Connecting Theory to Experiment in Poroelasticity

The variables controlled and measured in elastostatic laboratory experiments (the volume changes, shape changes, connning stresses, and pore pressure) are exactly related to the appropriate variables of poroelastic eld theory (the gradients of the volume-averaged displacement elds and the volume-averaged stresses). The relations between the laboratory and volume-averaged strain measures require the introduction of a new porous-material geometrical term. In the anisotropic case, this term is a tensor that is related both to the presence of porosity gradients and to a type of weighted surface porosity. In the isotropic case, the term reduces to a scalar and depends only on the surface-porosity parameter. When this surface-porosity parameter is identical to the usual volume porosity, the relations initially proposed by Biot and Willis are recovered. The exact statement of the poroelastic strain-energy density is derived and is used to deene both the laboratory strain measures and the laboratory elastic moduli. Only two restrictions are placed on the materials being treated: 1) the uid is homogeneous in each sample and 2) the material possesses a rigidity. However, the entire work is limited to linear deformations and long (relative to sample size) wavelengths of applied stress.