## 5 Conclusions  
In this paper, according to the different water conveyance conditions of the hydraulic tunnel, the theoretical method of calculating the internal force of the lining structure is given by using the mechanical analysis method. With this calculation method, the influence law of water level height and water conveyance pressure on the maximum value and distribution of lining internal force is further analyzed. The main conclusions are as follows:  
1. The hydraulic tunnel is greatly affected by the internal water pressure. This paper introduces the theory of structural mechanics, considers the operating conditions of different water levels and water conveyance pressures and derives a general formula for calculating the internal force of the lining structure. This calculation method can effectively calculate the value and distribution of internal forces. Based on the modified routine method, the calculation theory of tunnel structure is further improved, which provides a theoretical basis for the design and safe operation of hydraulic tunnels.
2. When water is delivered under pressure, the maximum internal force of the lining increases with the increase of water conveyance pressure and inner radius. When water is delivered without pressure, the maximum bending moment and axial force of the lining will inverse the increasing trend at the special water level. In addition, the maximum value of lining internal force of pressureless water conveyance is much smaller than that of pressurized water conveyance. Therefore, when the hydraulic tunnel has high requirements for water-passing capacity, it can strengthen the structural strength to carry out pressurized water conveyance or adopt the design scheme of increasing size and the carrying out of pressureless water conveyance.
3. When water is delivered under pressure, the distribution of lining internal force changes regularly with the increase of water conveyance pressure. The maximum value of internal force is in the fixed special position. When water is delivered without pressure, with the increase in water conveyance level the internal force value of the lining increases continuously and the difference in internal force value at different angles is more significant. The internal force of the lining is much stronger when water is delivered under pressure than when water is delivered without pressure, so the strength of the lining structure should be designed to be larger.
4. The calculation model ignores both the influence of internal water pressure in the vertical direction and the dynamic characteristics, which is inconsistent with the actual situation. In addition, the mechanism of abnormal maximum bending moment and axial force at special water levels is unclear. These problems need further study.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Maximum Internal Force**} & \multicolumn{2}{c}{**Pressureless Water Conveyance Level**} & \multicolumn{2}{c}{**Pressurized Water Conveyance Pressure**} \\ \cline{2-5}  & **Half Water Level** & **Full Water Level** & **0.2 MPa** & **0.4 MPa** \\ \hline Bending moment (kN-m) & 100.4 & 376.0 & 1771.6 & 3175.1 \\ Axial force (kN) & 120.8 & 172.0 & 1231.7 & 2291.7 \\ shearing force (kN) & 43.5 & 165.5 & 693.0 & 1222.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The maximum internal force of flood discharging tunnel lining.  
editing, Y.Z.; funding acquisition, Y.Z. and C.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (Grant No. 51508278).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The authors declare no conflict of interest.