TA 710 .577 1980 STRENGTH.STRESS-STRAINANDBULKMODULUS PARAMETERSFORFINITEELEMENTANALYSES OFSTRESSESANDMOVEMENTSINSOILMASSES by J.M.Duncan PeterByrne KaiS.Wong and PhillipMabry ReportNo.UCB/GT/BO-Ol August,19BO CollegeofEngineering OfficeofResearchServices UniversityofCalifornia Berkeley,California TABLEOFCONTENTS INTRODUCTION HYPERBOLICSTRESS-STRAINRELATIONSHIPS NonlinearStress-StrainCUrvesRepresentedbyHyperbolas Stress-DependentStress-StrainBehaviorRepresentedby VaryingEiand(al -a3) ult withConfiningPressure RelationshipBetweenEt andtheStresses InelasticBehmi"iorRepresentedByUseofDifferent ModulusValuesforLoadingandUnloading NonlinearVolumeChangeAccountedforByUsingConstant BulkModulus VariationofBwithConfiningPressure RestrictionsontheRangeofValuesofB SummaryofHyperbolicParameters TECHNIQUESFORDETERMININGVALUESOFTHEHYPERBOLICPARAMETERS FROMLABORATORYTESTRESULTS SelectingDataandEliminatingInconsistencies Evaluationofcand~forCohesiveSoils Evaluationof~and~ ~forCohesionlessSoils o EvaluationofKandn EvaluationofK ur Evaluationof~andm ComputerProgramforDeterminingParameterValues ii Page No. 1 4 5 7 11 11 13 16 18 18 22 22 25 30 32 40 41 46 COMPILATIONSOFPARAMETERVALUES ParametersforSoilsTestedUnderDrainedConditions ParametersforSoilsTestedUnderUndrainedConditions ConservativeParameterValues SUMMARY ACKNOWLEDGMENT REFERENCES APPENDIX- COMPUTERPROGRAMSP-5 iii Page No. 50 50 57 58 65 66 67 A-l 1 INTRODUCTION Thefiniteelementmethodprovidesapowerfultechniqueforanalysis ofstressesandmovementsinearthmasses,andit hasalreadybeenapplied toanumberofpracticalproblemsincludingembankmentdams,openexcava-tions,bracedexcavations,andavarietyofsoil-structureinteraction problems. Iftheresultsofsoildeformationanalysesaretoberealisticand meaningful,it isimportantthatthestress-straincharacteristicsofthe soilberepresentedintheanalysesinareasonableway.Thisisdiffi-cultbecausethestress-straincharacteristicsofsoilsareextremely complex,andthebehaviorofsoilisnonlinear,inelastic,andhighly dependentonthemagnitudesofthestressesinthesoil. Thehyperbolicstress-strainrelationshipsdescribedinthisreport weredevelopedinanattempttoprovideasimpleframeworkencompassing themostimportantcharacteristicsofsoilstress-strainbehavior,using thedataavailablefromconventionallaboratorytests.Theserelation-shipshavebeenusedinfiniteelementanalysesofanumberofdifferent typesofstaticsoil mechanicsproblems(11,12,13,22 ,23,24,31,32,35, 40),andvaluesofthehyperbolicparametershavenowbeendeterminedfor about150differentsoils. Thepurposesofthisreportaretodescribethehyperbolicrelation-ships,tooutlinetheproceduresforevaluatingthehyperbolicparameters, andtopresentparametervaluesdeterminedfromdrainedandundrained testsonanumberofsoils. Inapreviousreport,WongandDuncan(45)outlinedproceduresfor determinationofstress-strainandvolumechangeparametersforusein 2 nonlinearfiniteelementanalysesofstressesandmovementsinearth masses.Inthatreport,theparametersemployedtorepresentnonlinear andstress-dependentstress-strainandvolumechangebehaviorwere: (1)T a n g e ~ tvaluesofYoung'smodulus(Et)whichvarywith confiningpressureandthepercentageofstrength mobilized,and (2)Tangentvaluesofpoisson'sratio(Vt)whichvarywith confiningpressureandthepercentageofstrength mobilized. Subsequentstudieshaveshownthatthevolumechangebehaviorof mostsoilscanbemodelledwithequalaccuracybyassumingthatthebulk modulusofthesoilvarieswithconfiningpressure,andisindependent ofthepercentageofstrengthmobilized.Athighstresslevelsthis assumptionprovidesamorereasonablemeansofrepresentingthemechan-icalpropertiesofsoils. Thisreportoutlinesprocedureswhichmaybeusedtodetermine therequiredYoung'smodulusandbulkmodulusparametersfromconvention-allaboratorytest data.Specifically,thereportisconcernedwiththe useofthefollowingparameterstorepresentthenonlinearandstress-dependentstress-strainandvolumechangebehaviorofsoils: (1)TangentvaluesofYoung'smodulus(Et)whichvarywith confiningpressureandthepercentageofstrengthmobilized (exactlytheSameasinthepreviousreportbyWongand Duncan),and (2)Valuesofbulkmodulus(B)whichvarywithconfining pressureandwhichareindependentofthepercentageof strenqthmobilized 3 4 HYPERBOLICSTRESS-STRAINRELATIONSHIPS Thehyperbolicstress-strainrelationships(22)weredevelopedfor useinnonlinearincrementalanalysesofsoildeformations.Ineach incrementofsuchanalysesthestress-strainbehaviorofthesoilis treatedasbeinglinearandtherelationshipbetweenstressandstrain isassumedtobegovernedbythegeneralizedHooke'sLawofelastic deformations,whichmaybeexpressedasfollowsforconditionsofplane strain: 6.cr(3B + E) x (3B- E)06.0; x 6.cr 3B (3B- E)(3B+E)0 /:;.0; (1)= y9B- E Y /:;.T, 00E6.y xyxy inwhich OOx= normalstressincrement-/:;.cr = normalstressincrement y 6.1: = shearstressincrelllE!nt xy 6.0; = x normalstrainincrement 6.0;=normalstrainincrement y 6.y = shearstrainincrement xy E = Y01.Ulg'smodulus B = bulkmodulus 5 