Hierarchical Statistics-Based Nonlinear Vertical Velocity Distribution of Debris Flow and Its Application in Entrainment Estimation

Abstract

The vertical distribution of debris flow profile velocity is the key to studying debris flow, impulse and the sediment carrying process. At present, the linear distribution model based on flume test results cannot describe the vertical distribution of debris flow velocity effectively due to the limitation of measurement methods. In this paper, the smooth particle hydrodynamics (SPH) numerical model based on the Herschel–Bulkley–Papanastasiou (HBP) constitutive model is utilized to invert the three-dimensional dynamic process of debris flow based on a large-scale debris flow flume experiment. With a hierarchical statistical approach, a huge number of particle velocity data were analyzed and processed to obtain the vertical distribution law of velocity. We proposed a nonlinear vertical distribution model of debris flow velocity based on logarithm function accordingly. We also applied the proposed model to the existing debris flow entrainment estimation framework. A flume dam break test case was inverted to verify the performance of erosion calculations. The results show that the numerical simulation results of erosion depth are close to the experimental values. The error percentage of maximum erosion depth is 4.1%. The average error percentage of erosion depth simulation results is 15.5%.