## 3 Calculation
### Horizontal Voids Distribution  
As Figure 10 shows, a similar trend can be found as a vertical equivalent aperture range distribution. when the equivalent aperture is above 4 mm, the number of voids would decrease as then range increases. For the range from 0-2 mm and 2-4 mm, the numbers of voids are compatible. In addition, in Figure 10, it is more apparent that the number of voids with small equivalent aperture ranges account for a large proportion, which is more than 90% of the total voids number. The correlations between the parameters in Table 2 and the equivalent aperture were studied, and the results were shown in Table 2. It can be noticed that in horizontal sections, the number of voids still has a high correlation with the equivalent aperture ranging from 0-2 mm, whose R\({}^{2}\) is 0.71. As Figure 11 shows, as the total number of voids increases, the number of voids whose equivalent aperture ranges from 0-2 mm would increase. Therefore, in horizontal sections, the 0-2 mm equivalent aperture voids still account for a large proportion of the total voids. Similar to the vertical sections, the 0-2 mm equivalent aperture voids in the horizontal sections has a poor correlation with the air voids, while its R\({}^{2}\) is the highest among all equivalent aperture ranges. In addition, in horizontal sections, the total air voids would not be impacted by one or several sizes of voids, which is similar to vertical sections. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **0–2 mm** & **2–4 mm** & **4–6 mm** & **6–8 mm** & **8–10 mm** & **10–12 mm** & **12–14 mm** & **14–16 mm** \\
**R\({}^{2}\)** & **Voids** & **Voids** & **Voids** & **Voids** & **Voids** & **Voids** & **Voids** & **Voids** \\  & **Number** & **Number** & **Number** & **Number** & **Number** & **Number** & **Number** & **Number** \\ \hline Total Number & \multirow{2}{*}{(+) 0.71} & \multirow{2}{*}{(+) 0.55} & \multirow{2}{*}{(+) 0.05} & \multirow{2}{*}{(+) 0.04} & \multirow{2}{*}{(+) 0.02} & \multirow{2}{*}{(+) 0.05} & \multirow{2}{*}{(+) 0.39} & \multirow{2}{*}{(+) 0.22} \\ of voids & & & & & & & & \\ \hline Air voids of & \multirow{2}{*}{(+) 0.27} & \multirow{2}{*}{(+) 0.15} & \multirow{2}{*}{(+) 0.04} & \multirow{2}{*}{(+) 0.01} & \multirow{2}{*}{(+) 0.22} & \multirow{2}{*}{(+) 0.03} & \multirow{2}{*}{(+) 0.20} & \multirow{2}{*}{(+) 0.01} \\ each section & & & & & & & & \\ \((\%)\) & & & & & & & \\ \hline \hline \end{tabular} Note 2: The symbol in the bracket represents the positive (+)/negative (-) correlation.  
\end{table} 
Table 2: Coefficient Determinant Matrix. Figure 10: Voids number distribution along the horizontal section. The gradation of voids number in OGFC samples along the horizontal sections was drawn in Figure 12a,b. Each section in both samples shows a similar trend. As the equivalent aperture 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 is similar to the vertical cases. The relationship between the average accumulated voids area and the equivalent aperture is shown in Figure 12c, a high correlation can be also found in a quadratic polynomial with R\({}^{2}\) of 0.98. From Figure 12c, the speed to accumulate voids number would decrease as equivalent aperture increases, which is similar to the cases in vertical sections. Figure 11: Voids number distribution along the horizontal section. Figure 12: Cont. The relationship between the accumulated voids areas and equivalent aperture range along horizontal sections is shown in Figure 13a,b. It could be found that when the equivalent aperture ranges from 4-6 mm, 6-8 mm, 8-10 mm, 10-12 mm, and 12-14 mm, the accumulated voids areas have a relatively high fluctuation.