Upper bound limit analysis of soil slopes based on rigid finite element method and second-order cone programming

The upper bound approach based on rigid finite element method (RFEM) is one of the limit analysis methods, and it is an important method for stability analysis of soil slopes. However, there are still some key problems to be overcome in this method. Due to the assumption of rigidity, the plastic deformation energy of the system is stored only at the interfaces of all elements. Therefore, the accuracy of the approach is highly dependent on the alignment of the interfaces, which indicates that the accuracy is poor if an unstructured mesh is employed. To overcome this limitation, we propose a novel RFEM-based upper bound approach using perturbation method, according to the sequential limit analysis. Firstly, considering the rotation of elements, a novel second-order cone programming (SOCP) is put forward to construct the kinematically admissible velocity field based on RFEM. Secondly, a model for searching the critical slip surface is built by using sequential SOCP of RFEM-based upper bound approach and then solved by the nonlinear simplex and particle swarm optimization algorithm. From the analysis on stability problems of two benchmark soil slopes, the proposed method is verified. The main influence factors on computational efficiency and accuracy are also investigated in this paper. We have found that the type of mesh is a significant factor affecting the accuracy of the proposed method. It is necessary to consider the rotation of element in RFEM-based upper bound approach, which can not only improve the accuracy of the approach but also overcome the dependence of RFEM-based upper bound limit analysis on the alignment of interfaces.