Modeling of Entrainment in Debris Flow Analysis for Dry Granular Material

Abstract

Debris flow entrainment refers to the increase in mass by way of erosion of the channel beds or undermining the channel banks. Entrainment makes the calculation of travel distance and velocities of debris flow much more complex and difficult. Shear failure of the material in the channel bed is usually considered to be the dominant mechanism in entrainment analysis. However in granular flow, material at the surface of the channel bed can be eroded by progressive scouring under the base of the debris. This may result in more material being eroded and entrained than just considering the shear failure mechanism. A new analytical model is proposed to calculate entrainment in debris flow analysis by considering both rolling and shearing motion. Newton’s Law of Motion is used to calculate accelerations, velocities, and displacements of granular particles. To study the entrainment process inside granular flow and to verify the new entrainment model, numerical experiments have been carried out using the Discrete Element Method (DEM). Velocities, including translational velocity, rotational velocity and average velocity, total volume, shear stresses are monitored using measurement circles in the numerical experiment. Variations of the depth of erosion at specific locations along the debris flow channel are monitored and the average entrainment rates are calculated. By comparing the numerical experimental results with the analytical solutions, it is found that results from the analytical model agree well with that from the numerical experiments. In order to use the new entrainment model into debris flow runout calculation, the new entrainment model has been incorporated in a runout model based on an energy approach. Entrainment calculation governed by a second order partial differential equation is solved using the finite difference method. The total mass and profile of the channel bed are adjusted during the entrainment calculation. Sensitivity analyses have been carried out on the new model by varying the model parameters including internal friction angle, basal friction angle, turbulent coefficient and mean of Probability Density Function (PDF) etc. Back analysis of historical cases is carried out using the new model. Several case histories have been studied which include the Tsingshan debris flow, Niumian Rock Avalanche, Fjaerland debris flow, Faucon debris flow and Zymoetz River rock avalanche. An extremely large rock avalanche occurred on April 9, 2000 at Yigong is also studied in the thesis. Measurements obtained from site investigation, including flow velocity, flow height, entrainment depth at specific locations, run-out distance and total volume at deposition fan, have been used to evaluate the model. The results are encouraging based on comparisons of the run-out distance, front velocity and total volume of the debris. Improvements are required on the entrainment depth and total volume in some cases when lateral spreading of the debris is significant.