Investigation of fractal distribution law for the trace number of random and grouped fractures in a geological mass

A fractal study method of the number of geological mass fractures is introduced in detail in this paper. Three main aspects of the problem were studied: (1) The random distribution of fractures in a geological mass was in good agreement with the fractal law. The size scale of the studied geological mass ranged from 2400 m to 1 mm for the length of each side, and the geological mass samples were taken from 13 coal areas in China. (2) The geological mass fractures were evidently directional and anisotropic, having originated from tectonic movement. Observation and statistics for the data from the Xuangang, Fenxi and Dongshan coal areas in Shanxi, China, demonstrated that the fracture distribution of each group, classified by the strike of the strata, still follow the fractal law, even though the fractal dimension varies to a certain extent with different strikes. (3) The sedimentary strata containing the coal seams, as a geological mass, underwent almost similar tectonic movements in their geological history. The mechanical experiments on geological mass samples from Fenxi and Jiexiu in Shanxi demonstrated that the fractal dimension of the number of fractures in the same strata is in good power function with the product of strength and elastic modulus. The larger the product of the strength of the elastic modulus is, the larger is the fractal dimension, and vice versa.