## 4 A Case Study of Hidake Tunnel in Japan
### Results and Discussions  
According to the methods described above, the fractal dimensions for all the 65 spans of Hidake Tunnel were calculated and shown in Table 2. The TCIs of all the 65 spans were also calculated through the statistical method. According to the fractal dimension and TCI shown in Table 2, their correlation was presented in Figure 11. In addition, the results of 12 typical spans were marked in this figure. The results by two different methods can be fitted as a power function with a correlation coefficient of 0.8606. For most of the test spans, the results by the two different methods were consistent with each other. Obviously, there is a certain correlation between TCI and the new proposed index. However, for some points, the degree of risk is significantly different according to the two evaluation indices. For span 18, there are only three small cracks, and both the TCI and the fractal dimension are in quite small states. Obviously, it is in a safe state. For span 16, there are several cracks and no wide crack is found. Therefore, the calculated TCI is quite small. Since these cracks have almost penetrate the entire lining, it is clear that the risk is underestimated. As the cracks are connected together, the calculated fractal dimension is significantly larger. This behavior indicated that the result by the new index is more consistent with the actual risk of the tunnel lining. Similar phenomenon is found in the results of spans 36 and 63, where the risk is also underestimated by the TCI. While, some wide cracks were found in the two spans, and their risk is relatively large by both methods. For spans 34 and 42, the results were located below the fitting curve, which suggested that their risk was small according to the new index and large by the index of TCI. Since there are only some small and independent cracks in the two spans, the actual damage in the tunnel lining is not so serious. Therefore, the results by the new health assessment index are closer to the actual risk of the tunnel lining. For spans 46, 47, 50, 53, and 57, the risk of lining collapses is quite large by both health assessment indexes, which suggested that proper maintenance is extremely necessary. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Span** & **Lining** & **Inverted** & **Buried** & **Surrounding** & **Surface** & **Concrete** & **Construction** \\
**No.** & **Thickness** & **Arch** & **Depth** & **Rock Type** & **Prep** & **Type** & **Method** \\ \hline
16 & 0.55 m & No & 25 m & sand tuff & No & C20 & cast-in-place \\
18 & 0.55 m & No & 25 m & sand tuff & No & C20 & cast-in-place \\
34 & 0.70 m & No & 23 m & basalt & No & C20 & cast-in-place \\
36 & 0.70 m & No & 23 m & basalt & No & C20 & cast-in-place \\
42 & 0.55 m & No & 23 m & basalt & No & C20 & cast-in-place \\
46 & 0.55 m & No & 23 m & tuff breccia & No & C20 & cast-in-place \\
47 & 0.55 m & No & 23 m & tuff breccia & No & C20 & cast-in-place \\
50 & 0.55 m & No & 23 m & tuff breccia & No & C20 & cast-in-place \\
53 & 0.70 m & No & 23 m & lapilli tuff & No & C20 & cast-in-place \\
57 & 0.70 m & No & 23 m & lapilli tuff & No & C20 & cast-in-place \\
63 & 0.70 m & No & 2 m & lapilli tuff & No & C20 & cast-in-place \\
65 & 0.70 m & Yes & 0 m & lapilli tuff & No & C20 & cast-in-place \\ \hline \end{tabular}
\end{table} 
Table 1: The basic condition of the 12 typical spans. The above results suggested that the current method, which evaluates the health status of tunnel lining only by the index of TCI, is far from perfect. It is necessary to use a different method in which the distribution of cracks can be considered. The significance of the new evaluation index is that it can identify some unusual spans of tunnel lining and provide a basis for further internal testing. In addition, the calculation of fractal dimension is very simple and takes only a few minutes for one span. Meanwhile, a lot of time and work are need to get the TCI.