1-s2.0-S0266352X09001335-main

Computers and Geotechnics 37 (2010) 103–114

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Computers and Geotechnics

journal homepage: www.elsevier .com/locate /compgeo

Three-dimensional analysis of bearing behavior of piled raft on soft clay

JinHyung Lee a, Youngho Kim b, Sangseom Jeong b,*

a Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UKb School of Civil and Environmental Engineering, Yonsei University, Seoul 120 749, Republic of Korea

a r t i c l e i n f o a b s t r a c t

Article history:Received 23 February 2009Received in revised form 23 July 2009Accepted 26 July 2009Available online 20 August 2009

Keywords:Piled raftSoft clay3D finite element methodSlip interfaceLoad sharingFactor of safety

0266-352X/$ - see front matter � 2009 Published bydoi:10.1016/j.compgeo.2009.07.009

* Corresponding author. Tel.: +82 2 2123 2807; faxE-mail address: [email protected] (S. Jeong).

The piled raft has proved to be an economical foundation type compared to conventional pile founda-tions. However, there is a reluctance to consider the use of piled rafts on soft clay because of concernsabout excessive settlement and insufficient bearing capacity. Despite these reasons, applications of piledrafts on soft clay have been increased recently. Current analysis methods for piled rafts on soft clay, how-ever, are insufficient, especially for calculating the overall bearing capacity of the piled raft. This studydescribes the three-dimensional behavior of a piled raft on soft clay based on a numerical study usinga 3D finite element method. The analysis includes a pile–soil slip interface model. A series of numericalanalyses was performed for various pile lengths and pile configurations for a square raft subjected to ver-tical loading. Relatively stiff soil properties and different loading types were also used for estimating thebearing behavior of the piled raft. Based on the results, the effect of pile–soil slip on the bearing behaviorof a piled raft was investigated. Furthermore, the proportion of load sharing of the raft and piles at theultimate state and the relationship between the settlement and overall factor of safety was evaluated.The results show that the use of a limited number of piles, strategically located, might improve both bear-ing capacity and the settlement performance of the raft.

� 2009 Published by Elsevier Ltd.

1. Introduction

An increasing number of structures are constructed on softground, and the application of piled rafts on soft ground is becom-ing an important issue in foundation design. Less attention, how-ever, has been given to the behavior of a piled raft on soft claysoils because it is known as an unfavorable foundation type in softclay, which may be associated with excessive settlement and insuf-ficient bearing capacity [18,20]. Despite these concerns, a few suc-cessful applications of piled rafts on soft clay have been reported[11,20,25,26]. Recently, a few numerical methods have been devel-oped for the analysis of a piled raft on soft clay using analyticalmodels [20] or a three-dimensional (3D) finite element (FE)method [5,6]. However, current analysis and design proceduresfor piled rafts on soft clay under vertical loading are regarded asinadequate.

The behavior of a piled raft is affected by the 3D interactionbetween the soil, piles and raft. In addition, for soft clay conditions,the magnitude of settlement is larger than for stiff clay conditionsunder the same vertical applied load, so soil–structure (piles andraft) interaction is much more complicated. Therefore, a proper

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analytical model is needed to evaluate these interactions. Numer-ical methods, which are approximate, have been developed widelyin the last two decades because numerical methods are less costlyand may be used to consider many kinds of different soil and foun-dation geometries compared to field and model tests. According toPoulos [19], there are three broad classes of numerical analysismethods: (1) simplified calculation methods, (2) approximatecomputer-based methods and (3) more rigorous computer-basedmethods. He also noted that the most feasible method of analysiswas the three-dimensional linear/nonlinear FE method. Recently,nonlinear 3D FE analyses have been conducted [5,6,12,22,23];however, modeling problems related to the soil–structure interfacestill remain in the 3D FE analysis.

Therefore, the overall objective of this study focuses on investi-gating the bearing behavior of a piled raft on soft clay under verti-cal loading by using 3D FE analysis considering the pile–soil slipinterface model. No-slip (continuum) and slip analyses were con-ducted to examine the effects of the pile–soil interface model onthe behavior of a piled raft. The comparison of behavior for rela-tively stiff soil properties and different loading types was also car-ried out for the bearing behavior of a piled raft. Furthermore, theproportion of load sharing of the raft and piles at failure and therelationship between the settlement and overall factor of safetywere evaluated.

104 J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114

2. Finite element modeling

2.1. Finite element mesh and boundary conditions

The behavior of the piled raft was investigated by carrying out3D numerical analyses. The finite element package ABAQUS [1]was used. Fig. 1 shows a typical 3D FE mesh used in this parametricanalysis. The piles were taken to be 0.5 m in diameter D and 16 min length Lp. A square raft with width B of 10 m (thickness, 1 m)was considered. The pile head was connected to the raft rigidly.Due to symmetry, only a quarter of a whole mesh was modeledwith finite elements. The contact between the soil and pile was de-scribed as able to slip. The raft–soil interface was consideredsmooth with contact only. A relatively fine mesh was used nearthe pile–soil and raft–soil interface while a coarser mesh was usedfurther from the pile and raft. The mesh was assumed to be on arigid layer, and the vertical boundaries at the left- and right-handsides were assumed to be on rollers to allow downward movementof the soil layers. For the far-field boundaries, the distance of theboundary from the edge of the raft was set to 15 m since the ob-served influence zone based on the finite element analysis includ-

Rock

Pile

Soft clay

Raft

A

(a)

L p=

16m

tr =1m

Soft cl

rock

B/2=5m 1

(c

Fig. 1. A typical FE mesh used in 3D analysis (ex. 3 � 3, s = 3d, Lp = 16 m): (a) Typical 3D F

ing interface was at most 8–10 m [16]. After initial equilibrium, thevertical loading was applied on the top of the raft surface. Sincemodeling of the entire pile installation process is rather compli-cated, the pile was assumed to be in a stress-free state at the startof the analysis [10]. The stress change in the soil during pile instal-lation was therefore not included. In this study, the 3D model in-cluded very rigorous treatment of the soil and piled raft whichwere represented by 27 noded 2nd order hexahedral elements.

