ounce = 31.1034807 grams, 32.15 troy ounces = 1 kilogram, 1 troy ounce = 480 grains,
Mine Production Scheduling Optimization - The State of Art -
K. Dagdelen Professor Mining Engineering Department Colorado School of Mines Golden, Colorado 80401
OPEN PIT OPTIMIZATION
l
APCOM 2005
l l
For Each Block in The Model If a given block of material should be mined? When it Should be mined? Once it is mined what to do with the block of Material
OPEN PIT OPTIMIZATION Start
APCOM 2005
Physical Capacities Production Costs
Extraction Scheduling
Ultimate pit
Cutoff Grade Design Of Cuts
Steps of Traditional Planning by Circular Analysis
OPEN PIT OPTIMIZATION
APCOM 2005
ULTIMATE PIT LIMITS
OPEN PIT OPTIMIZATION ULTIMATE PIT LIMITS l Identifies What blocks should be mined and which l l APCOM 2005
l l
ones should be left in the ground. Defines the lateral and vertical extent to which a given deposit can economically be mined to 3-D Breakeven Analysis Moving Cone algorithm gives sub-optimum results Lerchs and Grossmann algorithm gives true breakeven pit that maximizes the undiscounted profits
OPEN PIT OPTIMIZATION
APCOM 2005
ULTIMATE PIT LIMITS The Lerchs and Grossmann Algorithm l Only finds the maximum profit pit boundary l No time value of money is considered l The pit that maximizes discounted profits (NPV) by taking into account time value of money is much smaller than the ultimate pit found by this technique
OPEN PIT OPTIMIZATION ULTIMATE PIT LIMITS l Common practice is to apply Lerchs and
Grossmann’s algorithm to the economic block model that is generated to discounted block values
APCOM 2005
l Economic block model is generated by discounting
block values based on a rough initial production schedule
OPEN PIT OPTIMIZATION ULTIMATE PIT LIMITS l If the schedule is not defined by identifying effect of
waste stripping on the overall cash flows then the ultimate pit limit may not be correct
APCOM 2005
l NPV analysis on the last incremental pushbacks
always results in elimination of non-contributing incremental pits
OPEN PIT OPTIMIZATION Start
APCOM 2005
Physical Capacities Production Costs
Extraction Scheduling
Ultimate pit
Cutoff Grade Design Of Cuts
Steps of Traditional Planning by Circular Analysis
OPEN PIT OPTIMIZATION
APCOM 2005
DESIGN OF PUSHBACKS Economic block models are developed by varying either l Metal Price l Cutoff Grade l Minimum profits required per ton of ore l Some ratio in block evaluation equation l As these variables change the pit outline also changes l Each outline is then used as pushbacks
OPEN PIT OPTIMIZATION
APCOM 2005
DESIGN OF PUSHBACKS
PHASE 1
PHASE 2 PHASE 3
OPEN PIT OPTIMIZATION DESIGN OF PUSHBACKS
APCOM 2005
l The concept is based on mining “next best ore”
without considering impact of stripping to be done ahead of time l First incremental pit contains the ore that has the highest average overall value per ton. The subsequent pits have lower and lower average value per ton of ore l The push back designs do not take into account effect of timing of waste stripping on the NPV l Blending requirements can not be taken into account
OPEN PIT OPTIMIZATION
APCOM 2005
DESIGN OF PUSHBACKS
OPEN PIT OPTIMIZATION Start
APCOM 2005
Physical Capacities Production Costs
Extraction Scheduling
Ultimate pit
Cutoff Grade Design Of Cuts
Steps of Traditional Planning by Circular Analysis
OPEN PIT OPTIMIZATION
APCOM 2005
CUTOFF GRADES
2005 SME Annual Meeting
Cutoff Grades l
A cutoff grade is the grade that is used to differentiate between ore and waste in a given mining environment. Although the definition of cutoff grade is straight forward, the determination of it is not.
l
To determine if a block of material should be milled or taken to the waste dump, breakeven mill cutoff may be used. Milling cutoff grade
McLaughlin Gold Mine California, USA Pit Ore and waste discrimination
Waste
2005 SME Annual Meeting
Waste dumps
Ore Cutoff grade
Stockpiles
Autoclave Mill
Round Mountain Gold Mine
Oxide
2005 SME Annual Meeting
Low grade stockpiles
Ore Sulfide
Crusher
Stockpiles
CIP Mill Leach Pads
Waste
Waste dumps
Breakeven Mill Cutoff Grade
2005 SME Annual Meeting
l
The lowest economic grade where mining, milling, and administration cost are equal to revenues obtained from the metal produced.
Breakeven cutoff grade =
Milling Cost (Price – Refining Cost - Sales Cost) * Recovery
l
Traditionally, this breakeven cutoff grade has been widely used in a production scheduling.
McLaughlin Mine Case Study
2005 SME Annual Meeting
l
The economic and operational parameters: Price
(P)
600
$/oz
Sales Cost
(s)
5
$/oz
Processing Cost
(c)
19
$/ton ore
Recovery
(y)
0.9
Mining Cost
(m)
1.2
$/ton
Fixed Cost
(fa)
8.35M
$/year
Mining Capacity
(M)
Unlimited
Processing Capacity
(C)
1.05M
tons
Discount Rate
(d)
15
%
Production Scheduling By Breakeven Cutoff Grade (Case1)
2005 SME Annual Meeting
l
If one uses breakeven cutoff grade for a production scheduling: Breakeven cutoff grade =
$19/ton ($600/oz - $5.0/oz) * 0.90
= 0.035 oz/ton
l
All the materials above 0.035oz/ton goes to process, and below goes to waste dump.
