## 3 Calibration and Verification of Model Mesoscopic Parameters  
### Calibration of Mesoscopic Parameters  
Accurate numerical simulations require the precise determination of microscopic parameters. In the Particle Flow Code 2D (PFC2D), the mesoscopic parameters of the linear parallel bond contact model encompass particle parameters and bonding parameters. The particle parameters primarily comprise the particle size range, particle size ratio (\(R_{max}/R_{min}\)), particle density (\(\rho\)), particle stiffness ratio (\(k\)), radius factor (\(\overline{\lambda}\)), particle dissipation energy (\(Damp\)), particle friction coefficient (\(\mu\)) and particle Young's modulus (\(E\)). On the other hand, the critical microscopic parameters pertaining to parallel bonding include the bond strength (\(pb\_\sigma_{l}\)), bond stiffness ratio (\(pb\_k\)), bond Young's modulus (\(pb\_E\)), and bond cohesion (\(c\)) [28]. The primary difference between the uniaxial compression in PFC2D and conventional triaxial compression lies in whether or not the left and right servo walls are required to provide the surrounding pressure. However, the microscopic parameters in the linear parallel bond model serve mainly for specimen formation and rock bonding, which are partially the same in uniaxial and conventional triaxial compression. Therefore, uniaxial compression indoor tests and simulations were carried out for perforated symmetrical fissure-hole sandstone specimens tested at \(\alpha=15^{\circ}\), \(45^{\circ}\) and \(75^{\circ}\). By systematically adjusting the microscopic parameters based on the macroscopic mechanical responses observed during indoor experiments [22], a set of microscopic parameters that accurately reflect the mechanical behavior of the selected perforated symmetrical fracture-hole sandstone specimens was obtained. This iterative process ensured that the simulated behavior closely matched the experimental results, enhancing the fidelity of the numerical modeling approach. The sandstone specimens loaded indoors were taken from Pingdingshan City, Henan Province, China, and consisted mainly of two minerals, quartz, and feldspar, and some geomechanical characteristics of the intact sandstone specimens are shown in Table 2. The specimens were brittle, and the holes were machined to a small size to prevent damage to the specimens during hole processing, and the size parameters of each defect are shown in Table 3. The indoor test system is shown in Figure 4. Uniaxial compression tests were carried out using the ZTR-276 rock triaxial test system with a displacement control method and a loading rate of 0.02 mm/s. For the simulation tests, the model size, defect size, and loading settings were replicated from the indoor tests. Subsequently, the microscopic parameters of the model underwent iterative adjustment using a 'trial and error' approach until the macroscopic mechanical behavior of the specimen in the simulation results closely matched that observed in the indoor uniaxial compression test results. The refined microscopic parameters selected at the end of this iterative process are presented in Table 4.  
Figure 3: Model settings and linear parallel bond model. Figure 5 compares the mechanical properties of the results simulated through the microscopic parameters in Table 4 and the indoor test results. In Figure 5a, the stress-strain curve of the indoor test can be divided into four distinct stages: the compaction stage, elastic stage, plastic stage, and failure stage. During the plastic phase, a significant drop in stress magnitude is negatively correlated with the fissure dip. This finding aligns with the test results reported by [PERSON] (2014). This is due to the lower load-bearing properties of the rock near the defect, which makes it more likely to fracture and sprout cracks during the loading process. Moreover, at \(\alpha=15^{\circ}\), a double peak appears in the stress-strain curve, which may be attributed to the horizontal orientation of the fissure, which leads to its closure under pressure during loading.