Damage and healing model of stiffness and permeability for salt rock: microstructure imaging, fabric processes and continuum mechanics

In this study, we proposed a fabric-enriched Continuum Damage Mechanics model to investigate the coupled influence of damage and healing on the mechanical and transport properties of salt rock. In order to infer the form of fabric tensors, we carried out creep tests on granular salt assemblies under constant temperature and humidity conditions and used microcomputed tomography for microstructure characterization. Using microscope imaging and micro-CT scanning, we analyzed the probability distributions of crack radius, void areas and crack spacing and used them as a basis to derive macroscopic evolution laws. A stress path comprising a tensile loading, a compressive unloading, a creep-healing stage, and a reloading was simulated. As expected, stiffness decreases (respectively increases) and permeability increases (respectively decreases) upon damage (respectively healing). Results also highlight the increased efficiency of healing with temperature. The micro-macro relationships established by statistical image analysis also provide the evolution of microstructure descriptors during the test. Simulations show that permeability changes are controlled by changes in crack connectivity, which dominate changes of porosity. The proposed framework is expected to improve the fundamental understanding of coupled processes that govern microstructure changes and subsequent variations of stiffness and permeability in salt rock, which will allow the assessment of the long-term performance of geological storage facilities. closure detected by an increment in wave velocity, rather than crack rebonding. The ultimate goal of this research work is to understand the fundamental microscopic mechanisms that cause stiffness and permeability evolution in salt rock during damage and healing processes. We use the thermomechanical model that we proposed in (Zhu and Arson, 2015a) as basis to predict the effect of crack opening, closure, and healing on the mechanical and transport properties. We explain the choice of fabric descriptors in Section 2. The multi-scale theoretical framework coupling damage and healing is presented in Section 3. In Section 4, we explain the upscaling method and the computation algorithm. Simulation results from a loading-unloading stress path are presented in Section 5 to show the influence of damage and healing on the coupled evolution of microstructure, stiffness, and permeability. 2. FABRIC CHARACTERIZATION Fabric evolution during damage and healing processes determines the mechanical and transport properties of salt rock. Nondestructive observation of fabric evolution under complex variations of stress, temperature, and moisture remains an experimental challenge. We carried out creep tests on table salt by confining those particles in tubes and loading them axially by a spring (Fig. 1a). We used an environmental chamber to maintain a constant humidity environment (relative humidity = 75%) at room temperature (22 o C). Table salt is a granular assembly that has the same crystallographic structure as salt rock. We used it as an analog of salt rock in this experimental study, because no large equipment is needed to apply creep loads required to study creep processes (as opposed to solid rock). Therefore in the following, open contacts at grain faces are considered as micro-cracks in the damage model. In our previous works, we did microscope observations of the salt assembly through the tube walls at regular time intervals in order ensure continuous microstructure characterization without taking out the sample (Zhu and Arson, 2015a). However, light reflection and transmission induced by transparent and cubic-shaped grains significantly impaired the image quality, which increased the difficulty to detect grain boundaries. To overcome this problem, we use micro-computed tomography (micro-CT) to observe and re-generate the 3D porous structure of the granular salt assembly. This technique can easily be used to distinguish the solid NaCl from voids, which have a strong density contrast. Micro-CT observations were conducted at the Guldberg Laboratory at Georgia Tech. The voxel size was 30 while the size of a single particle is . We used ImageJ (Abramoff et al., 2004) for 3D solid skeleton reconstruction (Fig. 1b). Cross-sectional views were produced throughout the sample (Fig. 1c), from which we extracted binary images with further image processing (Fig. 1d). Fig. 1. Image analysis during creep tests realized on table salt: (a) experimental set up; (b) micro-CT image of the solid skeleton; (c) cross-sectional view (original image); (d) crosssectional view (binary image). Voxel size = 30 . Sample diameter = 19 . Grain size = 300~400 . We performed statistical image analyses of the binary images to extract information on the fabric. In particular, we characterized pore connectivity by the studying the distribution of void centroid-to-centroid distances. Using the location of the void centroids (Fig. 2), we calculated the distance between this centroid and the centroid of the nearest void. We found that these relative distances follow a lognormal distribution (Fig. 3):