Experimental Study on Fracture Trace Extension Law of Coal Based on Acoustic Localization Time–space Cluster

During the working face mining, as the stress concentration occurs in the solid coal wall and the fracture structure develops on the coal pillar side, slippage and instability can be triggered easily in the coal, which brings a significant threat to the safety of the working staff. Through acoustic-optic-mechanical comprehensive monitoring equipment, this paper adopts digital binary processing technology and the digital speckle layer analysis method to investigate the extension law of different coal fracture traces. The proposed cross-quadrant nonlinear regression fitting method found that the fracture trace of instantaneous instability coal accords with the nonlinear distribution law of "step shape". The number of stages G of different types of coal was determined by employing the temporal-spatial multi-dimensional cluster analysis of coal fracture with acoustic location to obtain the distribution characteristics of their key lengths of damage. Further research on the key length damage relationship of different types of coal indicate that the macro fracture extension of coal is closely related to the damage of the middle key and medium-long key. Moreover, the average damage energy of long keys during instantaneous instability is less than medium-long keys, and the long key always shows a nonlinear growth trend. This provides a novel approach for predicting the damage characteristics of instantaneous instability and rupture of coal. In addition, the study is of great significance for avoiding the dynamic instability and sliding disasters of coal or rock to ensure mine safety and efficiency in production.