## 6 Conclusions  
In the design of hard rock single-layer lining tunnels, the flexural performance of the tunnel lining structure directly affects the safety, durability, and service life of the entire tunnel. This paper presents four-point bending tests of specimens with six different thickness ratios. The conclusions are as follows:  
1. The flexural ultimate load values of the specimens first increase and then decrease as the thickness ratio increases. The maximum flexural ultimate load occurs when the thickness ratio is 2, with a 20.9% increase in flexural ultimate load compared to the thickness ratio of 0.
2. The flexural toughness of the specimens increases and then decreases with the increase in the thickness ratio. When the thickness ratio is 2, the flexural toughness of the specimen reaches its maximum, which is 25% higher compared to the thickness ratio of 0 (unstratified specimen).
3. Layered construction affects the failure mode of the shotcrete single-layer lining structure. At thickness ratios ranging from one to five, cracks develop with a transverse abrupt change at the parting interface. All shotcrete beams exhibit mixed-mode failure, with the proportion of flexural failure cracks increasing as the thickness ratio increases.
4. Layered construction will cause the effective bending stiffness of shotcrete beams to be reduced, and the larger the thickness ratio, the more obvious the reduction in the effective bending stiffness of shotcrete beams. On this basis, the interface influence coefficient is proposed, and the bending stiffness correction is carried out by combining the theory of stacked beams, which supplements the insufficiency of single-layer lining in the calculation of structural bending stiffness and can provide theoretical support for the calculation related to tunnel support.  
The thickness ratio significantly impacts the flexural performance of fiber shotcrete beams. Reasonable control of the thickness ratio can optimize both the bending tensile strength and the bending stiffness. Combining the mechanical properties of concrete beams and the flexural stiffness correction method, it is recommended that the thickness ratio for single-layer lining tunnels be set between 1 and 2. Further research should focus on interface treatment technologies, such as increasing the roughness of the interface or  
Figure 15: Comparison between the calculated results of the modified method and the test results. **(a)** The mid-span deflections of fiber shotcrete beams. **(b)** Linear fitting of the calculation results of the correction method and the experimental results.  
applying adhesive to improve the interlayer cooperative deformation capacity, prevent interface detachment, and ensure structural stability.  
Conceptualization, M.W. and Z.Z.; methodology, Z.Z. and K.Z.; validation, M.W., M.X., X.H. and K.Z.; investigation, Z.Z., X.H. and P.C.; data curation, M.X., X.H., K.Z. and P.C.; writing--original draft preparation, M.W., Z.Z., M.X. and K.Z.; writing--review and editing, M.W., Z.Z., K.Z. and P.C.; project administration, M.W., Z.Z., X.H. and P.C.; funding acquisition, Z.Z. All authors have read and agreed to the published version of the manuscript.  
Not applicable.  
Data Availability Statement: Data associated with this research are available and can be obtained by contacting the corresponding author upon reasonable request.  
We want to express our thanks to the authors whose publications we cited and the efficient editor.  
[PERSON], [PERSON], and [PERSON] were employed by China Merchants Chongqing Communications Technology Research & Design Institute 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.