ByvaryingthevaluesofYoung'smodulusandbulkmodulusappro-priatelyasthestressesvarywithinthesoil,it ispossibleusing thesimpleequation(1)tomodelthreeimportantcharacteristicsof thestress-strainbehaviorofsoils,namely,nonlinearity,stress-dependency,andinelasticity.Theproceduresusedtoaccount'forthese characteristicsaredescribedinthefollowingparagraphs. NonlinearStress-StrainCUrvesRepresentedbyHyperbolas.Kondner andhisco-workers(29,30),haveshownthatthestress-straincurves foranumberofsoilscouldbeapproximatedreasonablyaccuratebyhyper-bolasliketheoneshowninFig.1.Thishyperbolacanberepresentedby anequationoftheform: = e: (2) Whileothertypesofcurvescouldalsobeused,thesehyperbolas havetwocharacteristicswhichmaketheiruseconvenient: (1)Theparameterswhichappearinthehyperbolicequationhave physicalsignificance.E.istheinitialtangentmodulus 1. orinitialslopeofthestress-straincurveand(crl-cr3)ult istheasymptoticvalueofstressdifferencewhichis relatedcloselytothestrengthofthesoil.Thevalueof (crl-cr3)ultisalwaysgreaterthanthecompressivestrength ofthesoils,asdiscussedsubsequently. (2)ThevaluesofEiand(crl-cr3)ultforagivenstress-strain 6 ----------------~ REAL If I b- {OJ-(J3) = _I + -E (OJ -(J3 )ult l TRANSFORMED FIG. IHYPERBOLICREPRESENTATIONOFASTRESS-STRAINCURVE curvecanbedeterminedeasily.Ifthehyperbolicequation istransformedasshowninthelowerpartofFig.1,it representsalinearrelationshipbetweenE/(Gl-G3)andE. Thus,todeterminethebest-fithyperbolaforthestress-straincurve,valuesofE/(Ol-03)arecalculatedfromthe testdataandareplottedagainstE.Thebest-fitstraight lineonthistransformedplotcorrespondstothebest-fit hyperbolaonthestress-strainplot. Whendatafromactualtestsareplottedonthetransformedplot, 7 thepointsfrequentlyarefoundtodeviatefromtheideallinearrelation-ship.Thedataforstiffsoils,suchasdensesands,usuallyplotona mildcurvewhichisconcaveupward,whereasthedataforsoftsoils,such asloosesands,usuallyplotonamildcurvewhichisconcavedownward. Experiencewithseveralhundredstress-straincurvesforwellovera hUndreddifferentsoilsindicatesthatagoodmatchisusuallyachieved byselectingthestraightlinesothat.it passesthroughthepOintswhere 70%and95%ofthestrengtharemobilized(22,32).Thus,inpractice, onlytwopointsforeachstress-straincurve(the70%pointandthe95% point)areplottedonthetransformeddiagram. StressDependentStress-StrainBehaviorRepresentedbyvaryingEi and(Ol-03)ultwithConfiningPressure.Forallsoilsexceptfullysatu-ratedsoilstestedunderunconsolidated-undrainedconditions,anincrease inconfiningpressurewillresultinasteeperstress-strainCUrveanda higherstrength,andthevaluesofEiand(Gl-03)ultthereforeincrease withincreasingconfiningpressure.Thisstress-dependencyistakeninto accountbyusingempiricalequationstorepresentthevariationsofE. ~ and(01-03)ultwithconfiningpressure. ThevariationofEiwith03isrepresentedbyanequationofthe followingform,whichwassuggestedbyJanbu(28): (3) 8 ThevariationofEiwith03correspondingtothisequationisshownin Fig.2.TheparameterKinequation(3)isthemodulusnumber,andnis themodulusexponent.Botharedimensionlessnumbers.pisatmospheric a pressure,introducedintotheequationtomakeconversionfromonesystem ofunitstoanothermoreconvenient.ThevaluesofKandnarethesame foranysystemofunits,andtheunitsofEiarethesameastheunitsof p.Tochangefromonesystemofunitstoanotherit isonlynecessary a tointroducetheappropriatevalueofpinequation(3). a Thevariationof(Ol-03)ultwith03isaccountedforasshownin Fig.3byrelating(01-03)ulttothecompressivestrengthorstressdif-ferenceatfailure,( O ~-03) f'andthenusingtheMohr-Coulombstrength equationtorelate(01-03)fto03'Thevaluesof(01-03)ultand(01-03)f arerelatedby: (4) inwhichRf isthefailureratio.Because(01-03)fisalwayssmaller than(Ol-03)ult'thevalueofRf isalwayssmallerthanunity,andvaries from0.5to0.9formostsoils. Thevariationof(01-o3)fwith03isrepresentedbythefamilarMohr-Coulombstrengthrelationship,whichcanbeexpressedasfollows: 9 FIG.2VARIATIONOFINITIALTANGENTMODULUS WITHCONFININGPRESSURE -r; cl... 0" (OJ-0"3'," 2 CCOS4>+2 0"3SIN4> I - SIN4> (OJ-0"3),=R,(OJ-0"3)ult FIG.3VARIATIONOFSTRENGTHWITHCONFININGPRESSURE .... o 11 sin (5) inwhichcand arethecohesioninterceptandthefrictionangle,as showninFig.3. RelationshipBetweenEt andtheStresses.Theinstantaneousslope ofthestress-straincurveisthetangentmodulus,EtBydifferentia-tingequation(2)withrespecttoEandsubstitutingtheexpressionsof equations(3),(4),and(5)intotheresultingexpressionforEt,the followingequationcanbederived: (6) Thisequationcanbeusedtocalculatetheappropriatevalueoftangent modulusforanystressconditions(a3 and(al-a3})ifthevaluesofthe parametersK,n,c,,andRf areknown. InelasticBehaviorRepresentedByUseofDifferentModulusvalues forLoadingandUnloading.If atriaxialspecimenisunloadedatsome stageduringatest,thestress-straincurvefollowedduringunloading issteeperthanthecurvefollowedduringprimaryloading,asshownin Fig.4.Ifthespecimenissubsequentlyreloaded,thestress-strain curvefollowedisalsosteeperthanthecurveforprimaryloadingandis