Variable-concentration and boundary effects on debris flow discharge predictions

The uniform flow of natural debris mixture is generally modeled assuming a uniform solid concentration and the absence of lateral walls. The resulting flow discharges are, however, higher than those observed and, in the case of erodible boundaries, the equilibrium between the moving and nonmoving mixtures cannot be simulated. Such a model also cannot simulate the effect of lateral rigid boundaries that generate lateral velocity and concentration gradients. This paper describes a numerical model to determine the concentration and velocity distribution in the two directions transverse to the flow. The model is applied to a uniform laminar flow of a mixture with a shear-thickening Herschel–Bulkley constitutive behavior, with rheological parameters expressed in terms of the local solid concentration, and allows the simulation of different conditions in the presence of both erodible and rigid boundaries.