## 4 Analysis and Discussion  
### Comparative Analysis of Field Measurements and Numerical-Analysis Results  
To evaluate the effect of track irregularities on the ballasted track on a serviced railway line due to adjacent excavation, the measured data of the vertical profile and track settlement and the numerical-analysis results were comparatively analyzed as shown in Figure 15.  
In terms of the position of the maximum vertical profile, there was a difference between the numerical-analysis and field-measurement results, and the maximum difference was approximately 3-7 mm. The field-measurement results measured by the RM sensor and the results measured by the Track master exhibited a similar trend. In all of the field-measurement results, which used the RM sensor and Track master, and the numerical-analysis results, the vertical profile was the largest at the center of the excavation site. Additionally, in the case of the HSR T1 section, the maximum vertical profile measured by the Track master was \(\sim\)6.9 mm, and the maximum vertical profile measured by the RM sensor was \(\sim\)4.7 mm, which was analyzed to be \(\sim\)31.8% smaller than the measurement value of the Track master. Figure 15: Comparative analysis between measurements of vertical profile, track settlement, and numerical-analysis results (HSR T1). (**a**) HSR T1 left rail; (**b**) HSR T1 right rail. As shown in Figure 16, in the case of HSR T2 section, the positions of the maximum vertical profile measured by the RM sensor and by the Track master (installed at the center of the excavation area) did not agree. Moreover, in the case of the RM sensor measurements and the numerical-analysis results, a large vertical profile was observed at the center of the excavation area. However, in the case of the Track master measurement, a large vertical profile was measured at a location \(\sim\)25 m away from the center of the excavation area. As a result of the vertical profile analysis, the maximum vertical profile measured by the Track master at the location at which the RM sensor was installed was \(\sim\)2.83 mm, and the maximum vertical profile measured by the RM sensor was \(\sim\)2.77 mm, which was \(\sim\)2% smaller than the value measured by the Track master. Comparative Analysis between Wheel-Rail-Interaction-Analysis Results and Field Measurements of Track Geometry  
We aimed to analyze the Wheel-Rail interaction force based on the track-irregularity data obtained from field measurements. According to previous studies [2,3], the irregularity in the vertical direction of the rail surface in contact with the wheel increases the Wheel-Rail interaction force, thus resulting in an increase in the impact force. The dynamic model considering the Wheel-Rail interaction is shown in Figure 17[2,17]. The dynamic Wheel-Rail interaction force was calculated using Equation (1) [2,3]. \[F_{dyn,\ max}=\beta\frac{M\
u^{2}}{L_{0}}\left|\frac{dz(x)}{dx}\right|_{max,\ actual} \tag{1}\]  
where \(M\) = equivalence mass (Wheel-Rail system), \(L_{0}\) = reference wavelength, \(z=z_{0}sin(2\pi vct/L)\), and \(\beta\) = dimensionless calibration factor. Figure 16: Comparative analysis between measurements of the vertical profile and track settlement and numerical-analysis results (HSR T2). (**a**) HSR T2 left rail; (**b**) HSR T2 right rail. The dynamic model of the track that considers the Wheel-Rail interaction force is based on a principle which allows the calculation of the increase in the inertia force caused by the irregularity of the rail surface in contact with the wheel attributed to the increase in the Wheel-Rail contact load. The Wheel-Rail interaction force was analyzed for each speed range as shown in Figures 18 and 19 using the vertical profile data obtained from the field measurement. Figure 17: Mass-stiffness combinations in the wheel- rail system. Figure 18: Analysis of Wheel-Rail interaction forces at different train speeds (HSR T1). (**a**) Left rail; (**b**) Right rail.