""'-

350 Mitchell andTseng

[13] Duncan,J.M., Byrne,P. andWong,KS., "Strength,Stress-StrainandBulk ModulusParametersfor Finite ElementAnalysesof StressesandMovementsin Soil Masses",GeotechnicalEngineeringReportNo. UCBjCTj80-01, Universityof California,Berkeley,August1980.De Alba, P., Seed,RB., and Chan,C.K, "SandLiquefactioninLarge-ScaleSimpleShearTests",Journ. Geot.Engrg.,ASCE, Vol.102,No.GT9,Sept.1976,pp.909-927.Seed, H.B. and Lee, KL., IIUndrained CharacteristicsofCohesionlessSoils",Journ.Soil Mech.andFound.Div.,ASCE, Vol.93,No.SM6,Nov.1967,pp.117-141.~y~ Corporation,IIFirstReport on In Situ Site InvestigationforDeterminationof LiquefactionPotential",Preparedfor the U.S.NationalBureauof Standards,theU.S.Bureauof Rec1amation,andtheJapanesePublicWorksResearchInstitute,March1984.

[14]

[15]

[16]

'/

17SPT-BasedAnalysisofCyclicPorePressure

GenerationandUndrainedResidualStrength

* **RaymondB. Seed andLeslieF. Harder,fr.

INTRODUCTION

Prominent among Professor Harry Seed's major contributionstogeotechnicalen~ineeringwasthedevelopmentof methodsfor evaluationoftheseismicstabllityandperformanceof damscomprisedof, or foundedon,soils potentiallyvulnerableto liquefaction. This subjectcontinuedtointerestbimoverthepasttwentyyears,andtbeanalyticalprocedureswhichheandhiscolleaguesdevelopedcontinuedtoevolvetbroughoutthisperiodoThis paper,basedonrecentstudiesandworkin progressat thetimeof hisdeath,presentsa surnmaryoverviewof the most currenttechniquesadvocatedby DI. Seedandhis colleaguesfor suchstudies.Thesewill bepresentedandillustratedbymeansof applicationtothere-evaluationof theperformanceof the Lower San FernandoDam during the 1971SanFernandoEarthquake,providinga c1eardemonstrationof the methodsadvocatedandfacilitatingassessmentof theirperformancewhenappliedtotbisimportantcasebistory.

SUGGESTED APPROACH

Numerousengineersandinvestigatorshavecontributedsignificantlyoverthepast20yearsto thedevelopmentof theengineeringmethodsdescribedberein.Manyof theseindividualsworkedcloselywitbDr. Seed,wbilemanyothersworkedindependently.Thoughtoo numerousto individuallyciteherein,theircontributionsaregratefullyacknowledged.

~:;:

*Assoc.Prof. of Civil Engineering,Universityof California,Berkeley,CA94720. **SupervisingEngineer,Calif. Dept.of WaterResources,1416NinthS1.,Sacramento,CA 94236.

351

352 SeedandHarder

The followingproceduresfor evaluationof the seismicstabilityandperformanceof damscomprisedof, or foundedon,potentiallyliquefiablesoilsareevolvedfromproceduresoriginallydevelopedbyDr. Seedandhiscolleaguesin the early1970's[1,2]. The mostslgnificantchangessincetheirearlyinceptionare: (a)increasedrelianceonin-situtestsasaprimarybasisfor evaluationofsoilconditions,and(b)morerecentincorporationofresidualor "steadystate"strengthevaluationasa partof overallstabilityandperformanceassessment.Numerousother,moresubtlerefinementsinanalyticalproceduresand recommendedcorrelationswill be presentedwithinthecontextoftheoverallpresentation.

In simple,conciseterms,the recommendedapproachfor evaluationofliquefactionpotentialand seismicstabilityand performanceof damsinvolvestenbasicstepsasfollow:

1.2.

