Stress fluctuations in granular matter: normal vs. seismic regimes in   uniaxial compression tests
  This paper is concerned with the trends of stress fluctuations in dry granular materials as functions of the sample size D and of the grain diameter d. Results are obtained in the plateau regime of large axial deformation, during axi-symmetric uni-axial compression. Two cases have to be distinguished depending on whether the material generates or does not generate stick-slip. When no stick-slip is generated (Fig.1), it is found that the relative stress fluctuations dq/q of the deviatoric stress q scales linearly with the ratio d/D >. The coefficient A relating dq/q and d/D ranges from 1 to 3 about, depending on the grain size d; this is probably due to the effect of the piston roughness. This result is compatible with a contact force network with a random force distribution and a short range correlation length L,i.e. L<3d; this leads to estimate the representative elementary volume REV to contain few grains (from 1 to 30) as it has been defended already in [1].   We turn now to cases exhibiting stick-slip (Fig. 2). It has been shown in [2] that the distribution of delays between events is rather "exponential" when the sample is small, and Gaussian-like when the sample is larger. The cross-over between the random to quasi periodic regime occurs for a typical sample which contains 10 000 000 grains [2]. In this paper we show an analogy between the statistics of stick-slip amplitude Dq/q and the seismicity of the Los Angeles area during 1979-1997 period [3]. Similarity of the two trends is quite surprising. The seismicity has been cut off at Magnitude M=3.5.   These results have to be handled with care since similarity may be fortuitous. 
F. Adj\'emian & P. Evesque