Adaptive finite element limit analysis incorporating steady state pore pressures

Abstract

This paper describes an adaptive method for incorporating the pore pressures associated with steady-state seepage in finite element limit analysis. The formulation can model both general seepage conditions, and locating the phreatic surface in unconfined flow presents no special difficulty [1]. Since the proposed method employs the same mesh for the upper analysis, the lower-bound analysis and the pore pressure computation, there is no need to import and interpolate the pore-pressures from another grid (or program). This is a significant practical advantage and leads to an efficient solution process. In the iterative solution method, a Hessian(curvature)-based error estimator is applied to the pore pressure field to generate a mesh which gives accurate pore pressures. Simultaneously, a variant of the ‘bounds gap’ error estimator of [2],[3] is employed to identify a separate mesh which gives accurate upper and lower bounds on the limit load. By combining these two strategies, a hybrid refinement strategy is developed which minimises both the bounds gap and the error in the computed pore pressures.