berkeley pile in liquefied soil

8/12/2019 Berkeley Pile in Liquefied Soil

1/5

AbstractSoil liquefaction and associateddeformation is a major cause of earthquake-related

damage to piles and pile-supported structures.

Computational procedures for nonlinear soil-pile

interaction response commonly employ a 1D pile-soil

system, and simplify the effect of soil pressure by

linear or nonlinear p-y springs.

This paper presents a pilot 3D Finite Element

study of dynamic pile response in liquefied ground.

The numerical model is formulated using CYCLIC, a

geomechanics nonlinear finite element program

developed to analyze cyclic mobility and liquefaction

problems. In the current analysis, the pile and soil

domains are discretized using 3D brick elements. The

soil stress-strain behavior is represented by aplasticity-based, effective-stress constitutive model.

This constitutive model is capable of simulating the

essential response characteristics of saturated

cohesionless soils, including shear-induced pore-

pressure generation (dilatancy) and cyclic mobility.

The computed results are compared to related

centrifuge testing results. Special attention is given to

the change in pile response characteristics due to

liquefaction and lateral spreading of the surrounding

soil.

KeywordsFinite Element Analysis, Pile,

Liquefaction

INTRODUCTION

Liquefaction and associated shear deformation is a

major cause of earthquake-related damage to piles andpile-supported structures. Pile foundation damage due to

lateral spreading induced by liquefaction is documented

in numerous reports and papers [1-3].

The recognition of the importance of lateral ground

displacement on pile performance has led to thedevelopment of analytical models capable of evaluating

the associated potential problems [4]. Modeling lateral

ground displacement and pile response involves complex

aspects of soil-structure interaction and soil behaviorunder large strains. Currently computational procedures

for nonlinear soil-pile interaction response commonlyemploy a 1D pile-soil system, and simplify the effect of

soil pressure by linear or nonlinear p-y springs. There is

not much effort devoted to the study of the piles inliquefaction-induced lateral spreading using finite element

method (FEM).

This paper presents a pilot three-dimensional (3D)

Finite Element study of dynamic pile response in liquefiedground. The numerical model is formulated using

CYCLIC, a geomechanics nonlinear finite element

program developed to analyze cyclic mobility andliquefaction problems [5,6]. In CYCLIC, the soil stress-

strain behavior is represented by a plasticity-based,

effective-stress constitutive model. This constitutivemodel is capable of simulating the essential response

characteristics of saturated cohesionless soils, including

shear-induced pore-pressure generation (dilatancy) and

cyclic mobility. Extensive calibration of CYCLIC hasbeen conducted with results from experiments and full-

scale response of earthquake simulations involving ground

liquefaction [7].

In this paper, salient features of the constitutive modeland the finite element formulation are presented first.

Thereafter, the numerical simulation procedures and

results are described and discussed.

FINITE ELEMENT FORMULATION

In CYCLIC, the saturated soil system is modeled as a

two-phase material based on the Biot [8] theory for porous

media. A numerical formulation of this theory, known as

u-p formulation (in which displacement of the soilskeleton u, and pore pressurep, are the primary unknowns

[9,10]), was implemented [5,6,11]. This implementation

is based on the following assumptions: small deformation

and rotation, density of the solid and fluid is constant inboth time and space, porosity is locally homogeneous and

constant with time, incompressibility of the soil grains,

and equal accelerations for the solid and fluid phases.

The u-p formulation is defined by Chan [9] as twoequations: i) the equation of motion for the solid-fluid

mixture, and ii) the equation of mass conservation for the

fluid phase, incorporating equation of motion for the fluidphase and Darcy's law. These two governing equations

may be expressed in the following finite element matrix

form [9]:

0fQpdBUM s

T =&& (1a)0fHppSUQ

pT =&& (1b)where M is the total mass matrix, U the displacement

vector, Bthe strain-displacement matrix, the effectivestress tensor (determined by the soil constitutive model

described below), Q the discrete gradient operatorcoupling the solid and fluid phases, p the pore pressure

