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Numerical modeling of liquefaction and comparison with centrifuge tests Peter M. Byrne, Sung-Sik Park, Michael Beaty, Michael Sharp, Lenart Gonzalez, and Tarek Abdoun Abstract: The prediction of liquefaction and resulting displacements is a major concern for earth structures located in regions of moderate to high seismicity. Conventional procedures used to assess liquefaction commonly predict the trig- gering of liquefaction to depths of 50 m or more. Remediation to prevent or curtail liquefaction at these depths can be very expensive. Field experience during past earthquakes indicates that liquefaction has mainly occurred at depths less than about 15 m, and some recent dynamic centrifuge model testing initially appeared to confirm a depth or confining-stress limitation on the occurrence of liquefaction. Such a limitation on liquefaction could greatly reduce remediation costs. In this paper an effective stress numerical modeling procedure is used to assess these centrifuge tests. The results indicate that a lack of complete saturation and densification at depth arising from the application of the high-acceleration field are largely responsible for the apparent limitation on liquefaction at depth observed in some centrifuge tests. Key words: liquefaction, dynamic centrifuge modeling, numerical modeling, depth limitation. Résumé : La prédiction de la liquéfaction et des déplacements qui en résultent est une préoccupation majeure pour les structures en terre localisées dans des régions de séismicité moyenne à forte. Les procédures conventionnelles utilisées pour évaluer la liquéfaction prédisent communément le déclenchement de la liquéfaction à des profondeurs de 50 m et plus. Le confortement pour prévenir ou réduire la liquéfaction à ces profondeurs peut coûter très cher. L’expérience sur le terrain durant les derniers séismes indique que la liquéfaction s’est produite principalement à des profondeurs infé- rieures de moins de 15 m, et des essais dynamiques récents sur modèle en centrifuge ont semblé confirmer une limita- tion de la profondeur ou de la contrainte de confinement pour la génération de la liquéfaction. Une telle limitation sur la liquéfaction pourrait réduire considérablement les coûts de confortement. Dans cet article, on utilise une procédure de modélisation numérique en contrainte effective pour évaluer les essais de centrifuge. Les résultats indiquent qu’un manque de saturation complète de même qu’une densification à une profondeur résultant de l’application du champ des fortes accélérations sont largement responsables de la limitation apparente sur la liquéfaction en profondeur observée dans certains essais au centrifuge. Mots clés : liquéfaction, modélisation dynamique centrifuge, modélisation numérique, limitation de la profondeur. [Traduit par la Rédaction] Byrne et al. 211 Introduction The prediction of liquefaction and resulting displacements is a major concern for earth structures located in regions of moderate to high seismicity. This is particularly so for earth dams where large displacements could lead to overtopping and sudden release of the reservoir, with life safety con- cerns. The standard procedure used to assess liquefaction com- monly predicts the triggering of liquefaction to depths of 50 m or more. Remediation to prevent or curtail liquefaction at these depths can be very expensive. Field experience dur- ing past earthquakes (Youd et al. 2001) indicates that lique- faction has mainly occurred at depths less than 15 m, and some recent dynamic centrifuge model testing (Steedman et al. 2000) suggests a depth or confining-stress limitation on the occurrence of liquefaction. Such a limitation on excess pore pressure development could greatly reduce remediation costs, but confirmation requires reliable data and an im- proved understanding of the liquefaction process through analysis. The seismic behaviour of soil structures to a design earth- quake is generally assessed from a three-stage total stress analysis involving (i) a dynamic analysis to compute the cy- clic stress ratios (CSR) for comparison with the cyclic resis- tance ratio (CRR) to identify zones that will liquefy; (ii)a Can. Geotech. J. 41: 193–211 (2004) doi: 10.1139/T03-088 © 2004 NRC Canada 193 Received 14 January 2003. Accepted 10 October 2003. Published on the NRC Research Press Web site at http://cgj.nrc.ca on 25 March 2004. P.M. Byrne 1 and S.-S. Park. Department of Civil Engineering, University of British Columbia, 2324 Main Mall, Vancouver, BC V6T 1Z4, Canada. M. Beaty. California Department of Water Resources, P.O. Box 942836, Sacramento, CA 94236, U.S.A. M. Sharp. Centrifuge Research Center, Engineer Research and Development Center, U.S. Army Corps of Engineers, Vicksburg, MS 39180, U.S.A. L. Gonzalez and T. Abdoun. Department of Civil Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, U.S.A. 1 Corresponding author (e-mail: [email protected]).
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Page 1: Byrne Model

Numerical modeling of liquefaction andcomparison with centrifuge tests

Peter M. Byrne, Sung-Sik Park, Michael Beaty, Michael Sharp, Lenart Gonzalez,and Tarek Abdoun

Abstract: The prediction of liquefaction and resulting displacements is a major concern for earth structures located inregions of moderate to high seismicity. Conventional procedures used to assess liquefaction commonly predict the trig-gering of liquefaction to depths of 50 m or more. Remediation to prevent or curtail liquefaction at these depths can bevery expensive. Field experience during past earthquakes indicates that liquefaction has mainly occurred at depths lessthan about 15 m, and some recent dynamic centrifuge model testing initially appeared to confirm a depth orconfining-stress limitation on the occurrence of liquefaction. Such a limitation on liquefaction could greatly reduceremediation costs. In this paper an effective stress numerical modeling procedure is used to assess these centrifugetests. The results indicate that a lack of complete saturation and densification at depth arising from the application ofthe high-acceleration field are largely responsible for the apparent limitation on liquefaction at depth observed in somecentrifuge tests.

Key words: liquefaction, dynamic centrifuge modeling, numerical modeling, depth limitation.

Résumé : La prédiction de la liquéfaction et des déplacements qui en résultent est une préoccupation majeure pour lesstructures en terre localisées dans des régions de séismicité moyenne à forte. Les procédures conventionnelles utiliséespour évaluer la liquéfaction prédisent communément le déclenchement de la liquéfaction à des profondeurs de 50 m etplus. Le confortement pour prévenir ou réduire la liquéfaction à ces profondeurs peut coûter très cher. L’expérience surle terrain durant les derniers séismes indique que la liquéfaction s’est produite principalement à des profondeurs infé-rieures de moins de 15 m, et des essais dynamiques récents sur modèle en centrifuge ont semblé confirmer une limita-tion de la profondeur ou de la contrainte de confinement pour la génération de la liquéfaction. Une telle limitation surla liquéfaction pourrait réduire considérablement les coûts de confortement. Dans cet article, on utilise une procédurede modélisation numérique en contrainte effective pour évaluer les essais de centrifuge. Les résultats indiquent qu’unmanque de saturation complète de même qu’une densification à une profondeur résultant de l’application du champ desfortes accélérations sont largement responsables de la limitation apparente sur la liquéfaction en profondeur observéedans certains essais au centrifuge.

