1. INTRODUCTION 1.1Background 1.1 Background A building is an enclosed structure that has walls, floors, a roof, an d usually windows. “A ‘tall building’ building’ is a multi-story multi-story structure in which most occupants depend on elevators [lifts] to reach their destinations. The most prominent prominent tall buildings are called ‘high-rise ‘high-rise buildings’ buildings’ in most countries and ‘tower blocks’ in Britain and some E uropean countries. The terms do not have internationally in ternationally agreed definitions.” definitions.” However, However, a high-rise building high-rise building can be defined as follows:
“Any structure where the height can have a serious impact on evacuation ” ( The
International Conference on Fire Safety in High-Rise Buildings).
“For most purposes, the cut-off cut-off point for high-rise buildings is around seven stories. Sometimes, seven stories or higher define a high-rise, and sometimes the definition is more than seven stories. Sometimes, the definition is stated in terms of linear height (feet or meters) rather than stories.”
“Generally, a high-rise high-rise structure is considered to be one that ex tends higher than the maximum reach of available fire-fighting equipment. In absolute numb ers, this has been set variously between 75 feet (23 meters) and 100 feet (30 meters),” or meters),” or about seven to ten stories (depending on the slab-to-slab distance between floors).
The foundations that designers are most likely to consider first for major structures on deep deposits of clay or sand are reinforced concrete rafts. Rafts spread the load from columns and load bearing walls over the widest possible area and the differential settlements can be minimized or controlled by varying the raft stiffness. Generally settlement consideration are the most important determinants of the final design and onl y in cases of extremely heavy structures must the possibility of bearing capacity failures can be seriously examined. To limit the settlement to the allowable value the practice is to use pile foundations. Conventional pile foundations are commonly designed by b y adopting a relatively high factor of safety for the piles. These piles are placed in such a manner that they will sustain the entire design load of the superstructure. Although the connection “cap” (often raft) is in close contact with the soil, its contribution to the total bearing capacity and general pile group behaviour is seldom considered.
Nevertheless, in the past few decades, there has been an increasing recognition that the use of pile groups in conjunction with the raft can lead to considerable economy without compromising the safety and performance of the foundation. Such a foundation makes use of both the raft and the piles, and is referred to here as a pile-enhanced raft or a piled raft. This concept makes clever use of deep foundation elements to selectively supplement and load share with mats and similar foundations.
Very often, the deep foundation elements (piles or shafts) are only placed beneath portions of a foundation and are intended to carry only a portion of the superstructure load. Thus this is fundamentally different from foundation application where the piles o r shafts are placed beneath the entire foundation and are assumed to carry all loads. An additional unique aspect of the piled - raft concept is that the deep-foundation elements are sometimes designed to reach their ultimate geotechnical axial compressive capacity under service loads.
The piled-raft concept has also proven to be an economical way to improve the serviceability of foundation performance by reducing settlements to acceptable levels. Although the piled-raft concept has been most notably n otably applied to new construction involving high-rise buildings it is also potentially useful for for remedial works and moderate height structures.
1.2 Objectives of the Research Despite the fact that piled raft foundations are recognized to be able to become a costeffective alternative to conventional pile foundations, piled rafts represent a lesser known and underutilized geo-technology in many areas, in fact the same also in Ethiopia. Prior P rior to introducing this intriguing foundation concept to the construction industry in the country, it is necessary to investigate the advantages and performance of piled raft for our cases.
The main objectives of this thesis is therefore, to design piled raft foundations for highrise building in Addis Ababa soils.
Chapter Two Literature Review 2.1 Introduction
In the design of foundations, shallow foundation is the first option where the top soil has sufficient bearing strength to carry the superstructure load without an y significant total and differential settlements to prevent damage of infrastructure and superstructure. However, in the last decades the need for high-rise buildings and high-loaded superstructures has been increased rapidly, even in the lands with poor subsoil conditions. Therefore, the need for foundations with high bearing capacity and showing low settlement values, both total and differential, has also been increased. These types of foundations can be constructed as a shallow foundation after the application of ground improvement techniques or as a piled foundation which transfers the excessive load to a deeper and stiffer stratum through the piles and reduces the settlements.
