## 4 Results and Discussion
### Parametric Studies
#### 4.2.2 Effects of Rail Pads  
Rail pads are used between rails and sleepers/bearers to increase the elasticity of the track. This affects the dynamic response of the track, such as vibration characteristics and stress distributions [6]. The dynamic response is a decisive factor with regards to safety, the lifecycle of components and passenger comfort. Based on the common assumption that track stiffness is the combination of rail pad, superstructure, and substructure stiffness [6; 47], a parametric study of varied rail pad stiffness is considered, using a vehicle speed of 50 m/s. In reality, rail pads have damping properties, but the effects of rail pad damping on impact responses have been found to be minimal in comparison to overall track damping of well compacted ballast bed [48]. Moreover, damping is a complex phenomenon and expected to be less effective under impact force that cannot be damped out in such a very short duration. As a consequence, rail pad stiffness is considered.  
Figures 9 and 10 show the influence of the rail pads on the longitudinal bending moment distributions together with contact forces. It is clear that the increase of rail pad stiffness causes higher positive and negative bending moments along the turnout. The maximum positive bending moment occurs at the sleepers under the crossing nose under all conditions. Nevertheless, the maximum negative bending moments could be observed at different locations. The reason seems to be the vibration response of the vehicle. For instance, the lowest rail pad stiffness produce higher contact forces while the train moves from the longest sleeper to shortest sleeper (see Figure 9b).  
Figure 8: Flexural responses of sleepers and bearers: **(a)** Sleeper at the entrance; **(b)** Sleeper under the switch blade; **(c)** Sleeper at the closure panel; **(d)** Sleeper under the crossing nose; **(e)** the longest Sleeper; **(f)** the shortest Sleeper.  
Figure 9: Dynamic effects: **(a)** Variations in dynamic factor which correspond to rail pad stiffness; **(b)** contact forces for minimum and maximum rail pad stiffness.  
The magnitudes of the maximum positive and negative bending moments, for the maximum rail pad stiffness, differ significantly from the minimum rail pad stiffness for most of the sleepers. The maximum gap between maximum positive bending moments for maximum and minimum rail pad stiffness is 10 kNm at the crossing section and similarly, it 5 kNm between maximum negative bending moments. Interestingly, the maximum gap becomes small at the sleepers after the crossing nose. The reason is that lower stiffness excites higher forces, on those sleepers, which closes the maximum gap between maximum positive bending moments as well as maximum negative bending moments for maximum and minimum rail pad stiffness. As can be seen from Figure 9a, the rail pad stiffness influences the dynamic factor to some extent such that the effect of the rail pad appears to be insignificant. Furthermore, contact forces on the wheel-rail interface before the crossing nose appear to be less sensitive to variations in rail pad stiffness Figure 9b. Consequently, it may be concluded that softer rail pads are efficient for the lifecycle of sleepers before the crossing nose.  
The bending moment distributions of specific sleepers, with different rail pad stiffnesses, are presented in Figure 11. The bending moment distributions mostly follow similar behaviors to those seen in previous sections, such as the location of maximum positive and negative bending moments at the particular time step. It seems that the longer sleepers are influenced more by rail pad stiffness variations. More interestingly, maximum negative moments show larger deviations. For instance, the maximum positive bending moment on the sleeper under the crossing nose ranges from 12 to 18 kNm. By contrast, the location of maximum negative moments for same sleeper changes and ranges from 1 to 9 kNm. Additionally, there is no negative bending moment between loaded rails when the rail pad stiffness is 20 kN/mm.