Determinethecross-sectionof thedamtobeusedforanalysis.Determine,withthecooperationof geologistsandseismologists,themaximumor mostseveretimehistoryof baseexcitationtowhichthedamanditsfoundationmightbesubjected.Determine,as accurately~,as possible,the stressesin theembankmentbeforetheearthquake;thisismosteffectivelydoneusingfiniteelementanalysistechniques.Determinethe dynamicpropertiesof the soilscomprisingthedam and foundation,such as shear modulus, dampingcharacteristics,and bulk modulusor Poisson'sratio, whichdeterminedynamicresponsecharacteristics. Since thesematerialcharacteristicsare nonlinear,it is also necessarytodeterminehowthepropertiesvarywithstrain.Compute,usingan appropriatedynamicfiniteelementanalysisprocedure,the acceleratlOnsandjor dynamicshear stressesmducedwithinthe embankmentandfoundation.For narrowcanyonswheretheratioof crestlength:maximumdamheightislessthanabout3:1,three-dimensionaleffectsassociatedwiththecanyonsidewallsmustbe accountedfor in theseanalyses.Two-dimensionalplane strain dynamicresponseanalysesaresufficientfor mostdamgeometrieswhere"crestlen~this longrelativeto embankmentheight. One-dimensional(columnar)analysesarenotgenerallyrecommendedfor dynamicresponseanalysisof dams,butcanprovidesufficientlyaccurateresultsforsomecases.Evaluatetheresistanceofpotentiallyliquefiablesoiltypeswithinthedamandfoundationtoporepressuregenerationundercyclicloadingconditions.This isprobablymosteffectivelydoneatthistimeusingStandardPenetrationTest(SPT) data,thoughrecentimprovementsin correlations between SPT and ConePenetrationTests(CPT) mayrenderCPT a viablealternativewhen soil conditions and geometryare already well-characterizedbymeansofboringsorotherinformation.Basedon the resultsof Steps6 and 7, evaluatelikely porepressuregenerationor cyclicstrainaccumulationwithinthedamandfoundation.This constitutesan evaluationof thepotentialfor "triggering"or initiatingsoilliquefaction.

3.

4.

5.

6.

7.

CyclicPorePressure 353

If porepressuregenerationin Ster 7 is foundto bepotentiallysignificant,evaluatethe residua undrained("steadystate")strengthsof thedamandfoundationsoils.This is probablymostreliablydoneat presentbasedon SPT data,or on CPT datacorrelatedwith SPT-basedrelationships.Using the resultingresidualstrengths,evaluatetheoverallstabilityof thedamandfoundation. This constitutesa "post-triggering"stabilityevaluation.If Step6 andjorStep8showthedamto besafewithrespecttoeither"triggering"or post-triggeringmanifestationof majorslidemovementsor deformations,evaluatethemagnitudeof (limited)overalldeformationslikelyto resultfrom combinedstaticanddynamicloads,andassesstheirpotentialimpactondamstabilityandperformance.Be sureto incorporatethe reguisiteamountof judgementineachof thesteps(1) through(9),beingguidedby a thoroughknowledgeof typicalsoil characteristics,theessentialsof finiteelementand dynamicresponseanalysisprocedures,and adetailedknowledgeof thepastperformanceof embankmentsinotherearthquakes.

The importanceof engineeringjudgmentat each step cannot beoveremphasized.A goodexampleis Step5: seismicresponseanalyses.Atthis stagethereis alwaysa needto weighand balancethe meritsofsimplificationandassociatedeaseofparameterdeterrninationandanalysisagamstthepotentiallossofaccuracyassociatedwithoversimplification.Forexample,talldamsin narrowcanyonsaresubjectto significant3-D effectsassoclatedwith the canyonsidewalls,andconventional2-D planestraindynarnicresponseanalysescanbernisleading.On theotherhand,fully3-Dresponseanalysesarerenderedextremelydifficultby theoverallsizeandcomplexityof theproblem,andtheinabilityto generateanddevelopfulIy3-D solutionswitha sufficiently"fine"meshcanalsoadverselyimpacttheresults.An optimumsolution(or somecasescanbe theuseof 2-D,planestrainanalysesbutwithfictitiouslyhighdynarnicshearmoduliusedtomodelthe additionalrestraintprovidedby the canyonsidewalls.The resultingcalculateddynamicshearstrainswithintheembankmentandfoundationcan then be "post-processed",using the actual (not fictitiouslyhigh)dynarnicshearmoduli,to generategoodestimatesof theactual,3-D cyclicshearstresses.This, of course,requiresconsiderablejudgment,andit isdifficulttoreducesuchaproceduretoasimplesetof "roles".

8.

9.di''i,;i~1

10.

Similarly,at the other extreme,simple one-dimensional(columnar)dynamicresponseanalysescanprovidesufficientlyaccuratecyclicshearstressesasto representa reliablebasisfor liquefactionanalysesfor somecases.~.houghthesesimplisticanalyses"tendto providenotoriouslypoorpredictionsof accelerations,strainsandcyclicstressesnearthecrestandslopingfacesof dams(dueto theirinabilityto correctlymodelthe localproblemgeometryandjor "topographicamplification"),theycanprovidereasonablya9curateestimatesof cyclicshearstressesdeepwithin theinteriorof anembankmentor itsfoundation,especiallyonewithrelativelyflatfaceslopesandahighratioofcrestlengthtodamheight.

