## 6 Conclusions  
In this study, to verify and demonstrate the longitudinal level irregularity suppression effect of the ladder sleepers at the structural boundary, full-scale model tests, numerical experiments, and the laying of the ladder sleepers on the commercial line were conducted. The findings obtained are as follows:  
1. Full-scale model test was conducted to quantify the load distribution effect of the ladder sleepers. 1. The natural frequency of the ladder sleeper was identified. The first mode is 75 Hz, the second mode is 151 Hz, the third mode is 293 Hz, the fourth mode is 480 Hz, and the fifth mode is 748 Hz, and the characteristics were clearly different from the PC sleepers. 2. Full-scale model tests verified and demonstrated that the ladder sleeper had the effect of reducing the transmission of vibration to the ballast compared to the PC sleeper track, except for the natural frequency of the ladder sleeper. 2. Numerical experiments were conducted using a three-dimensional numerical analysis model, and a comparison was made between the ballasted ladder track and the conventional PC sleeper track regarding the pressure on the sleeper bottom plane.  
Figure 21: Situation of the ladder sleepers on the commercial line (Support A).  
Figure 22: Comparison of the longitudinal level irregularity of the ballasted ladder track and PC sleeper track.  
As a result of static loading analysis, the pressure on the sleeper bottom plane of the ladder sleepers was reduced to about 67% in the ballasted ladder track compared to the PC sleeper track. In addition, the range of load distribution was five sleepers on the PC sleeper track. On the other hand, in the ladder sleeper, the range was about seven sleepers. As a result of train-running analysis, the ballasted ladder track was able to reduce the pressure on the sleeper bottom plane to about 66% compared to the PC sleeper track. 3. Tracks that simulate the structural boundary were modeled, which consists of a ballast section and a rigid support section. There was a \"step-up\" running analysis and a \"step-down\" running analysis. As a result, it was revealed that laying across the structural boundary may be more effective than laying in front of the structural boundary for reducing pressure on the sleeper bottom plane in the ballast section adjacent to the structural boundary.
3. Ladder sleepers laid on the commercial line and long-term measurement of longitudinal level irregularity was carried out to verify the effect of suppressing the longitudinal level irregularity. The subsidence progress coefficient \(\beta\) was 0.00178 for the ballasted ladder track and 0.00990 for the PC sleeper track, and the longitudinal level irregularity progressed significantly slower for the ballasted ladder track than for the PC sleeper track.  
In the future, we would like to increase the number of ballasted ladder tracks laid at the structural boundary and quantify the longitudinal level irregularity suppression effect under various conditions. In this way, we would like to propose a standard ladder sleeper structure according to the laying conditions.  
Conceptualization, T.W.; methodology, T.W., K.G. and K.M.; software, T.W. and K.G.; validation, T.W., K.M. and S.M.; formal analysis, T.W.; investigation, T.W.; resources, T.W.; data curation, T.W.; writing--original draft preparation, T.W.; writing--review and editing, T.W.; visualization, T.W.; supervision, T.W.; project administration, T.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors would like to thank the East Japan Railway Company for the significant cooperation in some field measurements of this study.  
The authors declare no conflict of interest.