## 2 Methodology and Materials  
### Design Standard of Monopile Grounded Connection  
A schematic diagram of a typical grouted connection between the TP and the MP is shown in Figure 1. These connections between two components are formed by filling the annulus between two members with dissimilar dimensions with grout, where the infill acts as a load transfer medium. These GCs are effectively used in offshore drilling and production platform jackets, as well as wind turbine structures. Generally, offshore wind turbine structures are designed according to ISO 19902 [17], IEC 61400-3-1 [18], DNV-OS-J101 [19], and other internationally accepted design standards and support structure protection standards (safety standards). In particular, the requirements for material certificates, as well as testing and handling procedures of DNVGL-ST-0126, provide clear analysis methods for GCs and the design criteria for shear keys that should be complied with, while the criteria for analysis and verification through the FE analysis of GCs are outlined in DNVGL-RP-0419. Equation (1) gives the maximum nominal radial contact pressure (\(P_{nom,d}\)) between the top and bottom of the GC due to the applied bending moment [20,21]. \[P_{nom,d}=\frac{3\pi M_{d}EL_{g}}{EL_{g}\cdot R_{p}L_{g}^{2}(\pi+3\mu)+3\pi\mu R _{S}^{2}L_{g}+18\pi^{2}k_{eff}R_{p}^{3}\left\{\frac{R_{p}^{2}}{T_{p}}+\frac{R_ {TP}^{2}}{T_{TP}}\right\}}, \tag{1}\]  
where \(k_{eff}\) is the effective spring stiffness of the shear key, \(\mu\) is the characteristic friction coefficient (=0.7), \(R_{p}\) is the outer radius of the MP, \(R_{TP}\) is the outer radius of the TP, \(t_{p}\) is the thickness of the MP, \(t_{TP}\) is the thickness of the TP, \(L_{g}\) is the effective length of the GC (\(=L-2t_{g}\)), \(L\) is the length of the GC, and \(t_{g}\) is the nominal thickness of the grout. Equation (2) expresses the effective spring stiffness per unit length around the GC for shear keys [22]. \[k_{eff}=\frac{2t_{TP}S_{eff}^{2}nE\psi}{4\sqrt[4]{3(1-v^{2})}t_{g}^{2}\left\{ \left(\frac{R_{p}}{T_{p}}\right)^{\frac{3}{2}}+\left(\frac{R_{TP}}{T_{TP}} \right)^{\frac{3}{2}}\right\}t_{TP}+nS_{eff}^{2}L_{g}}, \tag{2}\]  
where \(S_{eff}\) is the effective vertical distance of the shear key (\(=s-w\)), \(s\) is the vertical center distance of two adjacent shear keys, \(w\) is the width of the shear key, \(E\) is the Young's  
Figure 1: (**a**) Schematic diagram of GC connecting the transition piece and monopile, and (**b**) sectional view of the GC model used in this paper. modulus of the steel, \(\
u\) is the Poisson's ratio of the steel, \(n\) is the number of effective shear keys, and \(\psi\) is the design factor (1.0 when calculating the action force of the shear key and 0.5 when calculating the maximum nominal radial contact pressure). Equation (3) indicates the force per unit length in the circumferential direction of the shear key due to the bending moment and the axial force. \[F_{V\;Shk,\;d}=\frac{6p_{nom,d}k_{eff}}{E}\frac{R_{p}}{L_{g}}\left(\frac{R_{p} ^{2}}{t_{p}}+\frac{R_{Tp}^{2}}{t_{TP}}\right)+\frac{P_{d}}{2\pi R_{p}}, \tag{3}\]  
where \(P_{d}\) is the weight of the superstructure, including the total weight of the TP. At one shear key, the average force per unit length along the circumference is as expressed in Equation (4), and the characteristic interfacial shear capacity of the GC is as expressed in Equation (5). \[F_{V1\;Shk,\;d}=\frac{F_{V\;Shk,\;d}}{n}, \tag{4}\]  
\[f_{bk}=\left[\frac{800}{D_{p}}+140\left(\frac{h}{s}\right)^{0.8}\right]k^{0.6} f_{ck}^{0.3}, \tag{5}\]  
where \(h\) is the height in the radial direction from the interface between the grout and the tubular steel, \(D_{p}\) is the diameter of the pile, and \(k\) is the stiffness parameter in the radial direction, as defined by Equation (6) below.