An explicit material point and finite volume sequentially coupled method for simulating large deformation problems in saturated soil

Abstract

An explicit material point and finite volume sequentially coupled method (MPM-FVM) is developed using u-p form coupling formulations for the simulation of large deformations in saturated soil. In MPM-FVM, the momentum conservation equation is solved by MPM under the updated Lagrange framework, and the mass conservation equations are solved by FVM under the Euler framework. The numerical implementation of an explicit sequentially coupled algorithm is developed considering the tradeoffs between computational cost and numerical stability. The critical time step of u-p form governing equations is derived using the Von Neumann method, which is found to be much greater than the u-U form explicit MPM at low permeability, allowing for high numerical stability. Three numerical cases are presented to demonstrate the stability, efficiency, and effectiveness of the developed MPM-FVM method. The simulation of a saturated one-dimensional soil column subjected to quasi-static and dynamic loads validates the method, and highlights its greater efficiency and accuracy compared to standard solid–fluid coupled MPM methods. The large deformation simulation capability of the method is exhibited via simulation of a saturated slumping block. In real-world application, simulation results obtained using method achieves excellent agreement with the experiment measurements and observations of the Selborne landslide experiment.