Deformation and stresses upon drainage of an idealized granular material

A pore-scale numerical model is employed to simulate the primary drainage of a deformable assembly of spherical grains. The model combines the discrete element method and a pore-scale method, respectively, for the solid phase and the fluid phases. The evolution of strain along the simulated drainage in oedometer conditions is reported. The combined actions of phase pressures and surface tension lead the solid skeleton to first shrink and then to swell at the approach of residual saturation. The effective stress is examined through the Bishop’s coefficient \(\chi\), obtained by a back analysis of the simulated strain. It is found that \(\chi\) is relatively close to the degree of saturation, with an exception at very low saturation. Further, a contact stress obtained by averaging micromechanical quantities is found nearly exactly equal to the effective stress deduced directly from the strain, in contrast to previous findings. A detailed analysis of the heterogeneous fields of effective stress, saturation and pressure is offered, suggesting a unique relationship between \(\chi\) and saturation at a mesoscale.