proposed nonlinear 3-d analytical method for piled raft

Computers and Geotechnics 59 (2014) 112–126

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Computers and Geotechnics

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

Proposed nonlinear 3-D analytical method for piled raft foundations

http://dx.doi.org/10.1016/j.compgeo.2014.02.0090266-352X/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: [email protected] (J. Cho).

Sangseom Jeong, Jaeyeon Cho ⇑Department of Civil Engineering, Yonsei University, Seoul 120-749, Republic of Korea

a r t i c l e i n f o

Article history:Received 1 February 2013Received in revised form 5 February 2014Accepted 25 February 2014Available online 28 March 2014

Keywords:Piled raftSoil–structure interactionNumerical analysisField measurementLoad transfer approach

a b s t r a c t

The load distribution and deformation of piled raft foundations subjected to axial and lateral loads wereinvestigated by a numerical analysis and field case studies. Special attention is given to the improved ana-lytical method (YSPR) proposed by considering raft flexibility and soil nonlinearity. A load transferapproach using p–y, t–z and q–z curves is used for the analysis of piles. An analytical method of thesoil–structure interaction is developed by taking into account the soil spring coupling effects based onthe Filonenko-Borodich model. The proposed method has been verified by comparing the results withother numerical methods and field case studies on piled raft. Through comparative studies, it is foundthat the proposed method in the present study is in good agreement with general trend observed by fieldmeasurements and, thus, represents a significant improvement in the prediction of piled raft load sharingand settlement behavior.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years, a number of huge construction projects, such ashigh-rise buildings and long span bridges, are being undertaken.The piled raft foundations are especially being recognized as aneconomical foundation system for high-rise buildings. Here, pilesas settlement reducers have been discussed for over a quarter ofa century [2] and some significant applications have been reported[12,38,42]. Optimized design strategy is a major importance for aneconomic construction to be achieved. An optimized design of apiled raft can therefore be defined as a design with minimum costsfor the installation of the foundation and satisfactory bearingbehavior for a given geometry and raft loading [35]. The piled raftis a composite foundation system consisting of three bearing ele-ments: raft, piles and subsoil. Therefore, the behavior of a piled raftis affected by the 3D interaction between the soil, piles and raft,thus, a simple and convenient analytical method is needed to eval-uate these interactions.

Much work has been done to study load sharing and settlementbehavior of piled raft by many researchers. Numerical methodshave been developed widely in the last two decades becausenumerical methods are less costly and may be used to considermany kinds of different soil and foundation geometries comparedto field and model tests. Although these methods make slightlydifferent modeling techniques, they can generally be classified intothree groups: (1) simplified calculation methods [30,32], (2)

approximate computer-based methods [5,9,14,15,37] and (3) morerigorous computer-based methods [12,17,18,45,48].

The first type of method is based on the linear elastic analysis ofpiled raft subjected to axial loading. Generally, the simplifiedcalculation methods are most commonly used procedure for thepreliminary design of a piled raft foundation. However, it is notedthat these analytical methods are limited to elastic problem.Because this calculation procedure is developed for rigid raft andis assumed that the soil is perfectly elastic. Thus, it may not repre-sent the nonlinear behavior of actual piled raft in the field: it doesnot take into account the actual behavior of finite flexible raft andpile–soil interaction, etc.

The second type of method has been used to investigate thepiled raft system, which is analyzed as a continuous elasticmedium using finite element formulation. In these methods, theresearch by Poulos [29], Clancy and Randolph [5], Poulos [30]and Russo [37] also have some disadvantages. It did not predictthe membrane behavior of raft because the raft is generally mod-eled as plate element. Therefore, the raft used in these methodsmay not reflect the displacement due to membrane action of largesize raft foundations for high-rise buildings. In addition, most ofthe previous research is related to piled rafts subjected to verticalloading and only semi-infinite homogeneous single soil layer wasconsidered. The consideration of various loading condition and soillayer will be more realistic in design practice.

The third type of method is based on the three-dimensionalfinite-element or finite-difference techniques. Poulos [31] notedthat the most feasible method of analysis was the three-dimensional linear/nonlinear FE method. However, a rigorous

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강조

Fig. 1. Flat-shell element.

Fig. 2. Modeling of pile element.

S. Jeong, J. Cho / Computers and Geotechnics 59 (2014) 112–126 113

numerical approach of the piled raft system is computationallyexpensive and requires extensive training because of the three-dimensional and nonlinear nature of the problem. Therefore, a fi-nite element analysis is more suitable for obtaining benchmarksolutions against which to compare simpler analysis methods, orfor obtaining solutions of a detailed analysis for the final designof a foundation, rather than as a preliminary routine design tool[15].

In this study, an improved analytical method (YSPR) for the de-sign of piled raft has been proposed to overcome some limitationsof the existing methods. It is intermediate in complexity and theo-retical accuracy between the second and third type of method. Inthe present method, a numerical technique is used to combinethe soil and pile head stiffness with the stiffness of the raft. In order

to examine the validity of the proposed method, the analysis re-sults are compared with the available solutions from previous re-searches. In the field case study, comparative analyses betweenYSPR and a field measurement data are carried out for the pile loadand settlement behavior.

2. Method of analysis

2.1. Modeling of flexible raft

Finite element techniques have often been used for the analysisof raft by different researchers such as Clancy and Randolph [5],Zhang and Small [49], Kitiyodom and Matsumoto [14]. According

Fig. 3. Soil–structure interactions in piled raft foundation [13].

Fig. 4. Interactions between raft, piles, and subsoil in present method.

114 S. Jeong, J. Cho / Computers and Geotechnics 59 (2014) 112–126

to the former methods [5,49], the raft can be treated as a plate andthe soil can be treated as a series of interactive springs by using aMindlin’s solutions [22], in which the contact pressure at any pointon the base of the raft is proportional to the deformation of the soilat that point or as an elastic half-space in which the behavior of thesoil can be obtained from a number of closed-form solutions. In thelater method, the raft is modeled as thin plates and the piles aselastic beams and the soil is treated as interactive springs [14].The interactions between structural members are made by theuse of Mindlin’s solutions. The primary limitation of these methodsis that the membrane behavior of the flexible raft cannot be con-sidered because the nodal displacements (in the x- and y-direction)for the membrane action are not included. This limitation can beovercome by using a flat-shell element. An improved four-nodeflat-shell element proposed by the authors [48], which combinesa Mindlin’s plate element and a membrane element with torsionaldegrees of freedom, is adopted in this study. The flat-shell elementcan be subjected to the membrane and bending actions that areshown in Fig. 1. The displacement due to the membrane action isconsidered independent of the displacement due to the bending

action, therefore it can be considered separately. For the bendingaction, the displacement field for an individual element can be de-scribed in terms of the vertical nodal displacement and the rota-tions about the x and y axes. For the membrane action, thedisplacement field can be described in terms of the nodal displace-ments in the x and y directions.

2.2. Modeling of single and pile groups

In this study, piles are treated as beam-column elements. Thebehavior of soil surrounding the individual piles is representedby load–transfer curves (t–z, q–z, and p–y curves), and the interac-tion between piles is represented by p-multiplier (fm) and groupefficiency factor (Ge). The load–deformation relationship of individ-ual pile heads may be derived by a single pile analysis based onbeam-column method. In this method, a pile member is describedas a series of beam column elements with discrete springs to rep-resent the soil support condition as shown in Fig. 2. The governingdifferential equations for the axially loaded and laterally loadedpile can be expressed as:

1

2

P1

P2

u1 u2 u’2

P

u

1’

2’

ΔP1

ΔP2

0

(kt)1

(kt)2

u’1

Iteration

Load

incr

emen

t

(ks)2

(kt)i : tangential slope

(ks)i : secant slope

0

(ki)1

(ki)j

(u) i- 1

Fu

u

(ki)j : i = load incrementj = Iteration number

j=1 : tangential stiffnessj>1 : secant stiffness

f((u) i- 1)

Fu=f(u )

(ui)j

f((u i)i)

Δuj

(a)

(b)Fig. 5. Increment secant modulus method [48]. (a) Concept of increment secantmodulus method. (b) Estimating stiffness at ith load increment.


Fig. 6. Modeling of p

Axially loaded pile : EAd2w

dz2 � Cbzw ¼ 0 ð1Þ

Laterally loaded pile : EId4y

dz4 þ Qd2y

dz2 þ q� Ksy ¼ 0 ð2Þ

where EA, EI are the axial stiffness and the flexural rigidity the pile,w is the vertical deflection of the pile at point z, bz is the stiffness/circumference for the axial reaction represented by the modulusof the soil-response (t–z or q–z or both), which depends on thedepth z and pile movement w, and C is circumference of the pileat point z. Q is the axial load on the pile, q is the distributed loadalong the length of the pile, and KS is the stiffness for the lateral soilreaction represented by the modulus of the soil-response (p–y)curve.

In the next step, finite difference technique is used to solve thedifferential equations governing the compatibility between the piledisplacement and the load transfer along a pile. These techniquesare generally based on load tests on full-scale and parametric finiteelement analyses of pile–soil interactions, which are representedby load–transfer curves (t–z, q–z, and p–y curves).

2.3. Soil–structure interaction

The load-bearing behavior of a piled raft is characterized bycomplex soil–structure interaction between the piles, raft and thesubsoil, as shown in Fig. 3 [13]. The present method makes useof pile–soil–pile and raft–soil–pile interaction to simulate the realpiled raft–soil response under lateral and vertical loadings. Addi-tionally, for the raft–soil–raft interaction, this study uses a semi-empirical parameters proposed by many researcher [7,39,40] asthe modulus of soil reaction below the raft. The use of theseparameters as assumed in the derivation procedure, may be a lim-itation. However, these interactions are incorporated in a calcula-tion procedure that is computationally very efficient.

iled raft (YSPR).

Fig. 7. Flow chart of YSPR.


