Pseudo Static Approach for Seismic Analysis of Piles in Liquefying Soils

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University of Wollongong

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2005

Pseudostatic Approach for Seismic Analysis of Pilesin Liquefying Soil

D. S. LiyanapathiranaUniversity of Wollongong, [email protected]

H. G. PoulosUniversity of Sydney

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Publication DetailsTis article was originally published as: Liyanapathirana, DS & Poulos, HG, Pseudostatic Approach for Seismic Analysis of Piles inLiquefying Soil, Journal of Geotechnical and Geoenvironmental Engineering, 2005, 131(12), 1480-1487. Copyright AmericanSociety of Civil Engineers. Original journal availablehere.
http://ro.uow.edu.au/http://ro.uow.edu.au/engpapershttp://ro.uow.edu.au/eishttp://%22http/scitation.aip.org/gto%22http://ro.uow.edu.au/http://%22http/scitation.aip.org/gto%22http://ro.uow.edu.au/eishttp://ro.uow.edu.au/engpapershttp://ro.uow.edu.au/http://ro.uow.edu.au/http://ro.uow.edu.au/


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Pseudostatic Approach for Seismic Analysis of Pilesin Liquefying Soil

D. S. Liyanapathirana, M.ASCE,1 and H. G. Poulos, F.ASCE2

Abstract: The performance of pile foundations during an earthquake significantly influences the integrity of structures supported by

them. Therefore, in the overall seismic design process of the structures, modeling of the soilpile-superstructure interaction is an essential

part. Although finite element based coupled analysis of the soilpile-superstructure interaction models have the potential to provide

accurate results, they are computationally expensive and often complex to utilize. In practice, many geotechnical engineers tend to use

simple methods for obtaining the internal response of piles subjected to earthquake loading. Therefore this paper presents a simple

pseudostatic approach where a single pile is considered, including the contribution of the superstructure to the pile and the interaction

between the pile and the soil. The method involves two main steps. First a nonlinear free-field site response analysis is carried out to

obtain the maximum ground displacements along the pile and the degraded soil modulus over the depth of the soil deposit. Next a static

load analysis is carried out for the pile, subjected to the maximum free-field ground displacements and the static loading at the pile headbased on the maximum ground surface acceleration. The method has been verified using an independent dynamic pile analysis program

developed by the writers for the seismic analysis of piles in liquefying soil. It is demonstrated that the new method gives good estimates

of pile bending moment, shear force, and displacement, despite its relative simplicity. The method is then used to compute the response

of pile foundations during the Kobe 1995 earthquake and some centrifuge tests found in the literature where extensive soil liquefaction has

been observed. Very good agreement is observed between computed and recorded pile bending moments.

DOI: 10.1061/ ASCE 1090-0241 2005 131:12 1480

CE Database subject headings: Seismic analysis; Piles; Liquefaction; Earthquakes.

Introduction

Liquefaction of saturated soil subjected to earthquake loading isone of the major factors affecting the behavior of pile foundations

and subsequent building failure in seismically active areas. This

has been clearly demonstrated during past earthquakes that have

occurred in the USA e.g., 1989 Loma-Prieta , Japan e.g., 1995

Kobe , and Mexico e.g., 1995 Manzanillo . At many instances,

pile failure in liquefied ground occurred due to the inadequacy of

the pile to sustain large shear forces and bending moments devel-

oped during an earthquake event. Hence there is a great demand

for numerical procedures which can be used to predict pile

behavior in liquefying ground during an earthquake event.

Although one-dimensional Winkler models have become

popular for the seismic analysis of pile foundations, most of them

can be used only for the linear analysis of pilesoil interaction in

nonliquefying soil e.g., Novak 1974; Dobry et al. 1982; Kaynia

and Kausel 1982; Kavvadas and Gazetas 1993 . Winkler models

that take into account the nonlinear soil behavior have been de-

veloped by Penzien 1970 ; Kagawa 1980 ; Kagawa and Kraft 1981 ; Norris 1994 ; El Naggar and Novak 1996 ; Nogami and

Konagai 1988 ; and Tabesh and Poulos 2000, 2001a but they

lack the ability to predict pile behavior when the soil around the

pile starts to liquefy.

