numerical analysis of seismically induced liquefaction in earth embankment foundations. part i....

Numerical analysis of seismically inducedliquefaction in earth embankment foundations.Part I. Benchmark model

Ogun Aydingun and Korhan Adalier

Abstract: A numerical analysis has been performed for a clayey embankment founded on a liquefiable foundation soilusing an effective stress based, fully coupled, finite element code called DIANA-SWANDYNE II. The results werecompared with data obtained from centrifuge experiments. In Part I, the numerical method and the analysis procedureare explained. The results obtained for a series of three consecutive, increasing amplitude shaking events are presented.An attempt has been made to calibrate a benchmark model to be used in the application of different remedial measureswhich are discussed in Part II. The numerical predictions compared well with the experimental data and providedfurther insights into the dynamic behavior of embankment–foundation systems.

Key words: liquefaction, numerical modeling, coupled formulation, centrifuge, embankment, earthquakes.

Résumé : On a réalisé une analyse numérique pour un remblai argileux reposant sur un sol de fondation liquéfiable enutilisant un code d’éléments finis basé sur les contraintes effectives et complètement couplé appeléDIANA-SWANDYNE II. Les résultats ont été comparés avec les données obtenues d’expériences au centrifuge. Dans laPartie I, la méthode numérique et la procédure d’analyse sont expliquées. On présente les résultats obtenus pour unesérie de trois événements consécutifs de secousses à amplitudes croissantes. On a tenté de calibrer un modèle de pointsde repères à être utilisé dans l’application de différentes mesures de comfortement qui sera discuté dans la Partie II.Les prédictions numériques concordaient bien avec les données expérimentales et ont fourni des éclaircissements addi-tionnels sur le comportement dynamique des systèmes de fondation de remblai.

Mots clés : liquéfaction, modélisation numérique, formulation couplée, centrifuge, remblai, tremblements de terre.

[Traduit par la Rédaction] Aydingun and Adalier 765

Introduction

This is the first of two papers studying the seismic behav-ior of an earth embankment on a liquefiable foundation withand without retrofit measures. This paper (Part I) presentsthe results of numerical modeling and a comparison withdata from dynamic centrifuge tests on a cohesive embank-ment founded on a loose liquefiable deposit (constitutes thebenchmark case); the second paper (Part II) presents theresults on retrofitted embankment–foundation cases.

Liquefaction-induced ground displacements resultingfrom earthquake shaking are a major cause of damage toearth structures comprised of, or underlain by, loose satu-rated granular soils. Many liquefaction-induced failures ornear failures of structures such as river dykes, highway em-bankments, and earth dams have been reported around theworld during various earthquakes (Seed et al. 1990; Japanese

Geotechnical Society 1996; Adalier and Aydingun 2000).Such embankment damage was particularly destructivewhen the foundation soils liquefied (Duke and Leeds 1963;Yokomura 1966; McCulloch and Bonilla 1967; Seed 1968,1970; Matsuo 1996; Tani 1996; Krinitzsky and Hynes2002), resulting in cracking, settlement, lateral spreading,and slumping of the embankment. These and other reports,particularly those of liquefaction and lateral spreading of avast number of embankments on liquefied ground during the1995 Kobe earthquake, further emphasize the importance offoundation liquefaction as a potential source of damage toearth embankments.

Such an earthquake liquefaction hazard necessitates thedevelopment of appropriate remediation countermeasures(Ledbetter and Finn 1993; Marcuson et al. 1996). To experi-mentally investigate this problem, researchers frequentlyresort to the geotechnical centrifuge physical modeling tech-nique. This technique involves subjecting a small-scalemodel to a high level of confinement by the action of acentrifuge-induced gravitational field (e.g., N times the con-finement due to earth gravity (g), at Ng). In this fashion, thesmall model mechanically represents a much larger proto-type (e.g., N times larger in linear dimensions at Ng), due todependence of soil response on confinement. Centrifugemodeling data sets play a major role in the verification andrefinement of liquefaction countermeasures (Kimura et al.1995; Adalier et al. 2002). Such data also provide a basis for

Can. Geotech. J. 40: 753–765 (2003) doi: 10.1139/T03-025 © 2003 NRC Canada

753

Received 4 July 2002. Accepted 5 March 2003. Published onthe NRC Research Press Web site at http://cgj.nrc.ca on18 July 2003.

O. Aydingun. Department of Civil Engineering, EasternMediterranean University, Famagusta, Northern Cyprus.K. Adalier1. Department of Civil and EnvironmentalEngineering, JEC 4049, Rensselaer Polytechnic Institute,Troy, NY 12180, U.S.A.

1Corresponding author (e-mail: [email protected]).

I:\cgj\CGJ40-04\T03-025.vpJuly 15, 2003 11:03:03 AM

Color profile: Generic CMYK printer profileComposite Default screen

calibration of design and computational modeling proce-dures (Marcuson et al. 1996; Finn 2000).

An extensive work on using centrifuge modeling for theanalysis of liquefaction problems and verification withnumerical analyses has been the Verification of NumericalAnalysis by Centrifuge Studies (VELACS) Project(Arulanandan and Scott 1993) sponsored by the U.S.National Science Foundation. This project has provided ameans of verifying and calibrating various numerical meth-ods. The models mainly involved rather simple liquefiablesoil profiles, except a case with a quay wall. The resultswere mixed, but overall the effective stress based, fully cou-pled procedures made better predictions than empirical orloosely coupled methods. In another study, centrifuge modeltesting of a cohesive highway embankment founded on aliquefiable soil (fine-grained Nevada sand) with the applica-tion of different remedial measures has been carried out us-ing the centrifuge at Rensselaer Polytechnic Institute, Troy,New York (Adalier 1996; Adalier et al. 1998). First, abenchmark model with no remediation was tested. Thencountermeasures were applied to identical models and theeffect on soil response of each remedial measure wasobserved. The four additional countermeasures tested werelimited-zone densification of the sand layer, limited-zone so-lidification of the sand layer by deep soil mixing using ce-ment, gravel berm surcharge load, and sheet pile enclosure.Three increasing amplitude harmonic base input excitationsreferred to as shake 1, shake 2, and shake 3 were applied toeach model in succession, monitoring the accelerations, ex-cess pore pressures (EPP), and displacements throughout thetests. The study reported herein in a series of two papersaims to numerically analyze the problem of seismicallyinduced liquefaction including the remedial measures andprovide comparisons with centrifuge experiments. The capa-bilities and limitations of the employed numerical techniqueDIANA-SWANDYNE II to model such complex dynamicsoil–structure interaction problems were assessed. Currently,reliable computational modeling of earthquake-induced liq-uefaction and deformations in earth structure – foundationsystems still remains a major challenge (Arulanandan andScott 1993; Marcuson et al. 1996; Parra 1996; Matsuo et al.2000; Elgamal et al. 2003). In cases involving retrofit mea-sures, accurate computational simulation becomes an evenmore difficult task (Parra 1996; Cooke and Mitchell 1999).

