International Journal of Rock Mechanics and Mining Sciences
Experimental investigation and micromechanical analysis of damage and permeability variation in brittle rocks
Introduction
The damage induced by microcrack growth is an essential mechanism of inelastic deformation and failure in most brittle geomaterials such as rocks and concrete. The growth of microcracks leads to a series of consequences on macroscopic properties of material, for instance the diminution of elastic modulus, induced anisotropy, unilateral effects, volumetric dilation and hysteretic response, as well as the attenuation of wave velocity and permeability variation. This last point is of primordial importance for many engineering applications, for instance, the geological storage of nuclear waste, the durability of concrete structures in nuclear power plants, the sequestration of residual gas and enhancement of oil production.
The permeability determination in rock joints and fractured rock masses has been largely investigated in different cases ([1], [2], [3], [4], just to mention a few). However, only a few experimental works have been performed on the study of coupling between permeability and damage process in continuum rock mass. For instance, Suzuki et al. [5], Souley et al. [6] and Oda et al. [7] investigated the evolution of permeability in brittle rocks in triaxial compression tests. Suzuki et al. [5] further studied the relationship between the permeability change and microcrack growth in granite during immersion in hot water while Schulze et al. [8] were interested in the variation of permeability in rock salt. These works have shown that the permeability can significantly increase as a consequence of the nucleation and growth of microcracks under deviatoric stress. Guéguen and Schubnel [9] investigated the correlation between wave velocities and permeability of cracked rocks. Louis et al. [10] focused on micro-structural effects on the anisotropy of elastic and transport properties in sandstones. These works confirmed the inherent correlation between the permeability variation and microcrack growth. Similar investigations have been performed in cement-based materials, and showed significant variations of permeability due to growth of microcracks during mechanical loading, chemical degradation and thermal effects [11], [12], [13]. In situ investigations of permeability in excavation disturbed zone have also been performed [14], and the measurements showed that the permeability can increase by several orders of magnitude due to growth and coalescence of microcracks.
Based on this evidence, it appears necessary to develop theoretical and numerical modeling, taking into account the coupling between permeability and damage evolution. Oda [1] proposed a numerical model for the determination of permeability tensor in fractured rock masses by introducing the concept of probability density function of fracture distribution in space. The macroscopic permeability tensor is obtained by the volumetric averaging of local flow velocity which is described by an extended cubic law. This reference work has been largely used and extended in later investigations for the estimation of permeability of fracture networks in rocks. Different analytical and numerical models have also been developed for the description of permeability in continuous rock masses. However, in most models, the permeability variation is not or only indirectly coupled with damage process. The modeling of fully coupled process between damage and permeability is still an open issue. Recently, Dormieux and Kondo [15] proposed a micromechanical framework for the evaluation of macroscopic permeability of cracked materials using a self-consistent method. This model was limited to the isotropic case and its effective implementation does not appear easy. Shao et al. [16] proposed a phenomenological anisotropic model for brittle rocks. Choinska et al. [13] developed an isotropic damage-permeability model for concrete material including post-coalescence regime. Further, a number of empirical models have been proposed using various expressions of permeability with applied stresses or strains.
In the present work, some new experimental results are first presented in order to complete existing data on the permeability variation in brittle rocks under triaxial compression tests. Then, we propose a micromechanics-based model for the description of induced anisotropic damage and permeability variation. With such an approach, the permeability variation is directly related to the density and opening of microcracks.
Throughout the paper, will represent the unit second order tensor, and the following notations will be used in tensorial calculations:
Section snippets
Experimental investigation
A small number of experimental data is available on the characterization of permeability variation with microcrack growth in brittle rocks. Souley et al. [6] have performed a series of triaxial compression tests with the continuous measurement of permeability as a function of deviatoric stress for different confining pressures. Based on their results, we have compared the evolution of permeability and volumetric strain, as shown in Fig. 1. It is clear that the evolution of permeability is
Stress-based micromechanical anisotropic damage model
In this section, we present the formulation of a micromechanics-based anisotropic damage model. Note that most existing micromechanical and phenomenological models [17], [18] for anisotropic damage are generally developed in strain-based formulation. Taking into account in practical rock engineering application, in situ initial stresses and pore pressure are key factors for numerical modeling. Also it is preferable to express the damage evolution law in terms of stress and pore pressure. For
Coupling between damage and permeability variation
As shown by the experimental data presented in Section 2, the permeability of brittle rocks may be significantly modified by the growth of microcracks. The micromechanical model presented in the previous section should be extended for accounting for the coupling between the permeability variation and microcrack growth.
Experimental validation
In order to perform a first phase of validation of the proposed model, comparisons between experimental data and numerical simulations are presented in this section. In order to show the applicability of the model to different materials, three typical rocks are considered: granite, basalt and sandstone; these materials are differentiated by their microstructures and mineralogical compositions. Mechanical responses and permeability variations are successively investigated.
Conclusions
The coupling between permeability variation and growth of microcracks is investigated in this work. Some new experimental tests have been performed to complete existing data in literature. The experimental data have shown that the permeability in brittle rocks increases significantly due to the propagation of microcracks. Based on the experimental evidences, a micromechanics-based model is proposed for the description of induced anisotropic damage and permeability variation. The unilateral
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