Saturated granular flows: constitutive modelling under steady simple shear conditions

Abstract

In this paper, the authors analyse numerical and experimental results concerning either dry or saturated granular flows under steady, simple shear conditions. A new constitutive model is introduced, on the base of the mixture theory, according to which granular and liquid phases are considered separately. The constitutive relationship refers to the representative elementary volume and assumes that the mean values of all kinematic variables, of both granular and liquid phases, coincide. For the two phases, a parallel scheme is chosen. As regards the granular contribution, the authors employ an already conceived constitutive model where the critical state concept and the kinetic theory of granular gases are merged, and in which the granular temperature plays the role of state variable for the material. Under saturated conditions, the new model accounts for granular–liquid coupling effects. In fact, the liquid viscosity is a function of granular concentration, whereas the evolution of granular temperature is influenced by the liquid molecular viscosity. The model is validated against numerical results and critically discussed. For sufficiently small values of concentration, the transition from a Newtonian to a Bagnoldian regime, for increasing values of strain rate, is correctly reproduced.