## 5 Sensitivity Analysis of Thermal Conductivity
### Effects of Air Void  
In this article, the asphalt concrete was thought to be a biphasic heterogeneous material. However, when the asphalt mixture is not fully mixed, asphalt concrete may have air voids distributed nonuniformity. Due to the fact that air voids have an influence on the thermal conductivity of asphalt concrete, it is necessary to study this issue further.  
In total, 6 sets of three-dimensional heterogeneous asphalt concrete digital specimens were developed, and were marked as D1-D6. The dimensions and material parameters of these digital specimens were the same as those in Section 4. The thermal conductivity of air was set as 0.025 Wm\({}^{-1}\)K\({}^{-1}\). In these 6 groups of specimens, it is assumed that the air voids size was all 1 mm, and six different percentages of the air void were increased from 0% to 10% by 2%, respectively. The effective thermal conductivities of specimens D1\(\sim\)D6 with different air void contents were calculated through the method in this paper, as shown in Figure 12. In general, the prediction results indicated that the thermal conductivity gradually decreased as the air void content increased, which was the same as the results in previous study [25]. Furthermore, each 2% increase in air void reduced the effective thermal conductivity by approximately 3.5%.  
Figure 11: Effect of coarse aggregate type on asphalt concrete thermal conductivity.  
Figure 10: The effective thermal conductivity ratio of C1–C4 to A1.  
To study the distribution nonuniformity of air voids, three groups of cube asphalt concrete specimens were generated, which were noted as E1-E3, respectively. The air voids in specimen E1 were uniformly distributed, and the air voids in specimen E2 and E3 were evenly distributed across the 15% of the total volume of the specimens, as shown in the gray shaded part in Figure 13. All other variables, except the spatial distribution of air voids, were consistent with the stochastic model D4.  
Figure 14 illustrates the predicted effective thermal conductivity from each model. This study found that the air void distribution of asphalt concrete affects its thermal conductivity. Compared with the uniform model (E1), when the pores perpendicular to the thermal conductivity calculation direction (E2) are nonuniform, the effective thermal conductivity will increase, and when the pores parallel to the thermal conductivity calculation direction (E3) are nonuniform, the effective thermal conductivity will decrease.  
Figure 12: Effect of air void.  
Figure 13: Schematic diagram of air voids distribution in specimen (**a**) E2 and (**b**) E3.  
When viewing specimen E2 from a macroscopic perspective, it can be regarded as an approximate parallel model, as shown in Figure 13. On the contrary, specimen E3 can be regarded as an approximate series model. Thus, the effective thermal conductivity of specimen E2 could become closer to the theoretical maximum, while that of specimen E3 would be closer to the theoretical minimum. To summarize, the influence of air void nonuniformity on the thermal conductivity mainly depends on the concentration patten of the air voids.