# Seepage Characteristics Study of Single Rough Fracture Based on Numerical Simulation
## 2 Materials and Methods
### Numerical Simulation Model  
Figure 1 illustrates the effect of fracture wall roughness elements on seepage. It can be seen that the streamline (blue streamline) near the rough surface is significantly affected by the roughness elements (rough surface). The blue streamline is curved, and vortexes occur in front and behind the roughness elements. The streamline (yellow streamline) further away from the rough surface will also be affected by the roughness elements (rough surface), but the degree of influence has been weakened. The streamline (green streamline) furthest from the rough surface and near the smooth surface is hardly affected by the roughness elements (rough surface), and the flow line is almost smooth [10].  
The purpose of this study is to research the effect of rough wall surface of fracture on seepage flow, and to explore the seepage characteristics in symmetrical (but uncoupled) rough fractures [11]. The model with symmetrical-uncoupled rough wall surfaces was devised for this study (Figure 2). In order to simplify the calculation, the axisymmetric centerline was the symmetrical boundary, and there is no exchange of mass and heat on the symmetrical boundary.  
Fluent numerical simulation software was applied to simulate the seepage in rough fracture. The main variables included the distribution density and shape of roughness elements, and the fracture aperture. The length of the 2D fracture model (seepage path) was 100 mm, and the height (fracture aperture) was 3, 4, 5, 6, and 7 mm. Regardless of the width in the \(Z\) direction, it was 1000 mm by default. The dimension \(a\) was the height of roughness elements and \(a=1\) mm, \(b\) was the spacing between two adjacent roughness elements, and the distribution density of roughness elements was defined as \(A=b/a\). The value of \(a\) was a fixed value of 1 mm, and the value of \(b\) (roughness elements spacing) was set to 4 mm, 5 mm, and 6 mm, respectively, so the value of \(A\) was 4, 5, and 6, respectively. Different shapes roughness elements (triangular, rectangular, and sinusoidal) were selected to simulate the influence of rough fracture wall roughness on the change of flow field [10].  
Grid scale is a problem that should be paid attention to in the research. It is not appropriate to be too large or too small. When the grid size is too big, it will cause loss of simulation accuracy. The minimum fracture aperture is 3 mm, the roughness element height is 1 mm, and the minimum roughness element spacing is 4 mm, so the grid size should be much less than 1 mm. However, if the grid size is too small, calculation time would increase dramatically. Thus, in this study, the grid size selected 0.2 \(\times\) 0.2 mm. The grid size was much smaller than 1 mm (roughness element height), so the influence of grid size on the flow field could be ignored. The model and grid division structure are shown in Figures 3-5 [10].  
Figure 2: The symmetrical (uncoupled) rough fracture model. The dotted line is the symmetrical boundary.  
Figure 4: 2D model and grid structure diagram of single fracture with rectangular roughness elements and different densities: (**a**) \(A=6\), (**b**) \(A=5\), and (**c**) \(A=4\). In each figure, the upper black part is the schematic diagram of fracture rough surface, and the lower part is the diagram of fracture local roughness element and grid structure.  
Figure 5: _Cont._  
Figure 3: 2D model and grid structure diagram of single fracture with triangular roughness elements and different densities: (**a**) \(A=6\), (**b**) \(A=5\), and (**c**) \(A=4\). In each figure, the upper black part is the schematic diagram of fracture rough surface, and the lower part is the diagram of fracture local roughness element and grid structure.