## 4 Conclusions  
We investigated the cyclic behavior of a tripod foundation for OWT, particularly in terms of the permanent displacement and soil stiffness. Because it is difficult to predict the long-term cyclic behavior of on-site OWTs, centrifuge model tests were performed to assess the long-term stability of the structure under cyclic loading. To simulate the behavior of the demonstration turbine installed at the site using the centrifuge, a soil layer similar to that of the actual site was modeled, and the structure and environmental loads were simulated. The following conclusions were drawn based on the results of the tests:  
1. Large permanent displacement occurred when the first loading cycle was applied, and the amount of additional displacement gradually decreased as the load was reapplied. Moreover, it was found that the increase in permanent displacement was affected more by the loading level than the number of cycles;
2. The initial rotational stiffness of the tripod foundation decreased as the cyclic loading amplitude increased. In addition, the soil stiffness mainly increased in the first cycles and tended to gradually converge as the number of cycles increases. Moreover, the rotational stiffness rapidly increased as the number of cycles increased with 0.15 ULS, FLS, and SLS loadings, where the load magnitude was less than 50% of the ULS. On the other hand, in the case of the large-amplitude loading tests (ULS and 1.35 ULS), the increase in stiffness was relatively small;
3. The damping ratio also increased with the load level, which is consistent with the increased displacement. In particular, the damping ratio had a significant influence on the displacement;
4. The permanent rotation and the variation in the foundation stiffness due to the cyclic load increased logarithmically with the number of cycles. Therefore, the long-term performance of the OWT depending on the loading level and cycles can be predicted based on the trend. The long-term natural frequency of the structure was evaluated based on the predicted stiffness and mass of the system, and it was found that the long-term stability of the structure was not ensured when the structure was loaded with an FLS load \(10^{7}\) times.  
The long-term behavior of the OWT installed at the actual site was evaluated using centrifugal model tests. Although the actual OWT structure and in situ soil were properly modeled, the experimental results must be further verified because the actual OWT was simplified, and the soil preparation method cannot accurately simulate the on-site soils. Therefore, in the future, the results should be verified and expanded by comparing them with measurement results (change in the natural frequency and permanent rotational displacement) obtained from the on-site OWT. In addition, the experimental results with more loading cycles would be necessary to accurately predict the long-term behavior of the offshore wind turbine with a tripod foundation.  
Conceptualization, Y.-H.J. and J.-H.K.; data curation, Y.-H.J.; writing--original draft preparation, Y.-H.J.; writing--review and editing, J.-H.K.; supervision, J.-H.K.; project administration, S.-W.L.; Formal Analysis, Y.-H.J.; Investigation, Y.-H.J. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (Ministry of Science and ICT) (2017R1A5A1014883).  
Not applicable.  
The authors declare no conflict of interest.