quitesimilarinslopetotheunloadingcurve.Thusthesoilbehavioris inelastic,becausethestrainsoccurringduringprimaryloadingareonly partially recoverableonunloading.Onsubsequentreloadingthereis alwayssomehysteresis,butit isusuallyreasonablyaccurateto 12 .... tr FIG.4UNLOADING-RELOADINGMODULUS 13 approximatethebehaviorduringunloading-reloadingstresschangesas linearandelastic,ineffectignoringanyhysteresiseffects. Inthehyperbolicstress-strainrelationships,thesamevalueof unloading-reloadingmodulus,E,is usedforbothunloadingandreload-.ur ing.ThevalueofEisrelatedtotheconfiningpressurebyanequation ur ofthesameformasequation(3): n 03 ) E- K-ur- urPa(Pa InthisequationKistheunloading-reloadingmodulusnumber. ur (7) The valueofKisalwayslargerthanthevalueofK(forprimaryloading). ur Kmaybe20%greaterthanKforstiffsoilssuchasdensesands.For ur softsoils,likeloosesands,KmaybethreetimesaslargeasK.The ur valueoftheexponentnisalwaysverysimilarforprimaryloadingand unloading,andinthehyperbolicrelationshipsit isassumedtobethe same. NonlinearVolumeChangeAccountedforByUsingConstantBulk Modulus.Manysoilsexhibitnonlinearandstress- Co) c: "0 ... - en u ".:: -Ql E ::I g 14 High0"3 Intermediate Low0"3 AxialStrain,Ea AxialStrain,E ::I"'---------- Low0"3 ~ - - - - - - - __ Intermediote Fig"5NONLINEARANDSTRESS-DEPENDENTSTRESS-STRAIN ANDVOLUI\1ECHANGECURVES 15 inmeanstressis virtuallyunaffectedbythevalueof(ITI-IT3). Accordingtothetheoryofelasticity,thevalueofbulkmodulus isdef inedby B= (8) inwhichBisthebulkmodulus;llo l'llo 2'andllo 3arethechangesinthe valuesoftheprincipalstresses,andllEvisthecorrespondingchangein volumetricstrain.Foraconventionaltriaxialtest,inwhichthe deviatorstress(01-03)increaseswhiletheconfiningpressureisheld constant,equation(8)maybeexpressed (9) Thevalueofbulkmodulusforaconventionaltriaxialcompression test maybecalculatedusingthevalueof(01-03)correspondingtoany pointonthestress-straincurve,suchaspointAinFig.5,andthe correspondingpointonthevolumechangecurve(A'). Becauserealsoilsundergosomevolumechangeasaresultof changesinshearstressinadditiontothosecausedbychangesinnormal stress,thevaluesofBcalculatedusingequation(9)varysanewhat dependingonwhichpointsonthestress-strainandvolumechangecurves areemployedinthecalculation.Studyofthevolumechangebehavior ofawidevarietyofsoilshasledtothefollowingcriteriaforselect-ingwhichpointstouseincalculatingthevalueofB: (1)Ifthevolumechangecurvedoesnotreachahorizontal tangentpriortothestageatwhich70%ofthestrengthis 16 mobilized,usethepointsonthestress-strainandvolume changecurvescorrespondingtoastresslevelof70%. (2)Ifthevolumechangecurvedoesreachahorizontaltangent priortothestageatwhich70%ofthestrengthismobilized, usethepointonthevolumechangecurvewhereit becomes horizontal,andthecorrespondingpointonthestress-strain curve. VariationofBwithConfiningPressure.WhenvaluesofBarecal-culatedfortestsonthesamesoilatvariousconfiningpressures,the bulkmoduluswillusuallybefoundtoincreasewithincreasingconfining pressure.AsshowninFig.6,thevariationofBwithconfiningpres-surecanbeapproximatedbyanequationoftheform (10) inwhich~isthebulkmodulusnumberandmisthebulkmodulusexponent, bothofwhicharedimensionless.Paisatmosphericpressure,expressed inthesameunitsas(13andB.Formostsoilsthevaluesofmvary between0.0andLO.Inthecaseofundrainedtestsonclayscompacted dryofoptimum,valuesofmlessthanzerohavebeendetermined,which correspondstoadecreaseinthevalueofBastheconfiningpressure increases.Thisunusualbehaviorisbelievedtoresultfromabreakdown inthestructuralarrangementofthesoilparticlesduetotheapplication oflargerpressures. 17 (0"3)m BKbPoPo 0.110100 Fig.6VARIATIONOFBULKMODULUSWITHCONFININGPRESSURE 18 RestrictionsontheRangeofValuesofB.AsthevalueofB approachesEt/3,thecorrespondingvalueofVt (tangentPoisson'sratio) approacheszero,becauseVt =112 - Et/6B.Thereforeinfiniteelement computerprograms,thevaluesofVt mayberestrictedtopositivevalues byusingB= Et/3incaseswhereequation(10)indicateslowervalues. Similarly,byusingB=17Et whereequation(10)indicateshighervalues, thevalueofVt mayberestrictedtovalueslessthanorequalto0.49. SummaryofHyperbolicParameters.Inall.nineparametersare employedinthehyperbolicstress-strainrelationshipsdescribedinthis report.Theseparametersandtheirfunctionswithintherelationships, arelistedinTablel. Thehyperbolicrelationshipsoutlinedpreviouslyhaveprovenquite usefulforawidevarietyofpracticalproblemsforthefollowingreasons: (1)Theparametervaluescanbedetenninedfromtheresultsof conventionaltriaxialcompressiontests. (2)Thesamerelationshipscanbeusedforeffectivestress analyses(usingdatafromdrainedtests)andtotalstress analyses(usingdatafromunconsolidated-undrainedtests). (3)Valuesoftheparametershavebeencalculatedformanydif-ferenttypesofsoilsandthisinformationcanbeusedto estimatereasonablevaluesoftheparametersincaseswhere theavailabledataareinsufficienttodefinetheparameters forallofthesoilsinvolvedinaparticularproblem.The informationisalsoquiteusefulforassessingthereliability ofparametervaluesderivedfromlaboratorytestresults. 