## 6 Conclusions  
In this study, to simplify the deformation model of the sprayed polyurea-coated coal body, the influence of deformation-induced internal stress variations within the coal body was not considered. Future research will incorporate this effect to enhance the predictive accuracy of the model. Moreover, in practical coal mine roadway support, the polyurea coating on the roof is subjected to the downward pressure exerted by the overlying coal seam, necessitating the development of a tensile stress model. The main findings of this study are as follows:  
1. The spraying of polyurea significantly improves the mechanical load-bearing properties of coal specimens, particularly after brittle failure. The confining pressure exerted by polyurea on the coal enhances the frictional resistance between internal fractures, thereby delaying the occurrence of collapse and effectively increasing the residual strength of the coal. This finding underscores the critical role of polyurea in coal mine support.
2. Although a polyurea coating is generally thin, its effect on the mechanical performance of the specimen at the elastic stage is relatively limited. Our results show that the elastic modulus of polyurea is much lower than that of coal specimens. Hence, in the early loading phase, the coating has no significant influence on the stress-strain response. In engineering applications, balancing the coating thickness and material properties is essential to meet the requirements of different working conditions.
3. The theoretical model developed in this study successfully predicts the deformation behavior of coal specimens sprayed with polyurea. The model reflects the stress-strain relationship of the specimens during the loading process; it also explains the confining pressure effect of the polyurea coating and changes in the friction coefficient after brittle failure. The model provides valuable insights into the complex interactions between the coating and the coal body.
4. As a novel temporary support material, polyurea coatings demonstrate significant potential for widespread application in coal mining and other extraction operations. Our results are expected to promote the development of spraying support technology in optimizing the material properties, spraying technology, and application scenarios of polyurea coatings; they also provide guidance for engineering practice.  
Conceptualization, S.C.; methodology, S.C.; software, J.Y.; validation, J.Y.; formal analysis, S.C.; investigation, S.C.; resources, S.C.; data curation, S.C.; writing--original draft preparation, S.C.; writing--review and editing, D.H.; visualization, J.Y.; supervision, D.H.; project  
Figure 11: Incremental fracture growth at each stage of the loading and unloading process.  
administration, S.C.; funding acquisition, D.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the CCTEG Coal Mining Research Institute (KCYIY-2024-MS-02) and the National Natural Science Foundation of China (52204123).  
Not applicable.  
Data Availability Statement: Data will be made available on request.  
Authors [PERSON] and [PERSON] were employed by the companies Coal Mining Branch, China Coal Research Institute and CCTEG Coal Mining Research Institute. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.