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

Published by the American Geophysical Union as part of the Water Resources Monograph Series, Volume 18. Landslides are a constant in shaping our landscape. Whether by large episodic, or smaller chronic, mass movements, our mountains, hills, valleys, rivers, and streams bear evidence of change from landslides. Combined with anthropogenic factors, especially the development and settlement of unstable terrain, landslides (as natural processes) have become natural disasters. This book charts our understanding of landslide processes, prediction methods, and related land use issues. How and where do landslides initiate? What are the human and economic consequences? What hazard assessment and prediction methods are available, and how well do they work? How does land use, from timber harvesting and road building to urban and industrial development, affect landslide distribution in time and space? And what is the effect of land use and climate change on landslides? [Book Synopsis]

Landslides: Processes, Prediction, and Land Use

Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.

Multiscale Methods for Composites: A Review

A novel discrete model for granular material incorporating rolling resistance

The homogenization techniques allow the macroscopic constitutive equations of a given material to be derived from its microscopic behaviour. The case of granular material is difficult because the microscopic level must be described in discrete terms (contact forces and relative displacements). The present paper is devoted to a general discussion of this problem and to a presentation of different models for granular homogenization. Since we shall primarily be concerned with methodological issues and with comparison to the standard microcontinuous case, attention will be focussed to the simplest case of micro-elasticity assuming a linear contact law

Homogenization for granular materials

This paper analyzes relationships allowing global variables to be deduced from local ones in granular materials. This change of scale is now clear for static variables but rather confusing for kinematic variables. This paper compares the various established formulations for kinematic variables and also proposes original formulations. By running numerical simulations all the formulations in question are compared and the basic premises to define the change of scale for kinematic variables in granular media put forward.

B. Cambou

Papers

Homogenization for granular materials

Change of scale in granular materials

A computational procedure to assess the distribution of constriction sizes for an assembly of spheres

Anisotropy in granular materials at different scales

Soil-structure interaction in shield tunnelling in soft soil