Abstract
Physical properties of rock, such as strength, elastic wave velocities and permeability, depend largely on microcrack geometry. In particular, anisotropy of these properties is intimately related to the distribution of microcrack orientations. In this paper, an estimating method for three-dimensional distribution of microcrack orientations in rock is introduced by using the associated Legendre function. If a microcrack is expressed by a penny shaped disk, the distributions of crack orientations and diameters are expressed using probability density functions respectively and the intersection of cracks with a plane is geometrically modeled. Based on the model, the density function of three-dimensional orientations is characterized by observing traces of cracks, which have two-dimensional orientations, on some surfaces of a rock. A microscopic examination using a digital microscope under ultraviolet light is employed for visualization of microcracks on Inada granite filled with methylmetaacrylate combined with fluorescent paint. After a few steps of image processing, line elements on the digital images are automatically extracted as traces of cracks using the Segment Tracing Algorithm that is a lineament identification method. Once line elements are obtained, it is easy to characterize their two-dimensional orientations. An observation equation is constructed by using these two-dimensional orientations on three orthogonal surfaces of the granite, and then the probability density function of three-dimensional microcrack orientations is obtained by solving the equation. P-wave velocities in the Inada granite are also measured in the study. Anisotropy of the P-wave velocity is in harmony with the distribution of microcrack orientations. The orientation of the rift plane of the granite approximately agrees with the primary orientation of microcracks, while there is no obvious difference between grain and hardway planes.
