## 4 Results and Discussions
For intermediate L/D values, the deflection profiles exhibit a series of curved lines with nonzero values at the end of the pile, indicating a combination of rotation and flexure. Figure 10: Lateral load vs. L/D ratio at (**a**) 10 and (**b**) 1 percent of the monopile diameter based on the FE and 1D DNV results. Determining a minimum embedded length to ensure the stability of offshore monopile foundations under severe loading conditions is a crucial step in their design. While various criteria exist for geotechnical monopile design, there is no widely accepted standard for determining the optimal pile length. In many projects, a rigid grip of the pile in the subsoil under significant static loads is essential, which necessitates either a deflection profile with two zero-deflection points (zero-toe-kick criterion, \(L_{zik}\)) or at least a vertical tangent (vertical-tangent criterion, \(L_{vt}\)) [48; 49]. The aforementioned criteria may lead to excessively long embedded pile lengths for large-diameter monopile foundations with significant bending stiffness [50]. As an alternative, DNVGL-2016 proposes analyzing the influence of increased embedded length on pile head displacement and selecting an embedment length that places the design on  
Figure 11: The difference between the results of the FE model and 1D DNV method in (**a**) large and (**b**) small displacements. Figure 12: Deflection profile for the 8 m monopile in L/D ratios of 4, 6, 8, and 10 for the 5 MN load exerted at h = 40: (**a**) FE results and (**b**) 1D DNV p–y method results. the \"flat part of the corresponding displacement-length curve\". This means that the length (\(L_{const}\)) should be chosen such that further increases in monopile length have minimal impact on pile head deflection. Based on the descriptions provided, the critical lengths according to different criteria can be analyzed for both the 1D DNV p-y and FE methods using the data in Figures 12 and 13. According to Figure 13, the \(L_{const}\) for both methods is achieved at a pile length of approximately 48 m, beyond which further increases in pile length do not significantly reduce monopile head deflection. The results also show that the vertical-tangent criterion leads to almost-similar pile lengths, with approximately 48 m for the 1D DNV p-y method and 50 m for the FEM results. Although the vertical-tangent criterion offers embedded lengths similar to the DNV recommendation, previous research has highlighted its unreliability, as this criterion may result in shorter embedded lengths for higher load eccentricities. This is not desirable, as a suitable criterion should lead to a larger pile length for more critical loading conditions [50]. The zero-toe-kick criterion, on the other hand, leads to the longest pile lengths, with approximately 51 m for the 1D DNV p-y method and more than 80 m for the FE results, under the 5 MN load considered. The response of the monopile using p-y curves extracted from the FE model was also investigated using LPile software. This analysis was conducted for different L/D ratios of the 8 m monopile, the reference diameter in this study. The p-y curves can be extracted from the numerical model, y values through the direct output of the model, and p values from the numerical integration of normal and shear stresses on interface elements. The p-y curves were inserted into the LPile model using the user-defined p-y-curve option. Henceforth, these results will be referred to as the 1D model with FE-extracted p-y curves. Figure 14 compares the results of the FE analysis, 1D DNV p-y method, and 1D model with FE-extracted p-y curves. It can be seen from Figure 14a,b that in low slenderness ratios (i.e., L/D = 4), there is a clear difference between the results of the FE model and the 1D model with FE-extracted p-y curves for both small and large displacements, highlighting the influence of additional components contributing to the lateral capacity of the monopile.