Transient wave propagation in a one-dimensional poroelastic column

Biot's theory of porous media governs the wave propagation in a porous, elastic solid infiltrated with fluid. In this theory, a second compressional wave, known as the slow wave, has been identified. In this paper, Biot's theory is applied to a one-dimensional continuum. Despite the simplicity of the geometry, an exact solution of the full model, and a detailed analysis of the phenomenon, so far have not been achieved. In the present approach, an analytical solution in the Laplace transform domain is obtained showing clearly two compressional waves. For the special case of an inviscid fluid, a closed form exact solution in time domain is obtained using an analytical inverse Laplace transform. For the general case of a viscous fluid, solution in time domain is evaluated using the Convolution Quadrature Method of Lubich. Of all the inverse methods previously investigated, it seems that only the method of Lubich is efficies and stable enough to handle the highly transient cases such as impact and step loadings. Using properties of three widely different real materials, the wave propagating behavior, in terms of stress, pore pressure, displacement, and flux, are examined. Of most interest is the identification of second compressional wave and its sensitivity of material parameters.