## 6 Conclusions  
1. The failure of the rock mass around the borehole is the root cause of pressure relief, and the radius of the plastic zone around the borehole is the key factor affecting the failure of the rock mass. With the increase in the drilling radius and drilling depth, the strength of the rock mass and the stored elastic strain energy decrease. The larger the radius of the plastic zone around the hole is, the more obvious the surface main control crack propagation is. Additionally, the vertical stress at both ends of the hole top and bottom becomes smaller, the impact tendency of the surrounding rock of the roadway is reduced, and the pressure relief effect is better.
2. According to the analysis of the percentage reduction in the peak strength of the test block, it can be seen that larger borehole diameters are not better. If the aperture is too large, not only does the pressure relief effect not change significantly, but also the coal wall of the two sides of the roadway will be destroyed and the stability will be reduced. If the hole spacing is too small, it will become single-hole pressure relief, which will lead to an increase in the rock mass strength. The borehole pressure relief can only remove the stress near the borehole, and there is a new peak stress concentration not far from the borehole.
3. The change in borehole spacing has a significant effect on the failure mode of the rock mass. The smaller the spacing between the two holes, the easier the plastic zone around the two holes is to connect, and the rock mass is dominated by penetration failure, whereas the rock mass is dominated by independent failure. Different pressure relief parameters have different pressure relief efficiencies, and the priority should be given to multi-hole combined pressure relief, followed by expanding the aperture, and finally increasing the hole depth.
4. The mechanical model of drilling holes is established by classical mechanics. It is concluded that the radius of the drilled hole has a linear relationship with the radius of the plastic zone around the hole and has a quadratic relationship with the elastic strain energy stored in the rock mass; the deeper the borehole is, the farther the stress peak goes into the deep surrounding rock; when the borehole spacing is less than or equal to 3.286 cm, the plastic zones generated around the two boreholes are connected.  
Conceptualization, P.W., Y.J., P.L., J.Z. and Z.Z.; methodology, P.W., Y.J. and P.L.; software, Y.J. and P.L.; validation J.Z. and Z.Z.; formal analysis, P.W. and Y.J.; investigation, P.L. and J.Z.; writing--original draft preparation, Y.J.; writing--review and editing, P.W. and Y.J.; funding acquisition, P.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (52174110), key projects of the Hunan Provincial Department of Education (21A0313), the key laboratory of the Ministry of Education for Coal Mine Safety and Efficient Mining (JYBSYS2021203), the Hunan Natural Science Foundation (2020 JJ5186), and these projects are led by [PERSON]. This article is also funded by the Guizhou province science and technology support plan funded projects, and this project is led by [PERSON].  
Not applicable.  
The data presented in this study are available in the article.  
The authors declare no conflict of interest.