A method for Estimating three-dimensional Distribution of microcrack orientations in rock

摘要

Physical properties of rock, such as strength, elasticwave velocities and permeability, depend largely on microcrackgeometry. In particular, anisotropy of these properties is intimatelyrelated to the distribution of microcrack orientations. In this paper,an estimating method for three-dimensional distribution ofmicrocrack orientations in rock is introduced by using theassociated Legendre function. If a microcrack is expressed by apenny shaped disk, the distributions of crack orientations anddiameters are expressed using probability density functionsrespectively and the intersection of cracks with a plane isgeometrically modeled. Based on the model, the density functionof three-dimensional orientations is characterized by observingtraces of cracks, which have two-dimensional orientations, onsome surfaces of a rock.A microscopic examination using a digital microscope underultraviolet light is employed for visualization of microcracks onInada granite filled with methylmetaacrylate combined withfluorescent paint. After a few steps of image processing, lineelements on the digital images are automatically extracted as tracesof cracks using the Segment Tracing Algorithm that is a lineamentidentification method. Once line elements are obtained, it is easy tocharacterized their two-dimensional orientations. An observationequation is constructed by using these two-dimensionalorientations on three orthogonal surfaces of the granite, and thenthe probability density function of three-dimensional microcrackorientations is obtained by solving the equation. P-wave velocitiesin the Inada granite are also measured in the study. Anisotropy ofthe P-wave velocity is in harmony with the distribution ofmicrocrack orientations. The orientation of the rift plane of thegranite approximately agrees with the primary orientation ofmicrocracks, while there is no obvious difference between grainand hardway planes.