Three-Dimensional Finite Element Analysis of Dynamic Pile Behavior in

Liquefied Ground

Jinchi Lu1, Liangcai He1, Zhaohui Yang1, Tarek Abdoun2and Ahmed Elgamal11Department of Structural Engineering, University of California, San Diego, USA

2Geotechnical Centrifuge Research Center, Rensselaer Polytechnic Institute, Troy, NY


2/5

vector, S the compressibility matrix, and H the

permeability matrix. The vectorss

f andp

f representthe effects of body forces and prescribed boundaryconditions for the solid-fluid mixture and the fluid phase

respectively.In equation (1a) (equation of motion), the first term

represents inertia force of the solid-fluid mixture,

followed by internal force due to soil skeletondeformation, and internal force induced by pore-fluid

pressure. In equation (1b) (equation of mass

conservation), the first two terms represent the rate of

volume change for the soil skeleton and the fluid phaserespectively, followed by the seepage rate of the pore

fluid. Equations (1a) and (1b) are integrated in the time

domain using a single-step predictor multi-correctorscheme of the Newmark type [5,9]. In the current

implementation, the solution is obtained for each time

step using the modified Newton-Raphson approach [5].

SOIL CONSTITUTIVE MODEL

The second term in equation (1a) is defined by thesoil stress-strain constitutive model. The finite element

program incorporates a soil constitutive model [5,11-13]

based on the original multi-surface-plasticity theory forfrictional cohesionless soils [14]. This model was

developed with emphasis on simulating the liquefaction-induced shear strain accumulation mechanism in clean

medium-dense sands [6,7,12,13,15]. Special attention

was given to the deviatoric-volumetric strain coupling(dilatancy) under cyclic loading, which causes increased

shear stiffness and strength at large cyclic shear strain

excursions (i.e., cyclic mobility).

The constitutive equation is written in incrementalform as follows [14]:

)(: pE &&& = (2)

where & is the rate of effective Cauchy stress tensor, & the rate of deformation tensor,

p& the plastic rate of

deformation tensor, and E the isotropic fourth-order

tensor of elastic coefficients. The plastic rate of

deformation tensor is defined by:p& = P L , where Pis

a symmetric second-order tensor defining the direction of

plastic deformation in stress space, L the plastic loading

function, and the symbol denotes the McCauley's

brackets (i.e., L =max(L, 0)). The loading functionLis

defined as: L = Q:& /H where H is the plasticmodulus, and Q a unit symmetric second-order tensor

defining yield-surface normal at the stress point (i.e., Q=

ff / ), with the yield function f selected of the

following form [16]:

0

)())((:))((2

3 20

200

=

+++= ppMppppf ss (3)

in the domain of 0p . The yield surfaces in principal

stress space and on the deviatoric plane are shown in Fig.

1. In equation 3, s p is the deviatoric stresstensor, p the mean effective stress, a second-orderkinematic deviatoric tensor defining the surfacecoordinates, and M dictates the surface size. For

cohesionless soil, 0p is a small positive value (1.0 kPa inthis paper) such that the yield surface size remains finite at

0p for numerical convenience (Fig. 1). For cohesive

soil, 0p is related to cohesion. In the context of multi-surface plasticity, a number of similar surfaces with a

common apex form the hardening zone (Fig. 1). Each

surface is associated with a constant plastic modulus.

Conventionally, the low-strain (elastic) moduli and plastic

moduli are postulated to increase in proportion to the

square root of p [14].The flow rule is chosen so that the deviatoric

component of flow P = Q (associative flow rule in thedeviatoric plane), and the volumetric component P defines the desired amount of dilation or contraction in

accordance with experimental observations. Consequently,

P defines the degree of non-associativity of the flowrule and is given by [5]:

P1)/(

1)/(2

2

+

=

(4)

Where p/2/1):)2/3(( ss is effective stress ratio, a material parameter defining the stress ratio along the

phase transformation (PT) surface [17], and a scalar

function controlling the amount of dilation or contraction

depending on the level of confinement and/or accumulated

plastic deformation [12]. The sign of 1)/(2

dictates dilation or contraction. If negative, the stress pointlies below the PT surface and contraction takes place

(phase 0-1, Fig. 2). On the other hand, the stress point lies

above the PT surface when the sign is positive and dilationoccurs under shear loading (phase 2-3, Fig. 2). At low

confinement levels, accumulation of plastic deformation

may be prescribed (phase 1-2, Fig. 2) before the onset of

dilation [12].

