Von Neumann stability analysis of Biotʹs general two-dimensional theory of consolidation

Von Neumann stability analysis is performed for a Galerkin nite element formulation of Biotʹs consolida- tion equations on two-dimensional bilinear elements. Two dimensionless groups|the Time Factor and Void Factor|are identi ed and these quantities, along with the time-integration weighting, are used to explore the stability implications for variations in physical property and discretization parameters. The results show that the presence and persistence of stable spurious oscillations in the pore pressure are in uenced by the ratio of time-step size to the square of the space-step for xed time-integration weightings and physical property selections. In general, increasing the time-step or decreasing the mesh spacing has a smoothing e ect on the discrete solution, however, special cases exist that violate this generality which can be readily identi ed through the Von Neumann approach. The analysis also reveals that explicitly dominated schemes are not stable for saturated media and only become possible through a decoupling of the equilibrium and continuity equations. In the case of unsaturated media, a break down in the Von Neumann results has been shown to occur due to the in uence of boundary conditions on stability.