## 3 Application of Functionality Loss Evaluation Model for Railway Network Components
### Construction and Visualization of the Railway Network Model
#### 3.2.2 Derivation of Functionality Loss for Railway Network Components Under an Earthquake Scenario  
The calculated PGA and functionality loss values for each railway network component are presented in Figure 11 and Table 8. Functionality losses of <2%, >2%, >4%, and >10% are \begin{table}
\begin{tabular}{c c c c} \hline
**Structure** & **Soil Classification** & **Structure** & **Soil Classification** \\ \hline Bridge 1 & S2 & Embankment A & S2 \\ Bridge 2 & S3 & Embankment B & S4 \\ Bridge 3 & S4 & Embankment C & S3 \\ Bridge 4 & S4 & Embankment D & S5 \\ Bridge 5 & S5 & Embankment E & S2 \\ Tunnel 1 & S3 & Embankment F & S3 \\ Tunnel 2 & S3 & Embankment G & S4 \\ Tunnel 3 & S2 & Embankment H & S5 \\ Tunnel 4 & S3 & Embankment I & S3 \\ Tunnel 5 & S2 & Embankment J & S4 \\ \hline \end{tabular}
\end{table} 
Table 6: Ground condition for each railway network structure. \begin{table}
\begin{tabular}{c c c c c} \hline
**Ground** & **Description** & \multicolumn{2}{c}{**Short-Period Ground Amplification Factor, F\({}_{\text{a}}\)**} \\ \cline{3-5}
**Type** & **Description** & **S \(\leq\) 0.1** & **S = 0.2** & **S \(\geq\) 0.3** \\ \hline S\({}_{2}\) & Shallow and stiff ground & 1.4 & 1.4 & 1.3 \\ S\({}_{3}\) & Shallow and soft ground & 1.7 & 1.5 & 1.3 \\ S\({}_{4}\) & Deep and stiff ground & 1.6 & 1.4 & 1.2 \\ S\({}_{5}\) & Deep and soft ground & 1.8 & 1.3 & 1.3 \\ \hline \end{tabular}
\end{table} 
Table 7: Short-period amplification factors [21]. shown 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 1.8 to 6.7% for railway bridge sections, 2.4-17.2% for embankment sections on soft ground, 0.2-1.3% for embankment sections on stiff ground, and 1.0-4.6% for tunnel sections. However, this study applied the same seismic fragility function for bridges and classified tunnels only by depth, applying the same seismic fragility function for each category, which presents a limitation. Additionally, since a wide range of sections were not simulated, similar peak ground acceleration values were derived despite considering ground amplification, leading to similar functionality loss values for the same structures. The objective of this study is to propose and apply a methodology for determining functionality loss in railway networks based on previous studies. It is anticipated that establishing a classification system for structures based on various parameters and deriving seismic fragility functions for each classification will lead to more reasonable results in the future. \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 & 0.22260 & 6.28 \\ Bridge No. 2 & 2 & 22 & 0.20505 & 5.00 \\ Bridge No. 3 & 3 & 31 & 0.14736 & 1.78 \\ Bridge No. 4 & 2 & 17 & 0.22752 & 6.66 \\ Bridge No. 5 & 2 & 20 & 0.21858 & 5.98 \\ Embankment A & 3 & 17 & 0.22263 & 0.18 \\ Embankment B & 3 & 19 & 0.21246 & 0.96 \\ Embankment C & 4 & 20 & 0.21891 & 12.58 \\ Embankment D & 3 & 24 & 0.19882 & 2.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Calculated PGA value and functionality loss value at each structure (input PGA = 0.3 g). Figure 11: Functionality loss value for earthquake scenario (Input PGA = 0.3 g). 2.3 Derivation of Functionality Loss for the Railway Network System Under an Earthquake Scenario 0.3 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 (8). \[FL_{N}=\frac{L_{S}\times FL_{S}}{L_{N}} \tag{8}\]  
where \(FL_{N}\) is the railway network functionality loss ratio, \(FL_{S}\) is the functionality loss ratio of railway components, and \(L\) is the length of the component.