What does control Vp/V8 in granular rocks?

Abstract

The compressionnal Vp and shear Vs velocities of rocks are known to depend on composition and porosity. In the case of high porosity, poorly consolidated dry rocks, [Winkler, 1983] showed that VP/Vs is essentially constant and close to 1.56, in disagreement with theoretical predictions. Winkler suggested that this discrepancy could be attributed to either packing models or contact stiffnesses models. We have investigated first the influence of packing models using results derived directly for disordered packings [Digby, 1981] and for ordered ones. Identical Poisson's ratio values, lower than the experimental values, are obtained for close packings and random ones. This shows that the role of packing is a minor one. In agreement with the conclusion of [Palciauskas, 1992], the role of contact stiffnesses appears to be the main one. We show that experimental results can be explained by a simple and robust roughness model. Averaging over a distribution of microcontacts implies that only half of these contribute to shear so that the ratio of both stiffnesses has a value close to that previously derived by Palciauskas on the basis of a more complex oblique contact model. The observed average Poisson's ratio value of 0.14-0.15 and VP/Vs value of 1.56 is a consequence of a symmetric asperity distribution and of the asymmetry of shear.