Piles in such groups interact with one another through the sur-rounding soil, resulting in the pile–soil–pile interactions. In thisstudy, a set of nonlinear p–y curves which can be modified byreducing all of the p-values on each curve by a p-multiplier (fm)are used as input to study the behavior of the laterally loaded piles.The p-multiplier can be calculated for each pile in the group[3,6,19]. For each pile i in the group, the p-multiplier can be ex-pressed as:

fmi ¼ b1ib2ib3i � � � bji ð3Þ

where bji is the p-reduction factor due to the effect of pile j on pile i.In a group of closely-spaced piles, the axial capacity of group is

also dominated by variation in settlement behavior of individualpiles due to pile–soil–pile interaction. The most reliable data

concerning the efficiency of the piles in a group is derived by manyresearchers [11,21,41]. In this study, load–transfer curves in sideresistance (t–z curve) and in end bearing resistance (q–w curve)which can be modified by reducing all of the t- and q-values oneach curve by a group efficiency factor (Ge) are used as input tostudy the behavior of the vertically loaded piles.

In classical solution, the Winkler model [46] is used for analyz-ing raft foundation. However, the Winkler model could not predictaccurately the displacement of some solids, e.g. soil. The Winklermodel ignores the important interaction existing between adjacentpoints in the soil continuum. In other words, the soil springs areconsidered as isolated foundation elements. In order to overcomea limitation, much work has been performed to propose someimproved or refined models [8,10,27,43]. For the raft–soil–pile

Fig. 8. Schematic diagram of vertical and lateral loaded piled raft. (a) Pileconfiguration. (b) Section-view.


interaction, in this study a membrane-spring system originallyproposed by Filonenko-Borodich [8] was incorporated to involvethe soil spring-coupling effects. This system can provide a mechan-ical interaction between the individual soil spring and pileelements by using the flat-shell element. As shown in Fig. 4, the

Fig. 9. Soil spring constant for lin

present method proposed an improved raft–soil–pile system byconnecting the top ends of soil springs and pile elements with anelastic flat-shell element including membrane action. By usingflat-shell element, a realistic representation of the subgrade reac-tion can be established directly in terms of coupled soil resistancein which the response at any point on the interface affects otherpoints. The authors believe that a combination of the soil springand the elastic flat-shell element may be used to overcome therestrictions associated with conventional methods, and therebyalso used to analyze appropriately axially loaded piled raft, in soildeposits. Consequently, the proposed analytical method should bebased on the concept of soil–structure interaction under the lateraland vertical loadings.

2.4. Global stiffness matrix

The stiffness matrix of a flat-shell element (Kflat-shell=raft) in localcoordinate system was constructed through combining separatelythe stiffness matrix of a plate element (Kplate) and that of a mem-brane element (Kmembrane) as followings:

Kflat-shell ¼Kplate 0

0 Kmembrane

� �ð4Þ

The stiffness matrix of a plate element Kplate is represented inthe following form:

Kplate ¼Z

VBT

bDbBbdV þZ

VBT

s DsBsdV ð5Þ

where Bb is the bending strain matrix and Bs is the shear strain ma-trix. For an isotropic material, Db and Ds are given as follows:

Db ¼Et3

12ð1� m2Þ

1 m 0m 1 00 0 ð1� mÞ=2

264

375 ð6aÞ

Ds ¼WEt

2ð1þ mÞ1 00 1

� �; W ¼ 5

6ð6bÞ

where E is Young’s modulus, m is Poisson’s ratio, and t is constantthickness of the plate. On the other hand, the stiffness matrix of amembrane element Kmembrane is represented in the following form:

Kmembrane ¼Z

v½BmGR�T � C � ½BmGR�dV þ 1

cVhhT ð7aÞ

ear analysis of a single pile.

10

8

6

4

2

0

Dep

thfro

mG

.L.(m

)0.02 0.03 0.04 0.05

IwV

PRABFEM (K&M, 2003)PLAXIS 3DYSPR

10

8

6

4

2

0

Dep

thfro

mG

.L.(m

)

-0.1 0 0.1 0.2IuH


10

8

6

4

2

0

Dep

thfro

mG

. L.( m

)

-0.1 0 0.1 0.2CsH


10

8

6

4

2

0

Dep

thfro

mG

.L.( m

)

-0.4 -0.2 0 0.2CbH


(a) (c)

(b) (d)Fig. 10. Comparison of analysis result for piled raft: (a) Settlement and (b) lateral displacement, (c) shear force; and (d) bending moment.


h ¼Z

v½bg�b�g�T dV ; ð7bÞ

c ¼ E2ð1þ mÞ ð7cÞ

where C is the constitutive modulus, c is taken as the shear modu-lus. Bm, G, R are the strain matrices representing the relationship be-tween the displacements (the membrane displacement, therotation, and midside incompatible displacement respectively)and the strains. b, g, �b, and �g are also the strain matrices for theinfinitesimal rotation fields.

