Depth-averaged models for dry granular flows

Geophysical granular flows, such as snow avalanches and debris flows, represent a great hazard to man and infrastructures. These natural phenomena are characterized by the rapid flow of a granular solid phase, embedded in an ambient fluid. Since such events occur with little warning, in addition to investigating the triggering conditions, it is of crucial interest to predict their propagation and run-out distances. The main purpose of the present research is to better understand the flow dynamics of dry granular flows, in the presence of no-slip bottom boundary conditions, and predict their propagation by using a depth-averaged approach. In this case, a stratification of different flow regimes, such as quasi-static and dense collisional, occurs and makes the utilization of the classical single layer depth-averaged models insufficient, because of important uncertainties about the velocity and shear stress distributions along the flow depth. In the first part of the present work, an experimental-numerical study on dam-break flows of dry granular material is reported. It has been found that a modification to the formula, proposed in the Savage-Hutter model for calculating the earth-pressure coefficient, leads to an improved agreement with experimental data, in presence of no-slip bottom conditions. In the second part, an experimental study on steady state velocity profiles of dry granular flows is reported. The granular material, used in this experimental research, was Ottawa sand (ASTM C-778 20/30). The velocity profiles at the side walls and free surfaces have been obtained, through granular PIV techniques. The measurements are in accordance with other experimental works on different granular materials and suggest the occurrence of a rheological stratification along the flow depth, in case of no-slip bottom condition. In order to better describe such a complex flow dynamics, a two-layer depth-averaged model has been proposed. The dynamics of the two layers, ideally corresponding to dense-collisional and quasi-static regimes, have been considered independently. As well, mass exchanges between the layers have calculated through a physically based closure equation. The well-known mathematical issue of the hyperbolicity loss in two-layer models has been carefully addressed. In order to overcome it, a local modification of source terms of the original mathematical model has been proposed. Such a treatment consists of introducing an extra resistance at the interface, if necessary, to avoid the hyperbolicity loss. This approach has been found to be robust and yields reasonable results, as long as the asymptotic steady state solution and boundary conditions fulfil the hyperbolicity requirements of the original model. Through comparisons with experimental data, the two-layer approach turns out to be very promising to describe the complex flow dynamics in case of no-slip bottom boundary conditions, although a more detailed description of the basal shear stress seems to be required. In the third part of the present dissertation, the same two-layer approach has been used in order to rewrite the mathematical model in a curvilinear coordinates system, attached to the interface between the two layers. The model equations have been obtained, by using the same approach proposed in Tai and Kuo (2008). In the model derivation, the physically negligible quantities are identified in a more rational way than the previous model, by means of a scaling approximation.