Numerical Study of the Stress Response of Two-Dimensional Dense Granular Packings

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.Comment: 7 pages, 5 figure

Anisotropic permeabilities evolution of reservoir rocks under pressure: new experimental and numerical approaches

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Why Effective Medium Theory Fails in Granular Materials

Experimentally it is known that the bulk modulus, K, and shear modulus, \mu, of a granular assembly of elastic spheres increase with pressure, p, faster than the p^1/3 law predicted by effective medium theory (EMT) based on Hertz-Mindlin contact forces. To understand the origin of these discrepancies, we perform numerical simulations of granular aggregates under compression. We show that EMT can describe the moduli pressure dependence if one includes the increasing number of grain-grain contacts with p. Most important, the affine assumption (which underlies EMT), is found to be valid for K(p) but breakdown seriously for \mu(p). This explains why the experimental and numerical values of \mu(p) are much smaller than the EMT predictions.Comment: 4 pages, 5 figures, http://polymer.bu.edu/~hmaks

Sensitivity of the stress response function to packing preparation

A granular assembly composed of a collection of identical grains may pack under different microscopic configurations with microscopic features that are sensitive to the preparation history. A given configuration may also change in response to external actions such as compression, shearing etc. We show using a mechanical response function method developed experimentally and numerically, that the macroscopic stress profiles are strongly dependent on these preparation procedures. These results were obtained for both two and three dimensions. The method reveals that, under a given preparation history, the macroscopic symmetries of the granular material is affected and in most cases significant departures from isotropy should be observed. This suggests a new path toward a non-intrusive test of granular material constitutive properties.Comment: 15 pages, 11 figures, some numerical data corrected, to appear in J. Phys. Cond. Mat. special issue on Granular Materials (M. Nicodemi Editor

Stress response inside perturbed particle assemblies

The effect of structural disorder on the stress response inside three dimensional particle assemblies is studied using computer simulations of frictionless sphere packings. Upon applying a localised, perturbative force within the packings, the resulting {\it Green's} function response is mapped inside the different assemblies, thus providing an explicit view as to how the imposed perturbation is transmitted through the packing. In weakly disordered arrays, the resulting transmission of forces is of the double-peak variety, but with peak widths scaling linearly with distance from the source of the perturbation. This behaviour is consistent with an anisotropic elasticity response profile. Increasing the disorder distorts the response function until a single-peak response is obtained for fully disordered packings consistent with an isotropic description.Comment: 8 pages, 7 figure captions To appear in Granular Matte

Hydromechanical behavior of heterogeneous carbonate rock under proportional triaxial loadings

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