For the seismic analysis of piles in liquefying soil, Winkler

type models have been developed by Kagawa 1992 ; Yao and

Nogami 1994 ; Fujii et al. 1998 ; and Liyanapathirana and

Poulos 2005 . Although these models are one-dimensional, a dy-

namic finite element analysis has to be carried out to obtain the

pile response in liquefying soil.

Recently, pseudostatic approaches for the seismic analysis of

pile foundations have emerged. In pseudostatic approaches, a

static analysis is carried out to obtain the maximum bending mo-ment and shear force developed in the pile due to earthquake

loading. These methods are attractive for design engineers when

compared to difficult but more complex dynamic analyses. For

piles in nonliquefying soil Abghari and Chai 1995 and Tabesh

and Poulos 2001b have developed pseudostatic approaches.

When liquefaction is of concern, the stiffness of the soil is dra-

matically reduced and the effect of the reduced stiffness should be

incorporated in the analysis. Therefore in this paper a pseudostatic

approach, which requires relatively little computational effort, is

presented for the analysis of piles in liquefying soil. Results ob-

tained from the pseudostatic approach are compared with the re-

sults given by a dynamic analysis and centrifuge data and despite

its simplicity, the pseudostatic approach results, which are in goodagreement.

1Senior Lecturer, Dept. of Civil, Mining and Environmental

Engineering, Univ. of Wollongong, Northfields Ave., Wollongong, NSW

2522, Australia.2Senior Principal, Coffey Geosciences Pty. Ltd. and Emeritus

Professor of Civil Engineering, Dept. of Civil Engineering J05 , Univ. of

Sydney, Sydney, NSW 2006, Australia.Note. Discussion open until May 1, 2006. Separate discussions must

be submitted for individual papers. To extend the closing date by one

month, a written request must be filed with the ASCE Managing Editor.

The manuscript for this paper was submitted for review and possible

publication on December 23, 2002; approved on August 17, 2004. This

paper is part of the Journal of Geotechnical and Geoenvironmental

Engineering, Vol. 131, No. 12, December 1, 2005. ASCE, ISSN 1090-0241/2005/12-14801487/$25.00.

1480 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / DECEMBER 2005


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Pseudostatic Approach

The pseudostatic methods were presented by Abghari and Chai

1995 and Tabesh and Poulos 2001b for the nonliquefying soil,and the inertial force acting at the pile head is represented by theproduct of the cap-mass and the spectral acceleration Dowrick

1977 . By comparing the results given by the pseudostatic methodwith the results given by a dynamic finite element analysis, Ab-ghari and Chai 1995 concluded that the inertial force should bereduced to 25% for the pile deflection and to 50% for the bending

moment and shear force to obtain the results in agreement withthe dynamic finite element analysis. They made this conclusionby analyzing only one example and the method has not beengeneralized. However, they have taken into account the nonlinear

behavior of the soil in their analysis.Tabesh and Poulos 2001b compared results given by pseudo-

static and dynamic analyses for different pile and soil properties.

They applied the full inertial force at the pile head and observedan excellent agreement with the dynamic analysis for the caseswithout cap-mass, but when the cap-mass increased they showed

that the pseudostatic approach overestimates the maximum bend-ing moment and shear force developed in the pile. However, theycarried out an elastic free-field site response analysis and in thepile analysis the nonlinear behavior of the soil is also not takeninto account.

In the pseudostatic approach proposed by Ishihara and Cubrin-ovski 1998 for the pile foundations in the soil deposits subjectedto lateral spreading, inertial force at the pile head has not been

considered to obtain the maximum bending moment and shearforce developed in the pile.

Here the pseudostatic approach has been extended for a lique-fying soil, where the degradation of shear modulus of the soil

occurs with the generation of pore water pressure in the soil.Although spectral acceleration has been used by Abghari and

Chai 1995 and Tabesh and Poulos 2001b , it has been foundthat the inertial force at the pile head calculated using the spectralacceleration, based on the effective stress analysis, is overesti-mated when the surrounding soil starts to liquefy. The numericalstudies carried out using the dynamic finite analysis show that

when the surrounding soil starts to liquefy, maximum pile headacceleration closely agrees with the maximum ground surface ac-celeration. Hence pseudostatic analysis has been carried out byapplying inertial force at the pile head calculated based on the

maximum ground surface acceleration, instead of the spectralacceleration.

