2006Critical-StateSoilMechanicsForDummiesPaulW.Mayne,PhD,P.E.

Civil&EnvironmentalEngineering

GeorgiaInstituteofTechnology

Atlanta,GA30332-0355

Email:paul.PROLOGUE

Critical-statesoilmechanicsisaneffectivestressframeworkdescribingmechanicalsoilresponseInitssimplestformhere,weconsideronlyshear-inducedloading.Wemerelytietogethertwowell-knownconcepts:(1)one-dimensionalconsolidationbehavior,representedbye-logsv’curves;and(2)shearstress-vs.normalstress(t-sv’)fromdirectshearboxorsimpleshearing.Herein,onlythebareessenceofCSSMconceptsarepresented,sufficienttodescribestrength&compressibilityresponse.CriticalStateSoilMechanics(CSSM)

ExperimentalevidenceprovidedbyHvorslev(1936;1960,ASCE);Henkel(1960,ASCEBoulder)Henkel&Sowa(1961,ASTMSTP361)Mathematicspresentedelsewhere,including:Schofield&Wroth(1968);Burland(1968);Wood(1990).Inbasicform:3materialconstants(f',Cc,Cs)plusinitialstate(e0,svo',OCR)ConstitutiveModels,include:OriginalCam-Clay,ModifiedCamClay,NorSand,BoundingSurface,MIT-E3(Whittle,1993)&MIT-S1(Pestana)andothers(Adachi,Oka,Ohta,Dafalias)"Undrained"isjustonespecificstresspathYet!!!CSSMismissingfrommosttextbooksandundergrad&gradcurriculaintheUSA.DirectShearTestResultssv’tDirectShearBox(DSB)sv’tDirectSimpleShear(DSS)tdtgsCSSMforDummiesLogsv'Effectivestresssv'ShearstresstVoidRatio,eNCCCtanf'CSLEffectivestresssv'VoidRatio,eNCCSLCSSMPremise:“Allstresspathsfailonthecriticalstateline(CSL)”CSLfc=0CSSMforDummiesLogsv'Effectivestresssv'ShearstresstVoidRatio,eVoidRatio,eNCNCCCtanf'CSLCSLCSLSTRESSPATHNo.1NCDrainedSoilGiven:e0,svo’,NC(OCR=1)e0svosvoDrainedPath:Du=0tmax=c+stanfefDeVolumeChangeisContractive:

evol=De/(1+e0)<0Effectivestresssv'c’=0CSSMforDummiesLogsv'Effectivestresssv'ShearstresstVoidRatio,eNCNCCCtanf'CSLCSLCSLNote:AllNCundrainedstresspathsareparalleltoeachother,thus:su/svo’=constantEffectivestresssv'DSS:su/svo’NC=?sinf’VoidRatio,eCSSMforDummiesLogsv'Effectivestresssv'Effectivestresssv'ShearstresstVoidRatio,eVoidRatio,eNCNCCCtanf'CSLCSLCSLCSsp'sp'OCOverconsolidatedStates:e0,svo’,andOCR=sp’/svo’wheresp’=svmax’

=Pc’=preconsolidationstress;OCR=overconsolidationratioCSSMforDummiesLogsv'Effectivestresssv'ShearstresstVoidRatio,eNCNCCCtanf'CSLCSLCSLCSOCStressPathNo.3UndrainedOCSoil:e0,svo’,andOCRsvo'e0svo'StressPath:DV/V0=0NegativeExcessDuEffectivestresssv'svf'VoidRatio,eDuCriticalstatesoilmechanicsInitialstate:e0,svo’,andOCR=sp’/svo’Soilconstants:f’,Cc,andCs(L=1-Cs/Cc)ForNCsoil(OCR=1):Undrained(evol=0):+Duandtmax=su=cuDrained(Du=0)andcontractive(decrease

evol)

ForOCsoil:Undrained(evol=0):-Duandtmax=su=cuDrained(Du=0)anddilative(Increase

evol)There’smore!Semi-drained,Partlyundrained,Cyclic…..EquivalentStressConceptLogsv'Stresssv'ShearstresstVoidRatio,eNCNCCCtanf'CSLCSLCSLCSOC1.OCState(eo,svo’,sp’)svo'2.ProjectOCstatetoNClineforequivalentstress,se’3.se’=svo’OCR[1-Cs/Cc]svo'e0Effectivestresssv'VoidRatio,esp'sp'se'se'susvf'epDe=Cslog(sp’/svo’)De=Cclog(se’/sp’)Deatse’suOC=suNCCriticalstatesoilmechanicsPreviously:su/svo’=constantforNCsoilOnthevirgincompressionline:svo’=se’Thus:su/se’=constantforallsoil(NC&OC)Forsimpleshear:su/se’=?sinf’Equivalentstress:NormalizedUndrainedShearStrength:su/svo’=?sinf’OCRL

whereL=(1-Cs/Cc)se’=svo’OCR[1-Cs/Cc]UndrainedShearStrengthfromCSSMPorewaterPressureResponsefromCSSMYieldSurfacesLogsv'Normalstresssv'ShearstresstVoidRatio,eNCNCCSLCSLCSLOCNormalstresssv'VoidRatio,esp'sp'OCYieldsurfacerepresents3-dpreconsolidationQuasi-elasticbehaviorwithintheyieldsurfaceYieldSurfaceCavityExpansion–CriticalStateModelforEvaluating

OCRinClaysfromPiezoconeTests

whereM=6sinf’/(3-sinf’)andL

=1–Cs/Cc0.8qcfsubqTCriticalstatesoilmechanicsInitialstate:e0,svo’,andOCR=sp’/svo’Soilconstants:f’,Cc,andCs(L=1-Cs/Cc)Usingeffectivestresses,CSSMad