Solving Dynamic Soil Deformation-Fluid Flow Coupling Problems Using Material Point Method

In recent years, there has been an increasing amount of research on the Material Point Method (MPM) for modeling multi-phase coupled problems. Applying MPM in hydro-mechanical problems that interest geotechnical engineers have been explored in many of these studies . The explicit MPM method has been favored in dynamic large deformation problems due to its computational efficiency. However, numerically generated pore pressure oscillation has been a major issue. This paper presents a new formulation of MPM to model coupled soil deformation and pore fluid flow problems. The formulation is presented within the mixture theory framework, and pore water pressure is solved implicitly using a splitting algorithm based on the Chorins projection method. The splitting algorithm helps mitigate numerical instabilities at the incompressibility limit when equal-order interpolation functions are used. It reduces pressure oscillations and a time step size, which is independent of fluid compressibility and soil permeability. The proposed method is validated by comparing the numerical results with the closed form solutions of one dimensional and plane strain problems.