In the pseudostatic approach presented here, maximum pile

bending moment, shear force, and displacement are obtained byperforming a static load analysis for the pile, involving two mainstages as follows.1. A free-field site response analysis is carried out to obtain the

maximum ground displacement and the minimum effectivevertical stress at each depth of the soil deposit and the maxi-mum ground surface acceleration during the earthquake load-ing.

2. Next a static load analysis is carried out for the pile, sub-jected to the maximum free-field ground displacements andthe static loading at the pile head, which is given by the

maximum ground surface acceleration multiplied by the cap-mass.

Here the maximum ground surface acceleration, minimum ef-fective stress, and the maximum ground displacement at each

depth have been obtained from the free-field site response analy-sis developed by Liyanapathirana and Poulos 2002b,c . The

static load analysis of the pile is carried out by modeling the pileas a nonlinear beam. Soilpile interaction is modeled using themethod of a beam on a nonlinear Winkler foundation.

Cap-mass at the pile head represents the mass of the super-structure. Although the superstructure supported by pile founda-tions is a multi-degree of freedom system, in the design of pilefoundations, it is reduced to a single mass at the pile head, to

simplify the analysis. The partial differential equation of a beamon a Winkler foundation is given by

EPIP4UPz4 = Kx Uf f UP + M amax 1

where EP =Youngs modulus of the pile material, IP =inertia of

the pile, UP = pile displacement, Uf f= free-field lateral soil dis-placement, Kx=spring coefficients of the Winkler model,M= cap-mass, and amax=maximum ground surface acceleration.Eq. 1 is solved using the finite element method.

The spring coefficients of the Winkler model have been ob-tained by integrating Mindlins equation over a rectangular areaas explained in the companion paper by Liyanapathirana and Pou-

los 2005 . At each depth, the spring coefficients are calculatedbased on the minimum effective stress obtained from the free-field site response analysis.

Usually it is assumed that the liquefied soil does not have any

stiffness. However, due to the stiffness contrast between the pileand the liquefied soil, computationally it is difficult to carry outan analysis with a near-zero shear modulus. Therefore in the nu-merical studies, a lower limit has been set for the initial effective

vertical stress, below which effective vertical stress is not allowedto decrease and pore pressures are not allowed to build up. Byanalyzing field data recorded at the Port Island site during theKobe 1995 earthquake, Davis and Berril 1998 reported that the

shear wave velocity of the liquefied region is about 25 m/s. Ishi-hara and Towhata

1982

also suggested that since shear stress

application during earthquakes is multidirectional, even when

shear stresses are reduced to zero in one direction, there willalways be some shear stress left in the soil. This was demon-strated in the rotational simple shear tests performed by Ishiharaand Yamasaki 1980 . During the one-dimensional free-field site

response analyses carried out by Ishihara and Towhata 1982 ,this lower limit of effective stress is set at 3% of the initial effec-tive overburden pressure.

The degradation of soil modulus gives rise to nonhomogeneity

of the soil profile, even if it was initially homogeneous. The useof the Mindlin equation is of course approximate for soils, whichare not homogeneous and isotropic, but can give results of ad-

equate accuracy for many cases of nonuniform soil profiles

Poulos 1982 .The nonlinear behavior of soil at the pilesoil interface has

been modeled using a plastic slider in series with spring coeffi-

cients of the Winkler model, which represents the lateral pressureat the pilesoil interface, as shown in Fig. 1. This lateral pressureis monitored and an iterative procedure is used to keep it below

the ultimate lateral pressure of the soil. According to Broms 1964 , for noncohesive soils, the ultimate lateral pressure isgiven by

Pu = 3v1 + sin

1 sin 2

In this model, displacement of the soil adjacent to the pile wall is

represented by the displacement of the plastic slider, which isdifferent from the displacement of the soil away from the pile

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / DECEMBER 2005 /1481


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represented by the maximum displacement at each depth obtainedfrom the free-field site response analysis.

The calculation steps involved in this new approach can besummarized as below.

