2-D vertical modelling for shearing flow of a granular-fluid mixture

We propose a rheological model for a dense granular flow (e. g. debris-flow). It is based on the simultaneous presence of quasi static an dynamic stress components. The model leads to rather simple relationships, suitable for implementation in mathematical debris-flow models. The relative simplicity of the scheme is obtained uncoupling the problem of determining the concentration values from the rheological problem. Dynamic stress components are represented according to the relations originally proposed by Bagnold (1954) and the quasi static component are derived from more recent experimental works (Angeloni, Lamberti, Schippa 19971). The ratio between the quasi static stress components is assumed to be constant and independent on the interstitial fluid. The model is tested considering the velocity profiles measured in a set of experiments in a rheometer with glass spheres shearing in newtonian viscous fluids (Angeloni, Lamberti, Schippa 19971). In this experiments the mean bulk concentration was measured, and a granular concentration distribution along the vertical has been assumed to be of exponential type, with a given maximum at the fixed bottom. Rather satisfactory results have been obtained.