## 4 Fractal Study on Microscopic Pore Structure of Zhanjiang Formation Structural Clay
### Menger Fractal Analysis of Microscopic Pore Structure in Zhanjiang Formation Structural Clay  
Data on pore distribution were collected from the three-dimensional visualization images of the microstructure reconstructed with ArcGIS, based on SEM images. To facilitate comparison, study areas of soil samples (70 \(\times\) 70 \(\times\) 70 \(\upmu\)m\({}^{3}\)) from both undisturbed and disturbed states were segmented into 13 pore size levels based on the range of measured pore diameters. The fractal dimension of the microscopic pore structure volume was calculated using Equation (13). The slope \(k\) of the linear fit, with \(\ln\left(\frac{b_{1}}{b_{0}}\right)\) as the abscissa and \(\ln\left[1-\frac{V(\frac{b_{1}}{b_{0}})}{V_{g}}\right]\) as the ordinate, was used to calculate the fractal dimension (\(D\) = 3 \(-\)\(K\)), as illustrated in Figure 8. The results of the calculations are presented in Table 6.  
Figure 8: Fractal dimension of volume distribution of microscopic pores at a vibration frequency of 20 Hz: (**a**) \(RD\) = 0.22 (20 Hz–30 min); (**b**) \(RD\) = 0.28 (20 Hz–60 min); (**c**) \(RD\) = 0.28 (20 Hz–90 min); (**d**) \(RD\) = 0.29 (20 Hz–120 min).  
Figure 8 indicates that the fractal dimensions of the pore structure volume range from 2.753 to 2.936, with \(R^{2}\) values consistently above 0.9. According to fractal theory, the fractal dimension derived from three-dimensional SEM images should lie between 2 and 3. Consequently, the results calculated and presented in Table 6, which are derived from Figure 8, comply with established fractal principles. This demonstrates that the microscopic pore structure of the Zhanjiang Formation structural clay, as reconstructed using ArcGIS under various disturbance conditions, exhibits pronounced Menger fractal characteristics. Generally, a larger pore fractal dimension indicates a more complex pore system and a more intricate spatial distribution of pores. The red line in Figure 9 represents the fitting trend line of the fractal dimension (D) as a function of the disturbance degree. Due to the significant abrupt change at the data point where D = 2.884, to better reflect the trend of change, this data point was used as a demarcation point for fitting two different types of functions. Figure 9 reveals a positive correlation between the pore fractal dimension and the disturbance degree; with increasing disturbance degree, the fractal dimension rises, suggesting a trend towards greater pore structure complexity. The pore fractal dimension is closely associated with both the pore structure and complexity of the Zhanjiang Formation structural clay, rendering it a crucial parameter for quantitatively evaluating the structural clay's pore structure characteristics. Therefore, based on the three-dimensional Menger sponge model, the complexity of the pore structure of the engineering soil can be evaluated by the pore fractal dimension.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Disturbance Degree** & **Working Conditions (Hz-min)** & \(y\) & \(R^{2}\) & \(D\) \\ \hline
0 & 0–0 & \(y=0.247x-0.691\) & 0.934 & 2.753 \\
0.22 & 20–30 & \(y=0.230x-0.104\) & 0.959 & 2.7