Experimental and Parametric Study on Mechanical and Motion Responses of a Novel Air-Floating Tripod Bucket Foundation with Taut Mooring

Abstract

In the present study, a novel air-floating tripod bucket foundation (AFTBF) with taut mooring is proposed. The mechanical and motion response characteristics of this foundation were investigated through model tests. Furthermore, a parametric study was performed on the factors influencing the RAOs of mooring tension, air cushion pressure, as well as motion in the surge, heave, and pitch directions. The conclusion of this research is as follows: mooring tension, air cushion pressure, and pitch angle exhibit wave-frequency responses in small periods and low-frequency responses in large periods. Surge response is characterized by dual-peak features, while heave response predominantly demonstrates wave-frequency characteristics. As draft increases, the air cushion pressure inside the buckets exhibits a decreasing trend. Changes in water depth have more pronounced impacts on mooring tension and motion responses than on air cushion pressure. The impacts of changes in mooring distance and water depth on mechanical and motion responses are significantly more pronounced than those induced by changes in draft. These findings provide a critical foundation for the optimal design of this foundation in water depths of 30–50 m.

1. Introduction

The progressive depletion of nearshore marine resources has driven the global offshore wind industry to transition from near-shore to deep-water deployments [1]. Floating foundations, characterized by their independence from water depth and seabed conditions, have garnered widespread attention for their enhanced capacity to harness marine wind energy [2,3,4,5]. Decades of experience in offshore oil and gas platform development have demonstrated the long-term survivability of floating structures in marine environments. From a resource acquisition perspective, deep-water zones offer expansive areas with abundant wind resources, presenting significant development potential [6]. In terms of cost control, floating wind turbines exhibit reduced sensitivity to water depth compared to fixed-bottom foundations, with lower construction complexity, material consumption, and operational maintenance costs. Furthermore, the modular installation and flexible positioning of floating foundations enable minimized ecological impacts, such as noise and electromagnetic interference. China’s implementation of the “Single 30” policy in 2024, mandating new offshore wind projects to be located either ≥30 km from the coastline or in >30 m water depths, coupled with Norway’s strategic shift to suspend fixed-bottom developments, underscores the global trend toward deep-water floating solutions. Current research priorities focus on structural lightweight design optimization and advanced mooring system development to address the critical challenge of characterizing environmental adaptability through dynamic response analysis and motion prediction under operational conditions [7,8].

In recent years, air-floating structures have been widely applied in fields such as fixed foundations for offshore wind power, wave energy devices, and floating breakwaters, etc. During the air-floating process, unlike traditional bottom-closed structures, which are rigid structures supported on a water spring, air-floating structures are rigid structures supported on a series spring consisting of an internal air cushion and a bottom water plug, as shown in Figure 1. This challenges the well-recognized evaluation criteria for floating structures with free surfaces based on metacentric height or center of buoyancy [9]. Based on the isothermal process of ideal gases, Seidl proposed the design concept of air-floating structures and established a functional relationship between the airbag coefficient, draft, and geometric dimensions [10]. Bie et al. proposed the air buoyancy decrease coefficient to consider the difference in buoyancy changes between air-floating structures and rigid-bottom structures [11]. Based on the adiabatic process of ideal gas, Van Kessel et al. derived the correction of dimensionless parameters considering gas compression effects on the stiffness and initial metacentric height of air-floating box-type structures [12]. Thiagarajan proposed a correction formula for the metacentric height that incorporates the net effect of the air cushion on the static stability of a compartmented structure [13]. Ikoma et al. conducted numerical studies on flexible very large floating structures (VLFS) supported by air cushions using the potential flow theory model with zero-draft assumption. A profound reduction in elastic deformations and wave drift forces has been observed. The effects of air pressure distribution and drift forces on VLFS under fixed and floating conditions during wave excitation were investigated [14,15,16,17].

Combining the above parameters, Huang et al. studied the natural vibration characteristics of the world’s first composite bucket foundation (CBF) [18]. Among them, the theoretical and numerical simulation results of the heave natural frequency showed good agreement, but due to the large dispersion of the added mass coefficient for pitch, there were differences in the results. Zhang studied the heave and pitch natural periods of the composite bucket foundation [19]. As the draft increases, the heave natural period increases, but the pitch motion period decreases, which is mainly caused by the change in the center of gravity position. Min studied the natural vibration characteristics of CBF under no-load and top ballast conditions. Ballasting leads to an increase in draft, while the pitch natural period no longer changes when the draft exceeds a certain value [20]. Wang et al. conducted research on the CBF of the Jiangsu Dafeng Wind Farm and a certain offshore substation and found that the oscillating natural period of the CBF increases with the increase in draft [21,22]. Liu et al. studied the natural vibration characteristics of large-diameter multi-bucket foundations and determined that the added mass coefficient ranges from 1.2 to 1.8, with a larger value taken when the draft is small and a smaller value when the draft is large [23].

