An Upper-Bound SOCP-Based FELA Formulation for Plane Strain and Axisymmetric Problems: Incorporating Absolute Value of Tangential Velocity Jump along Velocity Discontinuities

Abstract

To solve plane strain and axisymmetric stability problems in geomechanics, a second-order cone programming (SOCP)-based upper-bound (UB) finite-element limit analysis (FELA) formulation is presented. The formulation incorporates the absolute value of the tangential velocities jump (Δut) while implementing the associated flow rule along velocity discontinuities. Note that the existing SOCP-based UB-FELA formulation is meant only for a plane strain case but not an axisymmetric one. The kinematic admissible velocity field and the computation of the power dissipation along the velocity discontinuities are both based on the absolute sign of Δut. Since the proposed formulation is based on SOCP, it has been found to be computationally very efficient in terms of the required CPU time to solve any axis-symmetric stability problem. Considering the absolute sign of Δut, it further improves the accuracy of the UB solution obtained, although the difference is very marginal. To show the implementation, the analysis was carried out to compute the bearing capacity of strip, circular, and ring foundations, and the solutions were found to be quite accurate.