# Seismic Reliability Assessment of Water Supply Systems Considering Critical Paths
## 3 Application and Results
### Application Results  
#### 3.4.1 System Serviceability (\(S_{\mathrm{s}}\))  
First, it was found that the supply capacity after the occurrence of an earthquake of magnitude \(7\) for the current system, which has not been made earthquake-resistant, was \(84.32\%\). This means that about \(15.68\%\) of the total supply would be unavailable after a magnitude \(7\) earthquake. The fact that high supply capability was observed following the occurrence of a relatively high-intensity earthquake suggests that the existing pipelines meet current design standards. The earthquake resistance of each of the nine critical paths and calculations of post-earthquake supply reliability are shown in Table 3 and Figure 6  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Entire**} & \multicolumn{6}{c}{**Critical Path (Pipeline)**} \\ \cline{2-10}  & **System** & **RES1** & **RES2** & **RES3** & **RES4** & **RES5** & **RES6** & **RES7** & **RES8** & **RES9** \\ \hline \(S_{\mathrm{s}}\) (\%) & 84.32 & 89.04 & 92.69 & 86.12 & 85.20 & 85.55 & 85.27 & 88.27 & 88.43 & 85.33 \\ Increase Rate (\%) & - & 4.72 & 8.37 & 1.80 & 0.88 & 1.23 & 0.95 & 3.95 & 4.11 & 1.01 \\ Rank & - & 2 & 1 & 5 & 9 & 6 & 8 & 4 & 3 & 7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: System Serviceability Results by Path.  
The reliability of the water supply system for all critical paths was, on average, about 3% higher than that of the current state. The reliability of supply capacity in the RES2 Pipeline was 92.69%, representing the largest increase in reliability (8.37%). The RES2 Pipeline, as shown in Table 2 and Figure 4b, has a relatively small number of pipes, but the individual pipes are longer and more widely dispersed than in other pipelines. In addition, since it is fulfilling a demand equivalent to 35.9% of the total supply, it is inevitably vulnerable to earthquakes. It was thus found that high reliability can be ensured if such a path is made earthquake resistant. Like the RES2 Pipeline, the RES1 Pipeline also significantly increases the reliability of the system when earthquake resistance is ensured. The seismic reliability results suggest that the RES1 and RES2 Pipelines should take precedence when conducting seismic reinforcement, since the amount of water supplied through the two is large and the pipes are long, even though these paths are composed of large-diameter pipes with a relatively high probability of failure.  
Next, the RES7 and RES8 Pipelines, which are composed of a number of different pipelines, also displayed good increases in reliability. In contrast to the RES2 pipeline, the amount of water supplied by the RES7 and RES8 Pipelines and the average pipe diameter are relatively small. Of course, during the hydraulic analysis of the water supply network, nodes may be generated in areas where there is no demand or bent in accordance with the judgment of the model constructor, but most nodes are generated according to a divergence of demand or a change in pipe diameter. In this case, when the corresponding path is a single path, the supply rapidly deteriorates if one of the relatively small-diameter pipes is damaged or leaks due to an earthquake. Therefore, except when the supply ratio is very small, and its effect on the system is insignificant, a path composed of a large number of small-diameter pipelines, such as the RES7 and RES8 Pipelines, must be carefully managed and made earthquake-resistant.  
The RES4 and RES6 Pipelines were the least affected by increasing their earthquake reliability. This is because these pipelines are composed of a relatively small number of short pipes, and the quantity of water demanded relative to the average pipe diameter is less than that of the other routes. Since most of the critical paths are made up of large-diameter pipes, it is clear that there is a limit to improving pipeline reliability with seismic reinforcement.  
Figure 6: System Serviceability Results by Path.