| In this work, we present a finite element formulation for variably-saturated porous geomaterials undergoing elastoplastic deformations. The deforming body is treated as a multiphase continuum, and the governing mass and momentum balance equations are solved in a fully-coupled manner. It is well-known, however, that mixed formulations of the type examined here may lead to unstable approximations unless the spaces chosen for the pressure and displacement interpolation satisfy stringent stability restrictions. Failure to choose a stable pair typically leads to spurious pressure oscillations and poor convergence behavior. Unfortunately, many seemingly natural combinations---including equal-order interpolation for all field variables---do not satisfy the necessary requirements. In this work, we propose a stabilized formulation, based on a minor modification of the variational equations, which allows one to circumvent these restrictions and employ equal-order mixed elements. Several numerical examples are used to demonstrate the computationally appealing features of this alternative formulation.;The resulting implicit, nonlinear algebraic systems are then solved using an inexact Newton algorithm. We discuss methods for solving the linearized systems using memory-efficient iterative solvers, both on serial and parallel computing platforms. In order to deal with inherent ill-conditioning, we propose a block-structured, multilevel preconditioner that both accelerates the convergence of the Krylov solver and exhibits excellent scaling properties as the number of unknowns and number of processors increase.;To demonstrate the effectiveness of these approaches, the analysis framework is applied to modeling hydrologically-driven slope failure. This analysis is motivated by a recent landslide that occurred at a steep experimental catchment (CB1) near Coos Bay, Oregon. Simulations are used to quantify the rainfall-induced slope deformation and assess the failure potential. Results of parametric studies suggest that for a steep hillside slope underlain by shallow bedrock similar to the CB1 site, failure would occur by a multiple slide block mechanism, with progressive failure surfaces forming at the bedrock interface and then propagating to the slope surface. A key observation is that significant computational resources are required to capture these complex solid/fluid interaction mechanisms at sufficient resolution, further justifying the use of the proposed approaches over conventional methods. |