.",.dl

354 SeedandHarder

THE LOWER SAN FERNANDO DAM SLIDE OF FEBRUARY 9,1971

TheLowerSanFernandoDamin Californiadevelopedamajorslidein theupstreamslopeanderestasa resultof the1971SanFernandoearthquake(ML::::6.6).An investigationof theslide,includingtrenchesandborings,insitudensitytests,undisturbedsampling,indextesting,staticandcyclieloadtesting,andanalyseswasperformedandreportedbySeedetal.[1,3,4]andLeeetal. [5].The fieldinvestigationshowedthattheslideoccurredduetoliquefactionof azoneof sandyandsiltyhydraulicfill nearthebaseof theupstreamshell.

Two erossseetionsof theLowerSanFernandoDamarepresentedin Fig.1,oneshowingtheobservationsmadein a trenchexeavatedthroughtheslideareaandtheothershowinga reconstructedcrosssectionof thedam,illustratingthe zone in which liquefactionoceurred. Large blocksofessentiallyintaetsoilfromtheupstreamsectionof thedammovedintothereservoir,ridingoveror "floating"on theliquefiedsoil. After movementsstopped,theliquefiedsoilwasfoundtohaveextIlldedoutbelowthetoeofthedamandup betweentheintactblocks,withmaximummovementsasmuehas200ft (61m)beyondthetoeof thedam.Theblockof soilwhicheontainedthetoeof thedammovedabout150ft (46m)intothereservoir.

Datafromseismoscopesloedted'on theabutmentandon theerestof theembankmentindieatedpeakaeeelerationsof about0.55gatbothloeations,andananalysisof theseismoscoperecordon thedamerestindicatedthattheslideoeeurredabout20to30seeondsaftertheearthquakeshakinghadstopped. Thus the largeslide movementsapparentlydevelopedin theabseneeof earthquake-inducedstressesandwereeausedonlybythestaticstressesdueto theweightof thematerialsin theembankment.It canthusbe inferredthattheearthquakeshakingtriggereda lossof strengthin thesoilscomprisingtheembankmentandthatitwasthislossof strength,ratherthanthemertiaforcesinducedbytheearthquakeshaking,whichledto theslidingoftheupstreamslope.. -"Whileit is readilyapparentthatslidingdueto liquefaciionoecurredin theupstreamshellof theembankment,performancedatafrom'thefilesof theCityof Los AngelesDepartmentof WaterandPowershowthatthewaterlevelsmeasuredin wells installedin the downstreamshellshowedonlysmallchangesin elevationasa resultof theearthquakeshaking[6]. Thesewellsreadingswereobtainedonefull dayaftertheearthquake,andso didnot providea reliableindicationof peak pore pressuredevelopment.Nonetheless,the well readings,alongwith the abseneeof significantdeformationsof thedownstreamshellof thedam,appearto indicatethatwhile the earthquakemayhavecausedat leastsomeincreasein porepressureratio.in the downstreamshell andits foundation,therewas nosignificantextentof soil liquefaetionin the downstreamportionof thehydraulicfill.

/ .

..J ~ z::! ..J

356 SeedandHarder

This sliderepresentsa uniquelyimportantcasehistoryfor calibrationandverificationof liquefactionandseismicstabilityanalysismethodologiesforslopesand embankments.Historical constructionrecordsas well asextensivepost-earthquakegeotechnicalinvestigationsprovideunusuallygoodinformationregardingembankmentandfoundationgeometryandsoilconditions.Instrumentalrecordingsprovidea goodbasisfor developmentof inputaccelerations,aswell asfor evaluationof theresultsof dynamicresponseanalyses.Most importantof all, however,is the fact thatthelargelysimilarupstreamanddownstreamzonesof the dambehavedinhighlydissimilarfashion,withtheupstreamsectionslidingmorethan100feetintothereservoir, whilethedownstreamsectionremainedstableandexperiencedonlyminordeformationsof less thana footatmostlocations.Accordingly,usingwell-definedconditions,a reliableanalysismethodologymustbeabletousetherelativelyminordifferencesbetweentheupstreamanddownstreamportionsof thedamas a basisfor accuratelypredictingthesesignificantlydifferentobservedmodesofperformance.

