## 2 Finite Element Modeling
### Constitutive Model  
In this study, an idealized clay soil profile, derived from a real offshore site near the South Korean peninsula, was utilized. The NGI-ADP elastoplastic constitutive model was applied to the clay soil, as described in references [37; 38]. This model is specifically designed to capture the anisotropy in the undrained behavior of clays, using a total stress approach. Unlike most constitutive models, the NGI-ADP model allows for the direct input of undrained shear strengths for active (A), direct-simple-shear (D), and passive (P) modes of loading. The NGI-ADP constitutive model has demonstrated decent performance for laterally loaded monopiles in clay soils [39]. Table 2 lists the required parameters for the NGI-ADP constitutive model along with their descriptions. The soil drainage type was set to Undrained (C) to enable a total stress analysis with the direct input of undrained parameters. When simulating laterally loaded monopiles in clay, it is crucial to address the gap created at the interface between the pile and the surrounding soil during loading. For onshore monopiles, where this gap remains dry, the soil's saturated unit weight should be used. Conversely, for offshore monopiles, where the gap fills with free water, the submerged unit weight should be applied, even in total stress analyses. This approach ensures that the effect of the water-filled gap on counteracting the water pressure on the opposite side of the monopile is included in the modeling. Therefore, the submerged unit weight was used for the soil, with the phreatic level set at the bottom of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Model Code** & **D\({}_{\text{out}}\) (m)** & **L (m)** & **L/D\({}_{\text{out}}\)** & **h (m)** & **t (mm)** \\ \hline
1 & D4 LD4 & & 16 & 4 & & 40 \\
2 & D4 LD6 & 4 & 24 & 6 & 40 & 40 \\
3 & D4 LD8 & & 32 & 8 & 40 & 40 \\
4 & D4 LD10 & & 40 & 10 & & 40 \\ \hline
5 & D6 LD4 & & 24 & 4 & & 60 \\
6 & D6 LD6 & 6 & 36 & 6 & 40 & 60 \\
7 & D6 LD8 & & 48 & 8 & 60 \\
8 & D6 LD10 & & 60 & 10 & & 60 \\ \hline
9 & D8 LD4 & & 32 & 4 & & 80 \\
10 & D8 LD6 & 8 & 48 & 6 & 40 & 80 \\
11 & D8 LD8 & & 64 & 8 & 40 & 80 \\
12 & D8 LD10 & & 80 & 10 & & 80 \\ \hline
13 & D10 LD4 & & 40 & 4 & & 100 \\
14 & D10 LD6 & 10 & 60 & 6 & 40 & 100 \\
15 & D10 LD8 & & 80 & 8 & 100 \\
16 & D10 LD10 & & 100 & 10 & & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of monopile dimensions studied. the model. The clay's submerged unit weight (\(\gamma^{\prime}\)) and the lateral earth pressure coefficient K0 were 8.5 kN/m\({}^{3}\) and 1, respectively. The value of \(\tau_{0}/S_{u}^{A}\) was determined from [38]:  
\[\tau_{0}/S_{u}^{A}=0.5(1-K_{0})\sigma_{V0}^{\prime}/S_{U}^{A}\geq 0 \tag{1}\]  
where \(\sigma_{V0}^{\prime}\) is the initial vertical effective stress, considered positive for compression. The ultimate plastic strains for each layer were calculated as follows [40]:  
\[\gamma_{f}^{C}=\gamma_{f}^{E}/2=\gamma_{f}^{DSS}/1.5=K_{f}\cdot S_{U}^{A}/G_{ur }\cdot 100 \tag{2}\]  
where \(K_{f}\) is the calibration parameter and was set equal to 60 [40]. The undrained shear strength (\(S_{U}^{A}\)) was assumed to vary linearly with depth (z) as it is given by (3):  
\[S_{U}^{A}=5.2+3.1z \tag{3}\]  
To take strength anisotropy into account, the ratios \(S_{U}^{P}/S_{U}^{A}\) and \(S_{U}^{DSS}/S_{U}^{A}\) were set to 0.5 and 0.75, respectively [40]. The variation in the small-strain shear modulus of soil, \(G_{ur}\), with depth is shown in Table 3.  
Accordingly, Table 4 lists the summary of the soil parameters for the NGI-ADP model. For the monopile material, the linear elastic constitutive model was considered, and typical steel properties (\(E=210.0\) GPa and \(\
u=0.3\)) were assigned to it.