A continuum-discrete model using Darcy's law: formulation and verification

Abstract

This paper presents a numerical scheme for fluid-particle coupled discrete element method (DEM), which is based on poro-elasticity. The motion of the particles is resolved by means of DEM. While within the proposition of Darcian regime, the fluid is assumed as a continuum phase on a Eulerian mesh, and the continuity equation on the fluid mesh for a compressible fluid is solved using the FEM. Analytical solutions of traditional soil mechanics examples, such as the isotropic compression and one-dimensional upward seepage flow, were used to validate the proposed algorithm quantitatively. The numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm. Sensitivity studies on the effect of some influential factors of the coupling scheme such as pore fluid bulk modulus, volumetric strain calculation, and fluid mesh size were performed to display the accuracy, efficiency, and robustness of the numerical algorithm. It is revealed that the pore fluid bulk modulus is a critical parameter that can affect the accuracy of the results. Because of the iterative coupling scheme of these algorithms, high value of fluid bulk modulus can result in instability and consequently reduction in the maximum possible time-step. Furthermore, the increase of the fluid mesh size reduces the accuracy of the calculated pore pressure. This study enhances our current understanding of the capacity of fluid-particle coupled DEM to simulate the mechanical behavior of saturated granular materials.