## 3 Validation of the Model
### Comparisons between Model Prediction and Laboratory Experiments  
Figure 4 illustrates the numerical model, which has a diameter of 0.15 m, a height of 0.3 m, and an outlet boundary width of 0.01 m. Figures 5 and 6 display the comparison of evolution curves for water flow rate and particle loss between the numerical simulations  
\begin{table}
\begin{tabular}{c c} Initial porosity \(\varphi_{0}\) & 0.35 \\ Initial fluidized grain concentration \(c_{0}\) & 0.01 \\ Pore pressure on the outer boundary \(p_{d}/\)MPa & 0 \\ Upper-pressure boundary \(p_{u}/\)MPa & 1.0/0.7/0.4 \\ Coefficient \(\lambda/\)m\({}^{-1}\) & 4 \\ Real density of fluid \(\omega^{2\omega}/\)kgm\({}^{-3}\) & 1000 \\ Real density of grains \(\phi^{\prime}/\)kgm\({}^{-3}\) & 2650 \\ Kinematic viscosity of fluid \(\eta_{\mathrm{L}}/\)m\({}^{2}\)s\({}^{-1}\) & \(1\times 10^{-6}\) \\ Initial permeability \(k_{0}/\)m\({}^{2}\) & \(5\times 10^{-12}\) \\ Initial porosity \(\varphi_{0}\) & 0.35 \\ \end{tabular}
\end{table}
Table 1: Physical parameters of the numerical verification model.  
Figure 3: Large\(-\)scale triaxial testing system [6; 36].  
and experiments, with water pressures fixed at 0.4, 0.7, and 1.0 MPa. The comparison results are illustrated as follows:  
Figure 5 provides the comparison results of water inflow rate under different water pressures. It can be observed that the numerical model simulations are consistent with the laboratory model experiment data, which generally have a similar variation trend. In particular, the nonlinear increase of the water flow after a certain time can be reflected in the numerical simulation, e.g., the water flow changes from a Darcy linear flow to rapid  
Figure 4: Numerical verification model.  
Figure 5: Time variation of the water flow rate.  
Figure 6: Time variation of the particle loss.  
flow after 5 min when \(p\) = 1.0 MPa. This result demonstrates that the proposed model is able to reproduce the nonlinear flow of the water inrush. Furthermore, the magnitude of the predicted values is also comparable. For example, the final water inflow rate from the numerical study for \(p\) = 0.4 MPa was 145 mL/min, which is similar to the test result of 110 mL/min.  
For the eroded mass of the particles (see Figure 6), similar behavior can be observed compared to the result of the water flow rate. The time variation of the particle losses between the numerical investigations and laboratory tests shows a similar trend. The predicted particle losses are generally accepted for different water pressures. For example, when \(p\) = 0.4 MPa, the final particle loss is about 50 g in the numerical simulation, being 85% of the result in a laboratory test. Comparison from the above results suggests that the proposed model can well predict the evolution of the water-mud inflow in the completely weathered granite in the fault zone.  
However, some differences between numerical investigations and laboratory tests could also be observed, possibly attributed to the modeling method of the outlet in the numerical investigation. An outlet water boundary with 1 cm length was used, which is different from the outlet with the uniform small hole in the flow piston.