## 4 Discussion
### Effect of the Skirt Length  
Figure 8 (\(\theta\) denotes the pile rotation, and N denotes the number of cycles) shows the comparison of the cumulative rotations of the monopile and skirt-piles I and II, and then analyzes the effect of different skirt lengths on the resistance to deformation. Three stages may be distinguished in the cumulative process of the model pile's rotation as the number of cycles increases. The model pile displays cumulative deformation characteristics under horizontal cyclic loading in saturated clay soil. The first stage is the rapid development stage, occurring within the first 100 cycles. In this phase, the cumulative rotation of the pile experiences a rapid increase with the progression of cycle numbers. The second stage is the slow development stage, which occurs between 100 and 500 cycles for the monopile, between 100 and 2000 cycles for skirt-pile I, and between 100 and 4000 cycles for skirt-pile II. In this stage, the cumulative rotation of the model pile grows gradually and slowly, and the slowdown trend increases continuously. The cumulative rotation of the monopile rapidly reaches equilibrium compared to skirt-piles, indicating that as the skirt length increases, the resistance to deformation increases. An interesting finding was that increasing the skirt length significantly increased the duration of the slow development stage, making it slower to reach equilibrium. After the end of the second stage, the stable development stage is entered. With the increase in cycle times, the cumulative rotation of the pile ceases to increase and tends to be stable. Similar observations have been made in previous studies conducted on loose dry sand [37] and dense saturated sandy soils [38]. At N = 300 cycles, the cumulative rotation of skirt-piles I and II are 0.455 and 0.45, respectively. At N = 4500 cycles, the corresponding values are 0.463 and 0.45, respectively. This phenomenon illustrates that the advantage of increasing the skirt length to resist the horizontal deformation of model piles under long-term cyclic loading is more obvious. The primary cause of the cumulative deformation of the model pile is the reshaping of the surrounding soil under horizontal cyclic loading. In the early stage of loading, rapid movement of soil particles occurs under horizontal cyclic loading, inducing a transformation in the original arrangement. The continuous rearrangement of soil particles and alterations in the soil skeleton contribute to the escalating cumulative deformation of the pile. With the increasing number of cycles, after the rapid development stage, the movement between soil grains weakens, the arrangement of soil grains re-enters the stable state, and the resistance to deformation of the soil around the pile increases, but the cumulative rotation angle of the pile continues to grow slowly. The soil particles essentially stop moving in the late stage of cyclic loading; at this time, the cumulative rotation of the pile enters the stable stage. According to the previous analysis, the cyclic accumulation process is divided into three stages. Thus, the pile bending moment at each stage is selected for comparative analysis at the characteristic moment (N = 10, N = 100, N = 1500, N = 4500). Figure 9 demonstrates that the maximum bending moment of skirt-piles I and II occurs at 30 cm below the mud surface. Before reaching 1500 cycles, skirt-pile I exhibits a higher maximum bending moment compared to skirt-pile II. However, as stability is achieved beyond  
Figure 8: Comparison diagram of cumulative rotation for different skirt lengths (monopile, skirt-pile I: L = 50 mm, skirt-pile II: L = 100 mm). 1500 cycles, there is a discernible shift, with the maximum bending moment of skirt-pile II progressively surpassing that of skirt-pile I. The maximum bending moment of the pile produces a large reduction in the first stage, i.e., the rapid development stage, indicating that during this process, the rapid softening of the soil occurs.