## 6 Conclusions  
Based on the 21,103 operating face of the Hulusu Coal Mine, our research conducted a comprehensive investigation into the manifestation characteristics of rockburst, the instability mechanism of hard roof failure, energy accumulation behavior, the design and numerical validation of pressure relief schemes, and field engineering applications. The main findings and conclusions are as follows:  
(1) Microseismic monitoring results revealed that microseismic events were primarily concentrated within 60 m to the west and 100 m to the east of the 21,103 Return Airway, as well as within 300 m ahead and 50 m in back of the operating face. These distributions indicate localized stress concentration and instability of the rock mass structure, emphasizing the need for enhanced support and anti-rockburst measures in these regions.  
(2) A theoretical analytical framework for total elastic energy in the roof was established based on the modeling of the roof flexure, volumetric strain energy, and deformation energy. The study shows that as the rock's mining depth and overhang length increase, the stored EE within the system rises sharply, serving as a major energy source for rockburst events. Therefore, the formation of a large overhanging roof structure behind the 21,103 working face tends to accumulate substantial elastic energy, posing a significant rockburst risk. This conclusion aligns well with the observed spatial distribution of microseismic energy, validating the applicability and scientific reliability of the theoretical model.  
(3) Nine pressure relief schemes with varying borehole inclination angles were simulated using FLAC3D. The results indicate that the optimal configuration involved boreholes inclined at 45\({}^{\circ}\), spaced 15 m apart, with a diameter of 65 mm. The boreholes extended 24 m above the coal pillar and 30 m above the working face. This scheme provided the best comprehensive stress regulation effect on the surrounding rock, successfully forming an effective pressure relief zone and enhancing the roof stability. Furthermore, the modeling approach established in this study offers theoretical guidance for developing pressure relief strategies in regions with diverse geological characteristics prone to cluster mine pressure.  
(4) The efficacy of pressure relief technologies was verified through monitoring of water pressure variations, the fracture propagation range, and acoustic emissions from roof fracturing during field hydraulic fracturing experiments at the 21,103 roadway. The results demonstrate that the energy aggregated within the roof could be effectively liberated through the propagation of induced fractures, confirming that the pressure relief technique offers a significant mitigation effect against rockburst hazards in hard and thick sandstone roofs.  
Conceptualization, Z.W. and Y.L.; methodology, Z.W. and Z.S; software, Z.W.; validation, Y.L., Y.N. and P.Z.; formal analysis, Z.S.; investigation, Y.N.; resources, Y.L.; data curation, P.Z.; writing--original draft preparation, Y.N.; writing--review and editing, Z.S.; visualization, Y.N.; supervision, Z.W.; project administration, Y.L.; funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Scientific and Technological Key Project of \"Revealing the List and Taking Command\" in Heilongjiang Province (2021 ZXJ02A03, 2021 ZXJ02A04).  
Not applicable.  
Data availability Statement: Data are contained within the article.  
The authors declare no conflicts of interest.