## 4 Results and Discussion
### Seepage Velocity Field Analysis of Dislocation Fracture  
Figure 12 presents the curve of the fracture permeability \(K\) as a function of fracture displacement d. The graph shows that with the increase in fracture displacement d, the fracture permeability \(K\) shows a nonlinear growth trend, and the growth trend slows down. This trend is consistent with the results obtained by [PERSON] et al. [47] in experiments and simulations of fracture shear seepage under normal stress conditions. Under stress conditions, fracture shear mainly occurs in the compaction stage, and the fracture aperture changes relatively little with fracture displacement, resulting in nonlinear growth in permeability \(K\), which eventually tends to flatten. When fractures experience fracture displacement under stress-free conditions, the average mechanical aperture of the fractures is more  
Figure 11: The relationship between fracture spatial fractal dimension and dislocation distance. (The red arrow leads to a comparison of fracture openings). significant than that under stress conditions. Similarly, the change in permeability \(K\) is more important than that under stress conditions, especially after the fracture displacement exceeds 5 mm, where the permeability is twice that of the shear permeability under stress conditions. Figure 12 shows that when the fracture displacement is 7 mm, the fracture permeability \(K\) deviates from the curve, and the permeability is lower than that under previous fracture displacement states. This is closely related to the increase in fracture complexity mentioned in Section 4.1. Further analysis of the fracture flow velocity field is conducted to understand better the relationship between permeability \(K\) and the void space variation caused by fracture displacement. Table 1 summarizes the parameters analyzed for the flow velocity field. Figure 13 illustrates the distribution of the flow velocity field in fractures at various fracture displacements, with 400 streamlines set at the inlet. A grayscale map of the local aperture distribution is filled on the lower surface to provide a more intuitive understanding of the influence of fracture displacement on fluid flow. Figure 13 shows that the flow velocity within the fracture gradually decreases with increasing fracture displacement and exhibits a distinct preferential flow phenomenon, with streamlines avoiding areas of smaller local apertures. Additionally, as the fault displacement \(d\) gradually increases from 1 mm to 4 mm,  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dislocation Distance** & \begin{tabular}{c} **Nonliner** \\ **Factor \(E\)** \\ \end{tabular}  & \begin{tabular}{c} **Critical Hydraulic** \\ **Gradient** \\ \end{tabular}  & \begin{tabular}{c} **Inertia** \\ **CoefficientB \(\times\)** \\ **1011/Pa \(\times\) S\({}^{2}\)\(\times\) m\({}^{2}\)** \\ \end{tabular}  & \ \begin{tabular}{c} **Seepage Pressure** \\ **Gradient \(\Delta\)P/Pa** \\ \end{tabular}  & \begin{tabular}{c} **Reynolds** \\ **Number Re** \\ \end{tabular}  \\ \hline
1 & 0.56 & 5.58 & 55.81 & 1006.5 & 210.53 \\
2 & 0.52 & 2.04 & 20.37 & 393.47 & 210.53 \\
3 & 0.54 & 1.80 & 17.96 & 329.6 & 211.75 \\
4 & 0.45 & 0.91 & 9.14 & 204.6 & 214.4 \\
5 & 0.58 & 0.82 & 8.24 & 143.1 & 222.61 \\
6 & 0.  
the contact between fracture surfaces along the Y-axis at approximately 70 mm gradually occurs, increasing the contact area. When the fracture displacement \(d\) increases from 5 mm to 10 mm, the contact region along the Y-axis at 70 mm becomes a lower aperture, and the aperture distribution becomes complex and variable. Considering the flow velocity field at various fracture displacements, it is observed that the mechanical apertures are more extensive along the Y-axis at 40 mm compared to other regions. When the fracture displacement \(d\) increases from 3 mm to 10 mm, vortices and other nonlinear phenomena occur in the fracture at approximately 40 mm and 70 mm along the Y-axis.