## 4 Numerical Simulation Test
### Different Porosity Model Test  
Porosity has a significant impact on the mechanical properties of rocks. To investigate the influence of pore structure on the mechanical properties of rock pore structure reconstruction models, a total of 21 reconstruction models with varying porosities were developed. Utilizing multiple independent CT scan datasets, this study successfully reconstructed digital rock models with controlled identical porosity (25.0 \(\pm\) 0.3%). Quantitative  
Figure 12: Boundary and loading conditions of the upper and lower platens. Figure 13: Comparison of uniaxial compression stress–strain curves between experimental test and reconstructed model. analysis demonstrated excellent reproducibility, with standard deviations of 1.2 MPa for uniaxial compressive strength (from 10 repeated tests), 0.45 GPa for elastic modulus (95% confidence interval), and 0.15% for porosity measurements (\(n=15\)). These minimal variations (all \(<3\%\) of mean values) confirm the robustness and reliability of our pore structure reconstruction methodology. Subsequently, a series of uniaxial compression tests were conducted on these models with different porosities. Initially, the rock CT images were denoised, followed by segmentation using varying thresholds to reconstruct the rock pore structure models, as illustrated in Figure 14. The porosities of each reconstruction model are presented in Table 4. Additionally, a separate reconstruction model M0 of the same size with a porosity of 0 was established to obtain the compressive strength and elastic modulus of the rock pore structure reconstruction model at zero porosity. Figure 15 depicts the stress contour plots after loading using the Mohr-Coulomb criterion. The simulation results indicate that as the porosity of the rock pore structure reconstruction models increases, the corresponding compressive strength decreases. Various models have been proposed to characterize the relationship between porosity and strength in different materials. Figure 14: Partial reconstruction models of rock pore structures with varying porosity. **(a)** The porosity is 0. **(b)** The porosity is 3.027%. **(c)** The porosity is 12.582%. **(d)** The porosity is 20.261%. The power law model [20] is expressed as  
\[\sigma=\sigma_{0}(1-p)^{b_{1}} \tag{1}\]  
where \(\sigma\) is the strength of the porous material, \(\sigma_{0}\) is the strength of the non-porous material, \(b_{1}\) is the empirical constant, and \(p\) is the porosity. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Model** & **M1** & **M2** & **M3** & **M4** & **M5** & **M6** & **M7** & **M8** & **M9** & **M10** \\ \hline Porosity/\% & 3.027 & 3.979 & 5.945 & 7.396 & 8.692 & 9.385 & 10.021 & 10.671 & 11.312 & 11.934 \\ Model & M11 & M12 & M13 & M14 & M15 & M16 & M17 & M18 & M19 & M20 \\ Porosity/\% & 12.582 & 13.243 & 13.972 & 14.747 & 15.538 & 16.341 & 17.153 & 18.107 & 19.030 & 20.261 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Reconstruction of the porosity of the model. Figure 15: Stress contour plots of partially reconstructed rock pore structure models under loading. (**a**) Stress cloud image with porosity of 0. (**b**) Stress cloud image with porosity of 3.027%. (**c**) Stress cloud image with porosity of 12.582%. (**d**) Stress cloud image with porosity of 20.261%. The logarithmic model [21] is expressed as  
\[\sigma=n\ln\left(\frac{p_{0}}{p}\right) \tag{2}\]  
where \(n\) is the empirical constant and \(p_{0}\) is the porosity when the material strength is 0. The exponential model [22] is expressed as  
\[\sigma=\sigma_{0}e^{-k_{1}p} \tag{3}\]  
where \(k_{1}\) is the empirical constant. The linear model [23] is expressed as  
\[\sigma=\sigma_{0}-c_{0}p \tag{4}\]  
where \(c_{0}\) is the empirical constant.