# Numerical Analysis of an Upstream Tailings Dam Subjected to Pond Filling Rates
## 2 Numerical Modelling and Methods
### Constitutive Models  
In this study, the UBSCAN constitutive model was used to simulate the tailings materials, whereas the Mohr-Coulomb (M-C) model was applied for moraine and rockfill materials. The M-C model is a linear elastic-perfectly plastic model. The UBCSAND model is an effective stress plasticity model used in advanced stress deformation analyses of geotechnical materials. A fully coupled analysis (mechanical and groundwater flow calculations) can be performed simultaneously in this model. It can predict the shear stress-strain behavior of soil using an assumed hyperbolic relationship [27]. Therefore, this model can overcome the drawback of the elastic-perfectly plastic M-C model with a possibility to capture the nonlinearity in the elastic part of the soil. In addition, the UBCSAND model is appropriate for tailings materials as excess pore water pressure can build up in tailings during pond filling and dam raising. Figure 3 presents the behavior of tailings materials during drained simple shear tests and simulations. The laboratory tests were performed by [PERSON] [28] at the Lulea University of Technology. Several simulation models were performed in this study to evaluate parameters for the UBCSAND model. As can be observed, while the stress-strain curves followed the nonlinear behavior of the experimental data well in the UBCSAND model, they overestimated the shear strength of the tailings materials significantly in the M-C model, regardless of the applied normal stresses (50 kPa, 100 kPa, 150 kPa) or the tailings types (layered tailings, compacted tailings). The UBCSAND model has also been used for materials in the development of excess pore water pressure-induced static liquefaction [29] or seismic liquefaction [15; 30].  
The M-C input parameter values of moraine and rockfill materials were adopted from previous works [31; 32], as summarized in Table 1, except for the Poisson's ratio and the dilatancy angle. In this study, the Poisson's ratio (\(\upsilon\)) and the dilatancy angle (\(\psi\)) were assumed to be 0.33 and 0, respectively. These assumed values have been used in many simulation works of tailings dams in Sweden by [PERSON] et al. [7; 11], [PERSON] et al. [21], and [PERSON] et al. [15]. The laboratory tests were performed on tailings materials taken from an iron mine in northern Sweden. In addition, the parametric sensitivity analyses (curve fitting method) for obtaining elastic shear modulus number (\(K_{G}\)\({}^{e}\)), plastic shear modulus number (\(K_{G}\)\({}^{p}\)), and elastic bulk modulus number (\(K_{B}\)\({}^{e}\)) were performed. In the curve fitting method, the friction angles and cohesion, which were evaluated based on the direct shear test results, were fixed. Elastic shear modulus number (\(K_{G}\)\({}^{e}\)) and plastic shear modulus number (\(K_{G}\)\({}^{p}\)) were varied to capture the stress-strain curves from the experiments. Finally, elastic bulk modulus number (\(K_{B}\)\({}^{e}\)) was estimated as 70% of elastic  
Figure 3: Behavior of tailings materials during drained simple shear tests and simulations: (a) layered tailings with dry density of 1.65 t/m\({}^{3}\) and (b) compacted tailings with dry density of 1.82 t/m\({}^{3}\).  
shear modulus number (\(K_{C}c\)), as recommended in [20] (material models part). As can be seen in Figure 3, there is a good agreement between the simulations (UBCSAND model) and experimental results, regardless of the tailings types used. The index parameters \(m_{e}\), \(n_{e}\), and \(n_{p}\) were assigned the values of 0.5, 0.5, and 0.4, respectively, as suggested in the original UBCSAND report by [PERSON] and [PERSON] [27]. The hydraulic conductivity of the tailings was adopted from previous studies [28; 31]. In the present study, the hydraulic conductivity values in the horizontal direction were assumed to be 10 times higher than those in the vertical direction due to the layered nature of the tailings [26; 31]. All input parameter values of the UBCSAND model used in the numerical analyses are tabulated in Table 2.