# Ballasted Track Status Evaluation Based on Apparent Track Stiffness Index
## 2 Main Concepts
### Field Test
#### 2.2.2 Apparent Stiffness Distribution Characteristics
Therefore, to investigate the effect of the substructure on the magnitude of the apparent stiffness, the average and standard deviation were calculated only for the supporting sleeper. The results are listed in Table 3. The supporting sleeper was set as a sleeper having an apparent stiffness of 80 kN/mm or more. When the earthwork and bridge were compared, it was found that the average and standard deviation of the bridge were slightly larger. In addition, the tunnel was clearly distinguished from other structures, showing the largest average and standard deviation. The same conclusion was drawn from the results of estimating the population mean considering the number of sleepers at each substructure. The 95% confidence interval of the population mean from the sample mean and sample standard deviation for each substructure was found to be 132 to 135 kN/mm in the earthwork, 135 to 138 kN/mm in the bridge, and 174 to 182 kN/mm in the tunnel. In general, the value of the substructure stiffness of the ballasted track was in the order of tunnel > bridge > earthwork. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Structure**} & \multicolumn{2}{c}{**Apparent Stiffness (kN/mm)**} & \multicolumn{2}{c}{**Number of**} \\ \cline{2-4}  & **Average** & **Standard Deviation** & **Measurement Sleepers** \\ \hline Earthwork & 98 & 54 & 4404 \\ Bridge & 118 & 50 & 2404 \\ Tunnel & 156 & 67 & 1186 \\ All & 112 & 58 & 7994 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Apparent stiffness average and standard deviation for sleepers. Figure 4: Relative frequency of apparent stiffness: (**a**) All; (**b**) Earthwork; (**c**) Bridge; (**d**) Tunnel. Therefore, it can be speculated that the apparent track stiffness reflects the stiffness of not only the ballasted track but also the substructure. However, further analysis is needed on how the substructure affects apparent stiffness. Table 4 lists the results of comparing the numbers of supporting and hanging sleepers for each substructure. The ratio of the numbers of supporting sleepers and hanging sleepers is 1:0.67 for earthwork, 1:0.27 for the bridges, and 1:0.27 for the tunnels. As mentioned earlier, owing to space-time limitations, the tests were performed mainly on sections where the bridge, earthwork, and tunnel are all adjacent. In general, for bridge-earthwork and earthwork-tunnel joints, the stiffness of the lower part constantly changes; therefore, these parts tend to be structurally vulnerable, and a majority of hanging sleepers are seen in this type of location. This could be the reason why the ratio of hanging sleepers in earthwork is relatively high. For bridges or tunnels, considering that the number of tests performed at the center of these parts was relatively small owing to space-time limitations, the ratio of hanging sleepers in the entire section of the bridge or tunnel is considered to be smaller than the calculation result in this study. This indicates that maintenance of bridges or tunnels is required mainly for the connection parts where the hanging sleepers show intensive distribution. Furthermore, earthwork has relatively evenly distributed hanging sleepers, which implies that maintenance is required over a wide area of earthwork.