## 4 Seepage Simulation Based on the Navier-Stokes Equation
### Analysis of Influencing Factors of Tailings Permeability  
The pore structure has a great influence on the distribution and flow of fluids in porous media, and the pore network parameters can well describe the transport characteristics of fluids in tailings. The permeability characteristics of tailings are determined by a combination of pore radius, pore number, coordination number, throat number, roar radius, throat length and other factors. In order to analyze the degree of influence of each factor on the permeability characteristics, a sensitivity analysis was performed.  
Grey correlation analysis is the main method used to study the correlation between different factors in the grey theory model, which can analyze the correlation between factor variables and behavioral variables [23]. The correlation degree is a quantitative value used to reflect the influence of different factors on the same thing, and the range value is between 0 and 1, the larger the value, the higher the correlation degree and the closer the relationship. The correlation degree can be calculated according to Equations (9) and (10) [24].  
\[\epsilon_{\mathrm{i}}(k)=\frac{m+\rho M}{\Delta_{0i}(k)+\rho M} \tag{9}\]  
\[r_{\mathrm{i}}=\frac{1}{5}\sum_{k=1}^{5}\epsilon_{i}(k) \tag{10}\]  
where \(\epsilon_{\mathrm{i}}(k)\) is the correlation coefficient of the first sample comparison series to the reference series, \(\rho\) is the resolution coefficient, and the range is between 0 and 1, In order to fully reflect the integrity of the association, \(\rho\) should be taken as more than 0.5, so the overall value is 0.8 [25]. The extreme values \(M\) and \(m\) of the absolute difference are 2.270 and 0.027, respectively. Table 7 shows the correlation between each structural parameter and the tailings permeability coefficient \(K\).  
From Table 7, it can be concluded that the top three parameters that have the greatest impact on the permeability coefficient of tailings are porosity, number of pores and number of throats. The sum of the correlation degrees of throat radius is greater than that of pore radius, which indicates that the roar radius has a greater impact on permeability than pore radius. This is consistent with the results of [PERSON] et al. [26], which showed that the radius of the roar channel plays a major role in controlling the flow of water in the soil.  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Sample Number**} & \multirow{2}{*}{\
\begin{tabular}{c} **Permeability** \\ **(md)** \\ \end{tabular} } & \multicolumn{2}{c}{**Permeability Coefficient (cm/s)**} & \multirow{2}{*}{
\begin{tabular}{c} **Relative Error** \\ **(\%)** \\ \end{tabular} } \\ \cline{3-3} \cline{5-5}  & & **Simulated Value** & & **Experimental Value** \\ \hline CLT & 5.55 & \(5.72\times 10^{-6}\) & 5.86 \(\times\) 10\({}^{-6}\) & 2.4 \\ FCT & 7.31 & \(7.53\times 10^{-6}\) & 7.15 \(\times\) 10\({}^{-6}\) & 5.0 \\ SCT & 8.52 & \(8.78\times 10^{-6}\) & 8.11 \(\times\) 10\({}^{-6}\) & 7.6 \\ STT & 2.52 & \(2.45\times 10^{-5}\) & 2.64 \(\times\) 10\({}^{-5}\) & 7.8 \\ SDT & 4.39 & \(4.26\times 10^{-5}\) & 4.55 \(\times\) 10\({}^{-5}\) & 6.8 \\ \hline \end{tabular}
\end{table}
Table 6: Permeation simulation calculations and measured results.  
Figure 18: Streamline diagram of each specimen (**a**) CLT; (**b**) FCT; (**c**) SCT; (**d**) STT; (**e**) SDT.