Mots clés : liquéfaction, modélisation dynamique centrifuge, modélisation numérique, limitation de la profondeur.

[Traduit par la Rédaction] Byrne et al. 211

Introduction

The prediction of liquefaction and resulting displacementsis a major concern for earth structures located in regions ofmoderate to high seismicity. This is particularly so for earth

dams where large displacements could lead to overtoppingand sudden release of the reservoir, with life safety con-cerns.

The standard procedure used to assess liquefaction com-monly predicts the triggering of liquefaction to depths of50 m or more. Remediation to prevent or curtail liquefactionat these depths can be very expensive. Field experience dur-ing past earthquakes (Youd et al. 2001) indicates that lique-faction has mainly occurred at depths less than 15 m, andsome recent dynamic centrifuge model testing (Steedman etal. 2000) suggests a depth or confining-stress limitation onthe occurrence of liquefaction. Such a limitation on excesspore pressure development could greatly reduce remediationcosts, but confirmation requires reliable data and an im-proved understanding of the liquefaction process throughanalysis.

The seismic behaviour of soil structures to a design earth-quake is generally assessed from a three-stage total stressanalysis involving (i) a dynamic analysis to compute the cy-clic stress ratios (CSR) for comparison with the cyclic resis-tance ratio (CRR) to identify zones that will liquefy; (ii) a

Can. Geotech. J. 41: 193–211 (2004) doi: 10.1139/T03-088 © 2004 NRC Canada

193

Received 14 January 2003. Accepted 10 October 2003.Published on the NRC Research Press Web site athttp://cgj.nrc.ca on 25 March 2004.

P.M. Byrne1 and S.-S. Park. Department of CivilEngineering, University of British Columbia, 2324 MainMall, Vancouver, BC V6T 1Z4, Canada.M. Beaty. California Department of Water Resources,P.O. Box 942836, Sacramento, CA 94236, U.S.A.M. Sharp. Centrifuge Research Center, Engineer Researchand Development Center, U.S. Army Corps of Engineers,Vicksburg, MS 39180, U.S.A.L. Gonzalez and T. Abdoun. Department of CivilEngineering, Rensselaer Polytechnic Institute, Troy,NY 12180, U.S.A.

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

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limit equilibrium analysis to assess post-liquefaction stabil-ity using residual strengths in the liquefied zones; and, if noflow slide is predicted, then (iii) a simple dynamic analysisusing the strength of the soil to assess permanent displace-ments induced by shaking. The prediction of liquefaction atdepth in dynamic analysis occurs largely as a result of thereduction in CRR with increasing confining stress, or the Kσeffect, which is noted in laboratory element tests.

The aforementioned analyses represent the current state ofpractice. Such analyses are not fundamental and are notlikely to improve our basic understanding of the liquefactionprocess because they do not directly consider pore pressuresin the prediction of liquefaction. Pore pressures are indi-rectly allowed for in the reduced strength and stiffness val-ues used after liquefaction is triggered.

Effective stress analyses for assessing liquefaction havebeen available for more than 25 years and are more funda-mental. Triggering of liquefaction and post-liquefaction sta-bility and resulting displacements can be considered in asingle time domain analysis. Such analyses are generallybased on capturing the element behaviour from laboratorytests and then considering the soil structure to comprise acollection of such elements with both generation and dissi-pation of pore water pressure occurring as shaking proceeds.In this way the weaker and (or) more heavily loaded ele-ments are predicted to liquefy first, and the resulting dis-placements increase with time in a phenomenon referred toas lateral spreading. If sufficient elements liquefy and theirresidual strength is insufficient for static stability, a flowslide will result. Effective stress analyses have the capabilityof predicting observed liquefaction response.

The validation of effective stress modeling is very impor-tant, but it is difficult to achieve from field case historiesbecause the soil conditions and input motion are seldomknown with sufficient accuracy. The best documented casehistories are those of the Upper and Lower San Fernandodams and their responses to the 1971 San Fernando earth-quake, but even for these cases there is considerable uncer-tainty about conditions and loading.

Model tests can be conducted in the laboratory under con-trolled conditions and their response observed. Because soilbehaviour is highly stress dependent, however, small modelsunder a 1g acceleration field are not representative of fieldconditions. On the other hand, centrifuge tests that utilize ahigh acceleration field preserve the stress–strain response ofthe prototype soil and can give a more realistic representa-tion of field behaviour. Such models, when subjected to acontrolled base motion, can provide a database for the vali-dation of numerical approaches.

Although centrifuge testing provides a seemingly idealtool for validating numerical models, its application is notalways straightforward. A major validation initiative (Arula-nandan and Scott 1993) using centrifuge tests was carriedout in the 1990s and was termed a mitigated disaster by Pro-fessor R. Scott in his oral presentation. Some of the reasonsfor this assessment were due to aspects of the centrifugetests, including the boundary conditions in the centrifugebox, the use of water as a pore fluid and the resulting highrate of drainage, and the lack of verification of saturation.The validation process also showed the necessity of modelsto rationally consider the generation and dissipation of ex-

cess pore pressure during shaking. At that time, a very lim-ited number of numerical models were successful in accom-plishing this task.

In this paper a numerical procedure is used in which bothgeneration and dissipation of pore fluid pressure are consid-ered. The procedure is applied to predict the results of cen-trifuge tests that investigate liquefaction at large depths. Thecharacteristic liquefaction behaviour of Nevada sand used inthe models was obtained from undrained cyclic simple sheartests and is the basis for the numerical predictions of thecentrifuge tests. Several factors had to be considered to ac-curately predict the centrifuge results, including the changein density caused by the confining stresses induced in thecentrifuge and the effects of degree of saturation.

A comparison of predicted and measured centrifugemodel response is presented in this paper. Prior to the pre-diction, a brief description of the numerical model is pre-sented. In addition, the effects of saturation and stressdensification on liquefaction response are discussed.

Effective stress numerical modeling ofliquefaction

Cyclic shear strains induce plastic volume compaction ingranular soils. Martin et al. (1975) presented quantitativedata in their landmark paper and showed that the amountof compaction per cycle is proportional to the cyclic shearstrain amplitude and accumulated volume compaction and isindependent of normal effective stress. They also showedthat the pore pressure generated per cycle is dependent onthe plastic volumetric strain, the rebound modulus of thesoil, and the stiffness of the pore fluid. They integrated theseconcepts in a loose-coupled effective stress analysis and suc-cessfully predicted liquefaction response.

Fully coupled effective stress approaches that considershear-induced pore pressures at each time step rather than ateach cycle or half cycle have been developed by manyresearchers, including Dafalias (1986), Prevost (1989), Zien-kiewicz et al. (1990), Byrne et al. (1995), Beaty and Byrne(1998), Elgamal et al. (1999), and Kramer and Arduino(1999). The numerical procedure used in this paper is a fullycoupled approach called UBCSAND (Puebla et al. 1997;Beaty and Byrne 1998). It is based on plasticity theory andthe characteristic sand behaviour observed in laboratory testsunder monotonic and cyclic loading conditions. It is pre-sented briefly in the following sections.

