Rock Stiffness and Permeability During Crack Opening and Closure: A Planar Transverse Isotropic (PTI) Model Using Pore Size Distributions (PSD)
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A micro-macro model is proposed to study opening and closure of parallel crack planes in a porous rock. Pore Size Distributions (PSDs) of natural pores and cracks are updated with volumetric fractions, defined as distinct components of volumetric deformation. Deformation components depend on total deformation and on the crack density tensor (damage). The expression of the free energy postulated in the model allows capturing damage-induced anisotropy of stiffness. A unilateral condition of damage is introduced to account for stiffness recovery in compression. The permeability tensor is related to PSDs by combining Darcy's law and Hagen-Poiseuille flow equation. The model captures Planar Transverse Isotropy (PTI) induced by crack openings in both stiffness and permeability and predicts the evolution of two partial porosities (natural and damage-induced). The model will be used to model the damaged zone around underground cavities, faults and hydraulic fractures.