关键词: 条形浅基础, 极限承载力, 有限元法, 二阶锥规划, 非关联塑性, 增量加载法

Abstract: Ultimate bearing capacity analysis of the strip footing is a classical topic in soil mechanics. Based on the Hellinger-Reissner mixed variational principle and finite element method, a geotechnical elasto-plastic problem involving the Mohr-Coulomb model can be casted into a second-order cone programming (SOCP) problem in the finite element framework. A second-order cone programming based incremental finite element method named FEM-SOCP is then proposed. The proposed approach can avoid the complex stress integration algorithms and the smoothing treatment of the yield surface edges and corners, which are often necessary in the traditional elasto-plastic calculations. For the casted SOCP problem, the commercial solver MOSEK with the primal-dual interior point method can be used. The FEM-SOCP method is applied to the ultimate bearing capacity analysis of a shallow strip footing, with the associated and non-associated Mohr-Coulomb yield criteria considered, respectively. The numerical results show that the bearing capacity coefficients and bearing capacity obtained by the incremental loading FEM-SOCP method is consistent with the traditional FEM solution, but the yield zone attained is generally smoother compared to that obtained from conventional FEM.

Key words: shallow strip footing, ultimate bearing capacity, finite element method, second-order cone programming, non-associated plasticity, incremental loading method