Diffusion compaction coupling controls pore pressure dynamics in granular fluid flows

Abstract

Excess pore pressure in granular--fluid mixtures can transiently suppress frictional contacts and dramatically enhance flow mobility, yet its evolution is commonly modeled using constant effective diffusivities. Here we show that the apparent diffusivity is not intrinsic but emerges from the coupling between pore-pressure diffusion and granular compaction. Starting from two-phase mass conservation for a deformable, gas-saturated granular assembly, we derive an evolution equation for excess pore pressure that captures deformation of the granular skeleton. In the thin-flow, small-excess-pressure limit, this reduces to a one-dimensional diffusion--compaction equation with a time-dependent source term controlled by porosity changes. A modal analysis yields a reduced basal equation that separates diffusive drainage from compaction-driven forcing and identifies the corresponding timescales. This framework introduces a dimensionless source-to-diffusion ratio, $Ψ_0$, which governs the competition between these processes and collapses effective diffusivities obtained from high-resolution two-fluid simulations over nearly two orders of magnitude in bed height. This scaling implies that the apparent diffusivity, and thus flow mobility, is not intrinsic but depends on flow thickness through the competition between diffusion and compaction. Incorporating this physics into a depth-averaged model demonstrates that the resulting closure reproduces the thickness dependence of pore-pressure decay and runout observed in experiments. These results provide a physically grounded description of pore-pressure evolution in granular--fluid flows and clarify how diffusion--compaction coupling controls their mobility.