THELOWERSANFERNANDODAM

The internalgeometryandsP!1conditionswithinthedamandfoundationarewell-establishedasa resultof extensivegeotechnicalstudiesperformedin theearly1970's,andasecondsetof studiesperformedoverthepastfiveyears[1,5,6,7,8]. Figurel(b) showsa typicalcross-sectionthroughtheLower San FernandoDam as it existedimmediatelyprior to the 1971earthquake.Embankmentconstructionbeganin 1912.The embankmentwasfoundedon an alluvialfoundationconsistingprimarilyof stiff clayeysoilswithlayersandlensesofsandandgravel.

The majorityof theembankmentconsistsof hydraulicfill placedbetween1912and 1915.This materialwassluicedfromthefloorof thereservoiranddischargedfromstarterdikeson.theupstreamanddownstrea~edgesof the embankment.The actualdlmenslOnsof thesestarterdlkesareunknown.The hydraulicfill processresultedin upstream,anddownstreamshellsconsistingprimarilyof sandsandsiltsanda centrarcoreconsistingprimarilyof clayeysoils. Constructionphotos of the hydraulicfillplacementandpastreportsindicatethattheupstreamand downstreamsectionswereraisedsymmetricallyand constructedin a similarmanner.Therefore,it isreasonabletoassumethatthegeneralcharacteristicsof theupstreamanddownstreamhydraulicfill shellsaresimilar.

A 10-to._15-foot-thickhydraulicfill layerconsistingof "ground-up"shalefromthe left abutmentwasplacedin 1916overthe initial hydraulicfilldescribedabove.Umitedsamplingof thegroundshalein 1985disclosedawidelygradedsandandsiltysand,andconstructionrecordsindicate thatthemaximumparticlesizeof thegroundshalewasabout3 inches.

Theembankmentwasraisedanumberof timesbetween1916and1930byplacementof rolledfills.Themaximumheightoftheembankmentofabout140feetwasreachedin 1930.A thinblanketwasplacedonthelowerpart

---: ,

CyclicPorePressure 357

of thedownstreamslopein 1929and1930,apparentlyfor seepagecontroland to provideadditionalstabilitydueto the raisingofthe crest. Thecomposltionof theblanketwasdescribedin apost-constructionreportasamixtureof shale and gravellymaterialplacedin 12-inchlayersandcompactedbytrucks.The finaladditionto thedamwasa 4.5H:1V(rolledfill) bermplacedonthedownstreamslopein 1940.

EVALUATION OF STATIC AND CYCLIC STRESSES

~

An earIystageof theanalysisprocessinvolvesevaluationof thestaticstressconditionswithintheembankmentandfoundation.Theseareimportantintwowayswithintheoverallanalyticalscheme:(a)staticstresses,especiallyeffectiveconfiningstresses,can significantlyinfluencedynamicresponsecharacteristics(e.g.dynamicshearmoduli),and so can influencecyclicstresscalculations,and(b) staticstresses,principlytheeffective(vertical)overburdenstress(a'o)andthestatic"drivmg"shearstressona horizontalplane (rhv)can exerta significantinfluenceon the resistanceto porepressuregenerationor "triggering"of liquefactionat anypointwithintheembankment.

Seedetal. [1]presentedresultsof staticfiniteelementanalysesof LowerSanFernandoDamperformedusingthecomputerprogramISBILD [9].Asecond,morerecentanalysisperformedin 1987is presentedbySeedetal.[6,10],usingthefiniteelementmeshshownin Figure2. Both analysesusedsimilarmodellingprocedures,andbothyieldedsimilarresults.Thistypeof analysisis, in general,relativelyinsensitiveto choiceof computercode,solutionmethodology,andeventypeof constitutivemodel. Thereare,however,severalvitalcomponentsto suchananalysis:(1)nonlinear,stress/and stress-Ieveldependentsoil behaviormust be adequatelymodelled,(2) soilmodelparametersmustprovideadequatemodellingofthe in situ soils, and (3) hydraulicforces(e.g./ bouyancyandseepagegradients)mustbeincludedin theanalyses.

The 1987analysesusedtheprogramFEADAM84 [11],a 2-D planestrainfinite elementcodeo Nonlinearsoil behaviorwas modelledwith the"hyperbolic"modelproposedbyDuncanetal. [12],asmodifiedbySeedandDuncan[11,13].Theanalysismodelledconstructionof theembankmentinaseriesof "steps",placingnewelementsin theactualconstructionsequence.

i1Fig.2: FiniteElementMesh-LowerSanFernandoDam

,,..

