## 4 Scenario 1: Determination of the Stability of the Tailings Dam in Its Initial State
### Studies, Results of Simulation, and Discussion  
Obtaining the results involved performing calculations by running separate studies:  
1. A first study using the Darcy's law interface;
2. A second study using the solid mechanics interface with the in situ stress initialization;
3. A third study using the solid mechanics interface taking into account the FOS. The computing of the first study enabled the pressure head (hydrostatic pressure) graphic representation (Figure 14) as it acts on the dam. A positive pressure head indicates a positive pore pressure and thus a saturated soil, while a zero pressure head means unsaturated soil. The phreatic surface that divides the unsaturated and saturate soil is indicated by the zero-pressure head line. The hydrostatic pressure can be expressed as:  
\[\psi=\frac{p}{\delta\cdot g} \tag{6}\]  
where \(p\) is the pressure [N/m\({}^{2}\)]; \(\rho\) is the density [kg/m\({}^{3}\)]; \(g\) is the gravitational acceleration [m/s\({}^{2}\)]. Figure 15 presents the slip area just before the slope failure, with the arrows highlighting the direction of displacement. For a more suggestive image of the soil slipping phenomenon, a combined contour and arrow representation diagram was used. It must be noted that Figure 15 presents the slipping for a FOS value of 1.45. This value was imposed in the third aforementioned study where the FOS was defined in the [1; 2; 3; 4; 5] interval with an increment step of 0.001. Figure 14: Pressure head (hydrostatic pressure) in the dam. Figure 13: The mesh generated for the dam model. For higher values, the simulation of the adopted model did not converge, which means that the 1.45 value of FOS is the upper limit where the slope fails due to increased plastic stresses and a subsequent reduction in shear strength. The arrows show the direction of the soil particles' displacement. In the bottom-right corner, the soil did not slip because of the base boundary fixed constraints. The pattern in Figure 16 shows the actual plastic strain just before the collapse, indicating the failure mechanism. The displacement is also shown in a tridimensional representation in Figure 17, obtained by using the extrusion datasets in the results menu. Figure 16: Presentation of the actual plastic strain just before collapse. Figure 15: Presentation of the slip area and direction of displacement. This result means that the soil slippage prediction using the plane strain approximation is a precise and effective way, with the tridimensional visualization being available after postprocessing thus avoiding the processing-intensive task of solving complex 3D problems. Figure 18 presents the displacement amplitude in a 2D view. Finally, the graphic of the maximum displacement function of the FOS is plotted in Figure 19, which indicated after further analysis that the displacement significantly increases when the FOS exceeds 1.4, indicating the start of the slope failure. As mentioned, three separate stationary studies were created and run in order to obtain relevant results for the pore pressure effect on the slope stability. In the first study, the hydrostatic pressure (pressure head) shape was obtained by computing Darcy's Law, considering the pore pressure. The obtained hydrostatic pressure combined with gravity was then added to simulate the slope stability in the second study. Finally, in the third study, the stress and strain features were added, along with the pore pressure from the first study and the initial stresses generated by gravity from the second study. By including the Mohr-Coulomb criterion, we could examine the elastic-plastic failure of the soil as a result of the gravity and pore pressure variation combined, and thus the FOS was determined for the slope. The internal friction angle for unsaturated and saturated soils is different, resulting in the use of pore pressure instead. Thus, in regions with unsaturated soil, due to the fact that pores are considered interconnected and subject to constant atmospheric pressure, no external stresses were applied.