## 1 Introduction  
In recent years, as offshore construction has developed from shallow to deep sea construction, floating offshore structures in deep waters require simple and efficient anchorage foundations. Floating offshore structure anchoring foundations include drag anchors, suction anchors, torpedo anchors, and screw anchors, among others. Drag anchors are suitable only for shallow waters, as their lightweight design and limited friction make long-term stabilization in deep waters challenging and pose significant risks if dislodged. Suction anchors installed in soft soil provide limited lateral friction resistance. Increasing the weight and surface area of suction anchors can enhance stability, but this complicates installation, thereby limiting their practicality. Torpedo anchors, commonly used in deep-sea applications, are prone to positioning inaccuracies. Soft soil provides limited lateral friction resistance, which can reduce their pull-out bearing capacity. The helical anchor has been widely adopted due to its simple structure, convenient installation, low cost, and high pullout resistance [1]. The size effect of helical anchors significantly influences their uplift bearing capacity. To enhance this capacity, both domestic and international researchers have extensively studied the size effect of helical anchors [2, 3, 4]. However, most research has focused on the ratio of the embedment depth to the anchor helix diameter (depth-to-diameter ratio) regarding the uplift bearing capacity of helical anchors. In contrast, the effects of the pitch-to-plate diameter ratio and shaft-to-plate diameter ratio on the uplift bearing capacity are less explored. To better understand the uplift bearing capacity of the helical anchor [5], the main design parameters are illustrated in Figure 0(a). These parameters include the anchor helix diameter (\(D_{H}\)), the anchor shaft diameter (\(D_{S}\)), the anchor helix embedment depth (\(H\)), and the anchor helix pitch (\(d_{m}\)). The main uplift force (\(Q_{T}\)) is depicted in Figure 1b and includes the anchor helix uplift bearing capacity (\(Q_{A}\)), the resistance provided by the anchor shaft (\(Q_{S}\)), the weight of the helical anchor (\(W\)), and the suction force generated beneath the anchor helix during the pullout process (\(U_{S}\)). Currently, both domestic and international researchers have extensively researched the uplift bearing capacity of helical anchors. Early research by [PERSON] (1980) [6] focused on experiments related to the depth-to-diameter ratio of helical anchors and proposed a formula for calculating uplift bearing capacity. The uplift bearing capacity of helical anchors can be represented by the uplift bearing capacity, \(N_{c}\), as illustrated in Figure 1c. The coefficient of the uplift bearing capacity, \(N_{c}\), increases with the depth-to-diameter ratio; however, the rate of the increase diminishes and eventually stabilizes. [PERSON] [7] proposed a formula for calculating the pullout resistance coefficient of shallow circular plate anchors and estimated the ultimate pressure between the circular plate anchor and the soil surface using this formula. [PERSON] (1987) [8] concluded from pullout resistance tests of helical anchors that the pullout resistance of the anchor helix increases with anchor depth. [PERSON] and [PERSON] (1993) [9] conducted tests on model piles and concluded that the optimal uplift bearing capacity is achieved when the ratio of the helical plate spacing to the plate diameter is maintained between 1.0 and 1.5. [PERSON] and [PERSON] [10] conducted centrifuge tests on anchor helixes to investigate factors affecting uplift bearing capacity. It was concluded that the bearing capacity of the anchor helix significantly depends on its embedment depth and shape. [PERSON] [11] conducted pullout tests on helical anchors of varying diameters and investigated the relationship between ultimate uplift bearing capacity and the diameter of single-plate helical anchors.