dynamic deformations in sand embankments: centrifuge modeling and blind, fully coupled analyses

Dynamic deformations in sand embankments:centrifuge modeling and blind, fully coupledanalyses

Kanthasamy K. Muraleetharan, Sachin Deshpande, and Korhan Adalier

Abstract: Prediction of deformations during earthquake loading is one of the critical aspects in the design of ageotechnical engineering structure. The dynamic behavior of two centrifuge model sand embankments including defor-mations is presented and compared with blind predictions made by a fully coupled analysis procedure, the computercode DYSAC2, using a bounding surface elastoplastic model. The centrifuge model embankments were constructedusing Nevada sand placed at 62% (dense) and 43% (medium dense) relative densities and consisted of a mild slope onone side and a steep slope on the other side. Both embankments showed substantial movements along the slopes,spikes in the upslope acceleration values, and corresponding dilation spikes in the pore-pressure values. These spikeswere more pronounced for the medium-dense sand embankment and on the mild-slope sides for both embankments.The observed behavior is related to the stress–strain behavior of sands undergoing cyclic mobility, and the importanceof accurately obtaining the initial static stresses is emphasized. The blind predictions using the computer codeDYSAC2 compared reasonably well with the measured results and provided further insight into the behavior of theseembankments. The blind predictions similar to those shown in this paper are expected to provide confidence for prac-ticing engineers to use fully coupled procedures for predicting deformations of geotechnical structures subjected toearthquakes.

Key words: centrifuge modeling, cyclic mobility, earthquakes, embankment, fully coupled analysis, sand.

Résumé : La prédiction des déformations durant une secousse sismique est un des aspects critiques dans la conceptiond’une structure géotechnique d’ingénieur. On présente le comportement dynamique de deux modèles de remblai desable dans un centrifuge, incluant les déformations, et on le compare aux prédictions aveugles faites au moyen d’uneprocédure d’analyse totalement couplée, du code d’ordinateur DYSAC2, utilisant un modèle élastoplastique de surfacesfrontières. Les remblais modèles au centrifuge ont été construits avec du sable du Nevada mis en place à des compaci-tés relatives de 62% (dense) et de 43% (moyennement dense) et comportaient une pente douce d’un côté et une penteabrupte de l’autre côté. Les deux remblais ont montré des mouvements substantiels le long des pentes, des pointes dansles valeurs d’accélération vers le haut des pentes, et des pointes de dilatation correspondantes dans les valeurs des pres-sions interstitielles. Ces pointes étaient plus prononcées dans le remblai de sable moyennement dense et sur les côtésdes pentes douces dans les deux remblais. Le comportement observé est en relation avec le comportement con-trainte-déformation des sables subissant un mouvement cyclique et on souligne l’importance d’obtenir avec précisionles contraintes statiques initiales. Les prédictions aveugles au moyen du code DYSAC2 d’ordinateur se comparaient rai-sonnablement bien avec les résultats mesurés et fournissaient un éclaircissement sur le comportement de ces remblais.On s’attend à ce que les prédictions aveugles semblables à celles montrées dans cet article donnent confiance aux ingé-nieurs en pratique pour utiliser les procédures totalement couplées pour la prédictions des déformations des structuresgéotechniques soumises à des tremblements de terre.

Mots clés : modélisation par centrifuge, mobilité cyclique, tremblements de terre, remblai, analyse totalement couplée,sable.

[Traduit par la Rédaction] Muraleetharan et al. 69

Can. Geotech. J. 41: 48–69 (2004) doi: 10.1139/T03-065 © 2004 NRC Canada

48

Received 7 July 2002. Accepted 18 July 2003. Published on the NRC Research Press Web site at http://cgj.nrc.ca on 12 January2004.

K.K. Muraleetharan1 and S. Deshpande.2 School of Civil Engineering and Environmental Science, University of Oklahoma,202 W. Boyd Street, Room 334, Norman, OK 73019, U.S.A.K. Adalier. Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, JEC 4049, 110 8th Street, Troy,NY 12180, U.S.A.

1Corresponding author (e-mail: [email protected]).2Present address: Sempra Energy Utilities, 555 West Fifth Street, GT25H4, Los Angeles, CA 90013-1011, U.S.A.

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Introduction

It has always been important for geotechnical engineers tounderstand the dynamic behavior of dams, embankments,levees, and dikes subjected to earthquakes. Recent devastat-ing earthquakes in India, Taiwan, and Turkey and the 1995Hyogoken-Nambu (Kobe) earthquake in Japan have clearlydemonstrated the importance of properly understanding thedynamic behavior of the aforementioned geotechnical engi-neering structures. For example, Matsuo (1996) and Tani(1996) reported damage to dikes and dams during theHyogoken-Nambu earthquake consisting of settlement,cracks, distortion, and lateral sliding. Similar behavior ofthese structures was also observed during the recent earth-quakes in India, Taiwan, and Turkey. Lower San Fernandodam failed during the 1976 San Fernando earthquake, result-ing in approximately 1.5 m of surface settlement, and thedam was barely able to contain the water after the earth-quake (Seed 1979). Based on these types of damage, one canconclude that the deformations are the most important infor-mation geotechnical engineers need to predict in designingdams, embankments, levees, and dikes against seismic loads.For example, the most important parameter in the seismicdesign of a dam is the available freeboard after the designearthquake. In other words, although predicting accelera-tions and pore-water pressures in an embankment may beimportant to fully understand its behavior during earth-quakes, prediction of deformations is the most critical ele-ment for design purposes. Prediction of deformations alsoplays a key role in the design of waterfront structures.Knowing the deformation of a rock dike or a caisson duringa design earthquake is critical to designing the adjoiningstructures such as wharves and gantry cranes. Iai et al.(1998) commented that the degree of displacement is one ofthe essential design parameters to characterize the seismicperformance of port structures, and a reasonable seismic re-sponse analysis should be used to obtain these parameters.

Traditionally, empirical procedures (Makdisi and Seed1978) or simplified analytical procedures (Newmark 1965)have been used to obtain deformation of geotechnical engi-neering structures during earthquakes. In recent years, how-ever, dynamic, fully coupled analysis procedures arebecoming popular among geotechnical engineers to calculatedeformations and provide insight into the seismic behaviorof geotechnical engineering structures. In a fully coupledanalysis, the coupled differential equations governing the dy-namic behavior of the pore fluid and the soil skeleton aresolved, typically using a finite element method. Usually anelastoplastic constitutive model is also used to describe thestress–strain behavior of the soil skeleton. The Port of LosAngeles’ US$480 million dollar Pier 400 project (Jones etal. 2001) is one of the largest port projects in the world inrecent times. Fully coupled analysis procedures, the com-puter codes DYSAC2 (Muraleetharan et al. 1988, 1997b)and DYNAFLOW (Prevost 1998), were used together withother traditional approaches in the seismic design of Pier400 (Wittkop 1993; Muraleetharan et al. 1994a, 1997a;Fugro West, Inc. 1999). Iai et al. (1998) used a fully coupledprocedure to investigate the seismic response of port struc-tures during the Hyogoken-Nambu earthquake. To buildconfidence among practitioners in these fully coupled proce-

dures, however, it is important that developers of numericalprocedures make blind predictions of the behavior of geo-technical engineering structures subjected to earthquakes.

