Renormalization group study on connectivity of fracture network of overlying strata in deep coal mining

This paper focuses on the analysis of the connectivity of fracture network of overlying strata in deep coal mining based on the renormalization group method. Firstly, the probability formula of transfixion fracture formation in fractured overlying strata is derived out. The critical probability of transfixion fracture formation presents a negative exponent relation with the Weibull shape parameter. Secondly, on the basis of geological conditions of No. 15-22060 coal mining face in No. 8 Mine of Pingdingshan Coal Mining Group, the physical model under lateral pressure is constructed. During the process of coal mining face advancement, fracture networks of different advancement distances are extracted and binarized. These fracture networks are then transformed into matrixes of "0" and "1" elements. After applying the renormalization group method to these matrixes, the in-plane, horizontal, and vertical connectivities of fracture networks in deep coal mining are studied when the coal mining face is advanced 180 m. As to in-plane fracture networks of different classes, the last four matrixes obtained with the renormalization group method are zero, indicating that these networks are not connected, which is induced by the low occupancy of fracture areas of fracture networks of different classes. The distribution shape of "1" representing fractures is consistent with that of strata-separating fractures, and it is possible that the horizontal fracture is connected only if strata-separating fractures are present in the whole area of interest. The fracture networks of different classes are not connected in the vertical direction. However, when the area of interest is decreased, the proportion of elements "1" reflecting the vertical connectivity of fracture networks in the matrix is increased, and the rank of the zero matrix is decreased. These results may serve as a reference to the reasonable methane exploitation in deep coal mining.