McLaughlin Case Study l l
Consider a case study from McLaughlin Mine in California where an epithermal gold deposit was mined by an open pit. The grade distribution within the ultimate pit limit is: From
Tons
2005 SME Annual Meeting
Grade Category
Grade intervals
0 0.02 0.025 COG 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.1
To
0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.1 0.358
midpoint 0.0100 0.0225 0.0275 0.0325 0.0375 0.0425 0.0475 0.0525 0.0575 0.0625 0.0675 0.0725 0.0775 0.0900 0.2290
Ktons 70,000 7,257 89,167 tons 6,319 5,591 4,598 4,277 SR=2.45 3,465 2,428 2,307 1,747 36,346 tons 1,640 1,485 @0.102oz/ton 1,227 3,598 9,576 125,515
Yearly Mining and Milling Rates
2005 SME Annual Meeting
l
Assuming the deposit is homogeneously distributed, yearly mining rate is given as follows:
l l
l l
Yearly ore tons: 1.05Mtons (Limited by process capacity) Yearly ounces recovered: 1.05Mtons x 0.102 oz/ton x 0.9 = 96.3koz Yearly waste tons: 1.05Mtons x 2.45 (SR) = 2.58Mtons Yearly mining rates: 1.05M + 2.58M = 3.62Mtons
Yearly Schedules by Breakeven Cutoff Grade (Cont.)
2005 SME Annual Meeting
l
Mining the deposit with breakeven cutoff grade of 0.035oz/ton at 1.05M tons process capacity: Avg
Qm
Qc
Qr
Profits
Year (i)
COG
Ore Grade
(Mtons)
(Mtons)
(ktons)
($M)
1
0.035
0.102
3.6
1.05
96.3
33.0
2
0.035
0.102
3.6
1.05
96.3
33.0
3
0.035
0.102
3.6
1.05
96.3
33.0
4
0.035
0.102
3.6
1.05
96.3
33.0
5
0.035
0.102
3.6
1.05
96.3
33.0
6
0.035
0.102
3.6
1.05
96.3
33.0
7
0.035
0.102
3.6
1.05
96.3
33.0
8
0.035
0.102
3.6
1.05
96.3
33.0
9
0.035
0.102
3.6
1.05
96.3
33.0
10
0.035
0.102
3.6
1.05
96.3
33.0
11 to 34
0.035
0.102
3.6
1.05
96.3
33.0
35
0.035
0.102
3.4
1.00
91.7
31.4
Total
125.8
36.7
3,365.9
1,154.2 (NPV@15%) $218.5
2005 SME Annual Meeting
Shortcomings of the Traditional Cutoff Grades l
They are established to maximizing the undiscounted profits from a given mining operation.
l
They are constant unless the commodity price and the costs change during the life of the mine.
l
They do not consider grade distribution of the deposit.
OPEN PIT OPTIMIZATION CUTOFF GRADES l Many open pit mines are still designed and operated
using cutoff grades based on breakeven economic analysis which maximizes undiscounted profits
APCOM 2005
l The cutoff grades should be set to much higher
levels than the breakeven cutoff during the initial years of the operation
OPEN PIT OPTIMIZATION CUTOFF GRADES l The heuristic algorithm to define optimum declining
cutoff grades that maximize the NPV of a given project was developed by Kenneth Lane in 1965
APCOM 2005
l Applying this method to a given project results in
higher NPV for a project specially if capacities are not in harmony with the grade distribution of the deposit
2005 SME Annual Meeting
Declining Cutoff Grade l
Traditional cutoff grade (constant cutoff grade) does not maximize the NPV.
l
Many approaches have been suggested to improve NPV of the project.
l
K. F Lane in 1964 suggested an heuristic algorithm to obtain cutoff grades higher than breakeven grades during the early years that maximize the Net Present Value (NPV) of a project
Optimum Cutoff Grades by Lane’s Algorithm
2005 SME Annual Meeting
l
l
l
Lane’s approach considers the mining operation to be constrained by the capacities of mine, mill, and refinery. The cutoff grades are optimized by considering the grade distribution of the deposit in providing highest quality of ore to the mill subject to three capacity constraints. This approach has been successfully used in the mining industry for many years.
Optimum Cutoff Grades by OptiPit ®
2005 SME Annual Meeting
l
l
l
Linear Programming (LP) based algorithm and software is being developed to optimize cutoff grades under complex mining and process constraints. Mathematical programming approach is very powerful and provides complete flexibility in modeling complex operating environments. This approach will be described and demonstrated using four case studies coming from gold mines in Western United States.
Round Mountain Gold Mine
Oxide
Low grade stockpiles
Ore Sulfide
APCOM 2005
Crusher
Stockpiles
CIP Mill Leach Pads
Waste
Waste dumps
COMPLICATED PROCESSES AND CAPACITIES limited by ROM Leach
Dump
10M tons/yr
crusher Cr Leach
1 oc r P
2 oc r P
Phase 1
Cr
Proc 3
Autoclave
APCOM 2005
Phase2
Mine
Pr oc 4
5M tons/yr
20% Flot.
1.05M tons/yr
80%
Mining Capacity: 12M tons/yr Refining Capacity: 350 koz/yr Stockpile available
2M tons/yr
Tailings
OPEN PIT OPTIMIZATION CUTOFF GRADES l Linear Programming (LP) based algorithm and
software is being developed to optimize cutoff grades under complex mining and process constraints.
APCOM 2005
l Mathematical programming approach is very powerful
and provides complete flexibility in modeling complex operating environments.
CUTOFF GRADE FORMULATION Index d Cutoff Grade
Tons
Dump
APCOM 2005
McLaughlin mine
l
Grade intervals
Decision variables: Mine
X
t
Index g
igd Index i
Index t: Years
Mill
OPEN PIT OPTIMIZATION FUTURE
APCOM 2005
l NO scheduler in the market that incorporates
shortcomings discussed l There are efforts to develop methods that will overcome these shortcomings l The advancements in hardware and software technology in recent years is providing an unique opportunity to solve this problem by way of “Linear – Integer Programming” techniques l In the mean time, the use of computer programs that optimizes sub-problems will give you higher NPV for a given project if not the optimum.
MNGN 433 Mine Systems Analysis
Push Backs or Phases •
Defines how the pit will evolve with time.
•
Defines ore tons and its quality for different time periods.
•
Defines waste tons for removal schedules.
