## 3 Results and Discussion
### Rail Seat Forces  
In railway applications, the vehicle load is transferred via fastening system to bearers and then the ballast bed. In the absence of ballast support, the support conditions totally change in the vicinity of the unsupported bearers and the load transferred by fastening system change dramatically over unsupported bearers and adjacent bearers. In this section, uneven load distributions over the bearers are investigated based on the force transferred via fastening system. In Figure 10, the force transferred via fastening system/ rail seat force (named here for simplicity) is shown for unsupported bearers at normal track section. Four cases (i.e., one, two and three unsupported bearers and reference case) and velocities ranging from 10 m/s to 50 m/s are illustrated in the figure. The ratio is defined as rail seat force over static wheel load. The results show that the significant loss of force is obvious for the unsupported bearers, despite slightly escalation with higher velocities. On the other hand, forces increase for the fully supported adjacent bearers in all cases. In Figure 10b, the ratio ranges from 0.5 to 1.3. Furthermore, the relative increase could be as much as 32%/33%, 77%/75% and 130%/134% higher for former/latter adjacent bearers of one, two and three unsupported bearers at speed of 10 m/s. This conclusion indicates that such an outcome as indicated in [5], which was that the sleeper next to the unsupported sleeper in travelling direction is most subjected to increasing dynamic forces, could be inaccurate. Furthermore, it shows the number of unsupported bearer has a considerable effect on the load distribution. The worst is the case where three bearers are unsupported, which is 1.3 times higher than static load. It is noteworthy that the ratio is 0.5 in reference case under same condition. In contrast to number of unsupported bearers, the effect of different velocities is unclear. The irregularities seem to be decisive on the load distributions. For instance, relative increase from 10 m/s to 50 m/s, is 32%/33%, 35%/36%, 25%/27%, 24%/37% and 24%/39% for former/latter adjacent bearers of one unsupported bearers. Similar results are obtained for adjacent bearers of two and three unsupported bearers, where the locations and magnitudes of the maximum load transfer show variations. Last but not least, most of the additional loads, due to unsupported bearers, are carried by adjacent bearers as recognizable in Figure 10. Other bearers in the vicinity of unsupported bearers seem to be less effective in order to support the track against additional loads (Figure 10a). Figure 10: The distribution of rail seat force over the bearers when unsupported bearers exist at normal track section: (**a**) at particular time when the front wheel is on the bearer with number 10; (**b**) when maximum occurs at each bearer. Unsupported bearers are assumed to emerge at the switch panel under switch blades in Figure 11. The lengths of the bearers are the same as the bearers at normal track section. A perceptible difference compared to the outcomes of normal section is that force transferred via fastening system is lower due to higher track stiffness introduced by switch blades. For instance, the ratio for one of the adjacent bearers is 24% less than normal track section at 50 m/s in three unsupported bearers case in Figure 11b. Furthermore, the discrepancy observed between adjacent bearers and other bearers at normal track section partially disappear here. That means loads are distributed more evenly after unsupported bearers (Figure 11a). Peculiarly, the first unsupported bearer in the facing direction (bearer no. 21) in three unsupported bearer case transfers forces significantly due to new supporting conditions created by the separation between stock rail and switch blade, where loaded rail pushes the bearer and unloaded pulls. The effect of speed seems to be unclear at this section in terms of the ratios.