2.2. Constitutive modeling

The material behavior of the soft clay and bearing layer weremodeled with a Mohr–Coulomb model, and to simplify the analysisprocess, constant (average) values of material parameters wereadopted for the soil layer. The raft and piles were modeled withan isotropic elastic model.

For the pile–soil contact, the interface elements between pileand soil gives an effect on the behavior of a vertically loaded piledraft and the modeling of the pile–soil interfaces is an importantconcern. The modeling techniques used for the pile–soil interfaceare generally divided into two types. One is a slip element and

d=0.5m

3d

(b)

L s=

20m

4m

ay

5m

)

E mesh and boundary condition; (b) detail A – plan view; (c) side view of piled raft.

J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114 105

the other is a thin-layer element. The former was used by Lee et al.[14], Jeong et al. [10] and Lee et al. [15], in which the slip behaviorcould be considered. The latter was used by Reul and Randolph[22,23] and de Sanctis and Mandolini [5,6]. In general the sameconstitutive model is used as that of the nearby soil for the thin-layer element. However, the establishment of the basis for thedetermination of thickness of a thin-layer is difficult. Thus, a slipelement was used in this study to represent the interface behaviorbetween the pile and soil elements. However, difficulties still existin the choice of slip interface properties.

For the pile–soil slip interface, 2D quadratic 18 node elements,which consisted of two 9 node surfaces compatible with the adja-cent solid elements (the two surfaces coincide initially), were con-sidered using Coulomb’s frictional criterion to clarify smallsettlement of the piled raft. The schematic diagram and Coulomb’sfrictional model are shown in Figs. 2 and 3, respectively. This mod-el was selected from the element library of ABAQUS [1]. As shownin Fig. 2, the interface elements of zero thickness can only transfershear forces across their surfaces when a compressive normal pres-sure p0 acts on them. When contact occurs, the relationship be-tween shear force and normal pressure is governed by amodified Coulomb’s friction theory. Thus, these elements are com-pletely defined by their geometry: a friction coefficient l in Eq. (1),an elastic stiffness and a limiting displacement ccrit are used to pro-vide convergence.

scrit ¼ l � p0 ð1Þ

As reported by Jeong et al. [10], the interface friction coefficient lfor clay generally ranges from 0.2 to 0.4 Therefore, in this study,an average interface friction coefficient l of 0.3 for clay wasadopted. In addition, a critical shear displacement ccrit of 5 mmwas adopted for full mobilization of skin friction as suggested byLee et al. [14].

ClayPile

1γ

ClayPile

2γ

Nodes at the interface

(Identical co-ordinate)SlidingNo sliding

= p′< p′

Fig. 2. Behavior at the interface.

Elastic behavior

τ (shear stress)

τcrit=μσ′

γ (displacement)γcrit

Fig. 3. Coulomb’s frictional law.

2.3. Post analysis

The vertical settlements from the 3D FE analyses were used di-rectly, and the average settlement savg was represented by Eq. (2)[23].

savg ¼ ð2scenter þ scornerÞ=3 ð2Þ

where scenter = settlement of raft center, and scorner = settlement ofraft corner.

The stresses obtained at the integration points of the pile ele-ments were used to analyze the axial pile load. Thus, the axial pileload Ppile was calculated from the summation of the vertical stressin the pile element using Eq. (3).

Ppile ¼ pr2rv ð3Þ

where r is the pile radius and rv is the vertical stress in the pile ele-ment. In the case of the piles in a 3D analysis, the vertical stress wasaveraged at the same elevation.

The piled raft coefficient apr describes the ratio of the sum of allpile loads RRpile to the total load of the foundation Rtot using Eq. (4).

apr ¼RRpile

Rtotð4Þ

A piled raft coefficient of one represents a freestanding pile groupwhereas the piled raft coefficient of 0 describes an unpiled raft.

2.4. Validation

The validation of the present pile–soil slip interface model wasdone by a comparison with a centrifuge model test for a circularpiled raft on a stiff clay, which was carried out by Horikoshi andRandolph [8]. The total number of piles was nine (a 3 � 3 arraywith a pile spacing of 2.5 m) with a length of 15 m and diameterof 0.32 m, which were located under a 14 m diameter circular raftwith a thickness of 0.05 m. A soil depth of 25 m was taken into ac-count. Note that the prototype scale is used in this analysis. Thematerial properties of the soil and piled raft, which were adoptedfrom the values as reported by Horikoshi and Randolph [9], areshown in Table 1. As mentioned in Section 2.2, for the soil layer,the constant (average) values of the drained Young’s modulusand drained shear strength parameters were also adopted to sim-plify the analysis. However, the interface friction coefficient wasnot provided. Therefore, in the analysis a mean interface frictioncoefficient of the clay of 0.3 was used. In addition, a comparisonof the effect of the interface to a continuum (no-slip) analysiswas also conducted. An applied load of 12 MN was applied as a uni-form load over the whole raft area.