In recent years, the unique air-cushion–water-plug coupled bearing form of air-floating structures has been widely adopted in offshore construction scenarios such as air-floated towing, integrated transportation and installation techniques, and air-storage lowering, which has significantly reduced construction costs and improved construction safety. Ding et al. analyzed the air-floated towing characteristics of an emergency repair platform composed of four bucket foundations, concluding that mooring points should be positioned as close as possible to the plane where the platform’s center of buoyancy is located [24]. Le et al. investigated the effects of towing speed, water depth, freeboard height, and wave direction on the air-floating towing of a multi-bucket foundation platform [25]. Ding et al. conducted numerical simulations on the towing motion characteristics of CBF and found that the surging/swaying, heave, and pitch/rolling RAOs of the CBF were all related to the foundation draft and fluctuated sharply within the wave period range from 6 to 9 s [26]. Yan et al. carried out research on the static characteristics and towing stability of the proposed triple-bucket jacket foundation (TBJF) [27]. This foundation has good static stability and is suitable for long-distance towing under grade 5 wind and wave conditions. Zhang et al. compared the differences in towing resistance and air pressure between the CBF with bulkheads and the CBF without bulkheads through experiments and numerical simulations. The study found that under the same test conditions, the towing force of the CBF without bulkheads is greater than that of the CBF with bulkheads, and the subdivision plates can effectively reduce the towing resistance of the structure [28].

Ding analyzed the on-site measured data of the composite bucket foundation using one-step installation technology and found that changes in water depth, towing speed, and air pressure in the compartments had minimal impact on the towing process [29]. Lian et al. proposed a synthetical prefabrication and transportation (P&T) technique and studied the dynamic characteristics and towing resistance under this technique. It is suggested that as the monopod-bucket foundation with subdivisions floats up, the water depth of the construction site should not be less than 6 m [30]. Wang et al. proposed the wide-shallow bucket jacket foundation as the foundation type for offshore substations and its installation mode. The results indicate that it is feasible to carry out long-distance wet towing of the foundation under the condition of grade 5 wind and waves [21]. Zhu et al. present a fast and practical simulation framework for evaluating wet towing systems for multi-bucket jacket wind turbines, considering air compressibility in suction caissons under realistic seaway conditions. The results further indicate that the presence of compressible air in the caissons increases the natural periods in heave and pitch by approximately 3.5%, while the heave damping is reduced by 16% and the pitch damping is increased by 25% [31].

Li, Gao, and Moan T et al. have conducted extensive research on the hoisting construction process of offshore structures. Utilizing their self-developed external dynamic link library that interfaces with the SIMO program in time-domain simulations, they investigated the effects of factors such as different wave directions, various numerical calculation methods, and types of crane vessels on the calculation results. The shielding effect of crane vessels was considered, and wave impact and immersion-related loads during the lowering process were calculated. Additionally, standards for offshore operations and assessment criteria for sling slackness were established [32,33,34,35,36,37]. Zhang et al. conducted a complete time domain simulation of the lowering process of the three-bucket jacket foundation through theoretical analysis combined with the hydrodynamic software MOSES V12 [38].

Kim et al. investigated the mooring and motion characteristics of a two-dimensional air-floated box structure with taut mooring systems. They analyzed the oscillating motion, wave transmission rate, reflectivity, and mooring tension characteristics of the structure under open, cross, and vertical mooring configurations; however, only two-dimensional structural analyses were conducted [39]. Qi et al. revealed that the mechanical and motion characteristics of bottom-open structures are superior to those of bottom-closed ones. Nevertheless, no investigation into influencing factors was performed [40]. He et al. experimentally investigated the hydrodynamic performance of floating breakwaters with and without pneumatic chambers under slack-mooring conditions [41]. Furthermore, He et al. analyzed a proposed configuration of floating breakwaters with asymmetric pneumatic chambers, which was designed to increase the amplitude of oscillating air pressures inside both chambers over a wide range of wave frequencies, thereby improving performance in wave energy extraction. It was found that power extraction was primarily driven by water column oscillation inside the chambers, such that a narrower chamber breadth, which facilitates water column oscillation, was preferable [42,43]. Zhang studied the heave motion characteristics of air-cushion floating bodies, moonpool floating bodies, and solid floating bodies, concluding that the heave natural frequency of air-cushion-supported floating bodies lies between that of moonpool floating bodies and solid floating bodies [44]. Hao et al. researched the initial stability of such platforms, suggesting that the presence of air cushions can cushion loads acting on the structure and reduce structural motion; however, no analysis of the mooring characteristics of air-cushion-supported structures was conducted [45].