This chapter presents a brief review of previous researches on piles, rafts, pile groups and piled raft foundations. However, the main attention is on design methods and analyses of piled raft foundations. Chapter may be outlined as;
Single Piles
Pile Groups
Raft Foundations
Piled Raft Foundations
General philosophies of piled raft design
Methods of analysis of piled raft foundations
As briefly mentioned in the Chapter 1; rafts are generall y considered only as a “cap” which structurally connects the heads of the piles. However, the positive contribution of rafts to the load/settlement behavior is disregarded. As structural elements, rafts are mostly in contact with the soil, therefore has/have a capacity to tran sfer the load comes from the superstructure to the soil beneath. Considering this contribution (or load sharing), the total le ngth of the piles may
be significantly decreased. So, piled raft foundations become an alternative to the piled foundations or foundations with “settlement reducing piles” for an econ omic/feasible design.
Piled raft foundations consist of three elements; piles, raft and the subsoil. Therefore, it is essential to mention the behavior of piled raft found ations starting from the single piles, pile groups and the raft only. In this study, piled raft foundations with friction piles, which are subjected to static vertical compression load, has b een taken into account. Therefore, piles, rafts, pile groups and piled raft foundations in cohesion-less soils and subjected to lateral/dynamic loadings are not mentioned.
2.2 Classification of Piles and Construction Techniques in Brief Piles, which are used for the foundations, can be classified according to the material, size (diameter), installation technique and behavior. Piles can be made of timber, plane or reinforced concrete, precast concrete, cast in place concrete or steel/sheet. Considering the diameter, piles can be classified as small (d≤250mm), medium (300mm≤d≤600mm) and large (d≥800mm). According the installation technique, piles can be subdivided into two main categories as displacement piles and replacement piles (Viggiani et al. 2012). The displacement piles, which have been using prior than the replacement piles, are constructed by pushing, screwing or driving. Steel sections/columns or timber can be used as displacement piles, when it comes to concrete, as a material, the piles are to be precast. On the other hand, the replacement piles are constructed by the removal of the soil from the ground and pouring concrete or placing precast concrete units/steel sections into the hole. Considering the behavior, p iles may be categorized as; floating/friction piles and end-bearing piles.
Installation/construction process of the replacement piles has a large number of details depending on the subsoil material, water level, equipment used and the excavation technique. Percussion or rotary drilling methods can be used for boring the soil. At the present, the most of the replacement piles are constructed by the rotary drilling, which is also valid for Turkey. If the soil profile consists of unstable material or water, a temporary steel casing or slurry is used to
support the hole which called as wet method. In other case the soil is self-supporting. The refore, the steel casing or slurry is not needed, which called as dry method.
2.3 Load Transfer Mechanism and Bearing Capacity of a Single Pile
Under axial compression loads, load transfer mechanism of a single pile is as shown in the Figure 1. In the case of floating piles, the shaft friction “q s” governs the capacity. However, as its name implies, capacity of end-bearing piles depends on tip resistance “qb”.
Figure 2.1: Load transfer mechanism of a single pile.
Considering the above entioned load sharing mechanism of a pile, there are mainly three approaches for the calculation of the pile capacity; from fundamental soil properties, from in situ test (SPT, CPT, etc.) results and from full-scale load tests on a prototype pile. The general focus of this study will be on the first one; fundamental soil properties.
The general concept of the evaluation of the ultimate resistance of a pile is b ased on the shaft friction and base resistance. Thus, the total failure load is formulated as:
= Qu + W p =Qb + Q f -W p Where Qu= load applied to the pile at failure Qb= base resistance Q f = shaft resistance W p= weight of the pile. The general equation for the base resistance may be written as: 1
Qb= cN c+ q’ o N q + d Ab 2
Where d = width or diameter of the shaft at base level q’ o = effective overburden pressure at the base level of the pile Ab= base area of pile c= cohesion of soil
= effective unit weight of soil N c , N q , = bearing capacity factors which take into account the shape factor.
