dynamic behavior of pile foundations under cyclic loading in liquefiable soils.pdf

7/25/2019 Dynamic behavior of pile foundations under cyclic loading in liquefiable soils.pdf

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Dynamic behavior of pile foundations under cyclic loading in liquefiable soils

Amin Rahmani , Ali Pak

Department of Civil Engineering, Sharif University of Technology, P.O. Box 11155-9313, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 5 March 2011

Received in revised form 12 September

2011Accepted 13 September 2011

Available online 11 November 2011

Keywords:

Liquefaction

Pile foundations

Fully coupled three-dimensional dynamic

analysis

Dynamic behavior of pile

a b s t r a c t

In this paper, a fully coupled three-dimensional dynamic analysis is carried out to investigate the

dynamic behavior of pile foundations in liquefied ground. A critical state bounding surface plasticity

model is used to model soil skeleton, while a fully coupled (uP) formulation is employed to analyze soildisplacements and pore water pressures. Furthermore, in this study, variation of permeability coefficient

during liquefaction is taken into account; the permeability coefficient is related to excess pore water

pressure ratio. Results of a centrifuge test on pile foundations are used to demonstrate the capability

of the model for reliable analysis of piles under dynamic loading. Then, the verified model is used for a

parametric study. The parametric study is carried out by varying pile length, frequency of input motion,

fixity of the pile head, thickness of the liquefying soil layer and relative density of liquefying soil layer.

Three different soil profiles have been considered in this study. In general, parametric studies demon-

strate that fixity of the pile head, thickness of liquefying soil layer and frequency of input motion are

the most critical parameters which considerably affect piles performance in liquefied grounds.

Crown Copyright 2011 Published by Elsevier Ltd. All rights reserved.

1. Introduction

The behavior of pile foundations under earthquake loading is an

important issue that widely affects the performance of structures.

Design procedures have been developed for evaluating pile behav-

ior under earthquake loading; however, application of these proce-

dures to cases involving liquefiable ground is uncertain since the

performance of piles in liquefied soil layers is much more complex

than that of non-liquefying soil layer not only because the super-

structure and the surrounding soil exert different dynamic loads

on pile, but also because the stiffness and shear strength of the sur-

rounding soil diminishes over time due to non-linear behavior of

soil and also pore water pressure generation.

Liquefaction represents one of the biggest contributors to dam-

age of constructed facilities during earthquakes[1]. This phenom-

enon was reported as the main cause of damage to pilefoundations during the major earthquakes such as Alaska, 1964,

Loma-Prieta, 1989, Hyogoken-Nambu, 1995 [1]. Prediction of

seismic response of pile foundations in liquefying soil layers is

difficult, and there are many uncertainties in the mechanisms in-

volved in soilpile-superstructure interaction. However, in recent

decades, a wide range of centrifuge and shaking table tests and

also various numerical methods have been employed in order to

provide better insights into the dynamic behavior of pile founda-

tions in liquefiable soils. These researches can be divided into

three categories: field observations, laboratory tests, and numeri-

cal modeling.

1.1. Field observations

These studies mainly investigate the distribution of the failure

patterns, settlement and lateral displacement of piles. During

Niigata Earthquake, 1964, many pile foundations failed to support

structures due to the liquefaction of the surrounding soil. Accord-

ing to Hamada[2], the ground in the vicinity of a four-storey build-

ing moved approximately 1.1 m, and the maximum lateral

displacement of concrete piles with a diameter of 35 cm and length

of 69 m was around 70 cm. The large amount of lateral displace-

ment caused severe damage to the pile at the interface of the liq-

uefied and non-liquefied layers. Mori et al. [3] conducted an

excavation survey and internal inspection of the damaged pilesof a silo which suffered severe damage due to the Hokkaido Nan-

sei-Oki Earthquake, 1993. They concluded that damage usually oc-

curs at three different locations: at the pile head (for fixed-head

piles), at a depth of 13 m below the pile cap (for free-head piles)

and at the interface of the liquefied and non-liquefied layers. This

observation has been confirmed by others such as Tachikawa

et al.[4], Shamoto et al.[5], and Onishi et al.[6].

1.2. Laboratory tests

These studies include some dynamic centrifuge tests and

also shaking table tests of pile-supported structures in which

0266-352X/$ - see front matter Crown Copyright 2011 Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.compgeo.2011.09.002

Corresponding author. Tel.: +98 21 6616 4225; fax: +98 21 6601 4828.

E-mail address:[email protected](A. Rahmani).

Computers and Geotechnics 40 (2012) 114126

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seismic response of pile, soil and superstructure are investigated.

Wilson et al. [7]conducted a series of centrifuge tests on single

piles and pile groups located in liquefiable soils in order to ob-

serve the py behavior of piles embedded in liquefying sands.

The centrifuge tests results indicated that py curves were

highly time-dependent in liquefiable soils; lateral resistance on

the pile decreased by increasing pore water pressure, and there

was very little lateral resistance on the pile even under largerelative displacements. Furthermore, Yao et al. [8] used large

shaking table tests and concluded that the transient state prior

to soil liquefaction was important in the design of piles because

dynamic earth pressure showed peak response in this state.

Other researchers such as Abdoun and Dobry [9], Suzuki et al.

[10], Dungca et al. [11], Bhattacharya et al. [12], Tamura and

Tokimatsu [13] and Han et al. [14] also investigated dynamic

behavior of pile foundations in liquefiable soils using shaking

table tests.

