Quantifying permeability in bidisperse granular media through sequential homogenisation

Abstract

Abstract Content of image described in text. Bulk permeability controls pore pressure build-up in a granular material and thereby the hydrological conditions under which it deforms. The resulting deformation, in turn, alters pore geometry and consequently the material’s permeability. When simulating deformation, models often update a material’s permeability using parametrisations developed for idealised materials consisting of approximately equisized grains. However, real Earth materials often have wide grain-size distributions with several distinct modes. Here, we derive a model to estimate bulk permeabilities for bidisperse granular materials based on their wide, bimodal grain-size distributions, making progress towards bridging the gap between idealised and Earth materials. By combining direct numerical simulations to simulate pore-scale Stokes flows with sequential homogenisation to exploit the scale-separation among many grain-size modes, we compute flow fields consistent with pore-scale physics with high computational efficiency. We identify when existing techniques for estimating permeability meet their limitations. We validate our model against laboratory measurements of permeability for a two-component mixture of idealised glass beads and sands with scale-separated grain sizes, producing estimates of permeability with quantified variability. We then test our model against laboratory measurements of permeability for subglacial sediments, achieving high accuracy without specific calibration. Our work provides a practical tool to estimate permeability in the presence of deformation for Earth materials using grain-size distributions as an invariant.