Assessment of Stability of Slopes under Drawdown C

JOURNALOFGEOTECHNICALANDGEOENVIRONMENTALENGINEERING/MAY2000/443ASSESSMENTOFSTABILITYOFSLOPESUNDERDRAWDOWNCONDITIONSByP.A.Lane1andD.V.Griffiths,2Member,ASCEABSTRACT:Thetraditionalapproachforestimatingthestabilityofslopesunderdifferentsubmergencecon-ditionsisthechartsofMorgernsternand,morerecently,proprietarycomputerprograms,bothutilizinglimit-stateanalyses.Thechartapproachislimitedbygeometryandmaterialpropertyconsiderationsandthelimit-stateapproachbyassumptionsaboutanalysismethodandfailuremechanism.Thefinite-elementmethodoffersapowerfulmethodforanalyzingcomplexgeometriesandpropertiesofslopestabilityproblems,butmaybeunattractiveforroutineusebysupervisorystaff.Bycomparisonachartbasedapproachisuseful,particularlywhensettingoperatingconditionson,forexample,drawdownratesfordamsandreservoirs.Thispaperseekstoexploretheuseofthefinite-elementmethodtoproduceoperatingchartsforsuchcircumstancesthatshouldbeapplicabletorealstructures.INTRODUCTIONThestabilityofaslopedependsonitsgeometry,itsmaterialproperties,andtheforcestowhichitissubjected.Theseforcesincludetheeffectsofwaterbothinternally,intheformofpore-waterpressuresandseepageforces,andexternally,intermsofhydrostaticandhydrodynamiceffects.Theeffectofwateronslopestabilitycanbeseenbyconsideringtheslopeunderdifferentdegreesofsubmergenceanddrawdown.Theimpli-cationsofthiswerefirstquantifiedbyMorgernstern(1963)andlaterinvestigatedby,forexample,Desai(1977)andCous-ins(1978).Allusedlimit-stateanalysesfortheestimationofthefactorofsafety(FOS)oftheslopeunderarangeofcon-ditionstoproduceaseriesofchartsforpracticingengineerstoutilize.Thefinite-elementprogramFE-EMB1developedbyGrif-fiths(1996)hasbeenextendedtoFE-EMB1LGbyLaneandGriffiths(1997)toincludeanycombinationofsubmergenceanddrawdownconditionsandtoallowfortheautomaticgen-erationofpore-waterpressuresortheinsertionofknownval-uesforbothpredictionandback-analysis.Theprogramutilizesthepowerofthefinite-elementmethodtoaccountforpoten-tiallycomplexgeometriesandmaterialproperties,butisusedheretodevelopachartbasedapproachfortheoperationofdamsandreservoirstominimizetheriskofslopefailureunderdrawdownconditions.BRIEFDESCRIPTIONOFFINITE-ELEMENTMODELThefinite-elementprogramisfor2D,planestrain,slopestabilityanalysisbyfiniteelementsusingeight-nodequadri-lateralelementsofelastic-visco-plasticsoilwithaMohr-Cou-lombfailurecriterionandanonassociatedflowrule.Thepri-marydevelopmenthasbeentheinclusionoffree-surfaceand/orexternalreservoirloading.Thesoil’sself-weightismodeledbyagravity‘‘turn-on’’procedure(SmithandGriffiths1988)withnodalloadsaddedinasingleincrement.TheFOSfortheslopeisdefinedbydivisionoftheoriginalshearstrengthparametersc9,f9togivetheirvaluesatfailure,,wherec9f9ff1Lect.,GeotechnicsRes.Group,Dept.ofCiv.andStruct.Engrg.,UMIST,ManchesterM601QD,U.K.2Prof.,GeomechanicsRes.Ctr.,ColoradoSchoolofMines,Golden,CO80401.Note.DiscussionopenuntilOctober1,2000.Toextendtheclosingdateonemonth,awrittenrequestmustbefiledwiththeASCEManagerofJournals.ThemanuscriptforthispaperwassubmittedforreviewandpossiblepublicationonNovember16,1998.ThispaperispartoftheJournalofGeotechnicalandGeoenvironmentalEngineering,Vol.126,No.5,May,2000.qASCE,ISSN1090-0241/00/0005-0443–0450/$8.001$.50perpage.PaperNo.19604.c9=c9/FOS(1)ftanf9f9=arctan(2)fSDFOSThereareseveralpossibledefinitionsoffailure,forexam-ple,(1)sometestofbulgingoftheslopeprofile(SnitbhanandChen1976);(2)limitingoftheshearstressesonthepotentialfailuresurface(DuncanandDunlop1969);or(3)noncon-vergenceofthesolution(ZienkiewiczandTaylor1989).ThesearediscussedinAbramsonetal.(1995)fromtheoriginalpaperbyWong(1984),butwithoutresolution.Intheexamplesstud-iedherethenonconvergenceoptioncoupledwithasuddenincreaseinnodaldisplacementsistakenasbeingasuitableindicatoroffailure.Whenthealgorithmcannotconvergewithinauser-specifiedmaximumnumberofiterations,theimplicationisthatnostressdistributioncanbefoundthatissimultaneouslyabletosatisfyboththeMohr-Coulombfailurecriterionandglobalequilibrium.Ifthealgorithmisunabletosatisfythesecriteria,failureissaidtohaveoccurred.Slopefailureandnumericalnonconvergenceoccursimultaneouslyandareaccompaniedbyadramaticincreaseinthenodaldisplacementswithinthemesh.Mostoftheresultsshowninthispaperusedaniterationceilingof500andarebasedonagraphofFOSversusE9dmax/gH2(adimensionlessdisplacement),wheredmaxisthemaxi-mumnodaldisplacementatconvergenceandHistheheightoftheslopeofunitweightandeffectiveYoung’sModulusE9.ThisgraphmaybeusedalongsidethedisplacedmeshandvectorplotstoindicateboththeFOSandthenatureofthefailuremechanism.Incomparison,theFOSgeneratedbytra-ditionalmethodsrepresentstheratiobetweenthedrivingandrestoringforces,butthisisessentiallythesamedefinitionofFOSasusedinthefinite-elementapproach.Theprogramproducesgraphicaloutputtoillustratethemechanismoffailure.Toemphasizethemechanismoffailuretheiterationslimitmaybeincreasedto1,000andtheplotteddisplacementvectorslimitedtoaboveascaledminimuminordertodifferentiatethemechanismfromthebackgroundmesh.Similarly,theplotsofdisplacedmeshhavebeenpro-ducedbyallowingthehigheriterationslimitinordertoem