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Fig.4.Slopeprofileandsoilparametersforexample2.

Can.Geotech.J.Vol.42,

2005

Table1.Valuesoffactorsofsafetyandrequiredloadfactors.

themostcriticalslipsurfaceisashallowsurface(No.11)passingthroughthetoeoftheslope.However,inthecaseof=0.00(i.e.,drainedcondition)forthisshallowslipsur-face,theincreasedfactorofsafetyisthelargest,andthere-quiredloadfactoristheleast.Inotherwords,thismostcriticalslipsurfacewithoutanchorloadistheleastcriticalaftertheapplicationofanchorloads.Iftheslopeistomeettheprescribedstabilityconditions,theanchorloadsshouldbedesignedwithdueconsiderationtothesecondmostcriti-calslipsurface(No.7),whichpassesbelowthetoeoftheslope:itisassociatedwiththelowestfactorofsafetyforthegivenanchorloads,anditalsorequiresthelargestanchorloadstoattainthespecifiedfactorofsafety.ItisevidentfromTable1thatwithanincreaseinporepressureparame-ters(thefactorofsafetydecreasesandtherequiredloadfactorincreases.Itshouldbenotedthatthelocationsandin-clinationsoftheanchorsshowninFig.3areselectedonlyforthepurposesofillustration.Inpracticalapplication,itisrecommendedthatanoptimizationprocessbeperformedtodetermineanoptimumcombinationofanchors.Theproce-dureproposedherewouldserveasausefultoolforthispur-pose.

ofconcentratedforces.Althoughtheextensionoftheconventionalmethodstoincludeanchorloadsisstraightfor-ward,anunreasonablenormalstressdistributionontheslipsurfacewouldariseasaresult.Analternativeprocedureisproposedinthispaperforamorerationalanalysisofanchor-reinforcedslopes.Withthisprocedure,thenormalstressontheslipsurfaceisassumedtobealinearcombina-tionoftwopartsinvolvingtwoauxiliaryunknowns:onepartcorrespondstotheunreinforcedslopeobtainedusingcon-ventionalmethods;theotherpartisinducedsolelybytheanchorloads,withanapproximateclosed-formsolution.Solvingthethreeequilibriumequationsyieldsexplicitsolu-tionstothefactorofsafetywithgivenanchorloadsandtotherequiredanchorloadswithaspecifiedfactorofsafety.Thedisadvantagesofconventionalproceduresindealingwithanchorloadscanthusbeovercome.Thismethodcanserveasapromisingtoolforthedesignofstabilizationmea-suresinvolvinganchorsorsoilnailandgeotextilereinforce-mentsforfailedslopesandforthosehavingunacceptablestabilityconditions.

Acknowledgements

ThestudywasfinanciallysupportedbytheResearchGrantsCouncilofHongKongandtheJockeyClubResearchandInformationCenterforLandslipPreventionandLandDevelopment,UniversityofHongKong.Theirsupportis

Conclusions

Thelimitequilibriummethodsofsliceshavebeenwidelyusedforanalysingthestabilityofslopeswithouttheaction