Elastic responseThe elastic component of response is assumed to be iso-

tropic and specified by a shear modulus, G e, and a bulkmodulus, Be, as follows:

[1] G K PP

B G

G

n

e ea

a

e e

e

= ′

=

σ

α

where KGe is a shear modulus number, which depends on the

density of the sand and varies from about 500 for loose sandto 2000 for dense sand; Pa is atmospheric pressure in thechosen units; ′σ is the mean stress in the plane of loading,

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

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where ′σ = (σx′ + σy′)/2; ne is an elastic exponent that variesbetween 0.4 and 0.6, or approximately 0.5; and α dependson the elastic Poisson’s ratio, which is in the range 0.0–0.2(Hardin 1978), with the result that α varies between 2/3 and4/3 or is approximately unity.

Plastic responsePlastic strains are controlled by the yield loci, which are

assumed to be radial lines starting at the origin of stressspace as shown in Fig. 1. For first-time shear loading, theyield locus is controlled by the current stress state, point Ain Fig. 1. As the shear stress increases, the stress ratioη τ/σ(= ′) increases and causes the stress point to move topoint B, where τ and ′σ are the shear and normal effectivestresses, respectively, on the plane of maximum shearstress. The yield locus is dragged to the new location pass-ing through point B and the origin. This results in plasticstrains, both shear and volumetric. The plastic shear strainincrement, d pγ , is related to the change in shear stress ratio,dη, as shown in Fig. 2 and can be expressed as

[2] d dpp

γσ

η=′

1G /

where Gp is the plastic shear modulus and, assuming a hy-perbolic relationship between η and γp, is given by

[3] G G Rip p

ff= −

1

2ηη

where Gip is the plastic modulus at a low stress ratio level

(η = 0); ηf is the stress ratio at failure and equals sin φf ,where φf is the peak friction angle; and Rf is the failure ratioused to truncate the best fit hyperbolic relationship and pre-vent the overprediction of strength at failure. Rf generallyvaries between 0.70 and 0.98 and decreases with increasingrelative density. It has been useful to relate Gi

p to G e and rel-ative density Dr through the approximate relationship Gi

p ≈3.7(Dr)

4G e + Pa.The associated increment of plastic volumetric strain, d v

pε ,is related to the increment of plastic shear strain, d pγ ,through the flow rule as follows:

[4] d dvp

cvpε φ τ

σγ= −

sin

where φcv is the constant-volume friction angle or phase-transformation angle. This flow rule can be derived from en-ergy considerations and is similar to stress dilation theory(Rowe 1962; Matsuoka and Nakai 1977).

The yield loci and direction of the plastic strains resultingfrom the flow rule are shown in Fig. 3. Figure 3 shows thatat low stress ratios, significant shear-induced plastic com-paction is occurring, whereas no compaction is predicted atstress ratios corresponding to φcv. For stress ratios greaterthan φcv, shear-induced plastic expansion or dilation is pre-dicted. This simple flow rule is in close agreement with thecharacteristic behaviour of sand observed in laboratory ele-ment testing. Upon unloading (reducing stress ratio), thesand is assumed to behave elastically. Upon reloading, thesand is assumed to behave plastically but with a plasticmodulus that is several times stiffer than that for first-time

loading until the prior maximum value is reached, at whichpoint it reverts to first-time loading.

The sign of the stress ratio is controlled by the sign of theshear stress on the horizontal plane, and positive and nega-tive values are tracked separately. This means that the plastichardening includes kinematic rather than simple isotropicbehaviour. The characteristic drained behaviour of sand un-der cyclic loading observed by Martin et al. (1975), andadditional data reported by Byrne (1991) in which plastic

© 2004 NRC Canada

Byrne et al. 195

Fig. 1. Yield locus.

Fig. 2. Plastic strain increment and plastic modulus.

Fig. 3. Directions of plastic strains (flow rule).

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

volumetric strains accumulate with cycles of load but at adecreasing rate, is well captured by the model.

The response of sand is controlled by the skeleton behav-iour. A fluid (air–water mix) in the pores of the sand acts asa volumetric constraint on the skeleton if drainage is cur-tailed. It is this constraint that causes the pore pressure risethat can lead to liquefaction. Provided the skeleton ordrained behaviour is appropriately modeled under monotonicand cyclic loading conditions and the stiffness of the porefluid and drainage are accounted for, the liquefaction re-sponse can be predicted. This is the approach taken here,and the concepts discussed previously are incorporated inUBCSAND.

This model was used with the computer code FLAC (fastLagrangian analysis of continua), version 4.0 (Itasca Con-sulting Group Inc. 2000). This program models the soil massas a collection of grid zones or elements and solves the cou-pled stress flow problem using an explicit time stepping ap-proach. The program has a number of built-in stress–strainmodels, including an elastic–plastic Mohr–Coulomb model,and UBCSAND is a variation of this model in which frictionand dilation angles are varied to incorporate the yield lociand flow rule described earlier. Pore fluid stiffness andDarcy hydraulic flow are basic to the FLAC program, soonly the skeleton stress–strain relation is needed to simulateliquefaction. Drained, undrained, or coupled stress flow con-ditions are specified by the user.

The key elastic and plastic parameters can be expressed interms of relative density, Dr, or normalized standard penetra-tion test values, (N1)60. Initial estimates of these parametershave been approximated from published data and model cal-ibrations. The response of sand elements under monotonicand cyclic loading can then be predicted and the resultscompared with laboratory data. In this way, the model canbe made to match the observed response over the range ofrelative density or (N1)60 values.

Model simulation of saturated undrainedsimple shear

A soil element under simple shear undrained loading con-ditions is shown in Fig. 4. The predicted response to a cyclicshear stress of 11 kPa is shown in Fig. 5 for an initial stressstate with σvo′ = 100 kPa, K = 0.5, and density correspondingto (N1)60 = 8. σvo′ is the initial vertical effective stress andK0⋅ ′σvo is the initial horizontal effective stress. For strainsless than 0.05%, Fig. 5a shows the predicted stress strain re-sponse and Fig. 5b shows the rising pore pressure as thenumber of cycles and amplitude of strain increase. The pre-dicted response at large strain is shown in Fig. 6. Figure 6shows that once the excess pore pressure reaches about 85%of the initial effective stress, successive dilation and contrac-tion pulses occur and the stress–strain loops (Fig. 6a) aremuch softer and have a different characteristic shape as com-pared to the pre-liquefaction response.

