Rigid Finite Element Method for Upper Bound Limit Analysis of Soil Slopes Subjected to Pore Water Pressure

The traditional approach for assessing the stability of slopes is using limit equilibrium methods. Recently, many efforts have been made to utilize limit analysis methods based on the upper bound and lower bound limit theorems in plasticity. In this paper, an upper bound limit analysis method using rigid finite elements is presented. Rigid finite elements are used to discretize the slope media. Kinematically admissible velocity discontinuities are permitted to occur at all interelement boundaries. The traditional definition of factor of safety is adopted in the present method so that the results from the limit analysis can be directly compared with those from methods of slices. The presence of water can be considered through work terms in the energy–work balance equation. To do this effectively, the pore water pressure is considered as an external force, similar to gravity and surface tractions. The proposed method formulates the slope stability problem as a nonlinear optimization problem with constraints based on the yield criterion, flow rule, boundary conditions, and the energy–work balance equation. The optimization problem is solved by a sequential quadratic algorithm. Two numerical examples are presented to illustrate the validation and potential applications of the present method.