## 3 Calibration and Verification of Model Mesoscopic Parameters
### Calibration of Mesoscopic Parameters
As a result, the specimen exhibits a substantial load-bearing capacity even after experiencing partial damage. Figure 5b illustrates that the peak strength and modulus of elasticity of the perforated symmetric fissure-hole sandstone specimens demonstrate varying degrees of reduction compared to the macroscopic mechanical parameters of the intact sandstone specimens outlined in Table 2. Moreover, the specimens' peak strength and elastic \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mesoscopic Parameters** & **Value** & **Mesoscopic Parameters** & **Value** \\ \hline Particle size range, (mm) & 0.2\(\sim\)0.3 & Particle friction coefficient \(\mu\) & 0.5 \\ Particle size ratio \(R_{max}/R_{min}\) & 1.5 & Particle Young’s modulus \(E\) (GPa) & 50 \\ Particle density \(\rho\), (kg/m\({}^{3}\)) & 2500 & Bond strength \(pb\_{T}\) (MPa) & 10 \\ Particle stiffness ratio \(k\) & 2.0 & Bond stiffness ratio \(pb\_{K}\) & 2.0 \\ Radius factor \(\overline{\lambda}\) & 1.0 & Bond Young’s modulus & 50 \\ Particle dissipation energy \(Damp\) & 0.7 & \(pb\_{E}\) (GPa) & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PFC2D mesoscopic parameters. Figure 4: Indoor test loading system and samples. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Compressive Strength** & **Elastic Modulus** & **Natural Density** & **Saturated Density** & **Porosity (\%)** \\  & **(MPa)** & **(GPa)** & **(kg/m\({}^{3}\))** & **(kg/m\({}^{3}\))** & \\ \hline Values & 75.92 & 38.87 & \(2.51\times 10^{3}\) & \(2.65\times 10^{3}\) & \(1.6\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Partial geomechanical characteristics of the selected intact sandstone specimen. modulus decrease as \(\alpha\) decreases. These observed phenomena indicate that the presence of symmetric fissure-hole combination defects deteriorates the mechanical properties of the sandstone. Specifically, the dip angle (\(\alpha\)) of the perforated symmetric fissure impacts the mechanical properties of hole-containing sandstone under uniaxial compression, with lower dip angles corresponding to a higher likelihood of rock damage. The stress-strain curves obtained through numerical simulations of various specimens are highly comparable to the results of indoor testing. The curves obtained from indoor tests and simulations exhibit a consistent trend, with a close agreement in terms of both the slope of the elastic phase and the peak values. However, it is worth noting that due to the rigid nature of the model particles and their close proximity, the simulated specimens enter the elastic phase at the onset of the loading stage. Consequently, the initial compaction phase, observed in the experimental curve, is absent in the simulated curve. This disparity causes a leftward shift of the simulated curve relative to the experimental curve. Peak strength and elastic modulus also closely resemble the two data sets, with both increasing as the fissure dip angle increases (as shown in Figure 5b). The errors in peak strength between the numerical simulation and indoor tests ranged from 1.10% (0.66 MPa) to 3.89% (1.5 MPa), while the errors in modulus of elasticity ranged from 2.25% (0.52 GPa) to 4.68% (1.51 MPa). These discrepancies indicate that the numerical simulation results agree with the test results. Therefore, the microscopic parameters selected in Table 4 are reasonable and reliable.