Pore boundary deformation and the Biot coefficient: a micromechanical analysis

Continuum poroelasticity theories provide a macroscopic description of fluid-saturated porous media so that pore-scale features only emerge in some averaged form.However, therein the specific signature of the underpinning micro-structure is not transparent in the constitutive material equations.For a regular lattice-type micromechanical model, we derive an exact formula for the Biot coefficient.As anticipated by experimental and numerical studies, the Biot coefficient embodies a nonlinear combination of the elasticity of the solid phase material and the geometry characterizing the pore space.This result allows us to exemplify the abstract concept of pore boundary deformation appearing in the continuum description of porous media including the ramifications of a geometrical self-similar deformation.Although this is certainly an oversimplified model for most porous rocks, our analysis may serve as benchmark for numerical upscaling based on digitized images to infer the poroelastic material parameters and thus to support ongoing experimental efforts to measure poroelasticity coefficients.