Pore Pressure Development in Moving Boundary Problems

This research note examines fixed and deforming finite difference grid approaches for solving problems involving moving boundaries. In order to make comparisons between the solutions effected by each approach, emphasis is placed on the prediction of deficient pore pressures which develop within a clay stratum which is being excavated. It is assumed that the linear partial differential equation which describes consolidation is applicable. In the deforming grid approach, the distribution of deficient pore pressures is defined by a set of nodal degrees of freedom (u 1 u2 , …un) which are allowed to move as the excavation front advances, thereby maintaining a constant number of unknowns at all times. In order to account for the influence of moving reference points, the rate of pore pressure change at a material point ∂u/∂t is replaced by du/dt-v∂u/∂x. In order to avoid spurious oscillations in the nodal degrees of freedom, which move with the reference points, upwinding is introduced. For the fixed grid approach, the influence of material removal at a boundary is taken into account by removing the nodes above the excavation level at discrete times. Owing to the loss of nodal degrees of freedom as excavation advances, a much greater number of nodes is required to complete the analysis when compared with the deforming grid approach. A comparison of the solutions from each model showed that the deforming grid approach performed better, as anticipated. Both models underestimated the deficient pore pressure dissipation when compared with the solutions provided by Koppula and Morgenstern (1984).