# Ballasted Track Status Evaluation Based on Apparent Track Stiffness Index
## 3 Ballasted Track Status Test Indicator
### Track Stiffness Index  
Based on the analysis of the correlation between the apparent stiffness average and standard deviation, TQI, and cumulative tamping length, it was concluded that the average apparent stiffness or standard deviation could not be used as a status evaluation indicator. For the mean, it can be said that there was some correlation in the tunnels; however, there was low correlation in the earthwork and bridges. For the standard deviation, there was no direct correlation in any section. Although the standard deviation was not directly related to track quality, it was judged that the track quality could be represented well if the standard deviation was combined with the apparent stiffness average. The larger the average and the smaller the standard deviation, the more evenly distributed the supporting sleepers, indicating better quality of the track. In addition, when the mean of the apparent stiffness is small and the standard deviation is relatively large, there are more hanging sleepers than supporting sleepers. Therefore, the concept of the track stiffness index, which can represent the track status by simultaneously considering the average and standard deviation of the apparent track stiffness, was introduced. The track stiffness index is defined as the difference between the average and standard deviation of the apparent track stiffness. As per this definition, the track status is good when the average is significant (e.g., 100 kN/mm or greater) and the standard deviation is small, and the track status is bad when the average is small and the standard deviation is relatively larger. \[Stiffness\ Index=\alpha\cdot Average-(1-\alpha)\cdot SD \tag{2}\]  
Because the effects of the average and standard deviation on track status evaluation are different, each factor is multiplied by a weight. To derive the track stiffness index that has the largest correlation with TQI and cumulative tamping length as a track status evaluation index, the weight \(\alpha\) of the average was changed in the range from 0.5 to 1, and the correlations with TQI and cumulative tamping length were compared and represented in Table 5. The result of the comparison of the correlation coefficient with the apparent stiffness average is shown in Figure 7. As can be seen from the graph, the correlation coefficient between the stiffness index and TQI increases until \(\alpha\) is 0.6 and then decreases gradually. In addition, the correlation coefficient between the stiffness index and tamping length decreases slightly when \(\alpha\) is 0.5 and then increases gradually; however, the increase is smaller than that in TQI. Therefore, when \(\alpha\) was 0.6, the track stiffness index was determined to be the most suitable to be used as the track status evaluation index. The results are shown in Figures 8 and 9. Based on the analysis of the correlation between the track stiffness index and TQI, it can be observed that R\({}^{2}\) is significantly increased compared with the case of using the average alone. For the earthwork and tunnels, the correlation coefficients increased significantly to 0.58 and 0.61, respectively. However, regardless of the substructure, the result of analyzing the correlation at once showed R\({}^{2}\) values as small as 0.39, which means that it is appropriate to analyze the correlation by substructure categorization because the characteristics of the substructure are reflected in the apparent track stiffness as described above. For the bridges, R\({}^{2}\) slightly increased to 0.24, although the correlation was still very low.