## 1 Introduction
### Methodology
#### 1.1.2 Convergence Study  
Once the final set of soil parameters were defined, the convergence analysis was carried out. The purpose of this convergence analysis was to test the FE sensitivity to the model domain boundaries and to increase the accuracy of the results, defining the reference geometry and mesh size that will be followed in the parametric analysis. Figure 3 shows the dimensions studied herein, while Figure 4 displays a typical set of results for the convergence analysis, and in this case, the effects of the model vertical boundaries in the y direction (transverse direction of the loading, Ly) on the displacement at the mudline, ulm (m). The same procedure was followed to define the length of the model, Lx, and depth of the model, Lz (Figure 3). In all the analyses considered, the global element size was set to be medium sized, and a refinement zone extending 3D, 5D, and 7D away from the center  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Clay1** & **Units** \\ \hline \(\mathrm{c^{\prime}}\) & 15 & kPa \\ \(\mathrm{\Psi}\) & 0 & Degrees \\ \(\mathrm{\phi^{\prime}}\) & 8 & Degrees \\ \(\mathrm{P^{\prime}_{pop}}\) & 15 & kPa \\ \(\mathrm{P^{\prime}_{ref}}\) & 41 & kPa \\ \(\mathrm{e_{ini.}}\) & 4.23 & - \\ \(\mathrm{Y}\) & 17.9 & \(\mathrm{KN/m^{3}}\) \\ \(\mathrm{E^{ref}_{ood}}\) & 1406 & kPa \\ \(\mathrm{E^{ref}_{50}}\) & 1758 & kPa \\ \(\mathrm{E^{ref}_{ur}}\) & 5000 & kPa \\ \(\mathrm{v_{ur}}\) & 0.2 & -of the monopile and extending to the base of the model (zone of refinement in Figure 5) was investigated with changing coarseness factor (cf). This was completed to produce a finer mesh within the proximity of a monopile, where most of the strains were anticipated to take place. Based on the aforementioned convergence analyses, the selected boundary conditions are 7D for x, y from the pile centerline in all directions, with a refinement zone of 3D and cf of 0.2, yielding approximately 25,000 elements. This discretization of the domain provided good agreement with the practice reported by [35].  
Based on the results of the sensitivity analysis, the vertical boundaries were placed at 7D from the center of the model and the bottom boundary was placed more than (3D)  
Figure 4: Sample of convergence analysis results.  
Figure 3: Boundary conditions varied in convergence analyses.  
below the pile tip. The vertical boundaries were restricted horizontally and allowed to move vertically, while the bottom boundary was fixed in all directions (i.e., x, y, and z). These are standard model boundary conditions in Plaxis 3D and are used to remove any effects from the model boundaries on the structure response. The global mesh size was chosen to be medium sized after performing the sensitivity analysis, in which the FEM comprised 25,000 elements approximately. This was to ensure higher quality, yet time-efficient modeling. The mesh was further refined within a zone of 3D adjacent to the pile to increase the accuracy of the results. Figures 5 and 6 show a typical mesh used in the study.  
The load-displacement curve obtained from the FE analysis is plotted in Figure 7, along with the field data. Figure 7 demonstrates that there is excellent agreement between the calculated and measured load-displacement curves, validating the ability of the developed finite element model to simulate the behaviour of the large-diameter piles installed in the cohesive soil. Bending-moment and inclinometer data are also compared and excellent agreement is obtained as shown in Figure 8.  
Figure 6: Cross section showing developed mesh.  
Figure 7: Load displacement curve using Hs undrained A parameters, GK04 field data from [PERSON] et al. [22].