The comparative results of the 3D FE analysis and the centrifugetest under the design load of 12 MN are shown in Table 2. The ana-lyzed and experimental average settlements under the design loadof 12 MN were 21 mm (present study with slip interface), 19 mm(present study with no-slip interface) and 22 mm (measured).The result of the present study considering a slip interface gavemore reasonable agreement. For the no-slip analysis, the averagesettlement was smaller than for the slip analysis and the experi-mental result. Thus, the 3D FE analysis with a slip interface can

Table 1Material properties used for 3D FE analysis.

Soil Pile Raft

Young’s modulus: E, MPa 16.8 40,000 40,000Poisson’s ratio: m 0.4 0.16 0.16Density: c, kN/m3 17.5 20 20Undrained shear strength: cu, kPa 41.4 – –

Table 2Comparison of the results.

Results(applied load of 12MN)

Average settlement(mm)

Load carriedby piles (%)

Measured 22 19Present study Slip analysis 21 22

No-slip analysis 19 28

106 J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114

be evaluated as a reasonable agreement of average settlement. Inaddition, for the proportion of load taken by piles (i.e., a piled raftcoefficient apr), 19% was found from measurement, whereas the FEanalyses yielded 22% (present study with slip interface) and 28%(no-slip interface). The slip and no-slip analyses were larger thanthe values observed from the measurements, but the result of slipanalysis gave reasonable agreement to measurements compared tothe no-slip analysis.

Table 3Summary of numerical analyses conducted.

Foundation type Raft Pile

B (m) t (m) d (m) Lp (m) Array Spacing (s)

UR 10 1.0 – – – –PR 0.5 8f 3 � 3 3d�, 9d�

12f 4 � 4 3d, 6d16f�

20eb 5 � 5 4dSP – – 0.5 Same as PR – –

Note: f: floating pile, eb: end bearing pile; �: no-slip analysis.

B

Pile

(a)

cente

(c)

ce

Fig. 4. Pile configurations: (a) n = 9, s = 3d; (b) n = 9, s = 9d

Table 4Material parameters used in the analyses.

Model E0 (MPa) c0 (kPa)

Pile Elastic 12,500 –Raft 30,000 –

Soft clay Mohr–Coulomb 5 3Stiff clay 45 20Rock 500 0.1

Note: E (pile) is an equivalent value considering a solid cylinder.

From these comparative results, the settlement and piled raftcoefficient obtained by the slip analysis were somewhat different,but there was good agreement with the trends of the measuredresults.

2.5. Types of analyses

A series of numerical analyses on piled rafts (PR) were per-formed for different pile lengths, pile spacings and configurations,as shown in Table 3 and Fig. 4. The piles were taken to be 0.5 m indiameter D and 8, 12, 16 m (floating) and 20 m (end-bearing) inlength Lp. A square raft with a width B of 10 m (thickness, 1 m)was considered. A series of single piles (SP) and unpiled rafts(UR) were also analyzed. Moreover, to clarify the effect of thepile–soil slip of the piled raft on clay, two cases of conventionalno-slip (continuum) analysis were conducted.

The material properties of the soil were adopted from some ref-erence values as reported by Jeong et al. [10] for soft clay and Reuland Randolph [23] for stiff clay, respectively. In this study, atten-tion was focused on the drained (long-term) response of a piledraft resting on a soft clay layer, so the clay was idealized usingthe drained shear strength parameters, c0 and /0. Thus, consolida-tion effects were neglected. Constant values of drained Young’smodulus and drained shear strength parameters were adoptedfor the soil layer. For the structural components, the pile was basedon a typical steel pipe pile but modeled with a solid section, so aYoung’s modulus of the pile was applied to an equivalent solid pileThe Young’s modulus as reported by Jeong et al. [10] and the raft

sider

corner

(b)

(d)

sidenter

corner

(e)

sidecenter

corner

; (c) n = 16, s = 3d; (d) n = 16, s = 6d; (e) n = 25, s = 4d.

/0(�) m0 K0 ct (kN/m3)

– 0.25 0.01 25– 0.2 0.01 25

20 0.3 0.65 1820 0.3 0.65 1945 0.3 0.5 20

J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114 107

was assigned general concrete material parameters. Table 4 sum-marizes the material parameters used in the analyses.

For an applied vertical loading P, Poulos [18] noted that a uni-form loading may be adequate for the preliminary design stage,but it is not adequate for considering more detailed design. Hence,in this study, for comparison of the effect of loading types, two dif-ferent types of load, uniformly distributed loading (i.e., uniformloading) and concentrated loading (i.e., point loading), were ap-plied. For a point load, the load was applied at the center of the raft,but the equivalent magnitude of the load in the two different loadswas the same. The vertical loading was applied on the top of theraft surface after initial equilibrium.

All analyses were carried out under drained conditions. Thus,hydrostatic water pressure distribution was assumed in a drainedcondition with the ground water table located on the top of theclay layer.

0 0.5 1 1.5 2

1

0.8

0.6

0.4

0.2

0

z / L

s

slipcentersidecorner

no-slipcentersidecorner

P/QUR_ult

0.2 0.6

(a)

3. Computed results

3.1. Effect of slip interface model

To clarify the effect of pile–soil slip at the interface, in this studytwo different pile configurations (3 � 3, Lp = 16 m, s = 3d, 9d, asshown in Fig. 4a and b) in soft clay were subjected to both theno-slip (continuum) and slip analysis. The uniformly distributedloading was applied on the top of the raft surface. Fig. 5 showsthe normalized load P/QUR_ult versus the average settlement savg/Bof the piled raft with both slip and no-slip (continuum) analyses.Additionally, the resistance of nine (the number of piles in thepiled raft) single piles was plotted with the piled raft. The ultimatebearing capacity of a square unpiled raft (QUR_ult), which was usedto normalize the applied load level (P/QUR_ult), was estimated by theload of settlement of 10% B [2–4] from the ABAQUS [1] analysis ofthe unpiled raft load–settlement relationships reported by Lee[16].

