## 3 Sensitivity Analysis of the NorSand and HSSmal Models Using SoilTest
The resulting information is key to establishing a more efficient and well-founded calibration, as it allows focusing adjustment efforts on the most sensitive parameters. This process aimed to capture exaggerated variations and understand the influence of each parameter. The procedure was designed to observe how these changes affected the deviatoric stress vs. axial strain curves, pore pressure vs. axial strain curves, and stress paths in the p'-q diagram. The following section presents the constitutive models addressed in this study, along with the parameters used in the calibration of the experimental curves. NS is an elasto-plastic model based on CSSM, designed to describe soil behavior under static liquefaction and dilatancy conditions. It uses the state parameter (\(\psi_{0}\)) as a key variable to represent dilatancy in dense soils and liquefaction in loose soils [32]. The calibrated parameters for the NS model are shown in Table 3.  
The most dominant parameter is the state parameter (\(\psi_{0}\)), which governs the stress path (see Figure 5). Figure 4: Error analysis concerning sample size in the stress path curve p’-q. (**a**) CIU 400 kPa. (**b**) CIU 200 kPa. (**c**) CIU 100 kPa. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline  & & & & & \multicolumn{6}{c}{**NS Model**} \\ \hline Parameter & G\({}_{\text{ref}}\) & P\({}_{\text{ref}}\) & n\({}_{\text{G}}\) & \(\
u\) & \(\Gamma\) & \(\lambda\)e & M\({}_{\text{tc}}\) & N & X\({}_{\text{tc}}\) & H\({}_{0}\) & H\({}_{\Phi}\) & R & S & \(\psi_{0}\) \\ \hline Value & 7900 & 87 & 1 & 0.2 & 1.09 & 0.02 & 1.7 & 3.3 & 3.33 & 15 & 100 & 1.06 & 1 & \(-0.03\) \\ \hline Unit & kPa & kPa & - & - & - & - & - & - & - & - & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calibrated parameters of the NS model. Subsequently, the hardening parameters (H\({}_{0}\) and H\(\Downarrow\)) are identified, which control the strength and pore pressure (see Figures 6 and 7, respectively). Two parameters have a significant impact on the calibration, namely the shear modulus (G\({}_{\text{ref}}\)), which controls the initial elastic stiffness of the soil (see Figure 8). Figure 5: Variation in the state parameter \(\psi\). (**a**) Stress-strain strength curve. (**b**) Pore pressure-strain curve. (**c**) p-q stress path curve. Figure 6: Variation in the initial plastic hardening modulus H\({}_{0}\). (**a**) Stress–strain strength curve. (**b**) Pore pressure–strain curve. (**c**) p’-q stress path curve. Figure 7: Variation in the plastic hardening modulus as a function of the state parameter H\({}_{\Downarrow}\). (**a**) Stress–strain strength curve. (**b**) Pore pressure–strain curve. (**c**) p’-q stress path curve. The critical friction ratio (M\({}_{\rm tc}\)) controls the soil's shear strength when it reaches the critical state, that is, when the material experiences no changes in volume or stress during deformation [33] (see Figure 9). The HSS model, based on plasticity theory and formulated as an elasto-plastic model, stands out for its ability to capture the nonlinear behavior of soils, especially at small strains [34]. Its main advantage lies in considering the dependency of the elastic modulus on the strain level, which improves accuracy in simulations under cyclic or static loading conditions [35]. Table 4 presents the calibrated parameters of the HSs model. The dependency of the curve on the friction angle (\(\phi\)) is evident. This parameter defines the shear strength and is critical for configuring the peak of the stress-strain strength curve (see Figure 10). It is worth noting that, regarding the deviatoric stress versus axial strain curve, although the curves initially follow the expected theoretical trend, beyond a certain strain (\(\sim\)2.5%), the curve with the highest \(\phi\) exhibits a relative decrease in deviatoric stress compared to the curves with lower \(\phi\).