A purely deviatoric kinematic hardening rule ischosen according to [14]:

bp =& (5)


3/5

Fig. 1: Conical yield surfaces for granular soils in principal

stress space and deviatoric plane (after [5,11,14,18])

Fig. 2: Shear stress-strain and effective stress path under

undrained shear loading conditions (after [5,11])

where is a deviatoric tensor defining the direction oftranslation and b is a scalar magnitude dictated by the

consistency condition. In order to enhance computational

efficiency, the direction of translation is defined by anew rule [5,12], which maintains the original Mroz [19]

concept of conjugate-points contact. Thus, all yield

surfaces may translate in stress space within the failureenvelope.

SIMULATION OF CENTRIFUGE EXPERIMENT

Centrifuge Experiment

In the centrifuge test reported by Abdoun [4], a single

pile model (model 3, Fig. 3) was tested to simulate theresponse of the pile foundation subjected to the lateral

pressure of a liquefied soil due to lateral spreading. The

experiment was conducted using the rectangular, flexible-

wall laminar box container shown in Fig. 3. The soilprofile consist s of two layers of fine Nevada sand

saturated with water: a top liquefiable layer of relative

density, Dr = 40% and 6m prototype thickness, and abottom slightly cemented nonliquefiable sand layer with

a thickness of 2m. The prototype single pile is 0.6m in

Fig. 3: Lateral spreading pile centrifuge model in two-layer soil

profile, model 3 (modified after [20])

diameter, 8m in length, has a bending stiffness, EI = 8000kN/m2, and is free at the top. The model has an inclination

angle of 2 and is subjected to a predominantly 2Hz

harmonic base excitation with a peak acceleration of 0.3g.The results of the test were documented in [4].

Numerical Modeling

The centrifuge test was simulated using the above-

described three-dimensional finite element programCYCLIC. As shown in Fig. 4, the soil domain and the

single pile were discretized using 3D 8-node brick

elements. A half mesh configuration is used due togeometrical symmetry. The boundary conditions were (i)

dynamic excitation was defined as the recorded baseacceleration, (ii) at any given depth, displacement degrees

of freedom of the downslope and upslope boundaries were

tied together (both horizontally and vertically using the

penalty method) to reproduce a 1D shear beam effect [5],(iii) the soil surface was traction free, with zero prescribed

pore pressure, and (iv) the base and lateral boundaries

were impervious.A static application of gravity (model own weight)

was performed before seismic excitation. The resultingfluid hydrostatic pressures and soil stress-states served as

initial conditions for the subsequent dynamic analysis [7].

Fig. 4: Finite element mesh of model 3


4/5

With a mild inclination of 2, model 3 attempts to

simulate an infinite slope subjected to shaking parallel tothe slope [21]. However, it was noted that, in the

centrifuge test, the soil surface gradually lost the slope

and became level during the shaking phase. To simulatesuch behavior of losing the surface slope, a horizontal

component of gravity varying with time was applied to

the finite element simulation. The load-time history of theapplied horizontal gravity component was calculated

based on the recorded lateral displacement at ground

surface (the second subplot in Fig. 7).Figs. 5-8 display the computed and recorded lateral

accelerations, displacement, and pore pressures. In

general, good agreement was achieved between thecomputed and recorded responses. At 2m depth,

accelerations virtually disappeared after about 4 seconds

due to liquefaction (A4, Fig. 6). Liquefaction wasreached down to a depth of 5.0m (Fig. 8), as indicated by

the pore-pressure ratio ru approaching 1.0 (ru = ue/v

where ueis excess pore pressure, and vinitial effectivevertical stress). The Nevada sand layer remained liquefied

until the end of shaking and beyond. Thereafter, excesspore pressure started to dissipate.