Part I (this paper) is aimed at describing the analysis pro-cedure used and presenting the results of the benchmarkmodel. The soil parameters were obtained from monotonicand cyclic laboratory sample test data, and foundation soilparameters were further verified with level ground centrifugeexperiments. The parameters gave satisfactory results for thefirst shake event, and calibrations to embankment soil pa-rameters and foundation soil permeability were done to ac-count for changes in the models for the subsequent shakes(i.e., shakes 2 and 3). The centrifuge model was not recon-structed between shakes and the whole experiment was con-ducted on the original model. Therefore, after shake 1 themodel was no longer virgin and the experiment became in asense “nonlinear.” Without any calibration, such nonlinearbehavior would be very difficult to model, since the resultsof the previous shake were used as the initial conditions ofthe next shaking event for the numerical analysis as well.

The calibrated benchmark model runs were intended to pro-vide a basis of comparison for the application of remedialmeasures. The introduction of remedial measures into thecalibrated benchmark model is aimed to numerically investi-gate the effect of these measures and make comparisonswith experimental results.

Numerical method

The numerical analysis was carried out using an effectivestress based, fully coupled, finite element program calledDIANA-SWANDYNE II (Chan 1993). This two-dimensionalfinite element program is capable of solving static and dy-namic problems under both drained and undrained condi-tions. A detailed formulation of the numerical method usedis available in Chan (1988) and Zienkiewicz et al. (1990,1999).

Following the Biot formulation governing the behavior ofporous media (Biot 1956) and neglecting the fluid accelera-tion relative to the solid, the following displacement (u) –pore pressure (p) formulation can be derived. For the solidphase at any time station,

[1] [ ]{��} [ ]{ } [ ]{ } { }M u K u Q p f u+ − =

where [M] is the global mass matrix; [K] is the global stiff-ness matrix; [Q] is the coupling matrix; {f u} is the force ma-trix for the solid phase; and {u} and {p} are the globaldisplacement and pore-pressure matrices, respectively. Forthe fluid phase,

[2] [ ]{��} [ ] {�} [ ]{�} [ ]{ } { }G u Q u S p H p f p+ + + =T

where [G] is the dynamic seepage force matrix, [S] is thecompressibility matrix, [H] is the permeability matrix, and{f p} is the force matrix for the fluid phase. Equations [1]and [2] are solved using a finite difference technique calledthe generalized Newmark (GNpj) time integration scheme(Katona and Zienkiewicz 1985). At time tn + ∆t, the acceler-ation, velocity, and displacement, respectively, are given by

[3] ün+1 = ün + ∆ün

[4] � � �� u u u t u tn n n n+ = + +1 1∆ ∆ ∆βd

[5] u u u t u t u tn n n n n+ = + + +12

221

212

� �� ∆ ∆ ∆ ∆βd

and the rate of pore-pressure change and pore pressure, re-spectively, are expressed as

[6] � � �p p pn n n+ = +1 ∆

[7] p p p t p tn n n n+ = + +1 � �∆ ∆ ∆βd

where βd1, βd2, and βd are coefficients of numerical dampingchosen in the range of 0–1. For the scheme to be uncondi-tionally stable, the conditions βd2 ≥ βd1 ≥ 0.5 and βd ≥ 0.5must be satisfied. If eqs. [1] and [2] are rewritten for time tn+ ∆t and the fluid accelerations are neglected, the followingrelations are obtained:

[8] [ ] [ ] �� ([ ] ) �M K t u Q t p fn n nu+

− = +12

22

1β βd d∆ ∆ ∆ ∆

[9] ([ ] ) �� ([ ] [ ] ) �Q t u S H t p fn n npT

d dβ β1 1∆ ∆ ∆ ∆+ + = +

© 2003 NRC Canada

754 Can. Geotech. J. Vol. 40, 2003



Equations [8] and [9] are coupled by the [Q] matrix andsolved using a staggered approach. It is also possible to in-corporate viscous damping into the dynamic equation of thesolid phase in the form of [C]{�u}, where

[10] [C] = α0[M] + α1[K]

is called the Rayleigh damping (Clough and Penzien 1993).The coefficients α0 and α1 can be obtained by selecting adamping ratio ξn and a certain frequency ωn such that

[11] ξ αω

α ωn

n

n= +0 1

2 2

Constitutive model for sand

The liquefiable foundation soil was modeled using a gener-alized plasticity, bounding surface type, non-associated modelcalled Pastor–Zienkiewicz Mark III (Pastor et al. 1985, 1990;Zienkiewicz et al. 1999). The model is aimed at producingthe behavior of sands under monotonic and cyclic loading.In this model both volumetric and deviatoric plastic strainsare included in the hardening parameter of the bounding sur-face. In addition, plastic volumetric and deviatoric strainsare introduced during unloading.

