## 4 Finite Element Analysis of Transition Zones with High Moisture
### Results of the Finite Element Analysis  
FE simulation results of the transition zones with and without high moisture are analysed in this section. The dynamic wheel loads of Wheel 1 are shown in Figure 14. The horizontal axis represents the distance along the transition zone model, where the bridge is located between 48 m and 72 m. Dynamic wheel loads on the bridge are not analyzed here, and therefore their responses are covered by the shaded area. The dynamic wheel loads are zoomed before and after the bridge in Figure 14b,c, respectively. Figure 14: Dynamic wheel load of Wheel 1: (**a**) overview; (**b**) zoom-in of the embankment-bridge side; and, (**c**) zoom-in of the bridge-embankment side (unit: KN). Figure 13: Simulation of the transition zone with high moisture: (**a**) the reference case; (**b**) the high moisture case. As shown in Figure 14, the dynamic wheel load of Wheel 1 in the reference case is increased near the bridge, which is caused by the differential stiffness and settlement existing in the transition zone. This is one of the sources of degradation in transition zones. In addition, the dynamic wheel loads are different in the embankment-bridge and bridge-embankment sides. In the embankment-bridge side, the dynamic wheel loads are increased at a closer location to the bridge (at 47.4 m, 0.6 m from the bridge), while in the bridge-embankment side, the dynamic wheel loads are increased at a further location (at 73.2 m, 1.2 m from the bridge). This is caused by the different vehicle dynamics between the elevation and drop-off, which are theoretically studied in [17] and numerically studied in [8]. When comparing to the reference case, the dynamic wheel loads of Wheel 1 in the high moisture case are slightly increased at most of the locations before and after the bridge (43-48 m and 72-78 m), while they remain the same at further locations. This is reasonable since the stiffness of ballast is reduced only at these locations (8-sleeper distances, corresponding to 43.2-72 m and 72-76.8 m). Similarly, the slight increase is also found in the dynamic wheel loads of the other three wheels at most of the locations before and after the bridge, as shown in Figure 15. It should be noted that the dynamic wheel loads in the high moisture case are lower than that in the reference case at some individual peaks. This is caused by the dynamic vibration of the vehicle. To study the overall effect of high moisture, the statistics of increased percentage of the peaks close to the bridge (the closest seven peaks to the bridge on both sides, negative towards the bridge and positive away from the bridge, as indicated in Figure 14b,c) is performed, as shown in Table 3. The increase percentages of the dynamic wheel loads in the high moisture case with respect to those at the same location in the reference case are calculated. Figure 15: Dynamic wheel loads: (**a**) zoom-in of the embankment-bridge side of Wheel 2; (**b**) zoom-in of the bridge-embankment side of Wheel 2; (**c**) zoom-in of the embankment-bridge side of Wheel 3; (**d**) zoom-in of the bridge-embankment side of Wheel 3; (**e**) zoom-in of the embankment-bridge side of Wheel 4; and, (**f**) zoom-in of the bridge-embankment side of Wheel 4 (unit: KN). As shown in Figure 15 and Table 3, the dynamic wheel loads of all the wheels in the high moisture case are increased, where average ranges are from 0.2% (Wheel 4) to 2.6% (Wheel 1). It should be noted that the negative values in Table 3 correspond to the peaks in Figures 14 and 15 where the dynamic wheel loads in the high moisture case are lower than that in the reference case. The increase of the front wheels is higher than that of the rear wheels (Wheel 1 \(>\) Wheel 2, Wheel 3 \(>\) Wheel 4), and the increase of the front bogie is higher than that of the rear bogie (Wheel 1 \(>\) Wheel 3, Wheel 2 \(>\) Wheel 4).