To summarize, air-floating bucket foundations with catenary mooring exhibit superior mechanical and motion performance compared to traditional bottom-closed platforms [40]. The uniform distribution of air pressure and gas compressibility in air-floating structures can effectively average the forces exerted by the external environment on the bottom [46,47]. In deep-water environments, under the same pretension conditions, the motion response amplitudes of taut mooring systems are smaller compared to those of catenary mooring systems. Based on this, this paper innovatively proposes a new type of air-floating tripod bucket foundation (AFTBF) with taut mooring. The impact of geometric dimensions, mooring parameters, water depth, environmental conditions, and static and dynamic responses on the taut mooring characteristics of this foundation has not been systematically analyzed. Scholars have mainly conducted a series of studies on the static stability, towing characteristics, and catenary mooring of air-floating structures. The lack of detailed analysis of this new foundation directly affects its water depth adaptability and large-scale development and application in offshore energy development. Therefore, it is imperative to carry out research on the mechanical and motion response characteristics of AFTBFs with taut mooring.

The main objective of this study is to investigate the mechanical and motion performance of AFTBFs with taut mooring under regular waves through model tests. A prototype structure suitable for water depths of 30–50 m was initially designed based on literature reviews. A scaled model with a geometric scale of 1:100 was fabricated in accordance with the geometric similarity and Froude similarity criteria, and free decay tests and regular wave tests were conducted in a test flume. The outline of this paper is as follows: In Section 2, the objectives and basis of the model tests, dimensions of the model and prototype, test systems and equipment, as well as the test scheme and procedures are described in detail. In Section 3, the variation laws of the response amplitude operators (RAO) of mooring tension and air cushion pressure with different draft, water depth, and anchor distance, obtained from the tests, are discussed in detail. In Section 4, the variation laws of RAO for representative motion with different draft, water depth, and anchor distance, derived from the tests, are analyzed in detail. In Section 5, the conclusions drawn from this study are summarized.

2. Experimental Description

2.1. Design of Prototype and Model

The present experiment is intended to investigate the influence laws of draft, water depth, and anchor distance on the motion responses and force characteristics of an AFTBF with taut mooring under the action of regular waves, thereby providing an experimental basis for the stability design and seakeeping assessment of such structures.

The prototype design of the experiment is based on the moored open-bottom platform proposed by Qi [40]. Optimizations regarding its stability and seakeeping performance have been implemented to propose the structural form of the AFTBF adopted in this experiment. The experiment is strictly conducted in accordance with the national standard of the People’s Republic of China, Technical Code for Simulation Tests of Water Transport Engineering (JTS/T 231-2021) [48]. In combination with the actual conditions of the test site, a geometric similarity ratio of 1:100 and the gravity similarity criterion are employed to establish the correlation between the model and the prototype, ensuring that the test results can be extrapolated to the prototype scale via similarity theory. However, the gravity similarity criterion ensures similarity in the fluid motion characteristics between the model and the prototype under the action of gravity and is particularly applicable to scenarios involving free water surfaces in design. Nevertheless, since the standard atmospheric pressure within the absolute pressure is constant, model tests need to be conducted in a low-pressure environment to achieve similarity in absolute pressure, which is difficult to realize in experiments [49]. Therefore, when extrapolating model pressure data to prototype pressure data, it is necessary to consider the influence of scale effects and the compressibility of the air cushion.

As shown in Figure 2, the prototype is composed of three identical bucket foundations and a connecting frame. Each bucket foundation has a diameter of 10 m and a height of 20 m, with a height-to-diameter ratio of 2:1. The center-to-center distance between adjacent buckets is 20 m. The connecting frame is formed by cylindrical members with a diameter of 1.5 m into an equilateral triangular frame with a side length of 20 m, which is positioned above the tops of the buckets. The model is designed based on a 1:100 geometric similarity ratio, with conversion relationships of physical quantities calculated using similarity theory formulas as presented in

Table 1. Similarity theory formula of prototype and model structures.

Parameter	Length	Width	Height	Mass	Weight	Moment of Inertia	Radus of Inertia	Velocity	Acceleration	Period	Force
Prototype	1	1	1	1	1	1	1	1	1	1	1
Model	$\lambda$	$\lambda$	$\lambda$	${\lambda }^3$	${\lambda }^3$	${\lambda }^4$	$\lambda$	$\sqrt{\lambda }$	1	$\sqrt{\lambda }$	${\lambda }^3$

. Specifically, the model bucket foundations have a diameter of 0.1 m and a height of 0.2 m, with a center-to-center distance of 0.2 m between adjacent buckets, the main parameters of prototype and model for AFTBF are shown in

Table 2. Main parameters of prototype and model for AFTBF.