The predicted effective stress path is shown in Fig. 7. Af-ter about five cycles, flow liquefaction occurs with an asso-ciated large decrease in effective stress, bringing the stressstate to the phase-transformation line (path A). At this pointthe element dilates and recovers resistance as shown by pathB in Figs. 6 and 7. Upon subsequent unloading, the stress

path passes through the origin (zero effective stress). Thisleads to a very low shear modulus that increases with anincrease in shear strain as the sample dilates. It is this alter-nating contraction–dilation response of sand that causes thecharacteristic post-liquefaction behaviour observed in labo-ratory test elements and predicted by the model.

Fig. 4. Element under simple shear loading.

Fig. 5. Undrained cyclic simple shear response for small strain.

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The model has also been calibrated to predict liquefactiontriggering response in terms of normalized standard penetra-tion resistance (N1)60 in agreement with the National Centerfor Earthquake Engineering Research (NCEER) chart (Youdand Idriss 1997). The predicted CSR to cause liquefaction in

15 cycles versus (N1)60 is shown in Fig. 8 along with theNCEER chart relationship based on field experience. Themodel is shown to be in close agreement with the field data.

Centrifuge tests overview

Centrifuge model tests to evaluate liquefaction response athigh confining stress have been carried out at the EngineerResearch and Development Center (ERDC), U.S. ArmyCorps of Engineers, Vicksburg, Mississippi. The modelscomprised a dense sand layer with Dr ≈ 80% overlying aloose sand layer with Dr ≈ 50%. High confining stresseswere achieved by application of a surface layer of lead.

Nevada sand was used for the tests. Preliminary centrifugeresults were presented by Steedman et al. (2000) and indi-cated that there is a cutoff confining pressure above whichliquefaction will not occur. The data suggest this pressure is

© 2004 NRC Canada

Byrne et al. 197

Fig. 9. Stress densification of Nevada sand, one-dimensional datafrom Arulmoli et al. (1992) and eq. 5.

Fig. 8. Comparison of predicted (UBCSAND) and field-observed(NCEER Chart) liquefaction resistance.

Fig. 7. Effective stress path.

Fig. 6. Undrained cyclic simple shear response for large strain.

Page 6: Byrne Model

about 300 kPa, and Steedman et al. contend that field evi-dence supports this finding. If this is the case, then hugesavings in retrofit costs for many existing dams and bridgesare possible, since present analyses procedures indicate thattreatment to curtail or prevent liquefaction is often necessaryto depths where pressures are well in excess of 300 kPa.

To verify such a cutoff, additional centrifuge tests werecarried out at Rensselaer Polytechnic Institute (RPI) (Gonza-lez et al. 2002). These tests indicated no cutoff confiningstress for stresses up to 380 kPa but did show trends in thedevelopment of pore pressure and liquefaction which werenot consistent with state of practice or with state-of-the-artliquefaction analysis.

There are a number of possible reasons for the differencesbetween the two sets of centrifuge data and current analysisprocedures, including (i) characteristics of the centrifugemodel containment box, (ii) saturation of the model and porefluid stiffness, and (iii) stress densification effects. Thesepossibilities are briefly discussed in the following sections,followed by a more detailed discussion of stress densifi-cation and pore fluid stiffness.

Characteristics of the containment boxIn both ERDC and RPI tests a laminar box comprised of

rings allowing lateral shear movements (lateral strain in thelong direction of the box, parallel to shaking) was used. TheERDC box had a stiff sealant between rings, whereas in theRPI box the rings were separated by linear roller bearings(free to slide laterally). Therefore, upon liquefaction, theERDC box could offer significant lateral resistance thatcould influence the dynamic response of the model and themeasured accelerations.

Model saturationThe RPI models were saturated using a process that in-

volved replacement of air with carbon dioxide gas and thendisplacement and dissolving of the gas by the introductionof high-viscosity water under vacuum. In the ERDC tests,the viscous fluid was introduced at the base of the samplewithout prior removal of air by carbon dioxide or applicationof vacuum. In neither case was the degree of saturation orstiffness of the pore fluid evaluated by measurement of thecompression wave or other means.

Stress densificationThe density of the sand in the model will change with

stress. The authors believe that at high confining stress suchchanges could be quite significant and impact the numericalmodeling of the soil response. The stress densification ofsands is discussed in more detail later in this paper.

Purpose of numerical analysesThe purpose of the effective stress analysis carried out

here is to obtain a measure of understanding of the impor-tance of various aspects of the testing, including the charac-teristics of the box, the degree of saturation of the pore fluid,and stress densification effects. Prior to examining the cen-trifuge data and the results of the analyses, the effect ofstress densification and pore fluid stiffness are addressed.

Stress densification

The sand in the centrifuge model is first placed in the testbox under a 1g acceleration field at a specific void ratio ordensity. At this stage the stresses in the model are very lowand the densities are as placed. Upon spin-up to 100g, thestresses increase 100-fold, with high stresses at the base andlow stresses at the surface. These stresses induce compactionin the model, causing a significant increase in density at thebase and little change at the surface. This density change cancurtail liquefaction in the high-stress region near the base ofthe model and can be responsible for unexpected liquefac-tion response if it is not taken into account. For example,consider a uniform sand layer with the water table at the sur-face subjected to base motion causing little or no amplifica-tion. Current analysis procedures would predict liquefactionto occur first at the base and perhaps base isolate the upperlayers. Yet, under these conditions in the centrifuge whenthe initial sand density is uniform, liquefaction always oc-curs at the surface first. This unexpected result is likelycaused by stress densification.

The amount of stress densification depends on thecompressibility of the soil and can be estimated from one-dimensional compression tests. The results of such compres-sion tests on Nevada sand are shown in Fig. 9. The increasein relative density, Dr, is approximately proportional to thesquare root of vertical effective stress. It also depends on theplacement density, with higher placement densities havingless subsequent stress densification.

Examination of compression data on a number of sands(Park and Byrne 2004) indicates that all sands examinedseem to behave in a similar manner and that the stress densi-fication effect can be expressed by

[5] D DP

r rv

a

= + ′

0 α σ

where Dr 0 is the initial relative density at 0 kPa; σv′ is thevertical effective stress; and

α = +−

−( ) ( )max

max min

1 20

0ee e

DD

Cr

r1.5

in which emax and emin are the maximum and minimum voidratio, respectively; and C is a sand stiffness number that isindependent of void ratio.

The range in sand stiffness number C for a few sands isshown in Table 1. The results indicate that Nevada sand hasa stiffness number in the middle range of the data for othersands and thus is moderately sensitive to stress densificationeffects. It may be of interest to note that Marcuson andBieganousky (1977) did consider stress densification effectsin their large-scale chamber tests when evaluating stress anddensity effects on penetration resistance.

Effect of pore fluid stiffness on generatedpore pressures

The pore pressures of concern for liquefaction are thosegenerated by plastic volumetric strain. Pore pressures mayalso be generated by transient changes in total stress, but

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

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these lead to small changes in effective stress unless the soilis partially saturated. An applied load increment will inducea total volumetric strain increment, dεv, that is the sum ofthe elastic and plastic increments, d v

eε and d vpε , respectively.

