# Numerical Analysis of an Upstream Tailings Dam Subjected to Pond Filling Rates
## 2 Numerical Modelling and Methods  
### General Description  
An idealized upstream tailings dam was simulated using the finite element software Plaxis 2D [20]. Note that the plane strain condition is commonly adopted in simulations of tailings dams as it is a long straight section (except for corners) [7; 12; 21]. A full model was 360 m wide and 55 m high after the last construction stage, as shown in Figure 1a. In general, the model size should be large enough to avoid boundary effects on simulation outputs. In this study, the left vertical boundaries were 205 m away from the dam in all models. The slope inclination of 2H:1V (horizontal to vertical) was adopted as in the previous work of a simplified upstream tailings dam simulation by [PERSON] and [PERSON] [12]. The model comprised six soil types: moraine (foundation), rockfill (downstream support), initial dike (starter dike), layered tailings, compacted sand tailings (dikes), and rockfill (Figure 1b). Figure 1b shows the initial pond filling step, which was located at 10 m above the initial ground level. From this level, five construction stages comprising a raising phase (R) and a consolidation phase (C) were simulated in the model. In each raising phase, a new dike was constructed on top of previously layered tailings, assumed to be completed in 10 days and followed by a 10-day raising period for both new layered tailings and rockfill. The consolidation analysis was carried out to investigate the transient system response allowing excess pore water pressure to dissipate gradually during the consolidation process. The time in the consolidation phase (consolidation time) depends on the pond filling rate. In this current work, four case studies corresponding to four pond filling rates of 10.0 m/year, 5.0 m/year, 3.3 m/year, and 2.5 m/year were used to investigate the effects of the pond filling rates on excess pore water pressure and the stability of the upstream tailings dam. Therefore, the consolidation times in each stage were set over 163 days, 345 days, 528 days, and 710 days corresponding to the pond filling rates of 10.0 m/year, 5.0 m/year, 3.3 m/year, and 2.5 m/year, respectively. The phreatic line was assumed to be located at the surface of the tailings impoundment (worst-case scenario). The locations of the phreatic lines were adapted depending on the pond filling steps. In each analysis step, a new set of hydraulic boundary conditions was imposed, i.e., closed boundaries at the bottom (\(Y_{min}\)) and the left vertical edge (\(X_{min}\)), and open boundaries for others. As for the mechanical boundary conditions, the model was assumed to be fully fixed at its bottom. The horizontal displacements were assumed to be zero along the lateral edges (i.e., both left and right vertical boundaries). These hydraulic and mechanical boundary conditions can be found in many previous works dealing with two-dimensional numerical simulations of upstream tailings dams [7; 11; 12; 13; 14; 15]. The finite element mesh of the upstream tailings dam after the last construction stage is shown in Figure 2. The finite element mesh in each cluster was composed of 15-node triangular elements. These elements give a fourth-order (quartic) interpolation for displacements [20]. A massive number of elements were generated in the areas of interest (structural zone), providing the finer mesh near the slope with embankments and rockfill. This is due to the fact that these areas would be affected by large strains during the stage of construction. The coarser mesh was then generated at the far-field areas to minimize computation time. Apart from the fully coupled analysis on deformation and consolidation, the global factor of safety (\(FoS\)) for slope failure was computed for every stage of construction. The global factor of safety is computed in the finite element software Plaxis 2D using the shear strength reduction method.