Upper-Bound Analysis for Stone Retaining Wall Slope Based on Mixed Numerical Discretization

Abstract

The ultimate bearing capacity of masonry retaining wall slope is studied by combining the upper-bound theorem, the mixed numerical discretization, and the linear programming. First, the soil mass is discretized by triangular finite elements to simulate its continuum mechanics characteristics, and the stone masonry wall is discretized by rigid finite elements (RFEMs) to simulate its noncontinuum mechanics characteristics. Meanwhile, constraint conditions for kinematically admissible velocity fields are established, and then the plastic flow conditions of interfaces between finite elements and RFEMs are established. The upper-bound linear programming model for the ultimate bearing capacity of masonry retaining wall slope is built by taking the overload coefficient as the objective function, and the dual simplex method is used to solve the linear mathematical programming problem. Last, the ultimate load (or the safety factor) of the slope and the corresponding velocity fields could be obtained directly. Two examples have proved the validity of the proposed method. The research effort in this article is an attempt to introduce the mixed numerical discretization into the limit analysis.