Plona (1980) observed two distinct compressional waves in a water-saturated, porous structure made from sintered glass beads. The speeds predicted by Biot's equations of poroelasticity are compared to the values observed by Plona shown in Figure 1.

The input parameters to the model are *K*_{s} = 40.7 GPa, GPa,
g/cc, *K*_{f} = 2.2 GPa, g/cc, centistoke, and kHz. The drained frame moduli *K*_{d} and were calculated assuming spherically shaped glass particles and
needle-shaped inclusions of voids, following Berryman (1980c). We use
for the tortuosity. The permeability variation
with porosity was taken to obey the Kozeny-Carman relation

= const^3/(1-)^2,
which has been shown empirically
to provide a reasonable estimate of the porosity variation of permeability.
We choose cm^{2} ( D)
at and then
use (GkGv) to compute the value of for all other porosities
considered. No entirely satisfactory model for the characteristic
length *h* has been found. However, dimensional analysis suggests that
*h ^{2}* must be comparable to , so we have taken

h^2/= h_0^2/_0 = const.
At , we choose *h _{0}* = 0.02 mm corresponding to an
average pore radius to of the grain radius
(the glass beads in Plona's samples were 0.21-0.29 mm in diameter before
sintering).

The theoretical results for the fast compressional wave and the shear wave agree with Plona's measurements within the experimental error ( relative error in measured speeds and and an absolute error of in measured porosity), showing that the Biot-Gassmann equations agree very well with data for these simple synthetic rocks.

11/17/1997