Characterization and modeling of fracture distribution in rock mass using fractal theory

During the preliminary planning of an active extraction system for geothermal energy, the proper estimation and modeling of fracture distribution at a selected site is very important due to its role in the circulation of hydrothermal fluids. Because the dimensions of fractures vary widely from microcrack of crystal size to tectonic lines in a large geologic body, it is difficult to quantify their distribution as a whole. We propose a method to estimate the existence probability of fractures longer than a defined length by assuming the fracture shape to be a disc and using a fractal expression. An automatic extraction method of linear features, which have some relationship with fractures, from digital images is also presented. These methods were applied to a fracture analysis of a granitic massif in Japan, and microcracks, joints, and lineaments of the body were investigated. A self-similarity concerning both direction and trace length was found in these fractures of different sizes. Additionally, the connectivity ratio of fractures penetrating through two production wells was calculated using this fractal relationship and a numerical simulation.