畢業(yè)設(shè)計(jì)論文外文文獻(xiàn)翻譯中英文對照土木工程簡要的分析斜坡穩(wěn)定性的方法

畢業(yè)設(shè)計(jì)論文外文文獻(xiàn)翻譯中英文對照土木工程簡要的分析斜坡穩(wěn)定性的方法INTERNATIONALJOURNALFORNUMERICALANDANALYTICALMETHODSINGEOMECHANICSInt.J.Numer.Anal.Meth.Geomech.,23,439}449(1999)SHORTCOMMUNICATIONSANALYTICALMETHODFORANALYSISOFSLOPESTABILITYJINGGANGCAOsANDMUSHARRAFM.ZAMAN*tSchoolofCivilEngineeringandEnvironmentalScience,UniversityofOklahoma,Norman,OK73019,U.S.A.SUMMARYAnanalyticalmethodispresentedforanalysisofslopestabilityinvolvingcohesiveandnon-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.INTRODUCTIONOneoftheearliestanalyseswhichisstillusedinmanyapplicationsinvolvingearthpressurewasproposedbyCoulombin1773.Hissolutionapproachforearthpressuresagainstretainingwallsusedplaneslidingsurfaces,whichwasextendedtoanalysisofslopesin1820byFrancais.Byabout1840,experiencewithcuttingsandembankmentsforrailwaysandcanalsinEnglandandFrancebegantoshowthatmanyfailuresurfacesinclaywerenotplane,butsigni"cantlycurved.In1916,curvedfailuresurfaceswereagainreportedfromthefailureofquaystructuresinSweden.Inanalyzingthesefailures,cylindricalsurfaceswereusedandtheslidingsoilmasswasdividedintoanumberofverticalslices.TheprocedureisstillsometimesreferredtoastheSwedishmethodofslices.Bymid-1950sfurtherattentionwasgiventothemethodsofanalysisusingcircularandnon-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.STABILITYANALYSISCONDITIONSANDSOILSTRENGTHTherearetwobroadclassesofsoils.Incoarse-grainedcohesionlesssandsandgravels,theshearstrengthisdirectlyproportionaltothestresslevel:''(1),,,,tanf/,f,whereistheshearstressatfailure,theeffectivenormalstressatfailure,/,andtheeffectiveangleofshearingresistanceofsoil.Infine-grainedclaysandsiltyclays,thestrengthdependsonchangesinporewaterpressuresorporewatervolumeswhichtakeplaceduringshearing.Underundrained,uconditions,theshearstrengthcuislargelyindependentofpressure,thatis=0.When''(,)c,drainageispermitted,however,both&cohesive'and&frictional'componentsareobserved.Inthiscasetheshearstrengthisgivenby(2)Considerationoftheshearstrengthsofsoilsunderdrainedandundrainedconditions,andoftheconditionsthatwillcontroldrainageinthefieldareimportanttoincludeinanalysisofslopes.Drainedconditionsareanalyzedintermsofeffectivestresses,using''(,)c,valuesofdeterminedfromdrainedtests,orfromundrainedtestswithporepressuremeasurement.Performingdrainedtriaxialtestsonclaysisfrequentlyimpracticalbecausetherequiredtestingtimecanbetoolong.DirectsheartestsorCUtestswithporepressuremeasurementareoftenusedbecausethetestingtimeisrelativelyshorter.Stabilityanalysisinvolvessolutionofaprobleminvolvingforceand/ormomentequilibrium.Theequilibriumproblemcanbeformulatedintermsof(1)totalunitweightsandboundarywaterpressure;or(2)buoyantunitweightsandseepageforces.Thefirstalternativeisabetterchoice,becauseitismorestraightforward.Althoughitispossible,inprinciple,tousebuoyantunitweightsandseepageforces,thatprocedureisfraughtwithconceptualdiffculties.PLANARFAILURESURFACEFailuresurfacesinhomogeneousorlayerednon-homogeneoussandyslopesareessentiallyplanar.Insomeimportantapplications,planarslidesmaydevelop.Thismayhappeninslope,wherepermeablesoilssuchassandysoilandgravelorsomepermeablesoilswithsomecohesionyetwhoseshearstrengthisprincipallyprovidedbyfrictionexist.Forcohesionlesssandysoils,theplanarfailuresurfacemayhappeninslopeswherestrongplanardiscontinuitiesdevelop,forexampleinthesoilbeneaththegroundsurfaceinnaturalhillsidesorinman-madecuttings.,,,圖平面破壞Figure1showsatypicalplanarfailureslope.FromanequilibriumconsiderationoftheslidebodyABCbyaverticalresolutionofforces,theverticalforcesacrossthebaseoftheslidebodymustequaltoweightw.Earthquakeeffectsmaybeapproximatedbyincludingahorizontalaccelerationkgwhichproducesahorizontalforcek=actingthroughthecentroidofthebodyandneglectingverticalinertia.1Forasliceofunitthicknessinthestrikedirection,theresolvedforcesofnormalandtangentialcomponentsNand?canbewrittenas(3)NWk,,(cossin),,(4)TWk,，(sincos),,whereistheinclinationofthefailuresurfaceandwisgivenbyLWxxdxHxdx,,，,,,,,,(tantan)(tan),,0(5)2H,,,(cotcot),,2,whereistheunitweightofsoil,Htheheightofslope,isLHlH,,cot,cot,,,,theinclinationoftheslope.SincethelengthoftheslidesurfaceABis,thecH/sin,resistingforceproducedbycohesioniscH/sina.ThefrictionforceproducedbyNis.Thetotalresistingoranti-slidingforceisthusgivenbyWk(cossin)tan,,,,(6)RWkcH,,，(cossin)tan/sin,,,,Forstability,thedownslopeslideforce?mustnotexceedtheresistingforceRofthebody.Thefactorofsafety,Fs,intheslopecanbedefinedintermsofeffectiveforcebyratioR/T,thatis1tan2,kc,F,，tan(7),skHk，，,tan(sincos)sin(),,,,,,Itcanbeobservedfromequation(7)thatFsisafunctionofa.ThustheminimumvalueofFscanbefoundusingPowell'sminimizationtechnique18fromequation(7).DasreportedasimilarexpressionforFswithk=0,developeddirectlyfromequation(2)F,,,/,byassumingthat,whereistheaverageshearstrengthofthesoil,andsfdf,theaverageshearstressdevelopedalongthepotentialfailuresurface.dForcohesionlesssoilswherec=0,thesafetyfactorcanbereadilywrittenfromequation(7)as1tan,k,(8)F,tan,sk，tan,ItisobviousthattheminimumvalueofFsoccurswhena=b,andthefailurebecomesindependentofslopeheight.Forsuchcases(c=0andk=0),thefactorsofsafetyobtainedfromtheproposedmethodandfromDasareidentical.CIRCULARFAILURESURFACESlidesinmedium-stifclaysareoftendeep-seated,andfailuretakesplacealongcurvedsurfaceswhichcanbecloselyapproximatedintwodimensionsbycircularsurfaces.Figure2showsapotentialcircularslidingsurfaceABintwodimensionswithcentreOandradiusr.Thefirststepintheanalysisistoevaluatethesliding'ordisturbingmomentMsaboutthecentreofthecircleO.Thisshouldincludetheself-weightwoftheslidingmass,andothertermssuchascrestloadingsfromstockpilesorrailways,andwaterpressuresactingexternallytotheslope.Earthquakeeffectsisapproximatedbyincludingahorizontalaccelerationkgwhichproducesahoriazontalforcekd=actingthroughthecentroidofeachsliceandneglectingverticalinertia.WhenthesoilaboveABisjustonthepointofsliding,theaverageshearingresistancewhichisrequiredalongABforlimitingequilibriumisgivenbyequation(2).Theslidemassisdividedintoverticalslices,andatypicalsliceDEFGisshown.Theself-weightofthesliceis.ThemethodassumesthatthedWhdx,,resultantforcesXlandXronDEandFG,respectively,areequalandopposite,andparalleltothebaseofthesliceEF.Itisrealizedthattheseassumptionsarenecessarytokeeptheanalyticalsolutionoftheslopestabilityproblemaddressedinthispaperachievableandsomeoftheseassumptionswouldleadtorestrictionsintermsofapplications(e.g.earthpressureonretainingwalls).However,analyticalsolutionshaveaspecialusefulnessinengineeringpractice,particularlyintermsofobtainingapproximatesolutions.Morerigorousmethods,e.g.finiteelementtechnique,canthenbeusedtopursueadetailsolution.Bishop'srigorousmethod5introducesafurthernumericalproceduretopermitspecialcationofintersliceshearforcesXlandXr.SinceXlandXrareinternalforces,mustbezeroforthewholesection.Resolving()XX,,lrprerpendicularlyandparalleltoEF,onegets(9)Thdxkhdx,，,,,,sincos(10)Nhdxkhdx,,,,,,coscsinxa,22(11),arcsin,rab,,，rTheforceNcanproduceamaximumshearingresistancewhenfailureoccurs:(12)Rcdxhdxk,，,sec(cossin)tan,,,,,TheequationsoflinesAC,CB,andABYaregivenbyy22yxyhybrxa,,,,,,tan,,(),(13)123ThesumsofthedisturbingandresistingmomentsforallslicescanbewrittenaslMrhkdx,，,,,(sincos)s,0ll(14),,，，,，ryykdxryykdx()(sincos)()(sincos),,,,,,1323,,0L,，rIkI(),sclMrchkdx,，,sec(cossin)tan,,,,,,,r,0ll,，,,rcdxryykdxsec()(cossin)tan,,,,,23,,00(15)l，,,ryykdx()(cossin)tan,,,,23,L2,，,rcrIkItan()cs,,,22LHlarbH,,，,,cot,(),(16)laa,(17),arcsinarcsin,，rrLlIyydxyydx,,，,()sin()sin,,1323s,,0L(18)2H1，，2,，,(cot)secabH,,,,23r，，LlIyydxyydx,,，,()cos()cos,,s1323,,0L22tantanbrb,,2222，，,,，,,,，，2()()()rLarLa，，623rr(19)rLara,,,,,，,，,(tan)arcsin(tan)arcsinaHab,,,,,,22rr,,,,rla,1222，，,,，,，,,()arcsin()4()()bHrlablaHa，，26rrThesafetyfactorforthiscaseisusuallyexpressedastheratioofthemaximumavailableresistingmomenttothedisturbingmoment,thatiscrIkI,,,，,tan()McsrF,,(20)sMIkI()，,sscWhentheslopeinclinationexceeds543,allfailuresemergeatthetoeoftheslope,chiscalledtoewhifailure,asshowninFigure2.However,whentheslopeheightHisrelativelylargecomparedwiththeundrainedshearstrengthorwhenahardstratumis0,,3underthetopoftheslopeofclayeysoilwith,theslideemergesfromthefaceoftheslope,whichiscalledFacefailure,asshowninFigure3.ForFacefailure,thesafety()Hh,factorFsisthesameas?oefailure1susinginsteadofH.0Forflatterslopes,failureisdeep-seatedandextendstothehardstratumformingthebaseoftheclaylayer,whichiscalledBasefailure,asshowninFigure4.1,3Followingthesameprocedureasthatfor?oefailure,onecangetthesafetyfactorforBasefailure:''crIkI，,tan(),,,csF,(21)s''IkI，,，，sc''IIwheretisgivenbyequation(17),andandaregivenbysclll01'Iyyxdxyyxdxyyxdx,,，,，,sinsinsin，，，，，，s031323,,,ll000(22)3HHblH222,，,,,,，,，cot()()(2)(33)lllllabbHH,0112223rrrlll01,,,,，，，，，，I,y,ycosd，y,ycosd，y,ycosd,,,xxxc031323ll010(23)Hl1r1,arba,,,,2220,，，,r,Hcot,b,Harcsin,arcsin，,,,,2r42r2r,,,,,HHcot1,,,,222，，，，,,ratan,arcsin，4rl,ab，l,aH,a,,,,,22r6r,,,,22其中，yyxyHybrxa,,,,,,,0,tan,,,(24)，，1231122(25),,,，,，,,,,laHlaHlarbHcot,cot,，，0122Itcanbeobservedfromequations(21)~(25)thatthefactorofsafetyFsforagivenslopeisafunctionoftheparametersaandb.Thus,theminimumvalueofFscanbefoundusingthePowell'sminimizationtechnique.Foragivensinglefunctionfwhichdependsontwoindependentvariables,suchastheproblemunderconsiderationhere,minimizationtechniquesareneededtofindthevalueofthesevariableswhereftakesonaminimumvalue,andthentocalculatethecorrespondingvalueoff.IfonestartsatapointPinanN-dimensionalspace,andproceedfromthereinsomevectordirectionn,thenanyfunctionofNvariablesf(P)canbeminimizedalongthelinenbyone-dimensionalmethods.Differentmethodswilldiferonlybyhow,ateachstage,theychoosethenextdirectionn.Powell"rstdiscoveredadirectionsetmethodwhichproducesNmutuallyconjugatedirections.Unfortunately,aproblemoflineardependencewasobservedinPowell'salgorithm.ThemodiffedPowell'smethodavoidsabuildupoflineardependence.Theclosed-formslopestabilityequation(21)allowstheapplicationofanoptimizationtechniquetolocatethecenteroftheslidingcircle(a,b).TheminimumfactorofsafetyFsminthenobtainedbysubstitutingthevaluesoftheseparametersintoequations(22)~(25)andtheresultsintoequation(21),forabasefailureproblem(Figure4).WhileusingthePowell'smethod,thekeyistospecifysomeinitialvaluesofaandb.Well-assumedinitialvaluesofaandbcanresultinaquickconvergence.Ifthevaluesofaandbaregiveninappropriately,itmayresultinadelayedconvergenceandcertainvalueswouldnotproduceaconvergentsolution.Generally,ashouldbeassumedwithin$?,whilebshouldbeequaltoorgreaterthanH(Figure4).Similarly,equations(16)~(20)couldbeusedtocomputetheFs.minfortoefailure(Figure2)andfacefailure(Figure3),exceptisusedinsteadofHinthecaseoffacefailure.Hh,，，0BesidesthePowellmethod,otheravailableminimizationmethodswerealsotriedinthisstudysuchasdownhillsimplexmethod,conjugategradientmethods,andvariablemetricmethods.ThesemethodsneedmorerigorousorcloserinitialvaluesofaandbtothetargetvaluesthanthePowellmethod.AshortcomputerprogramwasdevelopedusingthePowellmethodtolocatethecenteroftheslidingcircle(a,b)andtofindtheminimumvalueofFs.Thisapproachofslopestabilityanalysisisstraightforwardandsimple.RESULTSANDCOMMENTSThevalidityoftheanalyticalmethodpresentedintheprecedingsectionswasevaluatedusingtwowell-establishedmethodsofslopestabilityanalysis.Thelocalminimumfactor-of-safety(1993)method,withthestateoftheeffectivestressesinaslopedeterminedbythefiniteelementmethodwiththeDrucker-Pragernon-linearstress-strainrelationship,andBishop's(1952)methodwereusedtocomparetheoverallfactorsofsafetywithrespecttotheslipsurfacedeterminedbytheproposedanalyticalmethod.Assumingk=0forcomparisonwiththeresultsobtainedfromthelocalminimumfactor-of-safetyandBishop'smethod,theresultsobtainedfromeachofthosethreemethodsarelistedinTableI.Thecasesarechosenfromthetoefailureinahypotheticalhomogeneousdrysoilslopehavingaunitweightof18.5kN/m3.Twoslopeconfigurationswereanalysed,one1:1slopeandone2:1slope.EachslopeheightHwasarbitrarilychosenas8m.Toevaluatethesensitivityofstrengthparametersonslopestability,cohesionrangingfrom5to30kPaandfrictionanglesrangingfrom103to203wereusedintheanalyses(TableI).Anumberofcriticalcombinationsofcandwerefoundtobeunstableforthemodelslopesstudied.Thefactorsofsafetyobtainedbytheproposedmethodareingoodagreementwiththosedeterminedbythelocalminimumfactor-of-safetyandBishop'smethods,asshowninTableI.Toexaminethee!ectofdynamicforces,theanalyticalmethodischosentoanalyseatoefailureinahomogeneousclayeyslope(Figure2).TheheightoftheslopeHis13.5m;theslopeinclinationbisarctan1/2;theunitweightofthesoilcis17.3kN/m3;thefrictionangleis17.3KN/m;andthecohesioncis57.5kPa.UsingtheconventionalF,2.09methodofslices,LiuobtainedtheminimumsafetyfactorUsingthesminproposedmethod,onecangettheminimumvalueofsafetyfactorfromequation(20)asF,2.08fork=0,whichisveryclosetothevalueobtainedfromtheslicemethod.sminF,1.55,1.37Whenk"0)1,0)15,or0)2,onecanget,and1)23,respectively,whichsminshowsthedynamice!ectontheslopestabilitytobesignificant.CONCLUDINGREMARKSAnanalyticalmethodispresentedforanalysisofslopestabilityinvolvingcohesiveandnoncohesivesoils.Earthquakee!ectsareconsideredinanapproximatemannerintermsofseismiccoe$cient-dependentforces.Twokindsoffailuresurfacesareconsideredinthisstudy:aplanarfailuresurface,andacircularfailuresurface.Threefailureconditionsforcircularfailuresurfacesnamelytoefailure,facefailure,andbasefailureareconsideredforclayeyslopesrestingonahardstratum.Theproposedmethodcanbeviewedasanextensionofthemethodofslices,butitprovidesamoreaccuratetreatmentoftheforcesbecausetheyarerepresentedinanintegralform.Thefactorofsafetyisobtainedbyusingtheminimizationtechniqueratherthanbyatrialanderrorapproachusedcommonly.Thefactorsofsafetyobtainedfromtheproposedmethodareingoodagreementwiththosedeterminedbythelocalminimumfactor-of-safetymethod(finiteelementmethod-basedapproach),theBishopmethod,andthemethodofslices.Acomparisonofthesemethodsshowsthattheproposedanalyticalapproachismorestraightforward,lesstime-consuming,andsimpletouse.Theanalyticalsolutionspresentedheremaybefoundusefulfor(a)validatingresultsobtainedfromotherapproaches,(b)providinginitialestimatesforslopestability,and(c)conductingparametricsensitivityanalysesforvariousgeometricandsoilconditions.REFERENCES1.D.BrunsdenandD.B.Prior.SlopeInstability,Wiley,NewYork,1984.2.B.F.WalkerandR.Fell.SoilSlopeInstabilityandStabilization,Rotterdam,Sydney,1987.3.C.Y.Liu.SoilMechanics,ChinaRailwayPress,Beijing,P.R.China,1990.448SHORTCOMMUNICATIONSCopyright(1999JohnWiley&Sons,Ltd.Int.J.Numer.Anal.Meth.Geomech.,23,439}449(1999)4.L.W.Abramson.SlopeStabilityandStabilizationMethods,Wiley,NewYork,1996.5.A.W.Bishop.&Theuseoftheslipcircleinthestabilityanalysisofslopes',Geotechnique,5,7}17(1955).6.K.E.Petterson.&Theearlyhistoryofcircularslidingsurfaces',Geotechnique,5,275}296(1956).7.G.Lefebvre,J.M.DuncanandE.L.Wilson.&Three-dimensional"niteelementanalysisofdams,'J.SoilMech.Found,ASCE,99(7),495}507(1973).8.Y.KohgoandT.Yamashita,&Finiteelementanalysisof"lltypedams*stabilityduringconstructionbyusingthee!ectivestressconcept',Proc.Conf.Numer.Meth.inGeomech.,ASCE,Vol.98(7),1998,pp.653}665.9.J.M.Duncan.&Stateoftheart:limitequilibriumand"nite-elementanalysisofslopes',J.Geotech.Engng.ASCE,122(7),577}596(1996).10.V.U.Nguyen.&Determinationofcriticalslopefailuresurface',J.Geotech.Engng.ASCE,111(2),238}250(1985).11.Z.ChenandC.Shao.&Evaluationofminimumfactorofsafetyinslopestabilityanalysis,'Can.Geotech.J.,20(1),104}119(1988).12.W.F.ChenandX.L.Liu.?imitAnalysisinSoilMechanics,Elsevier,NewYork,1990.13.N.M.Newmark.