## 2 Methodology and Materials
### Design Standard of Monopile Grounded Connection
\[k=\Big{[}\left(2R_{p}/t_{p}\right)+\left(2R_{TP}/t_{TP}\right)\Big{]}^{-1}+ \left(E_{g}/E\right)\Big{[}\left(2R_{TP}-2t_{TP}\right)/t_{g}\Big{]}^{-1}, \tag{6}\]  
where \(E_{g}\) is the Young's modulus of the grout and \(f_{ck,\;cub/75}\) is the characteristic compressive strength (MPa) of a 75 mm cube. The characteristic capacity per unit length of one shear key is as expressed in Equation (7), and the design capacity is as expressed in Equation (8). \[F_{V1\;Shk\;cap}=f_{bk}\cdot s. \tag{7}\]  
\[F_{V1\;Shk\;cap,\;d}=\frac{F_{V1\;Shk\;cap}}{\gamma m}. \tag{8}\]  
According to other studies of pile-to-sleeve GC, typical shear key types are divided into a weld bead, flat bar with fillet weld, and round bar with fillet weld [23]. In this study, the shear key of the flat bar with fillet weld type was selected as the research model because it is the most commonly used among them. Moreover, we expect that it would be relatively difficult to manufacture the round shape of the shear key reflecting the precise radius of curvature of the elastomeric bearing. The requirements for the shape dimensions of the shear keys are as follows:  
\[P_{nom,d}=\frac{3\pi M_{d}EL_{g}}{EL_{g}\cdot R_{p}L_{g}^{2}(\pi+3\mu)+3\pi\mu R _{S}^{2}L_{g}+18\pi^{2}k_{eff}R_{p}^{3}\left\{\frac{R_{p}^{2}}{T_{p}}+\frac{R_ {TP}^{2}}{T_{TP}}\right\}}, \tag{1}\]0  
\[P_{nom,d}=\frac{3\pi M_{d}EL_{g}}{EL_{g}\cdot R_{p}L_{g}^{2}(\pi+3\mu)+3\pi\mu R _{S}^{2}L_{g}+18\pi^{2}k_{eff}R_{p}^{3}\left\{\frac{R_{p}^{2}}{T_{p}}+\frac{R_ {TP}^{2}}{T_{TP}}\right\}}, \tag{1}\]1  
\[P_{nom,d}=\frac{3\pi M_{d}EL_{g}}{EL_{g}\cdot R_{p}L_{g}^{2}(\pi+3\mu)+3\pi\mu R _{S}^{2}L_{g}+18\pi^{2}k_{eff}R_{p}^{3}\left\{\frac{R_{p}^{2}}{T_{p}}+\frac{R_ {TP}^{2}}{T_{TP}}\right\}}, \tag{1}\]2  
\[P_{nom,d}=\frac{3\pi M_{d}EL_{g}}{EL_{g}\cdot R_{p}L_{g}^{2}(\pi+3\mu)+3\pi\mu R _{S}^{2}L_{g}+18\pi^{2}k_{eff}R_{p}^{3}\left\{\frac{R_{p}^{2}}{T_{p}}+\frac{R_ {TP}^{2}}{T_{TP}}\right\}}, \tag{1}\]3  
\[P_{nom,d}=\frac{3\pi M_{d}EL_{g}}{EL_{g}\cdot R_{p}L_{g}^{2}(\pi+3\mu)+3\pi\mu R _{S}^{2}L_{g}+18\pi^{2}k_{eff}R_{p}^{3}\left\{\frac{R_{p}^{2}}{T_{p}}+\frac{R_ {TP}^{2}}{T_{TP}}\right\}}, \tag{1}\]4  
\[P_{nom,d}=\frac{3\pi M_{d}EL_{g}}{EL_{g}\cdot R_{p}L_{g}^{2}(\pi+3\mu)+3\pi\mu R _{S}^{2}L_{g}+18\pi^{2}k_{eff}R_{p}^{3}\left\{\frac{R_{p}^{2}}{T_{p}}+\frac{R_ {TP}^{2}}{T_{TP}}\right\}}, \tag{1}\]5  
\[s\geq min\bigg{\{} \begin{array}{c}0.8\sqrt{R_{p}t_{p}}\\ 0.8\sqrt{R_{TP}t_{TP}}\end{array} \bigg{\}}. \tag{15}\]The purpose of the GC is to transfer pressure between the two tubular members to provide capacity for the loads. According to DNVGL-ST-0126, the bending moment capacity depends on the radial contact pressure, the horizontal shear resistance between the steel and the grout, and the vertical shear between the steel and the grout. It is composed of the resistance and moment resistance of the shear key. Axial load capacity is achieved using horizontal shear keys. Furthermore, the vertical shear key can be arranged on the inside or outside as necessary to provide capacity for torsional load. The design standard for GC using the shear key is as follows:  
\[F_{V1\text{ }Shk,\text{ }d}\leq F_{V1\text{ }Shk\text{ }cap,\text{ }d}, \tag{16}\]  
where \(F_{V1\text{ }Shk}\) is the force per unit length in the circumferential direction due to the bending moment and the axial force, and it is transmitted by the shear key. Equation (17) gives the requirements for the maximum nominal radial contact pressure as follows:  
\[p_{nom,d}\leq 1.5\text{ MPa}. \tag{17}\]  
These GC capacity evaluations can be analyzed through FE analysis. However, uncertainties of several parameters exist in the capacity evaluation of GCs. Uncertainties relate to the element type, element quality in the stress concentration region, coefficient of friction, grout material properties, material modeling, and contact formulas. Therefore, to minimize these uncertainties, proper FE modeling is essential. The FE model covered in this paper can be found in Section 3.