## 3 Description of Location and Geometry of the Model  
Incidents caused by stability issues in waste dumps in the Oltenia coal mining region (Figure 1), manifested as landslides involving large volumes of waste material, amounting to millions of cubic meters and impacting both the natural and built environments, have been recorded at several external dumps at various open-pit mines. The issue of dump stability is not limited to the construction period during which the waste material is deposited and leveling and sloping works are carried out. As evidenced by the aforementioned incidents, the stability problem extends over a considerable period after the dumping activities have ceased. This necessitates the monitoring of movements in unstable areas within the exploitation perimeter, its surroundings, and the dumps themselves should be conducted both during the exploitation period and for a sufficiently long period after the cessation of dumping activities. To illustrate the method, we adopted a model that is morphologically and dimensionally compatible with most of the dumps in the Motru coal basin. Figure 2 shows the cross-section of the sloped mass model. The lengths \(L_{1}\) and \(L_{2}\) are 85 m and 20 m, respectively, while the heights \(H_{1}\) and \(H_{2}\) are 20 m and 10 m, respectively. The slope angle \(\alpha\) varies from 30\({}^{\circ}\) to 45\({}^{\circ}\), which corresponds to the range of both designed and real slope angles for most dumps in the Motru coal basin. Figure 1: Basins in the Oltenia coal mining region [Oltenia Energy Company internal documents]. Figure 2: Cross-Section of the rock mass model. The material properties for both non-associative plasticity--noted as Material 1--and associative plasticity--noted as Material 2--are summarized in Table 1. The values are the mean (average) values for the soil properties of the material dumped in the waste deposits from the analyzed Lupoaia and Rosiuta exploitations in the Motru coal basin and are based on a real data series that the Oltenia Energy Complex has in its records [88, 89], as determined during the mandatory periodic laboratory testing of soil samples [90]. In the modeling, the plane strain assumption is applied for the sloped mass in the cross-section (2D), and the calculations are performed taking into consideration the effects of gravitational acceleration. A sensitivity analysis is usually carried out by changing parameter values one at a time and checking how this affects a certain system. In order to verify our model, the sensitivity analysis was conducted by running one simulation with the same angles and flow rules, but with a change in the angle of dilatation \(\psi\) to a value of \(15^{\circ}\), which represents 50% of the maximum value of \(30^{\circ}\) used in the main simulation. The resulting FoS value and its variation are presented in Table 2. The change noted \(\Delta\) in FoS is between 0.95% and 1.96%, which means that the change in the angle of dilatation does not influence the result to a large degree, hence the model can be considered well calibrated and valid. The simulations were performed in COMSOL Multiphysics using a 2D model and the Structural Mechanics -> Solid Mechanics module, and using the values defined in Table. 1 for the material parameters for both considered scenarios--associative plasticity and non-associative plasticity. The difference between the two scenarios is given as the value of the dilatation angle parameter, which is 0 and 30 degrees, respectively. Next, in the Definiton menu of the software, the calculation formulas corresponding to the variables (parametrized and reduced cohesion and friction angle, and the reduction factor) used in the simulation were implemented. The general geometry of the model was constructed using Polygon type graphic primitives, which were later unified using the Form Union option. In the model construction, the region for geometry redefinition with finite elements (Mesh Control Domains) was also defined, as shown in Figure 3.