A variational theory of porous media

Abstract

A theory of porous elastic solids, either dry or saturated by a compressible fluid, is presented which is based upon Hamilton's extended variational principle. The theory uses a more extensive kinematical description of the materials than is used in the Biot theory and includes the effects of the local expansions and contractions of the porous structure (microinertial effects). Unlike Biot's formulation, the constitutive relations for the porous solid and for the fluid depend only upon kinematical variables associated with the solid and with the fluid, respectively. The relation of the present theory to the Biot theory is discussed and it is shown that the theories are equivalent in the limit of large wavelengths. Wave propagation results are presented based on data for Berea sandstone and it is shown that the microinertial effects substantially alter the dispersion and attenuation behavior predicted by the Biot theory.