The plastic potential surface is obtained from the dila-tancy relation proposed by Nova and Wood (1982) as

[12] dg = (1 + α)(Mg – η)

where the stress ratio η = q/p′. The equation of the plasticpotential surface can be derived from this dilatancy relationas

[13] G q M ppp

gg

= − ′ +

− ′

11

1α

α

and the yield or bounding surface is assumed to have a simi-lar shape, given by

[14] F q M ppp

fc

= − ′ +

− ′

1

11

α

α

where p′ is the mean effective stress; q is the deviatoricstress; Mg is the slope of the critical state line; α and Mf areconstants; and pg and pc are size parameters. These plasticpotential and yield surfaces for loose and dense sand areshown in Fig. 1.

If a generalized plasticity formulation as first introducedby Zienkiewicz and Mroz (1985) and further extended byZienkiewicz et al. (1985) and Pastor et al. (1985, 1990) isadopted, the yield and plastic potential surfaces need not beexplicitly defined. The complete elastoplastic behavior canbe defined by a relation between stress (σ) and strain (ε) in-crements as

[15] dσ = D dε

where the value of D (tangent matrix of the solid skeleton)depends on the state and history of stresses and strains andalso the direction of dε. If some direction of stress increment

exists differentiating between loading and unloading and thisdirection is defined by a unit normal n, then the followingexpressions can be written:

[16] d d if d (loading)L Tσ ε σ= >D n 0

[17] d d if d (unloading)U Tσ ε σ= <D n 0

Neutral loading is defined by nT dσ = 0 (nT is n trans-pose) when both loading and unloading moduli are identicaland the behavior is locally elastic. The loading (L) andunloading (U) tangent matrices, respectively, can then bewritten in the most general form as

[18] D Dn nL e gL

T

L

− −= +1 1

H

[19] D Dn nU e gU

T

U

− −= +1 1

H

The arbitrarily defined tensors ngL and ngU can be selectedto fit the experimental data and define the flow rule. If thesetensors differ from n, then the flow is nonassociative, lead-ing to nonsymmetric tangent matrices. De is the elasticmatrix, and HL and HU are plastic loading and unloadingmoduli, respectively. By prescribing n, ngL, ngU, De, HL, andHU for all states of the material behavior, the model can thenbe fully described. By defining the unit normals to the yield

© 2003 NRC Canada

Aydingun and Adalier 755

Fig. 1. Plastic potential and yield surfaces for (a) loose sandsand (b) dense sands (reproduced after Pastor et al. 1985). CSL,critical state line.



and plastic potential surfaces, the need for explicitly defin-ing these surfaces is eliminated.

Using the dilatancy relationship given by eq. [12], thedirection ngL can be defined as

[20] ngLT

g

g=+1

11

2dd( , )

Similarly, the direction of the unit normal n to the yieldsurface is given by (Zienkiewicz and Pande 1977)

[21] nT

f

f=+1

11

2dd( , )

where

[22] df = (1 + α)(Mf – η)

where df is the dilatancy at yield.The plastic modulus for loading is obtained from the rela-

tion introduced in Pastor and Zienkiewicz (1986):

[23] HL = H0 p′Hf{Hv + Hs}HDM

where H0 is the loading plastic modulus, and

[24] Hff

= −

1

4ηη

in which

[25] ηαf f= −

11

M

and

[26] HM

vg

= −

1

η

[27] H es0= −β β1

β ξ0

[28] ξ = εd sp∫

where ε sp is plastic shear strain.

For reloading, a discrete memory factor HDM is introducedto take into account the history of past events:

[29] HDMmax

DM

=

ζζ

γ

where γDM is a parameter for reloading discrete memory fac-tor, and

[30] ζ αα

ηα

= ′ − +

p

M1

11

is called the mobilized stress function.In the Pastor–Zienkiewicz Mark III model, it is assumed

that plastic strains develop during unloading. As observedin the experimental data (Ishihara and Okada 1982), theamount of plastic strain developing during unloading de-pends on the level of stress ratio from which the unloading

takes place. Therefore, the following relation was suggestedby Pastor et al. (1985) for the unloading plastic modulus:

[31] H HM M

U U0g

u

g

u

u

for=

>

η η

γ

1

[32] H HM

U U0g

u

for= ≤η

1

where HU0 is the unloading plastic modulus, and ηu u= ′( )q p isthe unloading stress ratio.

Determination of soil parameters

A detailed description of the procedure for parameteridentification for the Pastor–Zienkiewicz Mark III model isgiven by Chan (1988). The parameter determination processis based on drained monotonic, undrained monotonic, andundrained cyclic triaxial test results, since they are the mostcommonly available experiments in engineering practice.For determining the foundation soil parameters, the resultsof laboratory tests performed by Earth Technology Corpora-tion on this sand (i.e., Nevada sand) as part of the VELACSProject (Arulmoli et al. 1992) were used. The experimentaldata include monotonic and cyclic triaxial test results for rel-ative densities (Dr) of 40 and 60%. For determining the soilparameters, isotropically consolidated and undrained mono-tonic triaxial test results and isotropically consolidated, load-controlled, and undrained cyclic triaxial test results wereselected. Since in the centrifuge experiments Nevada sand ata relative density of about 40% was used, the triaxial test re-sults corresponding to this relative density were chosen. Thebehavior of the model with the selected parameters wascompared with experimental results using the soil modeltesting program SM2D (Chan 1988, 1993). The parameterschosen for the foundation soil are given in Table 1. Compar-isons of the monotonic triaxial test results with those pre-dicted by the soil model are shown in Fig. 2. In addition,prior to the actual numerical runs for the benchmark model,several level-ground models were analyzed to check the va-lidity of the parameters chosen for the foundation soil. Thelevel-ground (one-dimensional situation) runs were com-pared with centrifuge experimental data from Adalier (1996)and experimental and numerical results from the VELACSProject (Arulanandan and Scott 1993). The general behaviorof the soil with the chosen parameters was observed, andgood agreement with experimental results was obtained. Itshould be noted that no further adjustments were made tothe parameters listed in Table 1.

