## 4 Strength Prediction Model  
### Selection of Representative Model Parameters  
To ensure the high reliability of the rock-like material strength prediction model, model-dependent variables should include both pore size distribution and porosity parameters. However, there are many different characterization methods for material pore size distribution and porosity parameters. Therefore, the selection of representative factors has an important impact on the accuracy and operability of the model. Based on the correlation analysis of different pore volume ratio, pore fractal dimension and compressive strength in sandstone-like materials, the single factor linear regression analysis of each characterization parameter and strength is carried out, and then, the correlation analysis between dependent variables is carried out. The results are shown in Table 7.  
Table 7 shows that the linear regression coefficient of pore volume ratio and compressive strength is greater than 0.8319, the correlation coefficient between pore fractal dimension and strength is more than 0.90, and the value of \(p\) is 0.0000 (\(<\)0.05). The data show that both of the pore volume ratio and fractal dimension have a good linear relationship with compressive strength. To avoid the prediction model being not conducive to practical operation due to complex expression, this study carries out the correlation test of different pore parameters and selects the representative parameters to establish a simple strength prediction model. Test results are shown in Tables 8 and 9. The correlation coefficient between macroporous pore ratio and other parameters of porosity is higher, especially with mesopore. Moreover, the correlation coefficient between pore volume ratio and strength of macropores is 0.9582 in single factor regression analysis. In the same way, the fractal dimension of macroporous aperture has a high correlation coefficient with that of micropore and mesopore, and the correlation coefficient with the fractal dimension of the mesopore is 0.9555 particularly. Furthermore, the correlation coefficient between fractal dimension and compressive strength of macropores is also the highest. It has been proved in relevant literatures that pore size can affect \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter Type** & **Pore Structure Parameter Type** & **R2** & **F** & \(p\) **Value** \\ \hline \multirow{4}{*}{Percentage of porosity} & Porosity & 0.8731 & 171.9648 & \multirow{4}{*}{0.0000} \\  & Percentage of micro-pore & 0.8319 & 113.8068 & \\ \cline{1-1}  & Percentage of meso-pore & 0.9212 & 292.2251 & \\ \cline{1-1}  & Percentage of macro-pore & 0.9582 & 572.6658 & \\ \hline \multirow{2}{*}{Fractal dimension of pore radius} & Fractal dimension of micropore & 0.9010 & 227.5951 & \multirow{2}{*}{0.0000} \\  & Fractal dimension of mesopore & 0.9292 & 315.0203 & \\ \cline{1-1}  & Fractal dimension of macropore & 0.9360 & 292.2676 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summarizes the single-factor linear regression results of pore structure parameters and compressive strength. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pore Parameter** & **Porosity** & **Percentage of** & **Percentage of** & **Percentage of** \\ \cline{1-1}  & & **Micropore** & **Mesopore** & **Macropore** \\ \hline Porosity & 1 & \(-\)0.4766 (**) & \(-\)0.5709 (**) & 0.4856 (**) \\ Percentage of micropore & \(-\)0.4766 (**) & 1 & 0.7819 (**) & 0.7341 (**) \\ Percentage of mesopore & \(-\)0.5709 (**) & 0.7819 (**) & 1 & \(-\)0.8196 (**) \\ Percentage of macropore & 0.4856 (**) & 0.7341 (**) & \(-\)0.8196 (**) & 1 \\ \hline \hline \end{tabular} Note: (**) indicates that the correlation test is significant at a significance level of 0.01.  
\end{table} 
Table 8: Analysis of pore volume parameters. the elastic behavior and strength of rock. Under the condition of keeping the porosity of the porous material unchanged, the change of pore position will lead to the change of sample strength [45; 46].