For undrained conditions the resulting change in pore pres-sure, du, is

[6] d dfvu

B

n= ε

where Bf is the bulk stiffness of the pore fluid, and n is theporosity. The corresponding change in effective mean stress,d ′σ , to an increment of volumetric strain is

[7] d deve′ =σ εB

The increment of total mean stress, dσ, is equal to the in-crements of effective mean stress and pore pressure. If, forsimplicity, we assume dσ = 0, then du = − ′dσ . Substitutingfrom eqs. [6] and [7] gives

[8] d d de

e

f

vp

Skemptone

vpu

BB

B n

B B=+

=1

/

ε ε

where BSkempton is the Skempton value commonly used to as-sess the saturation of samples in the laboratory. It is clear

© 2004 NRC Canada

Byrne et al. 199

Fig. 11. Hydraulic conductivity of Nevada sand (Arulmoli et al.1992).

Fig. 10. Variation of fluid stiffness with initial saturation for var-ious current absolute (abs) pressures (p).

Fig. 12. Cyclic resistance of Nevada sand (Arulmoli et al. 1992;Kammerer et al. 2000). Ncyc, number of cycles to liquefaction.

Sand Gs

D50

(mm) Cu emax emin C

Brasted sand (BS) 2.68 0.25 2.42 0.790 0.480 500Ottawa sand (OS) 2.67 0.40 1.54 0.820 0.500 370Toyoura sand (TS) 2.65 0.19 1.24 0.963 0.605 300Nevada sand (NS) 2.67 0.17 2.00 0.887 0.511 220Fraser River sand (FRS) 2.72 0.30 1.56 1.000 0.680 270Volcanic sand (VS) 2.44 0.17 2.38 1.810 0.970 105Mine tailing sand (MTS) 2.68 0.40 1.67 1.060 0.690 150Quiou sand (QS) 2.71 0.70 4.50 1.200 0.780 100

Note: Cu is the coefficient of uniformity; D50 is the mean grain size; Gs is the specific gravity.

Table 1. Material properties and sand stiffness number C.

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that the ratio of the skeleton stiffness to pore fluid stiffness,B Be

f/ , is a major factor in pore pressure response.From Boyle’s law, and assuming the same pressure in

both water and air, Bf is found to be a function of p, the cur-rent absolute pressure of the fluid, and Sr0, the saturation atzero gauge pressure (p = 100 kPa), as given by

[9] BpS P

fr a

kPa≅−

< ×2

0

6

12 10

( )

Sr0 approximates the initial saturation in a centrifugemodel prior to spin-up. If the pores are completely filledwith water, then Bf = 2 × 106 kPa, the bulk stiffness of water.If Be = 6 × 104 kPa and n = 1/3, then BSkempton = 0.99 anddu = 0.99Be d v

pε . But if the degree of saturation were reducedto Sr0 = 0.98, then Bf drops to 5000 kPa at p = 100 kPa, withBSkempton = 0.2 and du = 0.2Be d v

pε .Poor saturation at low pore pressure will lead to a reduced

pore pressure response to load. This is particularly so if theskeleton stiffness is high. This may occur in a centrifugemodel near the water table when it is at depth or when a sur-face load is applied. For a water table at the surface and nosurface load, BSkempton may still be high, as the skeleton stiff-ness will be low.

If the water pressure p in the soil increases, as it wouldduring spin-up, then water will flow into the voids, compressthe air, and increase Bf. This increase in fluid stiffness withan increase in pressure is included in eq. [9] and the subse-quent numerical simulations. The fluid stiffness, Bf, for arange of initial saturation and pressure conditions is shownin Fig. 10. The initial degrees of saturation in excess of99.9% are required to obtain Bf > 5 × 105 kPa for pore pres-sures less than 100 kPa gauge. Such values of Bf will gener-ally produce a liquefaction response similar to that of a fullysaturated condition. Initial saturation is seen to be very im-portant and can have a very large effect on pore pressure riseand liquefaction response, which varies with depth in themodel.

Properties of Nevada sand

The hydraulic conductivity and liquefaction resistance ofNevada sand used in the centrifuge tests and the modelingare as follows.

The hydraulic conductivity, k, used in the analyses isbased on constant-head permeability tests carried out for theVELACS program (Arulmoli et al. 1992). The results areshown in Fig. 11, where k varies between 6.6 × 10–5 m/s atlow relative density to 2.3 × 10–5 m/s at high relative density.The values shown are for water as a pore fluid under a 1gfield. For centrifuge tests in an acceleration field N timesgreater than gravity, the effective k will be N times greater. Ifthe viscosity of the fluid is M times greater than water, as itmay be for the centrifuge tests, then k would reduce by afactor M. Thus,

[10] k kNM

* =

where k* is the effective hydraulic conductivity in the centri-fuge, and k is the hydraulic conductivity of the soil in a 1genvironment using water as a pore fluid.

The liquefaction response of Nevada sand was based oncyclic simple shear tests carried out for the VELACS project(Arulmoli et al. 1992) and tests carried out at the Universityof California at Berkeley (Kammerer et al. 2000). The re-sults of these tests are shown in Fig. 12 in terms of CSR ver-sus number of cycles to liquefaction for a range of relativedensities. The predicted liquefaction response of the sandfrom the numerical model for a fully saturated state is shownby the lines in Fig. 12, which capture the data quite well.For both the laboratory tests and the numerical model, lique-faction was assumed to occur when the cyclic strain ampli-tude reached 3.75%.

RPI test results and analysis

Three centrifuge model tests conducted at the RPI centri-fuge facility were examined in detail. The models used Ne-vada sand and simulate level ground conditions subjected toa harmonic base input motion. The frequency of the inputmotion was selected to reduce the potential for amplificationin the model. The conditions for the three models are listedin Table 2 and are described in the following sections.

Centrifuge model 1Model 1 is comprised of a uniform sand layer with a

placed relative density of Dr = 55%. It was subjected to anacceleration field of 120g, and the fluid viscosity was 60times that of water. The fluid table is at the surface of themodel. No surcharge was applied at the surface, and themaximum initial effective stress at the base was 380 kPa.

Centrifuge model 2Model 2 is comprised of a uniform sand layer with a

placed relative density of Dr = 55% but with a surchargeload that resulted in a pressure of 140 kPa at the applied 80gacceleration field. The surcharge load simulates a sand col-umn above the fluid table. This condition also gave an effec-tive stress at the base of 380 kPa.

Centrifuge model 3Model 3 is comprised of a dense layer (Dr = 75%) overly-

ing a looser layer (Dr = 55%). It was subjected to an acceler-ation field of 80g and had a surface load of 140 kPa. Thiscondition also gave an effective stress at the base of380 kPa.