1.3. Numerical modeling

The effectiveness of numerical simulation tools for analyzing

liquefaction problems have become more important and promi-

nent in the light of potential disadvantages of physical models

used in experimental simulation[15]. Since two and three dimen-

sional numerical modeling are computationally complex and

time-consuming, most of the researchers and designers prefer to

use one-dimensional Winkler method based on finite element or

finite difference methods for the seismic analysis of pile founda-

tions. Kagawa [16], Yao and Negami [17], Fujii et al. [18], and

Liyanapathriana and Poulos [19] developed this method so that

liquefaction of surrounding soil was taken into account during

analyzing process. Miwa et al. [20], Liyanapathirana and Poulos

[19,21], and Chang et al.[22]showed that one-dimensional meth-

od is approximately capable of predicting maximum lateral dis-

placement and maximum bending moment of pile foundations

in liquefied soils; however, it is obvious that Winkler modelsare not able to simulate the prototype model accurately because

it is difficult to estimate the accurate values for the springs and

dashpots coefficients which considerably change over time. Finn

and Fujita [23], Klar et al. [24], Oka et al. [25], Uzuoka et al.

[26], Cheng and Jeremic [15] Comodromos et al. [27] used

three-dimensional finite element method in order to simulate

piles in liquefying soil layers. Each of these models possesses

varying prediction accuracy and certainty. In some of these papers

fully-coupled formulation (uP or uPU formulation) has been

employed; while in others the uncoupled formulation, in which

soil skeleton displacements and pore water pressure generation

are computed separately, has been used. According to the studies,

three-dimensional models are able to simulate most of the phe-

nomena which have been observed in the field more accuratelythan that of one-dimensional models.

In general, considering previous studies on the performance of

pile foundations embedded in liquefiable grounds, one may come

to the conclusion that there is a significant lack of understanding

in involved mechanisms. Besides, it should be noted that in the

previous studies the variation of soil permeability during liquefac-

tion has not been considered in the modeling. However, it is com-

monly demonstrated that soil permeability considerably changes

during liquefaction. Therefore, in the present study, it is intended

to take permeability variation into account in the soilpile-super-

structure simulation. The work presented in this paper utilizes a

fully coupled three-dimensional dynamic analysis together with

a well-calibrated constitutive model and a verified numerical

methodology in order to simulate the behavior of piles embeddedin liquefiable soils more accurately.

2. Numerical formulation

In this study, auPfully coupled formulation, presented by Zie-

nkiewicz and Shiomi[28], is used for modeling of soil skeleton and

pore fluid. TheuPformulation captures the movements of the soil

skeleton (u) and the change of the pore pressure (P). This formula-

tion is applicable for dynamic problems in which high-frequency

oscillations are not important, such as soil deposit under earth-quake loading. Using the finite element method for spatial discret-

ization, theuPformulation is as follows[29]:

MU

ZV

BTr0dV QP fs

0 1

QT _U HP S _P fp

0 2

whereMis the mass matrix, Uis the solid displacement vector, B is

the straindisplacement matrix, r0 is the effective stress tensor, Q

indicates the discrete gradient operator coupling the motion and

flow equations, Pis the pore pressure vector, S is the compressibil-

ity matrix, andH is the permeability matrix. The vectors f(s) andf(p)

include the effects of body forces, external loads and fluid fluxes.

Numerical integration of the above-mentioned equations isdone using Newmark algorithm, and implementation of these pro-

cedures was performed using OpenSees[30]framework, which is

an object-oriented program for finite element analysis. The Open

System for Earthquake Engineering Simulation (OpenSees) is a

comprehensive and continually developing software that is used

in the simulation of seismic response of structural and geotechni-

cal systems. In this study, a number of elements and material mod-

els from UCD computational geomechanics toolset, available in this

software, are employed. The employed elements and material

models are discussed in the following sections.

3. Constitutive modeling of sand behavior

Material model is one of the most important parts of numericalsimulation of the dynamic behavior of liquefiable soils. Using a

comprehensive constitutive model which possesses the simulative

ability to model the behavior of drained or undrained saturated

sands under monotonic and cyclic loadings leads to accurate mod-

eling of problems where liquefaction is involved. Accordingly, in

this research a critical state two-surface plasticity model devel-

oped by Dafalias and Manzari[31]is used. The most striking fea-

ture of this model is its capability to utilize a single set of

material parameters for a wide range of void ratios and initial

stress states for the same soil. It should be noted that initial stress

states, void ratio and fabric evolve through all stages of loading

(see Ref.[29]for more details about the employed material model).

This model possesses 15 parameters divided into 6 categories

based on their functions. These parameters are calibrated for Neva-da sand by Shahir[32,33]using tests performed by Earth Technol-

ogy Corporation in the course of the VELACS project [34].The

calibrated parameters are listed inTable 1.

4. Variation of soil permeability during liquefaction

Many studies have demonstrated that permeability coefficient

significantly increases during liquefaction phenomenon due to

structural change in soil skeleton. At the onset of liquefaction, soil

particles lose full contact with each other, and this change creates

additional pathways for water. The creation of such new, larger

flow pathways reduces the pore shape factor and tortuosity

parameters, and consequently leads to a significant increase in per-

meability coefficient[32]. The amount of increase in permeabilitycoefficient during liquefaction has been reported in some

A. Rahmani, A. Pak / Computers and Geotechnics 40 (2012) 114126 115


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investigations. Arulanandan and Sybico [35], based on the mea-

surement of changes in the electrical resistance of saturated sand

deposit during liquefaction in the centrifuge tests, concluded that

in-flight permeability of saturated sand during liquefaction in-

creases up to 67 times greater than its initial value. Jafarzadeh

and Yanagisawa [36] by measurement of the volume of the ex-

pelled water from saturated sand columns in shaking table model

tests indicated that the average permeability coefficient during

excitation is 56 times greater than its static value. Manzari and

Arulanandan [37] used variable permeability in their numerical

simulation. In their study, predictions of excess pore pressure

and settlement were satisfactory, but lateral displacements were

not simulated reasonably well. Balakrishnan[38]employed a fac-

tor of 10 for increasing the permeability coefficient in numerical

model in order to adjust the results of the simulation with the cen-

trifuge test measurements for the soil settlement during liquefac-

tion. Also, according to Taiebat et al. [39] and Shahir and Pak

[40]using a constant value of permeability coefficient in numericalanalysis results in a much smaller value of soil settlement

compared to the measured value. Shahir and Pak[40]concluded

that incorporation of permeability variation in the numerical

model is necessary for capturing both pore pressure and settle-

ment responses of a liquefiable soil mass.

