## 3 Vertical Temperature Distribution
### Vertical Temperature Distribution  
To accurately describe the vertical temperature distribution in the CRTS-II ballastless track, the vertical temperature distributions of the EHT test and the CHT test are shown in Figure 5.  
From Figure 5a, it can be seen that at the initial state of the EHT test, the temperatures in the track layers were almost equal, and the temperature curves showed a vertical nonlinear three-stage trend. The temperature-time curves of the CA mortar layer which is at a distance of 50-80 mm from the top surface of the track slab were even, indicating that the CA mortar layer showed heat insulation effects to reduce the heat conducted from the track slab top surface to the bottom base. From Figure 5b, it can be seen that the vertical temperature distribution in the natural temperature dropping period of the EHT test was same as that in the temperature rising period, and also has a nonlinear three-stage trend. Because the natural temperature dropping rate of the CA mortar layer was slow, the thermal insulation effect on the bottom base was initiated, and when the temperature of the track slab decreased, the CA mortar reduced the heat loss from the bottom base. As the temperature of the track slab continued to decrease, the temperature of the upper part of the track slab became gradually lower than the middle part, and a negative temperature difference appeared in the track slab. According to Figure 5c, at different moments of the CHT test, the vertical temperature distributions in the track layers were similar, and the overall vertical temperature distribution curves were in the shape of \"S\". The distribution curves developed in the same direction at different moments, and the temperature was the smallest in the track layers at approximately 10:00. The highest temperature occurred in the layers between 20:00 and 0:00. To study and compare the vertical temperature distributions of the CRTS-II ballastless track on the HSR bridge under different test conditions, the vertical temperature distribution curves when the maximum temperatures occurred (the end of the temperature rising period in the EHT test and 20:00 in the CHT test) were listed, and quadratic multinomial fitting was performed by the least square method (the correlation coefficient of the fitting result was 1). Furthermore, the results were compared with the positive vertical temperature load model (Model 1) of the CRTS-II ballastless track in the Changsha area [30], as shown in Figure 6.  
Figure 5: Vertical temperature distribution curves of the track. Figure 6: Comparison of the vertical temperature distribution. The Figure 6 shows that the minimum and maximum temperatures are, respectively, 37.7 \({}^{\circ}\)C and 48 \({}^{\circ}\)C of those in the Model 1 [30]; 23 \({}^{\circ}\)C and 58.2 \({}^{\circ}\)C in the EHT test; and 35.6 \({}^{\circ}\)C and 37.5 \({}^{\circ}\)C in the CHT test. The temperature distributions obtained from the EHT test and CHT test in this paper have nonlinear, three-stage trends--which is quite different from the exponential distribution of Model 1. There are two main reasons for this difference: On one hand, the Model 1 lacked the thermodynamic parameters of the CA mortar and did not consider the influence of the CA mortar layer on the vertical temperature distribution. On the other hand, the ultimate high temperature could be simulated by the EHT test; thus, the temperature variation range in the EHT test was much larger than that of the Model 1. The CHT test simulated the no direct sunshine high temperature conditions in summer; thus, the temperature variation range was smaller than that of the Model 1.