Slope stability analysis by finite elements

Slopestabilityanalysisby®niteelementsD.V.GRIFFITHSandP.A.LANE{Themajorityofslopestabilityanalysesper-formedinpracticestillusetraditionallimitequilibriumapproachesinvolvingmethodsofslicesthathaveremainedessentiallyunchangedfordecades.ThiswasnottheoutcomeenvisagedwhenWhitman&Bailey(1967)setcriteriaforthethenemergingmethodstobecomereadilyaccessibletoallengineers.The®niteelementmethodrepresentsapowerfulalternativeap-proachforslopestabilityanalysiswhichisaccu-rate,versatileandrequiresfeweraprioriassumptions,especially,regardingthefailuremechanism.Slopefailureinthe®niteelementmodeloccurs`naturally'throughthezonesinwhichtheshearstrengthofthesoilisinsuf®-cienttoresisttheshearstresses.Thepaperdescribesseveralexamplesof®niteelementslopestabilityanalysiswithcomparisonagainstothersolutionmethods,includingthein¯uenceofafreesurfaceonslopeanddamstability.Graphicaloutputisincludedtoillustratedefor-mationsandmechanismsoffailure.Itisarguedthatthe®niteelementmethodofslopestabilityanalysisisamorepowerfulalternativetotradi-tionallimitequilibriummethodsanditswide-spreaduseshouldnowbestandardingeotechnicalpractice.KEYWORDS:dams;limitequilibriummethods;num-ericalmodelling;plasticity;slopes.EngrandemajoriteÂ,lesanalysesdestabiliteÂdepentemeneÂesdanslapratiquecontinuentaÁutiliserlesmeÂthodestraditionnellesd'eÂquilibrelimiteetdessysteÁmesdetranchesquin'ontpratiquementpaschangeÂdepuisdesdizainesd'anneÂes.Cen'eÂtaitpaslereÂsultatenvisageÂquandWhitmanetBailey(1967)onteÂtablidescriteÁrespourquecesmeÂthodesalorseÂmer-geantespuissentdevenirfacilementaccessiblesaÁtouslesingeÂnieurs.LameÂthoded'eÂleÂments®nisquirepreÂsenteunealternativepuissantepourlesanalysesdestabiliteÂdepente,estexacte,poly-valenteetdemandemoinsd'hypotheÁses`apriori',surtoutencequiconcernelesmeÂca-nismesderupture.LarupturedepentedanslemodeÁleaÁeÂleÂments®nisseproduit`naturelle-ment'aÁtraversdeszonesdanslesquelleslareÂsistanceaucisaillementdusolestinsuf®santepourreÂsisterauxcontraintestangentielles.CetexposeÂdeÂcritplusieursexemplesd'analysesdestabiliteÂdepenteutilisantleseÂleÂments®niseteÂtablitdescomparaisonsavecd'autresmeÂth-odes,commel'in¯uenced'unesurfacelibresurlastabiliteÂd'unepenteetd'unedigue.NousjoignonsunerepreÂsentationgraphiquepouril-lustrerlesdeÂformationsetmeÂcanismesderup-ture.NousavancËonsquelameÂthoded'eÂleÂments®nispouranalyserlastabiliteÂdespentesconsti-tueunealternativepluspuissanteauxmeÂthodestraditionnellesd'eÂquilibrelimiteetquesonutili-sationdevraitmaintenantdevenirunepratiquestandardengeÂotechnique.INTRODUCTIONElasto-plasticanalysisofgeotechnicalproblemsusingthe®niteelement(FE)methodhasbeenwidelyacceptedintheresearcharenaformanyyears;however,itsroutineuseingeotechnicalpracticeforslopestabilityanalysisstillremainslimited.Thereasonforthislackofacceptanceisnotentirelyclear;however,advocatesofFEtech-niquesinacadememusttakesomeresponsibility.Practisingengineersareoftenscepticaloftheneedforsuchcomplexity,especiallyinviewofthepoorqualityofsoilpropertydataoftenavailablefromroutinesiteinvestigations.Althoughthisscepticismisoftenwarranted,therearecertaintypesofgeotechnicalproblemforwhichtheFEapproachoffersrealbene®ts.Thechallengeforanexperi-encedengineeristoknowwhichkindofproblemwouldbene®tfromaFEtreatmentandwhichwouldnot.Ingeneral,linearproblemssuchasthepredic-tionofsettlementsanddeformations,thecalcula-tionof¯owquantitiesduetosteadyseepageorthestudyoftransienteffectsduetoconsolidationareallhighlyamenabletosolutionby®niteelements.Traditionalapproachesinvolvingcharts,tablesorGrif®ths,D.V.&Lane,P.A.(1999).GeÂotechnique49,No.3,387±403387Manuscriptreceived28May1998;revisedmanuscriptaccepted8December1998.Discussiononthispapercloses3September1999;forfurtherdetailsseep.ii.ColoradoSchoolofMines,Golden.{UMIST,Manchester.graphicalmethodswilloftenbeadequateforrou-tineproblemsbuttheFEapproachmaybevaluableifawkwardgeometriesormaterialvariationsareencounteredwhicharenotcoveredbytraditionalchartsolutions.Theuseofnonlinearanalysisinroutinegeotech-nicalpracticeishardertojustify,becausethereisusuallyasigni®cantincreaseincomplexitywhichismorelikelytorequirethehelpofamodellingspecialist.Nonlinearanalysesareinherentlyitera-tiveinnature,becausethematerialpropertiesand/orthegeometryoftheproblemarethemselvesafunctionofthe`solution'.Objectionstononlinearanalysesonthegroundsthattheyrequireexcessivecomputationalpower,however,havebeenlargelyovertakenbydevelopmentsin,andfallingcostsof,computerhardware.AdesktopcomputerwithastandardprocessorisnowcapableofperformingnonlinearanalysessuchasthosedescribedinthispaperinareasonabletimespanÐminutesratherthanhoursordays.Slopestabilityrepresentsanareaofgeotechni-calanalysisinwhichanonlinearFEapproachoffersrealbene®tsoverexistingmethods.Asthispaperwillshow,slopestabilityanalysisbyelasto-plastic®niteelementsisaccurate,robustandsimpleenoughforroutineusebypractisingen-gineers.PerceptionoftheFEmethodascomplexandpotentiallymisleadingisunwarrantedandignorestherealpossibilitythatmisleadingresultscanbeobtainedwithconventional`slipcircle'approaches.Thegr