Comparison of 3-D Limit Equilibrium Methods

H Lu

In the proceedings of: GeoVancouver 2016: 69th Canadian Geotechnical Conference

Session: FUNDAMENTALS - VIII Physical & Numerical Modelling

ABSTRACT: The factor of safety from four most commonly used limit equilibrium methods are comparedfor three-dimensional analysisofslopes with homogeneous and heterogeneous layers of soils, and for a typical range of inclination of slopes from 30ð°to60ð°.The results indicate that the simplified Bishop method can be conservative(i.e., the factor of safety can be low)fornon-circular failures, particularly when the slopes are steeper. Similarly, the Spencer•s method may overestimate the factorof safety for non-circular failures.R†SUM†Le coefficient de sécurité à partir de quatre méthodes d 'équilibre limite les plus couramment utilisés sont comparés pourl'analyse en trois dimensions des pentes avec des couches homogènes et hétérogènes des sols , et pour unegamme typiqued'inclinaison des pentes de 30ð°à 60ð°. Les résultats indiquent que la méthode de Bishop simplifiée peut être conservatrice(à savoir, le facteur de sécurité peut être faible) pour les échecs non-circulaires, en particulier lorsque les pentes sontplus raides . De même, la méthode de Spencer peut surestimer le facteur de sécurité pour les échecs non circulaires.1INTRODUCTIONTwo-dimensional (2-D)limit equilibrium (LE) methods havebecome the most common methods to study slope stabilityproblems due to their simplicity andease ofunderstanding.Thelimit equilibrium methods developed over the pastdecadesarebased oninterslice force function assumptionsto renderthe problem determinate. A comparison of thesemethods has been presented by Fredlund and Krahn(1977). Fredlund and Krahn(1977)unified the methods toa common framework of equations and recognized whethermoment and/or force equilibrium is explicitly satisfied.Alllimit equilibrium methods of slicesmakeassumptionsregarding the interslice forces(e.g., the interslice forcefunction).The 2-D analysis is generally considered to beconservative in that the three-dimensional influence ofslope and slip surfacegeometryis not accounted for in a 2-D analysis.Athree-dimensional (3-D) slope stability islessroutinely performed althoughthemajority of failures are 3-D in character. The ‡slicing method… used in 2-D analysisisextended to ‡columns… in three-dimensional space for most3-D analysis methods.Similarly,the limit equilibriummethodsusedfor 2-D analysis have been extended for 3-D analysis as well.Hovland(1979)is the first to analyze a three-dimensional slope using the method of columns. Hovland•smethod is an extension of the assumptions associated withthe two-dimensional ordinary method.That is, allintercolumn forces acting on the sides of the columns areignored.The normal and shear forces acting at the base ofeachcolumnarederivedas the components of the weightof the column.Hovland(1979)observed that the 3-Danalysis resulted in a smaller factor of safety than from the2-D analysis for some situations.Hungr(1987)proposed a method that was an extensionof Bishop•s(1955)simplified method to three dimensionalanalysiswithout any additional assumptions involved. Inother words, the vertical intercolumn shear forces acting onboth lateral and longitudinal faces of each column wereneglected. Hungr•s results indicated that the ratio ofFOS3-D/FOS 2-D was greater than 1.0 for all cases. Hungr(1987)suggested that the extended 3-D method would beintuitively expected to exhibit as good a performance as theoriginal Bishop method for 2-D analysis.Hungr et al.(1989)compared the three-dimensionalmethods that were an extensions of the assumptions inBishop•s(1955)simplified and Janbu•s simplified two-dimensional methods for a number ofsolutions. Favourableresults from Bishop•s method were obtained for rotationaland symmetric sliding surfaces.Bishop•ssimplified methodwas found to be conservative when used for somenonrotational and asymmetric surfaces, because itneglects internal strength.Lam and Fredlund(1993)presented the theory andimplementation of a more generalized three-dimensionalslope stability model extending the two-dimensionalgeneral limit equilibrium (GLE) formulation(Fredlund andKrahn 1977, Fredlund et al. 1981).The dominantintercolumn forcefunctions were found for the verticalshear forces acting on each faces of the column.The effectof other force functions was negligible for the studiedgeometries.A review of limit equilibrium methods used for three-dimensional slope stability analysiswas presented byKalatehjari and Ali(2013).This paper is primarilyconcerned with four of the most commonly used methodsfor 3-D slope stability solutions.(i)Simplified Bishop method(Bishop 1955)(ii)Spencer•s method(Spencer 1967)

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