The behaviour of dense assemblies of dry grains submitted to continuous shear deformation has been the subject of many experiments and discrete particle simulations. This paper is a collective work carried out among the French research group Groupement de Recherche Milieux Divises (GDR MiDi). It proceeds from the collection of results on steady uniform granular flows obtained by different groups in six different geometries both in experiments and numerical works. The goal is to achieve a coherent presentation of the relevant quantities to be measured i.e. flowing thresholds, kinematic profiles, effective friction, etc. First, a quantitative comparison between data coming from different experiments in the same geometry identifies the robust features in each case. Second, a transverse analysis of the data across the different configurations, allows us to identify the relevant dimensionless parameters, the different flow regimes and to propose simple interpretations. The present work, more than a simple juxtaposition of results, demonstrates the richness of granular flows and underlines the open problem of defining a single rheology.

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On dense granular flows.

Interparticle forces in granular media form an inhomogeneous distribution of filamentary force chains. Understanding such forces and their spatial correlations, specifically in response to forces at the system boundaries, represents a fundamental goal of granular mechanics. The problem is of relevance to civil engineering, geophysics and physics, being important for the understanding of jamming, shear-induced yielding and mechanical response. Here we report measurements of the normal and tangential grain-scale forces inside a two-dimensional system of photoelastic disks that are subject to pure shear and isotropic compression. Various statistical measures show the underlying differences between these two stress states. These differences appear in the distributions of normal forces (which are more rounded for compression than shear), although not in the distributions of tangential forces (which are exponential in both cases). Sheared systems show anisotropy in the distributions of both the contact network and the contact forces. Anisotropy also occurs in the spatial correlations of forces, which provide a quantitative replacement for the idea of force chains. Sheared systems have long-range correlations in the direction of force chains, whereas isotropically compressed systems have short-range correlations regardless of the direction.

Contact force measurements and stress-induced anisotropy in granular materials.

We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow 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. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.

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

We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) proportional to H(alpha), with alpha=1.52+/-0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.

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Granular flow down an inclined plane: Bagnold scaling and rheology

Even though dust coagulation is a very important dust-processing mechanism in interstellar space and protoplanetary disks, there are still important parts of the physics involved that are poorly understood. This imposes a serious problem for model calculations of any kind. In this paper, we attempt to improve the situation by including the effects of tangential forces on the contact in some detail. These have been studied in recent papers. We summarize the main results from these papers and apply them to detailed simulations of the coagulation process and of collisions between dust aggregates. Our results show the following: (1) the growth of aggregates by monomers will normally not involve major restructuring of the aggregates, (2) the classical hit-and-stick assumption is reasonably valid for this case, (3) collisions of aggregates with each other or with large grains can lead to significant compaction, and (4) the results can be easily understood in terms of critical energies for different restructuring processes. We also derive a short summary that may be used as a recipe for determining the outcome of collisions in coagulation calculations. It is shown that turbulent velocity fields in interstellar clouds are capable of producing considerably compressed aggregates, while the small aggregates forming early on in the solar nebula will not be compacted by collisions. However, compaction provides an important energy sink in collisions of larger aggregates in the solar nebula.

https://iopscience.iop.org/article/10.1086/303996/pdf

The Physics of Dust Coagulation and the Structure of Dust Aggregates in Space

1. Introduction 2. The analysis of stress and strain rate 3. The ideal Coulomb material 4. Coulomb's method of wedges 5. The method of differential slices 6. Determination of physical properties 7. Exact stress analysis 8. Velocity distributions 9. The conical yield function 10. The prediction of mass flow rate Problems Appendices Index.

R. M. Nedderman

Papers

Statics and Kinematics of Granular Materials