The verification of liquefaction analyses by centrifugestudies project (VELACS), funded by the U.S. National Sci-ence Foundation (NSF), is the first major project in whichpredictions of dynamic behavior of geotechnical engineeringstructures were attempted before the event (Arulanandan andScott 1993). Several centrifuge model configurations weresubjected to base shaking after various predictors had sub-mitted their predictions to an adjudication committee.Predictions of deformations in this project were mixed, how-ever. Overall, fully coupled procedures made better predic-tions than empirical or loosely coupled methods. Popescuand Prevost (1994) reported analyses of various predictionsmade for the VELACS project, including those made byDYSAC2 (Muraleetharan et al. 1988, 1997b) and DYNAFLOW(Prevost 1998). In loosely coupled methods, dynamic govern-ing equations are solved, but pore pressures are calculatedfrom an external empirical model and the effective stressesare updated incrementally. Liquefaction was observed in sig-nificant portions of all the VELACS centrifuge models dueto the high levels of base shaking used in the tests. A follow-up project, the VELACS Extension Project (Arulanandan1996), was initiated to investigate the capabilities of selectedfully coupled procedures to predict dynamic behavior ofgeotechnical engineering structures where liquefaction didnot occur, but still substantial pore-water pressures devel-oped during shaking. The VELACS Extension Project wasalso interested in investigating the response of geotechnicalengineering structures constructed of different densities ofsand. Loose sands and dense sands have been known tobehave differently in laboratory cyclic tests. For example,whereas loose sands liquefy and produce large strains, densesands undergo cyclic mobility and produce limited strains(Ishihara 1985). The VELACS Extension Project was inter-ested in investigating how this laboratory-observed stress–strain behavior translated into deformation of geotechnicalengineering structures.

Numerical predictors were invited to predict dynamic be-havior of two submerged sand model embankments con-structed of a fine uniform sand at approximately 60%(dense) and 40% (medium dense) relative densities, respec-tively, and subjected to base shaking in a centrifuge. Thecross sections of the embankments were asymmetric andcontained a mild slope on one side and a steep slope on theother side. The predictions for the VELACS Extension Pro-ject were made after the tests were performed, but withoutany knowledge of the measured results. This paper describesthe behavior of these two centrifuge model embankmentsand the blind predictions made by the University of Okla-homa group using the computer code DYSAC2. Centrifugemodel test results and fully coupled analyses provided notonly insight into how sand embankments at different densi-ties behave when subjected to earthquakes, but also insightinto how mild and steep slopes constructed of the same ma-terial behave during dynamic loading events. The primaryfocus of this paper is to understand the deformation behaviorof submerged sand embankments. Observed and predicteddisplacements of the embankments are related to accelera-tions, pore-water pressures, and laboratory stress–strain re-

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Muraleetharan et al. 49



sponse. The importance of initial static stresses in thedynamic behavior of soils is also highlighted, and the needto perform accurate static analysis prior to a dynamic analy-sis is emphasized.

Centrifuge tests

Validation of any numerical procedure depends heavily onreliable experimental data. In geotechnical earthquake engi-neering, centrifuge testing has been recognized as a usefultool to produce data for the validation of numerical proce-dures and insight into failure mechanisms. For the VELACSExtension Project, centrifuge tests were performed using theRensselaer Polytechnic Institute (RPI) 3.0 m radius centri-fuge (Adalier et al. 1997). The embankment tests that wereused in the blind prediction exercise are discussed in thispaper.

All the tests were performed using a fine, uniform sandcalled Nevada sand (median particle size D50 = 0.15 mm,maximum void ratio emax = 0.887, minimum void ratioemin = 0.511, specific gravity = 2.67). Extensive laboratorytest results are available for this sand (Arulmoli et al. 1992).The model configuration and instrument locations are shownin Fig. 1. One model was constructed using Nevada sandplaced at a relative density (Dr) of 62% (dense) and the otherat a Dr of 43% (medium dense). The asymmetric modelcross section consisted of sides with slopes of 1V:3H (18.4°to the horizontal) and 1V:1.75H (29.7° to the horizontal).Angles of internal friction for Nevada sand at Dr of 62% and43% are approximately 36° and 33°, respectively, ensuringstatic stability of these models. All the tests were performedat a centrifugal acceleration of 50g, where g is the gravita-tional acceleration. The dimensions of the model are shownin prototype scale (i.e., model scale × 50) in Fig. 1. Themodels were instrumented with accelerometers, pore-pressure transducers, and linear variable differential trans-formers (LVDTs). The locations of the instruments are givenin Table 1.

Water was used as the pore fluid in all the tests. When thesame soil and pore fluid are used in a model and a proto-type, the quantity k/γf remains constant in the model and theprototype, where k is the coefficient of permeability and γf isthe unit weight of the pore fluid. Under a centrifugal accel-eration of 50g, γf increases by a factor of 50, and thereforethe model coefficients of permeability will be 50 timeshigher than the prototype values.

The models were constructed on top of rough sandpaperglued to the base of the model container to prevent slippagealong the base. Oven-dried Nevada sand was pluviatedthrough a V-shaped funnel with a row of holes along thefunnel tip. The holes were 2 mm in diameter and 4 mmapart. To produce uniform samples, the funnel was movedmanually back and forth along the width of the model con-tainer at a frequency of approximately 0.5 Hz and free fall-ing distance of 50 ± 5 mm for Dr = 62% and 30 ± 5 mm forDr = 43%. Pluviation was interrupted periodically to placeinstrumentation within the soil model. Transducer wireswere taped to the container sides. Pluviation was stopped2–10 mm above the desired model height at various loca-tions along the cross section. The model surface was thentrimmed to the final profile by removing the excess sand

with a vacuum line and a guide. Following pluviation, thetop of the model container was sealed with a lid, anddeionized, deaired water was introduced under a suction of90 kPa. This saturation process was performed over approxi-mately 8 h. Before testing, red-colored spaghetti sticks wereinserted vertically into the soil at the central cross sectionusing a thin steel tube and a guide. Spaghetti sticks, softenedby submersion in water, moved with the sand during shak-ing, and their final locations were recorded during the post-shaking dissection of the models. The centrifuge wasbrought up to 50g gradually in about 30 min and then spunat this level for another 10 min before the base shaking wasapplied. The relative densities reported here are based onvolume and weight measurements before spinning the cen-trifuge. Based on past experience, these relative densitiescould have changed about 1%–3% during spin-up. The re-sults of the tests are discussed in a later section togetherwith the predictions.

