The mechanical behavior of dense flows of granular (visco-plastic) material is of a great importance in describing geophysical flows (rock-falls, rock or debris avalanches, etc.). They have been simulated mostly using thin layer depth-averaged models (two dimensional) to reduce the high computational costs related to the necessary description of the real flow. Natural avalanches and debris flows are often associated to complicated mountain topologies, which makes the prediction very difficult.
Very recently, a new depth integrated theory was obtained in Ionescu [I12] to model the flows of visco-plastic materials over a general basal topography using a Drucker-Prager type yield criterion (which includes the Bingham model). Ionescu [I13] have developed also a robust numerical algorithm for the visco-plastic Saint-Venant model proposed in [I12]. The mechanical model and the numerical approach were funded by the Romanian Ministry of Education and Research through the national research project PN-II-ID-PCE-2011-3-0045.
In this project we propose to continue the above theoretical (academic) investigation of the dense avalanches with a laboratory experimental study and with the elaboration of a user-friendly software useful for geophysicists and civil engineers. Even though granular flows at the laboratory scale may not involve the same physical processes as those acting at the natural scale, they provide a very useful way to investigate and quantify possible mechanisms and scaling laws as well as to test constitutive relations. Moreover, the results of such a small-scale analysis are often assumed to be valid at a large scale.
The degree of novelty and relevance of the preliminary results
We summarize here the principal features of Ionescu viscoplastic shallow flow model [I12] (used in the present project) by comparison with Savage and Hutter model [SH89], [SH91], the principal competitor model. The model presented in this proposal deals with an incompressible, viscous fluid/solid with a rather general plasticity condition for which the yield limit could have a general dependence on the pressure. It can include Drucker-Prager and Von-Mises /Bingham plasticity models excluded by the Savage and Hutter model. Morever, with an appropriate choice of the viscosity, the model described in this proposal recovers the visco-plastic model proposed by Jop, Forterre and Pouliquen [JFP06]. The bottom surface is described by its elevation in the Savage and Hutter model, while a general parametric description is given here. In the Savage and Hutter model the frictional terms and the plastic terms of the shallow model are introduced as external forces through "net driving acceleration" terms and "pressure coefficients" terms, respectively. In contrast, in our model the resulting shallow equations have the same structure as the three dimensional ones: the 2-D (tangent) momentum balance law is completed with a "shallow constitutive equation" which links the projection of the averaged stresses on the tangent plane to the rate of deformations (expressed through the tangent differential operators).