The mild inclination of model 3 imposed a static

shear stress component (due to gravity), causingaccumulated cycle-by-cycle lateral deformation. The

recorded and computed ue histories both displayed anumber of instantaneous sharp pore pressure drops after

initial liquefaction (Fig. 8). These drops coincided with

the observed and computed acceleration spikes thatoccurred exclusively in the negative direction.

-0.2

0

0.2

A1 (3.0m)

Experimental

Computed

-0.2

0

0.2

LateralAcceleration(g)

A2 (7.0m)

0 5 10 15 20 25 30

-0.2

0

0.2

A3 (Input)

Time (sec)

Fig. 5: Model 3 recorded and computed acceleration time

histories (along the laminar box boundary)

-0.2

0

0.2

A4 (2.0m)

Experimental

Computed

-0.2

0

0.2

LateralAcceleration(g)

A5 (4.0m)

0 5 10 15 20 25 30

-0.2

0

0.2

A6 (7.0m)

Time (sec)

(Experimental data unavailable)

Fig. 6: Model 3 recorded and computed acceleration time

histories (in the soil)

0

10

20

30

40

LVDT1 (Pile head)

Experimental

Computed

0

20

40

60

80

100

Surface (near LVDT2(.25m))

0

20

40

60

80

LateralDisplacement(cm)

2.0m (near LVDT3(2.5m))

0

20

40

60

80

4.0m (near LVDT4(3.75m))

-8

-4

0

4

8

LVDT5 (6.0m)

0 5 10 15 20 25

-8

-4

0

4

8

LVDT6 (7.0m)

Time (sec)

Fig. 7: Model 3 recorded and computed lateral displacement

time histories

The permanent lateral displacement of the ground

surface after shaking is approximately 100cm. All lateral

displacements occurred in the top 6.0m within the

liquefiable sand layer. The top graph of Fig. 7 shows the

recorded and computed pile lateral displacement at the soilsurface during and after shaking. The computed pile

lateral pile lateral displacement increased to 40cm, and

decreased to approximately 20cm at the end of shaking,indicating relative movement between pile and soil. The

bottom slightly cemented sand layer, as indicated in Fig.

7, did not slide with respect to the base of the laminar box.


5/5

0

2

4

6

8

10

12ru= 1.0

Excessporepressure(KPa)

PP1 (1.0m)

Experimental

Computed

0 5 10 15 20 25 30

0

10

20

30

40

50

PP2 (5.0m)

Time (sec)

Fig. 8: Model 3 recorded and computed excess pore pressure

time histories

CONCLUSIONS

A 3D finite element study of dynamic pile response inliquefied ground was presented in this paper. The results

from numerical simulation were compared to relatedcentrifuge testing results. In general, good agreement was

achieved between the computed and recorded responses.

The calibrated numerical model will be useful inconducting additional parametric investigations.

ACKNOWLEDGMENTS

The reported research was supported in part by thePacific Earthquake Engineering Research (PEER) Center,

under the National Science Foundation Award Number

EEC-9701568, and by the National Science Foundation

(Grant No. CMS0084616). This support is most

appreciated.

REFERENCES

[1] H. Mizuno. "Pile damage during earthquakes in japan (1923-

1983)." inProc. Session on Dynamic Response of PileFoundations, T. Nogami, ed., ASCE, Atlantic City, April 27,

1987, pp. 53-77.

[2] T. Matsui, and K. Oda. "Foundation damage of structures." Soils

and Foundations, Special Issue on Geotechnical Aspects ofthe January 17, 1995 Hyogoken-Nambu Earthquake, January,

, 1996, pp. 189-200.

[3] K. Tokimatsu, and Y. Aska. "Effects of liquefaction-inducedground displacements on pile performance in the 1995

hyogoken-nambu earthquake." Soils and Foundations,Special Issue on Geotechnical Aspects of the January 17,

1995 Hyogoken-Nambu Earthquake, No. 2, September,

1998, pp. 163-178.

[4] T. Abdoun. "Modeling of seismically induced lateral spreading ofmulti-layered soil and its effect on pile foundations," Ph.D.

