Lower bound analysis of rectangular footings with interface adhesion factors on nonhomogeneous clays

Abstract

Solutions based on lower bound limit analysis provide a safe estimate of stability, and thus they are valuable for design and analysis in practice. In this paper, new lower bound solutions of the undrained bearing capacity of rectangular footings are first presented with consideration of adhesion factors at soil–footing interfaces and linearly increasing strength with the depth of clays. The new solutions of the problem are numerically derived using three-dimensional lower bound finite element limit analysis with semidefinite programming. The new solutions are expressed in terms of dimensionless parameters, including footing aspect ratios, adhesion factors at soil–footing interfaces, and normalized strength gradient factors. A statistically algebraic equation of the undrained bearing capacity of rectangular footings is also proposed for the first time.