In cohesionless soils and the term becomes insignificant in comparison with the term for deep foundations. Thus, Qb = ′ N q Ab The net ultimate load in excess of overburden pressure load ′ Ab is: Qu +W p - qo Ab = ′ N q Ab + W p - ′ Ab +Q f For all practical purposes, and are assumed equal. Therefore: Qu =′ N q Ab + Q f
tanδ ′ Qu =′ N q Ab + A s Where A s = surface area of the embedded length of the pile
′ = average effective overburden pressure over the embedded depth of the pile s= average lateral earth pressure coefficient δ= angle of wall friction.
In the case of cohesive soils, such as saturated clays (normally consolidated), for ϕ=0, N q=1 and = 0. The ultimate base load:
= (cb N c + ′ )Ab
The net ultimate base load:
- ′ Ab =Qb = cb N c Ab
Therefore, the net ultimate load capacity of the pile: Qu=cb N c Ab+α̅ u A s Where α = adhesion factor
̅ u = average undrained shear strength of clay along the shaft cb= undrained shear strength of clay at the base level N c = bearing capacity factor
The value of the bearing capacity factor is accepted as 9 which is the value proposed by Skempton (1951) for circular foundations for a ratio greater than 4. The base capacity of a pile in clayey soils may now be expressed as: Qb =9cb Ab Skin Resistance By α – Method: For evaluating the adhesion factor, Dennis and Olson (1983) developed a curve
in Figure 2 giving a relationship between and undrained shear strength of clay. This curve is valid for the piles penetrating less than 30m. For embedment between 30 to 50m, a reduction factor should be applied linearly from 1.0 to 0.56 (Dennis and Olson, 1983).
Figure 2.2 Adhesion factor for piles with penetration lengths less than 50m in clay (Data from Dennis and Olson, 1983; Stas and Kulhawy, 1984)
By β-Method or the Effective Stress Method of Computing Skin Resistance: Unit skin
friction is defined as:
tan δ= β ′ ′ fs= By Meyerhof 's Method (1976): Meyerhof has suggested a semi-empirical relationship for
estimating skin friction in clays. For bored piles: f s=cutan ∅′
Where cu = undrained shear strength of the soil
∅′ = effective angle of internal friction
2.4Load Transfer Mechanism and Bearing Capacity of Pile groups As load-bearing structural elements, piles are mostly installed in groups. Based on the connectivity of the pile cap with the underlying soil, pile groups can be divided into two main types as; free-standing groups, in which the piles c ap is not in contact with underlying soil and piled foundations, in which the cap is in contact with the underlying soil (Poulos and Davis (1980)). For both types of the pile groups, it is naturally expected from piles to interact and to affect each other’s capacity. Interaction between the piles in a group is indicated by Fleming et al. (1992) as shown in Figure 4. Pile slenderness ratio, pile spacing ratio, pile stiffness ratio, homogeneity of soil and Poisson’s ratio are the factors which creates the interaction of piles in a group.
Figure 2.3 Interaction of piles in a pile group (after Fleming et al., 1992)
Due to the interaction effects within a group, be aring capacity of the group becomes lower than the total capacity of the individual piles. As a result, the bearing capacity of pile
groups is described as the sum of the bearing capacity of the single piles, which was summarized in the previous section, multiplying with an e fficiency coefficient, and formulated as below: QGu=E nQu where QGu= bearing capacity of pile group Qu= bearing capacity of the single piles n = number of piles
Efficiency of the pile group can be found by Feld’s Rule, which reduces the capacity of each pile by for each adjacent pile, by the empirical expression of Converse-Labarre or by the group reduction formula of Terzaghi and Peck (1948).