The pile head stiffness (K11 � K66) is assumed to be constantwithin each load increment and each iteration and then superposi-tion can be applied in order to develop a pile head stiffness matrix(Eq. (8)) in individual piles. Using load–displacement relationshipsrepresenting pile behaviors according to pile head movements[34], the relationship between the nodal force and nodal displace-ments can be expressed in Eq. (9). In addition, the stiffness matrix

for pile groups can be formed by sum of n single pile stiffness ma-trix (Eq. (10)).

Kpile ¼

K11 0 0 0 �K15 00 K22 0 K24 0 00 0 K33 0 0 00 K42 0 K44 0 0�K51 0 0 0 K55 0

0 0 0 0 0 K66

2666666664

3777777775

i

ð8Þ

½K�pileðiÞfdgi ¼ fFig ð9Þ

Kpilegroups ¼Xn

i¼1

½KpileðiÞ � ð10Þ

where [K]pile(i) is an individual pile head stiffness matrix, {di} a dis-placement or rotation, and {Fi} force or moment at the ith pile head.

600 mm

Pile capFh

(variable)

Sand

Pile

15 mm

2.5D, 5.0D, and 7.5D22 mm

Rock

600 mm

Pile capFh

(variable)

Sand

Pile

15 mm

2.5D and 5.0D22 mm

Rock

(a) (b)Fig. 11. Test pile group configurations [4] (a) 2 � 2 pile groups (b) 3 � 3 pile groups.


A component (K11 � K66) of pile head stiffness matrix is changed ateach load increment and iteration stage.

The soil support at various nodes of raft foundation is simulatedby a series of equivalent and independent springs in three direc-tions (x, y and z directions). The spring behavior can be linear ornonlinear. In linear case, soil behavior is defined by soil stiffness(K11 � K33) which is assumed to be constant within each loadincrement and each iteration. The soil reactions at any point canbe expressed as

k11 0 0 0 0 00 k22 0 0 0 00 0 k33 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

2666666664

3777777775

i

du

dv

dw

au

av

aw

8>>>>>>>><>>>>>>>>:

9>>>>>>>>=>>>>>>>>;

i

¼

Fu

Fv

Fw

Mu

Mv

Mw

8>>>>>>>><>>>>>>>>:

9>>>>>>>>=>>>>>>>>;

i

ð11Þ

½K�soilðiÞfdgi ¼ fFig ð12Þ

where [K]soil(i) = individual soil stiffness matrix, {di} = displacementor rotation, and {Fi} = force of soil at point i. In nonlinear case, springbehavior is defined by giving pairs of load–relative displacementvalues. At this point, soil stiffness is calculated by nonlinear solutionprocedure.

Finally, the stiffness matrix of a piled raft can be defined by thecombination of the foundation system and the supporting soil.Therefore, the stiffness matrix formulations of a piled raft systemcan be written as the following:

½Kpiled raft� ¼ ½Kraft� þ ½Ksoil� þ ½Kpilegroups� ð13Þ

2.5. Nonlinear solution procedure

To consider the nonlinear load–displacement relationship ateach pile head and soil (below the raft), an incremental secantmodulus method developed by Won et al. [48] is used. When this‘‘incremental secant modulus method’’ is used, the displacement u2

corresponding to load P2 is increased to u02 as shown in Fig. 5(a), sothat point (P2, u02) will be located on the curve and consequentlythe displacement will be close to the exact solutions.

The procedure for nonlinear solution in this study includes thefollowing step. In total, 10 (ten) load–displacement curves (axial 1;lateral 8; torsional 1) are estimated per each pile head. Fig. 5(b)shows the estimation method of stiffness at an ith load increment.In this method, external forces are first divided by N (number ofload increment). The stiffness at ith load increment and jth itera-tion is represented (ki)j. In each load increment, tangential slopeis adopted at first iteration (j = 1) and the secant modulus at j > 1for the stiffness of pile head, which is expressed as Eqs. (14) and(15), respectively.

ðkiÞj ¼df ðuÞ

du

� �u¼ðuÞi�1

ðj ¼ 1Þ ð14Þ

ðkiÞj ¼f ððuiÞjÞ � f ððuÞi�1ÞðuiÞj � ðuÞi�1

ðj > 1Þ ð15Þ

ðuiÞj ¼ ðuÞi�1 þ Duj ð16Þ

where (u)i�1 is an accumulated final displacement at a previousload increment and (ui)j is an accumulated displacement at the ithload increment and jth iteration.

At each load increment, displacements (Duj) are calculatedthrough structural analysis and then accumulated displacements(ui)j are estimated using Eq. (16). If the convergence criteria,Duj–Duj�1 < e is satisfied, the accumulated final displacements(u)i are calculated and continue to the next load increment. Thisprocess iterates until the load increment number reaches N. Inthe structure analyses, the tangential slope (df(u)/du) and load(f(u)) of individual piles are estimated using cubic spline method[1]. The procedure described above is iterated until the errorbetween the assumed and calculated displacements falls within atolerance limit.

As a final outcome, an improved numerical method (YSPR) wasproposed to analyze the response of a raft and a piled raft consid-ering raft flexibility and soil nonlinearity (Fig. 6). Fig. 7 shows theflow chart of present method.

