## 4 Construction of Equivalent Monopile Model for OC4 Jacket Support Structure  
As mentioned in Section 2, the goal of this work is to propose an analysis procedure for jacket substructure and to verify its efficacy. The second analysis stage is to build an equivalent (substitute) monopile model of OC4 jacket substructure. The OC4 jacket support structure is firstly built by Solidworks 2013 (Dassault Systems, Waltham, MA, USA), as shown in Figure 6. The essential information for equivalent monopile model construction, like the density, cross-sectional area, young's module and area moment of inertia, are all obtained from this CAD profile. With the aid of freeware BModes 3.0, the OC4 jacket support structure model is finally simplified to be a monopile model. The flowchart of equivalent monopile model construction is shown in Figure 7. The CAD model of jacket support structure will be divided into several segments along the vertical direction. The software BModes 3.0 is employed to calculate the equivalent material property for the segment of jacket substructure transferred to be a part of a monopile. In addition, the global analysis is to obtain the aerodynamic loadings of an OWTG supported by an equivalent monopile. These loadings will be the input of local analysis. According to the released OC4 data, the transition piece (tower base) is supposed to be a rigid body. The NREL 5 MW OWTG FAST model is further simplified based on the OC4 documents as follows:  
1. The tower base is remodeled to be a rigid concrete block of dimension 4 m \(\times\) 9.6 m \(\times\) 9.6 m and is placed on the top of OC4 jacket substructure. Figure 4: Power Spectra of Base Shear Force under Load Case 5.3 of OC3 Phase I.  
Figure 5: Power Spectra of Base Overturning Moment under Load Case 5.3 of OC3 Phase I. The mass of concrete block is about 666 tons. The block C.O.G. (Center of Gravity) and tower centerline are entirely overlapped. * The RNA is treated as a point mass in SAP2000. The weight of rotor nacelle assembly (RNA) is assumed to be 350 tons [21]. Figure 6: OC4 Jacket Substructure CAD Model (**a**); and Simplified Tower Model (**b**). Figure 7: Flowchart of the Construction of Equivalent Monopile Model for Jacket Substructure. The constructed models and masses of substructure components are shown in Figures 6 and 8, respectively. Ignorable error occurred (see Table 2) in comparison with the results by ABS (American Bureau of Shipping) [26]. Moreover, the hydrodynamic mass and marine growth, which are shown in Figures 9 and 10, respectively, are taken into consideration as well. The OWTG is expected to be installed in Taiwan Strait and the corresponding water depth is 50 m. The equivalent hydrodynamic mass is estimated at the water depth of 50 m below mean sea level (MSL) and the marine growth is only engaged within the water depth range of 2-40 m below MSL (see Table 3[27]). Similarly, a comparison between the simulation results by INER and ABS is accomplished in Table 4. It can be observed that nearly negligible errors exhibited between these results of the two research teams. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Items**} & \multirow{2}{*}{**ABS**} & \multicolumn{4}{c}{**INER**} \\ \cline{3-6}  & & **Jacket** & **Error (\%)** & **Equivalent Monopile** & **Error (\%)** \\ \hline Mass (tons) & 1724.6 & 1724.92 & 0.02 & 1724.75 & 0.01 \\ \hline \multirow{2}{*}{**Modal Analysis (Hz)**} & \multirow{2}{*}{**ABS**} & \multicolumn{4}{c}{**INER**} \\ \cline{3-6}  & & **Jacket** & **Error (\%)** & **Equivalent Monopile** & **Error (\%)** \\ \hline
1 st Side-to-Side & 0.3153 & 0.3129 & 0.76 & 0.3130 & 0.72 \\
1 st Fore-Aft & 0.3180 & 0.3134 & 1.45 & 0.3135 & 1.42 \\
2 nd Side-to-Side & 1.1116 & 1.1529 & 3.72 & 1.1559 & 3.98 \\
2 nd Fore-Aft & 1.1446 & 1.1579 & 1.16 & 1.1609 & 1.42 \\ \hline \hline \end{tabular}  
* ABS: American Bureau of Shipping; INER: Institute of Nuclear Energy Research  
\end{table} 
Table 2: Comparison of Model Properties.