## 1 Introduction
### Methodology  
The aim of this research is to establish a quick method for estimating monopile lateral ultimate capacity based on a few soil parameters and design inputs. This has been accomplished by studying monopile behavior under eccentric lateral loading similar to that of a 5 MW wind turbine in medium-depth water. To do so, several prototype dimensions of MP models were established. A series of finite element models employing displacement-controlled loading were conducted. Model responses were evaluated for their bending behaviour and lateral ultimate capacity. A new normalization study examines whether the lateral capacity of the pile can be characterized primarily using the L/D ratio, as a combination of L/D and normalized stiffness of the monopile with respect to the soil. The effects of footing rigidity on the lateral ultimate capacity of monopiles' foundations is studied by changing the ground conditions, and generic curves are established relating to the ultimate lateral capacity of the foundation with respect to L/D and the foundation's normalized stiffness \(\mathrm{E_{P}}^{\star}\) given by the following:  
\[\mathrm{E_{P}}^{\star}=\frac{\mathrm{E_{P}I_{P}}}{\mathrm{I_{scp}}} \tag{1}\]E\({}_{\text{p}}\) : normalized stiffness of the monopile; E\({}_{\text{p}}\): pile Young's modulus; I\({}_{\text{P}}\): pile moment of inertia; and I\({}_{\text{scp}}\): moment of inertia of a solid cross-section pile of same diameter as the actual pile. Specifically, we investigate the mode of contribution using a normalization procedure of the ultimate capacity of a monopile considering the effects of soil profile and pile/soil relative rigidity given using E\({}_{\text{p}}\) */E\({}_{\text{50}}\), where E\({}_{\text{p}}\) * is the foundation normalized stiffness and E\({}_{\text{50}}\) is the soil Young's modulus at 50% of the ultimate deviatoric load is that causing failure of a soil specimen in a triaxial apparatus, q\({}_{\text{f}}\). This approach enables the normalization of the lateral ultimate capacity by the soil shear strength and pile diameter. Design charts are established to develop the MP lateral ultimate capacity considering L/D and E\({}_{\text{p}}\) */E\({}_{\text{50}}\) ratios for a given eccentricity. Finally, predictive equations are proposed to calculate the MP lateral ultimate capacity based on best-fit data from finite element (FE) results. The normalization method used provides a pathway for use of the same framework with other eccentricities. Three-dimensional (3D) FE models (FEMs) were conducted to simulate the MP foundations. Tetrahedron 10-noded elements were used to discretize the soil, while plate elements were used to discretize the tower and the pile. The FEM was validated against the results of field tests from [22], and the pile was simulated using embedded beam elements confined with solid elements instead of plate elements, to enable the evaluation of the structural forces. To account for slippage and gap formation, 6-noded interface elements were used to simulate contact between the solid (pile) zone and soil. The strength of the interface elements was defined through a reduction factor, R\({}_{\text{int}}\), applied to the soil properties, which varied between 1 and 0.3 for soft and stiff soils, respectively. The tower was simulated as a beam element having unit weight, diameter, E and thickness of 77 kN/m\({}^{3}\), 6 m, 200 GPa and 0.035 m, respectively. It is rigidly connected to the surrounding solid elements to ensure that the load is transferred uniformly over the pile area. In all models, x and y boundaries were set at 7D from the model center and restricted to move horizontally, while being allowed to move vertically. The bottom, z, boundary was fixed and placed at least 3D below the pile tip to avoid any boundary effects and to model rotational stiffness correctly. The FEM had an average of 25,000 elements. The soil behaviour was simulated employing the hardening-soil (HS) model obeying the Mohr-Coulomb (MC) failure criterion [34].