## 3 Evaluation of Cyclic Behavior of OWT Foundation under Cyclic Loads
### Evaluation of Cyclic Behavior of OWT Foundation under Different Load Amplitudes  
In all the graphs for the cyclic loading tests, the values in the positive direction indicate downward displacement of the bucket and compressive load. All the experiments were performed at a centrifugal acceleration of 70 g. According to the established centrifuge scaling laws based on dimensional analyses, all values recorded in this study are converted to the prototype scales (i.e., \(F_{P}=F_{m}\cdot N^{2}\), where \(F_{P}\) and \(F_{m}\) are the force in prototype and model scale, respectively, and N is the centrifugal acceleration relative to the Earth gravity (g)). The definitions of cyclic stiffness (rotational stiffness) and displacements (permanent, incremental, and temporary displacement) are presented in Figure 8. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Load Condition**} & \multicolumn{2}{c}{**Moment Load**} & \multirow{2}{*}{**Number of Cycles**} \\ \cline{2-2} \cline{4-4}  & **Prototype (kN\(\cdot m\))** & & **Model (kN\(\cdot m\))** \\ \hline
0.15 ULS & 7050 & 1.44 & 50 \\
0.3 ULS (FLS) & 14,100 & 2.87 & 50 \\
0.5 ULS (SLS) & 23,500 & 4.80 & 50 \\ ULS & 47,000 & 9.66 & 50 \\
1.35 ULS & 63,450 & 12.95 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Cyclic loading tests program. Figure 8: Cont. Figure 7: Centrifuge testing setup for cyclic loading experiment. Figure 9 shows the typical moment-rotation relationship for different loading levels. All the experiments were progressed from low to high loading level sequentially, ensuring that the pullout force was applied only to the windward bucket (i.e., one-way loading), which is the most vulnerable load condition on the tripod. From Figure 9, it can be seen that at each cyclic loading level, the first cycles followed the preceding moment-rotation curve until they reach the preceding maximum load. Thereafter, the slope of the curve dramatically decreased from the point beyond the preceding maximum load. The degree to which the slope decreases relative to the existing curve increases as the loading level increases. The slope of the curve changes significantly during the initial cycle and then changes depending on the number of cycles. In other words, soil-foundation interactions vary depending on the number of cycles as well as the loading level. To evaluate the effects of the load level and cycles in more detail, the loading stiffness and damping curves are plotted based on this moment-rotation curve. Figure 8: Definitions of the cyclic stiffness and displacements: (**a**) schematic for the rotation behavior of tripod foundation and (**b**) plots of the cyclic characteristics. Figure 9: Moment–rotation curve of cyclic loading tests. Figure 10 shows the foundation stiffness measured with increasing load amplitude for all the experiments. From the figure, it can be seen that as the loading amplitude increases, the initial rotational stiffness (\(\text{k}_{\text{L(0)}}\)) of the foundation tends to decrease relative to the loading magnitude due to the soil nonlinearity [22]. [PERSON] and [PERSON] [23] discussed the effect of the cyclic loading amplitude on the dynamic properties (i.e., shear modulus and damping ratio) of the SM from the results of extensive cyclic triaxial tests. They found that the strain amplitude significantly affects both the shear modulus and the damping ratio. This is consistent with the observation that the rigidity of the bucket foundation decreases as the loading level increases [20; 24]. Figure 10: Loading stiffness responses with loading amplitudes: (**a**) ground stiffness–number of cycles curve; (**b**) normalized stiffness with respect to first cycle stiffness; (**c**) ground stiffness–normalized loading level curve. Furthermore, the stiffness changes the number of cycles and the loading amplitude. In the 0.15 ULS, FLS, and SLS test cases, where the load magnitudes were less than 50% of the ULS, the stiffness rapidly increased as the number of cycles increased.