•
Defines the cash flows and overall project economics.
1
MNGN 433 Mine Systems Analysis
Push Backs or Phases Example
Phase 1
Phase 2 2
MNGN 433 Mine Systems Analysis
Push Backs or Phases Example (Cont.)
Phase 3
Phase 4 3
MNGN 433 Mine Systems Analysis
Push Backs or Phases Example (Cont.)
Cross Section
4
MNGN 433 Mine Systems Analysis
Cutoff Grade •
Minimum grade of the material for processing.
•
Normally used to discriminate between ore and waste within a given orebody.
•
Cutoff grade is Dynamic.
Read “Cutoff Grade Optimization” by Dr. Dagdelen
5
MNGN 433 Mine Systems Analysis
Breakeven Cutoff Grade •
The lowest economic grade where mining, milling, and administration cost are equal to revenues obtained from the metal produced.
•
Cutoff grades in the pit are normally much higher than the breakeven cutoff grade.
•
Cutoff grades decline as the mine matures, and approaches the breakeven cutoff.
6
Hypothetical Case Study MNGN 433 Mine Systems Analysis
• •
Consider a hypothetical case study where an epithermal gold deposit will be mined by an open pit. The grade distribution within the ultimate pit limit is: Grade Category From
To
0 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.1
0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.1 0.358
midpoint 0.0100 0.0225 0.0275 0.0325 0.0375 0.0425 0.0475 0.0525 0.0575 0.0625 0.0675 0.0725 0.0775 0.0900 0.2290
Ktons 70,000 7,257 6,319 5,591 4,598 4,277 3,465 2,428 2,307 1,747 1,640 1,485 1,227 3,598 9,576 125,515
7
MNGN 433 Mine Systems Analysis
Mine Design Parameters •
Capacities and Costs are: Price (P)
600 $/oz
Sales Cost (s)
5.00 $/oz
Processing Cost (c)
19.0 $/ton ore
Recovery (y)
90 %
Mining Cost (m)
1.2 $/ton
Fixed Costs (fa)
8.35 $M/yr
Mining Capacity (M)
Unlimited
Milling Capacity (C)
1.05 M
Capital Costs (CC)
105 $M
Discount Rate (d)
15 %
8
MNGN 433 Mine Systems Analysis
Traditional Cutoff Grades •
Traditionally, a cutoff grade is used to determine if a block of material should be mined or not. Ultimate pit cutoff grade
•
And, another cutoff is used to determine whether or not it should be milled or taken to the waste dump. Milling cutoff grade
9
Ultimate Pit Cutoff Grade MNGN 433 Mine Systems Analysis
•
Ultimate pit cutoff grade is defined as the breakeven grade that equates cost of mining, milling, refining and marketing to the value of the block in terms of recovering metal and the selling price.
Ultimate pit cutoff grade =
Milling Cost + Mining Cost (Price – Refining Cost - Sales Cost) * Recovery
Ultimate pit cutoff grade =
$19/ton + $1.2/ton ($600/oz - $5.0/oz) * 0.90
= 0.038 oz/ton 10
Milling Cutoff Grade MNGN 433 Mine Systems Analysis
•
Milling cutoff grade is defined as the breakeven grade that equates cost of milling, refining and marketing to the value of the block in terms of recovering metal and the selling price.
Milling cutoff grade =
Milling Cost (Price – Refining Cost - Sales Cost) * Recovery
Milling cutoff grade =
$19/ton ($600/oz - $5.0/oz) * 0.90
= 0.035 oz/ton 11
MNGN 433 Mine Systems Analysis
Milling Cutoff Grade (Cont.) •
In the milling cutoff grade, no mining cost is included since this cutoff is basically applied to those blocks that are already selected for mining.
•
The depreciation costs, general and administrative costs (G & A) and the opportunity costs are not included in the cutoff grade.
•
The basic assumption is that all of these costs including fixed costs defined as G & A will be paid by the material whose grade is much higher than the established cutoff grades.
12
MNGN 433 Mine Systems Analysis
Summary of the Traditional Cutoff Grades •
The ultimate pit limit cutoff is used to ensure that no material (unless they are in the way of other high grade blocks) is taken out of the ground unless all of the direct costs associated with gaining the metal can be recovered. (This assurance is automatically built into the ultimate pit limit determination algorithms like Learchs – Grossmann and Moving Cone)
•
The milling cutoff is used to ensure that any material that provides positive contribution beyond the direct milling, refining and marketing costs will be milled. 13
MNGN 433 Mine Systems Analysis
Shortcomings of the Traditional Cutoff Grades •
They are established to satisfy the objective of maximizing the undiscounted profits from given mining operation.
•
They are constant unless the commodity price and the costs change during the life of the mine.
•
They do not consider grade distribution of the deposit.
