## 3 Numerical Simulation of the Seepage of Dislocated Fracture
### Numerical Models  
To investigate the changes in the seepage field of fractured rock masses with displacements ranging from 0 to 10 mm, the single-fracture seepage simulations were conducted based on the fracture cavity model morphology obtained from CT scans under different dislocation conditions. The simulations involved solving the N-S and continuity equations to get the seepage velocity field for dislocation ranging from 0 to 10 mm. The corresponding mesh models are presented in Figure 6. The analysis of cavity variations was combined with the simulation results to understand the causes of complex fluid seepage behavior. In the simulation process, the fluid was assumed to be an incompressible Newtonian fluid with constant density (\(1\times 10^{3}\) kg/m\({}^{3}\)) and dynamic viscosity (\(1\times 10^{-3}\) Pa\(\cdot\)s). The simulation focused on single-phase, saturated, and steady-state conditions for the single-fracture seepage. Considering granite's low porosity and permeability, fluid exchange between the granite matrix and fractures was neglected [46].  
Previous experiments and observations have indicated that roughness distribution on the fracture surfaces leads to complex fluid seepage behavior [19]. Solving the three-dimensional N-S equation remains challenging. Under certain conditions, where the fluid is in laminar or creeping flow, i.e., \(Re<2000\), the fracture permeability can be estimated using Darcy's law and the Forchheimer equation [45,47].  
ComosOL Multiphysics ([[https://www.comsol.com/](https://www.comsol.com/)]([https://www.comsol.com/](https://www.comsol.com/))) is a finite element-based multiphysics simulation software widely used for simulating fluid flow in rock fractures. Initially, the models of fractured cavities with various dislocation states are imported into the software. The Y-axis is set along the length of the fracture, the X-axis along the width, and the Z-axis represents the direction of the dislocation-induced uplift, as illustrated in Figure 7. The color filling indicates the local mechanical aperture size of the dislocation-induced fracture.  
Subsequently, a network is established for the dislocation-induced fracture space model. COMSOL's built-in mesh generator is employed to generate a discretized mesh automatically suitable for the solver. The mesh is optimized based on the pore size, and the optimal mesh size is selected based on the computation capacity of the workstation. Boundary conditions for the spatial model are then determined according to the physical area. Uniform inlet and outlet boundary conditions are applied to all dislocation fracture models, with the fluid injection flow rate set as the inlet condition (10 mL/s) and the outlet boundary condition set to 0 Pa. The fluid flows primarily along the direction of fracture length under the fluid pressure difference. Other boundaries are treated as no-slip boundary conditions, consistent with many laboratory experimental conditions [12,18].  
This study uses COMSOL's laminar flow module to solve the N-S equations. When fluid seepage is simulated, the mesh conditions at the inlet and outlet boundaries are further optimized. A fine mesh with a size of 0.001 mm is used at the inlet and outlet  
Figure 6: Grid models for the fractures at different dislocations from 1 mm to 10 mm.  
boundaries, while a coarse mesh with a size of 0.1 mm is applied internally. The total number of tetrahedral elements is typically on the order of \(10^{6}\). The seepage field for different dislocation states is exported, and the dimensionless Reynolds number Re for fracture flow under different dislocation states is calculated as lower than 300. Thus, the flow regime in the dislocation-induced fractures can be assumed to be linear flow. The permeability of dislocated fracture models can then be calculated by Equation (9).