Particle Size Segregation and Diffusion in Saturated Granular Flows: Implications for Grain Sorting in Debris Flows

Sorting of rocks, boulders, and silt/sand-sized particles according to their size is a characteristic feature of debris flow deposits and is an active process during flow which significantly affects the mobility. The degree at which size sorting occurs in debris flows depends on the relative magnitudes of granular processes such as particle size segregation and diffusion. Since debris flows are fluid-saturated phenomena, accurate modelling of size sorting requires the understanding of the influence of fluids on these processes, which have not been systematically studied. Here, we present simulation results and the associated empirical expressions for particle size segregation and diffusion which take into account fluid effects due to buoyant and drag forces. These expressions are developed through scaling analysis of data obtained from coupled granular-fluid simulations of saturated bi-disperse mixtures under simple shear. We further show that using these scaling relationships, an existing segregation-diffusion continuum equation can be extended to model particle sorting in debris flows with various types of fluids.