## 1 Introduction  
Many countries are attempting to reduce environmental pollution due to fossil fuels by utilizing alternative renewable energy sources such as water, wind, solar, and tidal power. In particular, wind power--one of the cleanest energy sources--has shown potential in meeting international renewable energy targets [1, 2, 3]. Because the levelized cost of energy of wind power has steadily decreased, offshore wind turbines (OWIs) have attracted considerable attention [4]. To secure the competitiveness of offshore wind-energy production, a safe and economical OWT foundation design is crucial because the foundation-construction cost constitutes a large portion of the total OWT cost [5]. Monopiles are frequently used as conventional OWT foundations. In recent years, the suction bucket foundation has been regarded as a highly competitive alternative to the conventional monopile foundation owing to its convenient installation without heavy equipment for penetration and no hammer noise from driving and shorter installation and construction times, leading to reduced cost of the overall installation operation. Tripod foundations, which consist of three suction buckets placed in a triangular shape, can increase the bearing capacity and overturning resistance of the foundation for OWTs. Numerous studies have focused on the behaviors of monopiles and hybrid monopiles. However, very few studies have been conducted on tripod foundations, which have different mechanisms compared to conventional foundations (i.e., monopile and monopods). In addition, design guidelines for tripod foundations have not been established [6; 7; 8; 9; 10]. In the past, the evaluation of the ultimate bearing capacity of the offshore foundation based on the limit state design method was considered to be a key design issue. However, the following issues of the OWT design have been highlighted in recent years: (i) the structural natural frequency of the OWTs with respect to the soil-foundation interaction; (ii) the in-service performance under the application of numerous cycles of low-amplitude loads within a service limit state (SLS); (iii) the permanent displacement and variation in the stiffness of the soil-foundation system due to cyclic loading. [PERSON] et al. [11] suggested that the design should be based on the serviceability requirements rather than the ultimate conditions. The critical design criterion is that the permanent displacement must be lower than the service limit. In addition, the wind turbine system has high stiffness, and the blade and rotor eigenfrequencies provide only a small range of frequencies suitable for the design [12]. [PERSON] et al. [13] proposed a 10-step design protocol for the foundation for OWTs, with emphasis on the necessity of the stability of natural frequency and long-term behavior of OWTs. In this study, we evaluated the SLS and fatigue limit state (FLS) of a tripod foundation under cyclic loads at a low amplitude and its ultimate limit state (ULS) under cyclic loads at high amplitude. Then, we evaluate the resulting permanent displacement and variation in stiffness of the foundation system. The objective of this study is to guide the assessment of the in-service performance of bucket foundations under cyclic loading. Recently, it has been declared that Korea plans to establish a 17 GW wind farm by 2030, in line with the government's renewable-energy policy. Since 2014, the Korea Electric Power Research Institute (KEPRI) has been working on the SUCCESS project, which is aimed at verifying the stability and technical capability of the tripod foundation and at enhancing its applicability by installing a full-scale commercial 3 MW turbine in the western coast of Korea [14]. Three different methods were used to evaluate the natural frequency of the structure: (i) on-site impact load tests, (ii) numerical analysis, and (iii) centrifuge model tests. By comparing the natural frequencies obtained from the three methods, the reliability of the results was analyzed.