For a close pile spacing s = 3d of the piled raft, the average set-tlement of the slip analysis was slightly larger than for a no-slipanalysis, but the effect of slip at the interface was insignificant.For a wide pile spacing s = 9d, the average settlement for the slipanalysis was larger than for the no-slip analysis. Additionally, fora single pile, the load–settlement curve of the slip analysis ap-

0 0.2 0.4 0.6P / QUR_ult

2.5

2

1.5

1

0.5

0

s avg

/ B

(%)

no-slips=3ds=9d9 x single

slips=3ds=9d9 x single

3x3 array, Lp /Ls=0.8

Fig. 5. Average settlements with the effect of pile–soil slip at interface, uniformloading.

proached the asymptotic value, but the no-slip analysis was stillincreasing under the same load levels.

Fig. 6 shows the normalized pile load distribution for piles be-neath a piled raft. In this figure, QP_PR is the pile load in a pile be-neath a piled raft, z is the depth from the ground level, and theultimate bearing capacity of single pile (QSP_ult) was estimated bythe British Standard (BS) regulation of 10% d (d: pile diameter, basisof total settlement) from the load–settlement relationships, asshown in Fig. 5. The pile load of the center pile was generally smal-ler than that of a corner pile for relatively low load levels. For slipanalysis, with increasing load level, the pile load of the center pilewas slightly larger than that of corner pile, irrespective of pile spac-ing. For no-slip analysis of close pile spacing s = 3d, however, thepile load of the center pile was still smaller than that of the cornerpile, irrespective of load level. However, for wide pile spacings = 9d, as the applied load increased, the pile load of the center pilewas larger than that of the corner pile, as in the slip analysis. Thepile load distributions of the no-slip analyses were more depen-dent on the pile spacing and pile positions, and the qualitative dis-tributions of pile load were similar to those reported using 3D FEanalysis with a thin-layer pile–soil interface model [21]. For max-

QP_PR / QSP_ult

0 0.5 1 1.5 2QP_PR / QSP_ult

1

0.8

0.6

0.4

0.2

0

z / L

s

slipcentersidecorner

no-slipcentersidecorner

P/QUR_ult

0.2 0.6

(b)

Fig. 6. Pile load distributions (Lp/Ls = 0.8) with the effect of pile–soil slip at interface,uniform loading: (a) 3 � 3, s = 3d; (b) 3 � 3, s = 9d.

0 0.2 0.4 0.6 0.8P / QUR_ult

0

20

40

60

80

100

pr (

%)

slips=3ds=9d

no-slips=3ds=9d

3x3 array, Lp/Ls=0.8

α

Fig. 7. Piled raft coefficient with the effect of pile–soil slip at interface, uniformloading.

QP_PR / QSP_ult

1

0.8

0.6

0.4

0.2

0

z / L

s

uniformcentersidecorner

pointcsc

0.2 0.4 0.6

P/QUR_ult

3x3 3d

(a)

0 0.4 0.8 1.2 1.6 2

QP_PR / QSP_ult

1

0.8

0.6

0.4

0.2

0

z / L

s

uniformcentersidecorner

pointcsc

0.2 0.4 0.6P/QUR_ult

4x4 3d

(c)

0 0.4 0.8 1.2 1.6 2

Fig. 8. Pile load distribution (Lp/Ls = 0.8) with different loading types in soft

108 J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114

imum pile load, the results of the no-slip analyses were generallylarger than those of the slip analyses, but the end-bearing capaci-ties were almost the same under the same applied load level.

Fig. 7 shows the variation of the piled raft coefficients. The def-inition of the piled raft coefficient is the ratio of the sum of all pileloads to the total load of the foundation, as shown in Eq. (4). Thepiled raft coefficient decreased with increasing load level due tothe nonlinear pile load–settlement behavior. The piled raft coeffi-cients for the slip analysis were smaller than those of the no-slipanalysis, because the pile load of the slip analysis was generallysmaller than that of the no-slip analysis, as shown in Fig. 7. Forwide pile spacing s = 9d beneath the piled raft, the decrease inthe piled raft coefficient was significant because the bearingbehavior of the piles of the piled raft was similar to that of a singlepile.

3.2. Pile load distribution

Fig. 8 shows an example of the pile load distribution of piles be-neath a piled raft on soft clay with various pile configurations(3 � 3 of s = 3d, 9d, 4 � 4 of s = 3d, 6d, Lp/Ls = 0.8) under uniformand point loading. The position of the piles and pile configurations

0 0.4 0.8 1.2 1.6 2QP_PR / QSP_ult

1

0.8

0.6

0.4

0.2

0z

/ Ls

uniformcentersidecorner

pointcsc

0.2 0.4 0.6

P/QUR_ult

3x3 9d

(b)

0 0.4 0.8 1.2 1.6 2QP_PR / QSP_ult

1

0.8

0.6

0.4

0.2

0

z / L

s

uniformcentersidecorner

pointcsc

0.2 0.4 0.6P/QUR_ult

4x4 6d

(d)

clay: (a) 3 � 3, s = 3d; (b) 3 � 3, s = 9d; (c) 4 � 4, s = 3d; (d) 4 � 4, s = 6d.

