Simulation of Incompressible Problems in Geomechanics

This article presents techniques for solving problems involving incompressibility in the context of low-order linear elements. It begins with describing a weak formulation that applies to both finite element and material point methods. Iterative solution schemes, including relaxation and explicit time stepping, are summarized. A strain enhancement procedure that is useful when incompressibility is introduced through plasticity is presented next, followed by a slope stability example that compares the iteration characteristics and vertical crest displacement corresponding to explicit and implicit matrix-free algorithms. Two procedures for dealing with pore pressure generation related to incompressibility and undrained conditions are described and an example is presented to compare pore pressures.