## 4 Discussion
### Effect of the Skirt Diameter  
Figure 10 compares the cumulative rotation of different skirt diameters (skirt-piles II and III), showing the varying resistance to deformation. The development of cumulative rotations in skirt-pile III is also categorized into three stages. The first stage occurs within the initial 100 cycles, the second stage spans from 100 to 1500 cycles, and the third stage takes place between 1500 and 4500 cycles. Figure 9: Comparison diagram of pile bending moment for different skirt lengths in different cycles: (**a**) N = 10; (**b**) N = 100; (**c**) N = 1500; (**d**) N = 4500. As can be seen from Figure 10, as the skirt radius increases, the cumulative rotation of the skirt-pile composite foundation decreases throughout the cycle. And it was found that the second stage of skirt-pile III was a shorter process compared to skirt-pile II and reached equilibrium faster. The cumulative rotation of skirt-piles II and III are 0.53 and 0.45 at N = 4500 cycles, indicating that the increased radius of the skirt further increases its resistance to deformation. The larger skirt diameter provides more lateral support for the foundation, making it more resistant to horizontal movement or deformation. In addition, the increased bearing area of the skirt helps to disperse the lateral load, reducing the stress placed on the soil and minimizing the possibility of soil damage or excessive settlement. Therefore, increasing the skirt diameter usually improves the deformation resistance of the skirt-pile foundation, making it better able to withstand lateral forces and maintain stability. Analyzed in conjunction with Figure 8, increasing the skirt length reduces the cumulative corner on the one hand, and on the other hand allows its corner development process to enter the stabilization stage earlier. However, increasing the skirt diameter only reduces the cumulative rotation angle, and the development trends of skirt-piles II and III are the same. Figure 11 compares the bending moments of skirt-piles II and III for different cyclic load cycles (N = 10, N = 100, N = 1500, N = 4500) to study the effect of skirt diameter on the internal force of the pile under cyclic loading. The maximum bending moment point of skirt-pile III appears 20 cm below the mud surface at the beginning of cyclic load loading, and the maximum moment point shifts down with the increase in the cyclic number and stabilizes 30 cm below the mud surface. For skirt-pile III, in the first stage (N = 10-100 cycles), the soil softens rapidly and the pile bending moment decreases sharply. During the second stage of cyclic loading (N = 100-1500 cycles), the bending moment gradually decreases and stabilizes as the number of cycles increases. During this stage, the softening rate of the soil remains constant. As the cyclic loading progresses to the third stage (N = 1500-4500 cycles), the bending moment of the pile increases in correlation with the number of cycles, signifying a soil rearrangement that leads to a new equilibrium state during the cyclic process. The whole development processes are consistent with skirt-pile II. Figure 10: Comparison diagram of cumulative rotation for different skirt diameters (monopile, skirt–pile II: D = 100 mm, skirt–pile III: D = 150 mm). The bending moment progression of skirt-pile III along the pile's depth direction closely resembles that of skirt-pile II. In the initial loading stage, the bending moment rises and subsequently decreases with increasing depth. After a specific loading duration, back-bending points emerge at depths of 20 cm and 60 cm below the mud surface. Notably, augmenting the skirt diameter has a more negligible impact on the pile moment shape compared to extending the skirt length. The influence of the skirt length and skirt diameter on the ultimate bearing capacity and deformation resistance was quantified. These parameters can be optimized in practical engineering to meet specific project requirements and environmental conditions.