./- ,.,- - .L:.---- '--I-r---.-/f' - 1.-1.>---

K.: f--r.-. .L'"I \--I I I r ---I I

358 SeedandHarder

Soilsbelowthewatertableweremodelledusingeffectiveor "bouyant"unitweightstoaccountforbouyancyin evaluatingeffectivestresses.Theeffectsof seepageforceswereevaluatedbasedonaninitialflownetanalysisfromwhichseepageforceswerederived;thesewerethenappliedasequivalentnodalforces. The final calculatedeffectivestresseswlthineachelementprovidedthe key staticstresses(ar';)and 1hv)necessaryfor subsequentstagesof theoverallanalyticalprocess.

Seedet al. [1,4] presenteddynamicresponseanalysesof theLowerSanFernandoDam performedin 1972using the programQUAD4 [14].Similaranalyseswereperformedmorerecentlyusingthe codeFLUSH[15],and the meshillustratedin Figure 2. Both analysesusedstaticstresses,calculatedas describedabove,as a basisfor modellingdynamicshearmoduliof cohesionlesszones,thoughslightlydifferentrelationshipswereusedto modelthenonlinearrelationshipsbetweenshearstrainanddynamicshearmodulusanddamping:[16]fortheearlieranalyses,and[17]for themorerecentanalyses.Similarly,therelationshipsproposedin [16]wereusedtomodelstrain-dependentmodulianddampingin thecohesivezonesin theearlieranalyses,and[18]in themorerecentanalyses.

The earlieranalysesusedtheinputmotionsdescribedbySeedetal. [1,4]:(a) an interpretationof the abutmentrecordby Scott [19],and (b) amodifiedversionof thetimehistoryrecordedatthePacoimastationduringthe 1971San Fernando!,/earthquake. The modificationsconsistedoftrimrningof accelerationpulsesof greaterthan0.9g, thenscalingtherecordtoamaximumhorizontalaccelerationof 0.6g,providingamotioningoodagreementwith.Scott's[20]interpretationof the 1971seismoscoperecordfromtheabutmentof theLowerSanFernandoDam,butwithouttheunusuallowfrequencycomponentsof theinterpretedabutmentrecord.The morerecentanalysesemployedthemodifiedPacoimainputmotionscaledto0.55g.

The resultsof the1973and1987analyseswerein closeagreement:bothproducedmaximumhorizontalcrestaccelerationson theorderof 0.5to0.55g,in goodagreementwiththeactualrecorded-peakcrestaccelerations.Bothanalysesalsocalculatedsimilarpeakcyclichorizontalshearstresses(1hv,cycliJwithinthehydraulicfill zonesof theembankine~:

\\

It is interestingto note that Jong [20] performedone-dimensional,columnar analysesof individual vertical soil columns through theembankmentusingtheprogramSHAKE [21]. Theseanalyses,modellin~verticalpropagationof shearwavesand usingthe samenonlinears011modelsand soil parametersas the 2-D FLUSH analyses,significantlyunderestimatedbothaccelerationsandcyclicshearstressesnearthecrestand upper facesof the embankment.These analysesalso, however,providedrelativelygood agreementwith the 2-D dynamicresponseanalyseswithregardto cyclicshearstresses(11vcy}:lidwithinthehydraulicfill zonesnearthebaseof theembankment,typlcallycalculatingpeakCYclicshearstressesonly5% to 15%lower thanthosecalculatedby the 2-Danalysesin thesezones.

CyclicPorePressure 359

EVALUATION OF LIQUEFACTION RESISTANCE

Havingcalculatedthecyclicshearstressesresultingfromtheearthquakeloadingat eachpointwlthinthehydraulicfill, thenextstepis to evaluatethe resistanceof this materialto cyclicpore pressuregenerationoraccumulationof cyclicshearstrain. This constitutesevaluationof theresistanceto "triggering"or initiationof potentialliquefactionfailure,definedas sufficientpore pressureor strainaccumulationto bringthematerialto a conditionat whichundrainedresidual(or "steadystate")strengthwill controlfurtherbehavior.

