## 3 Results and Discussion
### Changes of 3D Void Parameters of Asphalt Mixture during Freeze-Thaw Cycles  
3D void content, void number, average diameter, and void volume fractals of samples are employed to quantitatively evaluate the effect of freeze-thaw cycles on the internal structure of asphalt mixtures. All 3D internal structure properties for samples with different design air void contents, tested under freeze-thaw cycles, are shown in Figure 7. Figure 7a shows the void content of samples sharply rising when the design void content changes from 3% to 5%, which later becomes very smooth when the design void content changes from 5% to 7%. It matches well with the changes of reconstructed 3D images of samples with different design void contents, which increases the credibility of the 3D analysis on the internal structure of asphalt mixture during freeze-thaw cycles. Regardless of the air void content of samples, the void content increases with increasing number of freeze-thaw cycles. The magnitude of change under the initial five freeze-thaw cycles is largest, greater than the effect of the subsequent 10 freeze-thaw cycles. Those results indicate that the damage of asphalt mixtures during freeze-thaw cycles and the number of freeze-thaw cycles do not satisfy a linear relationship. It is similar to the loss law of the mechanical properties of asphalt mixtures that the damage variable can be divided into three stages, i.e., fast damage period, stable damage, and damage development period, during freeze-thaw cycles [28]. After 35 freeze-thaw cycles, the void content of the sample with a design air void content of 3% increased from 0.96% to 1.4%, the sample with design air void content of 5% increased from 4.35% to 5.92%, and the sample with design air void content of 7% increased from 6.61% to 8.31%. This reveals that the sample with higher design void content has a higher risk of damage under freeze-thaw cycles. In Figure 7b, the variation of air void number is not completely consistent with the change of void content. The air void number is not only irregular with the design air void content, but also contains disorder with the number of freeze-thaw cycles. The void number of samples with 3% design void content is the largest, followed by samples with 7% design void content and lastly samples with 5% design void content. It indicates that the void number of samples is not directly related to the design void content. The  
Figure 6: Comparison of air void in 3D of different specimens during freeze–thaw test (from left to right in Figure 5), the 3D air voids images of sample are stand for 0, 5, 15, 25, and 35 freeze–thaw cycles in order). formation of voids is random during the progress of sample preparation. Although the void number does not increase with increasing number of freeze-thaw cycles, variation of the air void number is still following a pattern. For example, the air void number of all samples increased their air void content sharply during the initial five freeze-thaw cycles. However, as the number of freeze-thaw cycles reaches 15 or 25, the air void number reduced regardless of the design air void content. Combined with results shown in Table 5, the increase in the air void number of samples under the action of initial five freeze-thaw cycles suggest that the formation of new voids exert a dominant effect to increase the air void content. Consolidation of separated air (new or existing) plays an important role on the effect of air void content with increasing number of freeze-thaw cycles.