Upper limit analysis of stability of rock and soil slopes using rigid finite elements

The development and application of a new upper limit method for 2D and 3D slope stability problems are presented. Rigid finite elements are used to construct a kinematically admissible velocity field. The proposed method formulates the slope stability problems as an optimisation problem based on the upper bound theorem. The objective function for determination of the minimum value of the safety factor has some unknowns, which are subject to a set of linear and non-linear equality constraints derived from an energy-work balance equation, the Mohr-Coulomb failure (yield) criterion, an associated flow rule and a number of boundary conditions. The objective function with constraints leads to a non-linear programming problem, which can be solved by a sequential quadratic algorithm. Four typical 2D and 3D slope stability problems selected from the literature are analysed with the presented method. The results of the presented limit analysis are compared with those produced by other approaches.