## 3 Results and Discussion
### Rail Seat Forces
For example, the ratios for one of the adjacent bearers are calculated as 0.64, 0.61, 0.62, 0.59 and 0.65 from 10 m/s to 50 m/s for one unsupported bearer in Figure 11b. This outcome is also visible when relative increase considered. Relative increase is 31%, 25%, 27%, 27% and 24% under same condition. The load distribution among the bearers under an assumption that the unsupported bearers are laid at closure panel is depicted in Figure 12. The most distinct property of the figure is that fastening systems of unsupported bearers transfer significant amount of force to the bearers, such that fastening system still carries the approximately 50% percent of the load in the reference case. This behavior has not been observed nor mentioned for fully unsupported sleepers in normal track section by current and other studies [4; 5; 8; 9]. The ratios in adjacent bearers are between 0.44 and 0.71 based on their velocities and the number of unsupported bearers. The maximum ratio is observed at bearer number 35 when vehicle moves at 40 m/s and three bearers are unsupported. Although higher velocities seem to increase the magnitude of force transferred via fastening system in general, there is no certain pattern. For instance, the ratios from 10 m/s to 50 m/s are 0.51, 0.50, 0.55, 0.56 and 0.69 for adjacent bearer in the case of one unsupported bearer. For the same condition, the reference case has the ratios of 0.45, 0.40, 0.57, 0.46 and 0.54, respectively. The fluctuation in the ratios results from irregularities. As can be seen from the figure, the redistribution of loads is more uniform as a result of force carrying unsupported bearers. In Figure 13, force transferred via fastening system is presented for unsupported bearers under the crossing nose. At this section, track stiffness is also relatively high due to additional rails and longer bearers, resulting in considerable force transfer between rails and unsupported bearers. As clearly present in the figure, vehicle velocity has a significant impact on force transferred via fastening system at crossing panel owing to accumulated impact forces. In terms of the effect of unsupported bearer on the force transfer, two different characteristics could be observed. At lower speed such as 10 m/s, unsupported bearers seem to have small positive effect and slightly mitigate impact forces. In this regard, the ratio for the bearer with number of 53, which is under the crossing nose, is 0.77 in the reference case whereas it is around 0.70 for unsupported scenarios. On the other hand, higher velocities cause significant force transfer. Consequently, the ratios for same bearer are at similar level (around 1.1) for one, two and three unsupported bearers and reference cases. Nonetheless, relative increase varies with respect to velocities and number of unsupported bearer since the location of impact changes also. Regarding Figure 13b, it seems that the missing ballast support has limited impact in terms of rail seat forces. This behavior becomes evident in Figure 13a, which presents the rail seat load distribution at a particular time when the front wheel is on the unsupported bearer 53. Figure 11: The distribution of rail seat force over the bearers when unsupported bearers exist under switchblades: (**a**) at a particular time when the front wheel is on the bearer with number 20; (**b**) when maximum occurs at each bearer. Figure 12: The distribution of rail seat force over the bearers when unsupported bearers exist at closure panel: (**a**) at particular time when the front wheel is on the bearer with number 37; (**b**) when maximum occurs at each bearer. Figure 13: The distribution of rail seat force over the bearers when unsupported bearers exist under crossing nose: (**a**) at particular time when the front wheel is on the bearer with number 53; (**b**) when maximum occurs at each bearer. The longest unsupported bearers among the bearers following the bearers under the crossing nose carry less rail seat forces owing to the low dependency between two tracks (Figure 14).