# Ballasted Track Status Evaluation Based on Apparent Track Stiffness Index
## 3 Ballasted Track Status Test Indicator  
### Apparent Track Stiffness vs. TQI  
The apparent stiffness average and standard deviation in the measurement section were used to determine the usability of the apparent track stiffness as an indicator of track status. The status of each sleeper can be distinguished between the supporting and hanging sleepers using the value of the apparent track stiffness for each sleeper. The apparent stiffness average should be used to evaluate the overall status of the ballasted track in a specific section. The larger the apparent stiffness average, the better the overall track quality of the section. Another indicator of the ballasted track status in a specific section is the standard deviation of apparent stiffness. The apparent stiffness standard deviation indicates how uniform the track quality is in the measurement section. When the standard deviation is significant, the relative difference in track quality for each sleeper is significant; when the standard deviation is small, the relative difference is small. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Structure**} & \multicolumn{2}{c}{**Number**} & \multirow{2}{*}{**Ratio of Hanging Sleepers**} \\ \cline{2-2} \cline{4-4}  & **Supporting Sleepers** & & **Hanging Sleepers** \\ \hline Earthwork & 2632 & 1772 & 0.67 \\ Bridge & 1887 & 517 & 0.27 \\ Tunnel & 935 & 251 & 0.27 \\ All & 5454 & 2540 & 0.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of supporting sleepers versus hanging sleepers. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Structure**} & \multicolumn{2}{c}{**Apparent Stiffness (kN/mm)**} & \multirow{2}{*}{**Number of**} \\ \cline{2-2} \cline{4-4}  & **Average** & **Standard Deviation** & **Measurement Sleepers** \\ \hline Earthwork & 133 & 40 & 2632 \\ Bridge & 136 & 39 & 1887 \\ Tunnel & 177 & 51 & 935 \\ All & 142 & 45 & 5454 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Apparent stiffness average and standard deviation for supporting sleepers. To verify the usability of apparent stiffness as a track status evaluation index, its correlation with TQI was analyzed. TQI is the standard deviation of vertical track irregularity and is an index that can quantitatively indicate the overall track status of a specific section. According to the Railway Track Maintenance Guidelines [1], track maintenance is divided into five steps by the absolute value difference between the reference line and the vertical track irregularity measurement or the standard deviation of the vertical track irregularity in a 200 m section. It can be said that the difference in the absolute value between the reference line and the vertical track irregularity measurement reflects the individual sleeper status rather than the overall track status within a specific section. Because the standard deviation of vertical track irregularity can be said to reflect the overall track status in the measurement section, we used TQI, the standard deviation of vertical track irregularity, to analyze the correlation with the apparent stiffness mean in this study. Because TQI is measured on the left and right rails, the average value of TQI calculated at the left and right rail positions was calculated as the representative TQI of the section. In Korea, track irregularity is measured once a month using a comprehensive track recording car. Because the date on which the measurement was obtained and the date on which the LFWD test was performed were not exactly the same, the data measured by the comprehensive track recording car at the LFWD measurement time and the closest matching time were used to calculate TQI. Figure 5 depicts the correlation between apparent stiffness and TQI. In the figure, R\({}^{2}\) is the coefficient of determination. R\({}^{2}\) is between 0 and 1; as R\({}^{2}\) gets closer to 1, the two variables become more dependent. As a result of comparing the apparent stiffness average and TQI, the overall correlation was found to be very low, with R\({}^{2}\) of 0.23.