## 3 Numerical Test Method and Scheme Design
After several times of calculation trials and comparison of the influence of the number of grids on the calculation results, it is finally determined that the formal analysis is conducted while the number of grids lies between 300,000 and 500,000 (Figure 3). A numerical calculation model of the indoor launder overflow dam failure test was established with a similar scale of 1:100 between the prototype of the planned tailings dam and the proposed reduced-scale model. Referring to the model tailings selection method recommended by [PERSON] et al. (2023) [PERSON] et al. (2023), the dam failure analysis of the reduced-scale model test was analyzed under three schemes: fly ash mixed with bentonite (4:1), fine-grained tailings and prototype tailings, respectively, and the similarity between the model and the prototype and the rationality of the sand selection scheme were verified by combining the characteristics of the dam failure, such as the change of the breach and the time of the dam failure. According to the gravity similarity law, the geometric parameters of the numerical test are designed as shown in Table 1.  
Gravity model, sediment scoring model and RNG turbulence model are selected in the numerical simulation, and the physical and mechanical properties of the model packed sand are defined by the tailings particle size, density, critical shields parameter, entrainment coefficient, bed load transport rate coefficient and angle of repose underwater, respectively. The particle size distribution and density of tailings sand can be determined by standard tests (according to ASTM D6913M-17 and ASTM D854-23 [24; 25]). In order to achieve a more ideal calculation result, considering the large span of the particle size of the tailings, the average particle size of each particle size range is taken according \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Program**} & **Height and Width of Dam Body** & \multirow{2}{*}{**Slope Ratio**} & **Computational Domain** & \multirow{2}{*}{**Flow Head (m)**} \\  & **H \(\times\) W (m)** & & & **L \(\times\) W \(\times\) D (m)** & \\ \hline Tailings dam prototype & 40 \(\times\) 26 & 1:5 & 260 \(\times\) 40 \(\times\) 26 & 0.5 \\ \hline Fly ash mixed with & & & & \\ bentonite (4:1) & 0.4 \(\times\) 0.26 & 1:5 & 2.6 \(\times\) 0.4 \(\times\) 0.26 & 0.005 \\ \hline Fine tailings & 0.4 \(\times\) 0.26 & 1:5 & 2.6 \(\times\) 0.4 \(\times\) 0.26 & 0.005 \\ \hline Prototype tailings & 0.4 \(\times\) 0.26 & 1:5 & 2.6 \(\times\) 0.4 \(\times\) 0.26 & 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design of numerical test parameters. Figure 4: On the left is the geometry depicted using the FAVOR method, and on the right is the geometry depicted using the traditional FDM method. to the grading curve of the tailings. The critical shields parameter is obtained from the Soulsby & Whitehouse equation. The angle of repose under water is approximated to that of the internal friction angle of tailings. Considering the difference of copper tailings and ordinary sediment properties, the entrainment coefficient is 0.003, which can achieve good test results. According to the physical and mechanical test of rock and soil and the grain grading curve, the sand content of each grain size in the tailings can be obtained, and the purpose of adjusting the reasonable grain grading of the sand can be achieved by setting the percentage content in the model setting. According to the principle of similarity, the physical and mechanical properties of the prototype tailings and the tailings used in the model are listed in Tables 2-4. Based on the relevant engineering data of the tailings pond, the initial condition settings primarily include the global pressure, water pressure calculation method, and the setting of upstream and downstream water levels. The water level in the tailings pond is set at the same elevation as the dam height, which is 26 m. In the model, the bottom is set as a rigid body wall boundary, while the sides are set as symmetric boundaries.