## 3 Results and Discussion
### Changes of 3D Void Parameters of Asphalt Mixture during Freeze-Thaw Cycles
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Volume Grades**} & \multicolumn{5}{c}{**Number of Freeze–Thaw Cycles**} \\ \cline{2-6}  & **0** & **5** & **15** & **25** & **35** \\ \hline \(<\)0.1 & 2031 & 2758 & 2119 & 1803 & 2003 \\
0.1–1 & 1206 & 1686 & 1722 & 1573 & 1517 \\
1–2 & 528 & 549 & 437 & 586 & 528 \\
2–5 & 243 & 176 & 236 & 398 & 409 \\
5–10 & 62 & 55 & 72 & 85 & 80 \\
10–20 & 17 & 11 & 15 & 19 & 26 \\
20–30 & 10 & 11 & 16 & 17 & 19 \\ \hline \(>\)30 & 6 & 7 & 11 & 13 & 14 \\ Total & 4103 & 5253 & 4628 & 4494 & 4596 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Design voids content = 5%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Volume Grades**} & \multicolumn{5}{c}{**Number of Freeze–Thaw Cycles**} \\ \cline{2-6}  & **0** & **5** & **15** & **25** & **35** \\ \hline \(<\)0.1 & 3434 & 4429 & 3494 & 3370 & 3275 \\
0.1–1 & 1006 & 1186 & 1360 & 1377 & 1403 \\
1–2 & 147 & 176 & 337 & 308 & 323 \\
2–5 & 118 & 125 & 136 & 179 & 208 \\
5–10 & 50 & 57 & 64 & 85 & 69 \\
10–20 & 17 & 20 & 25 & 29 & 34 \\
20–30 & 11 & 11 & 20 & 28 & 20 \\ \(>\)30 & 17 & 19 & 24 & 27 & 29 \\ Total & 4800 & 6023 & 5460 & 5403 & 5361 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Design voids content = 7%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Volume Grades**} & \multicolumn{5}{c}{**Number of Freeze–Thaw Cycles**} \\ \cline{2-6}  & **0** & **5** & **15** & **25** & **35** \\ \hline \(<\)0.1 & 2959 & 4347 & 3786 & 3311 & 3408 \\
0.1–1 & 1506 & 1986 & 1712 & 1707 & 1758 \\
1–2 & 328 & 349 & 437 & 454 & 467 \\
2–5 & 243 & 136 & 176 & 214 & 217 \\
5–10 & 62 & 52 & 77 & 73 & 67 \\
10–20 & 7 & 8 & 25 & 31 & 28 \\
20–30 & 1 & 4 & 8 & 6 & 7 \\ \(>\)30 & 6 & 10 & 13 & 15 & 15 \\ Total & 5112 & 6892 & 6234 & 5811 & 5967 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Design voids content = 3%. Figure 7c shows the changes of average 3D void diameter in asphalt mixtures with three types of design void content, compared before and after freeze-thaw cycles. Average air void diameter abruptly decreases at the initial stages of the test, but gradually increases during the subsequent freeze-thaw cycles regardless of the design void content. As shown in Equation (2), the change of average air void diameter is affected by the variation of void content and void number. Corresponding to the variation in void content, void number, and void volume grades during freeze-thaw cycles, the reduced void diameters in asphalt mixtures at initial stages are caused by increasing number of voids with a volume less than 0.1 mm\({}^{3}\). This demonstrates that it is the newly formed voids that greatly influence the void diameter during freeze-thaw cycles. Moreover, the average void diameter was observed to increase after the fifth freeze-thaw cycle. This result indicates that existing air voids coalesce and air void volume increases with increasing number of freeze-thaw cycles. Comparing Figure 7a,d, variations of air void content and void volumetric fractals with increasing number of freeze-thaw cycles are investigated. A strong correlation between the air void content and void volumetric fractals in the hot mix asphalt mixture is observed. According to the definition of void volumetric fractals, if the value is closer to 2, its shape approximates a sphere in 3D space. Considering both Figure 7d and Table 4, void volumetric fractals of the sample with design void content of 3% are close to 2, and the majority of air voids' volume is less than 1 mm\({}^{3}\). This demonstrates that void volumetric fractals are related to single void volumes during sample preparation, i.e., the smaller the void volume is, the higher similarity the shape possesses to a sphere. As the air void  
Figure 7: Effect of design void content on internal structure evolution during freeze–thaw cycles. content increases, larger voids emerge and hence, void volumetric fractals become larger.