1D numerical model of muddy subaqueous and subaerial debris flows

A 1D numerical model of the downslope flow and deposition of muddy subaeria l and subaqueous debris flows is presented. The model incorporates the Hers chel-Bulkley and bilinear rheologies of viscoplastic fluid. The more famili ar Bingham model is integrated into the Herschel-Bulkley rheological model. The conservation equations of mass and momentum of single-phase laminar de bris flow are layer-integrated using the slender flow approximation. They a re then expressed in a Lagrangian framework and solved numerically using an explicit finite difference scheme. Starting from a given initial shape, a debris flow is allowed to collapse and propagate over a specified topograph y. Comparison between the model predictions and laboratory experiments show s reasonable agreement. The model is used to study the effect of the ambien t fluid density, initial shape of the failed mass, and theological model on the simulated propagation of the front and runout characteristics of muddy debris flows. It is found that initial failure shape influences the front velocity but has little bearing on the final deposit shape. In the Bingham model, the excess of shear stress above the yield strength is proportional to the strain rate to the first power. This exponent is free to vary in the Herschel-Bulkley model. When it is set at a value lower than unity, the re sulting final deposits are thicker and shorter than in the case of the Bing ham theology. The final deposit resulting from the bilinear model is longer and thinner than that from the Bingham model due to the fact that the debr is flow is allowed to act as a Newtonian fluid at low shear rate in the bil inear model.