非饱和土力学大师Fredlund的演讲

WhatistheFutureforSlopeStabilityAnalysis?

(AreWeApproachingtheLimitsofLimitEquilibriumAnalyses?)Introduction

LimitEquilibriummethodsofsliceshavebeen“Good”forthegeotechnicalengineeringprofessionsincethemethodshaveproducedfinancialbenefitEngineersareoftensurprisedattheresultstheyareabletoobtainfromLimitEquilibriummethodsSoWhyChange?ThereareFundamentalLimitationswithLimitEquilibriumMethodsofSlices??TheboundariesforaFREEBODYDIAGRAMarenotknown-TheSHAPEfortheslipsurfacemustbeassumedTheLOCATIONofthecriticalslipsurfacemustbe foundbyTRIALandERRORSHAPEandLOCATIONarethedrivingforceforaparadigmshift

ObjectivesofthisPresentation:ToshowthegradualchangethatisemerginginthewaythatslopestabilityanalysescanbeundertakenToillustratethebenefitsassociatedwithimprovedproceduresfortheassessmentofstressesinaslopeOutlineofPresentationProvideabriefSummaryofcommonLimitEquilibriummethodsalongwiththeirlimitations(2-D&3-D)Takethe

FIRST

stepforwardthroughuseofanindependentstressanalysisTaketheSECONDstepforwardthroughuseofOptimizationTechniquesIsaLimitEquilibriumAnalysisanUpperBoundorLowerBoundSolution?LimitEquilibriumMethodsprimarilysatisfytherequirementsofanupperboundtypeofsolutionReason:theshape

ofslipsurfaceisselectedbytheanalystandtherebyadisplacementboundaryconditionisimposedLimitEquilibriumandFiniteElementBasedMethodsofAnalysesWWWWWWWWNLimitEquilibriumMethodofAnalysisSm=tadldlsndlFiniteElementBased

MethodofAnalysisldtadlQUESTION:HowcantheNormalStressatthebaseofaslicebemostaccuratelycomputed?ConsidertheFreeBodyDiagramsusedtocalculatetheNormalStress?AssumptionforallLimitEquilibriumAnalysisSoilsbehaveasMohr-Coulombmaterials

(i.e.,friction,f',andcohesion,c')Factorofsafety,Fs,forthecohesivecomponentisequaltothefactorofsafetyforthefrictionalcomponentFactorofsafetyisthesameforallslices()[]msnsSFuFc=-+bfsb'tan'SummaryofAvailableEquationsAssociatedwithaLimitEquilibriumAnalysisEquations(knowns): QuantityMomentequilibrium nVerticalforceequilibrium nHorizontalforceequilibrium nMohr-Coulombfailurecriterion n

4nUnknowns:

QuantityTotalnormalforceatbaseofslice nShearforceatthebaseofslice,Sm nInterslicenormalforce,E n-1Intersliceshearforce,X n-1Pointofapplicationofintersliceforce,E n-1Pointofapplicationofnormalforce nFactorofsafety,Fs 1

6n-2SummaryofUnknownsAssociatedwithaLimitEquilibriumAnalysisOneFsperslidingmassForcesActingonEachSliceFocusonSmbyxSmXREREXLSlipsurfaceGround

surfaceWhRN

=snbbfNLPhreaticlineMobilizedShearForce,Sm

for

Saturated-UnsaturatedSoils()[]()swasansmFuuFuFcSbfbfsbbtan'tan'-+-+=Onlynewvariablerequiredforsolvingsaturated-unsaturatedsoilsproblemsistheshearforcemobilizedφb

=Frictionanglewithrespecttomatricsuctionua=Pore-airpressureuw

=Pore-waterpressure[]Momentequilibrium,Fm:Forceequilibrium,Ff:ååå-ïþïýüïîïíì÷÷øöççèæ-+=NfWx'tanR'tantanuNR'cFbwmfffbbååþýüîíì÷÷øöççèæ-+=aafffbabsincos'tan'tantancos'NuNcFbwfPore-airpressuresareassumedtobezerogaugeNormalforceatbaseofslice:LimitEquilibriummethodsdifferintermsofhow(XR-XL)iscomputedandoverallstaticssatisfiedLimitEquilibriumproblemisindeterminate:Canapplyanassumption(Historicalsolution)Canutilizeadditionalphysics(Futuresolution)()FFuFcXXWNbwLR'tansincostansinsin'faafabab++---=sxbaArea=Interslice

normalforce(E)widthofslice,bsxtxysyDistance(m)Elevation

(m)txybaArea=Interslice

shearforce(X)Vertical

sliceDistance(m)Elevation

(m)ò=baxydyXtò=baxdyEsStressesontheBoundaryBetweenSlicesMorgenstern&Price,1965SummaryofLimitEquilibriumMethodsandAssumptionsMethod

EquilibriumSatisfied

Assumptions

Ordinary

Moment,tobase

EandX=0

Bishop’sSimplified

Vertical,Moment

Eishorizontal,X=0

Janbu’sSimplified

Vertical,Horizontal

Eishorizontal,X=0,empiricalcorrectionfactor,f0,accountsforintersliceshearforces

Janbu’sGeneralized

Vertical,Horizontal

Eislocatedbyanassumedlineofthrust

Spencer

Vertical,Horizontal,Moment

ResultantofEandXareofconstantslope

ForcesActingonOneSliceinOrdinaryorConventionalMethodhWbbaN=sb

nNSmForcesActingonOneSliceinBishop’sSimplifiedandJanbu’sSimplifiedMethods

hWbbaN=sb

nNSmERELSummaryofLimitEquilibriumMethodsandAssumptionsDirectionofXandEistheaverageofthegroundsurfaceslopeandtheslopeatthebaseofasliceVerticalHorizontalLoweandKarafiathDirectionofXandEisparalleltothegroundVerticalHorizontalCorpsofEngineersDirectionofEandXisdefinedbyanarbitraryfunction.PercentofthefunctionrequiredtosatisfymomentandforceequilibriumiscalledλVerticalHorizontalMomentMorgenstern-Price,GLEAssumptionsEquilibriumSatisfiedMethod

ForcesActingonOneSliceinSpencer’s,Morgenstern-Price,and

GLE

Methods

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Element

Analysis

for

StressesLimit

Equilibrium

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