14
MNGN 433 Mine Systems Analysis
Yearly Tons and Grades Schedules by Constant Cutoff Grades
•
Define: Qm: Amount of total material mined in a given year (Mtons) Qc: The ore tonnage processed by the mill (Mtons) Qr: The recovered gold (koz)
•
The annual cash flows: Profits ($M) = (P - s) * Qr – Qc * c – Qm * m 15
MNGN 433 Mine Systems Analysis
Yearly Tons and Grade Schedules by Constant Cutoff Grades
•
Mining the deposit with traditional milling cutoff grade of 0.035oz/ton at 1.05M tons milling capacity (Table3): Avg
Qm
Qc
Qr
Profits
Year (i)
COG
Ore Grade
(Mtons)
(Mtons)
(ktons)
($M)
1
0.035
0.102
3.6
1.05
96.3
33.0
2
0.035
0.102
3.6
1.05
96.3
33.0
3
0.035
0.102
3.6
1.05
96.3
33.0
4
0.035
0.102
3.6
1.05
96.3
33.0
5
0.035
0.102
3.6
1.05
96.3
33.0
6
0.035
0.102
3.6
1.05
96.3
33.0
7
0.035
0.102
3.6
1.05
96.3
33.0
8
0.035
0.102
3.6
1.05
96.3
33.0
9
0.035
0.102
3.6
1.05
96.3
33.0
10
0.035
0.102
3.6
1.05
96.3
33.0
11 to 34
0.035
0.102
3.6
1.05
96.3
33.0
35
0.035
0.102
3.4
1.00
91.7
31.4
Total
125.8
36.7
3,365.9
1,154.2 (NPV@15%) $218.5
16
MNGN 433 Mine Systems Analysis
Yearly Tons and Grades Schedules by Constant Cutoff Grades (NPV Calculation)
•
NPV of the project: 33.0 (1 + 0.15)1
+
33.0 (1 + 0.15)2
+
33.0 (1 + 0.15)4
+
33.0 (1 + 0.15)5
+
33.0 31.4 + (1 + 0.15)34 (1 + 0.15)35
NPV =
+
33.0 (1 + 0.15)3 …
= $218.5M 17
MNGN 433 Mine Systems Analysis
Summary of Constant Cutoff Grade •
Total 28.44M tons is mined (Avg. grade 0.102 oz/ton)
•
Overall stripping ratio: 1: 2.42
•
Mine life: 35 years
•
Undiscounted profits: $1154.2M
•
NPV: $218.5M 18
MNGN 433 Mine Systems Analysis
Declining Cutoff Grade •
Traditional cutoff grade (constant cutoff grade) does not maximize the NPV.
•
Many approaches have been suggested such that NPV is improved.
•
Using cutoff grade higher than breakeven grades during the early years for a faster recovery of capital investments and using breakeven grades during the later stages has been practiced in the industry. 19
MNGN 433 Mine Systems Analysis
Heuristic Cutoff Grade •
The traditional cutoff grade is modified so that they include depreciation, fixed costs and minimum profit per ton required for a period of time to obtain a much higher cutoff grade during the early years.
•
After the end of the initial period, minimum profit requirement is removed from the equation to lower the cutoff grades further until the plant is paid off.
•
At that point, the depreciation charges are also removed. 20
MNGN 433 Mine Systems Analysis
Concept of Heuristic Cutoff Grade •
The concept is demonstrated pictorially as follows:
Idealized cross section of a series of pits for various cutoff grades
21
MNGN 433 Mine Systems Analysis
Capital Cost •
Assume: Capital Cost: $105M (Depreciated during the first 10 years)
•
Depreciation cost per year $105M / 10 yrs = $10.5M / yr
•
Depreciation cost per ton $10.5M / 1.05M tons = $10 / ton of ore
22
MNGN 433 Mine Systems Analysis
Minimum Profit •
Assume: Minimum profit of $3.0 per ton will be imposed to increase the cash flows further during the first five years
23
MNGN 433 Mine Systems Analysis
Heuristic Cutoff Grade Calculation •
The milling cutoff grades will be:
Yr 1 to 5 g milling =
Milling Cost + Depreciation + Minimum Prof. (Price – Refining Cost - Sales Cost) * Recovery
Ultimate pit cutoff grade =
$19/ton + $10/ton + $3/ton ($600/oz - $5.0/oz) * 0.90
= 0.060 oz/ton 24
MNGN 433 Mine Systems Analysis
Heuristic Cutoff Grade Calculation (Cont.) Yr 6 to 10 g milling =
Milling Cost + Depreciation (Price – Refining Cost - Sales Cost) * Recovery
Ultimate pit cutoff grade =
$19/ton + $10/ton ($600/oz - $5.0/oz) * 0.90
= 0.054 oz/ton 25
MNGN 433 Mine Systems Analysis
Heuristic Cutoff Grade Calculation (Cont.) Yr 11 to Depletion Milling Cost
g milling =
(Price – Refining Cost - Sales Cost) * Recovery
Ultimate pit cutoff grade =
$19/ton ($600/oz - $5.0/oz) * 0.90
= 0.035 oz/ton 26
MNGN 433 Mine Systems Analysis
Yearly Tons and Grade Schedules •
The year by year tons and grade schedule obtained modified cutoff grade policy (Table4): Avg
Qm
Qc
Qr
Profits
Year (i)
COG
Ore Grade
(Mtons)
(Mtons)
(ktons)
($M)
1
0.060
0.153
6.9
1.05
144.6
57.8
2
0.060
0.153
6.9
1.05
144.6
57.8
3
0.060
0.153
6.9
1.05
144.6
57.8
4
0.060
0.153
6.9
1.05
144.6
57.8
5
0.060
0.153
6.9
1.05
144.6
57.8
6
0.054
0.141
6.0
1.05
132.8
51.9
7
0.054
0.141
6.0
1.05
132.8
51.9
8
0.054
0.141
6.0
1.05
132.8
51.9
9
0.054
0.141
6.0
1.05
132.8
51.9
10
0.054
0.141
6.0
1.05
132.8
51.9
11 to 27
0.035
0.102
3.6
1.05
96.3
33.0
28
0.035
0.102
0.3
0.09
8.1
2.8
Total
125.8
28.44
3,032.1
1,112.7 (NPV@15%) $355.7
27
MNGN 433 Mine Systems Analysis
Summary of Modified Cutoff Grade •
Again, a total 28.44M tons is mined (Avg. grade 0.106 oz/ton)
•
Overall stripping ratio: 1: 3.88
•
Mine life: 25 years
•
Undiscounted profits: $1112.7M (3.6% reduction from Table3)
•
NPV: $355.7M (63% increase from Table3) 28
MNGN 433 Mine Systems Analysis
Heuristic Cutoff Grade (Including G & A) •
In the previous calculations, the G & A costs were not included in the cutoff grade and profit calculations.
