## 4 Analysis Results and Discussion
### Applying Longitudinal Forces to Track Segments  
The longitudinal forces applied by track slab segments were analyzed to identify the track-bridge interaction depending on the friction coefficient of QHTs on the bridge. The longitudinal forces of fasteners were calculated by summing the loads delivered from eight rail fasteners installed on one track segment slab with a length of 5.12 m. The frictional longitudinal forces were calculated by summing the loads applied on friction springs under the track slab segment. When only the temperature load was applied (Figure 8a), the frictional longitudinal forces were smaller than the fastener longitudinal forces for all friction coefficients; thus, track segments slipped over the bridge deck. When both temperature and train loads were applied and the friction coefficient was 0.7 (Figure 8b), the frictional longitudinal forces were greater than the fastener longitudinal forces when the rail slipped over the fasteners. The maximum fastener longitudinal force, 307.2 kN, was calculated by multiplying the segment length of 5.12 m with the maximum fastener longitudinal forces of 60 kN/m under the train load. When the friction coefficient equaled 0.5 or less, the maximum frictional longitudinal forces were smaller than the maximum longitudinal forces of the rail fasteners. In this case, the track segment slipped over the bridge deck because a longitudinal load greater than the frictional resistance was applied. Figure 9 shows the applied longitudinal forces to each segment according to the friction coefficients. When the friction coefficient was 0.7 (Figure 9a), the bridge expanded in the negative direction when a temperature load was applied to the bridge and QHT, while the rail fasteners exhibited resistance in the negative direction because they resisted the movement of the bridge. The longitudinal load due to temperature load reached the maximum frictional resistance of 127.65 kN, thereby generating a track segment slip over the bridge deck. When the train load was applied, the rails were pushed in the negative direction. Fastener springs were applied with a longitudinal load in a negative direction for all sections. The maximum longitudinal load under a train load was 196.9 kN, which was less than the maximum longitudinal resistance of 307.2 kN with the train load taken into consideration, thereby not generating an additional slip. Figure 8: Maximum track longitudinal force with respect to friction coefficients under the QHT slab. When the friction coefficient was 0.5 (Figure 9b), the frictional resistance due to temperature load reached its maximum of 91.2 kN; thus, the track segments slipped. The maximum longitudinal load under a train load was 244.2 kN, which did not exceed the maximum longitudinal resistance of 296.0 kN under a train load, thereby not generating an additional slip due to train operation. When the friction coefficient was 0.3 (Figure 9c), the maximum frictional resistance was reduced to 54.72 kN; thus, track segments slipped under the temperature loads. The maximum resistance of 177.6 kN was reached when the train load was applied; thus, the track slipped additionally owing to the train load. When the friction coefficient was 0.1 (Figure 9d), the maximum frictional resistance was 18.24 kN, which is very small; thus, track segments slipped due to the temperature load. Even when the train load was applied, the maximum longitudinal resistance remained at 59.2 kN; thus, the track segments slipped additionally under the train load as well. When the friction coefficient equaled 0.5 or higher, the longitudinal load of the track due to temperature and train load was smaller than the maximum frictional longitudinal resistance, thereby not generating a slip due to train load. However, when the friction coefficient equaled 0.3 or less, the maximum frictional longitudinal resistance was smaller, wherein the longitudinal load to the track exceeded the frictional longitudinal resistance, thus generating a slip due to the train load.