Response of fluid-filled porous media to a transient input

The theory predicting the dynamic behavior of fluid-filled porous media is due to Biot. In the theory he accounts for the relationship between the friction force between the two phases, solid and fluid, and the average relative fluid velocity by means of what he calls a viscodynamic operator. Recognizing that the operator makes the solution of the equations difficult, he presents an asymptotic approximation of the operator and introduces it into the equations for linear momentum, which results in an approximate theory which can be used to study wave propagation in the media. Study of the approximation shows that it is particularly suitable when the velocity of the fluid relative to the solid varies gradually with time. This raises the suspicion that the theory may not predict accurately the behavior of transient waves, especially near the head of the pulse. Accordingly, in this paper another approximate theory is developed, following the lead of Biot, this one appropriate when the relative velocity varies abruptly with time. A problem involving transient responses in a fluid-filled porous half-space is solved and the responses predicted by the ’’gradual’’ and ’’abrupt’’ theories are compared. The uneasiness concerning the appropriateness of the Boit theory for transient-wave-propagation problems proves to be without foundation.