(65a) Applying Particle-Size Segregation Theory to the Erosion-Deposition Dynamics of Granular Avalanches

Debris flows, snow avalanches and pyroclastic flows, like almost all geophysical events involving granular materials, exhibit a continuous exchange of particles between a depositional flow and the erodible substrate that it propagates on. The balance between erosion and deposition can have a great influence on the flow duration and runout distance, which are important factors to consider for hazard risk assessment and mitigation. A perfect balance between erosion and deposition is even possible in certain conditions (Edwards, Viroulet, Kokelaar & Gray 2017), resulting in a flow that propagates steadily downslope whilst maintaining a constant shape and velocity. By releasing a small amount of yellow sand onto an erodible bed of the the same material, but instead coloured red, it is shown that the erosion-deposition process in a steady avalanche eventually results in the the flowing material consisting entirely of particles that have been eroded from the substrate layer. Furthermore, different steady state regimes are possible for a given slope inclination angle depending on the amount of sand released. The experiments are simulated using a depth-averaged avalanche model and a friction law that allows dynamic, static and intermediate flow regimes for angular materials (Edwards et al. 2017). This model is augmented with the large-particle transport equation (Gray & Kokelaar 2010) for the evolution of an inversely graded shock interface between an instantaneously and sharply segregated layer of large particles above a layer of small particles in a bidisperse flow. The inclusion of a segregation equation here allows the tracking of the interface between the two different coloured sands and therefore the redistribution of grains due to erosion and deposition. By plotting the colour of the sand according to the depth-averaged yellow concentration at each position, it is shown that all of the key experimental features are qualitatively reproduced by the numerics.