In Feld’s Rule, effect of the spacing of the piles is not taken into consideration. Widely used Converse-Labarre formula, for the efficiency of the group, is expressed as: (−1)+(−1)
E=1-
9
where =number of columns of piles in a group. n = number of rows,
= tan-1( ) in degrees.
d = diameter of pile. s = spacing of piles center to center.
In the group reduction formula of Terzaghi and Peck (1948), group capacity is the lesser of the bearing capacity for block failure of the group or the sum of the ultimate capacities of the individual piles. Block failure formula of Terzaghi and Peck (1948); QGu=Br Lr cN c+2(Br +Lr )L̅
where Br = overall width of the group Lr = overall length of the group L= depth of the piles below ground level c= undrained cohesion at the base of group N c= bearing capacity factor
2.5 Raft Foundations Raft foundations are commonly one-piece structural elements and cover an area at least equal to the projection of the structure. These types of foundations are suitable when large differential settlements are expected or the underlying soils have low bearing capacity. Due to large size of raft foundations, generally the differential settlements govern the design.
Basically two approaches have been suggested for analyzing the behavior of raft foundations as; 1. Rigid foundation approach 2. Flexible foundation approach
Rigidity or flexibility of a raft depends on the rela tive stiffness of itself and the subsoil. The behavior of the foundation also depends on the rigidity of the superstructure (Gupta (1997)). It should be noted that the contribution of the rigidity of the superstructure to the rigidity of the foundation is not considered within this study.
2.5.1 Load Bearing Capacity Terzaghi’s (1943) well-known expression may be used for the ultimate load bearing capacity of the raft foundations; qult =cN c sc + qN q+0.5B where c = cohesion sc= shape factor for cohesion q= overburden pressure ( ) B= least lateral dimension of the raft
= unit weight of soil = shape factor for soil wedge N c , N q , are the coefficients of bearing capacity as a function of internal friction angle of the soil ∅. For square foundations, formula becomes: qult =1.3cN c + qN q+0.4B
2.5.2 Settlement The load-settlement behavior or the stiffness of the raft is governed b y; raft dimensions c and d , soil shear modulus Gs and Poisson’s ratio υ of the subsoil according to Tan and Chow (2004). For the rectangular rafts, Richart et al. (1970) give the stiffness of the raft acting alone, as: k r= [
Gs
] β z (4)
1−υ
Where is the coefficient depending on the one-half of the raft dimensions and . Coefficient of has been shown in Figure 15 and can be chosen as 2.2 for square rafts. Tomlinson (1994) gives the general equation for the immediate/undrained settlement of a flexible foundation on clay as: 1−
i=qn*2B*(
)*l p
where i = settlement at the center of the flexible loaded area qn= net foundation pressure B=width of the equivalent foundation raft
=undrained Poisson’s ratio for clay E u= undrained deformation modulus l p= Steinbrenner’s influence factor. l p depends on the ratios on H/B and L/B. Where, H is the depth of compressible soil layer, B is the equivalent raft breadth.
2.6 Piled Raft Foundations Piled raft foundations are the composite structures which consist of three elements; piles, raft and the subsoil. Applied loads are transferred to the subsoil both through the raft and the piles. This load transfer mechanism can be simply shown in Figure 16. Load sharing between raft and piles is the main distinctive feature that diversifies this type of foundation from other type of piled foundations’ design.
Figure 2.4: Simplified load transfer mechanism of piled raft foundations.
Randolph (1994) has presented three design approaches for the piled raft foundations as: 1. The Conventional Approach: Piles are designed to carry the majority of the load. 2. Differential Settlement Control: Piles are located in order to reduce the differential settlement, rather than the overall average settlement. 3. Creep Piling: Piles are designed to operate at a working load (70-80% of the ultimate capacity) at which significant creep occurs.
