Location of Tension Cracks at Slope Crests in Stability Analysis of Slopes

Abstract

Over the conventional limit equilibrium method and limit analysis method, the finite element method is advantageous, especially for slopes involving complex failure mechanisms where the critical slip surfaces cannot be represented by log spirals and other similarities. In the presence of tension cracks at slope crests, however, the finite element method encounters difficulties in convergence while handling Mohr–Coulomb’s yielding surfaces with tensile strength cut-off. Meanwhile, the commonly used load-controlled method for the system of nonlinear equilibrium equations is hard to bring the slope into the limit equilibrium state. The two drawbacks drag down the finite element method in more extensive applications. By reducing the constitutive integration of plasticity with non-smooth yielding surfaces to the mixed complementarity problem, the convergence in numerical constitutive integration is established for arbitrarily large incremental strains. In order to bring the slope to the limit equilibrium state, a new displacement-controlled algorithm is designed for the system of nonlinear equilibrium equations, which is far more efficient than the load-controlled method. A procedure is proposed to locate tension cracks. Corresponding to the Mohr–Coulomb failure criterion with and without tensile strength cut-off, the failure mechanisms differ significantly, while the difference in the factor of safety might be ignorable.