Therefore, in this study, variation of permeability coefficient has

been considered in numerical modeling of liquefiable layers using

a formulation suggested by Shahir and Pak[40]in which a direct

relationship between the permeability coefficient and excess pore

water pressure ratio (ru) was proposed. This relationship is as

follows:

kpki

1 a 1rb1u During PWP build up phaseru < 1

kpli

a During liquefied stateru 1

kpki

1 a 1rb2u During consolidation phaseru < 1

3

wherekiis initial permeability coefficient,kbis permeability coeffi-

cient during excitation,ruis defined as the ratio of the difference of

current pore pressure and hydrostatic pore pressure over the initial

effective vertical stress (ru Du=r0v0).a;b1; b2 are positive materialconstant. These parameters are 20, 1.0 and 8.9, respectively for Ne-

vada Sand[40]. This basically means that the permeability coeffi-

cient increases up to 20 times during the initial liquefaction. It is

to be noted that the proposed value fora is consistent with the re-ported value by Balakrishnan[38]because the peak value of 20 is

nearly equivalent with average value of 10. Validity and efficiency

of the proposed formulation can be found in Refs.[33]and [40].

5. Pilesoil model development

In this research, soil layers are modeled by cubic eight-node

elements with uP formulation (called EightNodeBrick_u_p ele-

ment in OpenSees framework) in which each node has four de-

grees of freedom: three for soil skeleton displacements and one

for pore water pressure. Pile is modeled by beam-column ele-

ments which have six degrees of freedom for each node: threefor displacements and three for rotations. A lumped mass on the

pile head represents the superstructure. The finite element mesh

is presented inFig. 1.

One of the important and difficult steps in numerical simulation

of pile foundations in the soil media is the connection of pile ele-

ments to the surrounding soil elements. In the present work, the

connection is provided by means of rigid beam-column elements

which possess the same physical properties of pile elements. As

shown in Fig. 2, these elements connect each pile node to sur-

rounding nodes of soil elements at an equal depth. At the connec-

tion point, soil element nodes slaved to the connection element

node for three translational DOFs, while the three rotational DOFs

of the connection element are left unconnected. Furthermore, slip-

page between pile elements and surrounding soil elements is fea-

sible in all directions by using zero-length interface elements,

which are defined by two nodes at the same location where the

connection beam-column element is connected to the surrounding

soil (as shown inFig. 2). An elastic-perfectly plastic material model

is used for the interface elements. Some static field tests and also a

centrifuge test, discussed later in this paper, were simulated in or-

der to obtain suitable mechanical properties of the interface ele-

ment. Based on these studies, Youngs modulus and yielding

strain of this material are selected to be 2000 kPa and 0.04, respec-

tively and are used throughout the main simulations of pile behav-

ior in liquefiable soil layer. It is to be noted that values considered

for these parameters lead to immediate yielding of interface ele-

ment i.e. slippage at soilpile interface can take place.

However, further studies and simulations revealed that the ef-

fect of interface elements was not that significant for the centrifugetest that has been simulated in this study. Comparing the numer-

ical results of the model with and without employing interface ele-

ments revealed a maximum difference of 5%. This can be specific to

the kind of the problem that is studied in this research where the

saturated liquefiable ground is horizontal and the soil is cohesion-

less. Nevertheless, the above mentioned interface element proper-

ties were employed to improve the quality of simulations and

match the numerical results with the experimental values as much

as possible.

Due to the symmetry of the model, the model is halved at the

line of symmetry along the center-line of the pile, and all applied

static loads are halved. Soil elements are coarser far from the pile

and finer around the pile (seeFig. 1).

Boundary conditions are set in the following way:

Base of the mesh is fully fixed in all directions.

At the side planes, parallel to the excitation direction, nodes are

restrained from movement in they direction, and at the ones,

perpendicular to the excitation direction, the nodes at equal

depths are constrained to have equal displacements in the x

direction to simulate free-field ground motion.

All other internal nodes are free to move in any direction.

Pore water pressures are free to develop for all nodes except the

ones at the level corresponding to the ground water table

elevation.

Simulations are carried out in three loading stages. In the first

stage of loading where pile elements are not installed, self-weight,

Table 1

Material parameters used for DafaliasManzari Model [32,33].

Parameter function Parameter index Value

Elasticity G0 150.0

m 0.05

Critical state M 1.14

c 0.78

kc 0.027

e0 0.83

n 0.45

Yield surface m 0.02

Plastic modulus h0 9.7

ch 1.02

nb 2.56

Dilatancy A0 0.81

nd 1.05

Fabric-dilatancy zmax 5.0

cz 800.0

116 A. Rahmani, A. Pak / Computers and Geotechnics 40 (2012) 114126


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including both the soil skeleton and the pore water weight, are ap-

plied on soil elements. In this stage the initial stress state, void ra-

tio and soil fabric evolve. These values are used as initial values for

the next stage of loadings. The second stage includes pile installa-

tion and application of its self-weight and the superstructure

weight. Then, at the final stage, an acceleration time history is ap-

plied to the model as an input motion, and dynamic analysis are

performed for the soilpile-superstructure system.