J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114 109

are shown in Fig. 4. In this figure, QP_PR is the pile load in a pile un-der a piled raft, QSP_ult is the ultimate bearing capacity of a singlepile, and z is the depth from the ground level. As discussed in Sec-tion 3.1, the pile load distribution was affected by the pile config-urations, pile positions and loading types.

For a piled raft under a uniform loading, the pile load of the cen-ter pile was generally smaller than that of a corner pile at a lowload level. With increasing load level, however, the pile load ofthe center pile was slightly larger than that of a corner pile, irre-spective of pile spacing, for 3 � 3 (3d, 9d) and 4 � 4 (6d) arrays.It was estimated that the normal stress generated between the soiland pile shaft increased with increasing loading on the raft, as re-ported by Katzenbach et al. [12]. In addition, for close pile spacing(3 � 3 and 4 � 4, s = 3d), the upper portion of the load in the pileswas smaller than the wide pile spacing case (3 � 3, s = 9d and4 � 4, s = 6d), and, in particular, the pile load of the center pile ofthe 4 � 4 (3d) array was generally smaller than that of the otherpiles.

For point loading, the pile load distributions were similar to theuniform loading case. However, the upper portion of the piles didnot generate the negative skin friction, and the upper portion of

0 1 2 3QP_PR / QSP_ult

1

0.8

0.6

0.4

0.2

0

z / L

s

uniformcentersidecorner

pointcsc

0.2 0.4 0.6P/QUR_ult

(a)

0 1 2 3QP_PR / QSP_ult

1

0.8

0.6

0.4

0.2

0

z / L

s

uniformcentersidecorner

pointcsc

0.2 0.4 0.6P/QUR_ult

(b)

Fig. 9. Pile load distribution (Lp/Ls = 0.8) with different loading types in stiff clay:(a) 3 � 3 array, s = 3d; (b) 4 � 4 array, s = 3d.

the load in the piles was larger than for the uniform loading casesfor close pile spacing. Moreover, the center piles of wider pile spac-ing (s = 6d, 9d) arrays showed a slightly larger pile load than thosefor other positions of piles. The end-bearing capacity, however, wasalmost same under the same pile configuration and length, irre-spective of loading types.

Fig. 9 also shows an example of the pile load distribution ofpiles of a piled raft on stiff clay with various pile configurations(3 � 3 of s = 3d, 4 � 4 of s = 3d, Lp/Ls = 0.8) under uniform and pointloading. As expected, the typical pile load distributions of stiff claywere comparable with the soft clay case, but the ratio of the pileload was larger than in the soft clay cases under the same loadlevel.

In addition, Figs. 8 and 9 show the ratio of the pile load and theultimate bearing capacity of single piles. Near the settlement of50 mm (10% d, about 0.2 of the load level), which was the criterionof the ultimate bearing capacity of a single pile, the pile load ratiowas smaller than unity because of the contribution of raft to theload sharing. In most cases, however, the ratio was larger thanunity at load levels greater than 0.2 (i.e., increasing settlement).This was due to the fact that in a settlement-based design for piled

0 0.2 0.4 0.6 0.8

P /QUR,ult

0

20

40

60

80

100

pr (

%)

Point loadings=3ds=9d

Uniform loadings=3ds=9d

Lp/Ls=1.0

Lp/Ls=0.8

Lp/Ls=0.4

(a)

0 0.2 0.4 0.6 0.8

P /QUR,ult

0

20

40

60

80

100

pr (

%)

Point loadings=3ds=6d

Uniform loadings=3ds=6d

Lp/Ls=1.0

Lp/Ls=0.8

Lp/Ls=0.4

(b)

αα

Fig. 10. Piled raft coefficient with load level in soft clay: (a) 3 � 3 array; (b) 4 � 4array.

110 J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114

raft, the piles were there primarily to minimize settlement. There-fore, the number of piles might be relatively small, and their mobi-lization might be significant. Katzenbach et al. [13] and Poulos [18]showed that the piles within a piled raft develop more than twicethe shaft resistance of a single pile, with the center piles showingthe largest values. Thus, the usual design procedures for a piledraft, which assume that the ultimate pile capacity is the same asthat for an isolated pile, tend to be conservative, and the ultimatecapacity of the piled raft foundation system is greater than that as-sumed in design. The results also showed a comparable phenome-non. However, the application of this result may be difficult inpractice. This is because pile groups of a piled raft show differentbehavior to that exhibited by a single pile. With pile groups in piledraft, there is no clear bearing failure compared to the case of singlepiles.

3.3. Piled raft coefficient

Figs. 10 and 11 show the piled raft coefficient apr for the 3 � 3(s = 3d, 9d) and 4 � 4 (s = 3d, 6d) cases between uniform and pointloading under soft and stiff clay. The piled raft coefficient apr was

0 0.2 0.4 0.6 0.8P /QUR,ult

0

20

40

60

80

pr (

%)

Point loadings=3ds=9d

Uniform loadings=3ds=9d

Lp/Ls=1.0

Lp/Ls=0.8

Lp/Ls=0.4

(a)

0 0.2 0.4 0.6 0.8P /QUR,ult

0

20

40

60

80

pr (

%)

Point loadings=3ds=6d

Uniform loadings=3ds=6d

Lp/Ls=1.0

Lp/Ls=0.8

Lp/Ls=0.4

(b)

αα

Fig. 11. Piled raft coefficient with load level in stiff clay: (a) 3 � 3 array; (b) 4 � 4array.

represented by Eq. (4) in Section 2.3. Based on the analysis results,the piled raft coefficient for point loading was generally greaterthan that for uniform loading for both soft and stiff clay, and thedifferences between uniform and point loading under close spacedpile groups s = 3d for the piled raft were slightly larger than forwide pile spacing (s = 9d of 3 � 3, s = 6d of 4 � 4), but it was belowabout 5% for soft clay and about 10% of stiff clay. Thus, it was esti-mated that the type of loading had less effect, although it slightlyinfluenced the distribution of the load among the piles. This wassimilar to the result reported by Poulos [18] in the hypotheticalcase analysis.

