土木工程专业英语原文及翻译文档格式.docx

土木工程专业英语原文及翻译文档格式.docx

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StabilityofSlopes

Introduction

Translationalslipstendtooccurwheretheadjacentstratumisatarelativelyshallowdepthbelowthesurfaceoftheslope:

thefailuresurfacetendstobeplaneandroughlyparalleltotheslipsusuallyoccurwheretheadjacentstratumisatgreaterdepth，thefailuresurfaceconsistingofcurvedandplanesections．

Inpractice,limitingequilibriummethodsareusedintheanalysisofslopestability.Itisconsideredthatfailureisonthepointofoccurringalonganassumedoraknownfailuresurface．Theshearstrengthrequiredtomaintainaconditionoflimitingequilibriumiscomparedwiththeavailableshearstrengthofthesoil，givingtheaveragefactorofsafetyalongthefailuresurface．Theproblemisconsideredintwodimensions，conditionsofplanestrainbeingassumed．Ithasbeenshownthatatwo-dimensionalanalysisgivesaconservativeresultforafailureonathree-dimensional（dish-shaped）surface．

AnalysisfortheCaseofφu=0

Thisanalysis,intermsoftotalstress，coversthecaseofafullysaturatedclayunderundrainedconditions,.Fortheconditionimmediatelyafterconstruction．Onlymomentequilibriumisconsideredintheanalysis．Insection,thepotentialfailuresurfaceisassumedtobeacirculararc.Atrialfailuresurface（centreO，radiusrandlengthLa

whereFisthefactorofsafetywithrespecttoshearstrength．EquatingmomentsaboutO：

Therefore

Themomentsofanyadditionalforcesmustbetakenintoaccount．Intheeventofatensioncrackdeveloping，asshownin，thearclengthLaisshortenedandahydrostaticforcewillactnormaltothecrackifthecrackfillswithwater．Itisnecessarytoanalyzetheslopeforanumberoftrialfailuresurfacesinorderthattheminimumfactorofsafetycanbedetermined．

Basedontheprincipleofgeometricsimilarity，Taylor[]publishedstabilitycoefficientsfortheanalysisofhomogeneousslopesintermsoftotalstress．ForaslopeofheightHthestabilitycoefficient（Ns）forthefailuresurfacealongwhichthefactorofsafetyisaminimumis

Forthecaseofφu=0，valuesofNssdependsontheslopeangleβandthedepthfactorD，whereDHisthedepthtoafirmstratum．

GibsonandMorgenstern[]publishedstabilitycoefficientsforslopesinnormallyconsolidatedclaysinwhichtheundrainedstrengthcu（φu=0）varieslinearlywithdepth．

Example

A45°

slopeisexcavatedtoadepthof8minadeeplayerofsaturatedclayofunitweight19kN／m3:

therelevantshearstrengthparametersarecu=65kN／m2andφu

Inthecross-sectionalareaABCDis70m2.

Weightofsoilmass=70×

19=1330kN／m

ThecentroidofABCDismfromO．TheangleAOCis°

andradiusOCism．ThearclengthABCiscalculatedas．Thefactorofsafetyisgivenby：

Thisisthefactorofsafetyforthetrialfailuresurfaceselectedandisnotnecessarilytheminimumfactorofsafety．

TheminimumfactorofsafetycanbeestimatedbyusingEquation.

From，β=45°

andassumingthatDislarge，thevalueofNs

9.3TheMethodofSlices

αandtheheight,measuredonthecentre-1ine,ish.Thefactorofsafetyisdefinedastheratiooftheavailableshearstrength（τf）totheshearstrength（τm）whichmustbemobilizedtomaintainaconditionoflimitingequilibrium,.

Thefactorofsafetyistakentobethesameforeachslice，implyingthattheremustbemutualsupportbetweenslices，.forcesmustactbetweentheslices．

Theforces（perunitdimensionnormaltothesection）actingonasliceare：

totalweightoftheslice，W=γbh（γsatwhereappropriate）．

totalnormalforceonthebase，N（equaltoσl）．Ingeneralthis

forcehastwocomponents，theeffectivenormalforceN'

（equaltoσ'

l）andtheboundarywaterforceU（equaltoul），whereuistheporewaterpressureatthecentreofthebaseandlisthelengthofthebase．

shearforceonthebase，T=τml.

totalnormalforcesonthesides,E1andE2.

shearforcesonthesides，X1andX2.

Anyexternalforcesmustalsobeincludedintheanalysis．

TheproblemisstaticallyindeterminateandinordertoobtainasolutionassumptionsmustbemaderegardingtheintersliceforcesEandX：

theresultingsolutionforfactorofsafetyisnotexact．

ConsideringmomentsaboutO，thesumofthemomentsoftheshearforcesTonthefailurearcACmustequalthemomentoftheweightofthesoilmassABCD．ForanyslicetheleverarmofWisrsinα,

therefore

∑Tr=∑Wrsinα

Now,

Forananalysisintermsofeffectivestress，

Or

whereLaisthearclengthAC．EquationisexactbutapproximationsareintroducedindeterminingtheforcesN'

．ForagivenfailurearcthevalueofFwilldependonthewayinwhichtheforcesN'

areestimated．

TheFelleniusSolution

Inthissolutionitisassumedthatforeachslicetheresultantoftheintersliceforcesiszero．Thesolutioninvolvesresolvingtheforcesoneachslicenormaltothebase，.