6. Verification and validation of the numerical model

Verification is meant to identify and remove errors in computercoding and verify numerical algorithms and is desirable in quanti-

fying numerical errors in computed solution [15]. Accordingly, in

this study, due to the sophisticated methodology used to develop

a pile in a soil deposit together with an advanced constitutive

model for soil skeleton and the applied three-dimensional uP

formulation, a detailed verification is done. In the first step, the

numerical model is verified against some closed form elastic solu-

tions and benchmark problems in which a single pile is modeled in

non-liquefying soil layers under static vertical or horizontal load-

ings, e.g. Poulos and Davis[41], Aristonous et al.[42], and Kuchuk-

arsalan[43]. Comparison of results demonstrated the capability of

the numerical model to predict the result by the maximum error of

4%. In the next step, results of a centrifuge test on pile foundations

are used to demonstrate the capability of the model for reliableanalysis of piles under dynamic loading. For this purpose, the

dynamic centrifuge test of pile-supported structure in liquefiable

sand performed by Wilson et al.[7] is simulated.

The soil profile consists of two horizontal layers of saturated,

fine and uniformly graded Nevada sand (D50 = 0.15 mm, Cu= 1.5).

The lower dense layer (Dr= 80%) is 11.4 m thick, and the upper

medium dense layer (Dr= 55%) is 9.1 m thick at the prototype scale

(seeFig. 3). Furthermore, the single pile is equivalent to a steel pipe

pile with a diameter of 0.67 m and wall thickness of 19 mm at the

prototype scale. The pile is extended 3.8 m above the ground level

and carries superstructure load of 480 kN; the embedded length of

pile is about 16.8 m. The container is filled with a hydroxyl-propylmetyl-cellulose and water mixture whose viscosity is about 10

times greater than pure water.

The soilpile-superstructure system was spun at a centrifugal

acceleration of 30 g, and the pile remained elastic during earth-

quake loading.

As shown inFig. 1, the finite element mesh consists of 896 cubic

eight-node soil elements and 16 beam-column elements, four ele-

ments are used to model the free-standing length of the pile and

the rest are within the soil strata. Also, the pile head is free to move

in all directions. Properties of Nevada Sand used in the numerical

model are presented inTable 2. According to the laws of centrifuge

modeling, permeability coefficient is three times greater than the

value at the prototype scale.

The Kobe 1995 acceleration record is scaled to 0.22 g and usedas an input motion to shake the model; the base input acceleration

42.4(m)

21.0(m)

X

Y

Z

ZP

x

z

y

X : 3@5(m)[email protected](m)[email protected](m)+

[email protected](m)[email protected](m)

Y : [email protected](m)+1 @0.5(m)[email protected](m)

Z : 5@2(m) [email protected](m)+5@1(m)

ZP: 3@1(m)[email protected](m)

21.0

42.4

17.0

3.8

4.0

x

z

u-P Elements

Lumped Mass

Beam-Column Element

Input Motion

Fig. 1. Finite element mesh.

Connection Elements

Pile Elements

Interface Elements

Surrounding Soil Elements

y

x

Fig. 2. Outline of Connections between pile elements and surrounding soil

elements.

Fig. 3. Layout of the model for centrifuge test by Wilson et al. [7].



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is shown inFig. 4. Time history of the measured and computed ex-

cess pore water pressure ratio at three different depths in the free

field: 1, 4.5, 21 m, are presented in Fig. 5. It is important to note

that in this study, excess pore water pressure ratio (ru) is defined

as the ratio of the difference of current pore pressure and hydro-

static pore pressure over the initial effective vertical stress

ru Du=r0v0. The results indicate that there is generally a goodagreement between measured and computed pore water pressure.

Fig. 6shows the computed and measured acceleration time his-

tories of the superstructure. It is concluded that the applied meth-

od is also capable of predicting the acceleration values. It is

important to note that sharp acceleration spikes can be seen corre-

sponding to sharp excess pore pressure ratio decrease at the depthof 1 m. This is due to the temporary increase in stiffness of the soil

which results in large acceleration spikes transmission from the

ground to the superstructure.

Fig. 7 shows the measured and computed bending moment

time histories at two different depths; 1 and 2 m. It can be seen

that the results obtained from the numerical model agree reason-

ably well with the values recorded during the centrifuge test.

According to the computed and measured results, the maximum

bending moment at the depth of 1 m occurs at the timet= 3.5 s.

As depicted inFig. 5, this time corresponds to sudden increase of

pore water pressure which results in the softening of surrounding

soil; and also as shown inFig. 6, the timet= 3.5 s corresponds to

the peak value of superstructure acceleration which results in a

large amount of inertial forces induced to the pile shaft. Therefore,

it can be concluded that the maximum value of bending moment

recorded and computed att= 3.5 s is the consequence of the sur-

rounding soil softening and the large amount of inertial forces

developed at the pile head.

Finally, soil displacements are compared with those recorded

during the centrifuge test.Fig. 8shows the time history of ground

surface settlement at the distance of 3 m from the pile. It is ob-

served that there is a good agreement between the computed

and measured values.

7. Parametric study

In order to provide better insights into the dynamic behavior of

piles embedded in liquefiable soil layers, a parametric study hasbeen carried out on three different soil profiles by varying

Table 2

Material parameters for Nevada sand, Popescu and Prevost [44].

Parameter Unit Value for

Dr = 55%

Value for

Dr = 80%

Porosity (n) 0.409 0.377

Saturated unit weight kN/m3 19.87 20.41

Permeability coefficient m/s 6.05 105 3.7 105

Permeability coefficient

in the prototype scale

m/s 1.815 104 1.11 104

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 2 4 6 8 10 12 14 16 18 20

Acceleration(g)

Time (sec)

Fig. 4. Input earthquake ground motion (Acceleration record of Kobe (1995)

earthquake scaled to 0.22 g)[7].

