## 3 Effects of the Mortar Disengagement on Dynamic Performances of the Vehicle- Track System
### Impacts of Mortar Disengagement on the Vehicle Performances  
#### 3.1.1 Evaluation of the Vehicle Operation Safety  
The vertical wheel-rail contact force and the wheel load reduction rate are usually exploited to evaluate the vehicle operation safety. The vertical contact force is evidently influenced by the track dynamic unevenness induced by mortar disengagement. Since the wheel load reduction rate is deduced from the vertical wheel-rail contact force, formulated by Equation (9), it is susceptible to the mortar disengagement, as well:  
\[R=\frac{\Delta P}{P}=\frac{P_{d}-P_{st}}{P_{st}}, \tag{9}\]  
where \(R\) means the wheel load reduction rate, \(\Delta P\) is the amount of wheel load reduction, \(P\) is the average wheel load of the left and right wheels and \(P_{d}\) and \(P_{st}\) are the dynamic and static wheel loads, respectively. The vertical wheel-rail contact forces with and without mortar disengagement are shown in Figure 9. It demonstrates that the amplitudes of wheel-rail force both in the disengagement zone and in the adjacent undamaged zone are significantly affected because of the mortar disengagement. The maximum wheel-rail force appears when the vehicle passes through the disengagement zone. Therefore, in the following analysis, for investigating the influence of mortar disengagement on the wheel-rail system performance, the maximum dynamic responses of vehicle structures are obtained either in the disengagement zone or in the neighboring undamaged zone. Figure 10 shows the maxima of the vertical wheel-rail contact forces and wheel load reduction rates with different mortar disengagement lengths (LMDs) and mortar disengagement heights (HMDs). In Figure 10, the maxima of wheel-rail forces and wheel load reduction rates increase with the increase of LMD and HMD. The effect of mortar disengagement on the vertical wheel-rail contact force is basically the same as the wheel load reduction rate. When LMD is greater than 1 m, the wheel-rail contact force and wheel load reduction rate increase apparently with the increase of HMD. For a constant LMD, when HMD reaches a special value, the maximum wheel-rail contact force keeps constant with the increase of HMD. This is because the slab cannot come into contact with the mortar layer when HMD is larger than the special value even though the vehicle passes through the mortar damage zone, and the mortar layer no longer plays a role of support. Thus, the maximum wheel-rail contact force remains basically unchanged with the increase of HMD. The mortar disengagement develops into a mortar void and special values of HMD and LMD are the critical sizes of the mortar void. A mortar void is the result of the  
Figure 9: Vertical wheel–rail contact forces in the time domain. further development of mortar disengagement. As the LMD is 0.5 m, 1 m, 1.5 m and 2 m, the corresponding mortar void heights are 1 mm, 1.5 mm, 2 mm and 4 mm, respectively. In the following analysis of some figures, the results of the mortar void will no longer be displayed. Figure 10a,b illustrate that when LMD is no more than 1 m, mortar disengagement hardly exerts influence on the maximum wheel-rail contact forces and wheel load reduction rate. The maximum growth rates are only 1.3% and 7.6% with regard to the maximum wheel-rail contact forces and wheel load reduction rate compared with that without mortar disengagement. When LMD is 1.5 m and 2 m, respectively, the maximum wheel-rail contact forces increase by 10.77% and 38.35%, and the maximum wheel load reduction rates increase by 30.35% and 120.83%. Meanwhile, as LMD reaches 2 m and HMD reaches 2 mm, the maximum wheel-rail contact force exceeds the critical value of 170 kN. When LMD reaches 1.5 m and HMD is no more than 2 mm, the maximum wheel-rail forces and wheel load reduction rates linearly increase with the increase of HMD. The slopes of linear fitting are 11.28 kN/mm and 0.04/mm for the maximum wheel-rail forces and wheel load reduction rates, respectively.