## 3 Evaluation of Cyclic Behavior of OWT Foundation under Cyclic Loads
### Estimation of Long-Term Behavior of OWT
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{3}{c}{**Estimation of Stiffness**} \\ \cline{2-4}  & \multicolumn{2}{c}{**Number of Cycles**} & **Initial Rotational Stiffness \(\mathbf{k_{L}}\) (kN\(\cdot\)m/o\({}^{\circ}\))** \\ \hline \multirow{2}{*}{FLS} & 14,100 & \multirow{2}{*}{\(10^{7}\)} & \multirow{2}{*}{659,573} \\  & (kN\(\cdot\)m) & & \\ \hline \multirow{2}{*}{SLS} & 23,500 & \multirow{2}{*}{\(10^{2}\)} & \multirow{2}{*}{163,171} \\  & (kN\(\cdot\)m) & & \\ \hline \multirow{2}{*}{ULS} & 47,000 & \multirow{2}{*}{1} & \multirow{2}{*}{146,877} \\  & (kN\(\cdot\)m) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Example of estimation of long-term stiffness of on-site OWT. Figure 14: Prediction curves of cyclic stiffness of site demonstration OWT. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Item**} & \multicolumn{3}{c}{**Estimation of Long-Term Stability**} \\ \hline \multirow{2}{*}{**Loading Level**} & **Estimated Stiffness** & **Moment (kN\(\cdot\)m)** & **Temporary Rotation (o\({}^{\circ}\))** & **Natural Frequency (Hz) * \\ \hline FLS & 659,573 & \multirow{2}{*}{47,000} & \multirow{2}{*}{0.0713} & \multirow{2}{*}{0.42} \\ X \(10^{7}\) & (kN\(\cdot\)m\(\cdot\)/o\({}^{\circ}\)) & & \\ SLS & 163,171 & \multirow{2}{*}{47,000} & \multirow{2}{*}{0.1414} & \multirow{2}{*}{0.20} \\ X \(10^{2}\) & (kN\(\cdot\)m/o\({}^{\circ}\)) & & \\ ULS & 146,877 & \multirow{2}{*}{47,000} & \multirow{2}{*}{0.3200} & \multirow{2}{*}{0.19} \\ X \(1\) & (kN\(\cdot\)m\(\cdot\)/o\({}^{\circ}\)) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Example of estimation of long-term stability of on-site OWT. Additionally, the long-term natural frequency of the structure was evaluated based on the equivalent stiffness and mass of the system as follows [13]:  
\[f_{0}\ =\ \frac{1}{2\pi}\sqrt{\frac{k_{sys}}{m_{sys}}}, \tag{4}\]  
where \(f_{0}\), \(k_{sys}\), and \(m_{sys}\) is the natural frequency, equivalent stiffness, and equivalent mass of the system, respectively. Table 8 shows the results of the natural frequency of the structure calculated based on the stiffness estimated from the cyclic loading tests. According to [33], the OWT structure is stable in the natural frequency range of 0.17-0.35 Hz. When this structure is loaded with the FLS load \(10^{7}\) times, the natural frequency is approximately 0.42 Hz, which does not comply with the stability criterion of the OWT. In other words, it can be concluded that the long-term stability of the structure is not ensured based on the natural frequency, and the structure is therefore unsafe in a long-term perspective. This study has some limitations. Only 50 cycles were applied for each test. To accurately predict the long-term behavior, tests with more loading cycles (e.g., 100 cycles in the SLS state, \(10^{7}\) cycles in the FLS state) should be conducted. Nonetheless, [PERSON] et al. [5] found that the cyclic behaviors (i.e., permanent displacement; cyclic stiffness) are proportional to the number of cycles on a log scale. In other words, the trend of cyclic behavior mainly changes initially and tends to gradually converge as the number of cycles increases. In this study, we demonstrated the possibility of using centrifugal modeling research to predict long-term behaviors.