The paper presents a refined implicit two-phase coupled Material Point Method (MPM) designed to model poromechanics problems under static and dynamic conditions with stability and robustness. The key variables considered are the displacement and pore water pressure. To improve computational efficiency, we incorporate the Finite Difference Method (FDM) to solve pore pressure, stored at the center of the background grid where the material points reside. The proposed hydromechanical MPM cannot only effectively addresses pore pressure oscillation, particularly evident in nearly incompressible fluids-a common challenge with Galerkin interpolation, but also decreases the degrees of freedom of the system equations during the iteration process. Validation against analytical solutions and various numerical methods, encompassing 1D and 2D plane-strain poromechanical problems involving elastic and elastoplastic mechanical behavior, underscores the method's resilience and precision. The proposed MPM approach proves adept at simulating both quasi-static and dynamic saturated porous media with significant deformation.

In this study, an implicit stabilized material point method (MPM) based on the updated Lagrangian formulation has been developed to model soil-like two-phase coupled problems under undrained/drained conditions, in which the displacement of solid phase and pore water pressure are used as primary variables. Instead of using the Cauchy stress in the equilibrium equation, we employ the first Piola-Kirchhoff stress (PK1 stress) and rigorously implement the objective Jaumann stress to account for large deformations. To address numerical oscillation in (nearly) incompressible coupled problems, the finite difference method (FDM) is used to calculate the pore water pressure stored at the center of the background grid cells and the B-bar method proposed by Hughes (1980) is also incorporated into the proposed MPM to avoid the volumetric locking problem. Through simulations of various classic hydromechanical coupled problems and comparing them with analytical solutions or other numerical simulations, the reliability and robustness of the proposed implicit MPM are extensively validated. The method demonstrates its capability to accurately capture the large deformation behavior and hydromechanical interactions in geomaterials, resulting in stable and reliable simulation outcomes.