## 2 Numerical Analysis
### Analysis of Track Irregularities in Railway Structure  
The unmatched deviations in the track geometry on the rail-running surface due to the track deformation from the cyclic loading of the rolling stock are referred to as track irregularities. The types of track irregularities are generally classified in vertical profiles, alignments, twists, cross levels, and gauges. Figure 1: Modeling. (**a**) Ground conditions; (**b**) Schematic of numerical modeling. Table 1 lists the maintenance criteria of track irregularities for high-speed railways in South Korea. For urban railways, the maintenance criteria of track irregularities are set differently for each speed range, but in the case of high-speed railways, there is no classification based on speed. In the case of ballasted tracks on serviced railway lines, track irregularities may occur during public service of the railway line even before the onset of the adjacent excavations. Whether the speed is 90 km/h or 120 km/h may show a significant difference in terms of the effects of the variation in the load of the rolling stock, depending on the size of the track irregularities. In this study, the effects of track irregularities in the subway line and high-speed railway line were evaluated based on vertical and horizontal displacements of the rails. The locations of evaluation for the subway line and the high-speed railway line are indicated in Figure 2.  
The vertical profile, alignment, cross level, and gauge in the serviced railway line tracks of high-speed railway lines were analyzed according to the adjacent excavation. As a result of the analysis of track irregularities in the high-speed railway lines shown in Figure 3a, the maximum vertical profile of the HSR T1 track ranged from 0.32-0.35 mm in the case of a vertical profile (based on 10 m), and the maximum vertical profile of the HSR T2 track ranged from 0.42 to 0.57 mm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Maintenance Phase** & **Vertical Profile** & **Alignment** & **Twist** & **Cross level** & **Gauge** \\ \hline construction value (CV) & N\({}_{\text{10 m}}\leq 2\) target value (TV) & N\({}_{\text{10 m}}\leq 3\) & D\({}_{\text{10 m}}\leq 4\) & g\({}_{\text{3}}\leq 3\) & E\({}_{\text{d}}\leq 4\) & 1434 \(\leq\) E\({}_{\text{avg}}\leq 1438\) \\ warning value (WV) & 5 \(\leq\) N\({}_{\text{10 m}}\) \(<\) 10 & 6 \(\leq\) D\({}_{\text{10 m}}\)\(<\) 7 & 5 \(<\) g\({}_{\text{3}}\leq 7\) & 7 \(<\) E\({}_{\text{d}}\leq 9\) & 1433 \(\leq\) E\({}_{\text{avg}}<1434\) \\ action value (AV) & N\({}_{\text{10 m}}\geq 10\) & D\({}_{\text{10 m}}\geq 7\) & g\({}_{\text{3}}\)\(>\) 7 & E\({}_{\text{d}}\)\(>\) 9 & E\({}_{\text{avg}}\)\(<\) 1433 \\ speed reduction value (SV) & 18 \(<\) N\({}_{\text{10 m}}\)\(<\) 22 & 14 \(\leq\) D\({}_{\text{17}}\)\(=\) 15 \(<\) g\({}_{\text{3}}\leq 21\) & 15 \(<\) E\({}_{\text{d}}\leq 18\) & 1422 \(\leq\) E\({}_{\text{min}}\)\(<\) 1426 \\ value (170 km/h) & (170 km/h) & (170 km/h) & (170 km/h) & (170 km/h) & (170 km/h) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reference values for management and maintenance of track irregularities for high-speed railway infrastructure (unit: mm, based on 10). Figure 2: Conceptual diagram for numerical-analysis locations. Figure 3: Analyzed results of track irregularities in high-speed railway lines. **(a)** Vertical profile (based on 10 m); **(b)** Alignment (based on 10 m); **(c)** Cross level; **(d)** Gauge. As shown in Figure 3b, in the case of the alignment (based on 10 m), the maximum alignment of the HSR T1 track ranged from 0.74-0.75 mm, and the maximum alignment of the HSR T2 track ranged from 1.12-1.14 mm. As shown in Figure 3c, in the case of the cross level, the maximum cross level of the HSR T1 track was approximately 0.27 mm, and the maximum cross level of the HSR T2 track was approximately 0.24 mm. As shown in Figure 3d, in the case of the gauge, the maximum gauge of the HSR T1 track was approximately 0.033 mm and the maximum gauge of the HSR T2 track was approximately 0.025 mm.