Thesis, Dept. of Civil Engineering, Rensselaer Polytechnic

Institute, Troy, New York, 1997.

[5] E. Parra. "Numerical modeling of liquefaction and lateral grounddeformation including cyclic mobility and dilation response

in soil systems," Ph.D. Thesis, Dept. of Civil Engineering,Rensselaer Polytechnic Institute, Troy, NY, 1996.

[6] Z. Yang, and A. Elgamal. "Influence of permeability on

liquefaction-induced shear deformation."J. Engineering

Mechanics, vol. 128, no. 7, 2002, pp. 720-729,ASCE.[7] A. Elgamal, Z. Yang, and E. Parra. "Computational modeling of

cyclic mobility and post-liquefaction site response." Soil

Dynamics and Earthquake Engineering, vol. 22, no. 4, 2002,

pp. 259-271.

[8] M. A. Biot. "The mechanics of deformation and acousticpropagation in porous media."Journal of Applied Physics,

vol. 33, no. 4, 1962, pp. 1482-1498.

[9] A.H.C. Chan. "A unified finite element solution to static and

dynamic problems in geomechanics," Ph.D. Thesis, U.College of Swansea, U. K., 1988.

[10] O. C. Zienkiewicz, A. H. C. Chan, M. Pastor, D. K. Paul, and T.

Shiomi. "Static and dynamic behavior of soils: A rational

approach to quantitative solutions: I. Fully saturated

problems."Proceedings of the Royal Society London, Series

A, Mathematical and Physical Sciences, vol. 429, 1990, pp.285-309.

[11] Z. Yang. "Numerical modeling of earthquake site response

including dilation and liquefaction," Ph.D. Thesis, Dept. ofCivil Engineering and Engineering Mechanics, Columbia

University, New York, NY, 2000.

[12] A. Elgamal, Z. Yang, E. Parra, and A. Ragheb. "Modeling of

cyclic mobility in saturated cohesionless soils."Int. J.

Plasticity, vol. 19, no. 6, 2003, pp. 883-905.[13] Z. Yang, A. Elgamal, and E. Parra. "A computational model for

cyclic mobility and associated shear deformation."J.

Geotechnical and Geoenvironmental Engineering, vol. 129,

no. 12, 2003, ASCE.

[14] J.H. Prevost. "A simple plasticity theory for frictional cohesionlesssoils." Soil Dynamics and Earthquake Engineering, vol. 4, no.

1, 1985, pp. 9-17.

[15] A. Elgamal, E. Parra, Z. Yang, and K. Adalier. "Numerical

analysis of embankment foundation liquefactioncountermeasures."J. Earthquake Engineering, vol. 6, no. 4,

2002, pp. 447-471.

[16] A. Elgamal, Z. Yang, E. Parra, and A. Ragheb. "Modeling of

cyclic mobility in saturated cohesionless soils."International

Journal of Plasticity, vol. 19, no. 6, 2003, pp. 883-905.[17] K. Ishihara, F. Tatsuoka, and S. Yasuda. "Undrained deformation

and liquefaction of sand under cyclic stresses." Soils and

Foundations, vol. 15, no. 1, 1975, pp. 29-44.

[18] S. Lacy. "Numerical procedures for nonlinear transient analysis of

two-phase soil system," Ph.D. Thesis, Princeton University,NJ, U.S.A., 1986.

[19] Z. Mroz. "On the description of anisotropic work hardening."J.

Mechanics and Physics of Solids, vol. 15, 1967, pp. 163-175.[20] T. Abdoun, and R. Dobry. "Evaluation of pile foundation response

to lateral spreading." Soil Dynamics and Earthquake

Engineering, vol. 22, no. 9-12, 2002, pp. 1051-1058.

[21] R. Dobry, and V.M. Taboada. "Experimental results of model no.2

at rpi." inProceedings of the International Conference on the

Verification of Numerical Procedures for the Analysis of SoilLiquefaction Problems, Vol. 2, Aarulanandan K, Scott RF

eds., Rotterdam: Balkema, 1994, pp. 1341-1352.

berkeley pile in liquefied soil

Documents