# Numerical Investigation of Slurry Fracturing during Shield Tunneling under a Reservoir
## 4 Model Setup and Analysis of the Project
### Shield Slurry Fracturing Extension Process  
Take the section EK4 + 820 as an example to model and analyze the extension process of shield slurry fracturing in the formation. Figure 16 demonstrates the slurry fracturing morphology when the crack tip is at different distances from the tunnel vault during the slurry fracturing extension process. It can be observed that from the initial failure at the top of the excavation face to the complete penetration of the slurry fracturing, the fracturing maintains a stable angle and extends upward obliquely.  
In the process of slurry injection, the change curve of slurry pressure at the grouting port of the shield excavation face at section EK4 + 820 is provided in Figure 17. With the continuous injection of slurry, the slurry pressure reaches the maximum value when the formation cracks. After that, the pressure value oscillates and decreases, which is due to the increase of slurry pressure in the fracture caused by the injection of slurry when the fracture is not expanding. When the fracture begins to expand, the volume of the fracture increases suddenly, and the slurry pressure in the fracture also decreases sharply. With the continuous replenishment of slurry, the slurry pressure begins to increase again until the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Elastic modulus \(E\) & 21 MPa \\ Poisson’s ratio \(\mu\) & 0.36 \\ Cohesion \(c\) & 0.013 MPa \\ Internal friction angle \(\varphi\) & 16.8 \\ Tensile strength \(\sigma_{t}\) & 0.011 MPa \\ Type I fracture energy \(G_{l}\) & \(5.4\times 10^{-4}\) MPa\(\cdot\)mm \\ Type II fracture energy \(G_{ll}\) & \(5.4\times 10^{-4}\) MPa\(\cdot\)mm \\ Penetration \(k\) & \(1\times 10^{-6}\) m\({}^{2}\) \\ Void ratio \(e\) & 0.1 \\ Filter loss coefficient & \(1\times 10^{-14}\) m\({}^{2}\cdot\)s/kg \\ Pore flow viscosity coefficient & 0.001 m\({}^{2}\cdot\)s/kg \\ \hline \hline \end{tabular}
\end{table}
Table 4: The parameters of the cohesive soil layer at the position EK4 + 820.  
Figure 16: The shield slurry fracturing morphology when the fracturing tip extends to different heights (EK4 + 820). (a) 3 m; (b) 6 m; (c) 9 m; (d) 13.5 m.  
fracture further expands. With the oscillating process of this slurry pressure, shield slurry fracturing spreads to the surface. With the upward expansion of the fracture, the water and soil pressure on the fracture surface becomes smaller and smaller, so the slurry fracturing pressure also gradually decreases.  
Finally, the slurry pressure at the grouting port on the excavation face of the shield tunnel is stable in the range of about 180 kPa; this is mainly because, after the fracture completely penetrates the overlying soil layer, the tunnel and surface form a communication channel. The slurry pressure at this time will be the same as the water pressure at this position, and the water head height at the grouting port of the excavation face vault is about 18 m. At this time, a shield slurry blow-out occurred on the surface.  
In summary, the formation fracturing pressure at section EK4 + 820 is about 0.39 MPa, and the pressure required for the fracture to continue to expand gradually decreases after the initial formation failure occurs.