## 6 Conclusions  
In this study, the self-developed coupling model OlaFlow-ABAQUS for the fluid-structure-seabed interaction (FSSI) was used to explore the dynamic response characteristics of a jack-up offshore platform and its seabed foundations under three conventional wave conditions (wave height was 3, 5, and 7 m, respectively). Based on the numerical results, the following conclusions were obtained:  
(1) There was only periodic sloshing with a small amplitude occurring under the three conventional wave conditions for the jack-up platform. The maximum sloshing amplitude was up to 8 cm, and no obvious residual displacement occurred for the jack-up offshore platform. It was indicated that there was no plastic deformation zone in the seabed foundation surrounding the pile legs of the jack-up platform. It can thus be seen that the jack-up offshore platform has excellent stability under conventional wave conditions. However, whether the periodic sloshing of the platform structure affects its normal performance highly depends entirely on the requirements set by the engineering task itself, which needs to be analyzed on a case-by-case basis.  
(2) Under conventional wave loading, momentary liquefaction occurred in the seabed foundation around the pile legs of the jack-up platform, and the maximum liquefaction depth was about 1 m. The spudcans installed on the tips of the pile legs of the jack-up platform effectively inhibited the occurrence of liquefaction in their surrounding seabed soil, making the offshore platform structure more stable under wave impact.  
(3) An important assumption in this study is that the behavior of seabed soil can be described by the Mohr-Coulomb soil model. It implies that the seabed foundation is assumed to be a type of geotechnical material with ideal elastoplastic behavior. As a result, the pore pressure build-up, and the related softening and residual liquefaction of the seabed foundation, could not be captured in this study. More complicated elastoplastic soil models could be used in the future to more reliably investigate the wave-induced dynamics of the jack-up offshore platform.  
(4) It was indicated by this study that the coupling model OlaFlow-ABAQUS for the FSSI problem is feasible, and has some advantages to study the dynamic response and to evaluate the stability of large-scale marine structures and their seabed foundations under ocean waves.  
Conceptualization, H.Y. and J.Y.; Data curation, D.Y. and Z.Y.; Formal analysis, H.Y., D.Y. and J.Y.; Funding acquisition, H.Y. and Z.Y.; Investigation, H.Y. and D.Y.; Methodology, D.Y. and J.Y.; Project administration, Z.Y.; Supervision, J.Y.; Writing--original draft, D.Y.; Writing--review & editing, J.Y. All authors have read and agreed to the published version of the manuscript.  
This work is financially supported by the Chinese Military Logistics Scientific Research Program (CZZ19J013), as well as by the National Natural Science Foundation of China (No. 51879257).  
Not applicable.  
Data Availability Statement: Data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.