Limit Analysis of Soil Slopes Subjected to Pore-Water Pressures

The limit-equilibrium method is commonly used for slope stability analysis. However, it is well-known that the solution obtained from the limit-equilibrium method is not rigorous, because neither static nor kinematic admissibility conditions are satisfied. Limit analysis takes advantage of the lower- and upper-bound theorems of plasticity to provide relatively simple but rigorous bounds on the true solution. In this paper, three-noded linear triangular finite elements are used to construct both statically admissible stress fields for lower-bound analysis and kinematically admissible velocity fields for upper-bound analysis. By assuming linear variation of nodal and elemental variables, the determination of the best lower- and upper-bound solution may be set up as a linear programming problem with constraints based on the satisfaction of static and kinematic admissibility. The effects of pore-water pressure are considered and incorporated into the finite-element formulations so that effective stress analysis of saturated slopes may be done. Results obtained form limit analysis of simple slopes with different ground-water patterns are compared with those obtained from the limit-equilibrium method.