0 0.004 0.008 0.012 0.016Displacement (m)

0

0.01

0.02

0.03

0.04

Late

rall

oad

(kN

)

measured (2.5D)measured (5.0D)measured (7.5D)predicted (2.5D)predicted (5.0D)predicted (7.5D)

0 0.004 0.008 0.012 0.016 0.02Displacement (m)

0

0.02

0.04

0.06

0.08

Late

rall

oad

(kN

)

measured (2.5D)measured (5.0D)predicted (2.5D)predicted (5.0D)

(a)

(b)Fig. 12. Lateral load–displacement curves at pile head. (a) 2 � 2 pile groups. (b)3 � 3 pile groups.

Table 1Material parameters used for this study (case studies).

Case Material properties

Type Depth (m) E

Japan case [15] Pile Steel pipe 0 to �5.5 2Raft Concrete 0 to 2.2 3Soil Sandy silt 0 to �1.7 1

Silty clay �1.7 to �13.5 1Germany case [34] Pile Concrete �5.5 to �25.5 2

Raft Concrete �3 to �5.5 3Soil Sand �3 to �8 7

Frankfurt clay �8 to �113 4Korea case Pile Concrete 0 to �30 2

Raft Concrete 0 to 6.0 3Soil Gneiss Soil spring stiffness (kPa

0 to 204,250

a Note: M.C. is Mohr Coulomb elasto-plastic model, L.E. is linear elastic model used in


3. Verification of proposed method with previous studies

3.1. Kitiyodom and Matsumoto [14]

A series of linear piled raft analyses were performed to verifythe present method by comparison with other numerical methodswhich have been used in the preliminary design of piled raft. Aschematic diagram of a 2 � 2 piled raft is shown in Fig. 8. Thisstructure consists of a raft, and four identical vertical piles, whichare spaced by 1.5 m (=3.75D, where D is the pile diameter). Thepiles have an embedded length of 10 m, a diameter of 0.4 m. Pilehead conditions are fixed. A square raft of size 3 � 3 m with athickness of 0.9 m is rested on a homogeneous soil. The Young’smodulus and Poisson’s ratio of the soil are 12,500 MPa and 0.3.The raft and piles, with a Young’s modulus and Poisson’s ratio of125,000 MPa and 0.3 respectively, is subjected to a vertical andlateral load. Fig. 9 shows the spring constants were used for thelinear soil condition. The same axial spring constants were usedalong the pile depth, with a constant value of 7,527,867 kN/m2,which includes the pile perimeter. The end-bearing spring was8,692,180 kN/m2, and the tension part was neglected. The con-stants of the horizontal springs were increase from 0 to4,682,274 kN/m2 along the pile depth. Since the soil is assumedto be an elastic model, the p-reduction and group efficiency factorof unity were used [6,18,41].

The response of piled raft is presented in settlement, lateral dis-placement of pile, and in shear force and bending moment distri-bution at various depths. Fig. 10(a–d) shows representativeresults from the proposed method. In addition, these results weretested by comparing them with well-known three existing numer-ical methods: the PRAB [15]; the finite element method performedby Kitiyodom and Matsumoto and PLAXIS 3D [28]. The results areshown in terms of dimensionless parameters of IwV for the settle-ment, IuH for the lateral displacement of a pile respectively, CsH,CbH for the shear force, and the bending moment along the pilerespectively. These parameters can be calculated by Eqs. (17)–(20).

IwV ¼EsDw

qzBrLrð17Þ

IuH ¼EsDu

qxBrLrð18Þ

CsH ¼S

qxBrLrð19Þ

CbH ¼B

qxDBrLrð20Þ

(MPa) m c (kN/m3) / (�) c (kPa) Modela

.1E�08 0.2 75 – – L.E.0,000 0.2 25 – – L.E.3 0.3 18 0 25 M.C.5 0.3 18 0 29.64 M.C.3,500 0.2 25 – – L.E.4,000 0.2 25 – – L.E.5 0.25 18 32.5 0 M.C.7a 0.15 19 20 20 M.C.8,000 0.2 – – – YSPR3,234 0.15 – –/m)

PLAXIS 3D Foundation Frankfurt clay: E = 45 + [tanh((z � 30)/15) + 1] � 0.7z.

Fig. 13. Field test of piled raft [16]. (a) Plan-view and (b) section-view.

Table 2Properties used for estimating load transfer curves (Japan case).

Contents Sandy silt Siltyclay

t–z, q–z curves [39] Ultimate skin friction, s(kPa)

40 40

Initial shear modulus, Gi

(kPa)5000 5769

Poisson’s ratio, m 0.3 0.3Ultimate bearingcapacity, Qf (kN)

– 250

p–y curves [19,20] Undrained shear strength(kPa)

25 29.64

Unit weights (kN/m3) 18.0 18.0p–y modulus, k (kN/m3) 27,150 27,150

Subgrade reactionmodulus

Kx, Ky (kN/m3) 27,150 –Kz (kN/m3) 5291 –

50

40

30

20

10

0Se

ttlem

ent(

mm

)

0 0.5 1 1.5 2 2.5Load (MN)

Measured (K&I, 1967)Calculated (R & E, 2006)YSPRPLAXIS 3D

Fig. 14. Computed and measured response of piled raft settlement.


where w, u are the settlement and lateral displacement at the pilehead, qz and qx are uniform vertical and lateral load, the breadth,Br and length, Lr, S and B are the shear force and the bending mo-ment along the pile.