•
Assume: Fixed Costs per year: $8.35M / year Fixed Costs per ton: ($8.35M/year) / (1.05Mtons/year) = $7.95 / ton
29
MNGN 433 Mine Systems Analysis
Heuristic Cutoff Grade Calculation (With G & A) •
The milling cutoff grades will be:
Yr 1 to 5 g milling =
Milling Cost + Depreciation + Minimum Prof. + Fixed cost (Price – Refining Cost - Sales Cost) * Recovery
Ultimate pit cutoff grade =
$19/ton + $10/ton + $3/ton + $7.95/ton ($600/oz - $5.0/oz) * 0.90
= 0.075 oz/ton 30
MNGN 433 Mine Systems Analysis
Heuristic Cutoff Grade Calculation (With G & A) (Cont.) Yr 6 to 10 g milling =
Milling Cost + Depreciation + Fixed cost (Price – Refining Cost - Sales Cost) * Recovery
Ultimate pit cutoff grade =
$19/ton + $10/ton + $7.95/ton ($600/oz - $5.0/oz) * 0.90
= 0.069 oz/ton 31
MNGN 433 Mine Systems Analysis
Heuristic Cutoff Grade Calculation (With G & A) (Cont.) Yr 11 to Depletion g milling =
Milling Cost + Fixed cost (Price – Refining Cost - Sales Cost) * Recovery
Ultimate pit cutoff grade =
$19/ton + $7.95/ton ($600/oz - $5.0/oz) * 0.90
= 0.050 oz/ton 32
MNGN 433 Mine Systems Analysis
Yearly Tons and Grades Schedules •
The year by year tons and grade schedule obtained modified cutoff grade policy that includes fixed costs (Table5): Avg
Qm
Qc
Qr
Profits
Year (i)
COG
Ore Grade
(Mtons)
(Mtons)
(ktons)
($M)
1
0.075
0.182
9.2
1.05
171.6
62.8
2
0.075
0.182
9.2
1.05
171.6
62.8
3
0.075
0.182
9.2
1.05
171.6
62.8
4
0.075
0.182
9.2
1.05
171.6
62.8
5
0.075
0.182
9.2
1.05
171.6
62.8
6
0.069
0.169
8.2
1.05
160.0
57.1
7
0.069
0.169
8.2
1.05
160.0
57.1
8
0.069
0.169
8.2
1.05
160.0
57.1
9
0.069
0.169
8.2
1.05
160.0
57.1
10
0.069
0.169
8.2
1.05
160.0
57.1
11 to 17
0.050
0.132
5.4
1.05
124.8
39.5
18
0.050
0.132
1.3
0.26
30.5
9.6
Total
125.8
18.11
2,562.5
885.6 (NPV@15%) $357.1
33
MNGN 433 Mine Systems Analysis
Summary of Modified Cutoff Grade with Fixed Cost Included •
The policy of declining cutoff grades calculated with depreciation, minimum profit, and the G & A cost further improved the NPV of the deposit by 1% ($355.7M vs. $357.5M)
•
Overall undiscounted profits were adversely reduced by 20% ($1112.7M vs. $885.6M)
34
MNGN 433 Mine Systems Analysis
Lane’s Approach •
Declining cutoff grades throughout the mine life gives higher NPV.
•
The question is, “How should the cutoff grades be determined to obtain the highest NPV?”
•
K. F. Lane discussed the theoretical background, a general formulation, and a solution algorithm.
Read “Choosing the Optimum Cutoff Grade” by K.F. Lane 35
MNGN 433 Mine Systems Analysis
Lane’s Approach (Cont.) •
Lane showed that cutoff grade calculations that maximize NPV have to include the fixed costs associated with not receiving the future cash flow quicker due to the cutoff grade decision taken now.
•
Underlying philosophy in inclusion of the opportunity cost is that every deposit has a given NPV associated with it at a given point in time and that every ton of material processed by the mill during a given year should pay for the cost of not receiving the future cash flows by one year sooner. 36
MNGN 433 Mine Systems Analysis
Cutoff Grade Equation for Lane’s Approach •
The cutoff grade equation that maximizes the NPV of the deposit constrained by the mill capacity is: g milling (i) =
c + f + Fi (P - s) * y
Where i = 1, …, N (mine life), gmilling(i) is the cutoff grade to be used in Year i.
37
MNGN 433 Mine Systems Analysis
Cutoff Grade Equation for Lane’s Approach (Cont.) •
Fi is the opportunity cost per ton of ore in Year i and it is defined as: Fi = d * NPVi / C
•
f is defined as: f = fa / C
Where d is the discount rate; NPVi is the NPV of the future cash flows of the years (i) to the end of mine life; fa is the annual fixed costs 38
Yearly Tons and Grades Schedules MNGN 433 Mine Systems Analysis
•
The year by year tons and grade schedule resulted from Lane’s approach (Table6): Avg
Qm
Qc
Qr
Profits
NPV
Year (i)
COG
Ore Grade
(Mtons)
(Mtons)
(ktons)
($M)
($M)
1
0.161
0.259
18.0
1.05
245.2
95.9
413.8
2
0.152
0.255
17.2
1.05
241.0
94.4
380.0
3
0.142
0.25
16.5
1.05
236.4
92.6
342.6
4
0.131
0.245
15.7
1.05
231.3
90.5
301.4
5
0.120
0.239
14.9
1.05
225.7
88.1
256.1
6
0.107
0.232
14.1
1.05
219.6
85.4
206.4
7
0.092
0.213
12.1
1.05
200.9
76.7
152.0
8
0.079
0.188
9.8
1.05
177.9
65.9
98.1
9
0.065
0.163
7.6
1.05
153.6
53.9
46.9
Total
125.8
9.45
1,931.4
743.4 (NPV@15%) $413.8
39
MNGN 433 Mine Systems Analysis
Steps to Obtain Table 6 (1st Iteration) Year (i) 1 2 3 4 5 6 7 … 21 22 23 Total
NPVi 0 0 0 0 0 0 0
Cog 0.050 0.050 0.050 0.050 0.050 0.050 0.050
0 0 0
0.050 0.050 0.050
