Recent advances in the upper bound limit analysis of Tresca's material

Abstract

This chapter presents a generalized framework for developing three-dimensional-upper-bound solutions for materials satisfying Tresca's failure criterion, ensuring admissibility in respect of zero volumetric strains and adopting local orthogonal coordinate systems aligned with the streamlines of the velocity field. The bearing capacity of shallow foundations in clay under generalized loading is a classical problem with widespread applications, particularly in modem offshore engineering. While numerical techniques—such as the finite-element method—are capable of providing accurate solutions to specific situations, they are cumbersome in terms of their use for parametric studies. They can also lead to unacceptable errors for inexperienced users. Upper-bound limit analysis of Tresca's material helps to overcome these difficulties. However, computation of three-dimensional kinematic mechanisms presents a significant problem itself. The theoretical developments discussed in this chapter allow these computations to be simplified, and the derived yield envelopes offer good accuracy in comparison with finite-element solutions. The framework uses orthogonal curvilinear coordinates and allows derivation of kinematically admissible velocity fields with new streamline shapes, including derivation of new plane but nonplane-strain fields and new radial but nonaxisymmetric fields.