The calculated results of the proposed analysis method closelyapproach the computed data from the other numerical methods.It should be noted that the present method provides a very satisfac-tory prediction of the shear force and the bending moment in indi-vidual piles, when the flexibility of the raft is considered by usingthe combination of the membrane and bending actions. Althougha reasonably good agreement between the proposed and the exist-ing methods was obtained, the proposed method has a larger settle-ment those of the existing methods at the same load. Conclusively,it is thought that YSPR can be used with some confidence in the pre-liminary design of axially and laterally loaded piled raft.

3.2. Chung and Jeong [4]

In this section, the verification of lateral response of the presentmethod against laboratory load test is discussed. By Chung and

Table 3Calculated stiffness of single pile and piled raft (Japan case).

K11 (kN/m) K22 (kN/m) K33 (k

Single pile 0.4052E+02 0.4052E+02 0.3877Piled raft (w/o Ge) 0.2735E+05 0.2735E+05 0.3453Piled raft (w/Ge) 0.2735E+05 0.2735E+05 0.2492

Jeong [4], a series of small scale model tests were carried out tostudy the behavior of pile groups subjected to lateral loadings onsand. The test soil used in this study was: the unit weight15.3 kN/m3, cohesion 0 kN/m2 and drained friction angle 37�. Themodel piles made from PVC tubes were 0.6 m in embedded length,22 mm in diameter and 2.5 mm wall thickness and 28,265 kN m2

flexural rigidity(EI). Fig. 11 shows an idealization of the subsurfaceprofile and pile embedment for test piles.

Using present method the behavior of pile groups are predictedwith different group configurations and different center-to-centerpile spacing: 2.5D, 5.0D, and 7.0D. Back-fitted hyperbolic p–ycurves that are calculated at 5, 10, and 20 cm along the pile depthin model test of single pile are implemented. Initial tangent

N/m) K44 (kN/rad) K55 (kN/rad) K66 (kN/rad)

E+05 0.3434E+03 0.3434E+03 0E+06 0.2730E+06 0.2730E+06 0E+06 0.2208E+06 0.2208E+06 0

Fig. 15. Torhaus Der Messe: (a) profile view and (b) configuration of pile.

Table 4Properties used for estimating load transfer curves (Germany case).

Contents Quaternarysilt

Frankfurtclay

t–z, q–z curves [39] Ultimate skin friction, sf

(kPa)143 91.6

Initial shear modulus, Gi

(kPa)30,000 20,434

Poisson’s ratio, m 0.25 0.15Ultimate bearingcapacity, Qf (kN)

– 90

p–y curves [24,33] Internal friction angle (�) 32.5 20Unit weights (kN/m3) 18 19p–y modulus, k (kN/m3) 16,300 136,000

Subgrade reactionmodulus

Kx, Ky (kN/m3) 16,300 136,000Kz (kN/m3) 294,000 –

Table 5Calculated stiffness of single pile and piled raft (Germany case).

K11 (kN/m) K22 (kN/m) K33 (k

Single pile 0.3979E+03 0.3979E+03 0.3020Piled raft (w/o Ge) 0.1118E+08 0.1138E+08 0.1300Piled raft (w/Ge) 0.1117E+08 0.1137E+08 0.1242

Fig. 16. Pile load: (a) pile 1, 2, 3 and (b) pile 4, 5, 6.


stiffnesses (Ks) of the p–y curves at the depths of 0.05, 0.1, and0.2 m are 11, 14.3, and 50 kN/m2, respectively. Also ultimate capac-ities (Pu) of the p–y curves at the same depths are 0.0011, 0.0033,and 0.0033 kN/m, respectively.

To consider the detailed group effect, p-multipliers calculatedfrom the Chung’s experiment are implemented. For the 2 � 2group, p-multipliers are 0.86 for lead row and 0.45 for trail rowat 2.5D pile spacing; 0.95 for lead row and 0.67 for trail row at5.0D; 1.0, 0.83 for lead, trail row at 7.5D. For the 3 � 3 group,p-multipliers are 0.8, 0.3 and 0.4 for lead, middle, and trail rowsat 2.5D pile spacing; 0.93, 0.48, and 0.6 at 5.0D pile spacing.

Fig. 12 shows the predicted and observed lateral load–settle-ment curves. The analysis of pile groups was performed for a fixedhead condition and spacing-to-diameter ratios varying from 2.5 to7.5. The present method considering pile–soil–pile interaction rel-atively well predicts the general trend of the measured lateralloads for the pile groups studied if the measured deflections arerelatively small (say less than 15 mm).

