## 4 Numerical Simulation Results and Analysis  
### Characterization of Mechanical Parameters  
Figure 6 illustrates the stress-strain curves of symmetrical fissure-hole sandstone specimens. As the influence of fissure dip on the stress-strain curves was consistent across all specimens, only the curve for specimens with a fissure length of 8 mm is presented in the figure. Figure 6a shows the stress-drop phenomenon before the peak stress occurs at different magnitudes when the fissure dip angle ranges from 0\({}^{\circ}\) to 45\({}^{\circ}\). Figure 6b reveals a decreasing trend in stress drop as \(\alpha\) increases. This suggests that increasing the fissure dip angle can reduce the stress drop effect, as observed in the indoor experiment (Section 2.2). The cause of the stress drop was analyzed to be the change in stress distribution within the specimens due to the variation in the fissure dip angle. When the angle between the fissure and the axial principal stress direction was larger, stress concentration at the fissure tips was more intense, as demonstrated in [PERSON]'s study [26] on force chain distribution near the fissure.  
The relationship between the symmetrical fissure dip angle and the strength parameters of the hole-containing sandstone is depicted in Figure 7. An increase in fissure dip angle results in higher peak strength and elastic modulus values for the specimens, which gradually converge towards those of the non-fissure specimen. In addition, as the fissure dip angle increases, the specimens' peak strength and elastic modulus demonstrate a gradual, rapid, and then gradual growth trend. This trend is particularly pronounced when \(\alpha\) ranges from 30\({}^{\circ}\) to 75\({}^{\circ}\); with a dip angle of 45\({}^{\circ}\), the elastic modulus demonstrates the fastest rate of growth. Therefore, the presence of perforated symmetric fissures worsens the mechanical properties of hole-containing sandstones, while increasing the angle of the fissures helps to mitigate the worsening effect. The sensitivity of the specimens' mechanical properties to changes in fissure dip angle is highest within the range of 30\({}^{\circ}\) to 75\({}^{\circ}\), with the most sensitive point being around 45\({}^{\circ}\).  
Figure 8 shows the effect of fissure length on the strength parameters of sandstones containing pores. As depicted in Figure 8, there is an apparent linear decrease in both peak strength and elastic modulus of the specimens as fissure length increases. The slope of these linear regressions becomes steeper as fissure inclination decreases, with the best fit between peak strength and fissure length occurring at \(\alpha=0^{\circ}\) (\(R_{2}=0.9992\)). Conversely, \(\alpha=75^{\circ}\) and \(90^{\circ}\) exhibit the weakest linear fit between the elastic modulus and fissure length and a weaker negative correlation between peak strength and elastic modulus with increasing fissure length. This may be due to microcrack expansion within the specimen and variations in damage patterns. In summary, our results demonstrate that an increase in fissure length exacerbates the detrimental effect of symmetric fissures on the mechanical properties of hole-containing sandstones. However, the magnitude of this degradation decreases with increasing fissure angle.