Avg Waste Ore Grade (Mtons) 0.133 101.5 0.133 97.1 0.133 92.6 0.133 88.2 0.133 83.7 0.133 79.3 0.133 74.9 0.133 0.133 0.133
12.7 8.3 3.8
Ore (Mtons) 24.0 23.0 21.9 20.9 19.8 18.8 17.7
SR
3.0 2.0 0.9
4.2 4.2 4.2
4.2 4.2 4.2 4.2 4.2 4.2 4.2
Year 1:
Cog=
19+8.35/1.05+(0*0.15)/1.05 (600-5)*0.9
=
0.050
Year 2:
Cog=
19+8.35/1.05+(0*0.15)/1.05
=
0.050
Qm (Mtons) 5.5 5.5 5.5 5.5 5.5 5.5 5.5
Qc (Mtons) 1.05 1.05 1.05 1.05 1.05 1.05 1.05
Qr (ktons) 125.7 125.7 125.7 125.7 125.7 125.7 125.7
Profits ($M) 39.9 39.9 39.9 39.9 39.9 39.9 39.9
NPV ($M) $255.0 $253.4 $251.5 $249.3 $246.8 $243.9 $240.6
5.5 5.5 5.1 125.8
1.05 1.05 0.91 24.0
125.7 125.7 108.9 2,874.0
39.9 39.9 33.1 910.8 (NPV@15%) $255.0
$86.6 $59.7 $28.7
(600-5)*0.9
40
MNGN 433 Mine Systems Analysis
Steps to Obtain Table 6 (2nd Iteration) 2nd iteration Year (i) 1 2 3 4 5 6 7 8 9 Total
NPVi $255.0 $253.4 $251.5 $249.3 $246.8 $243.9 $240.6 $236.8 $232.4
Cog 0.118 0.118 0.117 0.117 0.116 0.115 0.115 0.114 0.112
Avg Ore Grade 0.238 0.238 0.236 0.236 0.236 0.236 0.236 0.235 0.234
Waste (Mtons) 116.6 102.9 89.1 74.5 61.6 48.2 34.8 20.0 7.0
Ore (Mtons) 8.9 7.9 6.8 5.7 4.8 3.8 2.7 1.6 0.5
SR 13.1 13.1 13.1 13.1 12.9 12.9 12.9 12.9 15.6
Qm (Mtons) 14.8 14.8 14.8 14.8 14.6 14.5 14.6 14.6 7.5 125.0
Qc (Mtons) 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 0.45 8.9
Qr (ktons) 224.9 224.9 223.0 223.0 223.0 223.0 223.0 222.1 94.8 1,881.8
Profits ($M) 87.8 87.8 86.6 86.7 86.8 86.9 86.9 86.3 30.5 726.4
NPV ($M) $399.5 $371.7 $339.7 $304.0 $262.9 $215.5 $160.9 $98.2 $26.6
(NPV@15%)
$399.5 Year 1:
Cog=
19+8.35/1.05+(255*0.15)/1.05 (600-5)*0.9
=
0.118
Year 2:
Cog=
19+8.35/1.05+(253.4*0.15)/1.05 (600-5)*0.9
=
0.118
41
MNGN 433 Mine Systems Analysis
Steps to Obtain Table 6 (3rd Iteration) 3rd iteration Year (i) 1 2 3 4 5 6 7 8 9 Total
NPVi $399.5 $371.7 $339.7 $304.0 $262.9 $215.5 $160.9 $98.2 $26.6
Cog 0.157 0.149 0.141 0.131 0.120 0.108 0.093 0.077 0.057
Avg Ore Grade 0.257 0.253 0.250 0.245 0.238 0.232 0.215 0.189 0.158
Waste (Mtons) 118.1 101.2 84.8 69.0 54.7 40.7 27.5 15.3 7.1
Ore (Mtons) 7.4 6.6 5.9 4.9 4.2 3.3 2.5 1.7 0.9
SR 15.9 15.4 14.4 14.1 13.2 12.3 11.1 9.0 8.4
Qm (Mtons) 17.7 17.3 16.2 15.8 14.9 14.0 11.7 9.5 8.8 125.8
Qc (Mtons) 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 9.5
Qr (ktons) 242.9 239.1 236.3 231.5 224.9 219.2 203.2 178.6 149.3 1,925.0
Profits ($M) 94.9 93.2 92.8 90.5 87.7 85.3 78.6 66.6 50.0 739.7
NPV ($M) $411.8 $378.7 $342.2 $300.7 $255.4 $206.0 $151.6 $95.7 $43.5
(NPV@15%)
$411.81 Year 1:
Cog=
19+8.35/1.05+(399.5*0.15)/1.05 (600-5)*0.9
=
0.157
Year 2:
Cog=
19+8.35/1.05+(371.7*0.15)/1.05 (600-5)*0.9
=
0.149
42
Steps to Obtain Table 6 (4th Iteration) MNGN 433 Mine Systems Analysis
4th iteration Year (i) 1 2 3 4 5 6 7 8 9 Total
NPVi $411.8 $378.7 $342.2 $300.7 $255.4 $206.0 $151.6 $95.7 $43.5
Cog 0.160 0.151 0.142 0.131 0.118 0.105 0.091 0.076 0.062
Avg Ore Grade 0.259 0.255 0.250 0.245 0.238 0.230 0.213 0.182 0.162
Waste (Mtons) 117.0 101.4 85.2 70.0 55.9 41.8 28.0 16.5 8.0
Ore (Mtons) 7.8 6.7 5.9 5.1 4.2 3.3 2.7 2.0 1.2
SR 15.0 15.1 14.4 13.7 13.3 12.7 10.4 8.3 6.7
Qm (Mtons) 17.8 17.0 16.2 15.6 14.6 13.9 12.0 10.2 8.5 125.8
Qc (Mtons) 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 9.5
Qr (ktons) 244.8 241.0 236.3 231.5 224.9 217.4 201.3 172.0 153.1 1,922.1
Profits ($M) 96.0 94.7 92.8 90.7 88.0 84.3 77.1 61.8 52.6 738.0
NPV ($M) $412.3 $378.2 $340.2 $298.4 $252.4 $202.3 $148.3 $93.5 $45.7
(NPV@15%)
$412.30 Year 1:
Cog=
19+8.35/1.05+(411.8*0.15)/1.05 (600-5)*0.9
=
0.160
Year 2:
Cog=
19+8.35/1.05+(378.7*0.15)/1.05 (600-5)*0.9
=
0.151
43
MNGN 433 Mine Systems Analysis
Table 6 Table 6 Year (i) 1 2 3 4 5 6 7 8 9 Total
NPVi $413.8 $380.0 $342.6 $301.4 $256.1 $206.4 $152.0 $98.1 $46.9
Cog 0.161 0.152 0.142 0.131 0.119 0.105 0.091 0.077 0.063
Avg Ore Grade 0.259 0.255 0.250 0.245 0.239 0.232 0.2131 0.188 0.163
Waste (Mtons)
Ore (Mtons)
SR
Qm (Mtons) 18.0 17.2 16.5 15.7 14.9 14.1 12.1 9.8 7.6 125.8
Qc (Mtons) 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 9.5
Qr (ktons) 244.8 241.0 236.3 231.5 225.9 219.2 201.4 177.7 154.0 1,931.7
Profits ($M) 95.7 94.4 92.5 90.6 88.2 85.2 77.0 65.7 54.3 743.7
NPV ($M) $413.8 $380.2 $342.8 $301.7 $256.3 $206.6 $152.3 $98.2 $47.2
(NPV@15%)
$413.82 Year 1:
Cog=
19+8.35/1.05+(413.8*0.15)/1.05 (600-5)*0.9
=
0.161
Year 2:
Cog=
19+8.35/1.05+(380.0*0.15)/1.05 (600-5)*0.9
=
0.152
44
MNGN 433 Mine Systems Analysis
Summary of Lane’s Approach •
Lane’s approach gives 90% higher NPV and 35% lower undiscounted profits than constant cutoff grade (Table3).
