## 4 Analysis Results and Discussion
### Relative Slips of Friction and Fastener Springs  
The longitudinal displacement generated in a fastener spring is the relative displacement between the rail and QHT slabs. The longitudinal displacement generated in a friction spring is the relative displacement between the bridge deck and the QHT segment slabs. Figure 11 presents an example showing the behavior of a nonlinear resistance spring in a sequential analysis. The first slip occurs due to temperature when the maximum longitudinal resistance is reached due to the temperature load; subsequently, the secondary slip due to the train load occurs when the train load causes the maximum longitudinal resistance to be exceeded. When the longitudinal relative displacement is examined, the spring with the largest first slip due to the temperature load was generated at the right-end segment, while the spring with the largest secondary slip due to the train load was generated at the central segment. Figure 12a illustrates the history of the relative displacement of a fastener spring at the right end. The secondary slip due to the train load did not occur when the friction coefficient was 0.3 or higher. When the friction coefficient was 0.1, the longitudinal displacement increased to 0.69 mm, and the train load was applied after the temperature load. Then, when the applied load at the friction spring exceeded its maximum resistance, the effect of the train load was redistributed to the embankment section; thus, the relative longitudinal displacement at the fastener spring decreased. Figure 12b illustrates the history of the relative displacement of a fastener spring located at the left end of the central segment. Rail slip due to  
Figure 11: Typical sequential behavior of friction spring. Figure 10: Concept of resistance-track longitudinal force relationship. both temperature and train loads occurred when the friction coefficient was 0.3 or higher. In contrast, when the friction coefficient was 0.1, a rail did not slip due to the train load. Figure 12(a) illustrates the history of the relative displacement of a friction spring under the track segment at the right end of the bridge. The secondary slip due to the train load did not occur when the friction coefficient was 0.5 or higher, while the secondary slip occurred when the friction coefficient was 0.3. A final slip of 10.67 mm occurred when the friction coefficient was 0.1. Figure 12(b) illustrates the history of the relative displacement of a friction spring at the left end of the central segment. The secondary slip due to the train load did not occur when the friction coefficient was 0.5 or higher, while the slip due to both the temperature load and train load occurred when the friction coefficient was 0.3 or less. The maximum slip of the QHT segment occurred in the roller support at the right end of the bridge (Figure 14). Longitudinal relative displacements of 7.46 mm and 0.01 mm occurred due to the temperature and train loads, respectively, when the friction coefficient was 0.7. Longitudinal relative displacements of 9.27 mm and 1.40 mm occurred due to the temperature load and train load, respectively, when the friction coefficient was 0.1. Figure 12: Longitudinal relative slip of a fastener spring. Figure 13: Longitudinal relative slip of a friction spring. The maximum slip due to the temperature load was less than 10 mm. The actual relative displacement in actual field applications will stay less than this, as the temperature is repeatedly altered on a daily basis. The secondary slip due to the train load was smaller in size than the first slip due to the temperature load; however, secondary slips may accumulate if trains are operated, as it continuously works in the same direction. When the friction coefficient was 0.5 or higher, only the first slip due to the temperature load occurred without the secondary slip due to the train load; hence, the longitudinal displacement from the train operation was not accumulated.