Fully coupled analysis procedure

The fully coupled analysis procedure used in the predic-tions is based on the finite element solution of the dynamicgoverning equations for a saturated porous media (soil skele-ton and pore fluid). The details of this formulation andnumerical implementation are given in Muraleetharan etal. (1994b). The two-dimensional numerical implementationof the formulation resulted in the computer code DYSAC2(Muraleetharan et al. 1988, 1997b). Four-noded isopara-metric elements with reduced integration for the fluid bulkmodulus terms are used in DYSAC2. Nodal variables pernode are two soil skeleton and two fluid displacements. Athree-parameter time integration scheme called the Hilber-Huges-Taylor α-method (Hilber et al. 1977) is used, togetherwith a predictor–multicorrector algorithm, to integrate thespatially discrete finite element equations. This time integra-tion scheme provides quadratic accuracy and desirable nu-merical damping characteristics to damp the high-frequencyspurious modes.

In DYSAC2, stress–strain behavior of the soil skeletoncan be described by the isotropic linear elastic model andbounding surface elastoplastic models. Two constitutivemodels based on the bounding surface plasticity theory(Dafalias and Popov 1976) are used in DYSAC2, one forcohesive soils (Dafalias and Herrmann 1986) and one fornoncohesive soils (Yogachandran 1991). If a normally con-solidated dense sample of a soil dilates during undrainedshear, that soil is classified as noncohesive; if the soil doesnot dilate, it is classified as cohesive. All the predictionsreported in this paper are made using the model for non-cohesive soils. Details of the constitutive model are given inthe next section. The energy dissipation caused by the elas-toplastic response of the soil skeleton and the drag forcescaused by fluid flow provide the necessary damping for thewave propagation. No external damping such as the Ray-leigh damping is added to the analysis.

Constitutive model and model parametersThe constitutive model for noncohesive soils used in

DYSAC2 (Yogachandran 1991) is based on the boundingsurface plasticity theory (Dafalias and Popov 1976), which

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50 Can. Geotech. J. Vol. 41, 2004



allows plastic strains to occur for stress points within thebounding surface. In contrast, the classical plasticity theorydoes not allow plastic strains to occur for stress points with-in the yield surface. A nonassociative flow rule is used topredict the contraction and falling stress path behavior ex-hibited by very loose noncohesive soils in undrained shear.The tendency to contract during unloading in sands leads tocyclic mobility of dense sands and liquefaction of loosesands. Plastic strains during unloading are taken into accountusing the bounding surface concept similar to that of loadingto account for the above described phenomena. Restrictionsare placed on the strain increment directional vector, how-ever, to make the volumetric strain during unloading alwayspositive. The shapes of the bounding and plastic potentialsurfaces are shown in Fig. 2. Stress invariants I (first invari-ant of the effective stress tensor) and J (square root of thesecond invariant of the deviatoric stress tensor), given inFig. 2, are defined by eqs. [1] and [2] using standard indicialnotations:

[1] I kk= ′σ

[2] J s sij ij= 12

where σij′ is the effective stress tensor, and sij is the devia-toric stress tensor.

The bounding surface consists of two surfaces. Ellipse 1 isdefined by the parameters R and N, and ellipse 2 is definedby the parameters δ and N. The plastic potential surface isanother ellipse defined by the slope of the critical state lineNu. The parameters N, Nu, and R are functions of the Lodeangle α. The size of the bounding surface (I0) evolves basedon the accumulated volumetric and deviatoric strains. De-pendence of I0 on deviatoric strains helps the model predictdilation behavior of dense, noncohesive soils.

For a particular noncohesive soil at a particular relativedensity, a minimum of four laboratory tests will be requiredto calibrate the model parameters. These tests include oneisotropic (or one-dimensional) consolidation–rebound test,one undrained triaxial compression test, one undrained tri-axial extension test, and one undrained triaxial cyclic test. Ina recent implementation of the bounding surface concept forsands (Manzari and Dafalias 1997), the state parameter con-cept (Been and Jefferies 1985) is used to derive modelparameters that are independent of relative densities. De-scriptions of all the model parameters that require calibra-tion and the values of these parameters for Nevada sand at40% and 60% relative densities are given in Table 2. TheLode angle dependence of parameters (Mu, M, R, and h)given in Table 2 is taken into account using the functional

© 2004 NRC Canada


Fig. 1. Centrifuge model configuration and locations of the instruments (all dimensions are scaled to prototype by multiplying themodel dimensions by 50). ACC, accelerometer; PPT, pore-pressure transducer; LVDT, linear variable differential transformers.

Instrument x (m) y (m)

ACC 1 Base horizontalACC 2 Base verticalACC 3 7.50 0.15ACC 4 16.00 0.15ACC 5 21.40 0.15ACC 6 7.50 2.00ACC 7 21.40 2.00ACC 8 16.00 4.25PPT A 5.00 0.15PPT B 16.00 0.15PPT C 22.90 0.15PPT D 10.00 2.50PPT E 16.00 2.50PPT F 19.40 2.50LVDT 1 16.00 5.00

Table 1. Locations of the accelerometers (ACC),pore-pressure transducers (PPT), and linear variabledifferential transformers (LVDT) in prototype scale.



© 2004 NRC Canada


form proposed by Dafalias and Herrmann (1986). The modelparameters for Nevada sand were obtained using a subset ofthe available laboratory test results (Arulmoli et al. 1992), asinstructed by the VELACS Extension Project coordinatingcommittee. The step by step calibration procedure for theconstitutive model is described as follows:(1) Obtain λ and κ from one-dimensional consolidation–

rebound tests or isotropic triaxial consolidation–reboundtests. Calculate the slopes in the stress range of interest.

(2) Obtain the value of (Mu)c from isotropically consoli-dated undrained triaxial compression (CIUC) tests. Thisis the maximum q/p′ ratio reached during a CIUC test,where q is the deviatoric stress, and p′ is the effectivemean normal stress.

(3) Similar to step 2, obtain an initial estimate of (Mu)e

from isotropically consolidated undrained triaxial exten-sion (CIUE) tests.

(4) Calibrate the value of Mc by matching the final slope ofthe stress path, on a q–p′ plot, between the model pre-dictions and the measured results for a CIUC test.

(5) Finalize the value of (Mu)e by matching the final slopeof the stress path, on a q–p′ plot, between the model pre-dictions and the measured value for a CIUE test.

(6) Calibrate the values of Rc and β1 by matching the mea-sured and predicted q–ε1 curves for a CIUC test (whereε1 is the axial strain).

(7) In theory, the value of Re, the parameter defining ellipse1 in extension, can be calibrated similar to that in step 6.Due to very early shear band formation in triaxial exten-sion tests, however, q–ε1 plots are not reliable. A value

Fig. 2. Schematic illustration of the bounding and plastic potential surfaces used in the elastoplastic constitutive model.

