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This work focuses on the behaviour of granular materials under unsteady, simple shear conditions and, in particular, on from solid- to fluid-like phase transition. The authors introduce a theoretical model, based on continuum mechanics, able of predicting the mechanical behaviour of granular media under both quasi-static and dynamic conditions. The model assumes a parallel scheme where confining and shear stresses are computed as the sum of two contributions: the quasi-static and the collisional one. The quasi-static contribution is obtained by employing an elastic–plastic model including the critical state concept, while the collisional one is derived from the kinetic theory of granular gases. In order to test the model under unsteady conditions, DEM numerical simulations of time evolving homogeneous shear flows have been performed by considering an assembly of frictional, deformable spheres, under constant volume conditions. Simulations have been performed by systematically changing both void ratio and shear rate. The comparison between theoretical model predictions and DEM results is done in terms of time evolution of stresses and granular temperature. Suitable initial conditions are imposed to reproduce both solid to fluid (liquefaction) and fluid to solid (solidification) phase transitions.

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.

The numerical simulation of rapid landslides is quite complex mainly because constitutive models capable of simulating the mechanical behaviour of granular materials in the pre-collapse and post-collapse regimes are still missing. The goal of this paper is to introduce a constitutive model capable of capturing the response of dry granular flows from quasi-static to dynamic conditions, in particular when the material experiences a sort of solid-to-fluid phase transition. An ideal assembly of identical spheres under simple shear conditions is considered. In the constitutive model, void ratio and granular temperature have been chosen as state variables, and both shear and normal stresses are computed as the sum of two contributions: the quasi-static one and the collisional one. The former is determined by using a perfect elasto-plastic model including the critical state concept, while the latter is derived from the kinetic theory of granular gases. The evolution of the granular temperature, fundamentally governing the material phase transition, is obtained by imposing the kinetic fluctuating energy balance. The constitutive relationship has been integrated, under both constant pressure and constant volume conditions, and the influence of shear strain rate, initial void ratio and normal pressure on the mechanical response has been investigated.

We use previous results from discrete element simulations of simple shear flows of rigid, identical spheres in the collisional regime to show that the volume fractiondependence of the stresses is singular at the shear rigidity. Here, we identify the shear rigidity, which is a decreasing function of the interparticle friction, as the maximum volume fraction beyond which a random collisional assembly of grains cannot be sheared without developing force chains that span the entire domain. In the framework of extended kinetic theory, i.e., kinetic theory that accounts for the decreasing in the collisional dissipation due to the breaking of molecular chaos at volume fractions larger than 0.49, we also show that the volume fraction-dependence of the correlation length (measure of the velocity correlation) is singular at random close packing, independent of the interparticle friction. The difference in the singularities ensures that the ratio of the shear stress to the pressure at shear rigidity is different from zero even in the case of frictionless spheres: we identify that with the yield stress ratio of granular materials, and we show that the theoretical predictions, once the different singularities are inserted into the functions of extended kinetic theory, are in excellent agreement with the results of numerical simulations.

SUMMARY This paper aims at extending the well-known critical state concept, associated with quasi-static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure-imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides. Copyright © 2013 John Wiley & Sons, Ltd.

International audience; We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.

This work focuses on the mechanical response of dry granular materials under steady, simple shear conditions. In particular, the goal is to obtain a complete rheology able to describe the material behavior within the entire range of concentrations for which the flow can be considered dense. The total stress is assumed to be the linear sum of a frictional and a kinetic component. The frictional and the kinetic contributions are modeled in the context of the critical state theory and the kinetic theory of dense granular gases, respectively; in the latter, the correlated motion among the particles, which is likely to occur at high concentration, is also included. In accordance with recent findings on disordered granular packings, the frictional component of stresses is assumed to vanish when the concentration is below the random loose packing. According to this approach, four nondimensional quantities govern steady, simple shear flows: the concentration, the shear to normal stress ratio, the ratio of the time scales associated with the motion perpendicular and parallel to the flow, and the ratio between the particle stiffness and the normal stress. The present theory allows us to reproduce, in a notable way, both numerical simulations on simple shear flows of disks and physical experiments on incline flows of glass spheres taken from the literature.