Numerical modelsThe centrifuge models were analyzed with a single

column of elements. This one-dimensional representation isequivalent to assuming the stresses and strains in the centri-fuge model are uniform across any horizontal plane. Bound-ary constraints were placed on the model so that the top ofeach soil element remained horizontal during loading andthe width of the model remained virtually constant. This al-lowed each element to compress or expand in a verticaldirection and to experience shearing deformations due tohorizontal shear stresses. Secondary response modes, suchas rocking, were not represented.

The only other effect of the containment box consideredin the analysis was its tendency to limit vertical deforma-tions of the sand through frictional resistance. This effect

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was only evaluated in ERDC test model 5a discussed afterthe RPI tests. The interface shear stresses on the boundarychange the total stresses experienced by the sand. This ef-fect, known as the silo effect, is a concern in centrifugemodeling due to the large increase in total stresses that oc-curs after placement of the sand in the box. This effect wasapproximately modeled by including interface elements oneach side of the sand column and assigning an interface fric-tion angle of 25°. Spin-up of the centrifuge was modeled bygradually increasing the gravitational force. The resultingstresses and strains in the sand elements were a function ofboth the induced gravitational load and the resisting inter-face stresses. These interface stresses, and their effect on to-

tal stress, can also change during model shaking because ofchanges in horizontal stress and pore pressures.

Initial saturation was not measured in any of the threemodels. An assumption of 100% saturation led to predic-tions of excess pore pressure rise that were significantlyfaster than those observed. Assumed saturation values ofabout 98.5% before spin-up were found to give the bestagreement with the measurements for the three RPI models.The precise values used are listed in Tables 3–5.

Results for RPI model 1A cross section of model 1, showing the locations of the

pore pressure transducers and accelerations, and the FLAC

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Byrne et al. 201

Relative density, Dr (%)

Layer

Initialsaturation,Sr0 (%)

Bf afterspin-up(kPa)

Permeability,k (m/s) Placed Spin-up

Top 99.0 2.5×104 3.1×10–5 75 79Middle 98.5 4.0×104 3.1×10–5 75 81Bottom 98.0 3.5×104 5.5×10–5 55 63

Table 5. Key input of model 3 in numerical analysis.

Relative density, Dr (%)

Layer

Initialsaturation,Sr0 (%)

Bf afterspin-up(kPa)

Permeability,k (m/s) Placed Spin-up

Top 99.0 1.3×104 5.5×10–5 55 60Middle 98.5 2.4×104 5.5×10–5 55 62Bottom 98.0 3.2×104 5.5×10–5 55 63

Table 4. Key input of model 2 in numerical analysis.

Relative density, Dr (%)

Layer

Initialsaturation,Sr0 (%)

Bf afterspin-up(kPa)

Permeability,k (m/s) Placed Spin-up

Top 98.5 0.2×105 8.2×10–5 55 55Middle 98.5 0.6×105 8.2×10–5 55 61Bottom 98.5 1.2×105 8.2×10–5 55 63

Table 3. Key input of model 1 in numerical analysis.

RPI

Model 1 Model 2 Model 3 ERDC, model 5a

Centrifuge acceleration (g) 120 80 80 50Fluid viscosity, µw 60 40 40 50Prototype soil depth (m) 38.0 24.0 24.0 26.3Surcharge load (kPa) 0 140 140 580Max σv′ (kPa) 380 380 380 836Relative density, Dr (%) 55 55 75 (top 16 m);

55 (bottom 8 m)72 (top 18 m);

51 (bottom 8 m)

Table 2. Centrifuge model tests.

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simulation model are shown in Fig. 13. The input motioncomprised 50 cycles of 0.2g at 1.5 Hz prototype scale. Theactual input motion amplitude varied somewhat with time,as shown in Fig. 14, and this was accounted for in the FLACsimulation. The effect of stress densification on relative den-sity Dr was estimated from eq. [5] and is shown in Fig. 15.This relationship indicates that Dr has increased from 55%to about 63% near the base of the layer.

The measured and predicted acceleration and excess porewater pressure time histories at prototype depths of 1.3, 6.3,13.1, 24.8, 30.8, and 37.0 m are shown in Figs. 16a and 16b.Apart from the 30.8 m depth, the patterns of predicted accel-erations in Fig. 16b are in good agreement with the measure-ments. It is apparent from the large reduction in accelerationamplitude with time that liquefaction has occurred first at ornear the surface and worked its way downward. Figure 16bshows that the predicted excess pore pressures are in goodagreement with the measured values. At a depth of 13.1 mthe excess pore water pressure has reached the initial verticaleffective stress corresponding to 100% pore pressure rise ata time of 6 s, indicating liquefaction. This time is in goodagreement with the change in acceleration pattern.

The time to reach 100% pore pressure rise increases withdepth, indicating that liquefaction occurs first near the sur-face and works its way downward. This is a somewhat sur-prising result, as the accelerations in the initial time phase

are about the same at all depths, perhaps somewhat higher atdepth. This leads to a constant applied stress ratio, and, if Drwere constant, standard practice would suggest that liquefac-

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

Fig. 15. Placed density and increased density of model 1.

Fig. 14. Base input motions of model 1.

Fig. 13. (a) Centrifuge model 1 setup and instrument locations. (b) FLAC model 1 measurement locations.

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tion should be triggered at the base first due to the Kσ effect.When the numerical simulation was carried out assumingconstant Dr with depth, the liquefaction did occur first at thebase and then worked its way upward. Only when increaseddensity at depth in accordance with stress densification wasconsidered did the analysis predict the observed pore pres-sure pattern.

The rate of excess pore pressure buildup was sometimesobserved to change with time. An example is shown inFig. 16b for a time of 4 s and a depth of 30.8 m. The rate ofpore pressure buildup is a function of the applied cyclicstress at the depth in question. This stress, in turn, is thesummation of the mass times the acceleration of all overly-ing masses. Hence, as the acceleration patterns change in theoverlying soil due to pore pressure changes, the rate of porepressure rise at the depth in question will also change. Dif-fering patterns of excess pore pressure rise with depth andtime are to be expected and are seen in both the measure-ments and predictions.

Figure 16b also shows that the measured cyclic pore pres-sure spikes after liquefaction are significantly larger thanpredicted. These spikes result from dilation, and the lowerpredicted values may be a result of assuming a rate of dila-tion at failure that was independent of effective stress level.Dilation is higher at the very low effective stresses that oc-cur at liquefaction, and this effect was not modeled.

Results for RPI model 2A cross section of model 2, showing the locations of the

pore pressure transducers and accelerometers, and the FLACsimulation model are shown in Fig. 17. In this model, the

placement Dr = 55% and a surface load is applied. The ap-plied base motion is shown in Fig. 18. The estimated effectof stress densification on relative density is shown in Fig. 19and indicates that Dr has increased from 55% to 60% nearthe surface and 63% near the bottom layer.

