Depth-resolved numerical model of dam break mud flows with Herschel-Bulkley rheology

Mud flows are common phenomena in mountainous areas, which can threaten human safety and cause property losses under certain extreme circumstances. Studying the dynamic characteristics of mud flows, especially in the vertical direction, is helpful for risk reduction and hazard mitigation. In this study, a 2D depth-resolved numerical model based on Herschel-Bulkley rheology was developed to study the vertical structures of unsteady mud flows with a free-surface. The numerical model was solved by the projection method, and the free surface of mud flows was captured through the VOF method. To fully validate this new model, a series of laboratory experiments involving dam break mud flows were conducted, and the mud flow heights, bottom pressures and envelopes of mud residuum were measured. The numerical model proposed in this study was first validated by the steady-state solution for uniform flows of Herschel-Bulkley fluid on an inclined plane. Additionally, the simulated and measured mud flow heights, bottom pressures at different x locations and envelopes with different bed slopes showed good agreement. Furthermore, the numerical results for a Herschel-Bulkley fluid dam break flow were used to validate the proposed model, which further revealed good agreements. After that, the scenarios in which mud flows impact on a structure were numerically studied, and the vertical profiles of the front velocity and impact pressure on the structure were analyzed and discussed. The results show that a plug layer was formed in the mud flow under unsteady and nonuniform flow conditions, and the impact pressure on the structure was dominated by the dynamic pressure. In addition, the vertical position with the maximum impact pressure acting on the structure was not at the bottom or the surface of the mud flows, and the normalized vertical position rose as the yield stress and consistency coefficient increase for Herschel-Bulkley fluids.