In conventional design approach, loads are assumed to be carried only by the piles or by the raft. However, in the design of piled raft foundations, the load sharing between piles and the raft is taken into account (Reul and Randolph (2003)). Naturally, this load sharing improves the underestimated load capacity of the foundation comparing with the conventional approach, considering the properties of the piles and the raft remain unchanged. In addition, the piles may be used to control the settlement rather than carry the entire load (Linag et. al. (2003)) in the piled rafts. Tan and Chow (2004) illustrated the usage benefit of piles and raft together in the design of foundations in Figure 17.
Figure 2.5: Concept of piled raft (Tan and Chow, 2004)
2.6.1 Design Concepts The piled raft foundation is a foundation concept, which acts as a composite construction consisting of the three bearing elements: piles, raft and sub soil. According to its stiffness the raft distributes the loads of the structure Stot over contact pressure, represented by R raft, as well as over the piles, generally represented by the sum of pile resistance ∑ R pile,i in the ground (Figure 2.1). So the total resistance of piled raft is: Rtotal = Rraft + ∑R pile,i ≥ S tot
( 2.1)
By conventional foundation design it has to be proved that the building load is transferred either by the raft or the piles in the ground. In each case it has to be proved that either the raft or the piles will support the working load of the building with adequate safety against bearing resistance failure.
Figure 2.6 Piled raft foundation as composite construction of the bearing elements piles, raft and subsoil (Poulos, 2000)
The piled raft foundation indicates a new understanding of soil – structure interaction because the contribution of the rafts as well as the piles is taken into consideration to satisfy the proof of the ultimate bearing capacity and the serviceability of a piled raft as an overall system. Besides this, the interaction between raft and piles makes it p ossible to use the piles up to a load level which can be significantly higher than the permissible design value for the bearing capacity of comparable single standing pile. This leads us to different design philosophies with respect to piled raft foundation.
2.6.2 Alternative Design Philosophies
Randolph (1994) according to Poulos (2001) has defined clearly three different design philosophies with respect to piled rafts:
The “conventional approach”, in which the piles are designed as a group to carry the major part of the load, while making some allowance for the contribution of the raft, primarily to ultimate load capacity.
“Creep Piling” in which the piles are designed to operate at a working load at which significant creep starts to occur, typically 70-80% of the ultimate load capacity. Sufficient piles are included to reduce the net contact pressure between the raft and the soil to below the pre-consolidation pressure of the soil.
Differential settlement control, in which the piles are located strategically in order to reduce the differential settlements, rather than to substantially reduce the overall average settlement.
In addition, there is a more extreme version of creep piling, in which the full load capacity of the piles is utilized, i.e. some or all of the piles operate at 100% of their ultimate load capacity. This gives rise to the concept of using piles primarily as settlement reducers, while recognizing that they also contribute to increasing the ultimate load capacity of the entire foundation system.
Clearly, the latter three approaches are most conducive to economical foundation design, and will be given special attention herein. Howev er, it should be emphasized that the analysis and design methods to be discussed allow any of the above design philosophies to be implemented. According to Poulos (2001), De Sanctis et al. (2001) and Viggiani (2001) have distinguished between two classes of piled raft foundations: 1. “Small” piled rafts, where the primary reason for adding the piles is to increase the factor of safety (this typically involves rafts with widths between 5 and 15m); 2. “Large” piled rafts, whose bearing capacity of the raft is sufficient to carry the applied load with a reasonable safety margin, but piles are required to reduce settlement or differential settlement. In such cases, the width of the raft is large in comparison with the length of the piles (typically, the width of the piles exceeds the length of the piles). These
two categories broadly mirror the conventional and creep-piling philosophies considered by Randolph. Figure 2.2 illustrates, conceptually, the load-settlement behaviour of piled rafts designed according to the first two strategies. Curve O shows the beh aviour of the raft alone, which in this case settles excessively at the design load. Curve 1 represents the conventional design philosophy, for which the behaviour of the pile-raft system is governed by the pile group behaviour, and which may be largely linear at the design load. In this case, the piles take the great majority of the load. Curve 2 represents the case of creep piling where the piles operate at a lower factor of safety, but because there are fewer piles, the raft carries more load than for Curve 1. Curve 3 illustrates the strategy of using the piles as settlement reducers, and utilizing the full capa city of the piles at the design load. Consequently, the load-settlement may be nonlinear at the design load, but nevertheless, the overall foundation system has an adequate margin of safety, and the settlement criterion is satisfied. Therefore, the design depicted by Curve 3 is acceptable and is likely to be considerably more economical than the designs depicted by Curves 1 and 2.
