# Numerical Investigation of Slurry Fracturing during Shield Tunneling under a Reservoir
## 3 Verification of Numerical Solution
### Analysis of Calculation Results and Comparative Validation  
During the slurry injection simulation, the slurry pressure at the injection point can be monitored in real-time. Taking the confining pressure of 0.2 MPa and the axial pressure of 0.2 MPa in the model test as an example, the change curve of slurry pressure during the grouting process is provided in Figure 7. It can be observed from this curve that the slurry pressure gradually increases with the injection of slurry, and the slurry pressure drops sharply after reaching the peak value. The peak value is the crack initiation pressure (0.45 Mpa) of the sample fracturing. The crack initiation pressure of the sample is significantly greater than the confining pressure. Under the action of higher triaxial stress, the clay sample exhibits certain brittle characteristics, and the failure develops so quickly that it is difficult to observe. The sudden drop in slurry pressure indicates that the fracture penetration process is extremely rapid (0.73 s). It is almost impossible to observe the slurry fracturing propagation process of the sample during the test. This simulation calculation result is consistent with the slurry fracturing test phenomenon of blind-hole samples described in the test study. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Elastic modulus \(E\) & 75 MPa \\ Poisson’s ratio \(\mu\) & 0.22 \\ Cohesion \(c\) & 0.375 MPa \\ Internal friction angle \(\varphi\) & 14\({}^{\circ}\) \\ Tensile strength \(\sigma_{t}\) & 0.13 MPa \\ Type I fracture energy \(G_{I}\) & 0.021 MPa\(\cdot\)mm \\ Type II fracture energy \(G_{II}\) & 0.045 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 1: Model Mechanical Parameters. Figure 6: Model loading condition settings. The pressure distribution of the slurry fracture surface is provided in Figure 8. It can be found that the distribution of slurry pressure on the entire fracture surface is basically the same; this is because the viscous resistance of slurry is small and the size of the sample is relatively small, so there is no obvious pressure gradient in the direction of the entire fracture depth. The fracture morphology of the model can be found in Figure 8. By comparing with the damaged sample (as illustrated in Figure 9) given in the test study [17], it can be observed that the fracture surface morphology obtained by the simulation is basically consistent with the experimental results. The comparative results demonstrate the feasibility of the XFEM-based slurry fracturing simulation method. The angle between the failure surface of slurry fracturing and the confining pressure is about 45\({}^{\circ}\), and the overall failure of the clay sample demonstrates shear failure characteristics. Figure 8: Pressure cloud diagram of fracture surface (unit: Pa). Figure 7: Injection point slurry pressure monitoring. Figure 9: Fracture morphology of the samples damaged in slurry fracturing test [17]. It can be observed from the previous simulation examples that the XFEM method proposed in this paper to simulate slurry fracturing can obtain a failure shape that is more consistent with the test samples. In order to verify the accuracy of the simulation calculation results of the fracture initiation pressure, the test conditions under different confining pressures were simulated, and the calculation results were compared with the test results from [PERSON] et al. [17]. According to the setting of the confining pressure in the tests, 6 working conditions are set for the confining pressure when the axial pressure is 0.35 MPa.