In this paper, the numerical limit analysis procedure, associating the cell-based smoothed finite element method (CS-FEM) with the (second-order cone) primal-dual interior point algorithm, for cohesive-frictional materials problem is described. The soil is modeled as a cohesionless frictional Mohr-Coulomb material with the associated flow rule. Kinematically admissible velocity fields are established using CS-FEM. The underlying non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm. The core purpose of this study is to evaluate collapse loads as well as failure mechanisms of footings on slope which will be obtained directly from solving the optimization problems. In this study, the properties of soil and the width of footing and distance from footing to the edge of the slope are considered. Several numerical examples of slope stability are given to show the performance of the proposed method.
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