Boundary stresses due to impacts from dry granular flows

Field data and laboratory experiments suggest that bedrock wear from debris flows is largely due to particle-bed impacts, rather than solely due to abrasion by sliding, and that the associated bedrock erosion rates are dependent on the particle size distribution in the debris flow. Here we use Discrete Element Method (DEM) simulations with an established contact mechanics model to explore grain-size influences on contact forces associated with particle-bed impacts in sheared granular mixtures. We first compare DEM simulations with experimental observations obtained from shallow granular flows in rotating drums of diameters 0.56 m and 4.0 m. Our simulations reproduce, without parameter tuning, experimentally measured segregation, boundary pressures, and height profiles. We perform additional simulations systematically varying particle size distributions in binary mixtures. We show that local time-averaged boundary pressures in thin flows are essentially the normal component of the weight of the flow, independent of particle size distribution. However, other statistical measures of boundary forces scale with mass-averaged particle size. We demonstrate that this is because individual particle-bed impacts, rather than impacts from multiple particle collisions, dominate the largest contact forces. We show that these largest impact forces vary as the square of grain size and the 1.2 power of impact velocity as predicted from the contact mechanics model underlying the DEM. These results support the particle size dependence of a recently proposed bedrock incision model and suggest that next steps for a predictive bedrock incision model require the statistics of the largest impact velocities.