Stress fluctuations and macroscopic stick-slip in granular materials

This paper deals with the quasi-static regime of deformation of granular matter. It investigates the size of the Representative Elementary Volume (REV), which is the minimum packing size above which the macroscopic mechanical behaviour of granular materials can be defined from averaging. The first part uses typical results from recent literature and finds that the minimum REV contains in general 10 grains; this result holds true either for most experiments or for Discrete Element Method (DEM) simulation. This appears to be quite small. However, the second part gives a counterexample, which has been found when investigating uniaxial compression of glass spheres which exhibit stick-slip; we show in this case that the minimum REV becomes 10⁷ grains. This makes the system not computable by DEM. Moreover, similarity between the Richter law of seism and the exponential statistics of stick-slip is stressed. Received 8 March 2002 and Received in final form 12 July 2002