## 2 Finite Element Modeling
### Verification  
The numerical model was validated against the results from the CL2 pile test conducted at the Cowden site during the PISA project [41]. The CL2 test monopile had the largest diameter among the tests; its geometric characteristics detailed are Table 5. Initially, a ground profile for the Cowden site was developed using site investigation data and the NGI-ADP constitutive model [27; 42]. This ground profile includes approximately 40 m of over-consolidated clay till, underlain by chalk, with the groundwater table 1 m below the surface. The saturated bulk unit weight (\(\gamma_{sat}\)) is reported as 21.19 kN/m\({}^{3}\). Figure 3 illustrates the variation in the small-strain shear modulus (\(G_{0}\)), undrained shear strength in compression (\(S_{\text{u}}\)), lateral earth pressure coefficient in terms of effective stress (\(K_{0}^{\prime}\)), and measured pore water pressures (U) with depth. A detailed description of the ground conditions can be found in the work of [PERSON] et al. (2020a) [42]. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Test** & **D\({}_{\text{OUT}}\) (m)** & **L (m)** & **L/D\({}_{\text{OUT}}\)** & **h (m)** & **t (mm)** \\ \hline CL2 & 2 & 10.6 & 5.3 & 10.1 & 25 \\ \hline \end{tabular}
\end{table} 
Table 5: CL2 monopile test dimension at Cowden site. Since the Cowden site is onshore, the saturated unit weight of the soil was used to generate the initial stresses. Additionally, there is a significant non-linear variation in soil parameters, particularly at near-surface depths, which can affect the accuracy of predicting the response of calibration monopiles. To account for this variation, soil layers with a thickness of 1 m were used to create an appropriate model. Table 6 lists the calibrated NGI-ADP model parameters for the Cowden site. Given the use of the saturated unit weight for the soil, the lateral pressure coefficient in the middle of each layer was calculated in terms of total stresses as follows:  
\[K_{0}^{total}=\left(K_{0}^{\prime}+U/\sigma_{V}^{\prime}\right)/\left(1+U/ \sigma_{V}^{\prime}\right) \tag{4}\]  
The value of \(\tau_{0}/S_{u}^{A}\) in each layer was determined from (1). The calibration parameter \(K_{f}\) is from [39] and ultimate shear strains were calculated using (2) [39]. Based on triaxial tests performed during the PISA project, the average \(S_{U}^{P}/S_{U}^{C}\) ratio is 0.841 [27,42] and ratios \(S_{U}^{P}/S_{U}^{A}\) and \(S_{U}^{DSS}/S_{U}^{A}\) were calculated as follows:  
\[S_{U}^{P}/S_{U}^{A}=\left(S_{U}^{P}/S_{U}^{C}\right)\left(S_{U}^{C}/S_{U}^{A} \right)=0.841\times 0.99=0.833\]  
Figure 3: Summary of initial conditions adopted for Cowden site: (**a**) small-strain shear modulus (\(G_{0}\)); (**b**) undrained shear strength in compression (\(S_{u}\)); (**c**) lateral earth pressure coefficient in terms of effective stress (\(K_{0}^{\prime}\)); and (**d**) pore water pressure (U) (data from [PERSON] et al. 2020,2020,2020,2020) [27,42]. and from [40]:  
\[S_{U}^{DSS}/S_{U}^{A}=0.5\times\left(S_{U}^{P}/S_{U}^{A}+S_{U}^{C}/S_{U}^{A} \right)=0.5\times\left(0.833+0.99\right)=0.911\]  
Figure 4 compares the calculated lateral-load-displacement curve with the observed field behavior from [42]. As can be seen, the calculation results show reasonable agreement with the measured response of the monopile. To assess the accuracy of simulation results compared to field observations, the accuracy metric \(\eta\) is defined as follows [27]:  
\[\eta=\left(A_{ref}-A_{diff}\right)/A_{ref} \tag{5}\]  
where \(A_{ref}\) is the area below the reference, i.e., field measurements, and \(A_{diff}\) is the delimited area between the reference and the simulated curve. Desired \(\eta\) values are in the range of 90-100% [40]. The \(\eta\) parameter was calculated to be 90%, which indicates acceptable accuracy. Superimposed on the figure is the PISA finite-element-modeling CL2 curve [27], which closely fits the 3D FEM results.