Parameter		Prototype	Model
Bucket diameter/m		10.0	0.1
Bucket spacing/m		10.0	0.1
Thickness/m	Bucket top	0.2	0.002
	Bucket wall	0.1	0.001
Bucket height/m		20.0	0.2
Total height/m		22.5	0.225
Total weight		2260 t	2.26 kg
Exhaust valve diameter/m		2.0	0.02
Connecting frame diameter/m		1.5	0.015
Center of gravity (CoG) relative to the AFTBF’s base center		(0, 0, 12.638)	(0, 0, 0.1264)
Pitch radius of gyration about CoG/m		10.922	0.109
Roll radius of gyration about CoG/m		10.922	0.109
Yaw radius of gyration about CoG/m		12.102	0.121

. The model connecting frame has a diameter of 0.015 m and a side length of 0.2 m. The entire model is fabricated from stainless steel with an elastic modulus of 200 GPa and a density of 7850 kg/m³. The manufacturing error is controlled within ±0.5% to meet the geometric similarity requirements. Meanwhile, three exhaust ball valves are installed at the triangular vertices of the connecting frame, aligned with the midpoints of the bucket tops, to adjust the internal air pressure and control the draft. Scale rulers with a precision of 0.5 mm are attached to the side of each bucket for real-time monitoring of draft changes, and the adjustment error is ≤±1 mm.

2.2. Equipment and Measurement System

As shown in Figure 3, the experiment was conducted in a wave flume with dimensions of 30 m in length, 0.5 m in width, and 1 m in height at the National Engineering Research Center for Inland Waterway Regulation, Chongqing Jiaotong University. One side of the flume was equipped with a coastal irregular wave test platform wave-making system developed by Tianjin Tengyue Automation Equipment Co., Ltd.(Tianjin, China), which is capable of generating regular waves with stable waveforms, featuring a wave height control accuracy of ±0.5 mm and a period control accuracy of ±0.01 s. The AFTBF with taut mooring was placed 15 m away from the wave maker, a region verified through pre-tests as a fully developed wave zone. The other side was provided with a sloped gravel energy dissipation zone with a reflection coefficient of <1% to eliminate interference from shoreline reflections.

A Cartesian coordinate system (x, y, z) was adopted, with the origin O located at the center of the connecting frame. The z-axis was oriented vertically upward, perpendicular to the still water surface, and the x-axis was parallel to the incident wave direction, with its positive direction corresponding to the wave propagation direction. Motion along the x-axis was defined as surge, motion along the z-axis as heave, and rotation about the y-axis as pitch.

As shown in

Table 3. The main parameters of mooring lines.

Parameter	Prototype	Model
Diameter/m	0.2	0.002
Unit mass per meter/kg·m−1	1140	0.0114
Breaking force/N	1.67 × 107	1670
Elastic modulus/GPa	12.04	12.04
Stiffness/N·m−1	6.594 × 109	6594

, the mooring system complied with the 1:100 geometric similarity, mass similarity, and elastic similarity criteria, and was composed of an upper anchor plate, tension shackles, anchor chains, steel mesh with 2.0 cm × 2.0 cm holes and a diameter of 2.8 mm, and anchor blocks of 30 cm × 30 cm × 3 cm. The upper anchor plate at the extension of the connecting frame’s diagonal was connected via a tension shackle to an HYLY-019 micro tension sensor, which has a measuring range of 0–50 N, an accuracy of ±0.2% FS, and a sampling frequency of 100 Hz. One end of the sensor was connected to the mooring line, and the other end to the anchoring shackle of the steel mesh, which was fixed by anchor blocks to prevent slippage.

The measurement system included a YWH200-D digital wave height meter, positioned between the AFTBF and the wave maker for real-time wave height monitoring; an IM948 gyroscope, installed at the center of the top of the connecting frame, with an angular displacement accuracy of ±0.1°, an acceleration accuracy of ±0.01 g, and a sampling frequency of 100 Hz, for measuring motion responses; and a PCM300D compact pressure transmitter, with a measuring range of −10 to 10 kPa, an accuracy of ±0.5% FS, and a sampling frequency of 100 Hz, for monitoring the air cushion pressure. The numbering of mooring lines, sensors, and bucket foundations was consistent, with numbers 1# to 3# assigned in clockwise order along the wave direction as shown in Figure 4.

2.3. Experiment Plan and Procedure

A multi-factor comprehensive design method was adopted in the experiment, with draft, water depth, and anchor distance as variables. Draft was adjusted via mooring line length to 0.14 m, 0.16 m, and 0.18 m. Water depth was set to 0.30 m, 0.40 m, and 0.50 m by adjusting the flume water level. Anchor distance, defined as the straight-line distance from the upper anchor plate on the diagonal of the connecting frame to the anchoring shackle of the steel mesh, was set to 0.03 m, 0.06 m, and 0.09 m. Detailed combinations of test conditions are presented in

Table 4. Combinations of test model.

Combination	Draft/m	Pretension/kg	Depth/m	Anchorage Distance/m	Wave Height/m	Wave Period/s
1	0.14	0.327	0.5	0.03	0.02	0.4~1.5
2	0.16	0.508	0.5	0.03	0.02	0.4~1.5
3	0.18	0.646	0.5	0.03	0.02	0.4~1.5
4	0.18	0.526	0.3	0.03	0.02	0.4~1.5
5	0.18	0.580	0.4	0.03	0.02	0.4~1.5
6	0.18	0.646	0.5	0.03	0.02	0.4~1.5
7	0.18	0.646	0.5	0.03	0.02	0.4~1.5
8	0.18	0.587	0.5	0.06	0.02	0.4~1.5
9	0.18	0.576	0.5	0.09	0.02	0.4~1.5

.

