## 3 Evaluation of Cyclic Behavior of OWT Foundation under Cyclic Loads
### Estimation of Long-Term Behavior of OWT  
For the design of the serviceability limit state of an OWT based on the load and resistance factor design, the evaluation and prediction of the permanent displacement must be ensured. According to [31], an offshore wind generator with a permanent displacement of 0.25\({}^{\circ}\) or more has very low-efficiency. In addition, the China Hydro and Water Research Institute [32] suggested that the displacement criterion should be less than 0.17\({}^{\circ}\). In this  
Figure 11: Damping ratio–rotation curve under different load amplitudes. Figure 12: Cyclic stiffness–rotation curve under different load amplitudes. study, as a part of the long-term behavior evaluation for the performance-based design of OWTs, the accumulated rotation of large-scale OWTs due to cyclic loads was experimentally analyzed and predicted. Figure 13 shows a permanent rotation trend with the load levels and cycles. It can be seen that the permanent rotation increases slightly with the number of cycles under the SLS, where the magnitude of the load is small, and the permanent displacement is large in the early cycles and gradually converges. Therefore, the evaluation of the permanent displacement in the early cycle is important to assess the safety of the long-term behavior. These results are to those of previous studies on the cyclic behavior of the tripod foundation [20; 30]. Table 6 presents some predictions of the permanent rotation made using the trend curve for the SLS test in Figure 13. These results were obtained with an SLS load of 23,500 kN\(\cdot\)m. In other words, based on the prediction method of permanent rotation, as shown in the example (i.e., Figure 13 and Table 6), it is possible to predict the long-term behavior of the offshore wind tower with respect to the loading levels and cycles. The prediction of the stiffness and permanent displacement (i.e., accumulated rotation) of the foundation is important to ensure stability because the stiffness affects the natural frequency of the OWT and the temporary displacement of the structure. In particular, the temporary displacement of the foundation is significantly larger than the permanent displacement even when the numbers of cycles and loading levels are small. Figure 14 shows a plot of the stiffness change of the foundation with respect to the number of cycles. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**Expectation of Accumulated Rotation**} \\ \cline{2-3}  & **Number of Cycles** & **Accumulated Rotation 0 (\({}^{\circ}\))** \\ \hline \multirow{4}{*}{SLS} & \multirow{2}{*}{23,500 (kN\(\cdot\)m)} & \(10^{2}\) & 0.0466 \\ \cline{3-3}  & & \(10^{3}\) & 0.0606 \\ \cline{3-3}  & & \(10^{4}\) & 0.0747 \\ \cline{3-3}  & & \(10^{5}\) & 0.0887 \\ \cline{3-3}  & & \(10^{6}\) & 0.1028 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Predictions of long-term permanent rotation of on-site OWT. Figure 13: Prediction curves of permanent displacement of on-site OWT. Table 7 presents some results of the stiffness predicted when the FLS, SLS, and ULS loads are repeatedly applied. Based on the predicted stiffness, the temporary rotation of the foundation can be expected. Table 8 shows the results of the corresponding temporary rotation prediction. The estimated stiffness values can be predicted based on the loading level and cycles. In this state, the estimated stiffness values represent the temporary rotation corresponding to the application of a particular moment load. As shown in Table 8, when a moment load of 47,000 kN\(\cdot\)m (ULS) is applied to the structure, the temporary rotation exceeds the OWT displacement criteria.