Frictional Hysteresis in Granular Avalanches

Debris flows and snow avalanches are typical of a wide range of natural hazards in which grains of rock, ice or snow are eroded from a mountain slope and flow rapidly downhill, eventually stopping to form a deposit. Although the general mass and momentum balances that govern such granular flows have been understood for several decades, there is still much about their behaviour that is poorly understood. In particular, predicting how far a flow will travel is a significant challenge, and one of considerable practical importance to those living near mountainous regions. In this talk I will use laboratory experiments and models based on the shallow-water equations to demonstrate how flowing granular material can interact with grains that have already deposited. This interaction profoundly changes the morphology and runout distance of an avalanche. I will show that granular avalanches flowing over an erodible layer can flow indefinitely, by forming a soliton wave that erodes granular material at its front and leaves a trail of deposited grains behind it. In the absence of an erodible layer, the deposition of grains at the edges of a debris flow or snow avalanche can confine the subsequent flow laterally, allow it to flow a much greater distance downslope. The physics underlying these phenomena is the unique frictional rheology of granular materials: when a shear stress is applied to grains, they may adopt either a static state or shearing state, with a hysteretic transition between these two behaviours. Incorporating this hysteresis into our model equations allows prediction of a remarkable amount of the diverse and complex flow behaviour observed in nature.