## 3 Results and Discussion
### Void Distribution Characteristics
#### 3.3.4 The Study on Void Fractal  
The study shows that the void of cement stabilized macadam is complex and irregular, and they have statistical self-similarity characteristics [23]. The degree of irregular void distribution is different in vibration compaction and static pressure, so fractal theory is used to quantitatively describe the irregular degree of void of cement stabilized macadam mixture. Fractal theory regards the collection of voids in the mixture as a fractal body, and the distribution characteristic parameters of the fractal body are solved by fractal theory, which is fractal dimension. The fractal dimension reflects the complex degree of the geometry, the larger the fractal dimension, the higher the complexity, the less evenly the distribution of the void. The methods of solving fractal dimension include the box counting dimension method, the three-dimensional box covering method, and the islet method, etc. [24]. The box counting dimension method is widely used and the accuracy is high, so this method is used in this paper to calculate the fractal dimension of cement stabilized macadam mixture. Although different methods cause different fractal dimension results, the variation and trend of the fractal dimension should be consistent if the parameters of scan and image processing are consistent, which can reflect the characteristics of the fractal dimension of different mixtures quantitatively. The box counting dimension method can be understood in this way [25]: \"Box\" is an abstract concept, which can be a line segment, a grid, or a cube depending on different dimensions of object, and the same size of grid is used to cover the void because the images are two dimensional. If the size of the grid changes, the number of grids required to cover the entire target area changes. The relationship between the two is similar to:  
\[D_{\text{b}}\ =\ \frac{\log(N_{\text{k}})}{\log(1/\text{k})}, \tag{4}\]  
where kis unit-size of \"box\", \(N_{\text{k}}\) is the minimum number of boxes required to cover the target area of the image, and \(D_{\text{b}}\) is the fractal dimension of the research object, which represents the quantitative relationship of \(N_{\text{k}}\) increasing with the decrease of \(k\). The fractal dimension is calculated for the images of the two types of gradation (XM, GM) as well as the two different molding methods, and the results are shown in Table 11. It can be seen that the fractal dimension of void of different sections for one test piece has little variability and the coefficient of variation is generally less than 0.5%, which indicates that the fractal dimension has certain stability in the vertical direction. Figure 7: The void types of the XM and GM graded mixture. The calculation formula of void fractal dimension of cement stabilized macadam mixture [26] is as follows:  
\[D_{\text{b}}\ =\ \frac{\sum_{i=1}^{n}D_{\text{bi}}}{n}, \tag{5}\]  
where \(D_{\text{b}}\) is the void fractal dimension of cement stabilized macadam mixture, \(D_{\text{bi}}\) is the void fractal dimension in a single section image, and \(n\) is the number of two-dimensional CT of specimens of cement stabilized macadam mixture. According to the above definition, the fractal dimensions of different specimens were counted, and the results shown in Figure 8.  
According to Figure 8, different molding methods have a great influence on the fractal characteristics of void inside the mixture. The fractal dimension of voids obtained by a static pressure method is 11% higher than that by vibration compaction, with it being more likely that the former method will cause more aggregate crushing than that by vibration compaction. Besides, the vertical variation coefficient of specimens obtained by static pressure method is obviously larger than that obtained by vibration compaction and the on-site sample among the fractal dimension results of each specimens, which indicates that void of the vibration compacted specimens and the on-site sample is more uniform and continuous in the vertical distribution.