## 3 Numerical Modelling
### Load Cases  
The non-operational FOWT dynamic response in an accidental limit state (ALS) during extreme wind and wave conditions were studied. Mooring line #1 was set to release at 2000 s to simulate the ALS. The total numerical simulation time of each case was set to 6000 s, with a time step of 0.1 s. A recurrence period of 50-year typhoon condition with misalignment wind and wave directions, as recommended by the offshore standards[31], was selected as the extreme environmental load. Table 6 shows different return periods of typhoon wave conditions from local government analysis of over 20 years of typhoon wave data[32] in offshore Hsinchu, Taiwan, the site of a potential wind farm. \(T\)s denotes the significant wave period and \(Hs\) the significant wave height. The wave condition in \(Hs\) = 9.1 m, \(T\)s = 12.7 s and \(\gamma\) = 2.08, and the spectral density of the sea elevation process is represented by the JONSWAP spectrum (shown in \begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Values** & **Unit** \\ \hline Depth of platform base below SWL (total draft) & 20 & m \\ Elevation of the main column (tower base) above SWL & 10 & m \\ Elevation of offset columns above SWL & 12 & m \\ Spacing between offset columns & 50 & m \\ Length of upper columns & 26 & m \\ Length of base columns & 6 & m \\ Depth to top of base columns below SWL & 14 & m \\ Diameter of the main column & 6.5 & m \\ Diameter of offset (upper) columns & 12 & m \\ Diameter of base columns & 24 & m \\ Diameter of pontoons and cross braces & 1.6 & m \\ Platform mass, including ballast & \(1.3473\times 10^{7}\) & kg \\ CM location below SWL & 13.46 & m \\ Platform roll inertia about CM & \(6.827\times 10^{9}\) & kg-m\({}^{2}\) \\ Platform pitch inertia about CM & \(6.827\times 10^{9}\) & kg-m\({}^{2}\) \\ Platform yaw inertia about CM & \(1.226\times 10^{10}\) & kg-m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Properties of the semi-submersible platform (Adapted with permission from Ref. [30]. NREL). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Values** & **Unit** \\ \hline Overall Integrated Mass & 347.46 & te \\ CM Location (above GL) & 38.148 & m \\ Material Effective Density & 8.5 & te/m\({}^{3}\) \\ Material Young’s Modulus & 210 & Gpa \\ Material Shear Modulus & 80.8 & Gpa \\ Poisson Ratio & 0.3 & - \\ Added Mass Coefficient & 1.0 & - \\ Drag Coefficient & 1.2 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Tower Physical Properties (Adapted with permission from Ref. [29]. NREL). Figure 7). The wind speed takes the 50-year return period typhoon event at 60 m/s [32]. All of the load cases in this study are provided in Table 7 and visualised in Figure 8. LC1-5 represent the various incident wind direction situations (Figure 8A), while LC6-9 represent the different direction conditions (Figure 8B) and LC10 shows the wind and waves coming from 180\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Return Period (Year)** & \multicolumn{2}{c}{**10**} & \multicolumn{2}{c}{**20**} & \multicolumn{2}{c}{**50**} \\ \hline
**Wave Directions** & **Hs (m)** & **Ts (s)** & **Hs (m)** & **Ts (s)** & **Hs (m)** & **Ts (s)** \\ \hline North-East, NE & 6.6 & 10.8 & 7.7 & 11.7 & 9.1 & 12.7 \\ (33–45 degrees) & 6.6 & 10.8 & 7.7 & 11.3 & 8.7 & 12.4 \\ North-Northeast, NNE & 6.1 & 10.4 & 7.3 & 11.3 & 8.7 & 12.4 \\ (12–33 degrees) & 4.5 & 8.9 & 5.5 & 9.8 & 6.7 & 10.9 \\ North-Northwest, NNW & 4.5 & 8.9 & 5.5 & 9.8 & 6.7 & 10.9 \\ (327–348 degrees) & & & & & & \\ \hline \hline \end{tabular}  
* Source: Planning of environment protection and promotion on Kang-Nan coast HsinChu City.  
\end{table} 
Table 6: Return periods of the typhoon wave conditions at Hsinchu offshore. Figure 6: Model set-up of the OC4 floating wind turbine and mooring system. Figure 8: Multi-directional incident wave and wind directions: **(A)** LC1 to LC5; **(B)** LC5 to LC9.