Poro-acoustoelasticity of fluid-saturated rocks

We generalize the classical theory of acoustoelasticity to the porous case (one fluid and a solid frame) and finite deformations. A unified treatment of non-linear acoustoelasticity of finite strains in fluid-saturated porous rocks is developed on the basis of Biot's theory. A strain-energy function, formed with eleven terms, combined with Biot's kinetic and dissipation energies, yields Lagrange's equations and consequently the wave equation of the medium. The velocities and dissipation factors of the P- and S-waves are obtained as a function of the 2nd- and 3rd-order elastic constants for hydrostatic and uniaxial loading. The theory yields the limit to the classical theory if the fluid is replaced with a solid with the same properties of the frame. We consider sandstone and obtain results for open-pore jacketed and closed-pore jacketed gedanken' experiments. Finally, we compare the theoretical results with experimental data.