## 5 Sensitivity Analysis of Thermal Conductivity  
### Effects of Coarse Aggregate Orientation Angle and Aspect Ratio  
The degree of anisotropy in asphalt concrete is highly correlated with the angle and aspect ratio of the coarse aggregate utilized in that material. To ascertain the impact of aggregate orientation and aspect ratio, three different aggregate orientation angles and five different aggregate aspect ratios were considered, as shown in Table 2. Except for the coarse aggregate in Table 2 having a different orientation and aspect ratio, the other parameters of the asphalt concrete models were the same as those used in the model validation section. The above virtual models were denoted as B1\(\sim\)B15, respectively. The angle between the Z-Axis and X-Axis was known as orientation angle.  
Figure 8: Effective thermal conductivity of three-dimensional meso-structure models of asphalt concrete.  
Figure 7: Experimental setup.  
The random generation algorithm of three-dimensional aggregate in this paper was used to obtain the three-dimensional aggregate with different orientation and aspect ratios by changing the parameter setting of the three-dimensional aggregate. Moreover, the effective thermal conductivity of various models with different aggregate orientation and aspect ratios was calculated through the combined prediction method developed in this paper. The result is shown in Figure 9.  
Figure 9 indicates that the combined influence of the aggregate orientation angle and aspect ratio, which was consistent with existing literature [26]. All things being equal, it was predicted that with a decreased orientation angle, effective thermal conductivity would increase. For a bigger aspect ratio, this trend is more pronounced. As long as the aspect ratio is one, the effective conductivity of the asphalt concrete was not significantly influenced by the orientation angle. While the aggregate orientation angles were between 0\({}^{\circ}\) and 30\({}^{\circ}\), the effective thermal conductivity of asphalt concrete rises as the aggregate aspect ratio increases. Contrarily, the effective thermal conductivity of the asphalt concrete specimens diminishes with increasing coarse aggregate aspect ratio when the aggregate orientation angles are between 60\({}^{\circ}\) and 90\({}^{\circ}\). When the orientation of aggregate was between 30-60\({}^{\circ}\), the aspect ratio has small influence on the effective thermal conductivity. As a result, the aggregate has a higher effective thermal conductivity than the asphalt binder does. The effective thermal conductivity of asphalt concrete parallel to the aggregate orientation is  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Specimen Label** & **Orientation Angle of Aggregate (\({}^{\circ}\))** & **Aspect Ratio of Aggregate** \\ \hline B1 & uniformly distributed between 0–30 & 1 \\ B2 & uniformly distributed between 0–30 & 1.5 \\ B3 & uniformly distributed between 0–30 & 2 \\ B4 & uniformly distributed between 0–30 & 2.5 \\ B5 & uniformly distributed between 0–30 & 3 \\ B6 & uniformly distributed between 30–60 & 1 \\ B7 & uniformly distributed between 30–60 & 1.5 \\ B8 & uniformly distributed between 30–60 & 2 \\ B9 & uniformly distributed between 30–60 & 2.5 \\ B10 & uniformly distributed between 30–60 & 3 \\ B11 & uniformly distributed between 60–90 & 1 \\ B12 & uniformly distributed between 60–90 & 1.5 \\ B13 & uniformly distributed between 60–90 & 2 \\ B14 & uniformly distributed between 60–90 & 2.5 \\ B15 & uniformly distributed between 60–90 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The aggregate orientation and aspect ratio of asphalt concrete models.  
Figure 9: Effects of aggregate orientation angle and aspect ratio on effective thermal conductivity.  
higher when the aggregate orientation is inclined. In the asphalt pavement, the aggregate orientation is closer to the horizontal direction. Thus, it is inferred that utilizing smaller particles reduces the effective thermal conductivity.