Figure 2.7: Load settlement Curves for piled raft foundation according to varies design philosophies. (Poulos, 2000)
2.6.3 Design Issues As with any foundation system, design of a piled raft foundation requires the consideration of a number of issues, including: 1. Ultimate load capacity for vertical, lateral and moment loadings 2. Maximum settlement 3. Differential settlement 4. Raft moments and shears for the structural design of the raft 5. Pile loads and moments, for the structural design o f the piles.
In much of the available literature, emphasis has been placed on the bearing capacity and settlement under vertical loads. While this is a critical aspect and is considered herein, the other issues must also be addressed. In some cases, the pile requirements may be governed by the overturning moments applied by wind loading, rather than the vertical dead and live loads.
The bearing behaviour of a piled raft is characterized by a complex soil – structure interaction between the elements of the foundation and the subsoil. In detail there are the following interaction effects illustrated in Figure 2.1. •
Soil – pile interaction
•
Pile – pile interaction
•
Soil – raft interaction
•
Pile – raft interaction
The interaction effects between the adjacent piles and between the piles and the raft indicate for example the important fact, that bearing behaviour as known from a comparable single standing pile. The awareness of this interaction effects and the development of an adequate calculation method taking into the most substantial interaction effects is the main condition for a reliable design of piled rafts.
2.6.4 Methods of Analysis Several methods of analyzing piled rafts have been developed, and some of these have been summarized by Poulos (2000, 2001). Three broad classes of analysis method have been identified: •
Simplified calculation methods
•
Approximate computer-based methods
•
More rigorous computer-based methods.
Simplified methods include those of Poulos and Davis (1980), Randolph (1983, 1994), van Impe and Clerq (1995), and Burland (1995). All involve a number of simplifications in relation to the modelling of the soil profile and the loading conditions on the raft. The approximate computer-based methods include the following broad approaches: •
Methods employing a “strip on springs” approach, in which the raft is represented by a series of strip footings, and the piles are represented by sp rings of appropriate stiffness (e.g. Poulos, 1991) _Methods employing a “plate on springs” approach, in which the raft is represented by a plate and the piles as springs (e.g. Clancy and Randolph, 1993; Poulos, 1994).
The more rigorous methods include: •
Simplified finite element analyses, usually involving the representation of the foundation system as a plane strain problem (Desai, 1974) or an axi-symmetric problem and corresponding finite difference analyses via the commercial program FLAC.
•
Three-dimensional finite element analyses and finite difference analyses via the commercial program FLAC 3D.
•
Boundary element methods, in which both the raft and the piles within the system are discretized, and use is made of elastic theory (e.g. Butterfield and Banerjee, 1971; Wiesner and Brown).
•
Methods combining boundary element for the piles and finite element analysis for the raft (e.g. Hain and Lee, 1978; Franke et al, 1994)
2.6.4.1 Simplified Analysis Methods 2.6.4.1.1 Poulos – Davis - Randolph (PDR) Method For preliminary estimates of piled – raft behaviour, a convenient method of estimating the load – settlement behaviour may be developed by Poulos and Davis (1980) and Randolph (1994). As a consequence, the method to describe below will be referred to as the Poulos – Davis – Randolph (PDR) method. The method involves two main steps: 1. Estimation of the ultimate load capacity of the foundation. 2. Estimation of the load – settlement behaviour via a simple tri – linear relationship. For assessing vertical bearing capacity of a piled raft foundation u sing simple approaches, the ultimate load capacity can generally be taken as the lesser of the following two values: •
The sum of the ultimate capacities of the raft plus all the piles
•
The ultimate capacity of a block containing the piles and the raft, plus that of the portion of the raft outside the periphery of the piles.
