## 1 Introduction  
Compared to onshore wind energy, offshore wind power exhibits higher energy efficiency coupled with advantages such as higher wind speeds, reduced dust, and extended turbine lifespan. Offshore wind turbines are subjected to long-term effects of ocean waves and horizontal wind loads in operation. Consequently, horizontal loads represent the predominant controlling factor in the design of wind power foundations. At present, offshore wind farms in China are primarily situated in coastal waters, with relatively modest installed capacities. However, as offshore wind power gradually expands into deeper waters and higher power ratings, there is an escalating demand for increased load-bearing capacity in wind power foundations. In response to these requirements, various novel foundation designs suitable for offshore wind power were proposed. [PERSON] et al. [1] proposed that the composite three-bucket foundation combined with a circular plate can effectively improve the foundation's anti-overturning ability and thus improve the overall bearing capacity of the structure; [PERSON] et al. [2] employed a horizontal monotonic loading model test on hollow conical foundations under medium-coarse sand conditions and explored the impacts of foundation dimensions and loading height on the horizontal bearing capacity, as well as the distribution patterns of soil pressure; and [PERSON] et al. [3] experimentally determined that the deflection and bending moments of large-diameter piles calculated using API specification were lower than the measured values. [PERSON] et al. [4] focused on the influence of pile-bucket structure dimensions and penetration depth on foundation-bearing capacity and deformation by a three-dimensional finite element model. The results indicated that increasing the depth of penetration of both the foundation pile and bucket effectively enhanced the structure resistance of overturning. [PERSON] et al. [5] highlighted that, relative to sandy soil, the enhancement in the overall bearing capacity of the structure is more pronounced in soft clay with a pile-bucket composite foundation in a comparative study involving a single-pile foundation, bucket-shaped foundation, and pile-bucket composite foundation; [PERSON] et al. [6] asserted that the diameter of the bucket has the greatest impact on the load-bearing performance of the pile-bucket composite foundation with an increase in bucket diameter proving to be an effective means of enhancing structural load-bearing capacity; [PERSON] et al. [7] studied the sharing of the load by different parts of the foundation and the failure mode under vertical loading, concluding that composite foundation can effectively improve load-bearing capacity; [PERSON] et al. [8] proposed a theoretical formula for the horizontal load-bearing capacity of a pile-bucket composite foundation considering varying numbers of piles based on the ultimate equilibrium method; [PERSON] et al. [9] studied the load-bearing capacity degradation patterns of the pile-bucket composite foundations under static and cyclic loading, indicating that, compared to bucket height, an increase in bucket diameter more significantly improved the load-bearing capacity of the foundation; [PERSON] et al. [10] investigated the response of the pile-bucket composite foundation under static and dynamic loads, demonstrating that the composite foundation can reduce the depth of the pile penetration and effectively decrease the rotation angle and horizontal displacement of the foundation; and [PERSON] et al. [11] conducted modal analysis on a pile-bucket composite foundation with ABAQUS software and highlighted optimal pile-bucket diameter ratios and bucket skirt height. [PERSON] et al. [12] found that, compared with single-pile foundations, the pile-bucket composite foundation significantly reduced the seismic response of offshore wind turbines (OMTs). In summary, composite foundations integrating pile and bucket effectively enhanced the load-bearing capacity of the foundations. [PERSON] et al.