N'

=WCOSα-ul

Hencethefactorofsafetyintermsofeffectivestress（Equationisgivenby

ThecomponentsWCOSαandWsinαcanbedeterminedgraphicallyforeachslice．Alternatively，thevalueofαcanbemeasuredorcalculated．Again，aseriesoftrialfailuresurfacesmustbechoseninordertoobtaintheminimumfactorofsafety．Thissolutionunderestimatesthefactorofsafety：

theerror，comparedwithmoreaccuratemethodsofanalysis，isusuallywithintherange5-2%.

ForananalysisintermsoftotalstresstheparametersCuandφuareusedandthevalueofuinEquationiszero．Ifφu=0,thefactorofsafetyisgivenby

AsN’doesnotappearinEquationanexactvalueofFisobtained．

TheBishopSimplifiedSolution

Inthissolutionitisassumedthattheresultantforcesonthesidesofthe

slicesarehorizontal，.

Xl-X2=0

Forequilibriumtheshearforceonthebaseofanysliceis

Resolvingforcesintheverticaldirection:

Itisconvenienttosubstitute

l=bsecα

FromEquation，aftersomerearrangement，

Theporewaterpressurecanberelatedtothetotal‘fillpressure’atany

pointbymeansofthedimensionlessporepressureratio，definedas

（γsatwhereappropriate）．Foranyslice,

HenceEquationcanbewritten:

AsthefactorofsafetyoccursonbothsidesofEquation,aprocessofsuccessiveapproximationmustbeusedtoobtainasolutionbutconvergenceisrapid．

Duetotherepetitivenatureofthecalculationsandtheneedtoselectanadequatenumberoftrialfailuresurfaces，themethodofslicesisparticularlysuitableforsolutionbycomputer．Morecomplexslopegeometryanddifferentsoilstratacanbeintroduced．

Inmostproblemsthevalueoftheporepressureratioruisnotconstantoverthewholefailuresurfacebut，unlessthereareisolatedregionsofhighporepressure，anaveragevalue（weightedonanareabasis）isnormallyusedindesign．Again，thefactorofsafetydeterminedbythismethodisanunderestimatebuttheerrorisunlikelytoexceed7％andinmostcasesislessthan2％．

Spencer[]proposedamethodofanalysisinwhichtheresultantIntersliceforcesareparallelandinwhichbothforceandmomentequilibriumaresatisfied．SpencershowedthattheaccuracyoftheBishopsimplifiedmethod，inwhichonlymomentequilibriumissatisfied,isduetotheinsensitivityofthemomentequationtotheslopeoftheintersliceforces．

Dimensionlessstabilitycoefficientsforhomogeneousslopes，basedonEquation，havebeenpublishedbyBishopandMorgenstern[].Itcanbeshownthatforagivenslopeangleandgivensoilpropertiesthefactorofsafetyvarieslinearlywithγuandcanthusbeexpressedas

F=m-nγu

where，mandnarethestabilitycoefficients．Thecoefficients，mandnare

functionsofβ,φ’，thedimensionlessnumberc'

/γandthedepthfactorD.

UsingtheFelleniusmethodofslices，determinethefactorofsafety，intermsofeffectivestress，oftheslopeshowninforthegivenfailuresurface．Theunitweightofthesoil，bothaboveandbelowthewatertable，is20kN／m3andtherelevantshearstrengthparametersarec’=10kN/m2andφ’=29°

.

W）ofeachsliceisgivenby

W=γbh=20×

×

h=30hkN／m

Theheighthforeachsliceissetoffbelowthecentreofthebaseandthe

normalandtangentialcomponentshcosαandhsinα

Wcosα=30hcosα

Wsinα=30hsinα

Theporewaterpressureatthecentreofthebaseofeachsliceistakentobeγwzw，wherezwistheverticaldistanceofthecentrepointbelowthewatertable（asshowninfigure）．Thisprocedureslightlyoverestimatestheporewaterpressurewhichstrictlyshouldbe）γwze，wherezeistheverticaldistancebelowthepointofintersectionofthewatertableandtheequipotentialthroughthecentreoftheslicebase．Theerrorinvolvedisonthesafeside．

Thearclength（La）iscalculatedasmm．Theresultsaregivenin

Table

∑Wcosα=30×

=525kN／m

∑Wsinα=30×

=254kN／m

∑（wcosα-ul）=525—132=393kN／m

AnalysisofaPlaneTranslationalSlip

Itisassumedthatthepotentialfailuresurfaceisparalleltothesurfaceoftheslopeandisatadepththatissmallcomparedwiththelengthoftheslope.Theslopecanthenbeconsideredasbeingofinfinitelength，withendeffectsbeingignored．Theslopeisinclinedatangleβmz（0<

m<

1）abovethefailureplane．Steadyseepageisassumedtobetakingplaceinadirectionparalleltotheslope．Theforcesonthesidesofanyverticalsliceareequalandoppositeandthestressconditionsarethesameateverypointonthefailureplane．

Intermsofeffectivestress，theshearstrengthofthesoilalongthefailureplaneis

andthefactorofsafetyis

Theexpressionsforσ,τandμare:

Thefollowingspecialcasesareofinterest．Ifc’=0andm=0.thesoil

betweenthesurfaceandthefailureplaneisnotf