1. First, a free-field site response analysis is performed by tak-ing into account the pore pressure generation and dissipationin the soil deposit due to the earthquake loading. From this

analysis, the maximum ground surface acceleration, maxi-mum ground displacement along the length of the pile, andthe minimum effective stress level attained during theseismic activity can be obtained.

2. The superstructure is modeled as a concentrated mass at thepile head. Generally the superstructures supported by pilefoundations are multi-degree of freedom systems, but in thedesign of pile foundations, the superstructure is reduced to a

single mass at the pile head to simplify the analysis.

3. The lateral force to be applied at the pile head is the cap-mass multiplied by the maximum ground surface accelera-

tion obtained from the free-field site response analysis, asshown in Fig. 1.

4. The pilesoil interaction is modeled using springs as shownin Fig. 1. Spring coefficients are calculated by integrating the

Mindlins equation as described by Liyanapathirana and Pou-los 2002a, 2005 , using the minimum shear modulus corre-sponding to the minimum effective vertical stress calculated

in Step 1. The maximum soil displacement profile calculatedin Step 1 is applied to the pile through these springs asshown in Fig. 1.

5. A plastic slider is used in series with each spring to limit thepressure at the pilesoil interface to the ultimate lateral pres-sure given by Eq. 2 .

6. A nonlinear static load analysis is carried out to obtain the

profile of maximum pile displacement, bending moment, andshear force along the pile by applying the lateral force at thepile head calculated in Step 3 and the maximum soil dis-

placement profile along the pile calculated in Step 1 simul-taneously to the pile as shown in Fig. 1.

Verification of the Proposed Method

The proposed pseudostatic approach has been verified for soil

deposits with uniform relative density and for two-layer soil de-posits using the dynamic benchmark analysis described in thecompanion paper by Liyanapathirana and Poulos 2005 .

Soil Deposits with Uniform Relative Density

In this section the proposed pseudostatic approach has been veri-fied for soil deposits with uniform relative density. Results have

been obtained for a soil deposit with 50% relative density bychanging the length of the pile and the diameter of the pile. It isassumed that the pile extends down to the bottom of the soildeposit. The shear modulus of the soil is assumed to vary with the

effective stress level of the soil as shown below

Gs = G01 + 2K0

3v

100

0.5

MPa 3

where v= effective stress level of the soil, K0 = coefficient of

earth pressure at rest, and the initial shear modulus, G0, is as-sumed to be 30.

Tables 1 and 2 show the maximum pile bending moment ob-tained for different pilesoil configurations. The depth of the soil

deposit ranges between 15 and 30 m and the pile diameter rangesfrom 0.3 to 1.2 m as given in Table 1. The concrete piles used forthe analysis have a Youngs modulus of 3104 MPa and a den-

Table 1. Maximum Bending Moment MN m Obtained from Dynamic and Pseudostatic Analyses Dr=50%

Length

m

d=0.3 m d=0.6 m d=0.9 m d=1.2 m

Dynamic Pseudostatic Dynamic Pseudostatic Dynamic Pseudostatic Dynamic Pseudostatic

15 0.13 0.12 0.86 0.93 4.11 4.39 12.1 13.4

20 0.07 0.06 0.46 0.46 2.16 2.16 6.08 6.08

25 0.10 0.95 0.57 0.57 2.30 2.55 7.0 7.27

30 0.14 0.14 0.53 0.69 2.50 2.70 7.41 7.41

Table 2. Maximum Bending Moment MN m Obtained from Dynamic and Pseudostatic Analyses Dr=60%

Length m

d=0.3 m d=0.6 m d=0.9 m d=1.2 m

Dynamic Pseudostatic Dynamic Pseudostatic Dynamic Pseudostatic Dynamic Pseudostatic

15 0.12 0.12 0.86 1.05 4.03 4.03 11.0 11.3

20 0.17 0.16 1.20 1.24 5.36 5.36 12.9 12.9

25 0.13 0.10 0.63 0.50 1.98 1.98 5.93 5.93

30 0.16 0.15 0.80 0.70 2.70 2.99 8.31 7.31

Fig. 1. Beam on Winkler foundation model for pseudostatic analysis



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sity of 2,400 kg/m3. The soil deposits used for the analysis havea density of 1,900 kg/m3, permeability of 5.5e5 m/ s, and a fric-

tion angle of 30. It is assumed that the water table is 2.0 m belowthe ground surface.

