Quantitative Determination of High-Order Crack Fabric in Rock Plane

An accurate measurement method of crack fabric is proposed. Considering the density, geometry and spatial distribution in cracks, a novel method suggests the formula of high-order fabric tensor in the orthogonal space to describe cracks quantitatively. The crack is automatically identified by morphology and determined by stereo scans of image processing techniques. The fabric tensor is defined based on the idea of probability and statistics. The zero-order tensor describes the average effect of the density of rectangular cracks, the second-order tensor describes the two dominant directions of spatial cracks, and the higher-order tensor more accurately describes the anisotropy of cracks. With the increase of the tensor order, the more accurate direction and degree of the anisotropy can be described, and the morphological automatic identification of crack and its physical meaning of quantitative determination are clear. The plane description of the crack can be described by the invariants of the plane tensor. One invariant describes the degree of the anisotropy, and the other invariant describes its direction. The scan line is rotated and scanned on the rock plane image to obtain the accurate distribution of plane cracks, and the distribution law can be accurately described by the proposed high-order fabric tensor. In this paper, the rationality and effectiveness of the proposed measurement method are well verified by CT image analyses.

Automated summary

An accurate measurement method of crack fabric is proposed based on the density, geometry, and spatial distribution in cracks. The crack is automatically identified and determined through image processing techniques. The method utilizes high-order fabric tensor to quantitatively describe the anisotropy of cracks, with higher-order tensor providing more accurate direction and degree of anisotropy. The proposed method is verified to be rational and effective through CT image analyses.