19 TABLE1.SUMMARYOFTHEHYPERBOLICPARAMETERS ParameterNameFunction K,Kur Modulusnumber RelateEiandEtoa3ur nModulusexponent cCohesionintercept Relate (al-a3)f toa3 ~ ,t , ~Frictionangleparameters Rf FailureratioRelates (al-a3lult to (al-a3)f I), BulklOOdulusnumberValueofBIPa ata3 =P a ChangeinBIPa forten-fold mBulkmodulusexponent increasein0') 20 Thesimplehyperbolicrelationshipshavesomesignificantlimitations whichshouldbeunderstoodanyanyonewhousesthem: (1)BeingbasedonthegeneralizedHooke'sLaw(equation1)the relationshipsaremostsuitableforanalysisofstressesand movementspriortofailure.Therelationshipsarecapableof predictingaccuratelynonlinearrelationshipsbetweenloads andmovements,andit' ispossibletocontinuetheanalysesup tothestagewherethereislocalfailureinsomeelements. However,whenastageisreachedwherethebehaviorofthe soilmassiscontrolledtoalargeextentbytheproperties assignedtoelementswhichhavealreadyfailed,theresults willnolongerbereliable,andtheymaybeunrealisticin termsofthebehaviorofrealsoilsatandafterfailure. Theserelationshipsarenotuseful,therefore,foranalyses extendinguptothestageofinstabilityofasoilmass.They areusefulforpredictingmovementsinstableearthmasses. (2)Thehyperbolicrelationshipsdonotincludevolumechangesdue tochangesinshearstress,or"sheardilatancy."Theymay thereforebelimitedintheaccuracywithwhichtheycanbe usedtopredictdeformationsindilatantsoils,suchasdense sandsunderlowconfiningpressures. (3)Theparametersarenotfundamentalsoilproperties,butonly valuesofempiricalcoefficientswhichrepresentthebehavior ofthesoilunderalimitedrangeofconditions.Thevalues oftheparametersdependonthedensityofthesoil,itswater content,therangeofpressuresusedintesting,andthe drainageconditions.Inorderthattheparameterswillbe representativeofthebehaviorofthesoilinthefield condition,thelaboratorytestconditionsmustcorrespondto thefieldconditionswithregardtothesefactors. 21 TECHNIQUESFORDETERMININGVALUESOFTHEHYPERBOLIC PARAMETERSFROMLABORATORYTESTRESULTS Thevaluesofthehyperbolicparameterscanbedeterminedina seriesofsimple,straightforwardstepsusingthedatafromeither drainedorunconsolidated-undrainedtriaxialtests.Theprocedures 22 forevaluatingtheparametersaredescribedinthefollowingparagraphs. SelectingDataandEliminatingInconsistencies.Thefirststepin evaluatingtheparametersistoselectdataappropriatetotheproblem beinganalyzed.Inthecaseofnaturalsoils,thelaboratorytests must beperformedusingundisturbedspecimens.Inthecaseoffill materials, thelaboratorytestsmustbeperformedusingspecimenscompactedtothe samedensityandwatercontentasinthefield.And,inbothcases,the drainageconditionsinthelaboratorytestsshouldcorrespondtothosein theproblembeinganalyzed. Testsperformedatpressuresmuchhigherormuchlowerthanthose ofinterestintheproblemshouldnotbeusedinevaluatingtheparameters, becausethevaluesoftheparameterswhichbestfittheresultsofthe testsdependtosomeextentontherangeofpressuresusedintesting. Thetestdatashouldbeinspectedcloselytoeliminateexperimental errorsandinconsistencies.Forexample,inFig.7,thestress-strain curveforcr3 =0.95kg/cm2 isinconsistentwiththedataf ~ o mtheremain-ingfourtests,andshouldbediscarded. Smoothcurvesshouldbedrawnthroughthedata,usinggoodjudgment tomakethemostreasonableinterpretationsofallofthetestdata.For example,inFig.B,thedatapointsdonotdescribesmoothvariationsof 23 16 ~ N cre = 8.00kg/em2 E ~ 0> ~ ~12 (/) (/) UJ ~ 3.99(/) a: 8 ~ 2.02 > UJ 0.95 c 1.00 048121620 AXIALSTRAIN(%) FIG.7STRESS- STRAINCURVESFORCDTRIAXIAL TESTS,CANYONDAMSILTYCLAY(CL-29C) 24 ------------ ----- TESTSRESULTS --CURVESAFTER ADJUSTMENT o4812162024 AXIALSTRAIN(%) FIG.8ADJUSTMENTOFSTRESS - STRAINCURVES 25 stressandstrainbecauseofdifferencesinthelengthoftimetheloads wereinplacewhentheaxialdeformationsweremeasured.Thesmooth curvesrepresentreasonableinterpretationsofthedata,corr.esponding toarelativelyslowrateofloading. Ifnecessary,thestress-strainandvolumechangecurvesshouldbe shiftedsothattheypassthroughtheorigin.Forexample,inFig.9, thestress-strainandvolumechangecurvesincludetheaxialstrainsand volumechangesresultingfromapplicationoftheconfiningpressures. InFig.10thesedatahavebeenreplottedwiththecurvesshiftedsothat theypassthroughtheorigin.Notealsothatthecurvesforthetest withthehighestconfiningpressurehavebeeneliminatedbecausethe pressuresinthistestwereoutsidetherangeofinterestforthedam. Evaluationof.candp forCohesiveSoils.Thevaluesofstrength parameterscand~whichappearinthehyperbolicstress-strainrelation-shipcanbeevaluatedusinganyconvenientprocedure.Thetwomethods usedmostfrequentlyareshowninFigs.11and12.InFig.11,theMohr's circleshavebeenplottedandthevaluesofcand~weredeterminedby drawingthefailureenvelopeandmeasuringtheinterceptandangleof inclination.Theactualfailureenvelopeforthismaterial(orovilleDam