Collapse analysis of soils by adaptive pseudo-static limit analysis

The prediction of failure load factor and stress distribution at limit state plays an important role in geo-technical engineering design. This paper develops a pseudo-lower bound numerical procedure for adaptive limit analysis of geo-mechanics problems governed by the Mohr-Coulomb failure criterion. Equilibrium equations for the residual stress are enforced in a weak manner, allowing the use of displacement-based elements within the static limit analysis framework. The method does not require the construction of stress-based elements, but the stress fields at limit state can still be obtained. Non-linear failure criterion is cast in the form of a standard conic constraint, enabling the use of the highly efficient second-order cone based solvers. A refinement indicator based on Mohr-Coulomb yield function values is proposed, and adaptive mesh refinement is performed to speed up the computational progress. The proposed method is applied to various soil engineering problems, providing accurate bearing capacity together with stress distribution at limit state.