## 3 Application of Functionality Loss Evaluation Model for Railway Network Components
### Construction and Visualization of the Railway Network Model
#### 3.3.2 Derivation of Functionality Loss for Railway Network Components Under the Earthquake Scenario  
The calculated PGA and functionality loss values for each railway network component are presented in Figure 12 and Table 9. Functionality loss values of \(<\)5%, \(>\)5%, \(>\)15%, and \(>\)20% are represented in yellow, green, orange, and red, respectively, to illustrate the extent of functionality loss. Overall, functionality loss occurred mainly in embankment sections on soft ground, while railway bridges exhibited the lowest functionality loss. The estimated functionality loss ranged from 6.9 to 18.9% for railway bridge sections, 4.3-24.0% for embankment sections on soft ground, 0.8-4.5% for embankment sections on stiff ground, and 5.1-12.9% for tunnel sections. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Label** & **Length (m)** & **Distance from Epicenter (km)** & **PGA Level (g)** & **Functionality Loss (\%)** \\ \hline Embankment E & 2 & 15 & 0.23297 & 1.29 \\ Embankment F & 3 & 13 & 0.28062 & 17.21 \\ Embankment G & 3 & 15 & 0.24415 & 0.25 \\ Embankment H & 1 & 16 & 0.23929 & 6.69 \\ Embankment I & 4 & 23 & 0.19866 & 4.64 \\ Embankment J & 2 & 27 & 0.16584 & 0.57 \\ Tunnel I & 1 & 18 & 0.23436 & 4.62 \\ Tunnel II & 2 & 23 & 0.19866 & 2.46 \\ Tunnel III & 4 & 27 & 0.14587 & 0.99 \\ Tunnel IV & 4 & 19 & 0.22643 & 4.04 \\ Tunnel V & 3 & 18 & 0.20397 & 2.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: _Cont._3.3 Derivation of Functionality Loss for the Railway Network System Under an Earthquake Scenario 0.5 g  
To evaluate the overall functionality loss of the railway network, two methods can be used: (1) using the maximum loss value or (2) calculating the average functionality loss of all network components using Equation (9). Figure 12: Functionality loss value for earthquake scenario (input PGA = 0.5 g). \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Label** & **Length (m)** & **Distance from Epicenter (km)** & **PGA Level (g)** & **Functionality Loss (\%)** \\ \hline Bridge No. 1 & 4 & 16 & 0.35377 & 18.85 \\ Bridge No. 2 & 2 & 22 & 0.30750 & 14.07 \\ Bridge No. 3 & 3 & 31 & 0.22918 & 6.89 \\ Bridge No. 4 & 2 & 17 & 0.32778 & 16.14 \\ Bridge No. 5 & 2 & 20 & 0.29069 & 12.41 \\ Embankment A & 3 & 17 & 0.35377 & 0.82 \\ Embankment B & 3 & 19 & 0.31071 & 2.94 \\ Embankment C & 4 & 20 & 0.32485 & 20.10 \\ Embankment D & 3 & 24 & 0.25740 & 4.28 \\ Embankment E & 2 & 15 & 0.36684 & 4.47 \\ Embankment F & 3 & 13 & 0.39631 & 24.01 \\ Embankment G & 3 & 15 & 0.34538 & 0.77 \\ Embankment H & 1 & 16 & 0.34450 & 12.18 \\ Embankment I & 4 & 23 & 0.29930 & 9.84 \\ Embankment J & 2 & 27 & 0.25227 & 2.13 \\ Tunnel I & 1 & 18 & 0.34344 & 11.45 \\ Tunnel II & 2 & 23 & 0.29930 & 9.75 \\ Tunnel III & 4 & 27 & 0.24312 & 5.10 \\ Tunnel IV & 4 & 19 & 0.33400 & 12.92 \\ Tunnel V & 3 & 18 & 0.32955 & 12.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Calculated PGA value and functionality loss value at for structure (input PGA = 0.5 g). \[\text{FLnetwork}=\frac{L_{structure}*FL_{structure}}{L_{network}} \tag{9}\]  
where _FL_ is the functionality loss ratio, and \(L\) is the length of the component. The functionality loss for the railway network, calculated using the same method as before, is as follows: Assuming that functionality loss in any single section causes an overall functionality loss for the entire network, the functionality loss ratios for Line 1 (20.1% at embankment section C), Line 2 (24% at embankment section F), and Line 3 (12.2% at embankment section H) can be evaluated. Notably, embankment section C has the greatest impact on the functionality of the entire network, as its functionality loss disrupts the connections between Line 1 and Lines 2 and 3. Thus, its functionality loss value of 20.1% can be considered the representative value for network functionality loss. If this evaluation method is considered to overestimate functionality loss, calculations using Equation (9) yield a railway network functionality loss ratio of 9.57%.