## 4 Results and Discussions  
This section examines and discusses the lateral load response of monopile foundations with varying pile geometries based on the results of FE analysis and the 1D DNV p-y method. In the FE model, the load is applied at a height of 40 m above the mudline, while in the 1D DNV p-y analysis, conducted using LPile software, the horizontal load is applied at the mudline, and the load eccentricity is considered by applying an equivalent moment to the monopile at the mudline. A diameter-to-thickness ratio (\(D_{out}/t\)) of 100 is maintained across all models in this study. Since the focus is on the lateral behavior of the monopile, no vertical load is considered. DNVGL-ST-0126 states that a criterion on displacement shall be considered as the accepting criterion for adequate lateral pile resistance. Therefore, a displacement of 10% of the monopile diameter is used to define the ultimate lateral capacity and ultimate limit state (ULS) criteria in this study [47]. Additionally, the serviceability limit state (SLS) criterion, based on the same code, is defined as an average rotation of 0.25 degrees at the mudline for a given load applied at an eccentricity above the mudline. The results of this study indicate that this rotation corresponds approximately to a lateral displacement  
Figure 6: Simulated stress–strain curve in undrained 3-axial compression test for a soil element at a depth of \(-35\) m.  
Figure 7: Profile of \(\varepsilon_{50}\) with depth. of 1% of the pile diameter at the mudline, for all geometries studied, with a maximum divergence of 5% (see Table 7). Consequently, for each monopile geometry analyzed, diagrams illustrating both large and small displacements will be presented and discussed. Table 1 details the dimensions studied in this research. The 8 m monopile serves as the reference diameter in this study. Figure 8 illustrates the load-displacement curves for the D8-LD4 monopile, including results from both the numerical model and the 1D DNV p-y method. As can be seen, the DNV p-y method predicts a lower capacity of the monopile in both small and large displacements. Notably, the difference between the two methods increases with greater pile head displacement. In Figure 8b, it can be observed that at very small displacements (less than 0.02 m), the curves overlap. However, as displacement increases, the difference between the two curves increases, eventually reaching a point where the amount of difference remains nearly constant. Figure 9 presents the load-displacement results for all L/D ratios considered for the 8 m monopile in this study. Graphs (a) and (b) display the results from the FE model, while graphs (c) and (d) show the results from the 1D DNV p-y method. Figure 9a,c indicate that monopile stiffness and capacity increase with the L/D ratio in both the FE and 1D DNV p-y methods. However, the rate of capacity increase diminishes as the L/D ratio rises. Specifically, the sharp increase observed from an L/D ratio of 4 to 6 turns into a more modest increase from an L/D ratio of 8 to 10. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**L/D**} & \multicolumn{4}{c}{**D (m)**} \\ \cline{2-5}  & **4** & **6** & **8** & **10** \\ \hline
4 & 0.236 & 0.240 & 0.242 & 0.243 \\
6 & 0.242 & 0.250 & 0.254 & 0.255 \\
8 & 0.259 & 0.262 & 0.265 & 0.263 \\
10 & 0.260 & 0.262 & 0.254 & 0.263 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Monopile rotation at 0.01D lateral mudline displacement (in degrees). Figure 8: Comparison between the 1D DNV and FE model’s mudline-load–displacement response of the D8-LD4 at (**a**) large displacements and (**b**) small displacements. This trend is more pronounced in small displacements (Figure 9b), where increasing the L/D ratio from 6 to 10 does not significantly enhance capacity. The 1D DNV p-y results, shown in Figure 9c,d, exhibit a similar trend and layout to the FEM results, particularly in the small displacements domain, albeit with a notably weaker load-displacement response.