# Numerical Analysis of an Upstream Tailings Dam Subjected to Pond Filling Rates
## 3 Simulation Results  
### Stability Analyses  
Stability analysis is an important component in the design of any earth structure, including tailings dams. Stability is usually expressed in terms of the factor of safety (\(FoS\)), which is defined as the ratio between the available shear strength of the soil and the minimum shear strength required against failure [12]. Figure 4 illustrates the factor of safety of the dam (pond filling rate of 5.0 m/year) during the pond filling, comprising raising phases (R) and consolidation phases (C). As shown, the \(FoS\) decreased gradually and dropped to less than 1.5 after the construction of three dikes of a height of 20 m from the initial pond filling level, i.e., \(FoS\) was 1.37 for R3 and 1.48 for C3. These values kept falling and even dropped to around 1.0 after the last construction stage. In addition, it was found that the \(FoS\) values decreased after every raising phase and then increased again due to the subsequent consolidation phase. This can be explained by the increase in effective stresses at the same rate as the excess pore pressure dissipates. The shear strength \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Symbols**} & \multicolumn{2}{c}{**Moraine**} & \multicolumn{2}{c}{**Moraine**} & \multirow{2}{*}{**Rockfill**} & \multirow{2}{*}{**Unit**} \\  & & **(Foundation)** & & **(Initial Dike)** & & \\ \hline Soil unit weight above phreatic level & \(\gamma_{tunst}\) & 20 & 20 & 18 & kN/m\({}^{3}\) \\ Soil unit weight below phreatic level & \(\gamma_{sat}\) & 22 & 22 & 20 & kN/m\({}^{3}\) \\ Young’s modulus & \(E\) & 20,000 & 20,000 & 40,000 & kN/m\({}^{2}\) \\ Cohesion & \(c^{\prime}\) & 1 & 1 & 1 & kN/m\({}^{2}\) \\ Friction angle & \(\varphi^{\prime}\) & 37 & 35 & 42 & degree \\ \hline Horizontal hydraulic conductivity & \(k_{x}\) & \(4.98\times 10^{-8}\) & \(1.0\times 10^{-7}\) & \(1\times 10^{-1}\) & m/s \\ Vertical hydraulic conductivity & \(k_{y}\) & \(1.0\times 10^{-8}\) & \(4.98\times 10^{-8}\) & \(1\times 10^{-1}\) & m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of Mohr-Coulomb (M-C) model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Symbols**} & \multirow{2}{*}{**Layered Tailings**} & \multicolumn{2}{c}{**Compacted Tailings**} & \multirow{2}{*}{**Unit**} \\  & & & & (Dikes) & \\ \hline Soil unit weight above phreatic level & \(\gamma_{tunst}\) & 17 & 18 & kN/m\({}^{3}\) \\ Soil unit weight below phreatic level & \(\gamma_{sat}\) & 20 & 20 & kN/m\({}^{3}\) \\ Elastic shear modulus number & \(K_{C}c^{\prime}\) & 130 & 130 & - \\ Plastic shear modulus number & \(K_{C}c^{\prime}\) & 50 & 75 & - \\ Elastic bulk modulus number & \(K_{B}c^{\prime}\) & 91 & 91 & - \\ Elastic bulk modulus index & \(m_{e}\) & 0.5 & 0.5 & - \\ Elastic shear modulus index & \(n_{e}\) & 0.5 & 0.5 & - \\ Plastic shear modulus index & \(n_{p}\) & 0.4 & 0.4 & - \\ Constant volume friction angle & \(\Phi_{\rm{0}}\) & 25 & 28 & degree \\ Peak friction angle & \(\Phi_{p}\) & 28 & 36 & degree \\ Cohesion & \(c^{\prime}\) & 0 & 0 & kN/m\({}^{2}\) \\ \hline Horizontal hydraulic conductivity & \(k_{x}\) & \(1.0\times 10^{-7}\) & \(1.0\times 10^{-6}\) & m/s \\ Vertical hydraulic conductivity & \(k_{y}\) & \(1\times 10^{-8}\) & \(1.0\times 10^{-7}\) & m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of UBCSAND model. increases gradually during the consolidation phase. In this sense, the lowest stability of the dam is expected immediately after a new dike construction (a raising phase). This observation is similar to that of many previous studies on the stability of an upstream tailings dam [7; 12; 21; 33]. The possible failure mechanism of the dam is shown in Figure 5. The slip surface most likely associated with the lowest _FoS_ occurred according to Figure 5. In this case, the _FoS_ did not meet the adopted code requirements of the Swedish dam safety guidelines.