## 1 Introduction  
Since the beginning of the 21 st century, there has been a significant increase in the extraction of metals and minerals, which has resulted in a substantial rise in mining waste and, consequently, in the number of TSFs [1, 2]. In Chile, several mining projects include the construction of tailings dams exceeding 100 m in height, such as Ovejeria (120 m), Las Tortolas (170 m), Quilayes (198 m), and El Mauro (237 m) [3]. These structures are essential for the controlled management of mining waste; however, they also pose a significant risk in the event of failure. Historical records of disasters associated with TSFs, as demonstrated by recent incidents around the world [4], highlight the potentially devastating impacts of such failures on the environment and nearby communities [5]. Notable examples include the failure of the Corrego do Feijao dam in Brumadinho, Brazil, in 2019, which resulted in 272 fatalities [6]; the collapse of the Fundao dam in Mariana, Brazil, in 2015, which is considered the most severe environmental disaster in the history of the global mining industry in terms of tailings volume released and extent of damage; and the recent tailings failure at Las Cenzias mine in Cabildo, Chile, in June 2024, which caused significant environmental impacts on water resources and agricultural soils in surrounding communities [7; 8]. The primary cause of these disasters is the onset of instability under monotonic loading in granular materials, commonly referred to as static liquefaction or flow failure [9]. Liquefaction is associated with the sudden loss of shear strength in soil, followed by large deformations [10]. This type of failure occurs when saturated soils experience a sudden loss of strength due to an increase in pore water pressure, potentially leading to TSF failure [11; 12]. In this context, the use of constitutive models emerges as a valuable tool for evaluating and predicting the behavior of TSFs under various loading conditions [13]. These models enable the assessment of stability, deformation analysis, and evaluation of static liquefaction potential [14]. This study compares two constitutive models to determine which is more suitable for simulating undrained stress paths and, therefore, for assessing the potential for static liquefaction. The constitutive models evaluated are HSS and NS. The HSS model has extensive empirical support for capturing soil stiffness and nonlinearity in the small-strain range [15]; it is based on plasticity theory and includes soil dilatancy. In contrast, the NS model is grounded in critical state soil mechanics and uses the state parameter to control soil behavior [16]. Over the past two decades, literature reviews have shown that various constitutive models have been developed to represent static liquefaction, such as Mohr-Coulomb, Hyperbolic, and Hardening Soil. The NS model is capable of capturing key aspects of plastic soil behavior, including critical state phenomena [17]. On the other hand, the HSS model excels at simulating elasto-plastic behavior and is versatile in modeling undrained conditions. These two models were selected for this research due to their respective abilities to address different aspects of soil behavior, allowing for a comprehensive comparison of their results against experimental data. In this regard, selecting the most appropriate model remains a challenge, as both have specific advantages and limitations [18]. CIU triaxial test data provided the experimental basis for calibrating the HSS and NS constitutive models in subsequent phases of this study. These experimental data were later used to perform parameter fitting to evaluate which constitutive model best reproduces the observed behavior in the laboratory tests. The calibration results indicate that the proposed methodology enables the simulation and representation of the experimental curves from a CIU test on a tailings sample classified as a silt-like soil.