An implicit stabilized material point method for modelling coupled hydromechanical problems in two-phase geomaterials

Abstract

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.