## 1 Introduction  
Since the dynamic behavior of a train traveling on a railway bridge is sensitive to changes in track geometry due to bridge deformation, there are strict restrictions on deformation amplitude [1, 2]. In addition to vertical deformation, longitudinal expansion or contraction of a bridge increases the axial force on the rail. To control this, it is necessary to restrain excessive longitudinal deformation and/or to install rail expansion joints or special fastening devices [2, 3]. For this reason, the fixed-end arch design is often chosen for long-span railway bridges, as this type effectively controls longitudinal deformation of the superstructure by restraining deformation and rotation at the supports. However, the restraints at the supports cause vertical displacement of the arch due to temperature change, causing track-geometrical errors (which is often referred to as \"track irregularities\"), increasing train vibration, and degrading ride comfort thereby. Bridge deformation due to temperature change and resulting track irregularities does not, as general track irregularities caused by long-term bridge deflection or subgrade settlement do, show gradual growth in a certain direction; rather, it shows annual fluctuation corresponding to seasonal temperature variation; therefore, permanent maintenance is difficult. Unlike ballasted track, the geometry of which can be periodically adjusted through ballast damping and track lifting, in the case of slab track, the rail is fixed to slabs that are integrated with the bridge superstructure, which design renders periodic track-geometrical changes very difficult to deal with. To date, a number of analytical studies on the dynamic behavior of bridges during train travel have been carried out [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. On the other hand, there are relatively few studies on the correlation between bridge-deformation-caused long-wavelength track irregularities and train response. [PERSON] et al. [16] analyzed the effects of the shape, wavelength and amplitude of track irregularity on the safety and riding comfort of trains, and found that vertical track irregularity greatly affects vertical train acceleration. However, they did not consider the interaction between train and bridge. [PERSON] and [PERSON] [17] proposed a dynamic analysis model that takes into account train-track-bridge interaction by the direct stiffness and mode-superposition methods. Using this model, they assessed the effect of steel-arch-bridge vertical deformation due to temperature change on the running safety and ride comfort of high-speed trains. Based on their results, they showed that a temperature-change-induced large vertical deformation has a great effect on the safety and ride comfort of high-speed trains, but that the effect of this deformation on bridge structural safety is not significant. [PERSON] and [PERSON] [18] used three-dimensional finite element analysis to show that long-wave track irregularity caused by long-term bridge deflection due to concrete creep causes low-frequency vibration close to the natural frequency of the train suspension system. They validated their model by comparing the theoretical results with the experimental results, and proposed a track-geometrical adjustment pattern through shim insertion for avoidance of the resonance of the train suspension system. In sum, the previous studies show that long-wavelength track irregularity caused by bridge deformation have a great influence on train vibration, which depends on the bridge span length, the characteristics of the vehicle suspension system, and the train speed. The present study aimed to evaluate the correlations among the vertical deformation of fixed-end arch bridge, long-wavelength vertical track irregularity and vehicle vibrations, and to propose a management strategy for track irregularity change in an appropriate range.