Static Limit Analysis of Reinforced Soil Structures by a Simple Finite Element and Second-Order Cone Programming

Abstract To discretize reinforced soil structures in plane strain and predict their collapse load, a simple three-node triangular finite element is formulated based on the static theorem of the limit analysis. The element satisfies the equilibrium equations and the mechanical boundary conditions in a weak sense. A modified Mohr-Coulomb yield surface is adopted to describe the reinforced soil behavior from a macromechanics point of view. It is also taken into account the possibility of tension failure of the reinforcement and failure of the reinforcement interface. The stated nonlinear convex optimization problem is cast as second-order cone programming. Numerical examples illustrate the predictive accuracy of the above scheme as well as the efficiency and speed of an interior-point method to reach optimal solutions.