Micro–macro approach of anisotropic damage: A semi-analytical constitutive model of porous cracked rock

Abstract

A semi-analytical constitutive model of a porous cracked rock is proposed based on the micro–macro approach within a thermodynamic framework. The representative volume element (RVE) of a porous cracked rock is divided into two subproblems, P1 and P2. The porosity evolution equation of a spherical pore is proposed for P1, whereas P2 is an inelastic problem containing numerous anisotropic penny-shaped cracks. First, the relationship between microscopic and macroscopic strains is established through homogenization. This relationship is introduced into the macroscopic free energy equation. A crack propagation criterion based on the Griffith release rate is proposed, and the evolution equations of the shear and tensile crack densities are proposed based on the surface energy function. Subsequently, the Gaussian numerical integration method is used to obtain a semi-analytical explicit expression of the macroscopic stiffness tensor. Finally, based on the proposed crack propagation criterion, a strength-prediction method is developed. A series of uniaxial and triaxial experimental data for different rocks from other references is used to validate the proposed constitutive model and strength prediction method. The results obtained using the proposed model agree well with the experimental curves obtained from uniaxial tension and triaxial compression tests performed on different rocks. The macroscopic mechanical behavior and evolution of microscopic parameters for different rocks with an increase in confining pressure are effectively demonstrated by the proposed model. Strength prediction method can accurately describe the failure strength of different rocks. Furthermore, a sensibility analysis of model parameters revealed that initial porosity e0 and dilation coefficient ζ have a deteriorating effect on the failure strength, and material constant η has an enhancing effect on the failure strength.