Figure 3 showsa recommendedrelationshipbetween"corrected"SPTpenetrationresistanceand the equivalentuniform cyclic stressratiorequiredto "trig~er"liquefactiondunnganearthquakewitha duration(ornumberof loadmgcycles)representativeof a typicalearthquakewith amagnitude of M ::::7~,as suggestedby Seedet al. [22,23]. In thisrelationship,cyclicstressratio (CSR) is definedas theratioof theCYclicshearstressactingon a horizontalplane (1hvc) to the initial (pre-earthquake)effectivevertical or overburdenstress(a'o), as CSR =(1hvc)ja'O'The relationshipspresentedin Figure3 representasignificantimprovementoverearlier,slIllilarrelationshipsdevelopedbyDr. SeedandhiscoUeagues,as(a)theydirectlyaccountfortheinfluenceof finescontenton the relationshipbetweenpenetrationresistanceand li~uefactionresistance,and(b) theyarebasedon a "corrected"or "standardlzed"SPTpenetrationresistance.

The standardizedpenetrationresistance(N1)60is a new"standard"SPTblowcount,basedonstandardizedequipmentandproceduresaspresented(inpart)in Table1[22,23]. Theuseof othertypesof harnmer(e.g.donutharnmers),or othertypesof mechanismsto ralseanddrop the harnmer(e.g.automaticmechanical"trip"harnmers,"freefaU"harnmers,ropeandcatheadwiththreeturnsof therapeaboutthecathead,etc.),canimpartdifferentlevelsof energyto thetopof thedrill stem.Thesenon-standardpraceduresandequipmentrequirecorrectionof theblowcountsin ordertodevelopthestandardizedblowcount.The (N1)60"standardized"systemandprocedures,combinedwitha "typical"ropeandcatheadsystem(withtwoturnsof therafe aboutthecathead)typicaUydeliverap'proximately60%ofthe theoretica"freefaU"harnmerenergyto the dnU stem. For othersystems,the measuredpenetrationresistances(N, blowsjft) shouldbecorrectedas

ERN60 =Nx 60%

'~

>'!Q

whereER or energyratiois the"efficiency"or percentof theoreticalfreefaUenergydeliveredbytheharnmersystemactuaUyusedto thetopof thedrill stem.This canbemeasureddirectly,usinga pileanalyzer,or canbeestimated(for the mostcornmonalternatesystemsin wldespreaduse)basedoncorrelationsanddatasummarizedbySeedetal. [22,23].

360 SeedandHarder

0.6.Z9 ..o

15II

~5I

0.51

04_o~g'

..:.

IIIIIII

"'

."

,,I,,,I

I

Noto:' Datashownonlylonlt.. with>5" tinos.oon~dorabl.datalor

362 Seedand Harder

00

CN0.8

'00

OA 1.2 1.6

80

g- 2ea..a.:;

iO

.~/!.

ee"

~6~ . D.''' """'O,'21~o/;:;oJ

O om, ' by..Id , ,e>~J! 8;;

. o , " -o'n

oO 00 60,o 20 30 .0

IN,'.o10

Fig.4: ChartforValuesofCN Fig.5: ApproximateRelationshipBetweenDR and(Nl)60 [25]

,'/

Table2: RelationshipBetweenMagnit~de,NumberofEquivalentUniformLoadCycles,andLiquefactionResistanceFactorCM

loadingcyclesrepresentingthe earth'l.uakein question(afterSeedet al.,[27]),andthenusethesecondandthlrdcolumnsof Table2 to selectanappropriatevalueofCM, Eitherof theseproceduresresultin relationshipsbetween(Nl)60andCSRforearthquakesofothermagnitudesthanM"",7~thatarein goodagreementwithavailablefielddata[22,23],thoughthefield (casehistory)databaseis less extensivefor eventsof otherrangesofmagnitude.

Virtuallyall of thefield (casehistory)datareflectedin Figure3 (andinsimilarcollectionsof datafor othermagnituderanges)arefor levelgroundconditionsandrelativelyshallowsoilswithrelativelysmallinitialeffective

10

CyclicPorePressure 363

overburdenstresses.At highereffectiveoverburdenstresses,a givenCSRandnumberof loadingcycleswillbemoredamaging.This isbecausewhilesoils generallydevelophigher cyclic load resistancewith. increasingconfinement,the normalizedresistanceas expressedin termsof cyclicstressratiousuallydecreaseswith increasingconfinement.Accordingly,valuesof CSRfromFigure3 canbeusedforin situconditionswherea'o::;1 tonjft2 (1 kgjcm2),but mustbe correctedfor conditionswith initialeffectiveoverburdenstressesgreaterthan1tonjft2as

CSR(a'o=a~)=CSR(a=1tsf). Ku

A recommendedrelationshipbetweenKu anda'ois presentedin Figure6,basedondatasummarizedbyHarder[28].

