## 7 Conclusions  
Aiming to resolve the issue where rock burst easily occurs during the initial mining of the 2102 working face in the Balasu coal mine, theoretical research, FLAC\({}^{\text{3D}}\) software, and the elastic strain energy fish model are used to analyze the temporal and spatial variation law of roof elastic strain in the mining process. The following conclusions are drawn:  
(1) In the case of the 2102 working face without hydraulic fracturing roof-weakening measures, the mechanical model calculates that the first weighting interval is 77 m, easily causing strong pressure and even dynamic disasters in the working face when it falls. The theoretical calculation shows that the main roof is the reasonable range of hydraulic fracturing in the vertical direction of the working face for the medium-grained sandstone in the upper 4.8-22.43 m of the roof of the 2102 working face, and the effective fracturing section in the horizontal direction is arranged within 30.8 m from the cutting side of the working face;  
(2) FLAC\({}^{\text{3D}}\) software and the elastic strain energy fish model are used for simulation: as the working face advances to 70 and 80 m, the hard roof begins to bend under the influence of excavation of the working face, and the strain energy in the rock layer is rapidly accumulated under the influence of deformation. The peak value of strain energy gradually increases, and the energy gradient also gradually increases. The maximum strain  
Figure 11: The roof collapse behind the support of the 2102 working face. Figure 10: The working resistance of the support during the mining of the 2102 working face. energy of the roof reaches 140.54 kJ/m\({}^{3}\). At this moment in time, the working face advances to the first weighting interval, and the sudden fracture of the roof will be accompanied by the release of elastic energy, resulting in roof vibration and inducing rock burst. Therefore, the main roof should be cut before the first weighting interval to release energy;  
(3) According to the temporal and spatial variation law of roof elastic strain in the process of mining, the principle of hydraulic fracturing was proposed, and the test was carried out in the 2102 working face. The field application shows that, after hydraulic fracturing, the continuous high-pressure water injection into the rock layer after fracturing causes the expansion of the cracks to continue and effectively weakens the integrity of the rock layer. The cracks are observed at depths of 8, 12.2, 18.3, 24.2, and 31 m. The 2102 working face begins to gradually collapse at the 20 m position, and a large area of the face begins to collapse at 55 m. There is no support-crushing accident, and hydraulic fracturing effectively reduces the first weighting interval. The research results provide reference for similar narrow-coal-pillar roadway control;  
(4) The crack propagation via hydraulic fracturing roof cutting is greatly affected by the stress environment. We can only detect the crack morphology on the surface of the borehole via drilling peeps. When the crack enters the rock mass, the expansion is not accurately detected at present. In the future, extensive in-depth research work should be carried out on the initiation and propagation law of hydraulic fractures in coal and rock mass, which is helpful in forming the crack propagation pattern needed in engineering. Conceptualization, C.W. and J.B.; methodology, C.W. ; software, C.W. and T.W. ; validation, C.W. and J.B.; formal analysis, C.W. ; investigation, W.W.; resources, T.W. ; data curation, C.W. and T.W. ; writing--original draft preparation, J.B.; writing--review and editing, C.W. ; visualization, J.B.; supervision, W.W.; project administration, W.W.; funding acquisition, J.B. and W.W. All authors have read and agreed to the published version of the manuscript. This research has been supported by the Key projects of the Joint Fund of the National Natural Science Foundation of China (No. U21A20107).