## 4 Combined Stress Analysis of Composite Lining
### Simulation Results and Discussion
#### 4.3.2 Pipe Piece Stress Analysis  
The top of the pipe piece in the diversion tunnel is subject to tension on the inside and compression on the outside as water passage time increases, as shown in Table 5 and Figure 13. The maximum principal (tensile) stress on the inside gradually increased from 0.167 Mpa to 0.572 Mpa. The pipe piece's ring arch waist's stress changes are also more evenly distributed on both sides. The inner and outer sides of the waist experience compression and tension, respectively. The highest principal stress on the outer side raised from 0.730 Mpa to 1.953 Mpa. The maximum primary stress on the inside of the pipe piece increased from 0.143 Mpa to 0.529 Mpa under tension on the inside and compression on the outside. The outer edge of the tube sheet waist needs special care during long-term diversion tunnel operation since this area experiences increased tensile stress and is vulnerable to tensile cracking. The pipe piece can share the internal water pressure when the liner is subjected to internal water pressure, and the stresses of the pipe piece and liner tend to be uniform under the condition of sharing the stress. This causes the maximum primary stress at the pipe piece's waist.  
In the pressure plate test, the deformation modulus obtained by the secant and fitting method is close. The average deformation modulus of the fitting method under the water conveyance pressure of the engineering design is 4.71 GPa. The deformation modulus of 4.6 GPa is consistent with the average value measured by the borehole deformation method at the same elevation. This shows that the deformation modulus obtained by the borehole deformation method is reliable.
2. The horizontal bedding of the surrounding rock is developed and the integrity of the surrounding rock in the local hole section is poor according to the borehole television. The number of steep dip fractures is limited, but the width is large and there is a corrosion phenomenon. The deformation modulus of surrounding rock at the location of the diversion tunnel measured by the borehole deformation method is 0.4 GPa-9.4 GPa. The deformation modulus and elastic modulus will increase with depth.
3. The deformation modulus by the borehole deformation method and wave velocity obtained is fitted, and the power function relationship is obtained. Based on the acoustic test results, the deformation modulus of politic siltstone with various weathering degrees is estimated by using the relationship.
4. In the combined stress analysis of composite lining, the reinforced concrete lining of the Nansha Branch tunnel has a maximum primary stress of 5.407 Mpa, which is found inside the top and bottom. The outside edge of the waist on both sides of the pipe piece has the highest primary stress of 1.953 Mpa in tension.  
Conceptualization, Y.J.; methodology, Y.J.; software, Y.J.; validation, Y.H.; investigation, G.Y.; data curation, Y.H.; writing--original draft preparation, W.W.; writing--review and editing, W.W.; project administration, J.Y. All authors have read and agreed to the published version of the manuscript.  
We thank the National Natural Science Foundation of China for the support of this research (52078143) and the Guangdong Provincial Science and Technology Program (2019B020208003).  
Not applicable.  
Details on all data supporting the reported results can be obtained in Tables 1-5 and Figures 3-13 in this original manuscript.  
We thank the Guangdong Research Institute of Water Resources and Hydropower for providing test materials and fields for the study.  
The authors declare no conflict of interest.