Numerical investigation about propagation characteristics and hydro-sediment-morphodynamic interactions of multi-sized debris flow with a two-phase continuum model

Debris flows are classical two-phase flows that can be enhanced by entraining multi-grain sizes of sediments from the bed as they rush down steep slopes, in which particle segregation is related to assessing the potential hazards. However, understanding the characteristics and fluid-particle interaction mechanisms remains challenging. Here an existing depth-averaged two-phase continuum flow model is further improved by incorporating the effects of pore-fluid pressure and bed sediment conditions on erosion. To demonstrate its reliability, we compare numerical solutions with measurements of thickness, front location, and bed deformation in two sets of USGS large-scale experimental debris flows over erodible beds. The following physical understandings are obtained. First, the positive effects of pore-fluid pressure and coarse bed materials on erosion rates are numerically reproduced. Moreover, an additional mechanism for this phenomenon has been revealed. Specifically, debris flows on steep slopes are likely to fall into a high shear stress regime, under which conditions the sediment transport capacity always takes a maximum value and is independent of the sediment size. Therefore, the sediment settling velocity that is proportional to the sediment size affects the erosion rate directly. Second, we probe into the non-dimension number and energetics of the debris flows to find it necessary to incorporate water-sediment and particle-particle interactions into reproducing the debris flow processes. Third, two kinds of mechanisms for particle size coarsening in the head region of the debris flow are resolved: on the one hand, they can be incorporated and retained there if the debris flow acquires sediment from the bed in transit due to considering the hiding/exposure mechanisms and on the other hand, they can migrate to the head by preferential transport. Furthermore, a series of idealized tests were conducted to explore the factors contributing to the segregation of particles within a debris flow. The longitudinal particle segregation was reproduced by incorporating the shear-induced non-uniform vertical distributions of velocity and sediment concentrations, the visco-inertial rheology, as well as the grain-size heterogeneity into the modelling. Sensitive analysis shows that the transport of fine particles is more inhibited by the interaction of the flow, contributing to the larger transportation velocity of the coarse particle. We further observed that the water content, the slope, and the particle size would have positive effects on the longitudinal size segregation in the head region, contrasting with the negative effects of the flow viscosity. These factors affecting the segregation ratio are attributed to the changes in the ratio of the Reynolds Number of the flow between fine and coarse particle.