土木毕业英文论文翻译.docx

土木毕业英文论文翻译.docx

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土木毕业英文论文翻译

INTERNATIONALJOURNALFORNUMERICALANDANALYTICALMETHODSINGEOMECHANICS

Int.J.Numer.Anal.Meth.Geomech.,23,439}449（1999）

SHORTCOMMUNICATIONS

ANALYTICALMETHODFORANALYSISOFSLOPE

STABILITY

JINGGANGCAOsANDMUSHARRAFM.ZAMAN*t

SchoolofCivilEngineeringandEnvironmentalScience,UniversityofOklahoma,Norman,OK73019,U.S.A.

SUMMARY

Ananalyticalmethodispresentedforanalysisofslopestabilityinvolvingcohesiveandnon-cohesivesoils.Earthquakeeffectsareconsideredinanapproximatemannerintermsofseismiccoe$cient-dependentforces.Twokindsoffailuresurfacesareconsideredinthisstudy:

aplanarfailuresurface,andacircularfailuresurface.Theproposedmethodcanbeviewedasanextensionofthemethodofslices,butitprovidesamoreaccurateetreatmentoftheforcesbecausetheyarerepresentedinanintegralform.Thefactorofsafetyisobtainedbyusingtheminimizationtechniqueratherthanbyatrialanderrorapproachusedcommonly.

Thefactorsofsafetyobtainedbytheanalyticalmethodarefoundtobeingoodagreementwiththosedeterminedbythelocalminimumfactor-of-safety,Bishop's,andthemethodofslices.Theproposedmethodisstraightforward,easytouse,andlesstime-consuminginlocatingthemostcriticalslipsurfaceandcalculatingtheminimumfactorofsafetyforagivenslope.Copyright（1999）JohnWiley&Sons,Ltd.

Keywords:

analyticalmethod;slopestability;cohesiveandnon-cohesivesoils;dynamiceffect;planarfailuresurface;circularfailuresurface;minimizationtechnique;factor-of-safety.

INTRODUCTION

OneoftheearliestanalyseswhichisstillusedinmanyapplicationsinvolvingearthpressurewasproposedbyCoulombin1773.Hissolutionapproachforearthpressuresagainstretainingwallsusedplaneslidingsurfaces,whichwasextendedtoanalysisofslopesin1820byFrancais.Byabout1840,experiencewithcuttingsandembankmentsforrailwaysandcanalsinEnglandandFrancebegantoshowthatmanyfailuresurfacesinclaywerenotplane,butsigni"cantlycurved.In1916,curvedfailuresurfaceswereagainreportedfromthefailureofquaystructuresinSweden.Inanalyzingthesefailures,cylindricalsurfaceswereusedandtheslidingsoilmasswasdividedintoanumberofverticalslices.TheprocedureisstillsometimesreferredtoastheSwedishmethodofslices.Bymid-1950sfurtherattentionwasgiventothemethodsofanalysisusing

circularandnon-circularslidingsurfaces.Inrecentyears,numericalmethodshavealsobeenusedintheslopestabilityanalysiswiththeunprecedenteddevelopmentofcomputerhardwareandsoftware.OptimizationtechniqueswereusedbyNguyen,10andChenandShao.Whilefiniteelementanalyseshavegreatpotentialformodellingfieldconditionsrealistically,theyusuallyrequiresigni"cante!

ortandcostthatmaynotbejusti"edinsomecases.

Thepracticeofdividingaslidingmassintoanumberofslicesisstillinuse,anditformsthebasisofmanymodernanalyses.1,9However,mostofthesemethodsusethesumsofthetermsforallsliceswhichmakethecalculationsinvolvedinslopestabilityanalysisarepetitiveandlaboriousprocess.

Locatingtheslipsurfacehavingthelowestfactorofsafetyisanimportantpartofanalyzingaslopestabilityproblem.Anumberofcomputertechniqueshavebeendevelopedtoautomateasmuchofthisprocessaspossible.Mostcomputerprogramsusesystematicchangesinthepositionofthecenterofthecircleandthelengthoftheradiustofindthecriticalcircle.

Unlesstherearegeologicalcontrolsthatconstraintheslipsurfacetoanoncircularshape,itcanbeassumedwithareasonablecertaintythattheslipsurfaceiscircular.9Spencer（1969）foundthatconsiderationofcircularslipsurfaceswasascriticalaslogarithmicspiralslipsurfacesforallpracticalpurposes.CelestinoandDuncan（1981）,andSpencer（1981）foundthat,inanalyseswheretheslipsurfacewasallowedtotakeanyshape,thecriticalslipsurfacefoundbythesearchwasessentiallycircular.Chen（1970）,BakerandGarber（1977）,andChenandLiumaintainedthatthecriticalslipsurfaceisactuallyalogspiral.ChenandLiu12developedsemi-analyticalsolutionsusingvariationalcalculus,forslopestabilityanalysiswithalogspiralfailuresurfaceinthecoordinatesystem.Earthquakee!

ectswereapproximatedintermsofinertiaforces（verticalandhorizontal）definedbythecorrespondingseismiccoe$cients.Althoughthisisoneofthecomprehensiveandusefulmethods,useof/-coordinatesystemmakesthesolutionprocedureattainablebutverycomplicated.Also,thesolutionsareobtainedvianumericalmeansattheend.ChenandLiu12havelistedmanyconstraints,stemmingfromphysicalconsiderationsthatneedtobetakenintoaccountwhenusingtheirapproachinanalyzingaslopestabilityproblem.

