# Creep Behavior of Rocks and Its Application to the Long-Term Stability of Deep Rock Tunnels
## 9 Convergence and Post-Creep Behavior of Rocks Surrounding the Tunnels  
Convergence of tunnels is the gradual closing of the openings with the evolution of time. It is caused by two types of deformations of surrounding rocks. The first one is the deformation provoked by the tunnel front advance and the second is that generated by the effect of rock creep [176, 177, 178]. However, the major contribution to tunnel convergence is that due to rock creep. Therefore, the creep behavior of rocks really has the merit of reflecting and describing the long-term life of tunnels. According to [PERSON] et al. [130], reduction of tunnel convergence is possible by two technical measures such as low tunneling sequence or increased thickness of linings and early placement of supports. However, under the influence of time and aging of the supports, the convergence deformation can become considerable. The rate of convergence evolves according to the type of rocks located around the underground openings. It is generally faster in soft rocks than in hard rocks. To improve  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\sigma\) (MPa) & \(E_{m}\) (GPa) & \(\eta_{M}\) (GPa-day) & \(E_{K}\) (GPa) & \(\eta_{K}\) (GPa-day) \\ \hline
10 & 1.71 & 1250 & 67.67 & 53.46 \\
12 & 1.36 & 400 & 7.54 & 9.05 \\
15 & 1.26 & 98.04 & 5.82 & 4.66 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Creep parameters of salt rocks. (Data are taken from Mansouri and Ajalloian [152], Copyright©2022, with permission from the publisher, License No. 5361920269706).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time (Year)** & **Creep Strain of 1 st Stress Level (\(\times 10^{-3}\))** & **Creep Strain of 2 nd Stress Level (\(\times 10^{-3}\))** & **Creep Strain of 3 rd Stress Level (\(\times 10^{-3}\))** \\ \hline
1 & 8.915 & 21.34 & 70.32 \\
2 & 11.83 & 32.29 & 126.16 \\
3 & 14.75 & 43.24 & 182.01 \\
10 & 35.18 & 119.89 & 572.92 \\
50 & 152.00 & 557.89 & 2806.7 \\
100 & 298.00 & 1105.39 & 5598.93 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Creep strain results for a deep salt mine or cavern based on Equation (26).  
understanding, an illustration of convergence tendency is presented through Figure 10 for a circular tunnel.  
Ideally, the convergence is severe when the rocks surrounding the openings exhaust their stable creep phase. When it reaches 400 cm, the tunnels are said to have large deformations [179]. As associated with rock creep, large deformations are time-dependent [180], and are greater at great depth [181], where they can be strongly influenced by groundwater [182]. Unacceptable convergences are generally observed in deep tunnels located in soft and weak rocks under the action of strong in situ stresses [183]. The extent of tunnel convergence increases over time if security and stability conditions are no longer guaranteed. Indeed, when the accelerated creep is reached, the tendency to convergence become more and more severe. At that time, the tunnels will no longer be able to perform their functions because the risks of considerable closure are enormous. In fact, ensuring the long-term stability of tunnels is linked to major difficulties with the occurrence of tertiary creep [23]. The evolution of tertiary creep will then be followed by the final rupture of the rocks, and the tunnels will be completely collapsed. As a result, there is appearance of the post-creep behavior of the rocks surrounding the tunnels. According to [PERSON] et al. [184], the life cycle of deep tunnels can be composed of four stages, the ultimate of which is total destruction where the natural water pressure slowly repairs itself and seeps through the existing cavities. It is therefore essential to accurately predict the life of tunnels by developing accurate and suitable constitutive creep models in order to prevent any early post-creep behavior of rocks near the underground openings.