## 3 Field Test
### Image Analysis Results  
#### 3.2.1 Applicability of Shape Indices  
The image analysis was performed for the samples collected from each location to calculate the average value of the four shape indices. Moreover, the abrasion of aggregates was estimated per location using the relationship between the shape index and abrasion derived in the previous study [11]. The estimated abrasion, the track quality index (TQI) of each sampling location, and the number of maintenance works were compared. TQI, i.e., standard deviation of track irregularity of a specific section, is an index representing the overall track condition of a certain length of track. In Korea, track irregularity is inspected once a month using a track inspection vehicle such as Roger-1000k. However, because the sampling and inspection dates do not always tally exactly, the track irregularity data on the date closest to the sampling date was used for calculating the TQI. The number of maintenance works is counted by the number of machine tamping performed at each location from April 2004, when the high-speed railway was first opened, to July 2018. If ballast replacement work was performed at the respective location at a specific period, only the number of machine tamping performed from that point until July 2018 was counted. Figures 7 and 8 show relationships abrasion loss based on shape indices versus TQI and maintenance history, i.e., number of tamping process. The results showed that roundness is highly correlated with TQI (Figure 7a), while sphericity has a high correlation with the number of maintenance works (Figure 8b). Moreover, aspect ratio and angularity did not have a significant correlation with any variables. These phenomena were caused by shape characterization of shape indices and limitation of datasets. high in the result. [PERSON] et al. (2020) also concluded that sphericity and friction angle are inversely proportional. As sphericity increases, which mean surface of particle become smoother, the friction angle is decreased. Aspect ratio belongs to the large scale, but it is a ratio of the major axis to the minor axis of gravel particles, which may be inadequate to represent the overall shape. Thus, its correlation with TQI or maintenance work also is relatively low. Angularity is an index representing the detailed features of the particle surface, and thus, it is significantly affected by the precision and resolution of the experiment. However, the image analysis method employed in this study was not conducted with the high precision and resolution; therefore, the accuracy of angularity was measured to be lower than that for the other shape indices. This can be verified through the coefficient of variation of each shape index. In Figure 9, the coefficient of variation shows the relative distribution in which the standard deviation is divided by average. The coefficient of variation of angularity is 35-50%, which is larger than that of the other shape indices. This implies that estimating the exact abrasion loss of the respective section using angularity is difficult, which is resulted in a low correlation with the TQI or maintenance work. Figure 7: Abrasion loss based on shape index vs. TQI: (**a**) roundness; (**b**) sphericity; (**c**) aspect ratio; (**d**) angularity. The limitation of datasets means that some shape indices have relatively large error range. The 95% confidence interval for the population mean is expressed as follow  
\[95\%\text{ Confidence Intervals}=\mu\pm 1.96\times\frac{\sigma}{\sqrt{n}}\]  
where, \(\mu\) is a sample mean, \(\sigma\) is a standard deviation of samples, and \(\mathbf{n}\) is the number of aggregates. If coefficient of variation of aggregates is small or the number of aggregates is big, error range could be minimized. As can be seen in Figure 9, the coefficient of variation is approximately 5% for sphericity, 15-20% for roundness and aspect ratio and 35-50% for angularity. In case of sphericity, error range for the population mean are \(\pm 2\%\) when the number of aggregates is 20.