corematerialtestedunderU-Uconditions)wassignificantlycurvedwith-intherangeofpressuresofinterestinthedam,andthereforetwosets ofstrengthparameterswereusedintheanalysisofstressesandmove-mentsinthedam(31).AsshowninFig.11,theseparameterscorrespond totwodifferentrangesofpressure. Asecondprocedurefordeterminingthevaluesofcand~isillus-, tratedinFig.12.Thisinvolvesplottingthevaluesoft(a1-cr3)at ~ 60 C/) l-en C/) ILl g: 40 .C/) a: 0 I- ILl a 0 0 u-- ~ a:o 1--S I L I ~ :i: FIG.9 26 : v + ~ I+--+-+-+- +-+ 4 I 3 t Jj 2 5101520 AXIALSTRAIN(%) 5101520 jI I 1-'::::::::: 2 3 ~4. IIII STRESS-STRAINANDVOLUMECHANGECURVES OFUUTRIAXIALTESTS,NEWDONPEDRODAM COREMATERIAL(SC-3) (BECHTEL,1969) IL. Ul I-40 30 -b'20 , t) 10 6TSF 10.8 5.4 173 =5.4TSF o468121416 IIII1- 1 G,(% 010.8 2 3 21.6 4 FIG.10STRESS-STRAINANDVOLUMECHANGECURVESOFNEWDONPEDRODAM COREMATERIAL(SC-3),(AFTERADJUSTMENT) IV " 5 0 ~ i - - - - - - r - - - - - ~ - - - - - - ~ - - - - ~ r - - - - - - r - - - - - - ~ - - - - - ' - - - - - - ~ IL. (I) .... 40 en30 CI) w a: t;; a: ~20 :I: (I) 10 GC-2A c"1.5TSF ~..23.70 GC-28 c=10.3 TSF ~..3.50 0''''" o10203040506070 NORMALSTRESS,KG/CM2 AG.IIMOHRENVELOPESFOROROVILLEDAMCOREMATERIAL(GC- 2A& B). (DATAFROMDEPARTMENTOFWATERRESOURCES,1969) r 80 IV 00 LL. 29

4>= Sin -I (Ton",)= 26.4 0 c= a/Cos.1/>=2.68 TSF 20 C\I I I:)10 -

o1020304050 FIG.12MODIFIEDMOHRENVELOPEFORUU:"TRIAXIAL TESTSONNEWDONPEDRODAMCOREMATERIAL (SC-3).(DATA.FROMBECHTEL,1969) 30 failureagainstthevaluesof;=10552 . (!) z w 2 0"3= 425 PSI 0"3=250 PSI 03=125PSI 0"3=125PSI 810 (%)

FIG.16REPLOTTEDSTRESS-STRAINANDVOLUME- CHANGECURVES FOROROVILLEDAMSHELLMATERIAL(GP-6). 03 (psi) 125. 250. 425. TABLE2.CALCULATIONOFTRANSFORMEDSTRESS-STRAINDATAFOR OROVILLEDAMSHELLMATERIAL(GP-6) 70%StressLevel95%StressLevel EE (01-03) f(01-0 3) a (01-03) a E (01-03) E (01-03)aa (psi)(psi)(psi) -1 (psi) (psi) _1 620.434.02 589.043

1100.770.025.324xl0-4 1045.055 1550.1085.03 276xl0-4 1472.063 w ..., 38 0.00008.----.....,.----,...---..,..-----,,..----,----, I -(f) Q. --0.00006 ~ Q O O O 0 4 I 0' '" ,.., w 0.00002 CT3 0Ei =I/ob (OJ-CT3)ult(OJ-CT3)f Rf (PSI!(PSU-'(PSI) (PSlr'(PSO (PSI) -1250.0000227440530.001168626200.72 0 2500.0000155645160.0006751481 11000.74 4250.0000141709220.00045222215000.70 AvERAGERf =0.72 o ~ - - - - ~ - - - - - - ~ - - - - - ~ - - - - ~ - - - - - ~ - - ~ o246810 AXIALSTRAIN,Eo(%) AG.17TRANSFORMEDSTRESS-STRAINPLOTFOROROVILLEDAM SHELLMATERIAL(GP-6). tothevalueof(Ei/Pa)atthepointwhere(CJ3/Pa)isequaltounity. Thevalueofnisequaltotheslopeofthelineonthisplot,andmay bedeterminedgraphically.Alternatively,thevalueofnmaybedeter-minednumericallyusingtheequation 40 (14) EvaluationofK ur ThevalueofKurisusuallydeterminedassuming thatthevalueofthemodulusexponentforunloading-reloading(equation7) isthesameasthevalueofthemodulusexponentforprimaryloading (equation3).Thishasbeenfoundtobeanaccurateassumptioninmost caseswheresufficientdatawereavailabletocheck,anditsimplifiesthe determinationofK ur Oncethevalueofnhasbeendeterminedasdescribed intheprecedingparagraph,thevalueofKmaybedeterminedusingdata ur fromasingleunloadingcurve.Thebeststraightlineisfittedtothe unloadingcurve,andthecorrespondingvalueofE(slopeoftheline)is ur determined.ThenthevalueofKiscalculatedusingtheequation ur K ur = E ur InthisequationCJ3 isthevalueofconfiningpressureduringunloading, andnisthemodulusexponentforprimaryloading. Frequently,dataforunloadingisnotavailable,andit isnecessary toassumethevalueofK ur Theavailabledataindicatethatthevalueof KisalwaysgreaterthanthevalueofK.TheratioK/Kvariesfrom urur 41 about1.2forstiffsoilssuchasdensesandsupto3orsoforsofter soilssuchasloosesands.Ifthezonesundergoingunloadingand/or reloadingarenotlargeanddonothaveadominanteffectontheresults oftheanalysis,assumingthevalueofKwithintherangefroml.2Kto ur 3Kisprobablysufficientlyaccurate. Evaluationof~andm.Twostepsareinvolvedindeterminingthe valuesofthebulkmodulusparameters~andm.Thef i r s ~istodeter-minethevalueofBusingthedatafromeachtest,andthesecondisto plotthesevaluesofBagainsta3 onlog-logscalestodeterminethe valuesof~andm. Forsoilswithvolumechangecurveswhichdonotreachhorizontal tangentspriortothestageatwhich70%ofthestrengthismobilized, thevaluesofBarecalculatedusingequation(9)togetherwith(al-a3)= 0.7{al-a3)f'andthecorrespondingvalueof~ v 'Thesepointsare indicatedonthestress-strainandvolumechangecurvesfortheMicaCreek Damcorematerial,whichareshowninFig.19. Forpurposesoforganizingthecalculationsinvolvedindetermining thevaluesof~andm,aswellasK,nandRf,itisconvenienttouse thecalculationformwhichisshowninFig.20.Anexampleoftheuseof thisformfortheMicaDamCoreMaterialisshowninFig.21.Thehyper-bolicstress-straincurvesareshownwiththetestdatainFig.22. Forhighlydilatantsoilshavingvolumetricstraincurveswhich reachhorizontaltangentspriortothestageofthetestatwhich70%of thestrengthis mObilized,thedatacorrespondingtothestageatwhich thevolumetricstraincurvesbecomehorizontalareusedincalculating valuesofB.ThevolumechangecurvesforMontereyNo.0sandwhichare ... Co . 