## 2 Temperature Field Fitting and Simulation of CRTS III Slab Track
### Simulation Analysis of CRTS III Slab Track Deformation  
The research on the thermal stress of an object is the process of obtaining the stress and strain of the object by knowing the temperature distribution inside the object. In this study, finite element software was used to fit the data results of the temperature field obtained by simulation. The vertical temperature load distribution of the slab track was applied according to the function formula fitting the relationship between the temperature and the slab track depth in MATLAB. The temperature division of the slab track model is shown in Figure 8.  
The temperature field of sequential coupling thermal stress determines the stress and strain field in the analysis, and the stress and strain field does not affect the temperature field. The obtained stress and strain field was used as a known condition for thermal stress analysis. The stress-strain simulation model of the ballastless track was established according to the parameters shown in Table 3 [27]. \begin{table}
\begin{tabular}{c c} \hline
**Material** & **Properties** \\ \hline \multirow{4}{*}{Fail} & Linear expansion coefficient: 1.2 \(\times\) 10\({}^{-5}\)/\({}^{\circ}\)C \\  & Elastic modulus: 2.1 \(\times\) 10\({}^{11}\) pa \\  & Density: 7850 kg/m\({}^{3}\) \\  & Poisson ratio: 0.3 \\ \hline \multirow{4}{*}{Fastener} & Vertical stiffness: 50 kN/mm \\  & Transverse stiffness: 35 kN/mm \\  & Fastener spacing: 0.65 m \\ \hline \multirow{4}{*}{Slab track} & Linear expansion coefficient: 1 \(\times\) 10\({}^{-5}\)/\({}^{\circ}\)C \\  & Elastic modulus: 3.6 \(\times\) 10\({}^{10}\) pa \\  & Density: 2500 kg/m\({}^{3}\) \\  & Poisson ratio: 0.2 \\ \hline \multirow{4}{*}{Self-compacting concrete (SCC)} & Linear expansion coefficient: 1\(\times\)10\({}^{-5}\)/\({}^{\circ}\)C \\  & Elastic modulus: 3.25 \(\times\) 10\({}^{10}\) pa \\ \cline{1-1}  & Density: 2450 kg/m\({}^{3}\) \\ \cline{1-1}  & Poisson ratio: 0.2 \\ \hline \multirow{4}{*}{Base plate} & Linear expansion coefficient: 1 \(\times\) 10\({}^{-5}\)/\({}^{\circ}\)C \\  & Elastic modulus: 3.25 \(\times\) 10\({}^{10}\) pa \\ \cline{1-1}  & Density: 2500 kg/m\({}^{3}\) \\ \cline{1-1}  & Poisson ratio: 0.2 \\ \hline \end{tabular}
\end{table} 
Table 3: Thermodynamic parameters of the ballastless track displacement simulation model. Figure 8: The temperature division of the slab track. Based on the above parameters, the stress-strain simulation model of ballastless track was established, and a slab was selected for stress and strain analysis. The size parameters of the model have been given. In the stress-strain simulation model of ballastless track, the rail mesh size is 200 mm. The mesh sizes of slab track, self-compacting concrete, and base plate are 50 mm. In the established finite element model, the lower surface of the slab track is bound to the upper surface of the self-compacting concrete, and the lower surface of the self-compacting concrete is bound to the upper surface of the base plate. The foundation can be divided into three types: elastic foundation, plastic foundation, and elastic-plastic foundation. The foundation under the ballastless track base plate is an elastic foundation. The model uses the grounding spring to simulate the ballastless track foundation, and its supporting stiffness is 76 MPa/m. The initial temperature of the model is set at 25 \({}^{\circ}\)C. Ballastless track is generally subjected to an overall temperature load and a positive/negative temperature gradient load. The temperature rise and fall of the track structure will lead to the expansion or contraction of the slab track, and the temperature gradient will cause warping deformation of the slab track. The combined action of the two cases may lead to varying degrees of deformation of the slab track. Table 4 shows the displacement changes in the middle and corner of the slab under the conditions of heating and cooling. It can be seen that the displacement of the slab is positive due to the thermal expansion of the slab during heating.