Modeling the progressive entrainment of bed sediment by viscous debris flows using the three-dimensional SC-HBP-SPH...

Recent reports and experimental data closely indicate that bed-sediment entrainment by debris flows strongly impacts the evolution of the topographic signature of a valley. However, it is difficult to constrain the physics of the entrainment process in numerical models. The challenge is deeply embedded in the shape of the velocity profile, whose knowledge is fundamental for estimating debris-flow basal shear stress exerting on bed sediment. Most two-dimensional models are restricted because the depth-integrated shallow water assumption is problematic in this aspect. One alternative is to combine a three-dimensional, particle-based numerical model with a progressive entrainment law. In this paper, we propose a three-dimensional, surface cell (SC)-based smooth particle hydrodynamics (SPH) model for simulating bed-sediment entrainment by viscous debris flows. The dynamic behavior of a debris flow is simulated by the open-source DualSPHysics scheme, into which the Herschel-Bulkley-Papanastasiou (HBP) rheology model is incorporated. Subsequently, the bed surface is meshed, over which the particles belonging to a certain cell at each time step are identified to represent the basal velocity and flow depth using a novel SC-based algorithm. With the extracted velocities of these basal particles, the sediment entrainment rate of each cell can be estimated using the optimized progressive entrainment law. The proposed SC-HBP-SPH method is tested by means of a full-scale flume experiment carried out in a previous study. The results show that the proposed model can adequately describe and reproduce the complex dynamic process of bed-sediment entrainment by overriding debris flows.