# Numerical Investigation of Slurry Fracturing during Shield Tunneling under a Reservoir
## 4 Model Setup and Analysis of the Project
### Model Setup  
It is extremely difficult to model and analyze the entire shield tunnel crossing the reservoir section. In order to obtain valid rules about shield slurry fracturing, it is necessary to select a typical cross-section of this shield tunnel before modeling. The longitudinal section view of the right shield tunnel is provided in Figure 14. The four typical sections marked in Figure 14 were selected for simulation and analysis, according to the characteristics of slurry shield tunneling. The four selected section positions are modeled respectively to analyze the risk of shield slurry fracturing in the project.  
The covering soil thickness and water depth of the four typical sections, according to the preliminary design, are illustrated in Table 3. It can be found that the buried depth of the shield tunnel in this project is shallow. The shallowest position is less than 1 times the tunnel diameter.  
Figure 14: The longitudinal section view of the right shield tunnel.  
The analysis process requires modeling and calculation of four typical sections, respectively. Taking the position EK4 + 820 as an example to display the numerical modeling calculation process in this paper, it can be observed from Figure 14 that there is a slope in the design line of the shield tunnel. Since the slope is small and only a small local area is selected for modeling, the tunnel line in the model is simplified to the horizontal direction. The shield tunnel excavation diameter is 15.76 m. The thickness of the covering soil is 13.5 m and the water depth is 5.1 m at the position EK4 + 820. The initial position of the fracturing is located at the vault of the excavation face. The shield slurry injection rate is 1 L/s. In order to improve calculation accuracy, the crack propagation area is densified when dividing the mesh, with a total of 16,543 units. The engineering overview and modeling dimensions of the position EK4 + 820 are provided in Figure 15. The element type is plane strain hole compression integral units (CPE4 RP). The bottom of the model has fixed constraints, and the two sides have normal constraints. The top surface of the model is a free surface. Water pressure (51 kPa) is applied to the top of the model in the form of a uniform load. Stress conditions with corresponding soil and water pressures are applied at the tunnel boundary.  
According to the geological survey report, the strata where the shield tunnel is located below the reservoir are all cohesive soil strata with similar properties. A single cohesive soil layer was used when modeling the sections. The parameters of the cohesive soil layer are selected according to the geological exploration data and engineering experience, as illustrated in Table 4.  
The simulation process of slurry fracturing in shield tunnels is also divided into two stages: earth stress balance and fracturing extension. The initial stress balance is carried out in the in-situ stress balance stage. The loading needs to be kept constant during the fracturing extension stage. The slurry is injected at the preset initial fracture, and the slurry pressurization process continues until the fracture penetrates the model.  
Figure 15: The section overview and model of the position EK4 + 820. (**a**) The section overview; (**b**) The section model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Section Location** & **Covering Thickness (m)** & **Water Depth (m)** \\ \hline EK4 + 820 & 13.5 & 5.1 \\ EK5 + 001 & 21.4 & 6.4 \\ EK5 + 915 & 24.5 & 6.2 \\ EK6 + 280 & 17.2 & 5.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Basic parameters of selected typical section.