Property Dr = 40% Dr = 60%

Traditional model parametersSlope of isotropic consolidation line in e – ln p′ plot, λ 0.017 0.009Slope of elastic rebound line in e – ln p′ plot, κ 0.003 0.002Slope of critical state line in q – p′ space (compression), Mu 1.33 1.44Poisson’s ratio, v 0.3 0.3

Bounding surface configuration parametersParameter defining the initial size of the bounding surface, Io/I 1.5 1.0Slope of the line passing through the origin and the intersection of ellipses 1 and 2

(OA in Fig. 2) in q – p′ space (compression), Mc

0.89 0.89

Ratio of extension to compression value of M (same as the ratio of (Mu)e/(Mu)c), Me/Mc 0.61 0.61Value of parameter defining ellipse 1 in compression, Rc 1.5 1.5Parameter defining the gradient of ellipse 2 on p′ axis, δ 5.0 5.0

Hardening parametersShape hardening parameter in triaxial compression, hc 2.0 2.0Ratio of triaxial extension to triaxial compression value of h, he/hc 0.05 0.05Deviatoric hardening parameter, β1 0.5 0.4Unloading hardening parameter, Hu 0.2 0.2

Note: e, void ratio; p′ and q, stress variables in triaxial space, where p′ = (σ1′ + 2σ3′ )/3, q = σ1′ – σ3′ , and σ1′ and σ3′ are the princi-ple effective stresses.

Table 2. Constitutive model parameters for Nevada sand.



of Re = Rc will give sufficiently accurate predictions formost noncohesive soils.

(8) The hardening parameters during loading, hc and he, canusually be calibrated using the portion of the stress pathon a q–p′ plot during the initial contraction portion. Ne-vada sand started its dilation very early in the tests,however. Therefore these parameters were calibrated us-ing a cyclic test.

(9) The parameter δ plays a major role only for very loosesoils that exhibit a falling stress path during undrainedshear. For other soils, a value of 5.0 can be used to pro-vide sufficient accuracy.

(10)The hardening parameters hc, he, and Hu and the param-eter Io/I are all calibrated using a cyclic triaxial test.Since each of these parameters affects different portionsof a cyclic test, they can be easily calibrated. For exam-ple, hc affects the stress path on a q–p′ plot during load-ing on the compression side (Fig. 3, portion AB);

similarly, Hu and he affect portions BC and CD, respec-tively (Fig. 3). The value of Io/I is adjusted to match thestrains and the number of cycles.

The calibrated model parameters for Nevada sand at 60%relative density are used to predict behavior along a stresspath not used in the calibration procedure. Predicted resultsfor an anisotropically consolidated drained test (p′ constant)are compared with measurements in Fig. 4. The ability ofthe model to predict the behavior along a stress path not

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Fig. 3. An undrained cyclic triaxial test (CIUC) used in the cali-bration of constitutive model parameters for Nevada sand with arelative density of 60% (initial confining pressure 80 kPa).

Fig. 4. Comparison of measurements and constitutive model pre-dictions for an anisotropically consolidated drained (p′ constant)compression test of Nevada sand at 60% relative density (p′ =80 kPa).

Fig. 5. Finite element mesh used in the DYSAC2 predictions.



used in the calibration shows the generalization capability ofthe model.

DYSAC2 predictions

The constitutive model parameters listed in Table 2 wereused in DYSAC2 to predict the dynamic behavior of the twocentrifuge model embankments. Model test results were pro-vided to the predictors only after they had submitted theirpredictions to the organizing committee, and therefore theseanalyses are termed blind analyses. The finite element meshused for the predictions is shown in Fig. 5 and contained152 elements and 153 nodes. The same mesh was used inboth the predictions. The predictions were carried out in themodel scale and the results are reported in the prototypescale. Model times and displacements were multiplied by afactor of 50, and model accelerations were divided by 50 toobtain the prototype quantities. Coefficient of permeabilityvalues of 2.72 × 10–3 and 3.30 × 10–3 m/s were used for Dr =62% and 43%, respectively, in the predictions. As explainedpreviously, due to scaling, these values are 50 times higherthan those measured in the laboratory at 1g.

Prior to dynamic analyses, static analyses were performedusing a companion computer code SAC2 (Herrmann andMish 1983) and the same constitutive model parameterslisted in Table 2. Static analyses simulated the centrifugespin-up and provided the initial stresses for the dynamicanalyses. Static analyses prior to dynamic analyses are oftenoverlooked but are extremely important to obtain the initialstresses accurately. The importance of static analyses is il-lustrated in a subsequent section.

Embankment with a relative density of 62%Measured results for the dense sand embankment are pre-

sented and compared with the predictions in this section.Only the base acceleration – time histories, placement den-sity, and instrument locations were provided to the predic-tors. Since the tests were performed prior to the start of the

predictions, the actual base motion and the density wereused in the predictions. It is deemed unnecessary to adjustthe constitutive model parameters, however, and the parame-ters corresponding to Dr = 60% given in Table 2 were used.

The horizontal and vertical input (base) acceleration–timehistories used in the predictions are shown in Fig. 6. Themaximum input horizontal acceleration (amax) is 0.42g. Themeasured and predicted deformation patterns of the model atthe end of the test are shown in Figs. 7 and 8. A photographof the final locations of the spaghetti sticks is shown inFig. 7. The measured final position of the surface of the em-bankment is shown together with the measured positions ofthe spaghetti sticks in Fig. 8. The deformation pattern pre-dicted by DYSAC2 is also shown in Fig. 8. To compare withthe measured deformation pattern, hypothetical spaghettisticks were drawn through the finite element mesh and theirdeformations were tracked by interpolating nodal displace-ment values. These hypothetical spaghetti sticks are alsoshown in Fig. 8. Since the static analysis using SAC2 pre-dicted very little deformation within the embankment, onlythe predicted dynamic deformations are plotted in Fig. 8.The predicted final shape of the surface agrees with the mea-sured shape very well. The predicted deformation patterns ofthe spaghetti sticks agree reasonably well with the measuredpatterns on the mild slope side; however, DYSAC2 under-predicted the movement of spaghetti sticks on the steepslope side. Considering the fact that the entire problem wasanalyzed as a boundary value problem, it is not clear whyDYSAC2 predicted deformations well along the mild slopebut not along the steep slope. It is also interesting to notethat if one sees only the final deformed shape of the em-bankment surface (Fig. 8), it might be perceived that the em-bankment underwent very little deformation. By looking atthe final positions of the spaghetti sticks, however, it is veryclear that substantial deformations occurred within the em-bankment parallel to the slopes.

The measured and predicted settlement–time histories atlocation LVDT 1 (Fig. 1) are shown in Fig. 9. DYSAC2 pre-

© 2004 NRC Canada


Fig. 6. Input acceleration (Acc.) – time histories for the 62% relative density model.



dicted the total crest settlement (35 cm) well, however, thepredicted rate is higher than the measured rate. Measuredand predicted acceleration–time histories are shown inFigs. 10 and 11. DYSAC2-predicted accelerations are in rea-sonably good agreement with the measured values. Themeasured and predicted quantities are plotted to the samescale but in different plots due the close agreement between

the two at several locations. The measured and predictedtime histories can be compared by overlaying the two plots.Measured and predicted accelerations at locations ACC 4and ACC 5 (not shown here) are similar to those shown atACC 3 in Fig. 10. Accelerometer 8 rotated during shaking,and therefore the measured values are considered to belower than the actual values. One of the missing features in

© 2004 NRC Canada


Fig. 7. Locations of the spaghetti sticks (initially vertical) after shaking for the 62% relative density model.