The piled raft coefficient was not only strongly dependent onthe system geometries of the foundation but also on the load levelfor most cases. Generally, the piled raft coefficient decreased withincreasing load level. For the same number of piles, a decrease ofthe piled raft coefficient was relatively large for a wide pile spacing(3 � 3 9d and 4 � 4 6d) for both soft and stiff clay, and these rangedbetween 10% and 40% for soft clay and about 10% for stiff clay. Incontrast, the piled raft coefficient of a close pile spacing (3 � 3 3dand 4 � 4 6d) decreased by 10% for soft clay and remained almostconstant for stiff clay. Similar results for the relation between loadlevel and pile spacing were reported by Horikoshi and Randolph [8]and Reul [21]. They reported that this decrease of the piled raftcoefficient was caused by nonlinear pile resistance-settlementbehavior. In addition, a decrease of the piled raft coefficient withlonger piles was relatively large, except the end-bearing piles Lp/Ls = 1.0.

The piled raft coefficient was also affected by the soil propertiessignificantly. The coefficient value for soft clay was mostly higherthan for stiff clay. For example, the coefficient for a 3 � 3 piled raftis about 30% in soft clay and 20% in stiff clay. This difference in thepiled raft coefficient was caused by the contribution of the raft,which was more efficient with stiff clay. Moreover, the raft sharedthe load even though end-bearing piles were used, and the ratioranged from 1% to 10% on soft clay and 20–40% on stiff clay,according to pile configurations.

Fig. 12 shows the piled raft coefficient apr according to the totalpile length n � Lp, with respect to the floating pile cases. The piledraft coefficient increased with increasing total pile length, becausethe load sharing of piles was related to the bearing capacity of thepile groups in a piled raft, which increased with increasing pilenumber n and pile length Lp. For example, as shown in Fig. 10,for the foundations with n = 9 (3 � 3), 16 (4 � 4) and 25 (5 � 5)piles with a pile length ratio of 0.4, the average piled raft coeffi-cients were about 30%, 45% and 80% under a load level of 0.5,respectively. In addition, under the same total pile length, the piledraft coefficient was comparatively similar, although it was slightlyinfluenced by the pile spacing.

3.4. Load–settlement relation and factor of safety

Fig. 13 shows typical load–average settlement curves for a piledraft with 3 � 3 pile configurations (see Fig. 4) under uniform andpoint loading. The ratio of pile lengths Lp/Ls ranged from zero(UR) to 1.0 (end-bearing). As expected, the settlement increasedwith the increasing load levels, and the settlement decreased asthe pile length increased. By comparing the load–settlementcurves of the uniform loading and point loading, the load–settle-ment behaviors were similar, and the effects of the different load-ing types on the average settlements were insignificant. Thus, theeffect of loading type was negligible. This was similar to results re-ported by Poulos [18]. Additionally, the effects of pile lengths onthe reducing average settlements of soft clay were much largerthan that of stiff clay under the same load level.

To assess the factor of safety of the piled raft, the ultimate bear-ing capacity of the piled raft QPR_ult had to be defined. It was conve-

0 4 8 12 16 20Total pile length (n*Lp/Ls)

0

20

40

60

80

100

pr (

%)

Soft3x3 3d3x3 9d4x4 3d4x4 6d5x5 4d

Stiff3x3 3d3x3 9d4x4 3d4x4 6d

(a)

0 4 8 12 16 20Total pile length (n*Lp/Ls)

0

20

40

60

80

100

pr (

%)

Soft3x3 3d3x3 9d4x4 3d4x4 6d5x5 4d

Stiff3x3 3d3x3 9d4x4 3d4x4 6d

(b)

0 4 8 12 16 20

Total pile length (n*Lp/Ls)

0

20

40

60

80

100

pr (

%)

Soft3x3 3d3x3 9d4x4 3d4x4 6d5x5 4d

Stiff3x3 3d3x3 9d4x4 3d4x4 6d

(c)

α

α

α

Fig. 12. Piled raft coefficient with equivalent total pile length: (a) P/QUR_ult = 0.27; (b) P/QUR_ult = 0.54; (c) P/QUR_ult = 0.81.

J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114 111

nient to calculate it using Eq. (5), as suggested by Liu et al. [17] andBorel [2], but the values of each component should be defined inEq. (5).

Q PR ult ¼ aPG � Q PG ult þ aUR � QUR ult ð5Þ

where QPR_ult, QPG_ult and QUR_ult are the ultimate bearing capacity ofa piled raft, pile groups and unpiled raft, respectively. aPG and aUR

are the load sharing coefficients of a pile group and unpiled raftwhen combined to a piled raft, respectively.

For the ultimate bearing capacity of the piled raft QPR_ult, basedon previous researches reported by Cooke [4], Borel [2], Conte et al.[3] and de Sanctis and Mandolini [5,6], QPR_ult for clay was esti-mated at the settlement of 10% B. In this study, however, the anal-yses were not carried out until a settlement of 10% B because of theinfluence of geometrical nonlinearity [7] and the large amount ofstorage and time required. It was estimated using a hyperbolicextrapolation to a settlement of 10% B, using the load–settlementcurves, as shown in Fig. 13, as well as in de Sanctis and Mandolini[5,6].

