## 4 Model Base Establishment  
To further investigate the influence of rainfall on the stability of the backfill slope, a numerical analysis incorporated in the software Geostudio was adopted in this study. The numerical simulation has the advantages of high efficiency, safety, and good repeatability. It can freely consider different conditions as compared with the physical model test. Test T-2 was used to calibrate the numerical model, including the relationship of the mass moisture content with the matric suction and permeability of the backfill soil [33]. Adopting the rest model tests T-1, T-3, and T-4 to validate a numerical model is a great step towards ensuring the accuracy and reliability of the simulation results. Accordingly, a large number of model bases were established considering the different surcharges, and the rainfall intensity and duration were established.  
A two-dimensional numerical model with the same geometry as test T-2 was created. The backfill slope was modeled as Mohr-Coulomb failure criteria, and the material properties are as shown in Table 1. The bottom boundary was fixed in both the horizontal and vertical directions. The lateral displacements on the side boundaries were set to zero but the vertical movement was free. A rainfall boundary condition was set along the slope surface with a rainfall intensity of 4 mm/h. The Fredlund-Xing method was adopted to estimate the functions of the mass moisture content with the matric suction and permeability. After the simulation of rainfall, the Morgenstern-Price method was adopted to calculate the stability of the slope under the determined instability critical surcharge from the model test.  
Figure 8b includes the calculated slip plane by the numerical analysis. Table 4 summarizes the calculated displacements of the backfill slope and factor of safety. It is indicated that the results by the calibrated numerical model T-2 agreed well with the model test. The calibrated model was used to further predict the stability of the tests T-1, T-3, and T-4. The numerical model had the same geometry, displacement boundary condition, and material properties instead of the rainfall boundary. As seen from Figure 8 and Table 4, the results of the numerical analysis were in good agreement with the model tests.  
Based on the calibrated model, a model base including 112 cases was established, considering the factors of surcharge load and rainfall intensity and duration, as listed in Table 5. The rain duration changes from 0 to 9 h. The rain intensity varies from 0.65 to  
\begin{table}
\begin{tabular}{c c c c} \hline
**Test No.** & **Horizontal Displacement/mm** & **Vertical Displacement/mm** & **Factor of Safety** \\ \hline T-1 & 18.0/19.0 * & 22.2/18.0 * & 1.117 \\ T-2 & 56.6/50.0 * & 58.4/54.0 * & 1.080 \\ T-3 & 61.8/53.0 * & 59.4/57.0 * & 1.044 \\ T-4 & 49.6/46.0 * & 50.9/47.0 * & 1.053 \\ \hline \end{tabular} Note: * denotes the data of the model test.  
\end{table}
Table 4: Test results of numerical analysis.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Test No.** & **Horizontal Displacement/mm** & **Vertical Displacement/mm** & **Shear Strain/\%** \\ \hline T-1 & 19 & 18 & 1.4 \\ T-2 & 50 & 54 & 4.6 \\ T-3 & 53 & 57 & 4.8 \\ T-4 & 46 & 47 & 4.2 \\ \hline \end{tabular}
\end{table}
Table 3: The maximum displacement and shear strain at failure.  
4.0 mm/h, which refers to the rain intensity changing from light rain to heavy rain in the prototype.