Finally,all of theabovehasbeenbasedon "levelgroundconditions",orconditionsin whichthereis no static"driving"shearstressactingon ahorizontal plane in the soil. Generationof pore pressuresandaccumulationof shearstrainsundercyclicloadingcan be significantlyaffectedbythepresenceof astatic(non-cyclic)drivingshearstress,andthistoomustbeaccountedfor in analyslsof liquefactionresistancewithindamsandembankments.

1.2 o

1.0

0.4

0.2

00 1.0 2.0 3.0 4.0 5.0 6.0EFFECTIVE CONFININGPRESSURE (1st)or (ksc)

7.0 8.0

Fig.6: RelationshipBetweenEffectiveVerticalStress(a'o)andKa

,Jj

MagnitudeorDurationEarthquake No.of representative CorrectionFactor:Magnitude,M cyclesat0.65r cyclic,max CM 0.8

81/2 26 .---. 0.8971/2 15

" 1.0" 0.663/4 10 1.13.6 5-6 .3251/4 2-3 1.5

- ..- -.- -.- ..- -. -.- ,,- -'-..,-

.0"o ." o "'-" " ,.'

oo .: oI ',' '- ) o. f.,'"ON'OA" -... LAKE ARROWHEAOOA" El -..

364 SeedandHarder

EarlyrelationshipssuggestedbyDr. Seedtoaccountforthissuggestedthatthe presenceof a staticdrivingshearstresson a horizontalplanewasstronglybeneficial,andthatit significantlyincreasedthesoil'sresistancetoliquefaction.This remainstruefor relativelydensesoils,or soilswhichwouldtendto dilateunderuni-directionalshearing.More recentstudies,however,haveshownthatfor veryloosesoils(soilswhicharelessdilatantor morecontractiveunderuni-directionalshearing),thepresenceof astaticdrivin~shearstresscanactuallydecreasetheresistanceof thesoil to theinitiatlOnof liquefaction.Good data regardingthis remainssomewhatlimited,andfurtherinvestigationsof thiswouldbeofsignificantvalue.TheoriginalmethodproposedbySeed[29]toaccountfor theeffectsof drivingstaticshearstressesemployedthefollowingequation

CSR(a=a) =CSRl(a=O). Ka(wherea is definedastheratioofstaticdrivingshearstressonahorizontalplaneto the initial effectiveoverburdenstressasa =r hv/a'o)Basedondataavailableat this time(datasummarizedby Harder [28],as well asresearchin progress),it is suggestedthatther~lationshipsbetweena and~ proposedby Seed[29]be replacedby the relationshipspresente~inFigure7. Thesearebasedondatafor conditionswherea' ::;3 tons/ft (3kgjcm2),andareappropriateonlyfor theseconditions.At higherinitialeffectiveoverburdenstresse~,soilswill belessdilatantor morecontractive,andKavalueswilldecrease.'./ .

2.0

1.5

CTo'

I . rv

-~......Koe

""'.,.oe ;I

~I, 0'0

0.5

Dr~ 35%

I(Yo ~3tsf

oO 0.1 0.2 0.3

o(0.4 0.5

Fig.7: RelationshipBetweena andKa

"'-

CyclicPorePressure 365

1140LOWER SAN FERNANDO DAM

DDwNSTREAM S"ELL ZONESSPT EXPLDRmONS IN MUO-FlLLED

ROTAR' BOREHOLES.

{8 o-, . F-, 8G-I

.." ..,., . F., ~ G"...,-,

{Osoo, o' '."" 0"' 7'''' oO

1120

1100 OO

~t...~

1080

ELEVATION(feen 7

MEAN~ 19d:

1060

MEAN~ 14.5

1040

7

1020

MEAN '"14.57 8

1000~. 77

. .OENO'"""

366 SeedandHarder

As shownin Figure8,theresulting(Nl)6Qvaluesfrom1971and1985showsimilartrends,andthehydraulicfill canbesubdividedintofourelevationzones of apparentlysimilar properties. Table 3 summarizesthecorresponding(N1)60valueswithineachof thesezones.As shownin thistable,two elevationzonesappearto havesignificantlylowerpenetrationresistancesthantheotherzones. It shouldbe notedthat,although"bestestimates"or meanvaluesof (N1)60areappropriatefor theseanalysesof acasestudyinvolvingcomparisonwith observedfield performance,moreconservative(lower thanmean)valueswouldnormallybe selectedforanalysesperformedin orderto predictthe likelyfuturebehaviorof anygivendamor embankment.

