## 3 Sensitivity Analysis of the NorSand and HSSmal Models Using SoilTest
This behavior is based on the fact that an increase in \(\phi\) can intensify the dilatant behavior of the material, leading to an over-strength followed by stiffness degradation associated with softening mechanisms [36]. This behavior is consistent with the formulation of the HSS model and justifies the observed curve behavior. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline  & & & & \multicolumn{6}{c}{**HSS Model**} & \\ \hline Parameter & P\({}_{\rm ref}\) & E\({}^{\rm ref}\)\({}_{\rm 50}\) & E\({}^{\rm ref}\)\({}_{\rm ur}\) & E\({}^{\rm ref}\)\({}_{\rm 0 ed}\) & m & \(\
u\) & G\({}^{\rm ref}\)\({}_{\rm 0}\) & \(\gamma_{\rm 0.7}\) & K\({}_{\rm 0}\)\({}^{\rm nc}\) & \(\phi\) & \(\psi\) & c & R\({}_{\rm f}\) \\ \hline Value & 60 & 1310 & 25,900 & 3912 & 1 & 0.18 & 12,000 & 0.0001 & 0.82 & 34 & 14 & 1 & 0.82 \\ \hline Unit & kPa & kPa & kPa & - & - & kPa & - & - & \(\circ\) & \(\circ\) & kPa & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calibrated parameters of the HSS model. Figure 10: Variation in the friction angle \(\phi\). (**a**) Stress–strain strength curve. (**b**) Pore pressure–strain curve. (**c**) P’-q stress path curve. Figure 9: Variation in the slope of the critical state line M\({}_{\rm tc}\). (**a**) Stress–strain strength curve. (**b**) Pore pressure–strain curve. (**c**) P’-q stress path curve. On the other hand, a significant impact is observed on the stress path curve with the variation in the parameter K\({}_{0}\)\({}^{nc}\) (see Figure 11c). This parameter relates to the distribution of lateral and vertical stresses in the soil under initial consolidation conditions (see Figure 11). The parameters presented in Tables 3 and 4 were estimated and adjusted using a sensitivity analysis to represent the dilative behavior of the CIU triaxial tests, without resorting to values estimated through empirical correlations or other tests. On the other hand, the initial state parameters (\(\psi_{0}\)) in NS and the reference shear modulus (G\({}_{\text{ref}}\)) in HSS were key in defining the initial stiffness, dilatancy, and peak strength. During the parameter adjustment process, the major challenge was to identify common variables between the models to avoid altering the intrinsic material parameters. For this reason, a correlation between the parameters of both constitutive models was performed to achieve consistent calibration. Although the models represent different approaches to simulating soil behavior, they share some variables that allow a smoother transition between them. One of the main correlatable parameters is the reference elastic shear modulus at a given pressure (\(G_{\text{ref}}\)). Additionally, the Poisson's ratio (\(\
u\)) appears in both models with the same role of describing lateral deformation relative to axial deformation under load. However, the configuration of these parameters cannot be identical, as they affect the shape of the stress-strain strength curve. \[sint\phi^{\prime}=\frac{3 Mtc}{6+Mtc} \tag{1}\]  
The effective friction angle (\(\phi^{\prime}\)) in the HSS model correlates with the critical state friction parameter (\(M_{tc}\)) in the NS model, as shown in Equation (1). While the latter specifically focuses on friction at the critical state, both parameters serve to represent the soil's shear strength. 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, fundamental aspects such as elasticity, friction, and dilatancy, present in both models, allow data consistency when switching between the two simulation approaches [37]. During calibration, parameter correlation allowed an initial approximation of the curves for both models.