Lower bound limit analysis of an anisotropic undrained strength criterion using second-order cone programming

Abstract

In this paper, the formulation of the lower bound limit analysis of an anisotropic undrained strength criterion using second-order cone programming is described. The finite element concept was used to discretize the soil mass into 3-noded triangular elements. The stress field was modeled using a linear interpolation within the elements while stress discontinuities were permitted to occur at the shared edges of adjacent elements. An elliptical yield criterion was adopted to model the anisotropic undrained strength of the clay. A statically admissible stress field was defined by enforcing the equilibrium equations within all triangular elements and along all shared edges of adjacent elements, stress boundary conditions, and no stress violation of the anisotropic strength envelope cast in the form of a conic quadratic constraint. The lower bound solution of the proposed formulation was solved by second-order cone programming. The proposed formulation of the anisotropic undrained strength criterion was validated through comparison of the model's predictions with the known exact solutions of strip footings, and was applied to solve undrained stability of a shallow unlined square tunnel. Computational performance between the proposed approach of second-order cone programming and linear programming was examined and discussed.