The clayey embankment was modeled using a modelcalled MOHR COULOMB FIVE (Chan 1993) implementedin DIANA-SWANDYNE II. The main parameters requiredby this model are Young’s modulus (E), Poisson’s ratio (ν),cohesion (c), and friction angle (φ). The model is capable ofgiving associated plasticity response for the Mohr Coulomb,Drucker Prager, Tresca, and Von Mises yield criteria. In thisstudy the Mohr Coulomb criterion was used. A nonlinearvariation of elastic modulus is also available in the model,but a constant Young’s modulus was used in this case. Theparameters for this soil obtained from direct shear tests were

© 2003 NRC Canada




(Adalier 1996) φ = 31° and c = 22 kPa; representative valuesof 20 MPa and 0.3 were used for E and ν, respectively.

For the calibration of the benchmark model, the embank-ment soil properties were changed after shake 1 to obtain the

correct embankment settlements for shakes 2 and 3 becausethe soil structure was destroyed and greatly changed due toembankment cracking and settlement (i.e., φ, c, and E werelowered to 28°, 12 kPa, and 12 MPa, respectively, to capture

© 2003 NRC Canada


Fig. 2. Comparison of monotonic triaxial results with those predicted by the model.

Parameter Description Value

Mg Slope of the critical state line (CSL) 1.15

Mf Yield surface parameter 1.03αf, αg Dilatancy parameters 0.45

Kev0c Bulk modulus at mean effective stress p0′ 8400 kPaKes0c Three times the shear modulus at mean effective stress p0′ 12 600 kPaH0 Loading plastic modulus 600HU0 Unloading plastic modulus 40 000 kPaγu Unloading plastic deformation parameter 2γDM Parameter for reloading discrete memory 0β0 Shear hardening parameter 4.2β1 Shear hardening parameter 0.2p0′ Initial mean effective stress 40 kPa

Table 1. Parameters used for Nevada sand at a relative density of Dr = 40%.



the overall embankment weakening). No modification to thefoundation soil parameters was done for the calibrationprocess. The only other calibration parameter was the foun-dation soil permeability, which is discussed in the next sec-tion.

Model configuration and analysis procedure

The centrifuge experiments were performed at a gravita-tional acceleration of 75g throughout. Under this gravityfield, the centrifuge models (Fig. 3) simulated a prototypeearth embankment of 4.5 m in height and 20.3 m in width,resting on a sand foundation deposit of 6 m thickness. Soilmodels were built in a rigid-wall model container with innerdimensions (model scale) of 0.6 m in length, 0.27 m inwidth, and 0.15 m in height. Extensive discussions on theexperimental study including the model preparation, instru-mentation, and testing equipment and procedures are givenin Adalier (1996) and Adalier et al. (1998). A series of threeconsecutive shaking events of 10 cycles with 1.6 Hz proto-type frequency were applied to each model. The peak cyclicexcitation was at a level of about 0.09g (shake 1), 0.18g(shake 2), and 0.30g (shake 3) for each shaking event, re-spectively. The configuration of the benchmark model pre-pared for the centrifuge experiments is shown in Fig. 3, thedimensions given in prototype scale. The locations of accel-erometers (ACC), pore-pressure transducers (PPT), and lin-ear variable displacement transducers (LVDT) are shown.An identical model was prepared for the numerical analysiswith a mesh of 90 elements as shown in Fig. 4a. The accel-erations, EPPs, and displacements were monitored duringthe centrifuge experiments and for the numerical analyses atthe locations shown in Fig. 3. In addition, the displacementsat appropriate locations to obtain the deformation of Fig. 4bwere carefully mapped at the end of the centrifuge tests(during the post-test dissection of the models) and comparedwith the final displacements from the numerical analyses.All numerical analyses were performed at model scale, andthe results are reported in the prototype scale. Model timesand displacements were multiplied by a factor of 75 andmodel accelerations were divided by 75 to obtain the proto-type quantities. A mixture of 60% glycerin and 40% water(by weight) was used as the pore fluid during the centrifugeexperiments, reducing the foundation permeability by aboutnine times compared with that with water. High-viscositypore fluid served to somewhat counterbalance the increase inthe soil hydraulic conductivity (prototype) that resulted in anelevated g field. The water permeability of the Nevada sandas given in the VELACS soil data report (Arulmoli et al.1992) is 6.6 × 10–5 m/s for a relative density of 40.2%. Forthe numerical runs, one ninth of this value was used as aninitial value. During shaking, however, the permeability ofsand increases to a significantly higher value than the onemeasured in a constant-head permeability test as raised byScott (1986), Hushmand et al. (1987), and Arulanandan andMuraleetharan (1989) and also stated by Ishihara (1994).Therefore, the foundation permeability was reserved as an-other calibration parameter for the benchmark model to cor-rectly model settlements and the pore-pressure buildup. Theoriginal permeability was increased as much as three times

within the range 0.73 × 10–5 to 2.20 × 10–5 m/s. For consoli-dation events a high value of 2.20 × 10–5 m/s was used. Fordynamic runs, the initial value was 2.20 × 10–5 m/s for shake1, and this value was reduced to 1.50 × 10–5 and 0.73 ×10–5 m/s for shakes 2 and 3, respectively. The fact that thesoil densified after each shaking event allowed for such rea-soning to be made.

During the centrifuge experiments the model was gradu-ally brought up to 75g before the base input was applied.Then a horizontal base excitation (in the direction orthogo-nal to the embankment axis) was applied as a uniform har-monic base input motion. Ample time was allowed betweeneach phase of shaking to allow for and monitor full excesspore-pressure dissipation. The centrifuge continued spinningand providing the 75g field throughout. In addition to moni-toring the instrumented quantities by ACCs, PPTs, andLVDTs, vertical soft spaghetti noodles were used as incli-nometers and post-test deformations were carefully mappedto obtain the deformed configuration.