Fig. 8. Measured and predicted deformations for the 62% relative density model (displacements are plotted without magnification). t,time.



© 2004 NRC Canada


Fig. 9. Measured and predicted surface settlement – time histories at location LVDT 1 for the 62% relative density model.

Fig. 10. Measured and predicted acceleration–time histories at locations ACC 6 and ACC 3 for the 62% relative density model.



the predictions is the large asymmetric peaks in the acceler-ometer records at locations ACC 6 (positive) and ACC 7(negative). These two locations are along the slope, and bycomparing the direction of shaking shown in Fig. 1 it can beseen that the observed large peaks are directed towards thecenter of the embankment. The reason for these accelerationpeaks is discussed later in the paper.

The measured and predicted excess pore-water pressure –time histories are shown in Figs. 12–14, which also show thecalculated initial effective vertical stresses, σvo′ . Overall, theDYSAC2 predictions are in reasonably good agreement withthe measured values in reference to magnitudes and trends atall locations. As expected, the highest excess pore-waterpressure was measured and predicted at location PPT B inthe center of the embankment. Only momentary liquefaction(excess pore-water pressure = initial effective vertical stress)was observed and predicted at some locations. It is interest-ing to note that, despite the permeability being 50 timeshigher than that at 1g, some liquefaction is measured andpredicted. Careful comparison of the time histories will

reveal that DYSAC2 predicted slightly higher overall (areaunder the time history and the time axis) positive excesspore-water pressures or slightly less dilation at locationsPPT D and PPT F along the slopes. This slightly lessdilative behavior seen in DYSAC2 is discussed in relation toaccelerations and settlements in a subsequent section.

Embankment with a relative density of 43%Measured results for the medium-dense sand embankment

are presented and compared with the predictions in this sec-tion. The predictors were requested to make their predictionsfor this model assuming a relative density of 40% and thesame base motion as shown in Fig. 6. Constitutive modelparameters corresponding to Dr = 40% and listed in Table 2were used in the predictions. The predictions were again car-ried out without any knowledge of the measurements. Theactual horizontal and vertical acceleration – time historiesmeasured during the test are shown in Fig. 15. The actualhorizontal base acceleration (amax = 0.48g) is slightly higherthan the input horizontal acceleration (amax = 0.42g, Fig. 6)

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used for DYSAC2 predictions. The relative density of themodel tested (43%) is also slightly higher than that used inthe predictions.

The measured and predicted deformation patterns of themodel at the end of the test are shown in Figs. 16 and 17. Aphotograph of the final locations of the spaghetti sticks isshown in Fig. 16, and the measured final position of thesurface of the embankment is shown together with the mea-sured positions of the spaghetti sticks in Fig. 17. The defor-mation pattern predicted by DYSAC2 is also shown inFig. 17. Again, DYSAC2 predicted the deformed shape ofthe surface and the deformation patterns of the spaghettisticks on the mild slope side reasonably well; however, simi-lar to the Dr = 62% embankment, deformations of the spa-ghetti sticks on the steep slope side were underpredicted. Bycomparing Figs. 8 and 17 (both measured and predicted),one can clearly see that there are increased movements alongboth sides of the embankment for the medium-dense sand.The difference in movements between both the embank-

ments is, however, substantially greater on the mild slopeside. This observation is somewhat counterintuitive. Somepossible explanations for this counterintuitive behavior aregiven later in the paper.

Measured and predicted settlement–time histories at loca-tion LVDT 1 are shown in Fig. 18. The measured crest set-tlement is 75 cm as opposed to the predicted value of 62 cm.This discrepancy could be explained by the lower input ac-celeration values used in the DYSAC2 predictions as men-tioned previously. It can also be seen that the predicted rateof settlement is closer to the measured value than for theDr = 62% case.

The measured and predicted acceleration–time historiesare shown in Figs. 19 and 20, and the excess pore-waterpressure – time histories in Figs. 21–23. Acceleration re-sponses at locations ACC 4 and ACC 5 are similar to thoseat location ACC 3 shown in Fig. 19. Accounting for the vari-ations in input motions, predicted acceleration–time historiescan be considered to match the measured ones reasonably

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Fig. 12. Measured and predicted excess pore-water pressure (PWP) – time histories at locations PPT D and PPT A for the 62% rela-tive density model.



well except for the large asymmetric peaks seen at locationsACC 6 and ACC 7. Larger peaks, in comparison with theDr = 62% case, can be seen at locations ACC 6 and ACC 7.Momentary liquefaction is again measured and predicted atseveral locations despite the permeability being 50 timeshigher than that at 1g. The predicted pore-pressure magni-tudes and trends are in good agreement with the measuredquantities. In general, less cyclic pore pressures were pre-dicted at all locations except PPT E, where slightly morecyclic pore pressure is predicted.

Discussion of the predictions and testresults

Some of the discrepancies seen between the measured andpredicted quantities pointed out in the previous sections arediscussed in this section, and further insight into the dy-namic behavior of these embankments is provided.

A schematic illustration of the stress–strain behavior of asand element undergoing cyclic mobility in undrained tri-

axial shear is shown in Figs. 24a and 24b. This behavior hasbeen well documented in the literature (for example, seeIshihara 1985). The expected excess pore pressure (∆u) –time history is shown in Fig. 24c. The quantities q and p′ aredefined earlier in the paper (see Table 2), and εq is thedeviatoric strain. This sand element has an initial deviatoricstress of q0 and is subjected to a cyclic loading of qd

+ and qd−.

The illustration shown in Fig. 24 is a simplified representa-tion of a sand element along a slope subjected to dynamicloading. Downslope and upslope directions are marked inFig. 24a. Along a slope, the initial stress state and the dy-namic loading will deviate from the triaxial case and therewill be partial drainage. The aforementioned representationis sufficient, however, to discuss the behavior in a qualita-tive sense. The initial shear stresses will be in the upslopedirection to counteract the gravity forces, resulting in a posi-tive q0 as shown in Fig. 24a. The cyclic deviatoric stresses,qd

+ and qd−, are a result of acceleration components of the

base motion in the upslope and downslope directions, re-spectively. Due to the initial shear stress bias, the phase

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Fig. 13. Measured and predicted excess pore-water pressure – time histories at locations PPT E and PPT B for the 62% relative den-sity model.



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Fig. 14. Measured and predicted excess pore-water pressure – time histories at locations PPT F and PPT C for the 62% relative den-sity model.

Fig. 15. Measured input acceleration – time histories for the 43% relative density model (DYSAC2 predictions were made using thetime histories in Fig. 6).



transformation line will be reached first on the upslope sideas shown in Fig. 24a. If q0 is greater than qd

−, then the phasetransformation line in the downslope direction will not bereached.

