Historically, geotechnical stability analysis has been performed by a variety of approximate methods that are based on the notion of limit equilibrium. These techniques have the major disadvantage of the need to presuppose an appropriate failure mechanism. This can lead to inaccurate predictions of the true failure load, especially for cases involving layered materials, complex loading, or three- dimensional deformation. This lecture will describe recent advances in stability analysis focused on new methods which combine the limit theorems of classical plasticity with finite elements to give rigorous upper and lower bounds on the failure load. These “finite element limit analysis” methods do not require assumptions to be made about the mode of failure, and use only simple strength parameters that are familiar to geotechnical engineers. The bounding properties of the solutions are invaluable in practice, and enable accurate solutions to be obtained through the use of an exact error estimate and automatic adaptive meshing procedures. The methods are extremely general and can deal with layered soil profiles, anisotropic strength characteristics, fissured soils, discontinuities, complicated boundary conditions, and complex loading in both two and three dimensions. Following a brief outline of the new techniques, stability solutions for a number of practical problems will be given including foundations, anchors, slopes, excavations, and tunnels.
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