# Safety Analysis of Secondary Lining of Yulinzi Tunnel Based on Field Monitoring
## 4 Analysis of Test Results
### Variation Law of Section Internal Force
#### 4.3.3 Time-Varying Law of Bending Moment of the Secondary Lining  
We extract the bending moment and axial force values of all sections at the end of the monitoring and drew the bending moment and axial force diagrams, as shown in Figures 15 and 16, where the numerical unit in the bending moment diagram is kN\(\cdot\)m, and the numerical unit in the axial force diagram is kN. Figure 15 shows the bending moment diagram of the secondary lining monitoring section. In the figure, the direction of the bending moment at the vault position is opposite to that at other positions. It shows that the longitudinal cracks in the tunnel result could be attributed to the inner side of the vault area, which was subjected to a large tensile stress. This caused the secondary lining concrete to crack and fail. Comparing the internal force values at different positions, the bending moment at the arch foot was the largest, and the bending moment values on the left and right sides were 593 kN\(\cdot\)m and 851 kN\(\cdot\)m, respectively, mainly because the arch foot was in contact with the inverted arch and was subjected to a large force stress concentration phenomenon. The bending moment on the right side of the tunnel was generally greater than the bending moment on the left side, indicating that the surrounding rock load on the structure was greater on the right side than on the left side. The main reason was that the right side of the monitored section was the interval between the left and right holes of the tunnel. The distance (about 20 m) between the two holes can be judged according to the drawings During the simultaneous excavation of the two tunnels, due to the simultaneous disturbance of the left and right holes to the surrounding rock, the surrounding rock on the right side of the section had  
Figure 16: Axial force of secondary lining. Figure 15: Bending moment of secondary lining. a large loosening range. During the long-term stress process, the surrounding rock on the right side of the tunnel, the pressure was greater than the surrounding rock pressure acting on the left side of the tunnel. The bending moment value of the structure increased gradually from top to bottom. Figure 16 shows the axial force diagram of the secondary lining monitoring section. From the axial force value, it can be seen that all sections of the tunnel structure were under compression. From the perspective of the overall distribution of the axial force, the axial force of each section of the secondary lining increased continuously from top to bottom, and the axial force of the structure on the right was greater than that of the structure on the left, which is consistent with the distribution of the bending moment of the structure. In addition, it can be seen that the axial force of the substructure of the secondary lining was much greater than that of the superstructure. Comparing the numerical values of the arch foot and the vault, the axial force values of D1 and D7 were approximately 11 times different, which shows that the upper part of the tunnel is affected. The vertical downward load was relatively large and was transmitted from the upper part of the structure to the lower part of the structure; then, the vertical downward load was transmitted to the tunnel base by the arch foot. The high compressive stress at the arch waist and side walls may cause the concrete to split and fail under greater pressure, thus explaining the oblique and longitudinal cracks at the side walls of the tunnel. On the whole, the internal force distribution of the secondary lining structure of the tunnel presented the form of \"big on the right and small on the left\" and \"big on the bottom and small on the top\". The load was mainly transmitted from the upper part of the structure to the lower part of the structure so that the axial force value of the arch foot was the largest.