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.