Hysteresis phenomenon within unsaturated granular assemblies: Capillary forces and matric suction

In this paper, we present a numerical approach to simulate the condensation and evaporation processes of capillary bridges within granular materials. The formation and dynamics of capillary bridges are captured using a phase-field-based framework implemented within the Lattice Boltzmann Method (LBM) to solve the Allen-Cahn and Navier-Stokes equations, while evaporation and condensation processes accounted for local changes in position of the capillary interfaces. Our model captures the emergence of hysteresis as a result of irreversible geometric transitions-such as bridge coalescence and snap-off-without prescribing any constitutive relation between suction and saturation degrees. This change in capillary regimes arises naturally from the interface dynamics and is not solved by the LBM. In particular, we can capture and analyze the discontinuities in capillary forces, when capillary bridges merge or split within small elementary assemblies of three or four spherical particles. Having validated our numerical results for the above elementary assemblies, a polydispersed granular assembly composed of 1000 spherical grains is next addressed. Our simulations capture well-known condensation and evaporation hysteresis phenomenon while offering the possibility to inspect the underlying topology of air and water clusters for the same water saturation along different hydraulic paths.