# Seismic Damage Analysis of Box Metro Tunnels Accounting for Aspect Ratio and Shear Failure
## 5 Conclusions  
The seismic failure mechanisms of single-story rectangular cut-and-cover tunnels with various aspect ratios were identified and their damage states were updated using the nonlinear frame model and a series of pushover analyses. The shear wave velocity of the soil was varied from 50 to 400 m/s. The numerical model was verified against published relationships between the racking ratio and the flexibility ratio. Based on the numerical analysis results, the following conclusions are drawn.  
* A collapse damage state was not observed for the single box tunnels even after plastic hinges formed at all corners, primarily due to the support from the surrounding soil medium. The shear plastic hinge did not form in the single tunnel.
* For double and triple tunnels, the shear plastic hinges formed at the interior columns after flexure plastic hinges developed at all outer frame corners. The shear failure at the interior column may lead to a brittle structural collapse for multi-box tunnels. This failure should be avoided in design practices.
* The aspect ratio did not significantly influence the damage index (DI) of the single box tunnels. For double and triple tunnels, DIs at which the inner column failed was dependent on the aspect ratio. The shear strains corresponding to the damage states were more sensitive to the aspect ratio compared with DI.
* Damage states of box tunnels and corresponding DIs were updated from the study of [PERSON] et al. [21]. DIs range from 1.0 to 2.3 for three damage states of single box tunnels, which were minor, moderate, and extensive states. The collapse damage state was newly proposed and the corresponding DI was presented for double and triple box tunnels. DIs ranged from 1.0 to 3.5.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Tunnel Type** & **Damage State** & **Number of Plastic Hinges (NPH)** & **DI of [PERSON] et al. [21]** & **Updated DI** \\ \hline \multirow{4}{*}{Single box} & None & 0 & DI \(<\) 1.0 & DI \(<\) 1.0 \\  & Minor & 1 \(\leq\) NPH \(<\) 2 & 1.0 \(\leq\) DI \(<\) 1.2 & 1.0 \(\leq\) DI \(<\) 1.4 \\  & Moderate & 2 \(\leq\) NPH \(<\) 3 & 1.2 \(\leq\) DI \(<\) 2.0 & 1.4 \(\leq\) DI \(<\) 2.3 \\  & Extensive & 3 \(\leq\) NPH & 2.0 \(\leq\) DI & 2.3 \(\leq\) DI \\ \hline \multirow{4}{*}{Double box Triple box} & None & 0 & DI \(<\) 1.0 & DI \(<\) 1.0 \\  & Minor & 1 \(\leq\) NPH \(<\) 2 & 1.0 \(\leq\) DI \(<\) 1.2 & 1.0 \(\leq\) DI \(<\) 1.2 \\ \cline{1-1}  & Moderate & 2 \(\leq\) NPH \(<\) 3 & 1.2 \(\leq\) DI \(<\) 2.0 & 1.2 \(\leq\) DI \(<\) 2.0 \\ \cline{1-1}  & Extensive & 3 \(\leq\) NPH \(<\) 5 & 2.0 \(\leq\) DI & 2.0 \(\leq\) DI \(<\) 3.5 \\ \cline{1-1}  & Collapse & 5 \(\leq\) NPH & N.A. & 3.5 \(\leq\) DI \\ \hline \end{tabular}
\end{table}
Table 1: Updated definitions of damage states and corresponding DIs. Damage state definitions and DIs of [PERSON] et al. [21] are listed for comparison purposes.  
**Author Contributions:** [PERSON] and [PERSON]-[PERSON] conceived the idea, outlined the work, and reviewed the manuscript; [PERSON]-[PERSON] performed the numerical analyses and wrote the manuscript; [PERSON]-[PERSON] supported in performing numerical simulations and summarizing the results.  
**Funding:** This research was supported by the National Research Council of Science & Technology (NST) grant number CRC-16-02-KICT funded by the Korean government (MSIP).  
**Conflicts of Interest:** The authors declare no conflict of interest.