An implicit coupled MPM formulation for static and dynamic simulation of saturated soils based on a hybrid method

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.