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Upper bound limit analysis of cohesive soils using mesh-free method

A mesh-free based limit analysis approach is proposed, to determine the upper bound solutions for the collapse loads associated with cohesive soils, under plane strain conditions. In the presented technique, the geometry of problem is just simulated by nodes and there is no need of mesh in the traditional sense. The process of finding an upper bound solution consists of combining limit analysis theory and a mesh-free numerical technique as a discretisation tool. To satisfy the required conditions for the admissibility of the discretised velocity field at the entire problem domain, a strain rate smoothing technique has been adopted. The outcome of proposed combination is a nonlinear optimisation problem which is solved by a direct iterative technique. The solution found by an iterative algorithm is an upper bound for limit load of the stability problem. The efficiency of the proposed method is demonstrated by solving different example problems in the soil mechanics engineering field, at the end of the paper.