# Ballasted Track Status Evaluation Based on Apparent Track Stiffness Index
## 2 Main Concepts
### Field Test
#### 2.2.2 Apparent Stiffness Distribution Characteristics  
A total of 7994 sleepers were tested. The results showing the relative frequency by size of the apparent stiffness are presented in Figure 4. The relative frequency graph is displayed in the form of a bimodal distribution with two peak points. The ballasted track sleepers are divided into hanging and supporting sleepers based on the size of the apparent stiffness. Therefore, the distributions indicating the hanging sleeper sections with small apparent stiffness and the supporting sleeper sections with significant apparent stiffness were combined to show the resulting bimodal distribution. As mentioned earlier, the apparent stiffness by LFWD reflects not only the track stiffness but also substructure characteristics. Therefore, the distribution characteristics of the apparent stiffness may vary depending on the substructure. The relative frequency by apparent stiffness was classified by substructure and illustrated in a graph. For earthwork, the bimodal distribution was clearly shown, whereas at the bridge, the hanging sleeper group vaguely showed a unimodal distribution. In the tunnel, the hanging and supporting sleeper groups were not as clearly distinguished as in the earthwork; however, they still appeared in the form of a bimodal distribution and distributed over a wider area than did those for the earthwork. Table 2 lists the number of sleepers for which the apparent stiffness was measured at each substructure, the calculation of the average apparent stiffness, and the standard deviation. As can be \begin{table}
\begin{tabular}{c c c c} \hline
**Year of Measurement** & **Section Name** & **Structure Category** & **Location** \\ \hline \multirow{8}{*}{2017} & Sandong Bridge 3 & BR \({}^{1}\)-EW \({}^{2}\) & T1 092k050-092k340 \\  & Yongwa tunnel-Sandong Bridge 1 & TN \({}^{3}\)-EW-BR & T1 089k200-098k580 \\  & Seelygae Bridge & BR-EW & T1 195k240-195k510 \\  & Palgok overpass–Bannvol tunnel & BR-EW-TN & T1 035k850-036k415 \\  & Pyeongrade overpass & BR-EW & T1 075k050-075k272 \\  & Paengseong overpass 2–Bunyong overpass 1 & BR-EW-BR & T1 077k40-078k530 \\  & Shinjeng Bridge–Wunju tunnel & BR-EW-TN & T111k5710-112k050 \\  & Galhang overpass–Geumoh tunnel & BR-EW-TN & T2 241k160-241k460 \\  & Daejeonbuk connection line & BR-EW & T2 153k814-154k012 \\  & Seobong tunnel 2 & TN & T1 053k250-054k350 \\ \hline \multirow{8}{*}{2018} & Galhang overpass–Geumoh tunnel & BR-EW-TN & T2 241k160-241k460 \\  & Shinluge overpass & BR & T2 085k400-085k640 \\  & Godeung tunnel & EW-TN & T1 107k030-107k600 \\  & Pungsae Bridge & EW & T2 099k600-099k635 \\  & Paengseong overpass 1 & EW-BR & T2 075k490-075k690 \\  & Geumgang Bridge & EW-BR & T1 182k950-183k480 \\  & Yongwa tunnel & TN-EW & T1 089k200-089k350 \\  & & T2 098j200-089k236 \\ \hline \multirow{8}{*}{2019} & Geumgang Bridge & EW-BR & T1 182k950-183k480 \\  & Pungsae Bridge-Godeung tunnel & BR-EW-TN & T1 107k032-107k479 \\ \cline{1-1}  & Wunyong overpass 2 & EW & T2 081k850-081k729 \\ \cline{1-1}  & Shinlue overpass & EW & T2 086k440-086k731 \\ \cline{1-1}  & Pungsae Bridge & EW-BR & T2 100k240-100k389 \\ \hline \end{tabular} \({}^{1}\) BR, Bridge; \({}^{2}\) EW, Earthwork; \({}^{3}\) TN, Tunnel.  
\end{table} 
Table 1: Details of field testing. seen from the data in the table, the average magnitude of the apparent stiffness was in the order of tunnel > bridge > earthwork. In the tunnel, the average apparent stiffness and the standard deviation were the largest. In the earthwork, the hanging and supporting sleeper groups are combined as a bimodal distribution. Therefore, the average apparent stiffness is smaller and the standard deviation is slightly larger than those for the bridge, which is in a unimodal distribution. The apparent stiffness reflects not only the track stiffness and substructure characteristics but also the degree of sleeper hanging.