Prototype wave parameters included a wave height of 2.0 m and a period ranging from 4.0 to 15.0 s [42,50]. Based on the 1:100 similarity ratio, the model wave height was converted to 0.02 m, with a period ranging from 0.4 to 1.5 s. Each working condition was repeated three times in accordance with JTS/T 231-2021. As shown in Figure 5, the experimental procedures were as follows: Firstly, the flume water level was adjusted to the target water depth. Secondly, the structure was adjusted to the target draft and pretension via air valves and mooring lines. Thirdly, the wave maker generated regular waves with the target period; after stabilizing for 30 s, sensors were activated to synchronously collect data for a duration of 120 s. Fourthly, after the experiment, the wave making system was turned off, and the next group of test conditions was conducted after the water surface calmed. Finally, each group of experiments was performed in triplicate, with the average of parameters from the three repetitions adopted as the final result to guarantee reliability, and a total of 927 groups of experiments were conducted.

3. Study on Factors Influencing the Motion Characteristics of the AFTBF with Taut Mooring

Based on the similarity ratios between the prototype and model structures as shown in Table 1, the accelerations for translational degrees of freedom and angles for rotational degrees of freedom both have a similarity ratio of 1:1. Additionally, since waves propagate along the surge direction, surge acceleration, heave acceleration, and pitch angle are thus selected to accurately reflect the variation patterns of motion responses of the prototype structure. In this section, the amplitude variations in surge acceleration, heave acceleration, and pitch angle of the TMAFTBF under all wave test combinations are presented.

3.1. Effects of Draft

Figure 6 illustrates the RAO variation curves of surge acceleration, heave acceleration, and pitch angle of the structure under combinations 1–3. As observed from Figure 6a, with increasing period, surge acceleration exhibits a trend of initial increase, subsequent decrease, further increase, and final decrease, with one peak observed at 0.5 s and another at 0.8 s. The RAO of surge acceleration under different drafts displays dual-peak characteristics, reflecting the amplified dynamic response of the structure within two characteristic period intervals. Within the period range from 0.4 to 0.6 s, the smaller the draft, the larger the RAO of surge acceleration. This is attributed to the fact that a reduced draft decreases the added mass participating in surging motion, thereby increasing the RAO of surge acceleration. In the period range from 0.6 to 1.5 s, however, the larger the draft, the larger the RAO of surge acceleration. This is due to the higher wave energy density under longer periods, where the influence of draft on added mass diminishes; an increased draft enhances the surge force acting on the structure, thus resulting in greater surge acceleration.

The following observations can be drawn from Figure 6b: First, with increasing period, the structural heave acceleration exhibits a trend of initial increase followed by decrease; beyond a period of 1.1 s, it stabilizes at a constant value that increases with draft, with amplitudes under all draft conditions remaining below 0.05 m/s². Second, within the wave-frequency response stage, the RAO of heave acceleration decreases with increasing draft. This arises from the fact that a larger draft reduces the heave force while increasing the added mass participating in heave motion, consequently leading to a decrease in heave acceleration.

As observed from Figure 6c, with increasing period, the structural pitch motion exhibits a trend of initial increase, subsequent decrease, and further increase. With increasing draft, wave-frequency motion dominates at small periods, where the RAO of pitch motion first increases and then decreases; at large periods, low-frequency motion prevails, and the RAO of pitch motion increases, with the pitch motion at a draft of 0.18 m being greater than that under other drafts. This is because an increased draft elevates mooring pretension, which enhances the structural pitch stiffness; however, it also enlarges the wave-facing area of the structure, leading to an increased pitch moment and thus an amplification of pitch motion.

3.2. Effects of Water Depth

Figure 7 presents the RAO variation curves of surge acceleration, heave acceleration, and pitch angle of the structure under combinations 4–6. As observed from Figure 7a, with increasing period, the surge motion of the structure overall exhibits a dual-peak variation characteristic, and this trend becomes more pronounced as water depth increases. With increasing draft, the RAO of surge acceleration within the period range of 0.4–0.6 s shows a trend of first increasing and then decreasing; within 0.6–1.1 s, it exhibits a decreasing trend, while for periods exceeding 1.1 s, it presents a trend of first decreasing and then increasing. As observed from Figure 7b, with increasing period, the heave motion of the structure overall exhibits a trend of first increasing, then decreasing, and subsequently increasing. The maximum RAO of heave motion occurs at a water depth of 0.3 m and remains relatively high across the entire period range, whereas it is relatively low at a water depth of 0.5 m.

