## 6 Application: Identification of the PFS  
Based on the results obtained during the calibration stage, the adjusted parameters were applied to a larger-scale analysis to evaluate the material behavior under more practical and realistic conditions. For this purpose, a plane strain model was developed in Plaxis 2D. A simple geometry was created to represent the behavior of the tailings storage facility, which has a height of 10 m and a slope of 29.7 degrees (1V:1.75H). For comparison purposes, an axisymmetric model with a height of 10 m and a slope of 29.7\({}^{\circ}\) was defined. This configuration does not respond to a specific design criterion but was established for demonstration purposes. The main objective was to evaluate the performance of the NS and HS constitutive models in identifying potential failure surfaces, confirming that both models are capable of adequately capturing this behavior, regardless of their internal formulation. The HSS constitutive model was used to simulate the construction sequence, and a \"Plastic\" analysis type was carried out, which allows modeling the nonlinear behavior of the soil by capturing its transition from elastic to plastic once stresses exceed the yield limit. This type of analysis is useful for predicting both local and global failures, enabling the visualization of failure surfaces and evaluation of stability [45]. Subsequently, a time-dependent incremental load was applied to trigger static liquefaction. The load was applied at the surface of the tailings storage facility to simulate a rapid deposition of material. The procedure followed is similar to that described by [PERSON] et al. (2023) [41]. In both models, a global failure surface was identified. In the HSS model, the triggering load at the point of failure was 200 kPa, while for the NS model it was 118.8 kPa. It is important to note that the NS model does not allow for an SRF analysis, as it mobilizes strength through a hardening variable instead of relying on a parameter that can be systematically reduced. For this reason, an alternative analysis was conducted in which the incremental surcharge allowed for visualization of the PFS in terms of shear deformation (see Figure 20). Control points were established along the PFS identified in the numerical analysis of the tailings storage facility for both models to evaluate and compare soil behavior under critical loading conditions. Points A, B, and C were strategically selected in representative locations within the failure surface: Point A near the base, Point B in an intermediate zone,  
Figure 19: The user interface was generated with Python programming code in Visual Studio Code. and Point C at the upper part of the surface. This distribution allows for analysis of how mechanical responses vary across different sections of the failure zone. It is worth mentioning that although the identified failure surfaces for both models exhibit slight differences due to the specific formulations of each constitutive model, the control points were chosen to match the same relative coordinates within the failure surface. Figure 20 shows the control points placed along the PFS for both models. From the control points, a deviatoric stress (q) vs. shear strain (\(\gamma_{\text{xy}}\)) graph was generated to assess how both models represent the evolution of shear deformations in response to applied stresses, as shown in Figure 21. The parameters used to generate the simulations presented in Figures 21-23 correspond to those reported in Table 2 for the NS model and in Table 3 for the HSS model. These parameters were previously calibrated using the procedure described in the methodology section. A steep slope is observed at control points A and B in the HSS model, indicating that the soil undergoes large deformations under relatively small deviatoric stresses. The low initial stiffness, as obtained during calibration, results in a rapid progression toward failure.