First, a free-field site response analysis is carried out to obtain

the maximum soil displacements along the depth of the soil de-posit, maximum ground surface acceleration, and the minimumeffective vertical stresses along the depth of the soil deposit. The1995 Kobe earthquake record given in the companion paper by

Liyanapathirana and Poulos 2005 scaled to 0.25g has been usedas the excitation source. As discussed in a previous section, soildeposits retain some shear strength even after liquefaction. There-fore, during the free-field site response analysis, effective stress of

the soil is reduced only up to 2% of the initial effective overbur-den pressure at each depth.

Fig. 2 shows the amount of pore pressure generation, positive

and negative ground displacement envelopes, and the maximumground surface acceleration for the four soil deposits consideredfor the analysis. The liquefied depth ranges between 6 and 8 mfor these soil deposits.

During the pseudostatic analysis of the pile, the pile head isassumed to be restrained against rotational movement and the piletip is assumed to be restrained against lateral movement. Thecap-mass carried by each pile configuration is calculated based on

the ultimate load carrying capacity of piles in sand with a factorof safety of 2.5.

Despite its simplicity, Table 1 shows that the pseudostaticanalysis gives results in close agreement with the benchmark dy-namic analysis. The agreement between results is not only con-

fined to the point of maximum bending moment but occurs alongthe whole length of the pile. Fig. 3 shows the maximum positiveand negative bending moment, shear force, and displacement en-velopes along the pile obtained from the dynamic analysis, for the

15 m pile with 0.3 and 1.2 m diameters, given in Table 1 duringthe earthquake loading. These figures also show the maximumbending moment, shear force, and displacement obtained from the

pseudostatic analysis, and they demonstrate the close agreementbetween the dynamic and pseudostatic analyses along the lengthof the pile. It is interesting to see that in some parts, the staticprofile matches with the maximum positive envelope and in other

parts, it matches with the maximum negative envelope.In Fig. 4, the maximum bending moment and shear force pro-

files along the 15 m long pile with Dr=50% are given for a free

head pile where the pile extends 1 m above the ground surface.The maximum ground surface acceleration, pore pressure ratio,and ground displacements at each depth are given in Fig. 2 a .The concrete pile used for the analysis and the soil have the same

properties as in the previous analysis. Maximum bending momentprofiles are given for pile diameters of 0.3, 0.6, 0.9, and 1.2 m.

When carrying out the pseudostatic analysis, the pile head is as-sumed to be at the ground surface. Hence in addition to the iner-

Fig. 2. Amount of pore pressure generation and free-field

displacement along the depth of the soil deposit and the maximum

ground surface acceleration Fig. 3. Variation of pile moment, shear, and displacement along

depth for 15 m pile with diameters 0.3 and 1.2 m Dr=50%



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tial force, the moment due to eccentricity of the inertial force

acting at the pile head is applied to the pile in the pseudostatic

analysis. Here the inertial force at the pile head is given by the

product of capmass and the ground surface acceleration. The cap-

mass is calculated based on the ultimate load carrying capacity of

piles in sand with a factor of safety of 2.5. The agreement be-tween dynamic and pseudostatic analyses confirms that, irrespec-

tive of the boundary conditions at the pile head and the pile tip,

the pseudostatic approach can be used to estimate the internal

response of the pile.

Fig. 5 shows the internal response for the 0.3 m diameter and

15 m long pile without cap-mass and with a 50 t cap-mass,

founded in the soil deposit shown in Fig. 4 a . In Fig. 3 a the

internal response for the same pile is given when the cap-mass is

20 t. When the pile does not carry a cap-mass, excellent agree-

ment between the pseudostatic and dynamic analyses can be ob-

served in Fig. 5. With the increase in cap-mass, the agreement

between the pseudostatic and dynamic analyses reduces and the

pseudostatic method overestimates the maximum pile bending

moment. In the proposed pseudostatic method, the inertial forcebased on the maximum ground acceleration and the maximum

ground displacement profile is applied to obtain the internal pile

response. In the dynamic analysis, the maximum free-field ground

displacment will not occur in phase with the maximum ground

surface acceleration. As a result, the pseudostatic method overes-

timates the maximum pile bending moment in some cases com-

pared to the pile response predicted by the dynamic benchmark

analysis.