The numerical runs of the benchmark model were carriedout using a procedure similar to that for the experiments. Aninitial static analysis with linear elastic material propertieswas first performed to determine the fluid hydrostatic pres-sures and soil effective stresses that satisfy static equilibriumunder the weight of the soil system at the 75g field. Dis-placements (which were negligible compared with thosecaused by shaking events) were zeroed at the end of thestatic run, since the static run was aimed at bringing themodel to the initial stress state with the appropriate hydro-static fluid pressures. Resulting soil effective stresses andfluid pressures were then considered initial conditions forthe subsequent dynamic run with the induced base input mo-tion. After the initial static analysis, a no-earthquake dy-namic analysis with actual soil parameters was performed tocheck the equilibrium of the initial stress state. Then the dy-namic analysis under drained conditions was carried out. Asbase input motion, the actual recorded data from the centri-fuge experiments were used. Each dynamic analysis was fol-lowed by a consolidation run with a slightly larger time stepthan the dynamic run to allow for EPP dissipation and the fi-nal settlements to take place. For shakes 2 and 3, the finalGauss point parameters of the previous consolidation eventwere taken as the initial conditions, and the displacementswere not reset to simulate the actual behavior of the centri-fuge model.

The saturated liquefiable foundation soil was modeled us-ing four-noded quadrilateral solid and fluid elements withfour Gauss points. No fluid phase for the embankment waspresent, and the domain was modeled again with four-nodedsolid elements. Appropriate boundary conditions were ap-plied. For the solid phase, horizontal input motion was spec-ified along the base and the two lateral sides as the recordedrigid container acceleration. All base nodes were fixed in thevertical direction. Along the lateral sides, vertical motionwas allowed. For the fluid phase, the base and the two sides(i.e., the container boundaries) were impervious (zero flowrate, which is a natural boundary condition). In addition,zero fluid pressure was prescribed along the foundation sur-face (at the water-table level) and within the entire embank-ment.

© 2003 NRC Canada




Results and comparisons

It is worth noting that the results presented herein mainlydemonstrate the performance of the numerical procedure.Thus, extensive discussions about the reasons behind the re-corded soil behavior are not included, with the purpose offocusing attention on the aspects of computational modelingand prediction. For a detailed discussion of the experimentalresults one may refer to Adalier (1996).

DeformationsThe most important factor affecting the performance of an

earth embankment subjected to an earthquake is the ex-pected movement of the embankment and the ground sup-porting it during and after the event. Accurate prediction ofearthquake-induced deformations and damage is the key tomaking well-informed seismic safety and remediation deci-sions for earth embankments. In this respect, the success ofdeformation prediction is of particular importance.

© 2003 NRC Canada


Fig. 4. No-remediation model: (a) undeformed and deformed finite element mesh (numerical); (b) comparison of predicted (values inbold) and measured (values in parentheses) deformations after shake 3 (i.e., cumulative after three shaking events).

Fig. 3. Configuration of the no-remediation (benchmark) model. ACC, accelerometer; LVDT, linear variable displacement transducer;PPT, pore-pressure transducer.



The undeformed finite element mesh and the deformedmesh obtained at the end of the consolidation analysis ofshake 3 showing the final deformations are given in Fig. 4a.A comparison of the mapped deformations obtained in thecentrifuge experiments with the numerically obtained valuesis shown in Fig. 4b. As seen in these figures, the measuredand predicted deformations were in good agreement both invalue and trend, except that the numerically predicted verti-cal and horizontal displacements underneath the embank-ment around the centerline were considerably less than themapped values. This is attributed to the inability of thenumerical integration to deal with a large strain increment(A.H.C. Chan, personal communication, 2001). The behav-ior can also be explained physically. The horizontal strainsoccurring at this location are large (due to large normal hori-zontal stress) compared with those at other locations. This isessentially an expansion zone. The soil structure is destroyedunder such large strains, and numerically the behavior is dif-ficult to model as continuum. As discussed later in the pa-per, the predicted EPPs at this zone are affected likewise.The vertical settlements under the embankment comparewell with the mapped values as locations away from the cen-terline are approached.

AccelerationsExperimentally recorded and numerically obtained accel-

erations are shown in Figs. 5, 6,and 7 for shakes 1, 2, and 3,respectively. In all cases, the computed accelerations were inreasonable agreement with the recorded counterparts. Signif-icant discrepancies also existed between the computed andexperimental accelerations, however. The most significantdiscrepancy is the lack of experimentally observed large,sharp acceleration spikes in the predicted response. In thecentrifuge experiments there was a peculiar asymmetric re-sponse with clear, large spikes underneath the embankmenttoe observed at ACC a9 for shake 1 and being more apparentalso for ACCs a3 and a6 (and to a lesser extent at so-calledfree-field ACCs a2 and a5) as the shaking amplitude was in-creased in shakes 2 and 3. Such an asymmetric spiky accel-eration response has been thoroughly investigated (Dobry etal. 1995; Elgamal et al. 1996; Adalier and Elgamal 2002)and has been attributed to the occurrence of significant post-liquefaction cyclic downslope (i.e., shear straining towardsfree-field associated mostly with initial static shear stresses)deformations and dilation. Note that the absence of signifi-cant initial static shear stress at the embankment centerline(i.e., ACCs a7 and a4) dictated an essentially symmetric ac-celeration response both numerically and experimentally.This deficiency in simulating strong dilation is widespread inmost currently available constitutive models (Arulanandanand Scott 1993; Parra 1996). This poor simulation of dilationeffects had an insignificant adverse effect on the success ofpredicted shear deformations, however, as suggested by theoverall good agreement between measured and computeddeformations.

Another noticeable discrepancy is with the free-field re-sponse. There is a severe attenuation of recorded accelera-tions after two to four cycles (depending on the shake event)of excitation, particularly at ACCs a5, a8, and to a lesser ex-tent a9 due to extensive liquefaction that was not capturednumerically to the full extent, although numerical results

also showed some attenuation. The reason for this is be-lieved to be mostly related to an experimental rather than anumerical error. In the centrifuge models, high EPPs inducesevere softening of the soil, especially at locations of lowinitial confinement. This soil softening resulted in relativedisplacements between the transducer and the soil body andconsequently underestimation of actual soil accelerations bythe accelerometers.

