Finite element-based upper bound and lower bound limit analysis are found to be an excellent tool for solving various stability structural problems with less computational cost. The accuracy and efficiency of the obtained solution is highly dependent on the intensity of elements in the high stress or stain gradient region. Therefore, an adaptive meshing procedure is required to reduce the gap between upper and lower bound solutions. The adaptive meshing procedure presented in this paper is based on two basic concepts (a) a posterior error indicator and (b) an unstructured mesh generator. The posterior error estimator is based on intensity of maximum shear strain rate (γmax) has been used. Open-source software TRIANGLE and TETGEN have been used to generate unstructured meshes for 2D and 3D problems, respectively. A plane strain and a 3D foundation problem have been analyzed and steps involve in calculation have been clearly mentioned in the paper. The present analysis method is found to be efficient and accurate.@en

By using the lower bound finite elements limit analysis, this paper presents a methodology to evaluate the bearing capacity of piles in cohesive soils. The non-homogeneous nature of soil has been assumed for which the cohesion increases linearly with depth. An axisymmetric formulation, comprising of a planar domain with a mesh of three noded triangular elements has been adopted. Here, Mohr–Coulomb (MC) yield criterion has been employed. The yield criterion is expressed in terms of three quadratic constraints so that the problem can be solved using second-order cone programming (SOCP). Bearing capacity factors have been generated as a function of (i) height to radius ratio of the pile, (ii) rate of increase of cohesion and (ii) roughness of base and shaft of pile. The results computed from the analysis have been compared thoroughly with that reported in literatures.@en