Although results are given here only for some selected cases,

the method has given reasonable agreement with the dynamic

analysis for different soil conditions and pile configurations. It has

been found that the maximum values are given at the same depth

and the difference in magnitude is less than 25%, which is gen-erally acceptable for practical pile design purposes.

Two-Layer Soil Deposits

In this section the psedostatic method proposed in a previoussection has been verified for two-layer soil deposits with a non-liquefying soil layer overlain by a liquefying soil. The relativedensity of the liquefying soil is 50% and that of the nonliquefying

layer is 90%. For the Dr=50% case, the friction angle is 30 andG

0Eq.

3

is 30 MPa, while for the Dr=90% case, friction angle

is 35 and G0 is 35 MPa. It is assumed that both layers have a

density of 1,900 kg/ m3 and permeability of 5.5e5 m/ s. Thewater table is considered to be at the ground surface.

Fig. 4. Variation of pile moment along depth for a free head pile with

diameters 0.3, 0.6, 0.9, and 1.2 m Dr=50%

Fig. 5. Variation of pile moment and shear along depth for a 15 m

pile with diameter 0.3 m with and without cap-mass Dr=50%

Fig. 6. Maximum ground displacement envelopes along the depth

and maximum ground surface acceleration for layered soil deposits



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The total thickness of the two-layer soil deposit is 25 m andthe analysis is carried out by varying the thickness of the topliquefying soil layer. The four cases considered have top liquefy-ing layers of 4, 8, 12, and 16 m. The 1995 Kobe earthquake

record scaled to 0.25g shown in Fig. 3 has been used as theexcitation source.

The free head piles used for the analysis extends up to the

bottom of the soil deposit and the spring coefficients used torepresent pilesoil interaction are calculated based on the mini-mum effective stress at each depth obtained from the free-fieldsite response analysis. Two pile diameters are considered, 0.6 and

0.9 m, and each pile carries a cap-mass of 8.4104 and 1.66105 kg, respectively. The concrete piles used for this analysishave a Youngs modulus of 3104 MPa and a density of

2,400 kg/m3.Fig. 6 shows the positive and negative ground displacement

envelopes and the maximum ground surface acceleration obtainedfrom the free-field site response analysis. Figs. 7 and 8 show the

bending moment along the pile obtained from the pseudostaticapproach and the maximum positive and negative bending mo-ment envelopes obtained from the benchmark analysis for pileswith diameters 0.6 and 0.9 m, respectively. It can be seen that for

all cases, the maximum bending moment given by the pseudo-static approach reasonably agrees with those given by thedynamic bench mark analysis.

Comparison with Field and Centrifuge Data

In this section, the proposed pseudostatic method has been used toestimate the maximum bending moments developed in a pile used

for a centrifuge test carried out by Abdoun et al. 1997 and thebored piles at Bridge Pier 211 in Uozakihama Island after the

Hyogoken-Nambu 1995 earthquake reported by Ishihara andCubrinovski 1998 .

The centrifuge test by Abdoun et al. 1997 was carried out tostudy the pile response during lateral spreading. Details of this

test are given in the companion paper by Liyanapathirana andPoulos 2005 . Fig. 9 shows the maximum bending moment en-velope obtained from the pseudostatic analysis and the measured

maximum bending moments at several depths during the centri-fuge test. In this case, pile does not carry a cap-mass and pilehead is free. Therefore the pseudostatic analysis is carried out byapplying only the maximum free-field ground displacements at

each depth along the pile. It can be seen that the calculated valuesagree well with the values recorded during the centrifuge test.

The field measurements made in the piles at Pier 211 inUozakihama Island after the Hyogoken-Nambu earthquake oc-

Fig. 7. Variation of pile bending moment along depth for a 25 m

long pile with diameter 0.6 m in a two-layer soil depositFig. 8. Variation of pile bending moment along depth for a 25 m

long pile with diameter 0.9 m in a two-layer soil deposit

Fig. 9. Comparison of maximum bending moment along pile with

centrifuge data from Abdoun et al. 1997



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curred on January 17, 1995, and reported by Ishihara and Cubrin-

ovski 1998 , have been simulated using the pseudostatic ap-proach presented in this paper. Fig. 10 shows the crackdistributions observed in piles after the earthquake. The concretepiles at bridge Pier 211 are 46 m long and the diameter is 1.5 m.

