This paper aims to take a review on the modeling of damage in quasi-brittle rocks based upon continuum micromechanics. The basic idea of continuum micromechanics is a representation of brittle porous rocks as a material with distributed microcracks. With a crack density parameter identified as the governing state variable for the description of damage, methods of continuum micromechanics, namely the Eshelby-based homogenization schemes, are used to obtain macroscopic quantities such as elastic stiffness tensor and stress and strain, respectively. A thermodynamics approach is finally employed to obtain a macroscopic elastoplactic damage model, in which the frictional dissipation on the lips of closed cracks and its coupling with damage can be treated. Overall, the approach is to substitute constitutive parameters, which have been defined a priori on macroscopic level, by micromechanically motivated parameters, which have more sound physical interpretations. Discussions on the future work related to micromechanics-based damage modeling are also carried out.
As a natural composite material, the formation of rocks can be treated as a multiphase and multiscale material system. The most complicated phase in natural composite materials is the porosity, i.e. the space left in between the different solid phases at various scales, ranging from interlayer spaces in between minerals filled by a few water molecules, to the macropore space in between microstructural units of the material in the micrometer to millimeter range (Coussy, 2004). This porosity is the key to understanding and predicting macroscopic behavior of the material, ranging from diffusive or advective transport properties to stiffness, strength and fracture behavior (Dormieux et al., 2006a).
The breakthrough with pioneering work that relates macroscopic laws to microstructural properties was achieved in the 1970s. Auriault and Sanchez-Palencia (1977) were the first to develop appropriate averaging schemes for poroelastic materials under the assumption that the microstructure of porous material has a periodic pattern. Since these early works, various methods have been applied in order to determine the macroscopic behavior of a saturated porous medium starting from the microscopic scale. A reformulation of the equations of anisotropic poroelasticity was proposed by Thompson and Willis (1991). The relationships between the macroscopic poroelastic constants and the properties of porous medium constituents at microscopic level have been established.