## 2 Methodology
### Model Establishment
#### 2.2.3 Vehicle Load Modeling  
In recent years, the proportion of heavy-duty vehicles is increasing year by year, and the pavement structure is subjected to greater axle loads. Vehicles were selected to be weighed at one of the toll plazas with a high volume of truck traffic in order to determine the distribution of traffic axle loads. And their axle loads were statistically analyzed according to the full load axle load distribution factor. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Cement Stabilized Gravel**} & \multicolumn{2}{c}{**Cement-Line Gravel**} & \multicolumn{2}{c}{**Soil Base**} \\ \cline{2-7}
**Temperature** & \multicolumn{2}{c}{**Base**} & \multicolumn{2}{c}{**Subgrade**} & \multicolumn{2}{c}{**Soil Base**} \\ \cline{2-7}
**(\({}^{\circ}\)C)** & \multicolumn{2}{c}{**Elastic**} & \multicolumn{2}{c}{**Temperature**} & \multicolumn{2}{c}{**Elastic**} & \multicolumn{2}{c}{**Shrinkage**} \\
**Modulus** & \multicolumn{2}{c}{**(MPa)**} & \multicolumn{2}{c}{**Coefficient**} & \multicolumn{2}{c}{**Modulus**} & \multicolumn{2}{c}{**Coefficient**} & \multicolumn{2}{c}{**Alastic**} \\
**Modulus** & \multicolumn{2}{c}{**(\({}^{\circ}\)C\({}^{-1}\))**} & \multicolumn{2}{c}{**(\({}^{\circ}\)C\({}^{-1}\))**} & \multicolumn{2}{c}{**(\({}^{\circ}\)C\({}^{-1}\))**} & \multicolumn{2}{c}{**(\({}^{\circ}\)C\({}^{-1}\))**} \\ \hline
50 & & 2.50 \(\times\)\(10^{-5}\) & & 5.50 \(\times\)\(10^{-5}\) & & & \\
35 & & 2.35 \(\times\)\(10^{-5}\) & & 4.80 \(\times\)\(10^{-5}\) & & & \\
25 & & 1.72 \(\times\)\(10^{-5}\) & & 2.53 \(\times\)\(10^{-5}\) & & & \\
15 & 1500 & 0.72 \(\times\)\(10^{-5}\) & 1000 & 1.38 \(\times\)\(10^{-5}\) & & & \\
5 & & 0.05 \(\times\)\(10^{-5}\) & & 1.25 \(\times\)\(10^{-5}\) & & & \\ \(-\)5 & & 0.83 \(\times\)\(10^{-5}\) & & 0.63 \(\times\)\(10^{-5}\) & & & \\ \(-\)15 & & 0.50 \(\times\)\(10^{-5}\) & & 4.00 \(\times\)\(10^{-5}\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Temperature stress parameters of base layer and soil-based materials. During the statistical process, it was found that there were multiple axle types for some of the axle counts, so the models with this type of axle count were approximated in the calculations. The results for different shaft types are shown in Figure 2.  
Axle-type parameters are based on toll station statistics and include single, double, and triple axles. The distance between the shafts of different shaft types is 1.311 m. Referring to the research results of previous papers [25; 26], the tire grounding shape is simplified as a rectangle. The same dimensions were used to characterize the grounded area of the three types of axle-type tires, and the schematic of their tire grounding dimensions is shown in Figure 3.  
At present, the driving load is simplified into a triangular wave load or a sine and cosine load, and these two different load simplifications have little influence on the calculation results. The load in this study is simplified to a triangular wave load, and its action form is shown in Figure 4.  
The single action time of the triangular wave load can be calculated using the following formula:  
\[t=\frac{12r}{V}\]  
where \(V\) is the driving speed (m/s); \(r\) is the tire contact length (m); and \(t\) is the time of a single load (s). Figure 1: The 3D model of pavement structure is divided into several cells. Figure 2: Schematic diagram of different axle loads. In this study, the approximate load action time is 0.02 s, the equivalent dynamic load coefficient is 1.13, and the grounding pressures of different axial types are 0.8221 MPa, 0.6216 MPa, and 0.7520 MPa, respectively. The mesh is divided into different axial loads according to the dimensions shown in Figure 1. A temperature-displacement-coupled analysis step is used. The global size is 0.05. The unit type is an eight-node thermally coupled hexahedral unit (C3D8T). Restart analysis is established during analysis, outputting one restart request per analysis step.