•
Total tons mined are the same.
•
Tons milled is lower (36.7Mtons vs. 9.45Mtons)
•
Ounces of gold recovered is lower (3.37Moz vs. 1.93Moz)
•
Mine life is significantly shorter (36yrs vs. 10yrs) 45
MNGN 433 Mine Systems Analysis
Cutoff Grade Optimization 2 •
How to determine a cutoff grade policy where Mining capacity, milling capacity, and refining capacity may be limited, And Maximizing NPV of the projects
Read “An NPV Maximization Algorithm For Open Pit Mine Design” by Dr. Dagdelen 1
Definition of the Problem MNGN 433 Mine Systems Analysis
•
The problem is to maximize the NPV subject to production constraints: N Maximize
NPV = ∑ profit(i ) * (1+1d ) i i =1
Subject to
Qm (i ) ≤ M
for i = 1,…N
Qc (i) ≤ C
for i = 1,…N
Q (i ) ≤ R
for i = 1,…N
r Where i: Year indicator
N: Mine life in years Qm: Amount of total metal mined in a given year (Ore + Waste) Qc: Ore tonnage processed in a given year Qr: Recovered metal (in tons) in a given year M: Annual mining capacity in tons C: Annual milling capacity in tons R: Annual refinery capacity in tons
2
Derivation of Opportunity Costs of Mining Low Grades MNGN 433 Mine Systems Analysis
•
Define:
V:
Maximum possible present value of future profits (cash flows) from the operation (NPV of total operation)
Profits ($M):
Profits (Cash flow) from mining Qm amount of material
Vq:
Maximum possible present value of future profits (cash flows) after the next Qm amount of material has been mined
v=V-Vq:
Marginal increase in present value to be achieved by mining next Qm of material
3
MNGN 433 Mine Systems Analysis
Derivation of Opportunity Costs of Mining Low Grades (Cont.) V=
( profits ($M ) + Vq ) (1 + d )T
V * (1 + d )T = ( profits ($ M ) + Vq)
If i is relatively small, then
(1 + d ) i = (1 + d * T )
V * (1 + d * T ) = profits ($ M ) + Vq V + V * d * T = profits ($M ) + Vq V − Vq = profits ($M ) − V * d * T 4
MNGN 433 Mine Systems Analysis
Derivation of Opportunity Costs of Mining Low Grades (Cont.) Let v=V-Vq then v = profits ($M ) − d * V * T
The opportunity cost of taking low grades now when higher grades are still available
We need to set cutoff grade so that we do not delay high grade 5
Basic Present Value Expression MNGN 433 Mine Systems Analysis
•
Annual profits can be calculated as follows: v = ( P − r − s ) * Qr − c * Qc − m * Qm − f * T − d * V * T Where P: Metal price per ton of product r: Marketing cost per ton of product s: Sales cost per ton of product c: Processing cost per ton of ore m: Mining cost per ton of ore f: Annual fixed administrative costs T: Number of time periods that will take to mine, concentrate and refine Qm amount of material from the pit (i.e. years)
6
MNGN 433 Mine Systems Analysis
Mine Limiting Case •
When the mining capacity is the bottleneck in the system: Qm T= M
( f + d *V ) vm = ( P − r − s) * Qr − c * Qc − m + * Qm M vm
vm is a function of cutoff grades COG
7
MNGN 433 Mine Systems Analysis
COG of Mine Limiting Case •
Cutoff grade of mine limiting case is: gm =
c (P − r − s ) * y
where y: Metallurgical recovery
8
MNGN 433 Mine Systems Analysis
Concentrator Limiting Case •
When the concentrator capacity is the bottleneck in the system: Qc T= C
( f + d *V ) vc = ( P − r − s) * Qr − c + * Qc − m * Qm C
•
Cutoff grade of concentrator limiting case is: ( f + d *V ) c+ C gc = ( P − r − s) * y 9
MNGN 433 Mine Systems Analysis
Refinery Limiting Case •
When the refinery capacity is the bottleneck in the system: Qr T= R vr = ( P − r − s −
•
( f + d *V ) ) * Qr − c * Qc − m * Qm R
Cutoff grade of refinery limiting case is: gr =
c ( f + d *V ) P−r −s − * y R 10
MNGN 433 Mine Systems Analysis
Balancing Cutoff Grade (Cont.) Mine - Mill
C/M
g mc
11
MNGN 433 Mine Systems Analysis
Balancing Cutoff Grade (Cont.) Mine - Refinery
R/M
g mr
12
MNGN 433 Mine Systems Analysis
