A modification of Biot theory for unconsolidated sediment.

A mechanism for bottom penetration at low grazing angle is conversion of sound into Biot slow waves. Experiments in unconsolidated sediments have not found Biot slow waves with expected parameter values, but have found them in consolidated sediments. These results led us to consider a modification of Biot’s model for unconsolidated, sandy sediment. In our model, unstrained grains touch at a single point, since two adjacent grain surfaces have relative curvature. As the grains are pressed together, the contact area and the stress/strain ratio increase. Under extension the grains separate and there is no stress. The model predicts (lattice strain) ∝(stress)^1/2 under compression. This scaling law should apply to any such medium, but the numerical coefficient depends on detailed properties of the lattice and grain geometry. Slow waves resulting from sound incident on the sediment are studied within the framework of this model. For simplicity, normal incidence is assumed. A positive effective lattice bulk modulus results from sediment overburden or from the pressure field of the sound. Numerical solutions and bounds on the production of slow waves in such a medium imply that the intensity of the slow wave is too low to have been observed by the experiments.