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

ExcessPorePressure

Ratio

Time (sec)

Depth = 1 m

Centrifuge Test

Simulation

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

ExcessPorePressure

Ratio

Time (sec)

Depth = 4.5 m

Centrifuge Test

Simulation

-0.2

0

0.2

0.4

0.6

0.8

1

ExcessPoreP

ressure

Ratio

Time (sec)

Depth = 21 m

Centrifuge Test

Simulation

0 5 10 15 20 25

0 5 10 15 20 25

Fig. 5. Comparison of time histories of excess pore pressure ratio in the free field at

the depths of 1, 4.5, 21 m with the centrifuge test by Wilson et al.[7].

-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15 20 25

Acceleration

(g)

Time (sec)

Centrifuge Test

Simulation

Fig. 6. Comparison of time histories of superstructure acceleration with the

centrifuge test by Wilson et al. [7].

-3

-2

-1

0

1

2

3

0 5 10 15 20 25

BendingMom

ent(MN.m)

Time (sec)

Depth Z = 1 m

Centrifuge Test

Simulation

-3

-2

-1

0

1

2

3

0 5 10 15 20 25

BendingMoment(MN.m)

Time (sec)

Depth Z = 2 m

Centrifuge Test

Simulation

Fig. 7. Comparison of time histories of bending moment with the centrifuge test byWilson et al.[7].



6/13

boundary condition of pile head, pile length (L), thickness of lique-

fying soil layer (HL), relative density of liquefying soil layer (Dr)

and frequency of input motion (f). In the first profile, the ground

consists of one homogenous and liquefiable soil layer. In the sec-

ond profile, the ground is two-layered: the upper layer is liquefi-

able while the lower layer is not, and in the third one, the

ground is two-layered: the upper layer is dry and the lower layeris saturated and liquefiable. In all cases, the ground is level, and lat-

eral spreading phenomenon is not plausible. Fig. 9 shows these

profiles. It is important to note that the amplitude of input acceler-

ation is larger for the third case due to the larger values of initial

effective stress at lower layer. Amplitude of the sinusoidal input

motion is 0.15 g for the first and second soil profiles and 0.5 g for

the third soil profile.

The finite element mesh used for simulation of the proposed

soil profiles is shown inFig. 10. It consists of 1024 cubic eight-node

soil elements. The concrete pile cross section is assumed to be

square with sides (B) of 50 cm, and it is also assumed to remain

elastic during the excitation. Two different boundary conditions

are assumed at pile head: free head boundary condition in which

pile head is free to move and rotate in any direction and fixed head

boundary condition in which pile head is free to move in any direc-tion but constrained against any rotation. The material properties

of the pile and Nevada sand are shown in Table 3. In all cases,

the superstructure is simulated by a single lumped mass with a

load of 1000 kN. The input acceleration record used for the analysis

is a sinusoidal acceleration time history with 10 s duration. The

analysis has been repeated for pile lengths of 15B, 25B and 40B,

and acceleration frequencies of 1, 3, 5 and 10 Hz. For the sake of

comparison, the fully fixed pile head (against displacement and

rotation both) has also been simulated, but the results will not

be demonstrated here. The interested reader may refer to[45].

Before going into the study of the effects of mentioned

parameters on piles dynamic behavior, it is important to study

the dynamic performance of piles in each soil profile.

7.1. Pile response

The analysis has been repeated for pile lengths of 15B, 25Band

40B.Fig. 11shows maximum lateral displacement of pile and max-

imum bending moment envelops for the 40Blength pile for cases I,

II and III, respectively (due to the similar results obtained for each

pile length, only the results of the pile length of 40Bare presented

-80

-60

-40

-20

0

20

0 5 10 15 20 25

Se

ttlement(mm)

Time (sec)

Centrifuge Test

Simulation

Fig. 8. Comparison of time histories of settlement at the distance of 3 m from the

pile.

25 m

Case I Case II Case III

Liquefiable Soil

Dry Soil

W = 1000 kN

PGA = 0.5g

Dr = 40 %

Dr = 40 %

Liquefiable Soil

Dr = 40 %

W = 1000 kN

PGA = 0.15g

Nonliquefiable Soil

Dr = 85 %

Liquefiable Soil

W = 1000 kN

PGA = 0.15g

Dr = 30,40,50 %

Fig. 9. Schematic of soil profiles in cases I, II, and III.

40.5(m

)

25.0

(m)

X

Y

Z

x

z

y

X : [email protected](m)[email protected](m)[email protected](m)[email protected](m)

Y : [email protected](m)[email protected](m)[email protected](m)

Z : [email protected](m) [email protected](m)[email protected](m)

Input Motion

25.0 (m)

x

z

Lumped Massu-P Elements Beam-Column Element

40.5 (m)

Fig. 10. Finite element mesh. (Dark zone represents the pile.)



7/13

here). A number of observations can be made about these results.

Firstly, for case I, the maximum bending moment invariably devel-

ops at the depth of about 2 m for free-head pile, and at the pile

head for fixed-head pile (only fixed against rotation). For case II,

the maximum bending moment develops at two locations; the first

one is at the place explained for case I, and the other one is ob-

served at the depth corresponding to the interface of liquefiable

and non-liquefiable layers; however, for the third case, the secondmaximum bending moments are attained inside the lower liquefi-

able layer. Secondly, by investigating time histories of lateral dis-

placements and bending moment, it can be concluded that for all

three cases, the maximum lateral displacement of pile is attained

after when the soil layers liquefaction takes place. This is true for

the maximum bending moment which is attained at the bottom

of liquefiable layer; however, the maximum bending moment near

the pile top, develops at the first moments of dynamic loadings be-

fore liquefaction.

Ishihara [46] indicated that inertial forces which are the pre-

dominant forces before liquefaction are mainly responsible for

development of maximum bending moment near the pile head,

and kinematic forces which are predominant after liquefaction

are responsible for the maximum bending moment observed atthe interface of liquefiable and non-liquefiable layers. This is con-

firmed by the numerical method; the results are shown inFig. 12

in which the maximum bending moment envelops of 25B and

40B length piles are obtained for piles with and without super-

structure mass. It is interesting to observe that when the super-

structure is removed, the maximum bending moment near the

pile head decreases significantly, and no peak values are observed

at that location; while values at depths below 5 m are approxi-

mately unchanged. In other words, the same kinematic forces have

been developed in piles with and without superstructure.