If we follow a stress path PQRSTUV soon after the up-slope phase transformation line has been reached, the sandwill initially contract during the unloading phase from P to

Q, positive pore pressure will develop, and there will be aconsiderable reduction in soil moduli. As soon as the load-ing begins downslope at Q, significant strains will accumu-late due to these low moduli (Fig. 24b). Dilation, whichcommences at R, will stiffen the soil and gradually arrestthis strain accumulation. During the unloading in the down-slope direction, soil will again contract along ST and will

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Fig. 16. Locations of the spaghetti sticks (initially vertical) after shaking of the 43% relative density model.

Fig. 17. Measured and predicted deformations for the 43% relative density model (displacements are plotted without magnification).



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Fig. 18. Measured and predicted surface settlement – time histories at location LVDT 1 for the 43% relative density model.




develop positive pore pressures and the moduli will reduce,but this reduction will be less than that along PQ. When theupslope loading begins at T, there will be accumulation ofupslope strains; however, smaller pore pressures generatedalong ST and larger dilation along UV will restrict the up-slope strains to values smaller than the downslope strains.The result is a net strain accumulation downslope as shownin Fig. 24b. As shown in Fig. 24c, two cycles of excess porepressure will result for each cycle of loading. If q0 is largerthan qd

−, then the downslope phase transformation line willnot be reached and each cycle of loading will produce only asingle cycle of excess pore pressure. Furthermore, contrac-tion along unloading segments will be smaller and, corre-spondingly, strain accumulation along subsequent loadingsegments will also be smaller. Larger values of q0, however,will bring a stress path to the phase transformation linequickly.

The aforementioned stress–strain response is reflected inthe measured pore-water pressure and acceleration recordsalong the slopes. Acceleration values along the slopes are re-lated to shear stresses (equivalent to qd

+ and (qd− – q0) shown

in Fig. 24a). Large spikes can be seen in the measured accel-erometer response along the slopes (ACC 6 and ACC 7), inthe upslope directions, for both Dr = 62% and Dr = 43%(Figs. 10, 11, 19, and 20). These large spikes are also ac-companied by dilation spikes in the measured pore-pressureresponses along the slopes (PPT D and PPT F) as shown inFigs. 12, 14, 21, and 23. Lee and Schofield (1988) also ob-served these acceleration and corresponding pore-pressurespikes in embankments and provided a similar explanation.As mentioned previously, the only major difference betweenthe DYSAC2 predictions and the measured results is thesmaller dilation peaks, such as at points similar to P and V(Fig. 24), and the corresponding smaller upslope accelera-tion peaks. Although the exact reason for this difference isnot yet known, it is suspected that the boundary conditionof no relative displacement between the soil and the baseimposed in DYSAC2 analyses restricted the upslope anddownslope cyclic movements and contributed to this dis-crepancy.

Larger dilation spikes during upslope loading generallymeans subsequently larger contraction, generation of sub-

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stantial pore pressures, and then large strain accumulationswhen loaded in the downslope direction as seen in Figs. 24aand 24b. Elgamal et al. (1996) also discussed these dilationspikes and pointed out that they only occur at large shearstrains. In other words, the presence of a large number of di-lation spikes is an indication of large strain accumulation.The mild slope in the Dr = 43% embankment showed sub-stantially more dilation spikes than the mild slope in theDr = 62% embankment. The observed spaghetti stick patternand the predicted DYSAC2 deformations confirmed thatlarger movements did indeed occur within the mild slope ofthe Dr = 43% embankment compared with those in the Dr =62% embankment. For a given embankment, by comparingthe response on both sides of the embankment, it can beseen that the mild slope side had a substantially larger num-ber of dilation spikes for both embankments. This impliesthat the mild slope side would have accumulated morestrains than the steep slope side. Testing Nevada sand slopesin a centrifuge, Pilgrim (1998) also observed that gentleslopes can deform more than steeper slopes under certain

conditions. Although the DYSAC2 predictions are inagreement with this observation, the measured spaghettistick patterns do not support this observation. In fact, themeasured spaghetti stick patterns indicate that the steepslope of the Dr = 62% embankment moved about the sameamount or slightly more than the steep slope of the Dr =43% embankment. Considering the fact that the entire prob-lem was analyzed as a boundary value problem, it is notclear why DYSAC2 predicted deformations well along themild slope but not along the steep slope. As mentioned pre-viously, no slip bottom boundary conditions used in theanalyses could have contributed to this discrepancy. Thereare also no plausible explanations for experimental errors inthe spaghetti stick patterns on the steep slope. The reasonsfor this discrepancy are being investigated further.

For a given cyclic stress ratio (qd+ to qd

−) and initial confin-ing pressure p0′ , the farther the initial stress state from the p′axis, the faster the stress path will reach the phase transfor-mation line on the upslope side and begin to accumulatestrains in the downslope direction. If the initial stress state is

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Fig. 21. Measured and predicted excess pore-water pressure – time histories at locations PPT D and PPT A for the 43% relative den-sity model.



substantially away from the p′ axis such as when q0 is high,the cyclic stress path may not reach the phase transformationline in the downslope direction. This will lead to dilationand contraction only on the upslope side and consequentlysmaller acceleration and pore-pressure spikes and associatedsmaller deformations in the downslope direction. This is thereason that the steep slope sides with large initial static shearstresses showed smaller and fewer spikes. A higher q0 valuehas two counteracting effects on the deformations. On theone hand, a higher q0 value brings the stress path quickly tothe phase transformation line and begins to accumulate sub-stantial strains. On the other hand, it limits the contractionduring unloading and associated softening and strain accu-mulation. These two counteracting effects can potentiallyproduce larger or smaller deformations within a steep slopethan a mild slope, depending on the level of shaking.

The distance of the initial stress state from the phasetransformation line (the quantity z shown in Fig. 24a) is anindicator of whether or not a stress path will reach the down-slope phase transformation line. For a given initial confining

pressure p0′ , the higher the value of z, the closer the initialstress state to the p′ axis, and therefore the cyclic stress pathwill likely reach the downslope phase transformation line. Inother words, the dynamic behavior is controlled by the ini-tial stress state. This is the reason the static analysis per-formed prior to a dynamic analysis is very important, asmentioned previously.

The amount of excess pore-water pressure developed priorto the stress point reaching the phase transformation line( )∆ud (the noncyclic component) will also depend on thisquantity z. The quantity z is equal to p0′ – q0/Mu, wherep0′ and q0 are the initial stresses and Mu is the slope of thecritical state line (related to the phase transformation line).A smaller value of z will result in a lower value of ∆ud . Thequantity equivalent to z in the general stress space is I –J/Nu, where I and J are defined by eqs. [1] and [2] and Nu isthe slope of the critical state line in I–J space (Fig. 2).

