## 3 Evaluation of Cyclic Behavior of OWT Foundation under Cyclic Loads
### Evaluation of Cyclic Behavior of OWT Foundation under Different Load Amplitudes
In other words, even with small loads, soil densification occurs substantially as the number of cycles increases, resulting in a significant increase in the ground stiffness. However, in the case of the large-amplitude loading tests (ULS and 1.35 ULS), the increase in stiffness is relatively small compared to that in the small-amplitude loading tests. Generally, fatigue failure may be one of the causes of the alleviation of the increase in cyclic stiffness. According to [25], fatigue failure may occur due to the accumulation of deformations. They found that the cyclic shear strain continuously increases with the ratio of the average shear stress to the cyclic shear stress, and fatigue failure occurs when the cumulative shear strain exceeds a limiting strain. Consequently, the number of cycles required to reach fatigue failure increases exponentially, and the fracture does not occur suddenly. In other words, fatigue failure may be one of the causes of the alleviation of the increase in cyclic stiffness. Another possible factor is the soil preparation method (i.e., the compaction method in this study), which affects the deformational behavior of the soil for the cyclic loadings [26; 27]. Moreover, the loss of shear strength due to gaps between the foundation and the soil could be one of the reasons for the decrease in the resistance. When cyclic pullout loads act on the soil, the soil softens owing to ground disturbance and the gaps at the side of the bucket [28]. Additionally, the pullout loads with rotational force cause a decrease in the frictional contact resistance between the sand and steel [29]. As a result, the stiffness does not noticeably increase further, unlike in the case with smaller loads. Figure 9(b) shows the increase in stiffness normalized to the initial stiffness. In contrast to the amount of increase in stiffness, the ratio of increase in stiffness to the initial stiffness does not depend on the load. Therefore, because the rate of stiffness change strongly depends on the initial stiffness, it important to predict the initial stiffness of the soil accurately. Figure 9(c) shows the stiffness as a function of the loading level with different numbers of cyclic loads. The results show that the stiffness change decreased with the loading level and increased with the number of cycles. These findings are similar to the results of previous studies on the cyclic behavior of tripod foundation for the wind turbine [20; 30]. The foundation stiffness is an indicator of the ability of the foundation to resist the temporary displacement when a load is applied to the structure (i.e., resistance to displacement). The damping ratio, which is determined by calculating the area under the load-displacement closed curve, indicating the degree of residual displacement caused by loading and unloading. In other words, the damping ratio generally matches the degree of permanent displacement due to cyclic loading and tends to be the opposite of the stiffness of the soil-foundation systems. Therefore, to understand the displacement induced by the external load, both the foundation stiffness as well as the damping ratio should be considered. Figure 11 shows a plot of the damping ratio as a function of the temporary rotation per cycle. For the various load amplitudes, the damping ratio increases significantly with the load level, which is consistent with the increased displacement. Moreover, it can be seen that the damping ratio decreases owing to soil densification due to the cyclic loads. This decrease is large in the early cycle and then reduces, which agrees with the results of [23]. In particular, in the case of the large loading tests (ULS and 1.35 ULS), there is a large difference in rotation displacement due to the change in damping ratio. In other words, when a large load is applied repeatedly, the difference in damping ratio, rather than the stiffness, has a significant influence on the displacement. This is because the stiffness does not differ much in the case of large loading tests.