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%.

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

“…This flume experiment has been simulated in our previous study (Han et al, 2022), where a total of 43,258 fluid particles were used to represent the discretized debris-flow mass in the experiment. Nevertheless, in order to better explore the velocity details, more fluid particles are necessary to minimize the uncertainties of particle distribution.…”

“…Therefore, a high-performance computational server, capable of 24 core Intel Xeon Scalable CPU, 2 pieces of NVIDIA Titan V GPU, and 128GB RAM, is employed to execute the numerical computing. Other configurations and values of key parameters are kept the same as we summarized and listed in the previous study (Han et al, 2022).…”

Investigating the bearing performance of the foundation under the combined effects of flood scouring and soaking

“…( 1), the erosion rate is inversely proportional to the basal flow rate of the flood, indicating that the variation of the basal flow rate greatly affects the accuracy of the erosion rate calculation. Therefore, based on this, the model for the vertical nonlinear distribution of fluid velocity 29 is introduced in this paper, as shown in Eq. ( 2).…”

“…In the above equation, y denotes the flow depth of a point in the fluid; a denotes the nonlinear distribution coefficient of flow velocity, with a suggested value of 0.30-0.35 29 . This model establishes the relationship between the mean flow velocity generated by the two-dimensional shallow water model and the basal flow velocity under the nonlinear distribution model.…”

“…In order to achieve the above demand, the research logic follows three main steps. Firstly, based on the findings of previous studies [28][29][30] , the paper discussed the rationality of erosion foundation model that considers vertical nonlinear flow velocity distributions for flood. Secondly, the paper analyzed the foundation's bearing performance before and after flooding by considering the combined effect of dynamic scouring and static soaking.…”