## 1 Introduction  
Jack-up offshore platform is a type of important marine structure, which is mainly used for satellite launch, oil exploitation, and other engineering tasks in the offshore area. Jack-up offshore platforms are generally composed of four pile legs and an upper platform, among which the four pile legs have the function of automatic lifting. When in an instructive state, the four pile legs are put down and inserted into the offshore seafloor to fix the platform structure. When the tasks of platforms are finished, the pile legs can be raised. Then, the entire platform structure can float on the surface of seawater due to the buoyancy provided by the platform itself, and then can be transported by tugboats. Offshore platforms could be subjected to various levels of wave action in the period of service, and the dynamic response characteristics of offshore platforms and their seabed foundation to ocean waves have an important influence on their performance. Therefore, the dynamic response of offshore platforms and their seabed foundation to ocean waves is an important engineering problem. On the wave-induced dynamics of floating offshore platforms, a lot of research works have been conducted [1; 2; 3]. However, the previous studies on the dynamics of fixed offshore platforms and their seabed foundation to waves are limited. Moreover, due to the shortage of numerical computational techniques, and the limitation on the understanding of the role of the seabed foundation, the important influence exerted by the seabed foundation is often ignored. Previous studies basically only paid attention to the interaction between offshore platforms and waves from the perspective of fluid dynamics [4; 5; 6]. Their attention was mainly focused on the characteristics of the wavefields around fixed offshore platforms, and the time history characteristics as well as the magnitude of wave impact on platform structures. In their study, the seabed foundation was considered to be a rigid boundary with an infinite bearing capacity. However, the real situation is that the offshore seabed is usually composed of quickly deposited stratum with low bearing capacity, which is prone to be liquefied or soften under cyclic loads, e.g., waves and earthquakes [7; 8; 9]. As a result, the marine structures built on them would be destroyed due to excessive settlement or inclination [10]. Therefore, the seabed foundation has a very important influence on the wave dynamic response, and the stability of offshore platforms. Finally, ocean wave, marine structures, and seabed foundation must be regarded as an integrated system, and the wave-induced dynamic response of the offshore platform and its seabed foundation should be quantitatively evaluated adopting a coupled model considering the fluid-structure-foundation interaction. On the coupled model for the fluid-structure-seabed interaction (FSSI), it is known that [PERSON] et al. [11] and [PERSON] et al. [12] firstly proposed and implemented a very simple coupling model. [PERSON] and [PERSON] [13] realized another coupling model adopting OpenFOAM as the development platform. However, the coupling models proposed by [PERSON] et al. [11], [PERSON] et al. [12], and [PERSON] and [PERSON] [13] could only be applicable to very dense, sandy, seabed soil with a linear por-elastic model. In fact, the dynamic behavior of real seabed soil is very complicated, and cannot be described by the linear poro-elastic model at all. To solve this problem, [PERSON] et al. [14; 15] and [PERSON] et al. [16] proposed another more advanced numerical coupling model FSSI-CAS-2D/3D for FSSI problems. Recently, it evolves into FssiCAS [17]. Additionally, the analysis function for the seismic dynamic response of marine structures and seabed foundation was developed and integrated into FSSI-CAS-2D/3D by [PERSON] and [PERSON] [18].