Grain-Scale Modelling of Swelling Granular Materials Using the Discrete Element Method and the Multi-Sphere Approximation

In granular materials, the Representative Elementary Volume (REV) is a direct result of the particle locations, particle size distribution, and the shape of the particles. To study the REV of granular materials at the grain-scale, the Discrete Element Method (DEM) is employed to generate packings of spheres. In DEM, packings can be constructed to match a given particle size distribution and either a given porosity value or a given state-of-stress inside the packing. From these packings, hydraulic properties such as porosity, permeability and the capillary pressure – saturation curve can be computed using direct simulations, pore unit approach and/or the pore morphology method. The minimum number of particles that are required for those hydraulic properties to be independent of the number of particles can be investigated using two methods: 1) a packing is generated that contains a large number of particles, from which hydraulic properties are determined in a sub-domain that is increased incrementally; 2) a variety of packings is generated for various numbers of particles, where for each packing the hydraulic properties are computed. The latter method is convenient as typically many packings are generated for various conditions. We found that approximately 4000 spheres are sufficient for a narrow and normal distributed granular material. An additional degree of freedom arises when the shapes of particle are included, not only the particle position is important, but also its rotation and its randomness in shape. In DEM, particle shapes can be included as sets of overlapping spheres. We found that the minimum number of particles is approximately 2000 (i.e. 20.000 spheres) and that a minimum of 20 shapes should be included as otherwise the number of shapes affects hydraulic properties.