## 2 Temperature Field Fitting and Simulation of CRTS III Slab Track
### Temperature Field Fitting
In the model, not only the influence of heat conduction and radiation on the upper surface and both sides of the base plate but also the influence of solar radiation on the temperature of the slab track are considered. Since the CFD software used can only load solar radiation energy on semi-transparent or transparent boundary conditions and cannot directly load solar radiation on opaque walls, it needs to use [PERSON]'s law, Formula (4) to calculate the need to load the temperature of radiation [26]:  
\[q_{rad}=\sigma\varepsilon\Big{(}T_{\rm max}^{4}-T_{\rm min}^{4}\Big{)} \tag{4}\]  
where \(\sigma\) is the Stefan-Boltzmann constant, with a value of 5.6704 \(\times\) 10\({}^{-8}\) W/(m\({}^{2}\cdot\)K\({}^{4}\)), and \(\varepsilon\) is the surface emissivity of the object, also known as the degree of blackness. The temperature field model of ballastless track was used to calculate the temperature field under solar radiation in the daytime in mid-August. As shown in Figure 3, the temperature of the track surface under the influence of solar radiation reached 46.6 \({}^{\circ}\)C at 12:00. The temperature around and at the bottom of the slab track is about 41 \({}^{\circ}\)C. It can be seen that the temperature of the base plate does not change much. Solar radiation causes the surface temperature of the slab track to rise rapidly and the slab track has poor heat transfer capacity, resulting in a large temperature gradient inside the slab track. \begin{table}
\begin{tabular}{c c c c} \hline  & **Length (mm)** & **Width (mm)** & **Height (mm)** \\ \hline Slab track & 5600 & 2500 & 210 \\ Self-compacting Concrete & 5600 & 2500 & 100 \\ Base plate & 5600 & 2900 & 200 \\ \hline \end{tabular}
\end{table} 
Table 1: Dimensional parameters of CRTS III slab track. Figure 3: Simulation results of the ballastless track temperature (12:00). Figure 4 is a three-dimensional diagram of temperature changes inside the slab track during the daytime. It can be seen that there was a negative temperature gradient inside the slab track at 6:00. The temperature gradient inside the slab track was the smallest at 8:00. After 8:00, the surface temperature of the slab track rose rapidly, and the interior of the slab track showed a positive temperature gradient. The surface temperature of the slab track formed an obvious peak at 14:00. Overall, the slab track surface temperature variation is greater than the internal temperature variation. To carry out the deformation simulation of the slab track, it was necessary to fit the internal temperature field of the slab track. The temperature distribution at each time point in the daytime of the slab track in mid-August was calculated, and the results are shown in Figure 5.  
To obtain specific temperature data for the follow-up study, the temperature data at different depths at the center of the slab track were exported and are shown in Table 2.  
Figure 4: Diagram of simulation results of temperature variation with time at different depths during the daytime. Figure 5: The overall temperature distribution of the slab track at each time. ((**a**). 6:00, (**b**). 10:00, (**c**). 14:00, (**d**). 18:00).