## 6 Conclusions  
In this study, the reinforcement effects of thin sleeve arches with various materials and thicknesses on differently damaged linings are investigated through numerical simulations and model testing. After organizing and analyzing the test data and simulation results, the following conclusions are drawn:  
(1) Comparative analysis of two kinds of materials for different damage lining reinforcement effects; both steel fiber-reinforced concrete and reinforced concrete can meet the requirements of structural stress. In the early stages of loading, the overall stiffness of damaged linings reinforced with reinforced concrete is greater than that of those reinforced with steel fiber-reinforced concrete. However, as the load increases, the overall stiffness of damaged linings reinforced with steel fiber-reinforced concrete becomes greater than that of those reinforced with reinforced concrete. Additionally, damaged linings reinforced with steel fiber-reinforced concrete exhibit plastic deformation under the design load without experiencing failure; however, damaged linings reinforced with reinforced concrete fail under the design load. In summary, the reinforcement performance of steel fiber-reinforced concrete is superior to that of traditional reinforced concrete.  
(2) Under the design load, the thin arches of different thicknesses are loaded on the medium-cracked lining, which can meet the force requirements. Through comparative analysis, under the same load, the 10 cm thin arch has the best reinforcement performance, followed by 7.5 cm and 8.5 cm, and the 5 cm and 6 cm thin arches have the worst reinforcement performance. If only economic benefits are considered, 6 cm thin arches can be used in the reinforcement of medium-cracked linings, but considering its long-term reinforcement performance and economy, 7.5 cm is optimal.  
In China, a significant number of operational tunnels have developed varying degrees of cracking and water leakage over time, seriously threatening structural integrity and traffic safety. In the field of tunnel lining reinforcement, the use of cast-in-place concrete arches is common; however, the long construction period presents challenges in ensuring construction quality. Experimental research on using prefabricated steel fiber-reinforced concrete arches for reinforcing cracked linings in confined spaces indicates that steel fiber-reinforced concrete has significant potential for the rapid and practical repair of deteriorated tunnels, and these findings underscore the importance of promoting this technology in the field.  
Y.Z.: conceptualization, supervision, validation, funding acquisition. Z.L.: conceptualization, methodology, investigation, and data curation. L.L.: writing--original draft, writing--review and editing. J.Z.: visualization, resources, and supervision. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Guangdong Province Key Areas R & D Program (2022B0101070001), and the National Natural Science Foundation of China (No. 520780890, No. 52274176, No. 52078090), and the Chongqing Natural Science Foundation (cstc2021 jcyj-mssmx1075), and the Chongqing Natural Science Foundation Innovation and Development Joint Fund (2022 NSCQ-LZX0285), and the Chongqing Municipal Education Commission \"Shuangcheng Economic Circle Construction in Chengdu-Chongqing Area\" Science and Technology Innovation Project (KJCX2020031).  
Not applicable.  
Data Availability Statement: The data will be made available upon request. The corresponding author should be contacted if someone wants to request the data from this study.  
Author [PERSON] was employed by the company Guangdong Hualu Transport Technology Co., Ltd. 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.