COMPARISON OF NUMERICAL-CALCULATIONS OF 2 BIOT COEFFICIENTS WITH ANALYTICAL SOLUTIONS

The Biot theory for the acoustics of porous media contains drag and virtual mass coefficients that depend on the physical properties of the fluid and solid constituents, the frequency, and the microstructure of the porous medium. Biot derived an equation for the drag coefficient as a function of frequency by assuming cylindrical pores. In this paper, the finite element method is used to obtain values of the drag and virtual mass coefficients for face-centered cubic granular materials with three different porosities and the numerical results are compared to Biot's analytical solutions. By making appropriate choices of three parameters in Biot's analytical solution for cylindrical pores-the pore size parameter, the Kozeny parameter, and the tortuosity-the analytical solution matches these numerical results very well. This suggests that with appropriate choices of these parameters the analytical approach can predict the dependence of the drag and virtual mass coefficients on frequency for an arbitrary pore geometry. These results support a relation suggested by Hovem and Ingram for approximating the pore-size parameter for spherical grains, and they also agree with a relation suggested by Berryman for the dependence of the tortuosity on the porosity.