Exploring the Temporal-Varying and Depth-Nonlinear Velocity Profile of Debris Flows Based on A Stratification Statistical Algorithm for 3D-HBP-SPH Particles

Abstract

Estimation of velocity profile through mud depth is a long-standing and essential problem in debris-flow dynamics. Until now, various velocity profiles have been proposed based on the regression of experimental measurements, but these are often limited by the observation conditions, such as the number of the configured sensors. Therefore, the resulting linear velocity profiles exhibit limitations in reproducing the nonlinear behavior and its temporal variation during the debris-flow process. In this study, we present a novel approach to explore debris-flow velocity profile in detail upon our previous 3D-HBP-SPH numerical model, i.e., the three-dimensional Smoothed Particle Hydrodynamic model incorporating with the Herschel-Bulkley-Papanastasiou rheology. Specifically, we propose a stratification statistical algorithm for interpreting the details of SPH particles, which enables the recording of temporal velocities of debris flow at different mud depths. To regress the velocity profile, we introduce a logarithmic-based nonlinear function with two empirical parameters, that controlling the shape of velocity profile and concerning its temporal evolution. We verify the proposed velocity profile and explore its sensitivity using 34 sets of velocity data from three individual flume experiments in previous literatures. Our results demonstrate that the proposed temporal-varying and depth-nonlinear velocity profile outperforms the previous ones.