For more clarification of the issue, the performance of a pile

embedded in a dry ground is compared with the dynamic perfor-

mance of a pile embedded in a saturated (i.e. liquefiable) ground.

The obtained results for a free-head and fixed-head pile in Case IIare shown inFig. 13. It is concluded that in dry grounds, the lateral

displacements of the pile are significantly less than the values cal-

culated in a saturated ground. This is due to the fact that lateral

displacement of dry soil is far less than lateral displacement of sat-

urated soil; so little kinematic forces are exerted to the pile embed-

ded in a dry ground.

7.2. Soil response

To investigate the effect of pile foundations on the surrounding

soil response, excess pore water pressure time histories computed

near the pile are compared with those computed in the free field at

two different depths. The results are shown in Fig. 14 for a pile

with a length of 40B (21 m) in case I. It can be seen that at thedepth of 1 m (near the pile head), the time history of excess pore

water pressure near the pile is significantly different from the

one in the free field during excitation period, while after excitation

(from 10 to 25 s), time histories are nearly identical. Since the dif-

ference between time histories decreases in the depth far from pile

head (i.e. depth of 15 m), the dynamic response of superstructure

seems to be responsible for the observed behavior. In other words,

inertial forces from the superstructure caused the pile top to vi-

brate in a completely different nature from the surrounding soil,and this leads to larger shear strains exerted to the soil which leads

to temporary dilation and contraction behavior. It is to be noted

that as seen inFig. 12 inertial forces only affect pile top sections.

For this, time histories of excess pore water pressure near the pile

and in the free field are approximately identical at deeper depths.

Furthermore, lateral displacement of soil near the pile is com-

pared with the lateral displacement of soil in the free field before

and after liquefaction of the ground. The results are shown in

Fig. 15 for case I and III (The results obtained for case I is same

as case II). It is noted that the lateral displacement envelope of

the soil near pile and the soil in the free field have an identical

trend before the ground liquefies while there is a significant differ-

ence between the lateral displacement of soil near the pile and the

soil in the free field after liquefaction occurs. Accordingly, it seemsthat dynamic response of pile entirely differs from dynamic re-

sponse of soil after liquefaction.

7.3. Effect of pile length on pile performance

In this section, results obtained from repetitive analysis for pile

lengths of 15B, 25Band 40Bfor three different soil profiles are dis-

cussed (B= pile width). Due to the similarity of results for three

cases, only the results of case II are presented inFig. 16. It is con-

cluded that for all three profiles and any pile head boundary con-

ditions, pile length has no effect on maximum lateral

displacement of pile during excitation (i.e. from 0 to 10 s) while

significant changes are observed after excitation period (i.e. from

10 to 25 s); a change of about 15Bin pile length results in a changeof 2040% in maximum value of pile lateral displacement. Ariston-

ous et al.[42] and many other researchers reported that for piles

embedded in dry soil layers, pile length has a little effect on pile

lateral displacements. However, in this study, it is concluded that

pile length significantly affects pile lateral displacements after

excitation. From t= 10 s to t= 25 s, inertial forces are minimum

not only because the excitation has finished but also because soil

layers have liquefied so the kinematic forces, which are predomi-

nant, are exerted to the longer pile since the longer pile is in touch

with greater amount of the liquefied soil.

Fig. 17shows the maximum bending moment envelops of free-

head and fixed-head piles with lengths of 15B, 25Band 40B. In all

cases, it can be concluded that pile length has no effect on the place

of maximum bending moment, and the maximum value always at-tained at pile head or at the depth of about 2 m.

Table 3

The material properties of the pile and Nevada sand used in the numerical model.

Material Parameter Value

Pile

Youngs Modulus, (kPa) Ep 3.0 107

Density, (ton/m3) qp 2.40Poissons Ratio mp 0.2

Material Parameter Value

Soil Dr = 30% Dr = 40% Dr = 50% Dr = 85%

Soil density (ton/m3) qsat 1.938 1.957 1.976 2.052Fluid density (ton/m3) qf 1.0 1.0 1.0 1.0Porosity n 0.438 0.427 0.415 0.370

Permeability (m/s) k 7. 5 105 6.6 105 5.9 105 3.7 105



8/13

7.4. Effect of frequency of excitation on pile performance

Fig. 18shows maximum lateral displacement of pile, maximum

bending moment and pile head settlement time histories for differ-ent frequencies of excitation; 1, 3, 5 and 10 Hz. It is noted that the

frequency has a significant effect on pile response. For example, by

increasing the frequency from 3 Hz to 10 Hz, maximum lateral dis-

placement, maximum bending moment and settlement decreases

about 75%, 90% and 70%, respectively. Since acceleration amplitudeof the input motion is the same in all analysis, displacement

(a)

(b)

(c)

-25

-20

-15

-10

-5

0

0 0.5 1 1.5 2

Depth(m)

Maximum Lateral Disp. (cm)

Fixed HeadFree Head

-25

-20

-15

-10

-5

0

0 50 100 150

De

pth(m)

Maximum Bending Moment

(kN.m)

-25

-20

-15

-10

-5

0

0 100 200 300

De

pth(m)


(kN.m)

-25

-20

-15

-10

-5

0

0 0.5 1 1.5 2

Depth(m)


Fixed Head

Free Head-25

-20

-15

-10

-5

0

0 50 100 150

Depth(m)


(kN.m)

-25

-20

-15

-10

-5

0

0 100 200 300

Depth(m)


(kN.m)

-25

-20

-15

-10

-5

0

0 2 4 6

De

pth(m)


Fixed Head

Free Head-25

-20

-15

-10

-5

0

0 100 200 300

Dep

th(m)

Maximum Bending Moment(kN.m)

-25

-20

-15

-10

-5

0

0 200 400 600

Depth(m)


(kN.m)

Free Head Fixed Head

Free Head

Free Head Fixed Head

Fixed Head

Fig. 11. Maximum lateral displacement and maximum bending moment envelops for a free-head and fixed-head (fixed against rotation) pile in (a) Case I (b) Case II

(Thickness of liquefiable layer is 11 m.) (c) Case III (Thickness of dry layer is 5 m.).

