Intrinsic poroelasticity constants and a semilinear model

Abstract This paper presents an intrinsic micromechanical model for poroelasticity that leads to an alternative set of material constants. In the intrinsic model, the deformations of the solid phase, the fluid phase, and the pore space are explicitly modeled, and porosity is considered as a primary variable. The averaging process distinguishes an external frame surface averaging and an internal phase volume averaging. The variational principle leads to a porosity equilibrium equation that defines the nonlinear deformation of pore volume. Three fundamental deformation modes with their intrinsic material constants are identified: the shape preserving volumetric deformation of the solid phase, the porosity change due to solid grain rearrangement, and the porosity change associated with the microanisotropy and microinhomogeneity of solid phase. The linearized model is fully consistent with the Biot theory of poroelasticity. A semilinear model considering only porosity deformation nonlinearity with linear material constant leads to a universal exponential strain hardening law. The theory is tested against laboratory data of sandstone. Copyright © 2007 John Wiley & Sons, Ltd.