Scaling laws of granular column collapse over varying base roughness: Insights from continuum modeling with Navier slip boundary condition

The mobility and runout scaling of granular flow have significant implications for geohazard assessment, which are largely controlled by the energy dissipation and shear resistance from base roughness. Although continuum models have proven effective for studying these problems, conventional boundary conditions remain limited: the no-slip boundary condition neglects basal slip entirely, whereas the Coulomb friction condition relies on back-analysis calibration and cannot easily handle arbitrary base roughness. Here, we introduce a roughness-informed Navier slip boundary condition for the continuum modeling of dense granular flows, which relates slip velocity to the local shear rate at the base via a dimensionless slip length. The proposed boundary condition is implemented into a Navier–Stokes continuum framework coupled with the μ(I)-rheology and the volume of fluid method. Benchmark cases of granular column collapse on horizontal and inclined planes demonstrate that the proposed model significantly outperforms traditional boundary conditions, accurately capturing the transition from basal slip to no-slip flow regimes. Furthermore, unified scaling laws incorporating roughness correction factors are derived for runout distance, deposit height, and collapse duration, encompassing a wide range of initial aspect ratios and inclination angles. Finally, a phase diagram is developed to delineate the boundary between deposited and non-deposited regimes on various slopes. This work provides a physically grounded scaling scheme for future consideration of substrate conditions (e.g., roughness and topography) and thereby enhances predictive modeling of geophysical mass movements. © 2026 Elsevier Ltd