-16

-12

-8

-4

0

0 50 100 150

Depth(m)

Maximum Bending Moment (kN.m)

Without SS Mass

With SS Mass

-25

-20

-15

-10

-5

0

0 50 100 150

Depth(m)


Without SS Mass

With SS Mass

Pile Length = 25B Pile Length = 40B

Fig. 12. Maximum bending moment envelops for pile lengths of 25B and 40B (B: pile width) with and without superstructure mass (Case I).



9/13


10/13

compared to that corresponding to dry soils. According to the re-

sults, if the pile head is fixed against rotations, maximum bending

moment increases about 95% for case I, 130% for case II and 95% forcase III. However, in dry ground, pile head fixity leads to nearly 20%

increase in maximum bending moment. In liquefying soils, when

the pile head is restrained rotationally, relative lateral displace-

ment of pile at upper and lower regions significantly increases

due to liquefaction of surrounding soil (it can be seen in Fig. 13);

larger relative lateral displacements lead to larger bending mo-

ment so boundary condition of pile head has a big effect on bend-

ing moment in the cases where the ground liquefies.

7.6. Effect of thickness of liquefiable soil layer on pile performance

In this section, results obtained from repetitive analysis for

thickness of liquefiable layers(HL) of 5 m, 11 m and 15 m for a

pile length of 40B (i.e. 21 m) are discussed. This parameter isinvestigated only for the Case II.Fig. 19 shows maximum lateral

displacement of the pile for various thicknesses of liquefiable lay-

ers. It is concluded that the thickness of liquefiable soil layer has a

little effect on maximum lateral displacement of pile during exci-tation (i.e. from 0 to 10 s) while significant changes are observed

after excitation period (i.e. from 10 to 25 s). According to the re-

sults, twice increase in the thickness of liquefiable layer leads to

about twice increase in the maximum lateral displacement of pile.

As mentioned before, after excitation period, piles are intensely un-

der the control of the surrounding liquefied soil, so thicker liquefi-

able layer considerably affects pile lateral displacements which can

be very important in performance-based design approaches.

Fig. 20 shows maximum bending moment envelops of free-

head and fixed-head pile for thickness of liquefiable layers(HL) of

5 m, 11 m and 15 m for a pile length of 40B (i.e. 21 m). The maxi-

mum bending moment developed at the interface is investigated. It

is concluded that when the thickness is 5 m, there is 40% difference

between the value obtained for free-head pile and the value forfixed-head pile. However, for the thickness of 11 m and 15 m the

-25

-20

-15

-10

-5

0

0 0.5 1 1.5 2

Depth(m)

Maximum Lateral Displacement (cm)

L/B= 15 ( HL = 4 m)

L/B= 25 ( HL = 6.5 m)

L/B= 40 ( HL = 11 m)-25

-20

-15

-10

-5

0

0 1 2 3

Depth(m)


L/B= 15 ( HL = 4 m)

L/B= 25 ( HL = 6.5 m)

L/B= 40 ( HL = 11 m)(a) (b)

Fig. 16. Comparison of pile maximum lateral displacement for different pile lengths in Case II (a) during excitation ( t= 010 s) and (b) after excitation (t= 1025 s) (L: pile

length, B: pile width, HL: thickness of liquefiable layer).

-25

-20

-15

-10

-5

0

0 50 100 150 200

Depth

(m)


L/B= 15 ( HL = 4 m)

L/B= 25 ( HL = 6.5 m)

L/B= 40 ( HL = 11 m)-25

-20

-15

-10

-5

0

0 100 200 300 400

Depth

(m)


L/B=15 (HL = 4 m)

L/B=25 (HL = 6.5 m)

L/B=40 (HL = 11 m)Free Head Fixed Head

Fig. 17. Comparison of maximum bending moment for different pile lengths for free-head and fixed-head(against rotation) pile in Case II (L: pile length, B: pile width, HL:

thickness of liquefiable layer).

-25

-20

-15

-10

-5

0

0 5 10 15

Depth(m)


f = 1 Hz

f = 3 Hz

f = 5 Hz

f = 10 Hz

-25

-20

-15

-10

-5

0

0 200 400 600 800

Depth(m)


f = 1 Hz

f = 3 Hz

f = 5 Hz

f = 10 Hz-0.2

-0.15

-0.1

-0.05

0

0 10 20

PileHeadSettlement

(m)

Time (sec)

f= 3 Hz

f=5 Hz

f= 10 Hz

Fig. 18. Variation of maximum lateral displacement, maximum bending moment and pile head settlement for different frequencies of input excitation in Case I.



11/13

difference is nearly 14% and 0%, respectively. Results of numerical

analysis indicate that when the thickness of the liquefying layer

exceeds about one-fourth of the pile length, bending moment at

the interface does not depend on the boundary condition at the

pile head. It is worth mentioning that Liyanapathirana and Poulos

[19]reported this conclusion for the thickness of one-third of the

total thickness of the soil deposit using one-dimensional WinklerModel.