As observed from Figure 7c, with increasing period, the pitch motion of the structure overall shows an increasing trend, and with increasing water depth, the RAO of pitch motion exhibits a decreasing trend. This is attributed to the “shallow water effect”: under shallower water depths, due to the presence of the structure, the velocity of fluid flowing through the bottom of the structure increases. According to Bernoulli’s equation, the bottom pressure decreases, leading to an increase in the structural draft, which increases the vertical motion of the structure and its wave-facing area, thereby enhancing the oscillating motion of the structure. With increasing water depth, the influence of the structure on bottom pressure weakens, the “shallow water effect” diminishes, and the oscillating motion of the structure tends to exhibit wave-frequency motion at small periods and low-frequency motion at large periods.

3.3. Effects of Anchor Distance

Figure 8 illustrates the RAO variation curves of surge acceleration, heave acceleration, and pitch angle of the structure under combinations 7–9. As observed from Figure 8a, the RAO of surging acceleration exhibits a decreasing trend with increasing anchor distance. This phenomenon arises from the fact that, under identical draft and water depth conditions, the vertical tension component of the mooring lines remains constant; an increase in anchor distance enlarges the opening angle of the mooring lines, and the enhanced horizontal tension component restricts structural surging motion, thereby increasing structural surge stiffness and consequently inducing a decreasing trend in surging acceleration.

As observed from Figure 8b, firstly, within the wave-frequency response stage, the RAO of heave acceleration presents a trend of initial decrease followed by increase with increasing anchor distance; in the low-frequency response stage, however, it exhibits a decreasing trend as anchor distance increases. Notably, variations in anchor distance lead to significant non-monotonic oscillatory changes in heave acceleration with period, where larger anchor distances correspond to greater oscillatory amplitude and frequency. The first plausible mechanism is that, under identical external loads, an enlarged opening angle of the mooring lines results in an increased structural pitch angle, and the coupled motion of heave and pitch further amplifies vertical motion. The second mechanism is that an increase in anchor distance enhances the surge restoring force, reducing surge motion, while the intensified wave energy acting on the structure also contributes to an increased pitch angle, which in turn amplifies heave motion.

As observed from Figure 8c, across both the wave-frequency and low-frequency response stages, the RAO of pitch angle increases with increasing anchor distance. This is attributed to the fact that an increase in anchor distance enlarges the opening angle of the mooring lines, which reduces the vertical tension component of the mooring lines. Such a reduction diminishes the pitch restoring moment, weakens the constraint on pitch motion, and thus leads to an increase in pitch angle.

4. Study on Factors Influencing the Mechanical Characteristics of the AFTBF with Taut Mooring

The amplitude variations in mooring tensions in the front line 1# and rear lines 2# and 3#, as well as air cushion pressures in the front bucket 1# and rear buckets 2# and 3# of the AFTBF with taut mooring, are presented for all test combinations in this section.

4.1. Effects of Draft

Figure 9 shows the RAO variation curves of tension for mooring lines 1#–3# and air cushion pressures under combinations 1–3. As observed from Figure 9a–c, the RAOs of mooring line tension generally exhibit a trend of first increasing, then decreasing, and subsequently increasing with increasing period. Wave-frequency response characteristics are observed within the short-period range from 0.4 to 0.6 s, with the amplitude occurring around 0.5 s. In the long-period range from 0.6 to 1.5 s, low-frequency response characteristics are displayed, where the amplitude increases monotonically with the period [51]. This phenomenon is attributed to the high overall stiffness and elevated natural frequency of the structure under the taut-mooring condition, rendering it susceptible to dynamic resonance induced by short-period waves. In contrast, long-period waves, characterized by higher wave energy density and stronger persistent disturbance to the structure, lead to increased structural rolling and pitch motions with increasing period. Consequently, greater mooring line tension is required to constrain these motions, resulting in a monotonic increase in mooring line tension with increasing period.

During the wave-frequency response stage, with increasing draft, the variation trends of tension in the front mooring line 1# and rear mooring lines 2# and 3# are opposite. This is because the structure is jointly constrained by the front and rear mooring lines: wave crests or troughs of incident waves act directly on the front bucket, and wave forces are in phase with wave surface displacement, causing the tension in the front mooring line to fluctuate in phase with the wave surface position. Specifically, when a wave crest arrives, the structure moves forward, leading to a decrease in the tension of the front mooring line; when a wave trough arrives, the structure moves backward, resulting in an increase in the tension of the front mooring line. However, the arrival time of wave crests or troughs at the rear mooring lines lags behind that at the front mooring line. When incident waves drive the structure forward, the rear mooring lines are required to “restrain” the structure, causing their tension to increase; conversely, when the structure moves backward, the tension in the rear mooring lines decreases. At the maximum amplitude, the tension in the front mooring line exhibits a trend of first increasing and then decreasing, while the tension in the rear mooring lines shows a trend of first decreasing and then increasing.

