# Influencing Factors of Motion Responses for Large-Diameter Tripod Bucket Foundation
## 1 Introduction
The basic mass in the motion equation should include both the mass of the structure and the mass of the water plug inside the buoy, where the added mass coefficient of heaving is 1.2 [8]. [PERSON] et al. showed that the introduction of an air cushion support into a concrete gravity structure (CGS) increases the pitch response, while slightly affecting the heaving motion [12]. [PERSON] et al. experimentally evaluated the effect of water plug height and compartmentalization of an air cushion on the metacentric height, heave, and pitch natural frequency and the added mass of an air-cushion-supported box model. The air cushion reduced the stability of vessel and influenced both the natural frequency and added mass in heaving and pitching [16]. [PERSON] developed a correction formula for the metacentric height incorporating the net effect of an air cushion on the static stability of a compartmented structure [17]. [PERSON] presented a non-dimensional parameter that considers the compressibility factor of an air cushion. The parameter can be used to correct the heave, roll, and pitch restoring coefficients [18]. In the hydrodynamic aspect, using the three-dimensional diffraction-radiation theory, [PERSON] et al. studied the motion of structures both partially and completely supported by air cushions in waves [19; 20; 21]. The results are consistent with those of [PERSON]'s model test [22]. [PERSON] and [PERSON] extended [PERSON]'s method and calculated and analyzed the hydrodynamic coefficients of the heaving motion of an air cushion support structure [23]. Using the boundary integral equation method, [PERSON] and [PERSON] extended [PERSON]'s and [PERSON]'s work and analyzed the hydrodynamic coefficients and internal free surface changes of an air-cushion-supported structure at zero speed in regular waves [24]. Using the three-dimensional potential flow theory and linearized adiabatic law, [PERSON] and [PERSON] calculated the motion responses and wave loads of a rectangular barge with partial buoyancy provided by an air cushion in waves. The effects of different forms of subdivision on the motions and loads of structure were evaluated by comparing with the results of model tests [25; 26]. Using a 1/20-scale physical model and hydrodynamic software MOSES, [PERSON] et al. experimentally evaluated the effect of towing speed, water depth, free-board height, and wave direction on the air floating towing behavior of a multibucket foundation platform [27]. Using MOSES, [PERSON] et al. studied the hydrodynamic motion of self-floating towing for a large prestressed concrete bucket foundation (LPCBF) [7]. The hydrodynamic response of large floater with an air cushion not only depends on the wave conditions but also on the mass of water column, the height of the air cushion, and air pressure distribution. Using MOSES and physical model experiments, [PERSON] et al. developed a one-step integrated transportation and installation technique to minimize the offshore operation and maximize the proportion of work carried out onshore with cost, quality, and safety benefits. The dynamic and kinematic characteristics for the transportation system with different drafts and air pressures in the bucket were obtained. A smaller draft and a larger air cushion contribute to safe transportation [7]. In the design stage, OWTs with a large power rate should be installed at deeper water than 20 m and subjected to strong horizontal and moment loadings by the wind, wave, and current [28]. Therefore, the large-diameter multi-bucket foundation (LDMBF) is well suited for OWTs at deeper water. The wave diffraction and hydrodynamic interactions between bucket foundations are more complex with increasing diameters of the bucket during air floating transportation. Although previous studies explained the draft, compartments, water depth, and wave effect on the motion of air-cushion-supported structures, the motion response of large-diameter tripod bucket foundations (LDTBFs) has been rarely studied.