## 3 Sensitivity Analysis of the NorSand and HSSmal Models Using SoilTest
Practice shows that correlated parameters do not necessarily replicate, as each constitutive model is based on different formulations and governed by different theories. Therefore, parameter variability depends exclusively on the material type and the specific model parameters under evaluation [38]. On the other hand, some model-specific parameters do not have direct correlations. NS includes plastic hardening parameters (H\({}_{0}\) and H\(\upmu\)), whereas HSS uses parameters (E\({}_{50}\) and E\({}_{\text{ur}}\)) to describe the soil's elasto-plastic response. Although these parameters cannot be directly interchanged,  
Figure 11: Variation in the non-cohesive consolidation coefficient \(K_{0}\)\({}^{nc}\). (**a**) Stress–strain strength curve. (**b**) Pore pressure–strain curve. (**c**) p’-q stress path curve. fundamental aspects such as elasticity, friction, and dilatancy, present in both models, allow data consistency when switching between the two simulation approaches [37]. Based on empirical experience and the development of this research, the NS model is capable of representing both contractive and dilative soil behavior, thus allowing analysis of the static liquefaction phenomenon. This is a feature that the HSS model cannot represent; instead, HSS simulates stiffness degradation under cyclic loading, making it more suitable for dynamic analysis [39]. However, the HSS model implements a flow rule [40] from dilatancy theory that relates volumetric change to the distance from the critical state line through the following formulation (Equation (2)):  
\[\psi(e,p)\rightarrow\Delta\psi=\frac{\partial\psi}{\partial e}\Delta e+\frac{ \partial\psi}{\partial p}\Delta p \tag{2}\]  
where dilatancy (\(\psi\)) is a function of the void ratio (e) and pressure (p), meaning dilatancy variation depends on changes in either variable. In the HSS constitutive model, the void ratio is not considered a state variable and can therefore be excluded from the model equations. To evaluate static liquefaction--a phenomenon that occurs only under undrained, constant-volume paths--the void ratio remains constant. This implies that the HSS model is applicable for static liquefaction analysis as long as undrained conditions are considered, as proposed in this research. Under these conditions, the void ratio does not change, allowing proper use of the model for this type of analysis [41]. A total of 250 points were used as the base, according to the sensitivity analysis developed in Section 5. This number proved to be optimal for faithfully representing the triaxial test curve. This selection allowed for efficient calibration of both constituent models. The results obtained from calibration via parameter adjustment show significant accuracy in representing soil behavior for both the NS and HSS constitutive models, as observed in Figures 12-14. Figure 12: Calibration results of the stress–strain strength curve. (**a**) Comparison of experimental curves and simulated curves from the HSS model. (**b**) Comparison of experimental curves and simulated curves from the NS model. Figure 13: Calibration results of the p-q stress path curve. (**a**) Comparison of experimental curves and simulated curves from the HSS model. (**b**) Comparison of experimental curves and simulated curves from the NS model.