## 4 Results and Discussions
Figure 10 shows the lateral load capacity of all monopile geometries studied in this research at displacements of 0.1D and 0.01D, based on the 1D DNV p-y and 3D FE methods. The results are categorized by small and large displacements for various L/D ratios (4, 6, 8, and 10 m) of the monopile foundations. The findings indicate that while there is a difference in capacity values between the FEM and DNV methods, both show a similar trend of increasing capacity with increasing pile embedment length. As is illustrated in Figure 10a, for large displacements, increasing the embedment length for all monopile diameters leads to a continuous increase in capacity, with the rate of increase declining at an L/D ratio of 8 for both the 1D DNV p-y and 3D FE results. For small displacements, this decline in the rate of increase occurs at an L/D ratio of 6. Beyond this point, further increases in the L/D ratio do not result in significant capacity increases, causing the trend line to stabilize. This suggests that when considering small displacement or service criteria for determining the monopile embedment length, a smaller embedment depth can be selected compared to what would be required for achieving ultimate lateral capacity. Another notable point is the significant effect of increasing the monopile diameter on lateral capacity in both small and large displacements. While this approach can always be considered a viable solution, it is not always the most economical option. Figure 9: **Mudline-load–displacement response of the D8 and L/D of 4, 6, 8, and 10 based on (a,b) FE model and (c,d) 1D DNV model in large and small displacements. **  
The differences between the results of the 1D DNV p-y and FE methods, as shown in Figure 10, are detailed in Figure 11a,b for large and small displacements in percentages, respectively. According to these graphs, the maximum and minimum percentage differences between the 3D FE and 1D DNV p-y results are 41% and 11% for large displacements, and 32.5% and 13.3% for small displacements, respectively. The results indicate that as the L/D ratio increases, the percentage difference between the FE and 1D DNV p-y results decreases. While this reduction in difference has a steady trendline for small displacements, in large displacements, the rate of reduction decreases as the L/D ratio increases and stabilizes at an L/D ratio of 8 and higher. At an L/D ratio of 10, the discrepancy between the two methods narrows to an average of 13% across all monopile diameters, in large and small displacements. This reduction in the percentage difference with increasing L/D ratio is reasonable, as more slender monopiles align more closely with the conditions for which the DNV p-y method is designed. On the other hand, employing the 1D DNV p-y method for monopiles with an L/D ratio of less than 10 can lead to a substantial underestimation of their lateral capacity, potentially by as much as 41%. It is important to note that these quantities and ratios can vary depending on different soil conditions, the choice of constitutive models, and the specific loading conditions applied. Figure 12a,b display the deflection profiles of the 8 m monopile at various L/D ratios, comparing the FE and 1D DNV p-y analyses, respectively. The deflection is obtained by exerting a 5 MN load at a height of 40 m above the mudline. As the L/D ratio increases from 4 to 10, the deflection at the pile toe decreases to nearly zero for both methods. At an L/D ratio of 4, the deflection profile is nearly linear with a constant slope, indicating rigid rotation with minimal flexure. The FEM results at L/D = 4 show slight flexure, while the DNV results indicate almost no flexure, suggesting nearly rigid behavior. As the L/D ratio increases to 10, the deflection at the pile toe approaches zero, being observed at L/D = 8 in the DNV p-y method and at L/D = 10 in the FEM results. [PERSON] et al., 2023, also reported zero deflection at depths of 7 to 9D in their experimental study [12].