During the low-frequency response stage, as draft increases, the tension in lines 1# and 2# tends to decrease, whereas the tension in line 3# presents a trend of first decreasing and then increasing. Moreover, the amplitude variation in line 3# is greater than that in lines 1# and 2#. This phenomenon arises because the increase in draft is achieved by reducing the length of the mooring lines: a shorter mooring line length leads to increased pretension. With enhanced pretension, the constraint of the mooring lines on structural displacement is strengthened, the amplitude of structural motion is reduced, and the disturbance of wave forces on the air cushion is weakened. As a result, the RAO amplitude of air cushion pressure in this stage decreases with increasing pretension. Furthermore, line 1# is arranged along the wave direction and directly bears the forward force of incident waves, while lines 2# and 3# form a certain angle with the waves. In addition to withstanding the forward action of wave loads, lines 2# and 3# also bear additional loads generated by the oscillating motion of the structure.

From Figure 9d–f, the following can be observed: Firstly, with increasing period, the RAO of air cushion pressure exhibits a trend of first increasing, then decreasing, and subsequently increasing again. Secondly, within the short-period range from 0.4 to 0.6 s, wave-frequency response characteristics are exhibited, with the amplitude occurring at approximately 0.5 s; in the long-period range from 0.6 to 1.4 s, low-frequency response characteristics are shown, and the amplitude increases as the period increases. Thirdly, both in the wave-frequency response stage and the low-frequency response stage, the air cushion pressure in buckets 1#–3# tends to decrease with increasing draft. This phenomenon arises because the variation in air cushion pressure is significantly influenced by heave motion. As draft increases, pretension is enhanced, leading to an increase in the overall heave stiffness of the structure. Meanwhile, the heave force acting on the structure is reduced, resulting in a decrease in the RAO of air cushion pressure.

4.2. Effects of Water Depth

Figure 10 presents the RAO variation curves of mooring lines 1#–3# and air cushion pressures under combinations 4–6. From Figure 10a–c, the following observations can be made: First, in the wave-frequency response stage, with increasing water depth, the tension in line 1# exhibits a decreasing trend, while the tension in lines 2# and 3# shows a trend of first decreasing and then increasing. In the low-frequency response stage, the tension in lines 1# and 2# tends to decrease, whereas the tension in line 3# presents a trend of first decreasing and then increasing. Second, with increasing period, the RAO of mooring line tension at a water depth of 0.3 m no longer follows the trend of first increasing, then decreasing, and subsequently increasing; instead, multiple maximum values appear around periods such as 0.5 s, 0.9 s, and 1.3 s. There is a sudden jump in line 1# and 2# within the wave period range of 0.7–1.0 s, and there are two key reasons for this phenomenon: Firstly, the dynamic response of mooring tensions is strongly coupled with structural motions. When the wave period approaches the natural frequency of the structure-mooring system, resonance and dynamic amplification effects occur. As observed in Figure 7a, the surge motion exhibits the second peak within 0.7–1.0 s, indicating significantly enhanced surge responses that directly amplify mooring tensions. Figure 7b,c further show that both heave and pitch motions increase within this period range, with a more pronounced trend in shallower water depths. This intensified structural motion requires greater restraining tensions from the mooring lines, leading to a distinct peak in the tension RAO and thus the observed sudden jump.

From Figure 10d–f, the following observations can be made: First, during the wave-frequency response stage, with increasing water depth, the air cushion pressure in buckets 1# and 3# exhibits a trend of first decreasing and then increasing, while that in bucket 2# shows a decreasing trend. In the low-frequency response stage, when the period exceeds 0.7 s, the RAO of air cushion pressure tends to increase with increasing water depth. Second, the amplitude of air cushion pressure at a water depth of 0.3 m is significantly larger than that at 0.4 m and 0.5 m, and this difference is more pronounced in the long-period range exceeding 0.7 s. Possible reasons for these phenomena are as follows: First, the reduction in water depth leads to a decrease in relative wave depth (the ratio of water depth to wavelength), enhancing the nonlinear effect of waves and increasing the hydrodynamic loads acting on the structure. Meanwhile, as water depth decreases, wave energy becomes concentrated and wave height increases significantly, resulting in increased amplitudes of heave and pitch motion, which in turn causes an increase in the RAO of air cushion pressure. Third, the peak air cushion pressure in the front bucket (bucket 1#) is higher than that in the rear buckets (buckets 2# and 3#). This is primarily attributed to the direct effect of increased wave elevation on the wave-facing side: incident waves generate a higher local wave surface on the wave-facing side, and the superposition of diffracted waves and incident waves leads to more significant dynamic changes in the draft of the bucket, increasing the fluctuation of air cushion volume. On the leeward side, the wave surface is attenuated by the shadowing effect of the front bucket, resulting in milder changes in draft and thus weaker amplitudes of air cushion pressure. The RAO curves of air cushion pressure for buckets 2# and 3# are symmetrically coincident, further verifying that the spatial distribution of wave diffraction exhibits mirror characteristics. The equilateral triangular arrangement enables “balanced distribution” of leeward loads, ensuring the force coordination of the structure.

