Shear strength reduction finite element method based on second-order cone programming theory and its application

For geotechnical stability problems, the limit equilibrium method (LEM) and shear strength reduction finite element method (SSRFEM) have been commonly used. In the traditional elasto-plastic finite element method, a large maximum allowable number of nonlinear iterations (such as 200 or 500) are often set in the SSRFEM, so that the calculation is generally time-consuming; besides, the equilibrium iteration and stress integration algorithm may probably lead to inaccurate calculation of plastic zone and stability. Based on the Hellinger-Reissner mixed variational principle and finite element method, a new shear strength reduction finite element method is proposed based on the finite element method of second-order cone programming (FEM-SOCP). In the mathematical programming finite element framework, the elasto-plastic finite element problem can be cast into a form of second-order cone programming (SOCP), and when being utilized in conjunction with the strength reduction technique, the resultant approach named SSRFEM-SOCP can be applied to geotechnical stability analysis. When being applied to plane strain problems, it is observed that SSRFEM-SOCP is reliable and efficient, and particularly the plastic zone attained by the SSRFEM-SOCP is generally smoother than that by the conventional SSRFEM method.