Thecircularslipsurfacesareemployedforanalysisofclayeyslopes,withintheframeworkofananalyticalapproach,inthisstudy.TheproposedmethodismorestraightforwardandsimplerthanthatdevelopedbyChenandLiu.Earthquakeeffectsareincludedintheanalysisinanapproximatemannerwithinthegeneralframeworkofstaticloading.Itisacknowledgedthatearthquakeeffectsmightbebettermodeledbyincludingaccumulateddisplacementsintheanalysis.Theplanarslipsurfacesareemployedforanalysisofsandyslopes.Aclosed-formexpressionforthefactorofsafetyisdeveloped,whichisdiferentfromthatdevelopedbyDas.

STABILITYANALYSISCONDITIONSANDSOILSTRENGTH

Therearetwobroadclassesofsoils.Incoarse-grainedcohesionlesssandsandgravels,theshearstrengthisdirectlyproportionaltothestresslevel:

（1）

where

istheshearstressatfailure,

theeffectivenormalstressatfailure,and

theeffectiveangleofshearingresistanceofsoil.

Infine-grainedclaysandsiltyclays,thestrengthdependsonchangesinporewaterpressuresorporewatervolumeswhichtakeplaceduringshearing.Underundrainedconditions,theshearstrengthcuislargelyindependentofpressure,thatis

=0.Whendrainageispermitted,however,both&cohesive'and&frictional'components

areobserved.Inthiscasetheshearstrengthisgivenby

（2）

Considerationoftheshearstrengthsofsoilsunderdrainedandundrainedconditions,andoftheconditionsthatwillcontroldrainageinthefieldareimportanttoincludeinanalysisofslopes.Drainedconditionsareanalyzedintermsofeffectivestresses,usingvaluesof

determinedfromdrainedtests,orfromundrainedtestswithporepressuremeasurement.Performingdrainedtriaxialtestsonclaysisfrequentlyimpracticalbecausetherequiredtestingtimecanbetoolong.DirectsheartestsorCUtestswithporepressuremeasurementareoftenusedbecausethetestingtimeisrelativelyshorter.

Stabilityanalysisinvolvessolutionofaprobleminvolvingforceand/ormomentequilibrium.Theequilibriumproblemcanbeformulatedintermsof

（1）totalunitweightsandboundarywaterpressure;or

（2）buoyantunitweightsandseepageforces.Thefirstalternativeisabetterchoice,becauseitismorestraightforward.Althoughitispossible,inprinciple,tousebuoyantunitweightsandseepageforces,thatprocedureisfraughtwithconceptualdiffculties.

PLANARFAILURESURFACE

Failuresurfacesinhomogeneousorlayerednon-homogeneoussandyslopesareessentiallyplanar.Insomeimportantapplications,planarslidesmaydevelop.Thismayhappeninslope,wherepermeablesoilssuchassandysoilandgravelorsomepermeablesoilswithsomecohesionyetwhoseshearstrengthisprincipallyprovidedbyfrictionexist.Forcohesionlesssandysoils,theplanarfailuresurfacemayhappeninslopeswherestrongplanardiscontinuitiesdevelop,forexampleinthesoilbeneaththegroundsurfaceinnaturalhillsidesorinman-madecuttings.

Figure1showsatypicalplanarfailureslope.FromanequilibriumconsiderationoftheslidebodyABCbyaverticalresolutionofforces,theverticalforcesacrossthebaseoftheslidebodymustequaltoweightw.Earthquakeeffectsmaybeapproximatedbyincludingahorizontalaccelerationkgwhichproducesahorizontalforcek=actingthroughthecentroidofthebodyandneglectingverticalinertia.1Forasliceofunitthicknessinthestrikedirection,theresolvedforcesofnormalandtangentialcomponentsNand¹canbewrittenas

（3）

（4）

where

istheinclinationofthefailuresurfaceandwisgivenby

（5）

where

istheunitweightofsoil,Htheheightofslope,

istheinclinationoftheslope.SincethelengthoftheslidesurfaceABis

theresistingforceproducedbycohesioniscH/sina.ThefrictionforceproducedbyNis

.Thetotalresistingoranti-slidingforceisthusgivenby

（6）

Forstability,thedownslopeslideforce¹mustnotexceedtheresistingforceRofthebody.Thefactorofsafety,Fs,intheslopecanbedefinedintermsofeffectiveforcebyratioR/T,thatis

（7）

Itcanbeobservedfromequation（7）thatFsisafunctionofa.ThustheminimumvalueofFscanbefoundusingPowell'sminimizationtechnique18fromequation（7）.DasreportedasimilarexpressionforFswithk=0,developeddirectlyfromequation

（2）byassumingthat

where

istheaverageshearstrengthofthesoil,and

theaverageshearstressdevelopedalongthepotentialfailuresurface.

Forcohesionlesssoilswherec=0,thesafetyfactorcanbereadilywrittenfromequation（7）as

（8）

ItisobviousthattheminimumvalueofFsoccurswhena=b,andthefailurebecomesindependentofslopeheight.Forsuchcases（c=0andk=0）,thefactorsofsafetyobtainedfromtheproposedmethodandfromDasareidentical.

CIRCULARFAILURESURFACE

Slidesinmedium-stifclaysareof