## 4 Discussion
### The Extension of the Influencing Mechanism in Different Ratios of Wavelength to Amplitude  
The wavelength of frost heave refers to the length over which there is a change in subgrade elevation in the longitudinal direction. The increase in the ratio of wavelength to amplitude leads to a decreased rate of change in elevation due to frost heave, which would promote compatible deformation between slab track and subgrade. According to the monitoring data, the maximum wavelength of frost heave detected in the field is up to 40 m, most of which is between 10 and 20 m. In this section, by setting the amplitude as the typical value of 10 mm, scenarios with wavelengths of 5, 10 and 20 m are calculated. The calculated results of the three models are analyzed to study how the ratio of wavelength to amplitude affects the influencing mechanism. The maximum vertical wheel-rail force of the first wheelset under different wavelengths is shown in Figure 17a. In Model-A and Model-C, the wheel-rail force decreases as the wavelength increases. When the wavelength is 5 m and the amplitude is 10 mm, the vertical force of Model-B is even smaller. This is because the irregularity is covered by the contact loss underneath the foundation plate at the first wheelset. Significantly, only the first wheelset in Model-B shows this phenomenon, and the results of other wheelsets in Model-B are similar to those of the other two models. As the wavelength increases, the differences between the results of the three models become more and more similar. For example, the maximum wheel-rail force of Model-B is 20.82% less than that of Model-A and 46.22% less than that of Model-C when the wavelength is 5 m. When the wavelength is 20 m, the result of Model-B is 6.90% less than that of Model-C and almost the same as that of Model-A. Figure 17: Typical dynamic response of different models under different wavelengths. (**a**) Maximum vertical wheel-rail force; (**b**) Maximum vertical acceleration of track slab; (**c**) Maximum vertical interlayer contact pressure. The effects of increasing the wavelength on the maximum vertical acceleration of the car body and the track slab are shown in Figure 17b, respectively. In Figure 17b, the acceleration is selected from the same position as in Figure 12. It can be seen that the increase in wavelength results in the decrease in the acceleration. With the contact loss area becoming smaller as a result of the longer wavelength, the results of acceleration of the slab in the three models grow closer. The maximum interlayer contact pressure change in the contact loss area for different wavelengths is shown in Figure 17c. According to the model assumption, only the result between Model-B and Model-C is compared. Figure 17c shows that there is a sharp drop in the interlayer contact pressure as the wavelength increases. In Model-C, for example, the contact pressure drops from 0.62 to 0.39 MPa when the wavelength increases from 5 to 20 m. The divergence in contact pressure between the two models becomes lower as the wavelength increases. The decreasing amplitude of the contact loss area may cause a reduction in contact pressure. It can be seen from the results that as the ratio of wavelength to amplitude increases, the slab track shows better adaptability to the deformation of subgrade, the contact loss area decreases and the bottom of the ballastless track almost fits with the subgrade. Therefore, even though the ballastless track is bent by subgrade at this time, the leverage effect is not apparent anymore. When the wavelength is 20 m and the amplitude is 10 mm, the track irregularity becomes the dominant influencing factor of the frost heave. An additional uncontrolled factor in the study is the possibility that, due to the granular property of the subgrade, the contact loss area underneath the structure may be gradually compacted and reduced in the long term. Therefore, the calculation results in this paper are more conservative.