## 4 Results and Discussion  
### Statistics of Fractures' Local Mechanical Aperture Based on CT Data  
Figure 8 shows the distribution pattern of local mechanical aperture data with the fracture dislocation distance varying from 0 to 10 mm as a visualization of the variation in the distribution pattern with dislocation distance. The horizontal axis represents the mechanical aperture size, while the vertical axis of each dislocation reflects the amount of corresponding aperture data. It can be observed that with the increase in fracture dislocation distance, the distribution of local mechanical aperture data undergoes a significant evolution from a relatively concentrated distribution in a small aperture to a more extensive local aperture distribution. For instance, when the fracture dislocation is at a distance of 1 mm, the distribution of local mechanical aperture data is relatively narrow, displaying a predominant normal distribution. The local aperture values are primarily concentrated around 1-2 mm. As the fracture dislocation distance increases, the distribution of local aperture data significantly widens. When the fracture dislocation distance reaches 10 mm, most local aperture values are between 1.5 and 3.5 mm. Figure 9 presents the variation in the average mechanical aperture with fracture dislocation distance under normal stress conditions and stress-free conditions. It is evident that, with the increase in fracture dislocation distance, the average mechanical aperture exhibits nonlinear growth, with the growth rate gradually slowing down, following a logarithmic relationship. This behavior aligns with the experimental and numerical simulation results of [PERSON] et al. [47] under normal stress conditions, represented by the red and blue curves in Figure 9. Furthermore, it can be observed that the values of calculated average mechanical aperture \(e_{\mathrm{m}}\) do not entirely align with the fitted curve, reflecting the influence of the actual fracture roughness on the average fracture aperture. Compared with the fitting results obtained by [PERSON] et al. [48] through shear experiments, the average mechanical aperture under stress-free conditions is notably lower than the values under certain normal stress conditions. Figure 7: The simulation model of seepage in dislocation fracture, where the color fills in the figure characterize the magnitude of local aperture. Figure 8: Statistical analysis of fractures’ local mechanical aperture. Figure 9: The relationship between the average mechanical aperture of the fracture and the dislocation distance [47]. Considering the curve in the graph variations of the average mechanical aperture \(e_{\text{m}}\) with fracture dislocation distance, it can be observed that when dislocation occurs on the fracture surface, the change in fracture aperture generally maintains a certain level. As the fracture dislocation distance increases, the growth of the average mechanical aperture \(e_{\text{m}}\) gradually slows down. However, for certain fracture dislocation distances, such as 7 mm and 10 mm, the average mechanical aperture \(e_{\text{m}}\) deviates from the curve's growth trend. To better understand the variation in fracture apertures, the roughness angle \(\alpha\) is calculated along the length of the rock core in Figure 10. Figure 10a presents a two-dimensional vertical height map of fracture sections along the radial direction of the core, obtained by stacking fracture surface segments taken every 2 mm in the horizontal direction. It shows that the undulation range of the fracture surface is about 4 mm, consistent with the trend of aperture changes when the fracture is uplifted. Figure 10b displays the distribution of the roughness angle along the fracture direction, indicating a relatively gentle variation in roughness angle along the fracture direction, with only local areas exhibiting a more inclined roughness angle. Fracture displacement involves altering the void distribution within a fracture and affects the connectivity of void spaces.