Experimental Investigation of Entrainment Rate by Debris Flows: from Shear Stress to Granular Temperature

Abstract:

Debris flows – flows of boulders, gravel, sand, fine particles, and fluids – erode sediment from steep hillsides and deposit them at lower slopes. Current model frameworks for erosion by debris flow vary significantly and include those that consider macroscopic fields such as excess shear stresses, similar to traditional models of bedload transport, to those that consider the “granular” physics, from force chains (related to bed fabric) to granular temperatures (related to random kinetic energy of the flow). We perform experiments to investigate the underlying mechanics associated with entrainment of bed materials by overlying flows in an instrumented laboratory debris flow flume. In particular, we investigate how the erosion rate of a flowing mass impinging on an erodible bed of particles depends on boundary conditions, dynamics of the flow, and the state of the bed. Using high speed imaging to capture average and instantaneous particle dynamics simultaneously with bed stress measurements, we investigate the effectiveness of a variety of model frameworks for capturing the relationships between flow dynamics and erosion rates. We find no correlation between the bed shear stress associated with the mass of the flow and erosion rate. Similarly, we found no correlation between the erosion rate and a Reynolds stress, that is, the stress associated with correlations between downstream and vertical velocity fluctuations. On the other hand, we found that granular temperature is well-correlated with entrainment rate during particular phases of our experimental debris flow. In particular, we found the instantaneous entrainment rate ε is linearly dependent on the ratio of the granular temperature T_g to the kinetic energy associated with the average flow velocity u: ε ~ (T_g / ρ_m u²) where ρ_m is the local instantaneous density of the flow. We present these results and discuss how they vary with the state of the flow, boundary conditions, and particle mixtures.