Balancing Cutoff Grade (Cont.) Mill - Refinery
R/C
g rc
13
MNGN 433 Mine Systems Analysis
Open Pit Copper Case Study Deposit Reserves (%Cu)
(Mtons)
14
MNGN 433 Mine Systems Analysis
First Year Production Reserves (%Cu)
(Mtons)
15
Open Pit Copper Case Study MNGN 433 Mine Systems Analysis
Unit of mining: ton
Price
(P):
$25/ 1%Cu of one unit of mining
(=$25/1%Cu*1ton = $25/0.01tonCu = $25/20lbsCu = $1.25/lbCu) Mining Cost
(m):
$1/ one unit of mining = $1/ton
Concentrator Cost
(c):
$2/ one unit of mining = $2/ton
Refinery Cost
(s):
$5/ 1%Cu of one unit of mining
Fixed Cost
(f):
$300M /yr
Mine capacity
(M):
100M one unit of mining /yr = 100Mtons/yr
Concentrator capacity (C):
50M one unit of mining /yr = 50Mtons/yr
Refinery capacity
40M of 1%Cu of one unit of mining /yr
(R):
(=40M*0.01tonCu /yr = 400k tons Cu /yr) Recovery
(y):
100%
Discount rate
(d):
15% 16
MNGN 433 Mine Systems Analysis
Mine Limited Case (V=0)
(V=1174)
17
MNGN 433 Mine Systems Analysis
Concentrator Limited Case (V=0)
(V=1174)
18
MNGN 433 Mine Systems Analysis
Refinery Limited Case (V=0)
(V=1174)
19
Balancing Cutoff Grades (V=0) gm
gr
500
gc
400 300 200 Profit
MNGN 433 Mine Systems Analysis
Balancing Cutoff Grade
vm
Gopt
100
vc vr
0 -100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-200 -300 COG
Feasible Region
20
Balancing Cutoff Grade 300 250 200 150 100 Profit
MNGN 433 Mine Systems Analysis
Balancing Cutoff Grades (V=1174)
vm
50
vc
0 -50 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
vr
-100 -150
Gopt
-200 -250 COG
21
MNGN 433 Mine Systems Analysis
Limiting Economic Cutoff Grades •
Cutoff grade of mine limiting case is (V=0):
c 2($ / ton) 2 gm = = = %Cu = 0.10%Cu ( P − s) * y ( 25 − 5)($ / 1%Cu *1ton) *1 ( 25 − 5) *1
•
Cutoff grade of concentrator limiting case is (V=0):
300 M ($ / yr ) ( f + d *V ) 300 2 ($ / ton ) + c+ 2+ 50 M (ton / yr) C 50 %Cu = 0.40%Cu gc = = = ( P − s) * y (25 − 5)($ / 1%Cu * 1ton) * 1 (25 − 5) * 1
22
MNGN 433 Mine Systems Analysis
Limiting Economic Cutoff Grades (Cont.) •
Cutoff grade of refinery limiting case is (V=0):
gr =
=
c 2($ / ton) = ( f + d *V ) 300M ($ / yr) P−s− * y (25 − 5)($ / 1%Cu *1ton) − *1 R 40 M (1%Cu *1ton / yr)) 2 300 25 − 5 − *1 40
%Cu = 0.16%Cu
23
MNGN 433 Mine Systems Analysis
Grade – Tonnage Curve
24
MNGN 433 Mine Systems Analysis
Average Grade Above Cutoff
25
MNGN 433 Mine Systems Analysis
Ore : Material Ratio
26
MNGN 433 Mine Systems Analysis
Product : Material Ratio
27
MNGN 433 Mine Systems Analysis
Product : Ore Ratio
28
MNGN 433 Mine Systems Analysis
Grade – Tonnage Relationship Cutoff (%Cu)
Quantity (Mtons)
Tons Below Tons Above Avg Grade Cutoff Cutoff Above Cutoff (Mtons) (Mtons) (%Cu) (C )
Cu Produced
Product to Material Ratio (R/M)
Product to Ore Ratio (R/C)
Ore to Waste Ratio
( R)
Ore to Material Ratio (C/M)
(%Cu of 1ton of Material)
0.00
100
0
1000
0.500
500
1.0
0.500
0.500
0.00
0.10
100
100
900
0.550
495
0.9
0.495
0.550
0.11
0.20
100
200
800
0.600
480
0.8
0.480
0.600
0.25
0.30
100
300
700
0.650
455
0.7
0.455
0.650
0.43
0.40
100
400
600
0.700
420
0.6
0.420
0.700
0.67
0.50
100
500
500
0.750
375
0.5
0.375
0.750
1.00
0.60
100
600
400
0.800
320
0.4
0.320
0.800
1.50
0.70
100
700
300
0.850
255
0.3
0.255
0.850
2.33
0.80
100
800
200
0.900
180
0.2
0.180
0.900
4.00
0.90
100
900
100
0.950
95
0.1
0.095
0.950
9.00
29
MNGN 433 Mine Systems Analysis
Balancing Economic Cutoffs gmc: Ore : Material
= C:M = 50M/100M =0.5
Then, from the table above gmc= 0.50 %Cu gmr: Product : Material
= R:M = 40M/100M =0.4
Then, from the table above gmr= 0.45 %Cu grc: Product : Ore
= R:C = 40M/50M =0.8
Then, from the table above grc= 0.60 %Cu
30
MNGN 433 Mine Systems Analysis
Choosing Optimum Cutoff Grade
31
MNGN 433 Mine Systems Analysis
Choosing Optimum Cutoff Grade
Gmc = 0.40%Cu Grc = 0.40%Cu Gmr = 0.16%Cu
Then, Gopt = 0.40%Cu
32
