## 3 Results and Discussion
### Void Distribution Characteristics
#### 3.3.2 The Study on Vertical Distribution of Void  
The images obtained by X-ray CT scan are two-dimensional images. Some studies have shown that the finite information of two-dimensional images can reflect the three-dimensional void information of the mixture when the number of scanned sections is greater than 32, with a guarantee rate of 95% and an error control of 2.5%. In this paper, for each specimen, 90 vertical cross-section images were selected for data collection after removing the upper and lower 5 mm images of the end sections. The results show that they could meet the research requirements. The size and number of voids of each section of GM and XM graded mixture specimens were calculated to study the uniformity of the vertical distribution of the void parameters of mixture. The specific parameters include [19]: The number and average diameter of cross-sectional void, where the diameter of cross-sectional void is the diameter of the equivalent circle of the average void of each section. The mathematical expression is as follows:  
\[d=\ 2\ \times\ \sqrt{\frac{A}{N\pi}}, \tag{1}\]  
where \(A\) is the total area of the void extracted from a cross-sectional image of the mixture, and \(N\) is the number of voids extracted from a cross-sectional image of the mixture. As seen from Figure 5, the size and number of voids of the specimens of GM and XM graded cement stabilized macadam mixture molded by static pressure and vibration compaction are generally characterized by uneven longitudinal distribution. The specimens can be divided into \"top\", \"middle\", and \"bottom\" in depth. According to different molding methods graded by GM and XM and on-site sample, the curve shape of the number of cross-sectional voids shows the characteristics of \"high at both ends and low at middle\". This is because the number and size of void of a top and bottom mixture \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**The Types of Gradation**} & \multicolumn{3}{c}{**Different Molding Methods**} \\ \cline{2-4}  & **SP** & **VC** & **OS** \\ \hline XM & 8.56 & 6.71 & 6.15 \\ GM & 9.32 & 7.13 & 6.46 \\ \hline \hline \end{tabular} SP is static pressure, VC is vibration compaction, and OS is on-site sample.  
\end{table} 
Table 10: The reconstructed void (%) of different molding mixtures. is large in the process of molding the cement stabilized macadam mixture due to the disturbance of the molding and cutting machine on the specimens. Different molding methods have a greater influence on the number and size of the void of mixture. The number and equivalent diameter of void of staticpressure specimens is larger than vibration specimens. And the two curves corresponding to staticpressure specimens show large fluctuations, which fluctuates with the depth of specimens, and there is a phenomenon that the distribution of top and bottom is obviously asymmetric. The reason is that traditional static pressure specimens are close-grained by the static pressure between aggregates, so the moving range of aggregates is limited, and the fine aggregate and binder cannot fill the void well. In particular, for GM gradation, the static friction force of the static pressure on coarse aggregate often causes the original aggregate to crush, which will form more void. Therefore, the static pressure specimens have a large void space, large number of void, and great variability of vertical distribution. For vibration specimens, the number and size of a void still fluctuate in the vertical distribution due to tamp the aggregate when molding specimens indoor and the uneven rolling of the base, but the numerical change is not significant and the difference between the two ends is small. In addition, indoor vibration compacted instrument and road vibration roller have great compaction power, so a high frequency vibration of the mixture makes the mixture liquefied and compacted, and the aggregate is filled closely after a full movement, which greatly reduces the number and size of the void.