For pile groups, collapse may occur by failure of the individualpiles or the overall piled block. Considering a number of individual

piles, the ultimate bearing capacity of the pile groups (QPG_ult) forindividual pile failure is generally evaluated by

QPG ult ¼ g � n � Q SP ult ð6Þ

where QSP_ult is the ultimate bearing capacity of a single pile, g is thegroup efficiency factor, and n is the number of piles.

A value of g = 1 was adopted, which was consistent with theexperimental findings on small scale pile groups described byCooke [4] for piles located at a spacing not less than some criticalvalue (ranging from s/d of 2.5 for a 3 � 3 array to 3.0 for a 5 � 5 ar-ray). A coefficient of the pile group aPG of one was adopted basedon the results obtained by de Sanctis and Mandolini [5,6]. They re-ported that the proportion of the total load taken by the piles atfailure is nearly constant and equal about to unity. Moreover, theincrease of the ultimate capacity of pile groups in piled raft wasnot clear, though the pile resistance within a piled raft was largerthan those of a single pile, as discussed in Section 3.2.

The ultimate bearing capacity of the unpiled raft QUR_ult wasestimated by the load of settlement of 10% B (Section 3.1), andthe coefficient of the unpiled raft aUR was finally evaluated byEq. (7).

0 0.2 0.4 0.6P/QUR_ult

4

3

2

1

0s a

vg /

B(%

)

UniformURs=3ds=3ds=3ds=9ds=9ds=9d

Point (Lp/Ls)URs=3d (0.4)s=3d (0.8)s=3d (1.0)s=9d (0.4)s=9d (0.8)s=9d (1.0)

Lp/Ls=1.0

Lp/Ls=0.8Lp/Ls=0.4

(a)

0 0.2 0.4 0.6P/QUR_ult

4

3

2

1

0

s avg

/ B

(%)

UniformURs=3ds=3ds=3ds=9ds=9ds=9d

Point (Lp/Ls)URs=3d (0.4)s=3d (0.8)s=3d (1.0)s=9d (0.4)s=9d (0.8)s=9d (1.0)

Lp/Ls=0.8

Lp/Ls=0.4

Lp/Ls=1.0

(b)

Fig. 13. Effect of loading types on load–settlement curves (3 � 3 cases): (a) softclay; (b) stiff clay. Pile–soil interface included.

Table 5Results of proportion of raft (aur and nUR).

Pile configuration Lp(m) aUR nUR

Soft Stiff Soft Stiff

3 � 3 3d 8 0.95 0.97 0.96 0.9712 0.97 0.98 0.97 0.9816 0.99 1.02 0.99 1.02

3 � 3 9d 8 0.97 0.99 0.97 0.9912 0.99 1.01 0.99 1.0116 1.01 1.03 1.01 1.03

4 � 4 3d 8 0.91 0.94 0.92 0.9512 0.93 0.98 0.94 0.9816 0.95 1.00 0.96 1.00

4 � 4 6d 8 0.94 0.96 0.95 0.9712 0.98 1.00 0.98 1.0016 0.98 1.01 0.99 1.01

5 � 5 4d 8 0.92 – 0.94 –12 0.97 – 0.98 –16 1.04 – 1.03 –

Average 0.97(�1.0) 0.99(�1.0) – –

0 4 8 12Factor of Safety (QPR,ult /Qworking)

0

0.4

0.8

1.2

1.6

2

Set

tlem

ent r

atio

(s a

vg/B

, %) 3x3

3d9d

4x43d6d

UR

Lp / Ls = 0.4

(a)

Lp / Ls = 0.8

0 4 8 12Factor of Safety (QPR,ult /Qworking)

0

0.4

0.8

1.2

1.6

2

Set

tlem

ent r

atio

(s a

vg/B

, %)

3x33d9d

4x43d6d

UR

Lp / Ls= 0.8

(b)

Lp / Ls= 0.4

Fig. 14. Typical average settlement ratio with overall factor of safety (Lp/Ls = 0.4 and0.8): (a) soft clay; (b) stiff clay.

112 J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114

aUR ¼Q PR ult � Q PG ult

Q UR ultð7Þ

The results are summarized in Table 5. The coefficient of the unpiledraft aUR varied in the range from 0.91 to 1.04, with an average ofabout 1.0, for both soft and stiff clay. The unpiled raft coefficientaUR increased slightly with increasing pile spacing and length forthe same number of piles, and the value for stiff clay was larger thanthe value for soft clay. At failure, the pile groups of a piled raftslightly affected the ultimate capacity of raft corresponded to pileconfigurations, at least for pile configurations considered in thisstudy, but the difference became very small. A similar result for apiled raft on clay soil was reported by Borel [2], who suggestedthe value of 1.1 from a full-scale test. On the other hand, relativelysmall values were reported by de Sanctis and Mandolini [6]. Theysuggested a value of 0.4–1.0, with an average of around 0.75, fromFE analyses that used the thin-layer pile–soil interface model forsoft clay. The difference between this study and that of de Sanctisand Mandolini [6] is that their raft load sharing was smaller thanthat found in this study because the thin-layer pile–soil interfacemodel tends to slightly overestimate the pile load sharing in con-trast to the slip interface model, as discussed in Section 3.1.