Contours of the quantity I – J/Nu obtained in the staticanalysis of the Dr = 40% case are shown in Fig. 25, whichshows that the I – J/Nu values under the mild slope are

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Fig. 22. Measured and predicted excess pore-water pressure – time histories at locations PPT E and PPT B for the 43% relative den-sity model.



larger, on average, than those under the steep slope. Porepressure transducer locations A–F are also plotted in Fig. 25.By observing these locations in the contour plot of I – J/Nu,it can be predicted that maximum positive dynamic porepressures will occur at location B, and locations A, E, and Cwill reach approximately the same positive dynamic porepressures but less than that at B. Locations D and F willhave approximately the same pore pressure, but less thanthose at locations A, E, and C. The measured pore pressuresconfirm this observation. Contours of I – J/Nu for the Dr =62% case are also very similar to those in Fig. 25, and this isthe reason that the maximum positive pore pressures reachedfor both the embankments are approximately equal. There-fore, quite a lot can be said about the dynamic behavior bystudying the initial static stresses. Furthermore, if one inte-grates the value of the quantity I – J/Nu under each slope, itcan be seen that the mild slope will generate more positivepore pressures during shaking and therefore will havesmaller soil moduli. In addition, more points under the mildslope will reach the downslope phase transformation line,

and this will result in larger acceleration and pore-pressurespikes and deformation. Smaller values of I – J/Nu, however,will bring the stress paths quickly to the phase transforma-tion line, resulting in earlier strain accumulation. These twocounteracting effects will result in the final dynamic defor-mation of a slope.

Summary and conclusions

The centrifuge model test results of two submerged sandembankments are presented and compared with blind predic-tions made by a fully coupled analysis procedure, the com-puter code DYSAC2. The centrifuge model embankmentswere constructed using Nevada sand placed at 62% (dense)and 43% (medium dense) relative densities and consisted ofa mild slope on one side and a steep slope on the other side.Both models were subjected to similar base motions. Thecomputer code DYSAC2 solves the coupled dynamic gov-erning equations for fluid-saturated porous media and usesbounding surface elastoplastic constitutive models to de-

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Fig. 23. Measured and predicted excess pore-water pressure – time histories at locations PPT F and PPT C for the 43% relative den-sity model.



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scribe the stress–strain behavior of soils. The followingobservations and conclusions can be made from both thecentrifuge model tests results and the DYSAC2 predictions:(1) The medium-dense sand embankment settled twice as

much as the dense sand embankment. Both embank-ments showed substantial movements along the slopes.If only the surface deformations were measured, itmight have been perceived that the embankments under-went much smaller deformations. Spaghetti sticks in-serted at the central cross sections of the embankmentsclearly showed the large movements along the slopes.Therefore, it is important to measure deformations with-in centrifuge and field embankments during earthquakesto better understand the deformation mechanisms.

(2) Although the movements along the steep slope sides ofboth embankments were comparable, the movementalong the mild slope side in the medium-dense sand em-bankment was substantially larger than that in the densesand embankment.

(3) Both embankments showed acceleration spikes alongthe slopes. These acceleration spikes were pointed in theupslope direction and corresponded to matching dilationspikes in the pore-pressure response along the slopes.These spikes were substantially more pronounced in themedium-dense sand embankment. Furthermore, in bothembankments there were more spikes on the mild slopeside than on the steep slope side.

(4) The aforementioned spikes and related deformation be-havior can be explained using the well-known labora-tory stress–strain behavior of sands undergoing cyclicmobility. Cyclic loading of sands undergoing cyclicmobility along slopes produces asymmetric stress pathssimilar to that shown in Fig. 24. These asymmetricstress paths cause the sand elements to reach the phasetransformation line on the upslope side first and producedilation during loading and contraction and relatedpore-pressure increase during unloading along theupslope direction. This pore-pressure increase reducesthe soil moduli and produces large strains during subse-quent loading along the downslope direction.

(5) The asymmetric stress paths are key to producing theaforementioned spikes. The asymmetric stress paths willbe produced when there is an initial static shear stressand loading takes place along the slopes. If the initialstatic shear stresses are large, however, the downslopephase transformation line may not be reached and thespikes will be smaller and fewer. This is the reason forless pronounced spikes on the steep slope sides of theembankments.

(6) The closer the initial stress state point to the phasetransformation line, the smaller the noncyclic compo-nent of the generated pore-water pressure, but theshorter the amount of time taken for the stress state toreach the phase transformation line.

(7) Since the initial static stress state influences subsequentdynamic behavior substantially, it is important to per-form accurate static analysis prior to a dynamic analy-sis.

(8) The blind predictions using the computer code DYSAC2compared reasonably well with the measured results.Overall, accelerations, pore-water pressures, and defor-mations within the mild slopes were predicted reason-ably well. DYSAC2, however, predicted much lesspronounced spikes in acceleration and pore-pressure re-cords and underpredicted deformations within the steep

Fig. 24. Stress–strain and excess pore-water pressure – time his-tory of a sand undergoing cyclic mobility in triaxial undrainedshear.



slopes. No slip bottom boundary conditions used in theanalyses could have contributed to these discrepancies.

The centrifuge test results and observations presented inthis paper should provide valuable insight into the behaviorof submerged sand embankments, such as those used forport facilities and offshore drilling operations, in seismic ar-eas. Prediction of deformations during earthquake loading isone of the important aspects in the design of a new geo-technical engineering structure or in the seismic evaluationof an existing structure. Fully coupled analysis proceduressuch as DYSAC2 provide not only the seismic deformations,but also invaluable insight into the overall seismic behaviorof geotechnical engineering structures. The blind predictionssimilar to that shown in this paper should go a long way inconvincing the practitioners to use such fully coupled proce-dures with confidence for design applications.

Acknowledgements

The writers would like to thank K. Arulanandan of theUniversity of California, Davis, the principal investigator ofthe VELACS Extension Project, for providing an opportu-nity to participate in this project. Discussions withA.W. Elgamal of the University California, San Diego, onthe behavior of sand along the slopes are appreciated.K.D. Mish provided the contouring package used to createFig. 25. N. Ravichandran and T. Vinayagam assisted in cre-ating some of the figures. Partial support for the work pre-sented in this paper was provided by a grant from the U.S.National Science Foundation to the University of Oklahoma(grant CMS-9501718).

References

Adalier, K., Elgamal, A.W., and Dobry, R. 1997. VELACS Exten-sion Project, RPI centrifuge tests. Technical report prepared forthe National Science Foundation, Department of Civil Engi-neering, Rensselaer Polytechnic Institute, Troy, N.Y.

Arulanandan, K. 1996. Summary of VELACS Extension Project.Technical report prepared for the National Science Foundation,Department of Civil Engineering, University of California, Da-vis, Calif.

Arulanandan, K., and Scott, R.F. (Editors). 1993. Verification ofNumerical Procedures for the Analysis of Soil LiquefactionProblems, Proceedings of the International Conference, Davis,Calif., 17–20 Oct. 1993. A.A. Balkema, Rotterdam, The Nether-lands.

