## 2 Methods
### Soil Model Parameter  
To model the subsoil profile realistically, one must consider the non-linearity of the soft soil layer. There are various models that have been developed to achieve a realistic model for field conditions, including the hardening soil model (HSM), soft soil model (SSM), modified cam clay model (MCC), etc. In this study, the sand layer soil model uses the hardening soil model (HSM). The hyperbolic elastoplastic model (HSM) takes into account the nonlinearity of the soil by showing how stiffness changes with stress but it does not look at viscous effects like creep and stress relaxation. HSM is based on the Mohr-Coulomb failure criterion and its yield surface can expand due to plastic strain. The hardening soil model uses plasticity theory, unlike the Mohr-Coulomb model, which uses an elasticity model. The hardening soil model considers both shear hardening and compression hardening of the soil. A detailed formulation of the hardening soil model is explained by [26]. The hardening soil model (HSM) is introduced to characterize the mechanical behavior of soil under loading, unloading, and consolidation phases. The HSS model incorporates the small strain properties of materials, enabling a more precise prediction of soil deformation. Usually, the HSS model utilizes drained soil parameters such as unit weight (\(\gamma\)), drained shear strength (\(c^{\prime}\)), effective internal angel friction (\(\varphi^{\prime}\)), and lateral limit compression (\(E_{S}\)) [27]. The hardening soil model can be used for modeling different types of soil, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & & & \\ \hline Parameter & Unit & Very Loose & Loose & Medium & Dense & Very Dense \\ \hline Relative density (Dr) & \% & 0–0.15 & 0.15–0.35 & 0.35–0.65 & 0.65–0.85 & 0.85–1.00 \\ Corrected N\({}^{\prime}\)-SPT & (blow) & 0–4 & 4–10 & 10–30 & 30–50 & \(>\)50 \\ \multicolumn{2}{c}{Internal angle} & & & & & \\ friction (\(\varphi\)) & (\({}^{\circ}\)) & 25–30 & 27–32 & 30–35 & 35–40 & 38–43 \\ Unit weight (\(\gamma\)) & (kN/m\({}^{3}\)) & 11.0–15.7 & 14.1–18.1 & 17.4–20.4 & 17.3–22 & 20.4–23.6 \\ \hline \multicolumn{2}{c}{Cohesion Soil} & & & & & \\ \hline Parameter & Unit & Very Soft & Soft & Medium & Stiff & Very Stiff & Hard \\ \hline Corrected N\({}^{\prime}\)-SPT & (blow) & 0–2 & 2–4 & 4–8 & 8–16 & 16–32 & \(>\)32 \\ value & (kN/m\({}^{3}\)) & \(<\)15.7 & 15.7–18.8 & 17.3–19.6 & 18.1–20.4 & 18.8–22 & \(>\)20.4 \\ \multicolumn{2}{c}{Unconfined compression (q\({}_{\text{u}}\))} & & & & & \\ Cohesion undrained (C\({}_{\text{u}}\)) & (kN/m\({}^{2}\)) & 12 & 12–24 & 24–48 & 48–96 & 96–192 & \(>\)200 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation parameter for cohesionless soil and cohesive soil [25]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Soil Type** & **Es (kPa)** \\ \hline Sand (normally consolidated) & 500 (N + 15) \\ Sand (saturated) & 250 (N + 15) \\ Gravelly sand & 1200 (N + 6) \\ Clayey sand & 320 (N + 15) \\ Silts, sandy silts, clayy silt & 300 (N + 6) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation for [PERSON]’s modulus parameter [25]. including granular and soft soil. Power \(m\) represents the stress dependency of soil stiffness, where for soft soil, \(m=1\). The hardening soil model needs three stiffness parameters at a chosen reference pressure (\(P_{\textit{ref}}\)). There are a (1) triaxial modulus/secant modulus (\(E_{50}\)/\(\pi\)), (2) oedometric modulus (\(E_{\textit{ood}}\)/\(\pi\)), and (3) unloading-reloading modulus (\(E_{\textit{vir}}\)/\(\pi\)). A series of laboratory tests determine this parameter [28]. However, some scholars have used statistical and inverse analysis to determine the stiffness parameter for this model [29; 30]. This is conducted considering the time and cost if only using a laboratory test. Furthermore, to model the clayey soil in this study, a soft soil model is employed. Some scholars have used the soft soil model (SSM) to analyze the behavior of soft soil [31].