## 6 Conclusions  
In this paper, damage tests under different unloading spans of coal rock and uniaxial reloading tests of critically damaged coal rock were carried out. The critical span of unloading damage of coal samples under different unloading spans, the load-bearing characteristics, and reloading performance of the critically damaged coal body were analyzed; the damage evolution characteristics of the critically damaged coal samples were analyzed using the acoustic emission signals collected during the loading process when the samples were reloaded. The main conclusions are as follows:  
Coal samples were damaged using a triaxial unloading test, and by analyzing the damage morphology of the damaged coal samples, it can be seen that with the decrease in unloading gradient, surface cracks on the coal samples developed from tensile cracks  
Figure 15: Proportion of dissipated energy under standardized axial strain.  
to the coexistence of tensile and shear cracks and then to shear cracks, and it was determined that the critical unloading damage of the coal samples was 60% of their triaxial compressive strength.  
Through the uniaxial reloading test on the critically damaged (nMpa-60%) coal samples, it was found that the larger the unloading span, the worse the mechanical properties of the damaged coal samples. The uniaxial compressive strength before and after the damage was used as an index to redefine the damage factor to characterize the damage degree of the mechanical properties of the coal samples, and it was found that the larger the confining pressure unloading span was, the worse the damage degree of the coal samples was.  
By analyzing the acoustic emission signals and \(b\)-value of acoustic emission during the uniaxial reloading process of critically damaged (nMpa-60%) coal samples, the uniaxial reloading process of critically damaged (nMpa-60%) coal samples was divided into four stages, namely, \"stabilization zone-growth zone-secondary stabilization zone-steep growth zone\", and it was found that the smaller the pressure unloading span, the smaller the primary cracks in the specimen, and the more the macroscopic cracks were.  
By analyzing the fractal dimension and energy of the broken debris after uniaxial reloading of the critically damaged (nMpa-60%) coal samples, it was found that with the reduction in peripheral pressure unloading span, the space for elastic deformation of the damaged coal samples gradually decreases, the ability to store energy is weakened, the specimen cracks and produces plastic deformation more easily, the large-size rock mass produced at the time of destruction increases, and the fractal dimension decreases.  
Conceptualization, P.W. and Y.Z.; methodology, P.W.; validation, P.W., Y.Z. and C.M.; formal analysis, C.M.; investigation, P.W.; resources, P.W. and Y.Z.; data curation, C.M.; writing--original draft preparation, C.M.; writing--review and editing, P.W.; visualization, C.M.; supervision, P.W.; project administration, P.W.; funding acquisition, P.W. All authors have read and agreed to the published version of the manuscript.  
This study received funding from the National Natural Science Foundation of China (NSFC) (No. 52174110) and the Provincial and Ministerial Key Laboratory of the Ministry of Education of China for Safe and Efficient Mining in Coal Mines. This research was supported by JYBSYS2021203, the Key Project of Scientific Research of the Department of Education of Hunan Province (No. 21A0313), the Hunan Province Scientific and Technological Talent Support Project (Project No. 2022 JT)-N06), and the Scientific Research and Innovation Program of the Department of Education of Hunan Province (No. CX20221048).  
Not applicable.  
The data presented in this study are available in this article.  
The authors declare no conflict of interest.