Rheophysics of dense granular materials: Discrete simulation of plane shear flows

Abstract

We study the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation and prescribing the pressure and the shear rate. We show that, in the limit of rigid grains, the shear state is determined by a single dimensionless number, called inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic regime of soil mechanics, while large values of I correspond to the collisional regime of the kinetic theory. Those shear states are homogeneous, and become intermittent in the quasi-static regime. When I increases in the intermediate regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. We also show that the relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains (restitution, friction and elasticity) have a very small influence in this intermediate regime. Then, we explain how the friction law is related to the angular distribution of contact forces, and why the local frictional forces have a small contribution to the macroscopic friction. At the end, as an example of heterogeneous stress distribution, we describe the shear localization when gravity is added.

Modeling of crack propagation in weak snowpack layers using the discrete element method

“…The corresponding mechanical parameters, namely the normal and shear stiffness k n and k s (elasticity parameters), the restitution coefficient e (viscous parameter) and the friction coefficient µ are summarized in Table 1. The value of the normal stiffness k n was chosen in such a way that the normal interpenetration at contacts are kept small, i.e., to work in the quasi-rigid grain limit (da Cruz et al, 2005;Roux and Combe, 2002). Concerning the normal restitution coefficient e, we verified that the results presented below, and more generally all the macroscopic mechanical quantities obtained from the simulations, are actually independent of this parameter (in the range 0.1-0.9).…”

“…Discrete element (DE) modeling (Cundall and Strack, 1979) allows computing the motion of a large number of small grains by solving dynamic equations for each and defining a contact law between the grains. In addition, the DE method allows assessing mechanical quantities such as stress, displacement, deformation rate, porosity, etc., computed over representative elementary domains at each material point within the sample.…”

“…The discrete element simulations were performed using the commercial software PFC2D (by Itasca), which implements the original soft-contact algorithm described in Cundall and Strack (1979). …”

Flash weakening is limited by granular dynamics

“…[4] Many studies on the frictional properties of dense granular matter have been conducted also in the field of statistical physics mainly by means of numerical simulation [GDR MiDi, 2004;da Cruz et al, 2005;Jop et al, 2006;Hatano, 2007]. These previous studies have revealed that the friction coefficient of granular matter is described as an increasing function of nondimensional velocity known as the inertial number I.…”

“…These previous studies have revealed that the friction coefficient of granular matter is described as an increasing function of nondimensional velocity known as the inertial number I. For example, a constitutive law proposed by da Cruz et al [2005] is…”