## 4 Numerical Simulation Test
### Model Validation  
The digital rock reconstruction workflow employed high-fidelity CT datasets processed through Mimics Research 21.0 (Materialize NV, Leuven, Belgium) to generate a mesoscale pore architecture model with 107,812 ten-node tetrahedral elements (T10). The reconstructed domain, geometrically constrained to \(\Phi\)50 mm \(\times\) H100 mm cylindrical  
Figure 10: Threshold segmentation of denoised images using the ResUNet model. Figure 9: ResUNet prediction results with segmentation maps and corresponding histograms. dimensions (Figure 11), incorporated CT-derived pore spatial distributions with 98.7% volumetric congruence relative to physical specimens. This study validated the correctness of the segmentation using the following methods: In terms of pore size distribution (PSD), the equivalent diameters of pore throats (based on the maximum inscribed sphere algorithm) were extracted from the segmentation results, and the distribution curves were compared with the \(\upmu\)CT gold standard to justify the realism of synthetic structures. For topological connectivity, the Euler characteristic (which should match the Betti numbers), coordination number, and permeability predictions (with errors \(<\) 15% compared to experimental values) were calculated to justify the realism of synthetic structures. Regarding structural tortuosity, the pore centerlines were extracted using the maximal ball algorithm, the principal directional tortuosity ratios were computed, and the results were compared with resistivity method measurements to justify the realism of synthetic structures. Given the reconstruction's homogenization assumption and omission of inherent anisotropy, direct parameter transfer from laboratory-measured properties proved inadequate. A multi-stage numerical calibration protocol was therefore implemented:  
1. Initialization with experimental bulk modulus (K) and shear modulus (G);
2. Iterative adjustment of micromechanical parameters through conjugate gradient optimization;
3. Convergence validation using strain energy equivalence criteria;
4. The calibrated constitutive parameters (Table 3) govern the finite element formulation, which integrates two critical computational mechanics considerations. Micromechanical compliance tensors were derived from nodal displacement fields to capture stiffness evolution. Non-conforming surface compensation occurred via rigid platens with penalty-based contact algorithms (friction coefficient \(\upmu\) = 0.15). To accommodate the irregular surface of the reconstructed model, rigid platens were employed for displacement loading. The bottom platen was fully constrained in displacement and rotation, while the top platen was fixed in the X/Y directions and all rotational degrees of freedom, with displacement applied along the \(Z\)-axis (Figure 12). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{Density (kg/m3)} & \multirow{2}{*}{**Young’s Modulus (GPa)**} & \multirow{2}{*}{**Poisson’s Ration**} & \multirow{2}{*}{**Cohesion (MPa)**} & \multicolumn{2}{c}{**Internal Friction**} \\  & & & & **Angle (\({}^{\circ}\))** \\ \hline
2700 & 10 & 0.33 & 8 & 36 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The calculation parameters used in the numerical simulation. Figure 11: Reconstructed finite element model. (**a**) Model visualization. (**b**) Model perspective. The mechanical response characteristics of the synthetic pore architecture under uniaxial confinement are quantified in Figure 13. Numerical simulations yielded a uniaxial compressive strength (UCS) of 30.33 MPa (\(\pm\)0.25% relative error), demonstrating remarkable congruence with experimental benchmarks across three critical metrics: Elastic modulus deviation: <2.8%, Peak strain discrepancy: 1.03 \(\times\) 10\({}^{-3}\), Post-failure behavior correlation coefficient: R\({}^{2}\) = 0.974. The digital twin's stress-strain hysteresis exhibits strong alignment with physical test data in both deformation phases:  
1. Pre-peak: Tangent stiffness matching within 5% tolerance;
2.