Wave propagation in an unconsolidated granular material: A micro-mechanical approach

We provide a theoretical analysis to support the presence of both slow and fast compression waves in an unconsolidated, fully saturated, granular material. We derive the constitutive relation for such an aggregate based upon a micro-mechanics analysis. In doing this, we take in account the coupling between the solid particles and fluid. As a consequence of this coupling, the lubrication layer provides a connection between particles, both when they are separating and when they are compressing. The predictions of the speed and attenuation of the fast compression waves compare well with experimental data over the range of frequencies for which the nonlinear dissipation associated with the relative velocities between solid and fluid is negligible. Slow waves are also predicted without comparison, because of the absence of clear experimental data. Predictions of the speed and attenuation for the shear wave are also provided and show a good agreement with experimental data when surface roughness is taken into account.