The predicted and measured acceleration and excess porewater pressure at prototype depths ranging from 0.7 to22.3 m are shown in Figs. 20a and 20b, respectively. Thepredicted and measured acceleration responses are in reason-able agreement, although the predicted accelerations in theupper 7 m decrease more quickly than the measured values.

The measured excess pore water pressures indicate thatliquefaction again occurs first at or near the surface andworks its way downward. In contrast, the predictions showliquefaction occurring first at some depth between 3.9 and13.0 m, with no subsequent liquefaction near the surface.The predicted pore water pressures below this depth are inreasonable agreement with the measurements but show afaster initial rise.

Predicted pore pressures at depth 7.4 m are shown inFig. 20b, but no measured pore pressures are available forcomparison. Liquefaction is predicted to occur first at a timeof 4 s at this depth. This has the effect of decoupling the pre-dicted accelerations above this depth, as shown in Fig. 20a.Once liquefaction occurs at any depth in this one-dimensional model, it causes a base isolation effect that re-sults in decoupling the accelerations at all depths above thezone of liquefaction. The predicted excess pore pressuresabove the depth of liquefaction may be quite low, yet theaccelerations at these depths still show a large reduction inresponse due to base isolation from the lower liquefied layer.

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Fig. 16. (a) Comparison between measured and predicted accelerations of model 1. (b) Comparison between measured and predictedexcess pore pressures of model 1.

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This is the case at 3.9 m depth, as shown in Fig. 20. Hereliquefaction is predicted to occur at depth 7.4 m, causing de-coupling at 7.4 and 3.9 m depths, even though liquefactionis not predicted at the 3.9 m depth.

The effect of the surface load in model 2 is to increase theapplied cyclic stress ratio (CSR) with depth, making lique-faction more likely to occur first at depth rather than at thesurface. The CSR for model 2 can be approximated by

[11] CSR v

v w

=′

= ++ −

ag

ag

hh

max max ( )( )

σσ

γγ γ

0

0

140140

where amax is the cyclic acceleration amplitude, g is theapplied acceleration field, 140 is the applied surface loadin kPa, h is the depth below the ground surface, γ is the unitweight of soil, and γw is the unit weight of water. Assumingamax is constant with depth prior to liquefaction, which wasthe intent of the experiments, CSR will increase with depth,varying from amax/g at the soil surface to about 1.6amax/g ata depth of 20 m. Triggering of liquefaction also depends onrelative density, which will increase with depth due to stressdensification. Hence, the location of first liquefaction de-pends on the importance of the CSR variation comparedto the relative density variation. The decoupling of bothmeasured and predicted acceleration and the measured andpredicted excess pore pressures (Fig. 20) suggest that lique-faction is first occurring at a depth of about 7 m at times of

7 and 4 s, respectively. The measured excess pore pressurealso shows liquefaction occurring at depth 3.9 m, whereasthe predicted pore pressures are significantly lower at thisdepth. It is possible that the higher measured pore pressures

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

Fig. 19. Placed density and increased density of model 2.

Fig. 18. Base input motions of model 2.

Fig. 17. (a) Centrifuge model 2 setup and instrument locations. (b) FLAC model 2 measurement locations.

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near the surface may result from impeded drainage resultingfrom the presence of the lead surface load.

Significant cyclic pore pressures are predicted prior to liq-uefaction in Fig. 20b for model 2. This is somewhat surpris-ing, as dilation effects would not be significant prior toliquefaction. Such pore pressure spikes were far less signifi-cant in Fig. 16b for model 1 where no surface load was ap-plied. The cyclic pore pressures observed in model 2 arelikely due to changes in total mean stress arising from rock-

ing rather than being induced by shear. This is indicatedfrom a comparison of measured pore pressure responses attransducers P5 and P6 located at depth 3.9 m, but left andright of centreline as shown in Fig. 17. The comparisonshowed pore pressure spikes that were 180° out of phase,i.e., the P5 positive spike occurred at the same time as theP6 negative spike. In the FLAC analysis the left and rightboundaries were forced to have the same horizontal and ver-tical displacements. This precluded any rocking effects and

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Fig. 21. (a) Centrifuge model 3 setup and instrument locations. (b) FLAC model 3 measurement locations.

Fig. 20. (a) Comparison between measured and predicted accelerations of model 2. (b) Comparison between measured and predictedexcess pore pressures of model 2.

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likely accounts for the difference in measured and predictedpore pressure response.

Results for RPI model 3A cross section of model 3, showing the locations of the

pore pressure transducers and accelerometers, and the FLACsimulation model are shown in Fig. 21. In this model thelower portion was placed at Dr = 55% and the upper at Dr =75% and a surface load was applied. The applied base mo-tion is shown in Fig. 22. The effect of stress densification onrelative density Dr is shown in Fig. 23 and indicates that Drhas increased from 75% to 81% in the dense layer and from55% to 63% in the bottom loose layer.

The predicted and measured accelerations and excess porewater pressures at prototype depths ranging from 0.6 to22.8 m are shown in Figs. 24a and 24b, respectively. Apartfrom at the depth of 13.4 m, the predicted and measured ac-celeration responses are in general agreement. The predictedinitial accelerations are significantly higher than the mea-sured values in the first few seconds at the shallower depths,however.

The predicted and measured excess pore pressures arealso in reasonably good agreement except for at the depth of19.3 m, where the predicted responses are too rapid com-pared with the measured values. Although the denser upperlayers generate significant pore water pressure, they do notliquefy.

The predicted accelerations in Fig. 24a indicate decoup-ling is occurring at about 4 s at depths above 13.4 m. Thepredicted pore pressures in Fig. 24b indicate high pore pres-sures occurred at depth 19.3 m after about 4 s, with Ru =70%, where Ru is the ratio of excess pore pressure to initialvertical effective stress. This is not enough to base isolateand cause decoupling. So why the decoupling at 4 s? Thelooser sand begins at depth 15 m and it is likely that lique-faction would first occur at or close to this depth. An exami-nation of predicted response at depths in addition to theobserved points shows that liquefaction, with Ru = 100%,first occurred at a depth of 15 m at a time of 4 s, and this ex-plains the predicted response.

The measured response of model 3 is more difficult to ex-plain. The measured pore pressures in Fig. 24b show a 100%pore pressure rise at depth 19.3 m after 20 s. This shouldhave caused decoupling of accelerations at all depths above19.3 m after 20 s. Instead, the measured accelerations indi-cate a gradual decoupling occurring above a depth of 7.4 m

during the time period 0–20 s. The abrupt reduction in rateof pore pressure generation at depth 19.3 m (Fig. 24b) afterabout 3 s indicates an abrupt reduction in CSR occurred atthis time. This could have been brought about by liquefac-tion occurring near the top of the loose layer at a time ofabout 3 s, in agreement with expected and predicted re-sponses.

