Analysis of Fracture Mechanics Theory of the First Fracture Mechanism of Main Roof and Support Resistance with Large Mining Height in a Shallow Coal Seam

Because the first-weighting of a main roof with a large mining height has obvious sudden characteristics and is more severe, which causes large-scale support crushing and has a great impact on the ecological environment of the mining area, it is necessary to conduct an in-depth analysis. This paper studies the mechanical mechanism and asymmetric fracture conditions of a main roof with a large mining height, with the first-weighting occurring in a shallow coal seam. In combination with an asymmetric three-hinged arch structural model, the main roof was regarded as a finite plate model with a crack, and a fracture-mechanics model was established. The conditions and main controlling factors of main roof fracture asymmetry were analyzed, and the determination methods of the first-weighting interval and support resistance were further analyzed. The results show that the stress concentration and the stress-intensity factor increase at the crack tip with the advancement of the face; when the stress-intensity factors increase beyond the critical value, the crack expands until the first-weighting. The sufficient condition for modeling the instability was the length s of the branch crack reaching the protection thickness H of the main roof, and the necessary condition was the activation of the crack. The calculation equations of the first-weighting interval and the support resistance were obtained. The influence weights of each parameter on the support resistance are ordered as follows: overburden load q > rock fracture toughness KC > crack length a > main roof thickness h > weighting interval l. Finally, the theoretical analysis results were verified by an in situ monitoring case of the no. 33,206 working face in the Bulianta coal mine, China. On this basis, a reasonable value of the support resistance is further calculated. The results mentioned above can provide a new method for researching the first-weighting of the main roof and can improve the accuracy of the roof control analysis. The research on the mechanisms of first-weighting and the support resistance can effectively promote the safety production of mine, which is in line with the concept of green and sustainable development of the mine.