DEM-LBM coupling for partially saturated granular assemblies

In this paper, we propose a phase-field-based Lattice Boltzmann Method (LBM) model coupled with the Discrete Element Method (DEM) for simulating unsaturated granular media over a large range of degrees of saturation. The formation of capillary bridges between grains is computed via an LBM scheme that solves Navier-Stokes and Allen-Cahn equations for multi-phase flow in complex geometries. As for the motions of the grains, these are computed within DEM where the contact behavior between spherical particles is based on a simple elastic- plastic contact law. Using an efficient DEM-LBM coupling framework, capillarity effects are explored at the pore scale with the collapse of a sandcastle as a classic illustration. This is done by considering an assembly of several thousands of spherical particles connected by capillary bridges for different degrees of saturation. It is shown that the mean capillary stress increases with the degree of saturation up to a certain threshold beyond which capillary stress drops until complete saturation. In addition, the Soil Water Characteristic Curve is qualitatively recovered and compared to a theoretical model. As such, the proposed DEM-LBM coupling scheme becomes a viable numerical tool that can explicitly model and explore pore-scale phenomena in unsaturated soils.