Stability and Deformation Analysis for Geotechnical Problems with Nonassociated Plasticity Based on Second-Order Cone Programming

Abstract

The second-order cone programming (SOCP) optimized FEM (named FEM-SOCP) is extended to solve the geotechnical problems involving nonassociated plasticity. When FEM-SOCP is used with strength reduction, FEM-SOCP generally can be more efficient because the shear strength reduction FEM (SSRFEM) is often used with a very large allowable maximum number of nonlinear iterations. The FEM-SOCP method cannot be directly applied to the geotechnical deformation analysis involving the nonassociated plasticity because only the geotechnical problem with associated plasticity can be cast into the SOCP problem. To remove the difficulty, a time-discrete method with automatic error control is proposed for the iterative scheme of approximating the nonassociated plastic problems with a series of associated plastic problems. Based on numerical investigations, the time step factor with the range of α = 0.1–0.4 generally may lead to an accurate solution with an optimized efficiency.