Another noticeable discrepancy is with the embankmentaccelerations. Embankment accelerations were somewhatoverestimated (particularly at the crest, ACC a11). The dis-crepancy is small, however, and can be mostly attributed tothe relative slip (i.e., due to accumulation of a water – loosesand interlayer at the relatively impermeable embankment –liquefied foundation interface) and cracking of the embank-ment. Both of these physical phenomena, which are beyondthe capability of the employed code to capture, appear tohave a major impact in limiting the experimentally observedembankment accelerations. In particular, the ACC a11 ex-perimental record during shake 3 cannot be trusted becausethe soil around the accelerometer was already deformed andcracked due to the shake 2 event. Less likely, the discrep-ancy may also be partly due to the rather simple constitutivemodel chosen for the embankment material. This issue cer-tainly warrants further in-depth investigation.

Hence, the numerical model was able to capture many ofthe model acceleration response characteristics. It is alsonoteworthy that, overall, there is a very good phase agree-ment, which is an indication that material stiffness degrada-tion was adequately modeled.

EPPComparisons of the recorded EPP with the numerical

counterparts are given in Figs. 8, 9, and 10 for shakes 1, 2,and 3, respectively. Also, the LVDT recordings for embank-ment crest settlement (location L3) are compared. A goodagreement with the LVDT recordings was obtained numeri-cally. Most of the computed and recorded embankment set-tlements were observed to take place during base excitation.These settlements were partly due to the deformation of theembankment itself and partly to settlements of its base as aresult of migration of underlying foundation soil towards thefree field, as indicated by the post-test deformed mesh. Post-shake consolidation settlements were relatively small.

As shown in Figs. 8–10, the numerical simulation of EPPin the soil is quite good except in the zone directly under-neath the embankment (PPT p9 during shake 1 and PPTs p9and p6 during shakes 2 and 3). A sudden drop in EPP wasobserved during shaking, becoming more dominant inshakes 2 and 3 as the shaking amplitude was increased. Thecause of this behavior is again attributed to the large hori-zontal strains occurring in this region and the inability of theprogram to cope with the large strain increment as previ-ously discussed. As shown in Part II, for sheet pile enclosureas a remedial measure, this behavior is eliminated, as thefoundation soil underneath the embankment is confined andlateral deformations are restrained. At other locations, thematches between experimental and computational EPP weresatisfactory. In general, the observed rates of EPP buildupand dissipation are well captured in the predictions. Theonly significant discrepancy is with the response at PPT p7.

© 2003 NRC Canada




© 2003 NRC Canada


Fig. 5. Computed and experimental acceleration (Acc.) – time histories for the no-remediation (benchmark) model during shake 1.

Fig. 6. Computed and experimental acceleration–time histories for the benchmark model during shake 2.



At this location EPP dissipation was predicted to occur morerapidly than actually occurred. This is mainly due to thesedimentation–solidification phenomenon (Adalier 1992),which is not accounted for in DIANA-SWANDYNE II (as

in the vast majority of other codes). More research is neededboth experimentally and numerically on this little-understood phenomenon, which is believed to be caused bythe suspension of the sand particles in water pending their

© 2003 NRC Canada


Fig. 8. Computed and experimental excess pore pressure (EPP) and embankment crest settlement – time histories for the benchmarkmodel during shake 1.

Fig. 7. Computed and experimental acceleration–time histories for benchmark model during shake 3.



sedimentation and restoration of intergranular contact. Intro-duction of an artificial, highly nonlinear bulk modulus in thecode may account for this phenomenon (a topic of currentongoing research). Another noticeable discrepancy is thatthe cyclic fluctuations of EPP in numerical results weresomewhat larger than the measured ones. It is noted here,however, that the magnitude of these fluctuations cannot becompared with the experimental results, in which theemployed PPTs were physically unable to respond to such

abrupt fluctuations (verified in independent tests of thetransducers; Adalier 1996).

It should be noted that this reasonably good numericalperformance was obtained despite the fact that most of thefoundation model parameters were identified based on theconventional unit element laboratory test results. Additional“fine-tuning” calibration based on model response in centri-fuge conditions might have further improved the predictions.The calibration of stress–strain features of the model for the

© 2003 NRC Canada


Fig. 9. Computed and experimental EPP and embankment crest settlement – time histories for the benchmark model during shake 2.

Fig. 10. Computed and experimental EPP and embankment crest settlement – time histories for the benchmark model during shake 3.



dominant loading path may also provide better predictions(i.e., different calibrations may be necessary for differentparts of the region being analyzed). These remain as topicsfor future research.

Summary and conclusions

The feasibility of using a fully coupled, effective stressbased, finite element code DIANA-SWANDYNE II to esti-mate the dynamic behavior of a cohesive earth embankmenton a liquefiable foundation was assessed by modeling aseries of highly instrumented centrifuge tests. Typicalmonotonic and cyclic laboratory tests results were used toobtain the initial state parameters and constitutive modelconstants representative of the soil model. The results of thedynamic analysis, such as acceleration and excess pore pres-sure time histories and liquefaction-induced deformationbehaviors observed during the centrifuge model tests, com-pared satisfactorily with the numerically predicted counter-parts. Moreover, these comparisons provided valuable insightsinto the dynamic behavior of the employed embankment–foundation systems. There were significant discrepancies, how-ever, between the computed and recorded foundation porepressures and vertical deformations at zones beneath the em-bankment centerline. These discrepancies are believed to berelated to the inability of the code to cope with large strainincrements. More effort needs to be directed toward thisaspect both computationally and experimentally. Further re-search work is also needed primarily for more accurate mod-eling of dilative acceleration spikes appearing during largeshear strain excursions. Despite a number of shortcomings,the results represent a very good comparison with the exper-imental results, accounting for possible experimental errors.

This paper demonstrates that the presented computationalprocedure DIANA-SWANDYNE II when combined withcarefully calibrated material properties and model parame-ters can be used to study liquefaction potential and the effectof an increase in pore-water pressure on the dynamic re-sponse of soil profiles and earth embankments. The verifiedand calibrated analysis procedure presented in this paper isused in Part II as a platform to computationally study severalremediated cases. The computational results are comparedwith experimental records to assess the capability of the nu-merical technique to model retrofitted embankment cases.

