A volume averaging technique for obtaining macroscopic equations of motion for materials that are microscopically inhomogeneous has been extended to the situation in which multiple solid constituents form a porous matrix while a uniform fluid fills the pores. The analysis for multiple solid constituents was complicated by the presence of internal interfaces between the solid constituents within the averaging volume. These interfaces are characterized by constants that measure the fraction of the interface on which solid touches solid, fluid touches one solid, fluid touches the other solid, or fluid lies on both sides of the interface. These fractions are easily computed if the interface fractions are assumed to be uncorrelated, but real materials may be expected to exhibit some correlation. Although the presence of these interfaces complicates our analysis, the interface fractions nevertheless do not appear in the volume average equations at the macroscopic level. To complete the derivation, it was found that the jacketed and unjacketed tests of Biot and Willis (1957) together with the thought experiments of Berryman and Milton (1991) for solid matrix composed of two constituents were required in order to obtain definite results. Results were then found to be in complete agreement with earlier work of Brown and Korringa (1975) concerning the most general possible form of the quasistatic equations for volume deformation and therefore of the equations of motion for wave propagation through such media. The results therefore provide independent confirmation of the form of the equations that has been assumed to be correct since the work of Brown and Korringa (1975) and Rice and Cleary (1976).

11/12/1997