Constitutive relation for dense granular flow

We propose an experimentally derived constitutive equation for dense granular-fluid mixture (e. g. debris-flow). It is based on frictional (quasi-static) and collisional (dynamic) stress component. The model has been compared with experiments carried out in an annular rheometer (Angeloni, Lamberti, Schippa 19971) using glass spheres and natural sand shearing in air and in newtonian viscous fluids (i. e. water and water-glycerol solution) having different viscosity. The measures of the velocity distribution inside the channel leads to the a characterization of the actual shearing layer and to the evaluation of the related parameters (e. g. concentration, shear rate, etc). Dynamic stress component is consistent with that originally proposed by Bagnold (1954) in the asymptotic grain-inertia regime, but in the macro-viscous regime the value of the constant scatter from the original one, because of the presence of the quasi static stress component. The weighted function related to the quasi-static and dynamic stress seems to be slightly dependent on the grain characteristics (i. e. mainly the shape) in the range of the experiments. The constitutive model herein proposed compare satisfactorily with our experiments.