A numerical model for heterogeneous and confined debris flows

The flow equation for a uniform debris flow can be obtained, analytically, from integration of the local constitutive equations only in very simple schemes, for example in the hypothesis of uniform solid concentration and absence of lateral walls. The flow discharges computed by these assumptions result to be extremely higher than the observed ones. In the present paper an attempt to remove these two hypotheses is presented. The fluid is assumed mono-phase (equal velocity of solids and fluid) and heterogeneous (solid concentration variable in the cross section). The effect of the mixture heterogeneity is described, in this mono-phase approach, as expressing the constitutive parameters depending on the local solid concentration. A computational code has been implemented for the estimation of the concentration and velocity distribution in the cross section. The code is applied to a viscoplastic (Herschel-Bulkley) mixture.