## 6 Conclusions  
1. In the high-temperature diversion tunnel at Bulunkou, the three principal stresses are characterized by \(\sigma_{\rm H}>\sigma_{\rm Z}>\sigma_{\rm h}\). Notably, the temperature, maximum, and minimum horizontal principal stresses exhibit an approximately linear increase with the depth of the tunnel borehole, with the maximum horizontal principal stress showing a more pronounced increase.
2. The boundary line equation for the plastic zone of the tunnel surrounding the rock, accounting for self-weight stress and considering the thermal stress of the rock body in the hydraulic fracturing method, was derived. Subsequently, the analytical solution for the radius of the plastic zone was obtained via an iterative method. This facilitated the analysis of the morphology of the plastic zone and its expansion law. 1. Under high geostress conditions, the lateral pressure coefficient notably influences the morphology and extent of the plastic zone. Specifically, when \(\lambda=1.0\), the plastic zone exhibits circular distribution; it adopts an elliptical shape for \(1.0\leq\lambda\leq 2.0\); meanwhile, \(\lambda\leq 1.0\) or \(2.0\leq\lambda\), a butterfly-shaped plastic zone emerges. Excessive or insufficient lateral pressure coefficients (compared to \(\lambda=1\)) are prone to irregular plastic zone formation, markedly expanding the plastic zone range. 2. Under the combined influence of high geothermal temperature and geostress, the shape of the plastic zone in tunnels resembles that observed in tunnels subjected primarily to high geostress. Thermal stress in the rock mass slows down the expansion of the tunnel's plastic zone shape while notably increasing both its radius and extent. Additionally, the plastic zone's shape shows a more moderated response compared to scenarios influenced solely by high geostress, leading to a broader range of plastic zones. While thermal stress has a lesser impact on the shape and extent of the plastic zone compared to lateral pressure coefficients, its importance should not be underestimated.
3. A comparison between the Xinjiang Bulunkou tunnel, affected by high geothermal temperature and geostress, and the theoretical outcomes of this study reveals a significant difference in the radius of the surrounding rock's plastic zone and the stress induced by thermal interaction. This emphasizes the considerable role of thermal stress in influencing the plastic zone, validating its substantial impact.  
Conceptualization, H.J. and Y.Y.; data curation, Y.Y.; formal analysis, Y.Y.; funding acquisition, H.J. and Q.L.; investigation, H.J., Y.Y., and Q.L.; methodology, H.J., Y.Y. and Q.L.; project administration, H.J. and Q.L.; resources, H.J. and Q.L.; software, Y.Y.; supervision, H.J., J.Z., G.L., and Q.L.; validation, Y.Y.; visualization, Y.Y.; writing--original draft, H.J., Y.Y., and Q.L.; writing--review and editing, Y.Y., H.J., J.Z., G.L., and Q.L. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Natural Science Foundation of China (52369021) and the Youth Fund of the National Natural Science Foundation of China (42102312).  
Not applicable.  
Data Availability Statement: Data is contained within the article.  
Authors [PERSON] as employed by the company Xinjiang Water Resources and Hydropower Survey Design and Research Institute Limited Liability Company. 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.