Acknowledgements

The authors gratefully acknowledge the contributions ofProfessor Andrew H.C. Chan of the University of Birmingham(U.K.) by providing his computer program (DIANA-SWANDYNE II) for this work and giving valuable guidanceon its use. This work is mostly sponsored by the Engi-neering School of Eastern Mediterranean University, North-ern Cyprus. The physical model experiments described herewere performed using the Geotechnical Centrifuge atRensselaer Polytechnic Institute (RPI), Troy, New York(Professor Ricardo Dobry, Director). The authors are alsograteful to Dr. Michael K. Sharp of the EngineeringResearch and Development Center, U.S. Army Corps ofEngineers, Vicksburg, Mississippi for many valuable discus-sions and review comments.

References

Adalier, K. 1992. Post-liquefaction behavior of soil systems. M.S.thesis, Rensselaer Polytechnic Institute (RPI), Troy, N.Y.

Adalier, K. 1996. Mitigation of earthquake induced liquefactionhazards. Ph.D. thesis, Rensselaer Polytechnic Institute (RPI),Troy, N.Y.

Adalier, K., and Aydingun, O. 2000. Liquefaction during theJune 27, 1998 Adana-Ceyhan (Turkey) Earthquake. Journal ofGeotechnical and Geological Engineering, 18(3): 155–174.

Adalier, K., and Elgamal, A.W. 2002. Seismic response of adjacentsaturated dense and loose sand columns. Soil Dynamics andEarthquake Engineering, 22(2): 115–127.

Adalier, K., Elgamal, A.W., and Martin, G.R. 1998. Foundationliquefaction countermeasures for earth embankments. Journal ofGeotechnical and Geoenvironmental Engineering, ASCE,124(6): 500–517.

Adalier, K., Abdoun, T., Dobry, R., and Phillips, R. 2002. GeorgeMassey Tunnel seismic safety retrofit final design — RPI centri-fuge tests results. Technical Report to Buckland and Taylor Ltd.,Vancouver, B.C.

Arulanandan, K., and Muraleetharan, K.K. 1989. Level groundsoil-liquefaction analysis using in-situ properties. Journal ofGeotechnical Engineering, ASCE, 114(7): 771–790.

Arulanandan, K., and Scott, R.F. (Editors). 1993. Verification ofnumerical procedures for the analysis of soil liquefaction prob-lems. Vols. 1 and 2. A.A. Balkema, Rotterdam, The Nether-lands.

Arulmoli, K., Muraleetharan, K.K., Hossain, M.M., and Fruth, L.S.1992. Verification of liquefaction analysis by centrifuge studieslaboratory testing program soil data. Technical Report, EarthTechnology Corporation, Irvine, Calif.

Biot, M.A. 1956. Theory of propagation of waves in a fluid satu-rated porous solid — Part I: low frequency range. Part II: highfrequency range. Journal of the Acoustic Society of America,28: 168–191.

Chan, A.H.C. 1988. A unified finite element solution to static anddynamic geomechanics problems. Ph.D. thesis, University Col-lege of Swansea, Swansea, Wales.

Chan, A.H.C. 1993. User manual for DIANA-SWANDYNE II.School of Civil Engineering, University of Birmingham, Bir-mingham, U.K.

Clough, R.W., and Penzien, J. 1993. Dynamics of structures.McGraw-Hill Press, New York.

Cooke, H.G., and Mitchell, J.K. 1999. Guide to remedial measuresfor liquefaction mitigation at existing highway bridge sites.Technical Report MCEER-99-015, Multidisciplinary Center forEarthquake Engineering Research, Buffalo, N.Y.

Dobry, R., Taboada, T., and Liu, L. 1995. Centrifuge modeling ofliquefaction effects during earthquakes. In Proceedings of the1st International Conference on Earthquake Geotechnical Engi-neering, Special Keynote and Theme Lectures, IS-Tokyo ‘95,Tokyo, Japan. Edited by K. Ishihara. A.A. Balkema, Rotterdam,The Netherlands. pp. 129–162.

Duke, C.M., and Leeds, D.J. 1963. Response of soils, foundations,and earth structures to the Chilean Earthquake of 1960. Bulletinof the Seismological Society of America, 53(2): 309–357.

Elgamal, A.W., Zeghal, M., Taboada, V., and Dobry, R. 1996.Analysis of site liquefaction and lateral spreading using centri-fuge testing records. Soils and Foundations, 36(2): 111–121.

Elgamal, A.W., Yang, Z., Parra, E., and Ragheb, A. 2003.Modeling of cyclic mobility in saturated cohesionless soils. In-ternational Journal of Plasticity, 19: 883–905.

© 2003 NRC Canada




© 2003 NRC Canada


Finn, W.D.L. 2000. State-of-the-art of geotechnical earthquake en-gineering practice. Soil Dynamics and Earthquake Engineering,20: 1–15.

Hushmand, B., Crouse, C.B., Martin, G.R., and Scott, R.F. 1987.Site response and liquefaction studies involving the centrifuge.In Proceedings of the 3rd International Conference on SoilDynamics and Earthquake Engineering, Princeton, N.J. ElsevierScience, Amsterdam. pp. 3–24.

Ishihara, K. 1994. Review of the predictions for Model 1 in theVELACS program. In Verification of numerical procedures forthe analysis of soil liquefaction problems. Edited by K.Arulanandan and R.F. Scott. A.A. Balkema, Rotterdam, TheNetherlands. Vol. 2, pp. 1353–1359.

Ishihara, K., and Okada, S. 1982. Effects of large preshearing oncyclic behaviour of sand. Soils and Foundations, 22: 109–125.

Japanese Geotechnical Society. 1996. Special Issue onGeotechnical Aspects of the January 17, 1995 Hyogoken–Nambu Earthquake, Tokyo, Japan. Soils and Foundations.

