Microporomechanics of quasi-brittle rocks: Theoretical formulations and analytical simulations

Abstract

Hydromechanical coupling is one of the essential theoretical and practical issues in rock mechanics and rock engineering. In geological context, it is critically important to incorporate the effect of pore pressure into the constitutive equations with full account of cracking-induced material anisotropies and friction-related plastic deformation. Focus here is put on poromechanical formulations for quasi-brittle rocks weakened by microcracks and saturated with pore fluid pressure. The linear homogenization method applied to derive the effective properties and system free energy is combined with the irreversible thermodynamics and the problem decomposition. Constitutive derivations include the determination of the system free energy, state equations associated with and evolution laws of the internal variables, closed-form failure criterion, etc. Inherent coupling between anisotropic unilateral damage, friction-induced plastic deformation and the fluid pressure constitutes one of significant novelties of the work. Continuities required for the total free energy, macroscopic stress and the global porosity are guaranteed at any opening-closure transition of cracks. Through strength and deformation coupling analyses, the effects of fluid pressure on material strength and deformation are elucidated and also validated by experiments we performed upon a sandstone.