800 600 42 0"3= 250 psi ~ - - . . ; ; : . 150 psi - 400 tr I -100psi 200 50psi 0 ~ - - - - ~ ~ - - - - - 4 ~ - - - - - 4 - - - - - - - 4 - - - - - - ~ 24810 :.I! o > II) 2 :3 Eo,% 100 psi ---_______- 150 psi --____--- 250 psi Note:~= pointsoncurvescorrespondingto{OJ-CT3yi:r,-0"3lf.=0.7 Fig.19STRESS-STRAINANDVOLUMECHANGECURVESFOR MICACREEKDAMCOREMATERIAL(SM-SC-IBl (INSLEYANDHILLIS.1965) Soil: CT3 CD Po (CT,- 0"3'ull Ei PO ..!. Po Dolo10'O,.IOIO,lcPo,om,I". DOlO'0' 70 -I.Sf,... L,.,I95 -I.SI,... L IBulkModulu.Po,om.I.,. !oj -CT3"(OJ -CT3'Eo Ell (OJ- CT3'Eo -..!L (OJ-CT3'bt. -------Poa @-@ =(!)'- @> @ (OJ-CT3' @@ ----.!!..!. PoPo R,= . @ A ,og.R, ' =2.0_..L @ + - @ [@>+ (!)]Po

Po (OJ -03'34 J!l 0 @ JiL0 (i) 5000 "...."",!,.11j;::::::.:::::.:: .. "" : : ; , , ; "',::;,.'..",";' or B/Po 100 50.' jl:I'::;j': 0.10.20.52 CT3/Pa 5 Fig.20FORMFORCOMPUTINGHYPERBOLICPARAMETERS 102050 " w Soil: 0010'0'Oe.iolo,icModulusPo,omele" CoreMoleriol 0010'0' 70 %SlressLevel95 %SI,e"Le.elBulkModulu.Po,om.'ers CTl\oj CT3',(OJ-CT3'0 11 (OJ- - 110\ \, LL= 35 a::\ ,0 , PI = 19 o \ '.5' \ \. , ''0 \ , '0,-;;-\J"I \J"I, 1051- r \"', , \',0'0\. 6'0 \.0 \..2-, \0 ,0 "-\ \. ___________L_________________L____________________ ____ 810121416182022242628 WATERCONTENT(%) FIG.25MOISTURE - DENSITYRELATIONSHIPSFORCOMPACTEDPITTSBURGSANDYCLAY. Ul '" 120 1151--+----,'" --

Q. ;:1051---f=-T-"'",,==i---+--+--""oI:-"'oC---I en z ILl o 681012141618202224 >- LL=35 120PI=19 681012141618202224 WATERCONTENT(%) 60 FIG.26STRENGTHPARAMETERSFORCOMPACTED PITTSBURGSANDYCLAYTESTEDUNDER UUTESTCONDITIONS. (KULHAWY.DUNCANandSEED.1969) >-I-(J) Z ILJ o LL :35 120PI=19 K II 0 6810141618202224

LL:35 120PI= 19 n 115105

681012141618202224 LL:35 120PI: 19 Rf \I

681012141618202224 WATERCONTENT(%) 61 FIG.27MODULUSPARAMETERSFORCOMPACTED PITTSBURGSANDYCLAYTESTEDUNDER UUTESTCONDITIONS. (KULHAWY,DUNCANandSEED,(969) 120 -U Q. 100 . >-812162024 -III c: Q) 0 I I >-.. 0 120 110 LL=35 ~ -PI=19 ~ " m -,/, 1'.,s= ( , \ ~ ~ O % '< \ i\ , v;-I -~~ 1/0 I '0.5 '" I' -1.0 100 812162024 WaterContent.% FIG.28BULKMODULUSPARAMETERSFOR COMPACTEDPITTSBURGSANDYCLAY TESTEDUNDERU-UTESTCONDITIONS. (CL-51. 62 varioustypesanddegreesofcompaction.Suchestilnatescanbemade usingthecompilationsofdataintheprevioussection.Usingthese data,conservativeparametervalueshavebeeninterpretedforvarious typesofsoils,andthesearesummarizedinTable7.Thesevalues arecalledconservativeinthesensethattheyaretypicalofthe 63 lowervaluesofstrengthandmodulus,andthehighervaluesofunit weightforeachtypeofsoil,basedonthedatacontainedinthisreport. TABLE7.SOILPROPERTIES Unified RC 4>0 ll4>C Classification Stand. Ym degdegk/ft2 AASHTOk/ft3 GW,GP1050.1504290 SW,SP1000.1453970 950.14036.50 900.1353330 SM1000.1353680 950.1303460 900.1253240 850.1203020 SM-SC1000.1353300.5 950.1303300.4 900.1253300.3 850.1203300.2 -CL1000.1353000.4 950.1303000.3 900.1253000.2 850.1203000.1 knRf 6000.40.7 4500.40.7 3000.40.7 2000.4.0.7 6000.250.7 4500.25 0.7 . 3000.250.7 1500.250.7 4000.60.7 2000.60.7 1500.60.7 1000.60.7 1500.450.7 1200.450.7 900.450.7 600.450.7 I), 175 125 75 50 450 350 250 150 200 100 75 50 140 110 80 50 m 0.2 0.2 0.2 0.2 0.0 0.0 0.0 0.0 0.5 0.5 0.5 0.5 0.2 0.2 0.2 0.2 '" .. 65 SUMMARY Iftheresultsofafiniteelementanalysisofstressesandmove-mentsinsoilaretobemeaningfulandrealistic,itisimportantthat thestress-straincharacteristicsofthesoilberepresentedinareason-ableway. Thehyperbolicstress-strainrelationshipsdescribedinthisreport canbeusedtorepresentthreeimportantcharacteristicsofthestress-strainbehaviorofsoils:nonlinearity,stress-dependency,and inelasticity.Thevaluesoftheparametersmaybedeterminedfromthe resultsofconventionallaboratorytests,andtheparametersmaybeused foranalysisofstressesandmovementsinstablesoilmasses. Thetechniquesusedtodeterminevaluesoftheparametersfrom theresultsoflaboratorytestsareexplainedindetail,andcompilations ofparametervaluesaregivenforsoilstestedunderbothdrainedand unconsolidated-undrainedtestconditions. ACKNOWLEDGMENT Manypeoplehaveparticipatedindevelopingtheconceptsandthe datacontainedinthisreport.Thewriterswishtoexpresstheir appreciationforthecontributionsofF.H.Kulhawy,C-Y.Chang,G.W. Clough,E.S.Nobari,PoulLade,J.M.Simon,andAntonioSoriano. TheresearchwassponsoredbytheNationalScienceFoundation underGrantNo.ENG73-08048A02. 66 REFERENCES 1.BechtelCOJ:Poration(1969)"ReportonSoilTestsfortheProposed NewDonPedroDam,"SanFrancisco. 2.Becker,E.,Chan,C.K.andSeed,H.Bolton(1972)"Strengthand DeformationCharacteristicsofRockfillMaterialsinPlaneStrain andTriaxialCompressionTests,"ReportNo.TE-72-3,Officeof ResearchServices,UniversityofCalifornia,Berkeley,California. 67 3.Bird,J.M.(1961)"UncertaintiesinEarthDamDesign,"Journalof theSoilMechanicsandFoundationsDivision,ASCE,Vol.87,No.SM3, June,pp.33-68. 4.Bishop,A.W.