## 3 Standard p-y Approach for Monotonic Loads  
The behavior of laterally loaded piles is typically analyzed using the p-y method according to the DNVGL-ST-0126 and DNV-RP-C212 guidelines [7; 43]. In this approach, the monopile is modeled as a beam with specific properties, connected along its embedded length to multiple springs, whose lateral-load-displacement behavior is defined by p-y curves. These p-y curves represent the ground response through a non-linear relationship between soil resistance and displacement at a given depth. For homogeneous soil conditions, both the ultimate strength (\(P_{u}\)) and initial stiffness (\(E_{py}\)) increase with depth [1]. DNV-RP-C212 recommends different p-y curves for soft and stiff clay [43]. For soft clay, defined as clay with an undrained shear strength up to 100 kPa, [PERSON]'s (1970) p-y curves are recommended [11]. For stiff clay, defined as clay with an undrained shear strength exceeding 100 kPa, the procedures proposed by [PERSON] et al. (1975) and [PERSON] and [PERSON] (2011) are recommended [44; 45]. In this regard, [PERSON]'s (1970) soft-clay p-y curves were used for the upper depth (up to \(-30.6\) m, where the soil's undrained shear strength (\(S_{u}\)) is less than 100 kPa), while [PERSON] and [PERSON]'s (1975) p-y curves for stiff clay were employed at greater depths (beyond \(-30.6\) m, where Su exceeds 100 kPa) [11; 36]. [PERSON] and [PERSON] (2011) proposed two p-y curve formulations for stiff clay based on whether free water is present ([PERSON] et al. 1975) or absent ([PERSON] and [PERSON] 1975) [36; 44; 45]. The p-y curve with free water corresponds to the cases where annular scour occurs around the pile during cyclic loading (see Figure 5). Considering that, in the present study, the monopile response under monotonic loading is of interest, the p-y curve without free water proposed by ([PERSON] and [PERSON] 1975) has been adopted for the layers. The monopile foundation analysis was performed using the commercial software LPile v2022, which is tailored for evaluating laterally loaded piles via the p-y method. LPile utilizes a finite difference approach to solve the beam-column differential equation, enabling the determination of the deflection, bending moment, shear force, and soil response along the pile's length. For both the Matlock soft clay and Reese and Welch stiff clay without free water, LPile requires three input parameters: undrained shear strength (\(S_{u}\)), effective unit weight (\(\gamma^{\prime}\)), and the strain corresponding to half of the maximum difference in principal stresses in the stress-strain curve of the undisturbed specimen of clay (\(\varepsilon_{50}\)). The profiles for effective unit weight and undrained shear strength are detailed in Table 4. To ensure consistency between the two approaches, i.e., the FE and standard p-y methods, \(\varepsilon_{50}\) values were directly derived from numerical simulations of undrained triaxial tests. PLAXIS software provides a single-element algorithm that allows the simulation of common geotechnical laboratory tests for a defined set of parameters in a given constitutive model. There is no need for meshing in this method, and only the initial stresses on a 3D single element are defined. Then, changes in stress or strain are applied to the element  
Figure 5: Annular gaps formed around the pile following cyclic loading [46]. according to the desired test. In this study, a 3-axis compression test was simulated in a displacement-controlled manner to determine \(\varepsilon_{50}\). After applying the initial stresses on a hypothetical element at the desired depth (based on the vertical in-situ stress and the lateral soil pressure coefficient), the axial strain was increased in small steps until the failure of the element (q = qu). Then, the strain corresponding to half of the failure deviatoric stress was determined as \(\varepsilon_{50}\).