The (N1)6Ovaluessummarizedin thesecondcolurnnof Table3 arebasedonpost-earthquakeblowcounts,andsomecorrectionis requiredtoaccountfor densificationlikelyto haveoccurreddueto theearthquakeshaking.Seedet al. [6]haveestimatedthatthepre-earthquakeblowcountsin thedownstreamhydraulicfill wouldhavebeenlower,ontheaverage,byabout2blows/ft,andthisis reflectedin thethirdcolurnnofTable3whichwill betakenasthevaluesfor thedownstreamzonesin theseanalyses.

There is some minar questionas to how thesevalues should beextrapolatedto theupstreamportionof thehydraulicfill withinwhichtheslide occurred. Sirnilarityand uniforrnityof constructionproceduressupporttheuseof thesame'(N1)60valuesfortheupstreamsection.On theotherhand,it hasbeensuggestedthattheupstreamsectionmayhavebeensomewhatless denselyconsolidateddue to reservoir bouyancyand theabsenceof thedownstreamberms. If reservoir fillinghadbeeninitiatedsufficientlyquicklyaftercompletionof constructionthatfull consolidationof the embankmentunderits ownweightwasnot completed,thenthemaximumdifferencein densitybetweenthe upstreamand downstreamhydraulicfill sectionswouldhavebeensuchthattheupstream(N)60valueswouldneedto be reducedby about1 blow/ft. As shownin Table 3, areductionof 1 blow/ft will be usedfor theanalysesdescribedherein. Itshouldbenotedthatthisrelativelyminordecreasein theupstreamsection's(N1)6Ovaluesdoesnot explainthesignificantdifferencesin performance

Table3: Representative(N1)ti

368 SeedandHarder

'f;]

o FSL > 1.4!ZJ FSL '" 1.1to 1.3. FSL < 1.1

CLAYEYCOREZONE

Fig. 9: Results of Analy'sesof Resistanceto lnitiation or "Triggering"ofLiquefaction Fmlure -Lower SanFernando Dam

Comparing the equivalent,uniform, earthquake-inducedcyclic stressratio(CSR q) with the uniform cyclic stress ratio necessaryto fully triggerliquera.ction,thefactorof safetyagainst"triggering"canbeca1culatedas

FSl =CSRt.field = 0.288 = 1.27CSReq 0.227-r --r /

Thisfactorof safetycanbeinterpretedin a numberof ways. Figure 10showsaplotof residualexcessporepressureratio(ru = !:J.uja'o)basedonlaboratorytestdatafor levelgroundconditions(a =O)assurnmarizedbyTokimatsuandYoshimi,[30]forsandysoils,andEvans[31]andHynes[32]forgravellysoils,assurnmar~zedbyMarcusonandHynes[33].For non-level groundconditions(a *" O), the effectiveverticalstressneed notnecessarilybe fullyeliminatedbyporepressureincreasesto initiate"large"deformationsin thepresenceof combinedcyclicand"driving"staticshearstresses. Accordingly,whena *"O,theresidualexcessporepressureratioisbestdefinedastheratioof cyclically-generatedporepressures(!:J.u) to thevalueof!:J.unecessarytoinitiatelargedeformations(!:J.Ul~) as

r _!:J.uup*"O- !:J.ulim

Lessdatais availableregardingtherelationshipsbetweenru.andFS fornon-Ievelgroundconditions,anddifferencesof opinionexistastohowthisdatacanbestbeinterpreted.Muchof thisisduetouncertaintyregardingthenatureofthetransitionfroma conditionwhereincyclicJ?orepressuregeneration(or cyclicstrainaccumulation)behaviorexertspnmarycontrolonperformance,to "post-triggering"conditionswhereinundrainedresidual(or IIsteadystate")strengthscontrolbehavior.

Nonetheless,at this time it appearsthat a reliable analysiscan beperformedbyconsideringthat:

1.,

Soil elementswith low factorsof safety (FSe ~ 1.1) would achieveconditions wherein soil liquefactionfailureshouldbe consideredto

CyclicParePressure 369

1.0

wa;::>

:z 0.6wa;Q.Wa;oQ.

~ 0.4w(j)(w....e 0.2UJwa;

,""'

LEGEND

777/ GRAVEL (EVANS 1987.:L.::L.: ANO HYNES 1988)

"a;O 0.8 ,.i=