Evaluation of rock anisotropy using 3D X-ray computed tomography
Introduction
Anisotropy in rocks originates from stratification, metamorphic foliation, and discontinuities, and grain fabrics affect the mechanical, thermal, hydraulic, and seismic behaviors of rock (Johnston and Christensen, 1995, Amadei, 1996). The significance of such anisotropy has been emphasized in studies of in situ stress (Adamei and Goodman, 1982), fracture propagation (Timms et al., 2010, Ajibade et al., 2012), and anisotropic fluid flow and heat transfer (Deming, 1994, Davis et al., 2007). It is also critical to determine the anisotropic parameters and symmetry plane in rocks in resolving the constitutive relations, which is a long-standing issue.
Anisotropic rock can be classified into two classes depending on the apparent visibility of anisotropy (Barla, 1974): class A includes rocks with anisotropic properties that may appear isotropic, and class B includes rocks with visible evidence of anisotropy. The symmetry plane in class B rocks (e.g., shale, gneiss, schist) is readily observable and is well matched with experimentally derived properties (Cho et al., 2012, Kim et al., 2012a), whereas in class A rocks (e.g., granite and sandstone) additional effort is required to identify the symmetry planes. Most methods of characterizing anisotropic rock require a priori knowledge of the symmetry plane through visible observations. It is therefore challenging to characterize anisotropy when it is not visually apparent.
Three-dimensional (3D) X-ray computed tomography (CT) enables the internal microstructures in a rock mass to be visualized. In studies of anisotropy, this technique has been applied to pore networks, fabrics, crack propagation, and the elastic modulus, using image-based characterization and stochastic simulations, which are commonly corroborated by systematic experiments and numerical investigations (Scholz and Koczynski, 1979, Pros et al., 1998, Inglis and Pietruszczak, 2003, Ketcham, 2005, Ketcham and Iturrino, 2005, Nakashima et al., 2008, Arad et al., 2010, Timms et al., 2010, Nasseri et al., 2011). These approaches generally involve the pre-processing of images to segment existing phases, and are applicable to a wide range of rock specimens, including volcanic rock, schist, granite, dolomite, marine sediment, and sandstone (Sun and Kodawa, 1992, Ruiz de Argandoda et al., 1999, Lindquist and Venkatarangan, 2000, Ketcham, 2005, Ketcham and Iturrino, 2005, Nasseri et al., 2011, Cnudde et al., 2011a). The petrophysical properties of construction materials have also been widely characterized using X-ray CT and associated image analysis techniques (Cnudde et al., 2011b, Lanzon et al., 2012, Yun et al., 2012). Although the specimen size for X-ray CT analyses should be less than a couple of centimeters, the anisotropy of resistivity, magnetic susceptibility, seismicity, and rock strength can also be evaluated in terms of grain shape, crystalline structure, and fractures to improve our fundamental understanding of the relation between anisotropy and the dominant properties of the rock mass (Uyeda et al., 1963, Gergoire et al., 1998, Luneburg et al., 1999, Zeng et al., 2008, Ben and Onwuemesi, 2009, Ajibade et al., 2012).
Because the X-ray attenuation values in reconstructed CT images depend on the internal density of the mineral fabric and the atomic weights of the elements in minerals, a particular clustering of 3D attenuation values can indicate the existence of anisotropy and its orientation. Here, we propose a novel method of determining the nature of anisotropy in rocks using 3D X-ray CT, based on the notion that anisotropy in a rock mass can be identified by the spatial distribution of attenuation values crossed by systematically oriented slicing planes, followed by statistical evaluation of variations in the form of planar clustering. The proposed method is applicable regardless of the visibility of the anisotropy or the origin of the symmetry plane, and utilizes the original X-ray attenuation values without any pre-processing of images. Here, we present and validate the proposed method, and discuss its application to samples of four different types of rock.
Section snippets
Validation of the proposed concept
X-ray attenuation value of every CT voxel is related to density of rock (solid and pores) and atomic weight of the elements comprised in that voxel. Any anomalous or heterogeneous internal structure within a rock specimen therefore exhibits uniquely clustered attenuation values. For layered structures, the clustering of similar attenuation values may define a planar geometry with a specific orientation, and should periodically alternate in the direction normal to the plane of the structure.
Distribution of attenuation values
Fig. 9a shows the relation between μG and σG when the slicing plane moves normal to the layered structure (e.g., along the highest cv orientation) for the four tested rock specimens. High mean values are accompanied by high standard deviations for given sliced planes. Despite the lack of causality in this observation, the quasi-linear relation observed in Fig. 9a suggests that the layered structure tends to have attenuation values with high variation. This observed relationship between two
Conclusions
We assessed the presence and orientation of anisotropy in rock using 3D X-ray computed tomographic images and performed a statistical evaluation of clustered attenuation values. Variation in the mean voxel values crossed by the slicing plane during systematic scanning enables identification of the number and orientation of embedded layered structures, regardless of their visibility. Unlike existing X-ray CT applications for rock materials, this method utilizes the original X-ray attenuation
Acknowledgments
This study was supported by a Korea CCS R&D Center (KCRC) grant funded by the Ministry of Education, Science and Technology of the Korean Government (no. 20120008929), and a grant from the New & Renewable Energy Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Ministry of Knowledge Economy of the Korean Government (no. 2012T100201733).
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