N/m) K44 (kN/rad) K55 (kN/rad) K66 (kN/rad)

E+06 0.4482E+05 0.4482E+05 0E+08 0.2583E+09 0.2115E+09 0E+08 0.2548E+09 0.2078E+09 0

140

120

100

80

60

40

20

0

Settl

emen

t(m

m)

0 50 100 150 200 250

Load (MN)

PLAXIS 3DYSPR (w/o Ge)YSPR (w/ Ge)

Smax = 124mm

Measuredsettlement

Fig. 17. Settlement behavior of large piled raft foundation.


4. Comparison with other case histories

The validity of the proposed method was examined by compar-ing the results from the present approach with some of the field-measured results. The pile and soil properties employed with theYSPR and PLAXIS 3D analyses for the case histories were the sameproperties mentioned in their research. In the field, the soil stiff-ness significantly depends on the stress level, indicating that thestiffness generally increases with depth. To account for the in-crease of the stiffness with the depth, the Young’s modulus of soil(Eincrement) value which is the increment of stiffness per unit ofdepth was used in FE analyses. Table 1 summarizes the materialproperties used in the case studies.

4.1. Japan case

The settlement behavior of axially loaded piled raft reported byKoizumi and Ito [16] are compared with the predicted values of theproposed method. This test site was located near the 1-chome, Ote-machi in Tokyo. A fully instrumented piled raft was installed in theclay soil, which consists of sandy silt with gravel and organic siltyclay. Fig. 13 shows the subsurface profile and pile configurations ofthe test piled raft. All of the test piles are 300 mm in dia. and 5.5 min length. The soil and material properties were determined byback-analysis of field load test results using PLAXIS 3D Foundation.From full-scale tests in clay soil presented by O’Neill [23] and Whi-taker [47], the group efficiency factor, Ge, was set at 0.7 for thereduction of side resistance (t–z curve) and end bearing resistance(q–w curve) of piles. The input parameter of soil used to generatethe load transfer curve and soil-spring are summarized in Table 2.

Table 3 shows the estimated stiffness of single pile and piledraft when a vertical load of unity is applied. Compared to the stiff-ness in which the group efficiency factor was 1.0, the stiffness ofpiled raft showed a significant decrease in K33 of about 28%. Thisis because the decrease of the pile resistance due to the pile–soil–pile interaction (i.e. group efficiency factor), change the globalstiffness of piled raft.

The proposed analysis method (YSPR) and a finite elementprogram analysis (PLAXIS 3D) results were compared with themeasured load–settlement curves in Fig. 14. All the methods

predicted the general trend of the measured values reasonablywell. However, the calculated results by Roberto and Enrico [36]have a relatively smaller settlement as the applied load increasedthan the results of the proposed solution. This clearly demonstratesthat for analysis result, YSPR gives more flexible results for nonlin-ear behavior of soil, because the Roberto and Enrico [36] use soilflexibility matrix(based on linear elastic analysis of pile groups)for soil–pile interaction and the proposed method does so usingnonlinear load transfer curves and solution algorithm. These dis-crepancies between predicted and measured behavior at the highload levels are because the assumptions of raft–soil relative stiff-ness and group efficiency factor are influenced on the settlementbehavior of piled raft. In addition, computational time to run thiscase saves 57 min of computer time, and is about 20 times fasterthan the 3D FE analysis.

4.2. Germany case

The settlement and load sharing behavior of instrumented,large, piled raft installed in stiff clay was compared with the pre-dicted values of the proposed and the FE analyses. Constructed be-tween 1983 and 1986, the 130 m high Torhaus was the firstbuilding in Germany with a foundation designed as a piled raft. Atotal number of 84 bored piles with a length of 20 m and diameterof 0.9 m are located under two 17.5 � 24.5 m large rafts. The bot-tom of the 2.5 m thick raft lies just 3 m below ground level(Fig. 15(a)). The subsoil comprises quaternary sand and gravel upto 2.5 m below the bottom of the rafts, followed by the Frankfurtclay [34]. And a schematic diagram of 7 � 6 piled raft structure isshown in Fig. 15(b). The maximum load of Peff = 200 MN for eachraft [37] minus the weight of the raft is successively applied bymeans of a uniform load over the whole raft area. In the presentmethod (YSPR), the soil around individual pile is modeled withnonlinear load transfer curves. The axial load transfer curves (t–z,q–z curves) are estimated using the equation developed by Wangand Reese [44], the lateral load transfer curve (p–y curve) is usedas an API model [25,32]. The group efficiency factor, Ge, was setat 0.73 for the average value of pile spacing: 3D � 4D [23,47].The input parameter of soil used to generate the load transfer curveand soil-spring are summarized in Table 4.

Table 5 summarizes the calculated stiffness for the single pileand the piled raft foundation. A decrease in the group efficiencyfactor from 1.0 to 0.73 results in about 4.5% decrease in stiffnessof piled raft. It is also noted that the stiffness of piles inside thegroup varied with a group effect. Fig. 16(a–b) shows a comparisonof the measured and calculated pile loads. The prediction of thepresent method is much more conservative than that of 3D FEanalyses and the measured one. However the proposed methodis in good agreement with general trend of pile load which increasefrom a center pile (pile1) to the edge (piles 2, 4 and 6) and to thecorner pile (piles 3 and 5). The computed results for the center,side, and corner piles show that the load distribution of the indi-vidual piles in a group is highly influenced by the flexibility ofthe raft. This finding was similar to what Won et al. [48] discussedabout correlation between the pile member force and the flexibil-ity of pile cap for a pile groups.