(1966)"TheStrengthofSoilsasEngineeringMaterials," Geotechnique,Vol.16,No.2,June,pp.89-130. 5.Broughton,N.o.(1970)"ElasticAnalysisforBehaviorofRockfill," JournaloftheSoilMechanicsandFoundationsDivision,ASCE,Sept., pp.1715-1733. 6.Casagrande,A.andHirschfeld,R.C.(1960)"FirstProgressReport onInvestigationofStress-DeformationandStrengthCharacteristics ofCompactedClays,"SoilMechanicsSeriesNo.61,HarvardUniversity, May. 7.Casagrande,A.andHirschfeld,R.C.(1962)"SecondProgressReport onInvestigationofStress-DeformationandStrengthCharacteristics ofCompactedClays,"SoilMechanicsSeriesNo.65,HarvardUni versi ty, April. 8.Casagrande,A.,Hirschfeld,R.C.andPoulos,S.J.(1963)"Third ProgressReportonInvestigationofStress-DeformationandStrength CharacteristicsofCompactedClays,"SoilMechanicsSeriesNo.70, HarvardUniversity,November,67p. 9.Casagrande,A.andPoulos,S.J.(l964)"FourthReportonInvestiga-tionofStress-DeformationandStrengthCharacteristicsofCompacted Clays ,"SoilMechanicsSeriesNo.74,HarvardUniversity,october. 10.Casagrande,A.(1965)"HoheStaudamme,"MitteilungendesInstitutes furGrundbauundBodenmechanik,TechnischeHochschu1e,Vienna,No.6, December,32p. 11.Chang,C-Y.andDuncan,J.M.(1970)"AnalysisofSoilMovements AroundaDeepExcavation,"JournalofSoilMechanicsandFoundations Division,ASCE,Vol.96,No.SM5,Proc.Paper7512,September, pp.1655-1681. 12.Clough,G.w.(1972)"ApplicationoftheFiniteElementMethodto Earth-StructureInteraction,"state-of-the-ArtReport,Proceedings oftheSymposiumonApplicationsoftheFiniteElementMethodin GeotechnicalEngineering,U.S.ArmyEngineersWaterwaysExperiment Station,Vicksburg,Mississippi,May. 13.Clough,G.W.andDuncan,J.M.(1971)"FiniteElementAnalysesof RetainingWallBehavior,"JournaloftheSoilMechanicsandFounda-tionsDivision,ASCE,Vol.97,No.SM12,December. 14.CorpsofEngineers,FortWorthDistrict(1961)"ProctorDam: Mem:>ran dum , "U.S.DepartmentoftheArmy,FortWorthDistrict, CorpsofEngineers,1961. 15.CorpsofEngineers,FortWorthDistrict(1961)"SomervilleDam: 68 DesignMemorandum,"U. S.DepartmentoftheArmy,FortWorthDistrict, CorpsofEngineers,1961. 16.CorpsofEngineers,JacksonvilleDistrict(1964)"RodmanDam,Cross FloridaBargeCanalProject:DesignMem:>randum,"U.S.Department oftheArmy,JacksonvilleDistrict,CorpsofEngineers,1964. 17.CorpsofEngineers,KansasCityDistrict(1966)"ClintonReservoir: DesignMemorandumNo.10,SupplementA,SoilDataandEmbankment Design,"U.S.DepartmentoftheArmy,KansasCityDistrict,Corps ofEngineers,August1967. 18.CorpsofEngineers,LouisvilleDistrict(1960)"MonroeReservoir: DesignMemorandumNo.2,AppendixI,LaboratoryTestData,"U.S. DepartmentoftheArmy,LouisvilleDistrict,CorpsofEngineers, February1960. 19.CorpsofEngineers,OmahaDistrict(1968)"ChatfieldDamandReservoir: DesignMem:>randumNo.PC-24,"U.S.DepartmentoftheArmy,Omaha District,CorpsofEngineers,1968. 20.CorpsofEngineers,TulsaDistrict(1972)"BirchDam:DesignMemoran-dumNo.6,Embankment,SpillwayandOutletWorks,"U.S.Department oftheArmy,TulsaDistrict,CorpsofEngineers,September1972. 21.DepartmentofWaterResources(1969)"ReportonUnconsolidated-UndrainedTriaxialShearTestsfortheCoreofOrovilleDam,"State ofCalifornia. 22.Duncan,J.M.andChang,C-Y.(1970)"NonlinearAnalysisofStress andStraininSoils,"JournaloftheSoilMechanicsandFoundations Division,ASCE,Vol.96,No.SM5,September1970. 23.Duncan,J.M.andClough.G.W.(1971)"FiniteElementAnalysesof portAllenLock,"JournaloftheSoilMechanicsandFoundations Division,ASCE,Vol.97,NO.5MB,Proc.Paper,August1971, pp.1053-1068. 69 24.Duncan,J.M.'andLefebvre,G.(1973)"EarthPressuresonStructures DuetoFaultMovement,"JournaloftheSoilMechanicsandFounda-tionsDivision,ASCE,Vol.99,NO.SM12,Proc.Paper10237,December 1973,pp.1153-1163. 25.Hall,E.B.andGordon,B.B.(1963)"TriaxialTestingwithLarge-ScaleHighPressureEquipment,"STP361- LaboratoryShearTesting ofSoils,ASTM,pp.315-328. 26.Hirschfeld,R.C.andPoulos,S.G.(1963)"High-PressureTriaxial TestsonaCompactedSandandanUndisturbedSilt,"STP361-LaboratoryShearTestingofSoils,ASTM,1963,pp.329-339. 27.Insley,A.E.andHillis,s.F.(196S)"TriaxialShearCharacteris-ticsofaCompactedGlacialTillUnderUnusuallyHighConfining Pressures,"Proceedings,6thInt.Conf.onSoilMechanicsand FoundationEngineering,Vol.1,Montreal,pp.244-248. 28.Janbu,Nilmar(l963)"SoilCompressibilityasDeterminedbyOedometer andTriaxialTests,"EuropeanConferenceonSoilMechanicsand FoundationEngineering,Wissbaden,Germany,vol.1,pp.19-25. 29.Kondner,R.L.(1963)"HyperbolicStress-StrainResponse:Cohesive Soils,"JournaloftheSoilMechanicsandFoundationsDivision,ASCE, Vol.89,No.SMl,February,1963,p.115. 30.Kondner,R.L.andZelasko,J.S.(1963)"AHyperbolicStress-Strain Formulation 'ofSands,"Proceedingsofthe2ndPanAmericanConference onSoilMechanicsandFoundationEngineering,Vol.1,Brazil,1963, p.289. 31.Kulhawy,F.H.andDuncan,J.M.(1972)"StressesandMovementsin OrovilleDam,"JournaloftheSoilMechanicsandFoundationsDivision, ASCE,Vol.98,No.SM7,Proc.Paper9016,July1972,pp.653-665. 32.Kulhawy,F.H.,Duncan,J.M.andSeed,H.B.