An approach to limit analysis with cone-shaped yield surfaces

The paper presents an algorithm for limit analysis with mixed approach by finite elements with application to geotechnical problems. The emphasis is on a special technique to deal with the singularity at the apex of a cone-shaped yield surface. The approach is based on the direct application of the sub-differential concept to the flow law and is essentially different from the Lagrange multipliers technique. The proposed algorithm does not require the regularization usually adopted for the singularities at the boundary of the plastic admissible stress region that occur in soil models. The case of a Drucker–Prager model is particularly considered, as well as the Mohr–Coulomb model in plane strain conditions. The algorithm is applied to a footing and a shallow tunnel.