&E!ectsofearthquakesondamsandembankments',Geotechnique,15,139}160(1965).14.B.M.Das.PrinciplesofGeotechnicalEngineering,PWSPublishingCompany,Boston,1994.15.A.W.SkemptonandH.Q.Golder.&Practicalexamplesofthe/"0analysisofstabilityofclays',Proc.2ndInt.Conf.SMFE,Rotterdam,Vol.2,1948,pp.63}70.16.L.Bjerrum,andT.C.Kenney.&E!ectofstructureontheshearbehaviorofnormallyconsolidatedquickclays',Proc.Geotech.Conf.,Oslo,Norway,vol.2,1967,pp.19}27.17.A.W.Skempton,&Long-termstabilityofclayslopes,'Geotechnique,14,77}102(1964).18.D.G.Liu,J.G.Fei,Y.J.YuandG.Y.Li.FOR?RANProgramming,NationalDefenseIndustryPress,Beijing,P.R.China,1988.19.W.H.Press,B.P.Flannery,S.A.TeukolskyandW.T.Vetterling,NumericalRecipes:?heArtofScienti,cComputing,CambridgeUniversityPress,Cambridge,1995.20.M.G.AndersonandK.S.Richards.SlopeStability:GeotechnicalEngineeringandGeomorphology,Wiley,NewYork,1987.21.R.Baker.&Determinationofcriticalslipsurfaceinslopestabilitycomputations',Int.J.Numer.Anal.Meth.Geomech.,4,333}359(1980).22.A.K.Chugh.&Variablefactorofsafetyinslopestabilityanalysis',Geotechnique,?ondon,36(1),57}64(1986).23.B.M.Das.PrinciplesofSoilDynamics,PWS-KentPublishingCompany,Boston,1993.24.S.L.HuangandK.Yamasaki.&Slopefailureanalysisusinglocalminimumfactor-of-safetyapproach',J.Geotech.Engng.ASCE,119(12),1974}1987(1993).25.S.L.Kramer.GeotechnicalEarthquakeEngineering,PrenticeHall,EnglewoodCli!s,NJ,1996.26.D.LeshchinskyandC.Huang.&Generalizedthreedimensionalslopestabilityanalysis',J.Geotech.Engng.ASCE,118(11),1748}1764(1992).27.K.S.LiandW.White.&Rapidevaluationofthecriticalsurfaceinslopestabilityproblems',Int.J.Numer.Anal.Meth.Geomech.,11(5),449}473(1987).28.D.W.Taylor.FundamentalsofSoilMechanics,Wiley,Toronto,1948.29.U.S.FederalHighwayAdministration,Advanced?echnologyforSoilSlopeStability,U.S.Dept.ofTransportation,Washington,DC,1994.30.Spencer(1969).31.CelestinoandDuncan(1981).32.Spencer(1981).33.Chen(1970).34.BakerandGarber(1977).35.Bishop(1952).簡要的分析斜坡穩(wěn)定性的方法JINGGANGCAOs和MUSHARRAFM.ZAMAN諾曼底的俄克拉荷馬大學(xué)土木環(huán)境工程學(xué)院摘要本文給出了解析法對邊坡的穩(wěn)定性分析,包括粘性和混凝土支撐。地震被認(rèn)為是用和振動相似的方式產(chǎn)生的地震從屬效應(yīng)。這篇論文涉及到了兩種破壞面:一個(gè)平面的破壞面,一個(gè)圓形的破壞面，這個(gè)合適的方法可以被視為切割方法的延伸，但是它提供了更加精確的計(jì)算力的方法，因?yàn)樗捎玫氖欠e分的方法。安全的方法是利用最小化的技術(shù),而不是一般的由一個(gè)反復(fù)的試驗(yàn)方法。安全的因素所獲得的分析方法是符合最初最低基本安全因素的方法—切割法。推薦的方法是基于最危險(xiǎn)滑動面的直接的，最簡單的去用并且最快的計(jì)算，和計(jì)算該斜坡的最小安全系數(shù)。關(guān)鍵詞:解析方法;巖質(zhì)邊坡穩(wěn)定性;有粘性和無粘性土;動力學(xué)因素;平坦的破壞面;圓形破壞面;估算最小值的方法;影響安全性的因素介紹最早的用在分析土應(yīng)力的方法被認(rèn)為是庫倫在1773年提出來的。他的解決擋土墻土應(yīng)力的方法用的是滑動面，在1820年法國這個(gè)被延伸用來分析邊坡。直到1840年，英國和法國的鐵路和隧道的鉆鑿和路堤經(jīng)驗(yàn)表明了許多泥土中的破壞面不是平的，而是沒有規(guī)律的彎曲的。1916年，不規(guī)則的破壞面在碼頭結(jié)構(gòu)破壞中出現(xiàn)在瑞典。