Arulmoli, K., Muraleetharan, K.K., Hossain, M.M., and Fruth, L.S.1992. VELACS, verification of liquefaction analyses by centri-fuge studies — laboratory testing program — soil data report.Technical report prepared for the National Science Foundationby The Earth Technology Corporation, Irvine, Calif. Availablefrom http://geoinfo.usc.edu/gees/velacs/ [cited XXXX].

Been, K., and Jefferies, M. G. 1985. A state parameter for sands.Géotechnique, 35(2): 99–102.

Dafalias, Y.F., and Herrmann, L.R. 1986. Bounding surface plastic-ity II: application to isotropic cohesive soils. Journal of theEngineering Mechanics Division, ASCE, 112(12): 1263–1291.

Dafalias, Y.F., and Popov, E.P. 1976. Plastic internal variables for-malism of cyclic plasticity. Journal of Applied Mechanics,98(4): 645–650.

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.

Fugro West, Inc. 1999. Geotechnical study — Pier 400, Stage 2 —Phase 1 container wharf, Port of Los Angeles, California. Tech-nical report prepared for Port of Los Angeles. Vol. 1. FugroWest, Inc., Ventura, Calif.

Herrmann, L.R., and Mish, K.D. 1983. User’s manual for SAC2: atwo-dimensional, nonlinear, time dependent, soil analysis codeusing the bounding surface plasticity model. Technical Report,Department of Civil Engineering, University of California, Da-vis, Calif.

Hilber, H.M., Hughes, T.J.R., and Taylor, R.L. 1977. Improved nu-merical dissipation for time integration algorithms in structuraldynamics. Earthquake Engineering and Structural Dynamics, 5:283–292.

Iai, S., Ichii, K., Liu, H., and Morita, T. 1998. Effective stress anal-yses of port structures. In Soils and Foundations, Special IssueNo. 2 on the Geotechnical Aspects of the January 17, 1995Hyogoken-Nambu Earthquake), Japanese Geotechnical Society,Tokyo. pp. 97–114.

Ishihara, K. 1985. Stability of natural deposits during earthquakes.In Proceedings of the 11th International Conference on SoilMechanics and Foundation Engineering, San Francisco, Calif.,

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Fig. 25. Contours of the quantity I – J/Nu (distance from the critical state line to the initial stress state in the invariant stress space) atthe end of the static analysis for the 43% relative density model (values are in kPa). A–F, pore pressure transducer locations.



12–16 Aug. 1985. Vol. 1. A.A. Balkema, Rotterdam, The Neth-erlands. pp. 321–376.

Jones, S.G., Buzzoni, G., Foxworthy, J., Menendez, A., andShahrestani, S. 2001. Twenty-first century terminal. Civil Engi-neering Magazine, ASCE, 71(12): 38–41.

Lee, F.H., and Schofield, A.N. 1988. Centrifuge modeling of sandembankments and islands in earthquakes. Géotechnique, 38(1):45–58.

Makdisi, F.I., and Seed, H.B. 1978. Simplified procedures for esti-mating dam and embankment earthquake-induced deformations.Journal of the Geotechnical Engineering Division, ASCE,104(7): 849–867.

Manzari, M.T., and Dafalias, Y.F. 1997. A critical state two-surfaceplasticity model for sands. Géotechnique, 47(2): 255–272.

Matsuo, O. 1996. Damage to river dikes. In Soils and Foundations,Special Issue No. 1 on the Geotechnical Aspects of the Janu-ary 17, 1995 Hyogoken-Nambu Earthquake, Japanese Geo-technical Society, Tokyo. pp. 235–240.

Muraleetharan, K.K., Mish, K.D., Yogachandran, C., and Arula-nandan, K. 1988. DYSAC2 (version 1.0): dynamic soil analysiscode for 2-dimensional problems. Computer Code, Departmentof Civil Engineering, University of California, Davis, Calif.

Muraleetharan, K.K., Arulmoli, K., Jagannath, S.V., Wittkop, R.C.,and Foxworthy, J.E. 1994a. Validation of a computer code forthe analysis of dike retaining structures. In Centrifuge 94, Pro-ceedings of the International Conference, Singapore, 31 Aug. –2 Sept. 1994. Edited by C.F. Leung, F.H. Lee, and T.S. Tan.A.A. Balkema, Rotterdam, The Netherlands. pp. 203–208.

Muraleetharan, K.K., Mish, K.D., and Arulanandan, K. 1994b. Afully-coupled non-linear dynamic analysis procedure and its ver-ification using centrifuge test results. International Journal forNumerical and Analytical Methods in Geomechanics, 18:305–325.

Muraleetharan, K.K., Arulmoli, K., Wittkop, R.C., and Foxworthy,J.E. 1997a. Use of centrifuge and numerical modeling in the de-

sign of Port of Los Angeles’ Pier 400. In Centrifuge modeling,intelligent geotechnical systems, and reliability-based design.Transportation Research Record 1582. pp. 13–21.

Muraleetharan, K.K., Mish, K.D., Yogachandran, C., and Arula-nandan, K. 1997b. User’s manual for DYSAC2 (version 7.0):dynamic soil analysis code for 2-dimensional problems. Techni-cal Report, School of Civil Engineering and Environmental Sci-ence, University of Oklahoma, Norman, Okla.

Newmark, N.M. 1965. Effects of earthquakes on dams and em-bankments. Géotechnique, 15(2) : 139–160.

Pilgrim, N.K. 1998. Earthquake-related deformation beneath gentlyinclined ground. Géotechnique, 48(2): 187–199.

Popescu, R., and Prevost, J.H. 1994. Comparison betweenVELACS numerical ‘class A’ predictions and centrifuge experi-mental soil test results. Soil Dynamics and Earthquake Engi-neering, 14: 79–92.

Prevost, J.H. 1998. DYNAFLOW user’s manual. Technical Report,Department of Civil Engineering and Operations Research,Princeton University, Princeton, N.J.

Seed, H.B. 1979. Consideration in the earthquake-resistant designof earth and rockfill dams. Géotechnique, 29(3): 215–263.

Tani, S. 1996. Damage to earth dams. In Soils and Foundations,Special Issue No. 1 on the Geotechnical Aspects of the January17 1995 Hyogoken-Nambu Earthquake, Japanese GeotechnicalSociety, Tokyo. pp. 263–272.

Wittkop, R.C. 1993. Applications of VELACS philosophy to Portof Los Angeles Pier 400 project. In Verification of Proceduresfor the Analysis of Soil Liquefaction Problems, Proceedings ofthe International Conference, Davis, Calif., 17–20 Oct. 1993.Vol. 2. Edited by K. Arulanandan and R.F. Scott. A.A. Balkema,Rotterdam, The Netherlands. pp. 1647–1655.

Yogachandran, C. 1991. Numerical and centrifuge modeling ofseismically induced flow failures. Ph.D. dissertation, Universityof California, Davis, Calif.

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dynamic deformations in sand embankments: centrifuge modeling and blind, fully coupled analyses

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