  The paper provides a macro-microscopic coupled constitutive model for
fluid-saturated porous media with respect to the compressibility of the solid
skeleton, the real solid material and the fluid phase. The derivation of the
model is carried out based on the porous media theory and is consistent with
the second law of thermodynamics. In the present paper, two different sets of
independent variables are introduced to implement the coupled behavior between
the compressibility of the solid skeleton and the real solid material.
Altogether the proposed model exploits five independent variables, i.e. the
deviatoric part of the right Cauchy-Green deformation tensor, the partial
density of solid phase, the density of the real solid material, the density of
the real fluid material and the relative velocity of the fluid phase.
Subsequently, the linearized version of the proposed constitutive model is also
presented and compared with some models by other authors. It is found that
Biot's model can also be derived based on the linearized version of the
proposed model, which indicates that the present work bridges the gap between
the porous media theory and Biot's model. Compared with Biot's model, the
present model can provide the evolution of the porosity by considering the
volumetric strain of the solid skeleton and the volumetric strain of the real
solid material.
