## 3 Calculation  
Given that the resolution of images was consistent during the image process and the resolution unit was ppi, the area of each air voids can be calculated according to the number of pixels and the area of each pixel. Since each inch has a specific number of pixels, which depends on the resolution. Thus, the area of each pixel can be calculated on the area of each inch divided by the resolution, as shown in Equation (1). The area of each air voids can be calculated based on Equation (2). Alternatively, applying software Image J could also achieve the same results, the area of each air voids could be calculated automatically in the software. \[A_{p}=\left(\frac{25.4}{r}\right)^{2} \tag{1}\]  
where:  
\(A_{p}\) = The area of each pixel, mm\({}^{2}\),  
\(r\) = resolution, ppi. \[A=nA_{p}=n\left(\frac{25.4}{r}\right)^{2} \tag{2}\]  
where:  
\(A\) = The area of each air voids, mm\({}^{2}\),  
\(n\) = the number of pixels in each air voids. In this study, all materials were considered to be non-spherical, and this is because the aggregates are non-spherical due to its corner angle, the air voids are almost all non-uniform after the mixture being compacted. In order to compare different non-uniform voids characteristics, the equivalent aperture  
Figure 5: Image Process, (**a**) Image segmentation, (**b**) Voids extraction. voids content of each section and voids with equivalent aperture ranging from 0-2 mm, indicating that although there are a lot of small voids in materials, they do not affect the air voids content remarkably. In fact, the void number with different equivalent aperture ranges in vertical sections has no apparent correlation with the air voids of each section and the highest R\({}^{2}\) is only 0.29. It means the number of each vertical equivalent aperture range may not significantly impact the total air voids. From the determinant coefficient perspective, there is no significant difference between the small size voids which have a large amount and large size voids which only have a small amount. Therefore, it can be inferred that the overall air voids content may not be influenced by a single or several sizes of voids significantly. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**R\({}^{2}\)**} & **0-2 mm** & **2-4 mm** & **4-6 mm** & **6-8 mm** & **8-10 mm** & **10-12 mm** & **12-14 mm** & **14-16 mm** \\  & **Voids** & **Voids** & **Voids** & **Voids** & **Voids** & **Voids** & **Voids** & **Voids** \\  & **Number** & **Number** & **Number** & **Number** & **Number** & **Number** & **Number** & **Number** & **Number** \\ \hline Total Number of & (+) 0.79 & (+) 0.49 & (+) 0.47 & (+) 0.16 & (+) 0.13 & (-) 0.01 & (-) 0.22 & 0.00 \\ voids & & & & & & & & \\ \hline Air voids of each section (\%) & (+) 0.16 & (+) 0.02 & (+) 0.09 & (+) 0.02 & (+) 0.21 & (+) 0.29 & (+) 0.01 & 0.00 \\ \hline \hline \end{tabular} Note 1: The symbol in the bracket represents the positive (+)/negative (-) correlation.  
\end{table} 
Table 1: Coefficient Determinant Matrix. Figure 6: Voids number distribution along the vertical section. Figure 7: Correlation between the number of voids and that with 0–2 mm equivalent aperture. To further explore the relationship between voids and the equivalent aperture, the gradation of the voids number along the vertical section was drawn in Figure 8a,b. Each section in both OGFC samples shows a similar trend, which means the air voids number distribution of the material is relatively even. As the equivalent aperture range increases, the speed to accumulate voids number would decrease. When the equivalent aperture range reaches 8-10 mm in each section, the accumulated number of voids is close to the total number, which means that voids with the equivalent aperture below 10 mm account for almost all the voids. The relationship between the average accumulated voids and equivalent aperture range is shown in Figure 8c, a high correlation can be found in a quadratic polynomial with R\({}^{2}\) of 0.98.