# Grouting Process Simulation Based on 3D Fracture Network Considering Fluid-Structure Interaction
## 3 Case Study
### Grutting Simulation Considering Fluid-Structure Interaction
#### 3.2.1 Analysis of Fluid Calculation  
1. Analysis of Grout Diffusion Process  
Driven by grouting pressure, the injected grout penetrates into the primary fractures intersecting with grouting borehole and then migrates into the fracture network. As shown in Figure 9, the grout \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Fracture**} & \multicolumn{3}{c}{**Coordinate/m**} & \multirow{2}{*}{**Radius/m**} & **Dip** & **Dip** & **Apferure/m** \\ \cline{2-7}  & **X** & **Y** & **Z** & & **Direction/Deg** & **Angle/Deg** & **Apferure/m** \\ \hline
**1-1724** & **19.874** & **9.182** & **56.403** & **0.835** & **344.432** & **18.027** & **0.0089** \\
**1-1647** & **19.053** & **9.902** & **55.445** & **1.213** & **347.699** & **13.503** & **0.0129** \\
**1-872** & **19.157** & **8.701** & **55.255** & **0.726** & **347.079** & **14.107** & **0.0077** \\
1-952 & 17.818 & 10.036 & 52.685 & 0.543 & 349.080 & 15.092 & 0.0058 \\
2-220 & 20.193 & 7.555 & 57.400 & 1.246 & 41.687 & 80.996 & 0.0132 \\
2-562 & 18.444 & 14.515 & 54.789 & 0.755 & 41.635 & 86.409 & 0.0080 \\
2-121 & 17.862 & 13.714 & 51.170 & 1.162 & 39.079 & 85.291 & 0.0124 \\
3-1755 & 18.708 & 7.543 & 56.899 & 1.150 & 9.167 & 14.944 & 0.0122 \\
3-2007 & 16.190 & 8.332 & 56.259 & 1.099 & 13.901 & 11.962 & 0.0117 \\
**3-2881** & **19.736** & **7.530** & **55.015** & **0.784** & **7.736** & **10.360** & **0.0083** \\
3-699 & 19.515 & 9.665 & 54.138 & 1.035 & 9.766 & 19.581 & 0.0110 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Geometric parameters of the computation fracture mode. Figure 8: Fluid calculation model: (**a**) fracture geometrical model, (**b**) fracture grid model, and structural calculation model: (**c**) rock mass geometrical model, (**d**) rock mass grid model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Medium**} & **Density** & **Elastic Modulus** & **Poisson Ratio** & **Cohesion \(C\)** & **Internal Friction** \\  & **(kg/m\({}^{3}\))** & **(MPa)** & **\(\mu\)** & **(MPa)** & **Angle \(\varphi\) (\({}^{\circ}\))** \\ \hline Slate & 2690 & 4000 & 0.25 & 9.5 & 37.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Physical mechanical parameters of rock masses. Figure 7: Selected grouting simulation area. diffusion length increases gradually over time. After 60 s, most of the primary fractures have been filled with grout except primary fracture 1-1647; this is because the radius of fracture 1-1647 is larger and there are two secondary fractures intersecting with it, which hinders the further diffusion of grout in it. After grouting, primary fractures are completely filled with grout, secondary fractures are mostly filled, and other fractures are filled with a little grout. For details, five primary fractures (1-1724, 1-1647, 1-872, 3-2881, 1-952) intersecting directly with the grouting borehole are the main passages of the grout, and then the grout diffuses from the primary fracture to the secondary fractures. From Figure 9, it can be seen that there are secondary fractures intersecting with primary fractures, and the grout diffusion at the intersection presents a non-uniform spread shape. Thus, the filling of the primary fractures is influenced by the number of intersecting secondary fractures. As shown in Figure 9, the filling rate of secondary fracture 2-220 is 100%, this is due to the aperture of fracture 2-220 being 13.2 mm, which is bigger than other fractures, and it intersects with two primary fractures, of which the intersecting length with primary fractures 1-1647 is relatively large, reaching 1.6447 m. Secondary fracture 2-562 is basically filled with grout because it intersects with three primary fractures (1-1647, 1-872, 3-2881), but the length of intersection is short, and its aperture is 0.8 mm which is relatively small resulting in incomplete grout filling. Secondary fracture 2-121 is not fully filled with grout due to the hindrance of fracture 3-699 and the small intersections with fracture 3-2881 and 1-952.