## 5 Long-Term Stability and Lining Safety of Surrounding Rocks in Tunnels
### Timing of Lining
#### 5.2.1 Latest Timing of Lining  
The deformation of the surrounding rocks and deformation rate corresponding to 1, 2, 3, and 4 in Figure 13 are demonstrated in Table 8. The deformation and deformation rate satisfy the requirement that the displacement should be 80-90% of the expected total displacement, the horizontal convergence rate of tunnel is less than 0.1-0.2 mm d\({}^{-1}\), or the settlement rate of arch is less than 0.07-0.15 mm d\({}^{-1}\). For determining the latest timing of lining, the deformation of the surrounding rocks should converge, and the supporting force should not exceed the limit. The stress of the rock mass during creep is simulated. The maximum tensile stress of XZ43+090 127 days after the completion of the support installation is 134 kN and the maximum compressive stress of the steel arch is 210 MPa; these values are close to the ultimate levels, suggesting a great risk for the support safety. Therefore, it is not appropriate to determine the latest timing of lining based on the deformation that is 80% of the maximum deformation. When the latest timing of lining is moved forward to 110 days after completion, the maximum tensile stress of the bolt is 124.6 kN, which is 90.9% of its ultimate bearing capacity. The maximum compressive stress of the steel arch is 178.2 MPa, which is 82.7% of its ultimate bearing capacity. In this case, the supporting structure plays a prominent role and is still in a safe state. The latest timing of lining for XZ43+090 is 110 days. The maximum tensile stress of the bolt 100 days after the support is installed in XZ67+070 is 128 kN, which is 93.4% of its ultimate bearing capacity. The maximum compressive stress of the steel arch is 183 MPa, which is 85.1% of its ultimate bearing capacity. It is still in a safe state. Therefore, the latest timing of lining in this section is determined to be 100 days. The deformation \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Arch**} & \multicolumn{3}{c}{**Sidewall**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Final**} & \multicolumn{2}{c}{**0.8 U**} & \multicolumn{2}{c}{**0.9 U**} & \multicolumn{2}{c}{**Final**} & \multicolumn{2}{c}{**0.8 U**} & \multicolumn{2}{c}{**0.9 U**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Deformation**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**Rate**} & \multicolumn{2}{c}{**Time (day)**} & \multicolumn{2}{c}{**Rate**} & \multicolumn{2}{c}{**Deformation**} & \multicolumn{2}{c}{**Time (day)**} & \multicolumn{2}{c}{**Rate**} \\ \cline{2-10}  & \multicolumn{2}{c}{**(mm-d\({}^{-1}\))**} & \multicolumn{2}{c}{**Time (day)**} & \multicolumn{2}{c}{**(mm-d\({}^{-1}\))**} & \multicolumn{2}{c}{**(mm)**} & \multicolumn{2}{c}{**Time (day)**} & \multicolumn{2}{c}{**(mm-d\({}^{-1}\))**} & \multicolumn{2}{c}{**(day)**} & \multicolumn{2}{c}{**(mm-d\({}^{-1}\))**} \\ \hline XZ43+090 & 53.64 & 127 & 0.078 & 195 & 0.073 & 42.99 & 145 & 0.083 & 210 & 0.05 \\ \hline XZ67+070 & 54.67 & 100 & 0.1 & 177 & 0.071 & 43.77 & 127 & 0.092 & 189 & 0.054 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Deformation of the arch and sidewall and the deformation rates. curves of the surrounding rocks after the support installation and lining are shown in Figure 14.  
We can observe that the lining constrains the development of creep even though the creep characteristics of the mudstone exist after the pouring of reinforced concrete lining. For XZ43+090 and XZ67+070, the deformation limit is 10 mm, and the surrounding rock will exert deformation pressure on the reinforced concrete lining. The long-term stress in the concrete and steel of the lining is shown in Figures 15 and 16, respectively. For XZ43+090, when the lining is poured 110 days after the support installation, the creep effect in the surrounding rocks causes the reinforced concrete lining to generate compressive stress with increasing operation time.