## 3 The Index System of Risk Assessment for Tunnel Failure
### Correlation Between Evaluation Indicators and Damage Levels  
The correlation between the damage levels and the nine evaluation indexes was analyzed to verify the reliability of the evaluation indexes. Table 4 displays the number of angles and lithology occurrences at different damage levels. It was observed that more slight damage observations occurred in tuff and the moderate damage observations were prone to occur in pyrite. In addition, 77 damage observations occured where the tunnel was oriented perpendicular to the maximum principal stress (angle = 90\({}^{\circ}\)), and only 13 damage observations occurred when the tunnel was oriented parallel to the maximum principal stress (angle = 0\({}^{\circ}\)). This indicates that tunnel orientation has a strong correlation to tunnel damage.  
Figure 6 displays the distribution of the other seven evaluation indexes, including the accumulated MS events, the accumulated released energy from the MS events, the MS events density, the displacement, the apparent stress, distance between the tunnel and its nearest slope, and the buried depth. There are many outliers within the upper part of the boxplot for accumulated MS events and the accumulated energy. This may indicate that some sample data of the two indexes deviate from the data distribution center. If these data were used in the tunnel damage risk assessment, the accuracy of the results would be significantly affected. Due to this dispersion, the uppermost and lowermost 5% of the data were removed from each of the seven indexes prior to implementation in tunnel damage risk assessment. The data distribution of these seven evaluation indexes and their mean values after truncation are shown in Table 5. The boundaries of the statistical parameters of each evaluation index overlap between the three damage levels. However, from the scatter diagram of the distribution of evaluation indexes with different damage levels (Figure 7), it can be seen that, although the distribution of the MS events, MS events density, displacement, the apparent stress overlap in each damage category to some extent, each damage level has a distinct cluster of observations. The boundaries of distributions  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Damage Level** & **Pyrite** & **Tuff** & **Angle/0\({}^{\circ}\)** & **Angle/90\({}^{\circ}\)** \\ \hline No damage & 13 & 11 & 5 & 19 \\ Slight damage & 21 & 23 & 5 & 39 \\ Moderate damage & 13 & 9 & 3 & 19 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Statistics results between the damage levels and the angle and lithology.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Accumulated** & **Accumulated** & & & & & & \\
**MS Events** & **Energy/\(lg\)E(J)** & **Distance/m** & \(\sigma_{a}\)**/MPa** & **u/m** & **Density/m3** & **Depth/m** & **Angle/\({}^{\circ}\)** & **Lithology** & **Damage Level** \\ \hline
8 & 23.6 & 35.3 & 0.20 & 0.002 & 11.79 & 709 & 90 & Pyrite & Slight \\
1 & 4.35 & 105.88 & 0.02 & 0.002 & 0.32 & 609 & 90 & Tuff & No \\
2 & 7.15 & 76.35 & 0.36 & 0.003 & 2.47 & 758 & 0 & Pyrite & No \\
16 & 50.5 & 83.95 & 0.44 & 0.008 & 4.89 & 759 & 0 & Pyrite & Moderate \\
10 & 25 & 58.91 & 0.26 & 0.003 & 13.68 & 659 & 90 & Pyrite & Slight \\
11 & 32.4 & 60.28 & 0.22 & 0.004 & 8 & 908 & 0 & Tuff & Slight \\
13 & 29.8 & 85.98 & 0.39 & 0.005 & 3.42 & 659 & 90 & Pyrite & Slight \\
22 & 69.1 & 55.3 & 0.87 & 0.007 & 20.26 & 810 & 90 & Tuff & Moderate \\
7 & 23.4 & 121.37 & 0.20 & 0.004 & 8.79 & 709 & 90 & Tuff & Slight \\
10 & 25.8 & 155.1 & 0.10 & 0.002 & 9.55 & 910 & 90 & Pyrite & Slight \\ \hline \hline \end{tabular}
\end{table}
Table 3: Example of observation data that includes the evaluation indexes and the damage level.  
of the other three indexes (the angle, distance, and buried depth) are indistinct at the three damage levels. Because of this, it is not possible to conduct the tunnel damage risk assessment by using a single evaluation index, and a comprehensive analysis by using multi-indexes is necessary to improve the accuracy of the evaluation results.