## 5 Conclusions  
The present study investigated the correlations among the vertical deformation of fixed-end arch railway bridges, long-wavelength track irregularities, and train vibration. Based on the results, the present study suggests how to evaluate the suitability of track geometry and how to prepare the maintenance plan. The conclusions drawn from this study are as follows.  
* Field measurements and a numerical analysis were used to clarify the phenomenon by which large vertical long-wavelength track irregularity is periodically generated by the thermal expansion of the bridge arch rib fixed at both ends due to seasonal temperature changes in fixed-end arch bridges. As a result, the dominant wavelength of the track irregularity is determined by the span length of the main arch.
* Long-wavelength track irregularity increases the vertical acceleration of the train body, especially in the daytime on summer days when the track irregularity is the largest. On the other hand, in winter, the temperature increases during the daytime relative to nighttime, and track irregularity becomes smaller than at nighttime, the result being that the measured train acceleration is lower than that in summer, but is expected to increase in the early morning and at night.
* When track irregularity is represented by the chord versus method with a 30-m chord, the waveform with the train body acceleration is very similar to that of the track irregularity, and the peak acceleration magnitude is also highly correlated with the peak value of the 30-m-chord track irregularity. It is considered that this is due to the fact that amplification factors of the 30-m chord in the critical wavelength band for the vertical train body acceleration are close to or larger than 1; it is also considered that it is appropriate to manage long-wavelength track irregularity with the 30-m chord when the bridge span length is less than 70 m. If the bridge span is longer than 70 m, the dominant wavelength of the track irregularity might, depending on the train speed, be close to the critical wavelength band corresponding to the natural frequency of the train suspension, and so it is necessary to further extend the chord length.
* Unlike train vibration, excitation frequency due to long-wavelength track irregularity to the bridge structure is very small compared with the natural frequency of the bridge, so that the acceleration of the bridge is hardly affected by track irregularity.
* To control long-wavelength track irregularity due to seasonal temperature changes and to prevent the degradation of passenger comfort, it is necessary during the design stage to predict vertical deformation of the bridge due to temperature change and the corresponding long-wavelength track irregularity. Also, it is preferable to determine the main span length in such a way that it does not coincide with the critical wavelength of the train.
* At the maintenance stage or before the start of train operation, readjustment of the rail height can be carried out to reduce long-wavelength track irregularity. To do so, it is recommended to measure track-geometrical errors at different temperatures and to obtain the correlation between long-wavelength track irregularity and train body acceleration from a test run.  
S.H.H. implemented in-situ measurements and data analysis for the track. S.K. contributed planning and data analysis. K.-C.L. implemented in-situ measurements and data analysis for the bridge and train, S.Y.J. developed the main research plan, implemented numerical analysis, and contributed the data analysis, S.H.H., S.K., K.-C.L. and S.Y.J. collaborated for collecting the measurement data, discussing the analysis results, and organizing the manuscript.  
This research was funded by a grant from the R&D Program of the Korea Railroad Research Institute, Republic of Korea.  
The authors acknowledge the support of Korea Railroad Corporation (KORAIL) for their cooperation during field measurements.  
The authors declare no conflict of interest.