## 4 Results and Discussion
### Parametric Studies  
#### 4.2.1 Effects of Train Speed  
Dynamic excitations along a railway track are a function of the vehicle velocity. In this study, an investigation into the effects of train speed on a turnout and sleepers was also conducted. The train speeds used ranged from 10 to 55 m/s, which respectively approximately correspond to the minimum (32 km/h) and the maximum (200 km/h) permissible speeds through switches and crossings in the UK [42]. It is noted that a movable crossing nose is commonly used at speeds over 55 m/s [6]. The relation between dynamic factor together with contact forces against speed is presented in for two cases: where the track is perfectly smooth, and a track with irregularities. The definition of the dynamic factor is the maximum dynamic force over the static load and; therefore, both the impact-induced, so called P1 and P2 forces, and dynamic wheel forces are considered. P1 is defined as the high frequency impact force due to irregularities with small wavelengths and is mostly higher than the P2 forces. Moderate frequency impact force (P2) is defined as an impact force following P1 forces and cannot exceed the threshold of 322 kN according to Rail Safety and Standards Board (RSSB) [43]. Indeed, several definitions of P2 forces exist in the literature. The definition used here is selected for clarity. By contrast, dynamic forces are defined as track forces in the range between static and impact forces. It is expected that impact forces are higher than dynamic forces on an ideal track where dynamic forces are equal to static forces. Nevertheless, dynamic forces could be higher than static values or even P1 forces, on the track with irregularities, based on the severity of the irregularity and the vehicle speed. This possibility is noticeable in Figure 5a. In ideal cases, the dynamic factor is purely due to impact forces. Conversely, dynamic forces prevail at lower speeds (up to 30 m/s) with irregularities present; therefore, the dynamic factor fluctuates around the ideal case below 30 m/s. Furthermore, the maximum forces could exist anywhere along the turnout at speeds below 30 m/s. Contrarily, the dynamic behaviors under both track conditions show similar properties over the speed of 30 m/s. The case with irregularities has a slightly higher dynamic factor than the ideal case. This is due to the selected track irregularities and the contact force formulation. Here, track irregularities have extra contributions to contact forces, which may be accepted as degradation. As can be seen from the figure, the non-linear correlation between dynamic factor and velocity shows that higher velocities cause higher impact forces for both cases and dynamic factors could reach up to 3.2. It is worth mentioning that the instant wheel load or impact force, here approximately 318 kN, is close to the limit of the permissible wheel force which is defined as 322 kN by RSSB [43]. However, the P1 portion of the impact induced wheel forces could be higher [36; 44; 45] than this threshold, but they are mostly acceptable as the duration of the impact is small. As aforementioned, both numerical studies and field measurements [7; 11; 32; 40] show that the highest contact forces and vertical accelerations of the wheelsets are observed at the crossing panel, particularly at the crossing nose. The common insight in these studies is that the most critical part of a turnout is the crossing panel. Nevertheless, such a conclusion seems inaccurate; in [31] where it is shown that sleepers at closure panels are subjected to the highest bending moments under moving constant loads. Interestingly, the findings in the previous section confirm both results, which show that the critical section could be either at closure panel or crossing panel based on vehicle speed. To understand the origin of the discrepancy between studies, it is crucial to investigate the longitudinal bending moment distributions of turnout components for different vehicle speeds.