For estimating the load-settlement behaviour, an approach similar to that described by Poulos and Davis (1980) can be adopted. However, a useful extension to this method can be made by using the simple method of estimating the load sharing between the raft and the piles, as outlined by Randolph (1994). The definition of the pile problem considered by Randolph is shown in Figure 2.3. Using his approach, the stiffness of the piled raft foundation can be estimated as follows:
K pr = [K p + K r (1-αcp )]/ [1-α2cp*K /K r p ] Where K pr = stiffness of piled raft K p = stiffness of the pile group K r = stiffness of the raft alone αcp = raft – pile interaction factor.
(2.2)
Figure 2.8: Simplified representation of a pile-raft unit (Poulos, 2001)
The raft stiffness r K can be estimated via elastic theory, for example using the solutions of Fraser and Wardle (1976) or Mayne and Poulos (1999). The pile group stiffness can also be estimated from elastic theory, using approaches such as those d escribed by Poulos and Davis (1980), Fleming et al (1992) or Poulos (1989). In the latter cases, the single pile stiffness is computed from elastic theory, and then multiplied by a group stiffness efficiency factor which is estimated approximately from elastic solutions. The proportion of the total applied load carried by the raft is:
P r / P t = K r (1-αcp ) / (K p + K r (1- αcp )) = X
(2.3)
Where P r = load carried by the raft P t = total applied load. αcp =Raft – pile interaction factor αcp = 1 - ln (r c / r o ) / ζ
(2.4)
Where r c = average radius of pile cap, (corresponding to an area equal to the raft area divided by number of piles r o = radius of pile ζ = ln ( r m / r o )
r m = {0.25 + ξ [2.5ρ(1−υ ) − 0.25]}*L ξ = E sl / E sb ρ = E sav / E sl υ = Poisson’s ratio of soil L = pile length E sl = soil Young’s modulus at level of pile tip E sb = soil Young’s modulus of bearing stratum below pile tip E sav = average soil Young’s modulus along pile shaft.
2.6.4.1.2 Burland’s Approach When the piles are designed to act as settlement reducers and to develop their full geotechnical capacity at the design load, Burland (1995) has developed the following simplified process of design:
•
Estimate the total long-term load-settlement relationship for the raft without piles (see Figure 2.5). The design load 0 P gives a total settlement S o.
•
Assess an acceptable design settlement S d , which should include a margin of safety.
• P l is the load carried by the raft corresponding to S d . •
The load excess P o - P l is assumed to be carried by settlement-reducing piles. The shaft resistance of these piles will be fully mobilized and therefore no factor of safety is applied. However, Burland suggests that a “mobilization factor” of about 0.9 be applied to the ‘conservative best estimate’ of ultimate shaft capacity, P su.
•
If the piles are located below columns which carry a load in excess of P su , the piled raft may be analyzed as a raft on which reduced column loads act. At such columns, the reduced load Qr is: Qr = Q − 0.9 P su
•
(2.6)
The bending moments in the raft can then be obtained by analyzing the piled raft as a raft subjected to the reduced loads Qr .
•
The process for estimating the settlement of the piled raft is not ex plicitly set out by Burland, but it would appear reasonable to adopt the approximate approach of Randolph (1994) in which: S pr = S r * K r / K pr
(2.7)
where S pr = settlement of piled raft S r = settlement of raft without piles subjected to the total applied loading K r = stiffness of raft K pr = stiffness of piled raft. Equation 2.2 can be used to estimate pr K pr
2.6.4.2
Approximate Computer Methods
The approximate computer-based methods are based on elastic theory and mainly have two approaches (Poulos 2001) as; strip on springs and plate on springs. In these approaches, the raft is treated as a strip and as a thin plate respectively. Additionally, piles are treated as springs and the soil as an elastic continuum, which are also simplified into springs, for the foundationstructure interaction analyses. Furthermore, the combination of these two methods is also possible. Sonoda et al. (2009) modeled of a raft of a building in Japan, composed of a mat having a thickness of 0.6m and beams having height of 1.2m, by a combination of thin plates and beams and as a combination of pile springs and soil springs as shown in Figure 19.