Katona, M.G., and Zienkiewicz, O.C. 1985. A unified set of singlestep algorithms Part 3: the Beta-m method, a generalization ofthe Newmark scheme. International Journal of NumericalMethods in Engineering, 21: 1345–1359.

Kimura, T., Takemura, J., Hiro-oka, A., Okamura, M., andMatsuda, T. 1995. Countermeasures against liquefaction of sanddeposits with structures. In Proceedings of the 1st InternationalConference on Earthquake Geotechnical Engineering, IS-Tokyo‘95, Tokyo, Japan. Edited by K. Ishihara. A.A. Balkema, Rotter-dam, The Netherland. pp. 163–184.

Krinitzsky, E.L., and Hynes, M.E. 2002. The Bhuj, India, earth-quake: lessons learned for earthquake safety of dams on allu-vium. Engineering Geology, 66(3–4): 163–196.

Ledbetter, R.H., and Finn, W.D.L. 1993. Development and evalua-tion of remediation strategies by deformation analysis. InGeotechnical Practice in Dam Rehabilitation, Proceedings of theSpecialty Conference, Raleigh, N.C. Edited by L.R. Anderson.ASCE Geotechnical Special Publication 35, pp. 386–401.

Marcuson, W.F., Hadala, P.F., and Ledbetter, R.H. 1996. Seismicrehabilitation of earth dams. Journal of Geotechnical Engi-neering, ASCE, 122(1): 7–20.

Matsuo, O. 1996. Damage to river dikes. Soils and Foundations,36(1): 235–240.

Matsuo, O., Shimazu, T., Uzuoka, R., Mihara, M., and Nishi, K.2000. Numerical analysis of seismic behavior of embankmentsfounded on liquefiable soils. Soils and Foundations, 40(2):21–39.

McCulloch, D.S., and Bonilla, M.G. 1967. Railroad damage in theAlaska Earthquake. Journal of the Geotechnical Engineering Di-vision, ASCE, 93(5): 89–100.

Nova, R., and Wood, D.M. 1982. A constitutive model for soilunder monotonic and cyclic loading. In Soil mechanics —transient and cyclic loads. Edited by G.N. Pande and O.C.Zienkiewicz. John Wiley & Sons Publishing Company,New York. pp. 343–374.

Parra, E. 1996. Numerical modeling of liquefaction and lateralground deformation including cyclic mobility and dilation re-sponse in soil systems. Ph.D. thesis, Rensselaer Polytechnic In-stitute, Troy, N.Y.

Pastor, M., and Zienkiewicz, O.C. 1986. A generalized plasticityhierarchical model for sand under monotonic and cyclic loading.In Proceedings of the 2nd International Conference on Numeri-cal Models in Geomechanics, Ghent, Belgium. Edited by G.N.Pande and W.F. Van Impe. M. Jackson & Son Ltd., Cornwall,U.K. pp. 131–150.

Pastor, M., Zienkiewicz, O.C., and Leung, K.H. 1985. Simplemodel for transient soil loading in earthquake analysis — II.Non-associative models for sands. International Journal of Nu-merical and Analytical Methods in Geomechanics, 9: 477–498.

Pastor, M., Zienkiewicz, O.C., and Chan, A.H.C. 1990. General-ized plasticity and the modeling of soil behaviour. InternationalJournal of Numerical and Analytical Methods in Geomechanics,14: 151–190.

Scott, R.F. 1986. Solidification and consolidation of a liquefiedsand column. Soils and Foundations, 26(4): 23–31.

Seed, H.B. 1968. Landslides during earthquakes due to soil lique-faction. Journal of the Geotechnical Engineering Division,ASCE, 94(5): 1055–1123.

Seed, H.B. 1970. Soil problems and soil behavior. In Earthquakeengineering. Edited by R.L. Weigel. Prentice-Hall Inc.,Englewood Cliffs, N.J. Chapter 10.

Seed, R.B., Dickenson, S.E., Riemer, M.F., Bray, J.D., Sitar, N.,Mitchell, J.K., Idriss, I.M., Kayen, R.E., Kropp, A.,Hander, L.F., and Power, M.S. 1990. Preliminary report on theprincipal geotechnical aspects of the October 17, 1989 LomaPrieta Earthquake. Report UCB/EERC-90/05, Earthquake Engi-neering Research Center, University of California-Berkeley,Berkeley, Calif.

Tani, S. 1996. Damage to earth dams. Soils and Foundations,36(1): 263–272.

Yokomura, S. 1966. The damage to river dykes and related struc-tures caused by the Niigata Earthquake. Soils and Foundations,6(1): 38–53.

Zienkiewicz, O.C., and Mroz, Z. 1985. Generalized plasticity for-mulation and its application to geomechanics. In Mechanical en-gineering materials. Edited by C.S. Desai and R.H. Gallagher.John Wiley and Sons Press, Chichester, U.K. Chapter 33,pp. 655–680.

Zienkiewicz, O.C., and Pande, G.N. 1977. Some useful forms ofisotropic yield surfaces for soil and rock mechanics. In Finiteelements in geomechanics. Edited by G. Gudehus. John Wileyand Sons Press, Chichester, U.K. Chapter 5, pp. 179–190.

Zienkiewicz, O.C., Leung, K.H., and Pastor, M. 1985. Simplemodel for transient soil loading in earthquake analysis. I — Ba-sic model and its application. International Journal of Numericaland Analytical Methods Geomechanics, 9: 453–476.

Zienkiewicz, O.C., Chan, A.H.C., Pastor, M., Paul, D.K., and Shiomi,T. 1990. Static and dynamic behaviour of geomaterials — A ratio-nal approach to quantitative solutions. Part I — Fully saturatedproblems. Proceedings of the Royal Society of London, Series A,429: 285–309.

Zienkiewicz, O.C., Chan, A.H.C., Pastor, M., Schrefler, B.A., andShiomi, T. 1999. Computational geomechanics. John Wiley andSons Press, Chichester, U.K.



numerical analysis of seismically induced liquefaction in earth embankment foundations. part i....

Documents