(1969)"FiniteElement AnalysisofStressesandMovementsinEmbanJanentsDuringConstruction," ReportNo.TE69-4,OfficeofResearchServices,universityof California,Berkeley,California. 33.Lade,P.(1971)"TheStress-StrainandStrengthCharacteristicsof CohesionlessSoils,"Ph.D.Dissertation,UniversityofCalifornia, Berkeley,California,August1972. 34.Lee,K.L.(196S)"TriaxialCompressiveStrengthofSaturatedSand UnderSeismicLoadingConditions,"Dissertationpresentedtothe UniversityofCalifornia,Berkeley,inpartialfulfillmentofthe requirementsforthedegreeofDoctorofPhilosophy. 70 35.Lefebvre,G.,Duncan,J.M.andWilson,E.L.(1973)"Three-Dimensional FiniteElementAnalysesofDams,"JournaloftheSoilMechanicsand FoundationsDivision,ASCE,Vol.99,No.SM7,Proe.Paper9857,July, 1973,pp.495-507. 36.Linell,K.A.andShea,H.F.(1960)"StrengthandDeformationChar-acteristicsofVariousGlacialTillsinNewEngland,"Research ConferenceonShearStrengthofCohesiveSoils,ASCE,Boulder, Colorado,pp.275-314. 37.Marachi,N.(1969)"StrengthandDeformationCharacteristicsofRock-fillMaterials,"DissertationpresentedtotheUniversityofCalifornia, Berkeley,inpartialfulfillmentoftherequirementsforthedegreeof DoctorofPhilosophy. 38.Marsal,R.J.,Gomez,E.M.,Nunez,A.,Cuellar,R.andRamos,R.M. (1965)"ResearchontheBehaviorofGranularMaterialsandRockfill Samples,"ComisionFederaldeElectricidad,Mexico,D.F.,February, 1965,76p. 39.Marsal,R.J.(1967)"LargeScaleTestingofRockfillMaterials," JournaloftheSoilMechanicsandFoundationsDivision,ASCE,Vol.93, No.SM2,March1967,pp.27-43. 40.Nobari,E.S.andDuncan,J.M.(1972)"EffectofReservoirFilling onStressesandMovementsinEarthandRockfillDams,"ReportNo. TE-72-1,UniversityofCalifornia,Berkeley,January1972. 41.ShannonandWilson(1961)"ReportonSoilTests:RoundButteDam Project,"ShannonandWilson,SoilMechanicsandFoundation Engineers,Seattle,Washington,July,1961. 42.ShannonandWilson(1963)"ReportonConstructionControlandRecord TestsforRoundButteDam,"ShannonandWilson,SoilMechanicsand FoundationEngineers,Seattle,Washington,1 9 6 3 ~ 43.ShannonandWilson(1964)"ReportonConstructionControlandRecord TestsforRoundButteDam,"ShannonandWilson,SoilMechanicsand FoundationEngineers,Seattle,Washington,1964. 44.Sherman,W.C.andTrahan,C.C.(1968)"AnalysisofDatafrom InstrumentationProgram,PortAllenLock,"TechnicalReportS-68-7, U.S.ArmyEngineers,WaterwaysExperimentStation,Corpsof Engineers,Vicksburg,Mississippi,September1968. 45.Wong,KaiS.andDuncan,J.M.(1974)"HyperbolicStress-Strain ParametersforNonlinearFiniteElementAnalysesofstressesand MovementsinSoilMasses,"ReportNo.TE74-3,Universityof California,Berkeley,July1974. A-I APPENDIX- COMPUTERPROGRAMSP-5 Thiscomputerprogramevaluatesthestrengthandstress-strain parametersc,~ ,~ ~ ,K,n,andRf usingstress-straindata,andthebulk modulusparameters~andmusingvolumechangedataforconventional triaxialtestsatvariousconfiningpressures.Theprogramwasdeveloped byKaiWongattheUniversityofCalifornia,Berkeleyin1977. Thefollowingdataarerequiredfortheprogram: Card1(10A8) Columns1-80TITLE1.TitleCardforprogramidentification. Card2(6IS,F10.0) Columns,1-5M.Numberofstress-straincurves. 6-10L.Numberofvolume-changecurves. 11-15JJ.Ifstress-straindataaregivenintermsofcrl/cr3 vs,JJ= 0,Ifstress-straindataaregiveninterms of(crl-cr3)vs,JJ=1. 16-20IPUNCH.If nopunchedoutputisdesired,IPUNCH= O. Ifpunchedoutputisdesired,IPUNCH=1. 21-25ICHECK.IfICHECK=1,correspondingvaluesof(cr1-cr3) andwillbecalculatedusingtheparametersdetermined andthevaluesprinted.Theseareusefulinchecking thecorrespondenceofthedataandtheparameters.If ICHECK=0,thesevaluesarenotcalculatedorprinted. 26-30ICOND.ForICOND= 0,astraight-linefai'lureenvelope isfittedtothedata,andvaluesofcand~aredetermined. ForICOND=1,acurvedenvelopeisfittedtothedata,and valuesof~ oand~ ~aredetermined.(Seeequation14and Figs.13and14.) 31-40Atmosphericpressure,expressedinthesystemofunits usedinthetests. Pa = 14.7Ib/in2 Pa = 1.033kg/crn2 Pa = 2116Ib/ft2 Pa = 10.33metricton/rn2 Pa = 2.116 k/ft2 Pa = 101. 4kN/rn2 Pa = 1.058t/ft2 Card(s)3(6F10.0) Columns1-10Confiningpressure,03, 11-20Stressratioatfailure,(01/03)forstressdifference atfailure,(01-03)f' 21-30Axialstrainat70%stresslevel(percent). 31-40Axialstrainat95%stresslevel(percent). 41-50Volumetricstrainat70%stresslevel(percent). A-2 Theinputvolumetricstrainat70%mustbecompressiveandbelessthan orequaltothemaximumcompressivevolumetricstrain. Repeat,onecardforeachtest,totalofM cards. c PROGRAMSF'S(INPUT, OUTPUT, PUrICH,TAPE 1 = HIPUTl COMMONM, L, Kk. JJ, XIN (20) "'IN (20) , XSLOPE. 'y' HiTER, lP(201.DPA(20),DP8(20),DPF(2B).PR, 2ERA(201.EA8(20) .EVR(20l.EV8(20) ,ERA(201 ,ER8(20), 3COHESN, ANGL 1 DRNGL 1, 4XK. XN. RAVE, >,KB, XM, 5TITLE 1 (10). 6EI(20l.PPA(20l.8(20) CHIPUTINFORMATIONOFEACHSO IL C c [ READ100.TITLE 1 IFCEOF(12,3.2. 2STOP 3CONTINUE READ120.M.L.JJ. IPUtICH,ICHECK.ICOND.PA MM=M PRINT130 PRINT200, TITLE 1 PR INT190 rEVALUATIONOFEIANDRF c c c c KB=0 XM=0.0 XKB=0.0 XHAX=0..0. ).."*X) YZ=(""'*>