## 4 Discussion
### Effect of Vertical Track Irregularities on Train Body Accelerations  
In Korean high-speed railways, as noted above, the track geometry is measured based on the chord versus method, not the absolute geometry. Ten (10)-m and 30-m chords are used in Korea. The 10-m-chord track irregularity underestimates the long-wavelength components, which are closely related to train vibration and passenger comfort. On the other hand, the 30-m-chord track irregularity better reflects the long-wavelength components of track irregularity [25]. Thus, it is necessary to investigate 30-m-chord track irregularity in order to control the temperature deformation of the bridge in terms of train vibration and passenger comfort. Figure 10: Vertical track irregularities caused by thermal deformation of bridge superstructure: (a) south-bound; (b) north-bound. Figure 11 shows 30-m vertical track irregularities converted from the measured track geometry. The blue line represents the upper and lower limits beyond which more \"attention\" should be paid [26]. Meanwhile, to examine the influence of the amplitude of track irregularities for train and bridge accelerations, the track irregularity waveform should be measured at the time of train passing. However, in this study, the track geometry was measured during the night repair time, and thus the track geometry in the test run could only be estimated from the measured data. If we assume that the track geometry is linearly proportional to the temperature of main arch rib, the track-geometrical change \(dy_{r}/dT\) (mm/\({}^{\circ}\)C) can be estimated by the relationship  
Figure 11: Vertical track irregularities based on 30-m chord: (**a**) south-bound, summer; (**b**) north-bound, summer; (**c**) south-bound, winter; (**d**) north-bound, winter. \[dy_{r}/dT=\frac{y_{rs}-y_{r,w}}{T_{s}-T_{w}} \tag{1}\]  
where \(T_{s}\), \(T_{w}\) are the temperatures (\({}^{\circ}\)C) of the main arch rib in summer and winter, respectively, and \(y_{r,s}\), \(y_{r,w}\) are the rail levels relative to the reference point (mm) at the measuring point in summer and winter, respectively. Using Equation (1), the track-geometrical data at a certain temperature other than the temperature of measurements can be obtained, and the chord-length-based track irregularity can also be estimated. Figures 12a and 13a show the rail levels, and Figures 12b and 13b show 30-m-chord track irregularities obtained by this method in the test run. Figure 12: Vertical accelerations of train body and track vertical irregularities in test run (south-bound line, summer): (**a**) vertical track irregularities from absolute geometry at peak temperature; (**b**) 30-m-chord vertical track irregularities at peak temperature; (**c**) vertical accelerations of train body. In comparing the 30-m-chord track irregularities in Figures 12b and 13b with those in Figure 11, one can find that the difference between those for nighttime and those for daytime temperatures is not large in summer, and so the waveforms look similar. On the other hand, since the temperature of the daytime is higher relative to nighttime in winter, the waveform is not clear. This is why the train body accelerations measured in summer are higher than those in winter. However, this also implies that in winter, the train body accelerations in the early morning and nighttime are larger than those measured in the daytime. Figure 13: Vertical accelerations of train body and track vertical irregularities in test run (south-bound line, winter): (**a**) vertical track irregularities from absolute geometry at peak temperature; (**b**) 30-m-chord vertical track irregularities at peak temperature; (**c**) vertical accelerations of train body. It can be found from the comparison of Figure 12b,c and Figure 13b,c that the waveforms of the train body vertical accelerations in the time domain coincide very well with those of the 30-m-chord track irregularities.