## 5 Conclusions  
In this study, an analysis model for the interaction of a rail-track-bridge system was proposed. A fastener spring between the rail and the track and a friction spring between track and bridge were defined. An analysis on the track-bridge interaction was consistently performed based on a sequential analysis scheme. In particular, the following conclusions have been deduced by faithfully analyzing the longitudinal behavior when only frictional resistance exists before anchors are installed.  
The frictional longitudinal resistance can be replicated by a bilinear spring similar to the longitudinal resistance of a fastener. Its maximum resistance is determined by the friction coefficient between the track slab and the bridge deck.  
A separate analysis scheme overestimates the maximum resistance because the longitudinal resistances for the temperature and train load are simply summed. Accordingly, the possibility of a slip occurring due to the train load is underestimated. The QHT without anchors has only the frictional resistance between the track and bridge and can slip over the bridge in the longitudinal direction. Therefore, applying a sequential analysis scheme where temperature and train loads are considered sequentially is appropriate.  
The additional rail stress can adversely increase due to the relative displacement in the track segment when train traction/braking load is applied. The friction coefficient under the QHT should be maintained at 0.3 or higher before anchor installation. When the frictional coefficient may become excessively small, low-speed operation should be guided so as to not induce traction/braking loads.  
A relative slip between the track and bridge due to the temperature load occurs in all cases regardless of the friction coefficient because it is only supported by the frictional resistance from the self-weight of the track slab. In contrast, a relative slip due to train traction load occurs at the critical friction coefficient of 0.3 or below.  
The maximum slip due to the temperature load was less than 10 mm. The final relative displacement will be less than this maximum value, as the temperature is repeatedly altered on a daily basis. The secondary slip due to the train load is smaller in size than the first slip due to the temperature load; however, the secondary slip may accumulate if trains are operated, as it continuously works in the same direction. When the friction coefficient is 0.5 or higher, only the first slip due to the temperature load occurs without the secondary slip due to the train load; hence, the longitudinal displacement from the train operation does not accumulate. When the friction coefficient is 0.3 or less, the secondary slip occurs from the train operation, which eventually accumulates if trains are operated repeatedly, thereby making it difficult to control the longitudinal displacement.  
As constantly maintaining the friction coefficient at actual sites is difficult, anchors should be installed promptly after constructing QHTs to fix on the bridge. In this study, the proposed sequential analysis in which the frictional resistance at the underside of the track segment is taken into consideration can be useful for determining the critical friction coefficient and the appropriate longitudinal resistance of a rail fastener, as well as for verifying track safety.  
Formal analysis and writing, S.C.; methodology and writing, K.-C.L.; validation, S.Y.J.; project administration, I.L.; supervision and investigation, W.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the R&D Program of The Korea Railroad Research Institute, grant number PK2004B1.  
The authors declare no conflict of interest.