A stabilized semi-implicit material point method for coupled hydromechanical large deformation problems in unsaturated porous media

This paper presents a stabilized semi-implicit material point method (MPM) for simulating coupled hydromechanical large deformation processes in unsaturated porous media. The governing equations are comprehensively formulated to incorporate the spatial gradients of saturation and porosity, capturing key features of solid–fluid interaction. To improve the numerical stability of the semi-implicit scheme, a cell-based averaging strategy is introduced to suppress stress oscillations in both the solid and fluid phases. Furthermore, a surface layer correction is developed to improve the velocity gradient near infiltration boundaries, which is particularly beneficial for modeling unsaturated flow behavior. The proposed method effectively addresses common numerical challenges associated with fluid incompressibility and low permeability, such as time step constraints and instability. The MPM framework is implemented with GPU acceleration, substantially enhancing computational efficiency. The accuracy and robustness of the proposed method are validated through three benchmark problems: one-dimensional infiltration, two-dimensional footing consolidation, and collapse of a partially saturated sand column. Finally, the practical applicability of the proposed method is demonstrated in simulating rainfall-induced slope failure and seepage in an embankment dam.