Figure 2.9: Strip on springs approach (Sonoda et al, (2009))
2.6.4.3 More Rigorous Computer Methods 2.6.4.3.1 Two – Dimensional Numerical Analysis Methods in this category are exemplified by the analyses described by Desai (1974), Hewitt and Gue (1994) and Pradoso and Kulhawy (2001). In the former case, the commercially available program FLAC has been employed to model the piled raft, assuming the foundation to be a two-dimensional (plane strain) problem, or an axially symmetric three-dimensional problem. In both cases, significant approximations need to be made, especially with respect to the piles, which must be “smeared” to a wall and given an equivalent stiffness equal to the total stiffness of the piles being represented. Problems are also encountered in representing concentrated loadings in such an analysis, since these must also be smeared. Unless the problem involves uniform loading on a symmetrical raft, it may be necessary to carry out analyses for each of the directions in order to obtain estimates of the settlement profile and the raft moments. As with the plate on springs approach, this an alysis cannot give torsional moments in the raft.
2.6.4.3.2 Three – Dimensional Numerical Analysis 3D Finite Element Method
A complete three-dimensional analysis of a piled raft foundation system can be carried out b y finite element analysis (e.g. Katzenbach et al, 1 998). In principle, the use of such a program removes the need for the approximate assumptions inherent in all of the above analyses. Some problems still remain, however, in relation to the modelling of the pile-soil interfaces, and whether interface element should be used. If they are, then approximations are usually involved in the assignment of joint stiffness properties. Apart from this difficulty, the main problem is the time involved in obtaining a solution, in that a non-linear analysis of a piled raft foundation can take several days, even on a modern computer running at high frequencies. Such analyses are therefore more suited to obtaining benchmark solutions against which to compare simpler analysis methods, rather than as routine design tools. Plaxis 3D
Plaxis is a company based in the Netherlands, developing software under the same brand name; Plaxis. The Plaxis 3D program is a three-dimensional finite element program used to make deformation and stability analysis for various types of geotechnical applications (Reference Manual, Plaxis). The user interface of the Plax is 3D consists of two sub-programs as Input and
Output. Properties of soil and other elements (boreholes, embedded piles, plates etc.) are assigned to the elements by using material data sets by the Input interface.
Sap2000
Sap2000 is general-purpose civil-engineering software for the anal ysis and design of any type of structural system developed by Computers and Structures, Inc. based in Berkeley, California. Frame elements, shell elements and spring supports are used in this stud y to define the model in Sap2000. As stated in the Reference Manual of Sap2000, the Frame element uses a general, three-dimensional, beam- column formulation which includes the effects of bi axial bending, torsion, axial de formation, and bi axial shear deformations. In this study, piles are modeled using the frame section properties. Shell elements are used to model the raft behavior. In Sap2000, three-node or four-node shell elements are available. Both the four-node and three-node shell element may be used in this study; however, the four-node shell elements are chosen. The main difference of four-node element is that, it does not have to be planar. Shell elements involve three types; membrane, plate and shell. Within these types, shell type of shell element is chosen, which supports all type of forces. However, plates support only the b ending moments and the transverse forces and membranes support only the in-plane forces and the normal (drilling) moments (Sap2000 Reference Manual). In addition, shell type elements involve thin and thick types. Shear strain is assumed to be zero for the thin type elements. Therefore, thick shell elements are used in this study. The piles (frame elements) and the raft (shell elements) has been connected without any constrains in the joints. The bottom of the model is supported by the spring supports, which is one of the possible joint connections.
