## 5 Conclusions  
In this study, physical model tests were performed to scrutinize the mechanical behavior of skirt-pile foundations under horizontal loads, and the characteristics of the ultimate bearing capacity, cumulative deformation, bending moment, and cyclic stiffness were investigated. Derived from the experimental results, the following conclusions can be drawn:  
* Enlarging the skirt diameter can greatly enhance the load-bearing capacity of the composite pile, and extending the skirt length can effectively improve the deformation resistance. Optimizing the skirt-pile size achieves desired performance in offshore engineering, minimizing material and construction costs.
* In saturated clay soil, the cumulative deformation of the model pile primarily results from the rearrangement of the soil around the pile during horizontal cyclic loading. The cumulative rotation of the pile can be categorized into rapid development, slow development, and stable development stages, providing aid in the design and evaluation of pile foundations in clay.
* Throughout the cyclic loading process, the bending moment of the pile initially experiences a decrease followed by an increase. Extending the skirt length is found to be effective in improving the overall stiffness of the skirt-pile, indicating the potential for improving structural integrity and stability through appropriate design modifications.
* The horizontal cyclic stiffness increases with an increase in both the skirt length and diameter, and this enhancement is particularly pronounced when increasing the skirt diameter. Meanwhile, the horizontal cyclic stiffness decreases as the number of cycles increases, stabilizing after 3000 cycles. Analyzing foundation degradation mechanisms informs accurate long-term behavior predictions in practical engineering.  
This study still carries certain limitations. Assumptions related to soil properties, boundary conditions, or loads may not fully reflect the complexity of the actual offshore  
Figure 13: Horizontal cyclic stiffness history curve.  
environment. Future studies could investigate the effects of additional parameters such as soil properties, water depth, and environmental loading conditions on foundation performance. Additionally, advanced numerical modeling techniques could be employed to simulate the behavior of skirt-pile foundations under more complex loading scenarios.  
Conceptualization, L.D. and M.F.; data curation, M.F.; formal analysis, B.Z.; funding acquisition, L.D.; investigation, M.F.; methodology, L.S.; project administration, D.W.; resources, L.D.; software, [PERSON]; supervision, D.W.; validation, M.F.; visualization, B.Z.; writing--original draft, M.F.; writing--review and editing, L.D. All authors have read and agreed to the published version of the manuscript.  
The authors are grateful for the financial support from the National Natural Science Foundation of China (grant no. 52108268), the Chongqing Natural Science Foundation (cstc2021 jcyj-msxmX1123), and the State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University (HESS-2119).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.