The water table is 2.0 m below the ground surface and the upper20 m of this site consists of Masado sand with an initial shearmodulus of 57.8 MN/m2 and density of 2,000 kg/ m3 Tokimatsu

et al. 1998 . Soil liquefaction was observed in the Masado sandlayer below the water table only. Therefore only the top 20 mlayer was analyzed using the effective stress method and incorpo-

rating pore pressure generation and dissipation. For this analysisthe cyclic shear strength curve for the Masado sand given byIshihara 1997 was used. It was assumed that the base rock had adensity of 2,200 kg/m3 and shear modulus of 75 GN/m2. Thelower end of the RC pile was assumed to be fixed while the pile

head was assumed to be fixed to the footing but free to move inthe horizontal direction.

Fig. 11 shows the maximum ground displacement at eachdepth obtained from the site response analysis and the free-fieldground displacements used by Ishihara and Cubrinovski 1998 .

During the earthquake, only the ground surface displacementswere recorded. Based on these data, the lateral ground surfacedisplacement at the vicinity of bridge Pier 211 was about 1.0 m,which agrees well with the maximum ground surface displace-

ment obtained from the numerical model. Ishihara and Cubrin-ovski 1998 used a cosine function through the liquefied layerdown to a depth of 20 m to distribute the ground surface displace-ment, as shown in Fig. 11. There is a slight discrepancy between

this assumed displacement distribution and the displacement dis-tribution obtained from the numerical model.

Fig. 12 shows the maximum bending moment profile along the

pile obtained from the pseudostatic approach and those calculatedby Ishihara and Cubrinovski 1998 . The predictions made by thepseudostatic approach agree well with Ishiharas results. Theyield moment for these piles was about 5 MN m. The computed

maximum bending moment profile exceeds the yield momentnear the pile head and around the boundary between the liquefiedand nonliquefied layers. This is consistent with the location of

cracks observed after the earthquake shown in Fig. 10.

Conclusions

This paper has described a pseudostatic approach that can be usedto compute the maximum bending moment and shear force devel-oped in a pile founded in liquefying soil. An effective-stress-

based free-field site response analysis is first carried out and theresulting ground displacements, degraded soil stiffness, and iner-tial force at the pile head, based on the cap-mass and the maxi-

mum ground surface acceleration, are applied to the pile staticallyto obtain the internal pile response. The spring coefficients of theWinkler model used in the pseudostatic analysis are derived fromMindlins equations.

The results presented in the paper suggest that the new methodhas promise in practical applications. For a few cases the newmethod overestimated the pile bending moment and shear forcebut the values were within 25% of those obtained from the dy-

namic analysis. Both dynamic and pseudostatic analyses give

peak values at the same locations. Also the pseudostatic methodhas been verified for two layer soil deposits with liquefying and

Fig. 10. Cracks observed in the piles at bridge pier 211 in

Uozakihama Island Ishihara and Cubrinovski with permission, 1998

Fig. 11. Maximum ground displacement at each depth obtained from

the site response analysis and estimated by Ishihara and Cubrinovski

1998 based on field measurements

Fig. 12. Bending moment of the pile at Bridge Pier 211 in

Uozakihama Island calculated from the pseudostatic approach and

Ishihara and Cubrinovski 1998 results with = 1102



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nonliquefying soil layers. The pile performance observed during acentrifuge test and a real earthquake has been simulated using thepseudostatic approach. It is found that the pile response calculated

from the pseudostatic approach is consistent with the observedpile behavior.

Acknowledgments

This work is part of a project on Design of Pile Foundations forSeismically Active Areas funded by the Australian ResearchCouncil and this support is gratefully acknowledged. Also the

writers would like to thank the reviewers for their thorough re-view and useful comments.

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Documents

Pseudo Static Approach for Seismic Analysis of Piles in Liquefying Soils