分析了這些破壞面之后，圓柱體截面被采用，并且滑移土體被分成了一定數(shù)量的條形體。這個(gè)解決程序有時(shí)候也被稱為“瑞典條分法”。到十九世紀(jì)五十年代中期，人們的注意力轉(zhuǎn)移到了用圓形和非圓形滑動面的分析上了。近些年來，隨著電腦的硬件和軟件史無前例的發(fā)展，數(shù)值分析法已經(jīng)被用在了邊坡穩(wěn)定性分析上。最好的方法是Nguyen,andChenandShao用的，當(dāng)有限元分析有模擬真實(shí)的土質(zhì)情況的時(shí)候，他們一直需要巨大的人力和物理，這些可能是沒有結(jié)果的。這個(gè)方法的滑動到數(shù)片仍然在被使用,它形成了許多現(xiàn)代分析基礎(chǔ),然而,大多數(shù)的這些方法的使用條款所有切片使計(jì)算邊坡穩(wěn)定性分析中所涉及的重復(fù)性和艱苦的過程。定位的滑動面具有最低的安全系數(shù)的分析,是一個(gè)邊坡穩(wěn)定問題重要的一部分。大量的計(jì)算機(jī)技術(shù)已經(jīng)發(fā)展到自動化許多這樣的過程。大多數(shù)的計(jì)算機(jī)程序在中心的位置,利用半徑的長度使用系統(tǒng)的變化找到臨界圓。除非有地質(zhì)控制去約防止動面稱為一個(gè)圓形狀,它可以被認(rèn)為是某一個(gè)合理的圓形邊坡。承擔(dān)合理的滑動面是circular.9斯潘塞(1969)發(fā)現(xiàn)考慮的圓形滑移面和對數(shù)螺旋滑動面是同樣臨界的使用目的。Celestino和鄧肯(1981年)、斯潘塞(1981年)的研究發(fā)現(xiàn),在分析滑動面形狀可以發(fā)生任何變形的地方滑動面被證明基本上都是圓形的。陳(1970),貝克和Garber(1977年)、陳、Liu12堅(jiān)持滑動面實(shí)際上是一個(gè)切削螺旋型的。為解決邊坡穩(wěn)定性分析，陳和Liu12發(fā)表的解析在坐標(biāo)系里是利用,,變分微積分,和對數(shù)螺旋線破裂面的來分析的。地應(yīng)力是幾乎按照地震系數(shù)定義,,的慣性力來估計(jì)的。雖然利用坐標(biāo)系來解決方案是一個(gè)綜合的測驗(yàn)和有用的方,,法,但是這種方法是十分復(fù)雜的。同時(shí),采用數(shù)值方法最后也能解決問題。陳和劉列出了對邊坡穩(wěn)定性分析時(shí)需要考慮的很多,出于物理因素的限制。在此研究中圓形滑動面是用于粘土質(zhì)斜坡分析框架內(nèi)的一個(gè)。分析方法。所提出的方法比陳和劉提出的方法更直接、更簡單地震效應(yīng)也包含在相似的總體框架相對靜載的方法中。地震效應(yīng)可以在位移模擬的分析方法中被更好的模擬是公認(rèn)的。平緩的滑動面用來分析砂性的斜坡。一個(gè)安全系數(shù)的解析表達(dá)式發(fā)展并且被應(yīng)用了，這是不同于Das所提出的分析方法的。穩(wěn)定性分析條件和土壤應(yīng)力有兩種級別的土壤。在無粘性土和砂石中，剪切力是和應(yīng)力成正比的:''(1),,,,tanf//,f,,是破壞時(shí)的剪切力，是破壞時(shí)的正應(yīng)力，是土壤的摩擦角。在粉質(zhì)粘土和細(xì)粘土中，應(yīng)力取決于孔隙水壓力或者是水在剪切過程中占cu得體積。在沒有排水措施的前提下，剪切力很大程度上是和壓力無關(guān)的，也就,''u(,)c,是說=0.當(dāng)有排水設(shè)施時(shí)，不管是密實(shí)的或者是有摩擦的，他們的系數(shù)都是遵循上述規(guī)律的。這種情況下，剪切強(qiáng)度如下式:考慮到剪力強(qiáng)度在排水和不排水條件下的不同，所以排水情況在邊坡分析中是非常重要的。排水條件是依據(jù)應(yīng)力值確定的，用的是排水和不排水條件下的孔隙壓''(,)c,力測試來確定系數(shù)的。對粘土采用三周壓縮試驗(yàn)的排水方法通常是不合適的，因?yàn)樗枰臏y試時(shí)間可太長了。經(jīng)常采用直剪試驗(yàn)或CU測試孔隙水壓力是因?yàn)闇y試時(shí)間是相對較短的。穩(wěn)定性分析包括解決涉及力和力矩平衡的問題。公式(1)利用容重和水壓力界限可以來解決平衡問題，或者通過公式(2)利用浮容重和滲流壓力。第一個(gè)方案是比較好的選擇，是因?yàn)樗又苯樱牟襟E只是存在概念上的不同。二維破壞面均勻的或者是不均勻的砂性邊坡的破裂面是二維的。在一些重要的二維滑坡的應(yīng)用是可以應(yīng)用的。這種方法可以用在可滲透性的土壤，比如砂性土和礫石，或者是有內(nèi)聚力的砂性土，這種土的剪切力是由摩擦力提供的。對于無粘性的砂性土，邊坡的二維破壞面可能發(fā)生在較大的二維間斷點(diǎn)發(fā)育的地方，比如在自然或者是人工的山體土壤的下面是自然的土質(zhì)中。,,,圖平面破壞圖1顯示一典型的平面失敗的斜坡。把滑動體ABC上的平衡力豎向分解，作用在滑動體上的垂直力一定是平衡與滑動體的自重W的。振動力是接近包括同一水平線上的重力加速度，它產(chǎn)生了一個(gè)水平方向的作用在滑動體重心上的力KW，并且不考慮豎直方向的慣性。對于作用力方向的一個(gè)單位層厚度，已知常力及其分量N、T可以按下式:(3)NWk,,(cossin),,(4)TWk,，(sincos),,其中為破壞面的傾斜角，W按照下式計(jì)算:LWxxdxHxdx,,，,,,,,,(tantan)(tan),,0(5)2H,,,(cotcot),,2,式中，是土壤的容重，H是邊坡的高，，是邊坡的LHlH,,cot,cot,,,,傾斜。滑動面長AB為，摩擦阻力為，N產(chǎn)生的摩擦力是H/sin,cH/sin,，總的抗滑力按下式給出:Wk(cossin)tan,,,,(6)RWkcH,,，(cossin)t