Both the measured and predicted pore pressures show thatliquefaction did not occur in the denser sand above a depthof 7.4 m. Liquefaction did occur in the denser sand at depth13.4 m after 30 s due to upward drainage from the looserlayer below 15 m. Liquefaction also occurred in the loosersand below a depth of 15 m at the two measurement loca-tions after about 20 s.

Pore pressure spikes are much more noticeable in models2 and 3, which include a surcharge load, and may arise frominduced rocking that was not modeled in the numerical anal-ysis.

ERDC centrifuge tests

A number of centrifuge tests simulating earthquake load-ing under level ground conditions were conducted at ERDC,Vicksburg, Mississippi, and these have been described bySteedman et al. (2000). The main purpose of these tests was

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Fig. 23. Placed density and increased density of model 3.

Fig. 22. Base input motions of model 3.

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to investigate liquefaction response at high overburden pres-sures. The tests were conducted under a range of conditionsand can be broadly grouped into three categories: (1) uni-form loose sand, (2) dense over loose sand, and (3) denseover loose sand with a lead surface load.

Typical tests in each category were numerically modeledand the results compared with the test data (Byrne et al.2001). The comparison showed that the predicted and mea-sured accelerations and pore pressures were in reasonableagreement for categories 1 and 2, provided allowance was

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Fig. 25. (a) Centrifuge model 5a setup and instrument locations. (b) FLAC model 5a measurement locations.

Fig. 24. (a) Comparison between measured and predicted accelerations of model 3. (b) Comparison between measured and predictedexcess pore pressures of model 3.

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made for lack of saturation. The placed saturation was esti-mated at about 98% to get best overall agreement. For cate-gory 3 tests with lead loading, however, the agreement wasnot good, as shown in the next section for model 5a.

Model 5aA cross section of model 5a, showing the locations of the

pore pressure transducers and accelerometers and the FLACsimulation model, is shown in Fig. 25. In this model thelower portion was placed at Dr = 51% and the upper at Dr =72% and a surface load of 580 kPa was applied. The appliedbase motion is shown in Fig. 26. Results from the FLACsimulation are shown for two different assumptions for ini-tial saturation: 98% (Fig. 27) and 97% (Figs. 28, 29).

The predicted and measured accelerations and excess porewater pressures at prototype depths ranging from 5.5 to

25.3 m are shown in Figs. 27a and 27b, respectively. Thepredicted pore pressures are significantly higher than themeasured values, and the predicted accelerations are higherthan the measured values for an initial saturation of Sr0 =98%.

An initial Sr0 = 97% results in significantly lower porepressures that are in reasonable agreement with the measure-ments (Fig. 28b), but the predicted accelerations are higherthan the measured values (Fig. 28a). When stress den-sification is considered, the predicted pore pressures are sig-nificantly lower than the measured values in the loose layerat depth, as shown in Fig. 29b. Figures 27–29 clearly dem-onstrate the importance of both initial saturation and stressdensification.

Side friction in the ERDC box is a possibility and couldlead to significantly lower stresses, both total and effective,

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

Fig. 27. (a) Comparison between measured and predicted accelerations of model 5a. Sr0 = 98% without densification. (b) Comparisonbetween measured and predicted excess pore pressures of model 5a. Sr0 = 98% without densification.

Fig. 26. Base input motions of model 5a.

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Fig. 29. (a) Comparison between measured and predicted accelerations of model 5a. Sr0 = 97% with densification. (b) Comparison be-tween measured and predicted excess pore pressures of model 5a. Sr0 = 97% with densification.

Fig. 28. (a) Comparison between measured and predicted accelerations of model 5a. Sr0 = 97% without densification. (b) Comparisonbetween measured and predicted excess pore pressures of model 5a. Sr0 = 97% without densification.

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particularly near the base of the box, as discussed earlier.The predicted acceleration and pore pressure responses foran angle of wall friction of 25° and Sr0 = 97% consideringstress densification are shown in Figs. 30a and 30b, respec-tively. The predicted pore pressures are in reasonable agree-ment with the measurements, although the predictedaccelerations are high. It is possible that the curtailment andflattening off of the observed pore pressures could in fact bea liquefaction response resulting from lower than expectedtotal stresses due to side friction or the silo effect. Liquefac-tion was not predicted in the model, as the silo effect re-duced with shaking, in agreement with the observation ofWhitman and Lambe (1986).

Summary

Conventional liquefaction assessment procedures indicatethat liquefaction can occur to considerable depths in loose tomedium-dense sand strata. This is based on dynamic analy-sis and the results of element tests showing that the liquefac-tion resistance ratio reduces with an increase in confiningstress, the Kσ effect. Pore pressure measurements in bettersaturated centrifuge models conducted at RPI indicate that

liquefaction occurred at considerable depths (correspondingto an overburden stress of 300 kPa or more) in loose ormedium-dense sand strata. In centrifuge models where lique-faction occurred at large depths, the models did show trendsin the development of pore pressure and liquefaction thatwere not consistent with state of practice or with state-of-the-art liquefaction analysis. Numerical analyses wereperformed that indicate the centrifuge findings can be ex-plained in terms of the densification that occurs when highconfining stresses are imposed. Thus a sand that was placedat Dr = 55% densifies to Dr = 63% at an applied confiningstress of 380 kPa. This change in density can explain the de-velopment of liquefaction at the ground surface first, withlater propagation downward through the rest of the model.

Some ERDC centrifuge tests simulating the response of alevel ground sand system to seismic loading indicated thatliquefaction was curtailed at high confining stress in the300 kPa region. Thus the results of these centrifuge tests ap-peared to be in conflict with both standard procedure andRPI centrifuge tests. Numerical analyses indicate that thesecentrifuge findings can be explained in terms of stress den-sification, lack of saturation, and (or) the possibility that liq-uefaction is occurring at pore pressures significantly below

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

Fig. 30. (a) Comparison between measured and predicted accelerations of model 5a. Sr0 = 97% with densification and silo effect.(b) Comparison between measured and predicted excess pore pressures of model 5a. Sr0 = 97% with densification and silo effect.

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the overburden pressures as a result of reduced verticalstress arising from side friction or the silo effect.

Stress densification will also occur under field conditionsand will improve liquefaction resistance. But stress densifi-cation is accounted for in principle in conventional liquefac-tion assessment techniques that are based on penetrationresistance by correcting for confining stress. Penetration re-sistance values so corrected are a measure of relative densityand so should reflect density changes arising from stressdensification and other factors such as changes in the depo-sitional environment.

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Arulmoli, K., Muraleetharan, K.K., Hosain, M.M., and Fruth, L.S.1992. VELACS laboratory testing program, soil data report. Re-port to the National Science Foundation, Washington, D.C., bythe Earth Technology Corporation, Irvine, Calif.

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