## 1 Introduction  
The energy crises in the 1970s led to the birth and development of large-scale wind turbines, which were further commercialized in the 1980s. Nowadays, environment-friendly wind power is at a rapidly developing stage, with land-based wind power accounting for a large proportion [1, 2, 3]. Onshore wind power had started earlier, with a large installed capacity at present. In comparison, the installed capacity of offshore wind power generation keeps growing, owing to its advantages such as favorable wind conditions and high applicability. Among the offshore wind power support structures, the single-pile foundation is most widely applied. Other multipile foundations, gravity foundations, and suction bucket foundations also account for a certain proportion [4, 5]. Wind turbines, towers, and foundations belong to high-rise structures, which need to withstand complex external environmental loads during their operation, and face problems such as structure vibration [6, 7, 8, 9, 10], soil-structure coupled vibration [11], seismic dynamic response [12, 13], and vibration reduction control [14, 15, 16]. Offshore wind turbines, especially, have to face many challenges in complex ocean environments, including waves, currents, and erosion. The interaction between the support structure and soil and the dynamic response analysis method involves the safe operation of the structure. Up to now, scholars around the world have conducted a number of in-depth studies on single- and multiple foundations, which are frequently applied to offshore wind power generation [17, 18]. Along with the large-scale construction of onshore wind farms, the form of onshore wind power infrastructure is constantly being improved and optimized, thereby forming the base structures that are adapted to different geological conditions. The wind power generation system belongs to a towering structure; however, due to the particularity of its structural form, it is slightly different from the ordinary tower structure in terms of mass distribution. For example, the wind turbine on the top has a large mass, so the bottom foundation structure is subjected to the coupling of torque-vertical load-horizontal load-bending moment load (i.e., \(T\)-\(V\)-\(H\)-\(M\)) under the external random wind conditions [19; 20; 21; 22]. Therefore, the stability of a wind power foundation structure is the key to ensuring the normal operation of wind power generation. Since the upper load has to be transferred to the base, the connection between the bottom of the tower and the top of the base is a key component, which is usually embedded on the top of the base. The commonly used structures of connection include the foundation ring and the anchor bolt. Note that the former is mostly used because of its simple structure, massive production, easy quality control, and convenient installation and construction [23; 24; 25]. The main loads that a wind turbine foundation bears include vertical, horizontal, and bending moment loads transferred from the upper tower tube, wind turbine, and fan blade. At present, the corresponding design and research mostly focus on the stress state of the structure under the coupling effect of these loads. In order to obtain the maximum wind energy in practice, the angle needs to be adjusted quickly and smoothly to align with the wind direction. At this time, the foundation structure will bear the horizontal torque load, which is transmitted by the wind turbine yaw [26; 27; 28]. Since the horizontal torque load caused by fan yaw is relatively small compared with the bending moment load, it is often not considered separately in the conventional foundation design. However, it is still not clear how the torque load is transmitted within the wind turbine foundation and which part mainly bears the torque load.