  The paper is concerned with dynamics of multi-phase media consisting of a
solid permeable material and a compressible Newtonian fluid. Governing
macroscopic equations are derived starting from the space-averaged microscopic
mass and momentum balances. The Reynolds stress models (i.e., momentum
dispersive fluxes) are discussed, and a suitable model is developed. In the
case of granular media the solid constituent is considered as an
elastic-plastic matrix, and the yield condition is approximated by Coulomb
friction law. It is revealed that the classical principle of maximum plastic
work is not, in general, valid for granular media, and an appropriate
variational principle is developed. This novel principle coincides with the
maximum plastic work principle for the case of cohesionless and free from
internal friction granular media.