Also, the effect of thickness of liquefiable soil layer on pile head

settlement is investigated in this study.Fig. 21shows variation of

pile head settlement by the increase of thickness of liquefying layer

for the pile lengths of 13 m and 21 m. It is noted that the increase

of the thickness of the liquefying layer has a little influence on pile

settlement when bottom of the liquefiable layer is far from the pile

toe while the settlement sharply increases by approaching the liq-

uefiable layer to the pile toe. It is commonly known that total set-tlement of piles is mainly due to the settlement of the soil in the

vicinity of pile toe. Therefore, when the liquefiable layer gets closer

to the pile toe, settlement of pile head considerably increases.

7.7. Effect of relative density of liquefiable soil layer on pile

performance

In this section, results obtained from repetitive analysis for

three different relative densities; 30%, 40% and 50% for a pile length

of 40B are discussed.Fig. 22shows the maximum lateral deflection

and maximum bending moment envelops for different relative

densities. It is observed that for the pile embedded in Nevada sand

layers, about 10% increase of relative density causes 15% decreasein maximum value of lateral displacement and an average value of

-25

-20

-15

-10

-5

0

0 0.5 1 1.5 2

D

epth(m)


HL = 5 (m)

HL = 11 (m)

HL = 15 (m)-25

-20

-15

-10

-5

0

0 1 2 3 4 5

D

epth(m)


HL = 5 (m)

HL = 11 (m)

HL = 15 (m)(b)(a)

Fig. 19. Variation of maximum lateral displacement for various thicknesses of liquefiable layers in Case II (a) during excitation ( t= 010 s) and (b) after excitation (t= 10

25 s).

-25

-20

-15

-10

-5

0

0 100 200 300

Depth(m)


Fixed Head

Free Head-25

-20

-15

-10

-5

0

0 100 200 300

Depth(m)


Fixed Head

Free Head

-25

-20

-15

-10

-5

0

0 100 200 300

Depth(m)


Fixed Head

Free Head

HL= 5 m

HL= 15 m

HL= 11 m

Fig. 20. Bending moment envelops for a 40B length (B: pile width) free-head and fixed-head pile in Case II.

0

5

10

15

20

25

0 5 10 15 20 25 30

Pile

HeadSettlement(cm)

Thickness of Liquefiable Layer (m)

L = 13 (m)

L = 21 (m)

Fig. 21. Variation of pile head settlement by the increase of thickness of liquefying

layer for the pile lengths(L) of 13 m and 21 m (Case II).



12/13

30% decrease in the value of the bending moment. This is due to

the increase of the liquefiable soil stiffness and smaller values of

soil displacement.

8. Conclusions

This paper tries to provide better insight into the performance

of pile foundations embedded in liquefiable soil deposits. For this,

an accurate methodology for numerical modeling of piles in lique-

fiable soils is employed. A fully coupleduPformulation is used to

analyze soil displacements and pore water pressures, and a bound-

ing surface critical state elasticplastic model that accounts for

fabric change is employed to model the soil skeleton. Moreover,

the permeability coefficient is updated in each time step as a func-

tion of excess pore water pressure ratio. Results from a centrifuge

test are simulated and the obtained results demonstrate that the

numerical model has the ability to simulate pile behavior in lique-

fying soil reasonably well.

Parametric studies are carried out for three different soil pro-

files. For each profile, the effect of pile length, fixity of the pile

head, frequency of input motion, the thickness of liquefying soillayer and the effect of relative density of liquefying soil layer on

pile performance are investigated. A summary of the findings are

mentioned below:

It is found that for any values of the mentioned parameters and

for all three soil profiles, the maximum lateral displacement of

free-head pile develops at pile head. Also, it is concluded that in

all cases the maximum bending moment develops at about 2 m

from pile top for free-head piles and at pile head for fixed-head

piles. Besides, for case II and III there is other peak values of bend-

ing moment at the interface of liquefiable and non-liquefiable lay-

ers and inside the liquefying layer, respectively.

Due to the fact that pile dynamic response near the ground sur-

face is approximately under the control of dynamic response of

superstructure, the pile has a significant influence on the seismicresponse of the surrounding soil near the ground surface. Further-

more, the results of the numerical model demonstrate that pile re-

sponse is different from the response of soil in the free field after

liquefaction while before liquefaction there is a little difference.

For all cases, it is shown that pile length and the thickness of liq-

uefiable layer have little influences on the maximum lateral dis-

placements during excitation; however, when the input

excitation finishes there are considerable differences in the maxi-

mum values of the lateral displacements for different pile lengths.

It is also shown that pile length has no effect on the location of the

maximum bending moment.

For all cases, it is concluded that natural frequency of earth-

quake highly affects pile performance in liquefiable soil deposits.

It is shown that if the frequency of the input motion increaseswhile the amplitude of acceleration remains constant, lateral

displacement, bending moment and pile head settlement signifi-

cantly decrease.

When the pile head rotation is fixed in all directions, the max-

imum lateral displacement of pile embedded in dry soil layers re-

duces much more compared to that in saturated liquefiable soil

layers. But maximum bending moment in saturated soil deposits

significantly increases. Generally, it is concluded that in liquefiableground, restraining pile head results in the development of larger

bending moment at the pile head although it decreases pile lateral

displacements; therefore, it is recommended that if the allowable

lateral displacement of superstructure and pile embedded in lique-

fiable ground is large enough, the application of hinge joint at pile

head is much more efficient than the application of restrained

joint.

It is also shown that if the thickness of the liquefying layer

exceeds one-fourth of pile length, the bending moment at the

interface does not depend on the boundary condition at the pile

head. Moreover, it is found that 10% increase in relative density

of liquefiable soil layer results in approximately 1530% decrease

in the maximum lateral displacement and maximum bending

moment.In general, parametric studies have shown that frequency of

excitation, pile head fixity and the thickness of liquefiable layer

have higher effects on pile response compared to the other param-

eters. Therefore, the key to good designs is reliable estimates of

these parameters.

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-20

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-10

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0

0 1 2 3 4

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-20

-15

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