# Deformation Law and Control Limit of CRTSIII Slab Track under Subgrade Frost Heave
## 3 Mapping the Relationship of Track Irregularity under Frost Heave
### The Influence of Frost Heave Parameters  
According to field investigations of subgrade frost heave displacements in frozen soil regions [53], it has been found that the frost heave amplitude of existing high-speed railway subgrade mainly ranges from 15 to 25 mm (and up to 40 mm in particular sections), and the frost heave wavelength is generally lower than 40 m. Consequently, these frost heave parameters (a frost heave amplitude of 0-40 mm and wavelength of 0-40 m) have been analyzed in this paper.  
Given that the change rate of track irregularities reaches its maximum in the middle part of the track slab (position C), the influence of position C subgrade frost heave parameters on track irregularity has been studied. When the frost heave wavelength is set at 10 m, the effect caused by amplitudes 5 mm, 20 mm and 40 mm are analyzed. When the frost heave amplitude is set at 10 mm, the effect caused by wavelengths 5 m, 20 m and 40 m are analyzed.  
As shown in Figure 11a, when the frost heave amplitude is small, the rail's deformation curve is basically symmetrical. Moreover, the rail's deformation amplitude is basically consistent with the frost heave amplitude. When the frost heave amplitude increases, the rail's deformation increases accordingly. As shown in Figure 11b, when the frost heave wavelength is 40 m, the rail's deformation curve is basically symmetrical. When the frost heave wavelength decreases, the rail's deformation curve gradually becomes asymmetrical. When frost heave parameters increase, the range of non-uniform rail deformations gradually increases.  
As shown in Figure 11c, when the frost heave amplitude is small, the track slab's deformation is relatively small, which does not jack up the rails; as a result, the amplitude transfer ratio is less than 1.0. When the frost heave amplitude increases, both the rail's deformation and amplitude transfer ratio increase. The track irregularity's change rate increases linearly along with the increase of frost heave amplitude. When the frost heave amplitude is 5 mm, the track irregularity's change rate is only 1.8; when the frost heave amplitude is 40 mm, the track irregularity's change rate increases to 7.94, an increase of approximately 4.4 times. As shown in Figure 11d, when the frost heave wavelength is short, the track slab's warping deformation is obvious, the rail's deformation amplitude is greater than the frost heave amplitude, and the amplitude transfer ratio is greater than  
Figure 10: Change rate of track irregularity at different positions. (**a**) Distributed along the route; (**b**) maximum change rate of track irregularity.  
1.0; when the frost heave wavelength exceeds 10 m, the amplitude transfer ratio remains almost unchanged. The track irregularity's change rate decreases with the increase in frost heave wavelength, and the curve slope first increases and then decreases. When the frost heave wavelength is 5 m, the track irregularity's change rate is 3.27, and when the wavelength is 40 m, it is 0.95, a reduction of approximately 3.4 times. Both frost heave amplitude and wavelength lead to changes in the track irregularity rate, which in turn affect the rail's smoothness. The greater the frost heave amplitude and the shorter the frost heave wavelength, the greater changes in the track irregularity rate.