4.3. Effects of Anchor Distance

Figure 11 presents the RAO variation curves of mooring lines 1#–3# and air cushion pressures under combinations 7–9. From Figure 11a–c, the following observations can be made: First, in the wave-frequency response stage, with increasing anchor distance, the tension in the front line 1# exhibits an increasing trend, while the tension in line 3# shows a decreasing trend. Although the tension in line 2# presents a trend of first decreasing and then increasing, the overall magnitude of its amplitude variation is insignificant. Second, in the low-frequency response stage, as anchor distance increases, the tension in lines 1# and 2# tends to increase, whereas the tension in line 3# shows a decreasing trend. Possible reasons for this are as follows: Line 1#, being in the wave-facing state, experiences an increase in the opening angle of the mooring line due to the increased anchor distance under stable wave action, which leads to enhanced structural pitch motion and thus an increase in the RAO of mooring line tension. Third, the magnitude of amplitude variation when the anchor distance increases from 0.03 m to 0.06 m is greater than that when it increases from 0.06 m to 0.09 m.

From Figure 11d–f, it can be observed that with increasing anchor distance, the RAO of air cushion pressure in buckets 1#–3# exhibits an increasing trend. Although the amplitude in the low-frequency response stage is larger than that in the wave-frequency response stage, the magnitude of its amplitude variation decreases. This is because, with the increase in anchor distance, during the wave-frequency motion stage, under steady wave action, the same draft results in identical external loads. Under such identical external loads, the increased opening angle of the mooring lines leads to a larger structural pitch angle, and the coupled motion of heave and pitch causes an enhancement in vertical motion, thereby increasing the RAO of internal bucket air cushion pressure. In the low-frequency response stage, however, the structure exhibits a “wave-following” behavior. The increased anchor distance leads to an increase in surge restoring force and a reduction in surge motion, while the energy of wave action on the structure increases, causing enhanced structural pitch motion. Consequently, the RAO of air cushion pressure inside the bucket in this stage exceeds that in the wave-frequency response stage.

5. Conclusions

A novel type of floating offshore foundation, namely the taut-moored AFTBF, is proposed in this paper. The mechanical and motion response characteristics of this foundation were investigated through model tests. Furthermore, a parametric study was performed on the factors influencing the RAOs of mooring tension, air cushion pressure, as well as motion in the surge, heave, and pitch directions. The main conclusions are as follows:

(1) With varying periods, mooring tension, air cushion pressure, and pitch angle exhibit wave-frequency responses in small periods and low-frequency responses in large periods. In contrast, surge response is characterized by dual-peak features, while heave response predominantly demonstrates wave-frequency characteristics.

(2) As draft increases, the air cushion pressure inside the buckets exhibits a decreasing trend. In the wave-frequency response stage, the mooring tension of the front line and rear lines shows opposing variation trends; in the low-frequency response stage, the variation trends of mooring tension for lines 1# and 2# diverge from that of line 3#.

(3) The shallow water effect amplifies the variation amplitudes of mooring tension, air cushion pressure, and motion responses of the AFTBF with taut mooring. Changes in water depth have more pronounced impacts on mooring tension and motion responses than on air cushion pressure.

(4) With increasing mooring distance, mooring tension, air cushion pressure, heave motion, and pitch motion all exhibit an increasing trend; however, the enhanced surge stiffness reduces the surge motion.

(5) The impacts of changes in mooring distance and water depth on mechanical and motion responses are significantly more pronounced than those induced by changes in draft.

Although this paper presents a preliminary investigation into the force and motion response characteristics of a taut-moored AFTBF, several limitations remain for practical engineering applications: Firstly, the model scale employed is 1:100, and the influence of scale effects has not been accounted for under the current experimental conditions, particularly the impact of air cushion compressibility on structural motion and force responses. Secondly, only the effects of regular waves with a single incident angle and unit wave amplitude on RAOs have been considered; factors such as wave direction angles, wave heights, and irregular waves have not been incorporated. Thirdly, the analysis has focused solely on the force and motion response characteristics of the foundation structure under regular waves, without addressing the variation laws of force and motion responses of the superstructure (e.g., wind turbine blades, nacelles, and towers) and the overall structure under the influence of complex marine environments. Finally, the present work is purely experimental, which provides solid physical insights but also has a limitation: the absence of complementary numerical analysis. In particular, no use of standard hydrodynamic tools (e.g., MOSES, WAMIT Version 7, ANSYS 2025) was made to validate or extend the experimental findings. More importantly, future research should aim to incorporate air-cushion stiffness effects into numerical models, such as through coupled fluid–structure interaction solvers, compressible air chamber models, or hybrid CFD–potential flow approaches.

Nevertheless, these findings provide a critical foundation for the optimal design of this foundation in water depths of 30–50 m. Future work should extend to irregular wave conditions and full-scale validation to enhance its engineering applicability.