Deep excavation-Stability analysis

StabilityanalysisFailureofanexcavationmayarisefromthestressonthesupportsystemexceedingthestrengthofitsmaterials,forexample,whenthestrutloadexceedsthebucklingloadofstrutsorthebendingmomentoftheretainingwallexceedsthelimitingbendingmoment.Failurecanalsoarisefromtheshearstressinsoilexceedingtheshearstrength.Themethodsofanalyzingwhetherthesoilsattheexcavationsiteareabletobearthestressgeneratedbyexcavationarecalledstabilityanalyses,andarethemainsubjectmatterofthischapter.Stabilityanalysesincludeoverallshearfailureanalysis,sandboilinganalysis,overturning,slidingandupheavalanalysis.Theoverallshearfailureanalysiscanbefurtherdividedintopush-inandbasalheavefailureanalyses.1.Introduction2.TypesoffactorsofsafetyThestrengthfactormethodTheloadfactormethodThedimensionfactormethodthreemethodstodeterminethefactorofsafety:Strengthfactormethod:Themethodconsidersthesoilstrengthinvolvingmuchuncertaintyandhasthestrengthreducedbyafactorofsafety.(Theparameterfortheundrainedanalysis)(after-reductionparameters)Loadfactormethod:Thefactorofsafetyfortheloadmethod,FSl,canbedefinedasfollows:whereRrepresentstheresistantforceandDisthedrivingforce.RandDcanbeeithertheresistantmomentandthedrivingmoment,orthebearingforceandtheexternalforce.Dimensionfactormethod:Supposethatretainingwallsareinthelimitingstateandthesoilstrengthsarefullymobilized.Withtheforceequilibrium(thehorizontalforceequilibrium,themomentequilibriumorothertypeofforceequilibrium),thepenetrationdepthofretainingwallsinthelimitingstatecanbefound.Thepenetrationdepthfordesignis:3.OverallshearfailureDefinition:Whentheshearstressatapointinsoilexceedsorequalstheshearstrengthofsoilatthepoint,thepointisinthefailurestateorlimitingstate.Whenmanyfailurepointsconnectupintocontinuitiesandformaplane,thefailuresurfaceisthusproduced.Oncethefailuresurfaceisproduced,theexcavationfailureorcollapsewilloccur.Thisiscalledtheoverallshearfailure.Thepush-inmethodThebasalheavemethodThepush-inmethodThebasalheavemethodDifferences:push-inreferstothestabilityoftheretainingwall.ThebasalheavemethodreferstothestabilityofthesoilFreeearthsupportmethodandfixedearthsupportmethodfreeearthsupportmethodassumesthattheembedmentoftheretainingwallisallowedtomovetoacertaindistanceundertheactionoflateralearthpressure.Thefixedearthsupportmethodistoassumethattheembedmentoftheretainingwallseemstobefixedatapointbelowtheexcavationsurface.Thus,whentheretainingwallisinthelimitingstate,thelateralearthpressurearoundthefixedpointonthetwosidesoftheretainingwalldoesnotnecessarilyreachtheactiveorpassivepressures.4.OverallshearfailureofstruttedwallsPush-inmethodthefactorofsafetyagainstpush-inMs=allowablebendingmomentoftheretainingwallEqcanbeusedeithertoobtainthefactorofsafetyagainstpush-inforacertaindepthofwallortherequiredpenetrationdepthofaretainingwallwithacertainvalueofsafetyfactor.BasalheaveTheanalysesofthebasalheavefailureareonlyapplicabletoclayeysoilsthesoilweightabovetheleveloftheexcavationsurface(planeabc)canbeseenastheloadtocauseexcavationfailure.SupposingatrialfailuresurfacecausedbythesoilweightwithinthewidthofB1actsonplaneabcasisshowninFigure,wecanfindtheultimateloadforthewidthofB1followingTerzaghi'sbearingcapacitymethodwiththeshearstrengthalongsidebdconsidered.TheratiooftheultimateloadtotheweightofsoilwithinthewidthofB1isthefactorofsafetyforthetrialfailuresurface.BearingcapacitymethodNegativebearingcapacitymethodThenegativebearingcapacitymethodassumesthattheunloadingbehaviorcausedbyexcavationisanalogoustothebuildingfoundationbeingsubjecttoanupwardloadingandthattheshapeofthefailuresurfaceissimilartothefailuremodeofthedeepfoundation.Then,usingthebearingcapacityequationforthedeepfoundation,wecanobtaintheultimateunloadingpressure.Thefactorofsafetyistheratiooftheultimateunloadingpressuretotheunloadingpressure.whereqsisthesurchargeonthegroundsurfaceandNcisSkempton'sbearingcapacityfactorSlipcirclemethodLetthetrialfailuresurfacesofthebasalheavefailurebeassumedtobebasicallycirculararcs,andseparatelycomputetheratiosoftheresistantmomentstothedrivingmomentsforthetrialcirculararcfailuresurfaces.Thesmallestfactorofsafetyamongthemisthenthefactorofsafetyagainstbasalheavefortheexcavation.Themethodisdesignatedastheslipcirclemethod.Theslipcirclemethod,withoutsettingthecenterataspecificposition,istotryoutthecirclesforvariouspositionsandsizesandtofindthecorrespondingfactorsofsafety.Thecirclewiththesmallestfactorofsafetyisthecriticalcircle.Accordingtotheanalysisresults,thefactorofsafetycorrespondingtothefailurecirclewhosecenterissetatthelowestlevelofstrut(point0)issmallerthanthatattheexcavationsurface(pointB)andisclosetothefactorofsafetyofthecriticalcircle(Liuetal.,1997).Thus,thecirculararcfailuresurfacewhosecenterissetatthelowestlevelofstrutisoftenadoptedforanalysis.thefactorofsafetyagainstbasalheave,theratiooftheresistantmomenttothedrivingmomentwithregardtothepointatthelowestlevelofstrutwillbe:Forsoilswithconstantstrengthorstrengthincreasingwithdepth,thecirclepassingthroughthebottomofaretainingwallisthecriticalcirclewiththesmallestfactorofs