## 2 Methodology  
### Structural and Material Parameters  
The thermal property parameters of the materials in each layer of the pavement structure are provided in Table 1. These parameters of materials are collected from other verified literature [22; 23; 24]. The analysis of temperature stresses in asphalt pavements is based on the temperature field, which is mainly influenced by the modulus of elasticity and temperature shrinkage coefficient. In addition, Northwest China has a large temperature difference, and the asphalt surface layer is directly exposed to the atmospheric environment, so the temperature changes it suffers cannot be ignored. The temperature stress parameters for each structure of the asphalt pavement are shown in Tables 2 and 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **AC-16** & **AC-20** & **AC-25** & \multicolumn{2}{c}{**Cement-Treated Base**} & \multicolumn{1}{c}{**Subgrade**} & \multicolumn{1}{c}{**Soil Base**} \\ \hline Thicknesses (m) & 0.04 & 0.05 & 0.06 & 0.30 & 0.20 & - \\ Density (kg/m\({}^{3}\)) & 2300 & 2100 & 2050 & 2200 & 2100 & 1800 \\ Poisson’s ratio & 0.25 & 0.25 & 0.25 & 0.25 & 0.25 & 0.40 \\ Thermal conductivity & 3240 & 3960 & 4680 & 5616 & 5148 & 5616 \\ (J/m\(\cdot\)h\(\cdot\)\({}^{\circ}\)C) & 800 & 850 & 900 & 911.7 & 1040 & 1040 \\ \multicolumn{2}{c}{Solar radiation absorption} & & & 0.90 & & \\ Road surface emissivity & & & & 0.81 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Thermal properties of pavement materials.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**AC-16**} & \multicolumn{2}{c}{**AC-20**} & \multicolumn{2}{c}{**AC-25**} \\ \cline{2-7}
**Temperature** & **Elastic** & **Temperature** & **Elastic** & **Temperature** & **Elastic** & **Temperature** \\
**(\({}^{\circ}\)C)** & **Modulus** & **Shotificate** & **Modulus** & **Modulus** & **Shotificate** & **Modulus** & **Shotificate** \\  & **(MPa)** & **(\({}^{\circ}\)C\({}^{-1}\))** & **(MPa)** & **(\({}^{\circ}\)C\({}^{-1}\))** & **(\({}^{\circ}\)C\({}^{-1}\))** & **(MPa)** & **(\({}^{\circ}\)C\({}^{-1}\))** \\ \hline \(-30\) & 12,467.5 & 1.20 \(\times\)\(10^{-5}\) & 12,530.8 & 1.30 \(\times\)\(10^{-5}\) & 9200.3 & 1.20 \(\times\)\(10^{-5}\) \\ \(-20\) & 8580.2 & 1.40 \(\times\)\(10^{-5}\) & 8367.6 & 1.60 \(\times\)\(10^{-5}\) & 5421.7 & 1.50 \(\times\)\(10^{-5}\) \\ \(-10\) & 5741.3 & 1.70 \(\times\)\(10^{-5}\) & 4810.5 & 2.10 \(\times\)\(10^{-5}\) & 3345.6 & 1.80 \(\times\)\(10^{-5}\) \\ \(0\) & 3828.5 & 2.00 \(\times\)\(10^{-5}\) & 3142.4 & 2.60 \(\times\)\(10^{-5}\) & 2958.2 & 2.20 \(\times\)\(10^{-5}\) \\ \(10\) & 2693.5 & 2.30 \(\times\)\(10^{-5}\) & 1978.4 & 2.40 \(\times\)\(10^{-5}\) & 1637.2 & 2.00 \(\times\)\(10^{-5}\) \\ \(20\) & 1756 & 2.50 \(\times\)\(10^{-5}\) & 1441 & 2.10 \(\times\)\(10^{-5}\) & 1285.3 & 1.80 \(\times\)\(10^{-5}\) \\ \(30\) & 1188.1 & 2.30 \(\times\)\(10^{-5}\) & 1185.6 & 1.80 \(\times\)\(10^{-5}\) & 1073.2 & 1.60 \(\times\)\(10^{-5}\) \\ \(40\) & 824.6 & 1.70 \(\times\)\(10^{-5}\) & 857.6 & 1.50 \(\times\)\(10^{-5}\) & 890.3 & 1.40 \(\times\)\(10^{-5}\) \\ \(50\) & 564.3 & 1.40 \(\times\)\(10^{-5}\) & 616.5 & 1.20 \(\times\)\(10^{-5}\) & 610.2 & 1.40 \(\times\)\(10^{-5}\) \\ \(60\) & 383.8 & 1.20 \(\times\)\(10^{-5}\) & 384.7 & 1.00 \(\times\)\(10^{-5}\) & 364.2 & 1.00 \(\times\)\(10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Temperature stress parameters of surface material.