## 4 Simulation of Temperature Field and Thermal Stress in HMAC Pavement  
### Analysis of Temperature Field  
The following assumptions were made in the establishment of the temperature field model: (1) the pavement layers were homogeneous and isotropic continua; (2) the temperature gradient in the horizontal direction was zero, and only the transfer of heat flow in the vertical direction was considered; and (3) there was continuous contact between the layers of the pavement, and the temperature and heat flow between the layers was continuous. The temperature parameters of each layer of pavement materials were obtained from related literature [35; 36; 37; 38; 39]. The results are shown in Table 7.  
Air temperature data over a 24-h span in summer, as shown in Table 8, was applied in ABAQUS to calculate the temperature field of HMAC pavement. The temperature changes of each structural layer over the 24-h period are shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Structural** & **Depth** & **Density** & **Theml Conductivity** & **Heat Capacity** & **Solar** & **Road Surface** & **Absolute** \\
**Layer** & **(cm)** & **(kg-m-\(\mathbf{\hat{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{   }}}}}}}}}}}}}\))** & **(\(\mathbf{\hat{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{   }}}}}}}}}}}}}}}\))** & **(\(\mathbf{\hat{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ }}}}}}}}}}}}}}}}\))** & **(\(\mathbf{\hat{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ }}}}}}}}}}}}}}}}}\))** & **Absorption** & **Consissivity \(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ }}}}}}}}}}}}}}}}\)** & **Zero T\({}_{\mathbf{Z}}\) (\({}^{\circ}\)C)** \\ \hline AC-13 & 4 & 2 500 & 3 600 & 900 & 0.9 & 0.81 & \(-\)273 \\ HMAC-20 & 10 & 2 500 & 4 680 & 925 & 0.9 & 0.81 & \(-\)273 \\ ATP-25 & 18 & 2 450 & 3 600 & 800 & 0.9 & 0.81 & \(-\)273 \\ CTB & 52 & 2 400 & 5 600 & 910 & 0.9 & 0.81 & \(-\)273 \\ LFTB & 72 & 1 800 & 5 200 & 940 & 0.9 & 0.81 & \(-\)273 \\ Soil & - & 1 850 & 5 600 & 1 000 & 0.9 & 0.81 & \(-\)273 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Temperature parameters of HMAC pavement. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Time (h)** & **Air Temperature** & **Time (h)** & **Air Temperature** & **Air Temperature** & **Air Temperature** \\  & **(\({}^{\circ}\)C)** & & **(\({}^{\circ}\)C)** & **Time (h)** & **(\({}^{\circ}\)C)** \\ \hline
1 & 24.5 & 9 & 29.2 & 17 & 33.7 \\
2 & 23.7 & 10 & 31.8  
As shown in Figure 9, because of the decreasing of air temperature, tensile stress was generated by the shrinkage of pavement materials and reached its peak at about 4:00 from 0:00 to 6:00. In contrast, the pavement material began to expand, and generated compressive stress with the gradual increasing of air temperature after 6:00. The maximum compressive stress was reached at the same time as the maximum temperature. Since the surface layers were most affected by the outside air temperature, the temperature field in these layers had the greatest change over the time period; therefore, the thermal stress in the surface layers had the greatest range of values. The maximum thermal stress appeared on the surface of the pavement and had a value of \(-\)0.7 MPa. As the depth of the pavement increased, the thermal stress decreased continuously to approximately 0 in the base and sub-base layers.