General scaling law for the velocity of steady, homogeneous granular flows down rough inclines

Avalanches of dry granular materials, such as rocks, snow, and ice, are chief contributors to hazardous geophysical flows in nature. A key problem hampering progress in predicting the destructiveness of such hazards is the poorly understood dependence of the flow velocity on the physical properties of the grains constituting a given material. In particular, their usually irregular, non-spherical shapes prevent application of rigorous theories, which were derived for spherical grains. In addition, we do not have a good empirical grasp of the issue, as evidenced by the failure of existing scaling laws across flows of different granular materials when applied to measurements and numerical simulations for idealized flow geometries. Here, we report a scaling law for the steady-state velocity of homogeneous granular flows down rough inclines. It holds for granular materials consisting of irregularly-shaped but relatively uniformly-sized grains descending rough slopes. Laboratory chute experiments and numerical simulations for a diverse range of granular materials corroborate its validity and generality. It exhibits a power-4/3 dependence on the flow thickness, as opposed to the power-3/2 dependence suggested by previous scaling laws. It is also unique in the aspect that it depends only on a single parameter characterizing the granular material: the dynamic angle of repose. This suggests that, quite surprisingly, most of the physical complexity associated with the composition and shape of a material's grains boils down to its bulk ability to resist externally-driven shearing.