J. Lee et al. / Computers and Geotechnics 37 (2010) 103–114 113

Table 5 also summarizes the values of coefficient nPR. The coef-ficient nPR was evaluated by

nPR ¼Q PR ult

Q UR ult þ Q PG ultð8Þ

The values were within the range from 0.92 to 1.03 for soft clay andfrom 0.95 to 1.03 for stiff clay. These were similar to those deducedfrom the experiments and numerical analysis results. Cooke [4] re-ported that, in a 1 g model test of clay, these range between 0.81and 1.03. Conte et al. [3] reported that the values range between0.83 and 1.04 from a centrifuge test of soft clay. Sales [24] and Borel[2] suggested the values of 0.89 and 1.02 from the results of full-scale tests, respectively. In addition, de Sanctis and Mandolini [6]reported values within the range from 0.82 to 1.0 based on theresults of FE analysis of soft clay. The coefficient nPR of this studyranged between 0.92 and 1.03, which means that the ultimatecapacity of the piled raft was at least 91% of the sum of the ultimatecapacities of the separate components.

From the results of the bearing capacity of a piled raft, the typ-ical relationship between the average settlement and the overallfactor of safety is shown in Fig. 14. The factor of safety was definedas the ultimate bearing capacity of a piled raft divided by an ap-plied load, and it depended on the pile length and pile configura-tion. However, for stiff clay, pile length and configuration hadless effect on the factor of safety against pile geometries than softclay. For the same factor of safety, the average settlement of softclay was generally larger than that in the case of stiff clay. For long-er piles Lp/Ls = 0.8 in soft clay, however, the relationship betweenthe average settlement and the overall factor of safety was similarto that of stiff clay.

Cooke [4] collected data on the settlements of piled and unpiledrafts on London stiff clays and reported that the settlements ofpiled foundations (0.11% B) are about one third of the settlementof shallow foundations (0.35% B). However, the real safety factorof the piled rafts is substantially higher than for shallow founda-tions because the raft contribution was ignored in this design. Hefound that the real factor of safety for the piled rafts was withinthe range of 6–14. He finally concluded that the settlements ofpiled rafts, designed with a true safety factor of three, are veryclose to those observed for shallow foundations (0.35% B).

Based on parametric study, a chart has been developed accord-ing to the pile geometries and soil properties, as shown in Fig. 15.In this study, where a settlement criterion of 0.35% B was applied,

0 2 4 6 8Factor of Safety (QPR,ult/Qworking)

0

0.4

0.8

1.2

1.6

2

s avg

/B (

%)

Pile array3x34x4

End-bearing

UR (soft)

- increase pile length 1) Lp/Ls= 0.4, 0.6, 0.8 2) Lp = 16d, 24d, 32d

Stiff clay

Soft clay

UR (stiff)

[0.35%B]

- Raft width (B)= 20d

Fig. 15. Average settlement ratios with overall factor of safety.

the factor of safety of the piled raft was about 4–8 on soft clayand about four on stiff clay. The result for stiff clay was similarto that proposed by Cooke [4]. For soft clay, the required factorof safety was generally greater than those of reported by Cooke[4] because of the characteristic of high compressibility for softclay, which is associated with excessive settlement. Therefore,for light weight (or low-rise) superstructures, it could be possibleto use a piled raft on soft clay. It was shown that the use of a lim-ited number of piles, strategically located, might improve bothbearing capacity and the settlement performance of the raft. Inaddition, the settlement criterion of the piled raft could be chan-ged to acceptable levels according to the safety and serviceabilitylimit of the superstructure.

4. Conclusions

A series of 3D elasto-plastic finite element analyses were con-ducted to investigate the bearing behavior of a square piled raftsubjected to vertical loading. In this study, the main characteristicof these analyses was to permit soil slip at the pile–soil interface.Pile positions, pile number, pile length and loading distributionson the raft were varied, and the effects of pile–soil slip, pile geom-etries and loading types were examined.

As expected, the development of settlements and pile loads fora piled raft was dependent on the slippage at the pile–soil interfaceand the pile configurations. The average settlements using slipanalysis were generally larger than those using no-slip analysis,whereas the maximum pile loads and pile load sharing using slipanalysis were smaller than those using no-slip analysis. However,the pile load distributions varied according to the pile spacing, aswell as the slippage at pile–soil interface.

The loading type (uniform or point load) influences the pile loaddistribution according to pile position within the piled raft. In addi-tion, the pile load distribution was affected by the pile configura-tions, pile positions and loading types.

The piled raft coefficient was not only highly dependent on thepile configurations but also on the load level and the loading type.Generally, the piled raft coefficient decreased with increasing loadlevel (i.e., increasing settlement), and the decrease of the piled raftcoefficient was relatively large for a wide pile spacing under thesame number of piles for both soft and stiff clay The piled raft coef-ficient of a point loading was substantially greater than that of auniform loading for both soft and stiff clay, and it was below about5% for soft clay and about 10% for stiff clay. In addition, the piledraft coefficient depended on the total pile length n � Lp. The piledraft coefficient increased with increasing total pile length at thesame load level, but it has comparatively similar values underthe same total pile length.

It was also found that the proportion of the load taken by theraft at failure was not highly dependent on the pile configurations,and the coefficients of pile groups within a piled raft and unpiledraft at failure were approximately equal to 1.0 for both soft andstiff clay, respectively. Using the results, the relationship betweenthe average settlement and the overall factor of safety was alsoevaluated. In this study, by comparing the settlement of 0.35% Breported by Cooke [4], the factor of safety of a piled raft was about4–8 on soft clay and about four on stiff clay, and this relationshipwas judged to be very useful in design practice.

An analytical solution was of interest to examine the safety fac-tor of a piled raft corresponding to a certain settlement and it couldbe used as an outline for preliminary design stages.

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