## 3 Analysis of Test Results  
Based on the calculated results of pore classification and fractal dimension of pore size, the variation range of pore volume ratio and fractal dimensions of pore size of sandstone-like materials is calculated. Statistical results are shown in Table 6.  
Table 6 shows that the pore distribution in sandstone-like materials is mainly macroporous. macropores occupy the biggest proportion of total porosity, account for 73.65 % of total porosity, then followed by mesoporous pore, account for 15.54 %, and microporous pore is the least, account for only 10.82% of the total porosity. Except for the fractal dimension of individual micropore is lower than 0.70, the correlation coefficient \(\mathbb{R}^{2}\) of fractal dimension of other apertures are greater than 0.70, which indicates that calculation results of fractal dimension of aperture have high reliability in this study. Meanwhile, the fractal dimension and correlation coefficient of pore size increase with the growth of pore radius. The mean fractal dimension of mesopores and macropores are higher than 0.9436, and the mean value of correlation coefficient are higher than 0.9425, while mean values of fractal dimension and correlation coefficient of microporous pore are only 1.5406 and 0.7026. The data difference shows that the mesopore and macropore of sandstone-like materials have obvious fractal characteristics. To verify the correlation between the ratio of different pore volume, the fractal dimension of pore size and the compressive strength of materials, the correlation coefficient between variable factors and strength are calculated, and the corresponding scatter plot are drawn and shown in Figures 3 and 4. According to the correlation analysis of fractal dimension and strength of different pore sizes, correlation coefficients of fractal dimension and strength of micropore, mesopore and macropore are 0.95, 0.80 and 0.76, respectively. Combined with the scatter plot of fractal dimension and compressive strength of Figure 3, it can be found that the fractal dimension of micropore, mesopore and macropore are positively correlated with compressive strength, in which the fractal dimension of micropore has a high linear correlation with compressive strength, while the fractal dimension of the mesopore and macroporous aperture has low correlation coefficient with the strength, and the distribution of most scattered points is consistent with the trend of linear increase, but individual points deviate from the main trend line. To simplify the model calculation, the relationship between fractal dimension and compressive strength of mesopores and macropores is considered as a linear positive correlation. \begin{table}
\begin{tabular}{c c c c} \hline
**Pore Classification** & **Micropore (r < 0.1\(\mu\)m)** & **Mesopore (0.1 \(\mu\)m < r < 1\(\mu\)m)** & **Mecropore (1 \(\mu\)m < r < 100 \(\mu\)m)** \\ \hline Percentage of porosity & 0.0117–0.2496 & 0.0662–0.2460 & 0.6085–0.8563 \\ Average percentage of porosity & 0.1082 & 0.1554 & 0.7365 \\ Fractal dimension of pore radius & 1.3042–1.8055 & 2.8211–2.9791 & 2.9762–2.9990 \\ Average of fractal dimension of pore & 1.5406 & 2.9436 & 2.9934 \\ radius & 0.6627–0.8967 & 0.8483–0.9844 & 0.8891–0.9956 \\ Fractal dimension calculation & 0.7029 & 0.9425 & 0.9438 \\ Average of calculation correlation & 0.7029 & 0.9425 & 0.9438 \\ \hline \end{tabular}
\end{table} 
Table 6: Statistics of different pore fractal dimension ranges. From Figure 4, it can be seen that the pore ratio of micropore and mesopore are also positively correlated with the strength, while both the proportion of macroporous in pore volume and porosity show different change rules. The correlation coefficient between the macroporous pore ratio and compressive strength is \(-0.85\), and the correlation coefficient between porosity and strength is \(-0.93\). By analyzing the comprehensive scatter diagram, the correlation between compressive strength and the proportion of macroporous pores and porosity are highly negative linear.