Fig. 17 shows a settlement behavior of the piled raft. The mea-sured maximum settlement is about 124 mm, the calculated set-tlements using YSPR and PLAXIS 3D are 106.7 (with Ge; 111.5)mm and 117 mm respectively. This curve demonstrates the effectof pile–soil–pile interaction by considering group efficiency. Theproposed method with an interaction factor is more appropriateand realistic to represent a pile–soil–pile interaction for closely-spaced piles than on that of no-interaction analysis. In Both valuesof YSPR and 3D FE analyses are smaller than the measured one.However, these two numerical methods provide an acceptable

Fig. 18. Preliminary design case of large piled raft: (a) plan view and (b) profile view.


design prediction. Despite the approximate assumptions involved(i.e., loading condition, construction process, consolidation of clay),the present method when used in nonlinear analysis is useful forpredicting the settlement behavior of a piled raft foundation takingaccount of soil nonlinearity, the flexibility of the large raft, and thepile arrangement. The time taken for the computer to run this casesaves 115 min of computer time, and is about 24 times faster thanthe 3D FE analysis. For large problems this computational savingcan be very significant.

4.3. Korea case

As shown in Fig. 18, preliminary design case of a piled raft (OOsuper tower) conducted at high-rise building construction sites inKorea were representatively selected for the design application.The construction site is comprised mainly of normally bandedgneiss, brecciated gneiss and fault core zones. Based on the resultsof pressure meter, Goodman Jack and plate load tests carried out inthe field, a nonlinear elastic modulus design line is established to

represent the stiffness of the ground. A schematic diagram of a raftfoundation with piles is shown in Fig. 18(b). This structure consistsof a raft, and 112 of ground strengthen piles. The piles have anembedded length of 30 m, a diameter of 1.0 m. A large raft size71.7 � 71.7 m with a thickness of 6.0 m is resting on a bandedgneiss. The raft and ground strengthen piles, with a Young’s mod-ulus of 30 GPa and 28 GPa respectively, is subjected to a verticalload (Ptotal = 6,701 MN).

Fig. 19(a–d) shows the raft settlement at different sections pre-dicted by GSRaft [26] and YSPR. Agreement between the GSRaftand YSPR of settlement is generally good; however there is a slightdifference in prediction of settlement in the faulting zone wherethe sudden drop of the magnitudes were occurred. This can beattributed to the inappropriate assumption of material propertiesdue to no accurate ground investigation data on this section. Thecalculated raft settlement has some difference between theproposed method and the existing solution, based on the sameanalysis conditions. This is because the conceptual methodologyof the present method is completely different from that of general

Fig. 19. Raft settlement distribution: (a) section 1, (b) section 2, (c) section 3; (d) section 4.


structural models. The raft is modeled as a grillage and the piles aretreated as bar element with axial stiffness only in GSRaft whileYSPR is adopted flat-shell element and 6 � 6 pile head stiffness.Although there are no measured profiles of raft settlement, theproposed analysis method showed reasonably good correspon-dence with well-known in-house program.

5. Conclusions

The primary objective of this study was to propose an improvedanalytical method for a pile raft foundations. The conceptual meth-odology of the proposed method is completely different from thatof general continuum method. A series of analytical studies wereconducted. Through comparisons with case histories, it is clearlydemonstrated that the proposed method was found to be in goodagreement with measurement data. From the findings of thisstudy, the following conclusions can be drawn:

1. By taking into account the raft flexibility and soil nonlinearity,the proposed analytical method is an appropriate and realistic

representation of the settlement and load sharing behavior ofpiled raft foundation. It provides results that are in good agree-ment with the field measurement and numerical analyses.

2. Proposed analytical method produces a considerably larger set-tlement of piled raft than the results obtained by the linear elas-tic analysis. Additionally, the analytical method is intermediatein theoretical accuracy between general three-dimensional FEanalysis and the linear elastic numerical method. The settle-ment of piled raft obtained by the present method is similarto that obtained by the PLAXIS 3D, while it shows smaller val-ues than those obtained by existing method based on linearelastic analysis of pile groups.

3. From the example case histories, the proposed method is shownto be capable of predicting the behavior of a large piled raft.Nonlinear load–transfer curve and flat-shell element can over-come the limitations of existing numerical methods, to someextent, by considering the realistic nonlinear behavior of soiland membrane action of flexible raft.

4. Additionally, the comparative studies demonstrated that thepresent method, when used in analysis of large scale piled raft,


is useful for computational saving and improving performancein engineering practice.

Acknowledgements

This work was supported by the National Research Foundationof Korea (NRF) grant funded by the Korea government (MSIP) (No.2011-0030040).

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