The Anti-Overturning Response of Tripod Bucket Foundation for Offshore Wind Turbines

Abstract

The tripod bucket jacket foundation is proven to be a practicable solution for offshore wind turbines (OWTs) to withstand huge environmental loads in deep water. This paper presents model tests for a scaled tripod bucket jacket foundation with reference to a prototype applied in China to obtain its lateral load bearing behavior in medium-dense sands. Extended finite element analyses were conducted by ABAQUS to compare anti-overturning responses for the tripod bucket foundation in both sand and soft clay, and the influences of loading direction and aspect ratio were also taken into account. The results showed that the failure modes of the laterally loaded tripod bucket foundation are the pull-out of the windward bucket in sand and the settlement of the leeward bucket in soft clay, respectively. Thus, the unfavorable loading direction of the foundation changes with soil type. It is also shown that the bearing capacity for the foundation in soft clay will be enhanced more effectively as the bucket diameter increases. Instead of the rotational soil resistance resulting from the rotation of the bucket, the vertical soil resistance governs the anti-overturning bearing capacity of a tripod bucket foundation. As the tilt created by the overturning moment rises, the rotational stiffness of the foundation dramatically declines.

1. Introduction

With the increasing demand for renewable energy, offshore wind energy has been proven to be a feasible option to achieve carbon neutrality worldwide with a global installation of 55.9 GW [1]. Generally, the fabrication and installation cost of OWTs foundation accounts for about 30% of the overall cost [2]. Therefore, it is essential to adopt an appropriate OWT foundation type to reduce the cost of construction and promote the development of the offshore wind industry in China.

At present, monopile foundations are widely used in nearshore areas with a water depth of less than 30 m [3,4]. However, the jacket foundation, with multi-pile or multi-bucket, is more suitable for offshore wind farms in deeper water than the monopile foundation due to its strong bearing capacity [5]. Given the convenience of installation for suction buckets, the multi-bucket jacket foundations are recommended as an alternative solution to replace the traditional piled jacket foundation [6,7]. As shown in Figure 1, the multi-bucket jacket foundation, especially the tripod type, has been successfully applied to several offshore wind farms in China, with detailed information summarized in

Table 1. Detailed information on multi-bucket jacket foundations installed in China.

Location	Height of Structure (m)	Total Weight (Tons)	Water Depth (m)	Wind Turbine Capacity (MW)
Shapa, Guangdong	52.0	1560	27–32	5.5
Houhu, Guangdong	63.1	1800	23–26	5.5
Changle, Fujian	85.7	1936	32–45	10.0
Zhuanghe, Liaoning	45.5	1200	30	5.0

.

To ensure the in-place stability of OWTs, the evaluation of the anti-overturning response of the tripod foundation is one of the key factors to be considered in the design practice [8]. Nevertheless, there is no detailed guidance for designers in the widely used design codes, e.g., DNV-GL code [9] and API code [10].

A few model tests were reported in the literature with a focus on the overturning moment-rotation response of tripod bucket foundations under lateral loads [11,12,13,14]. Wang et al. [11], Jeong et al. [12], and Kim et al. [13] studied the monotonic and cyclic behavior of the tripod foundation by performing centrifuge tests in sand. They found that the bucket had a weak bearing capacity for the pullout load, resulting in the dominant pullout behavior of the tripod foundation. Faizi et al. [14] conducted a series of small-scale tests in loose sand under 1 g condition to analyze the influence of both loading direction and footing spacing on the anti-overturning capacity of the tripod. They showed that the overturning capacity is influenced by the loading direction. However, the movement responses of the tripod foundation were not systematically reported in these works.

Considering the high time and economic costs of carrying out model tests, extensive studies were conducted numerically. Wang et al. [15] reported a comparison study of the bearing capacity for two tripod bucket jacket foundations with varied L/D in sand under monotonic loads. The results showed that the overturning moments on the tripod foundation are resisted by the inside and outside bucket soil friction. Tran et al. [16] and Kim et al. [17] performed parametric studies for the tripod foundation in sand and clay, respectively. They agreed that the spacing ratio S/D (where S is the spacing between footing and D is the diameter of the bucket) and aspect ratio L/D (where L is skirt length) are the key factors affecting the anti-overturning bearing capacity. Furthermore, Qiu et al. [18] systematically examined the kinematic mechanisms of the whole foundation system against spacing and embedment and developed an efficient method to predict overturning bearing capacity considering the influence of geometrical factors. Extended work was undertaken by Hung et al. [19], He et al. [20], and Barari et al. [21] to investigate the ultimate bearing capacity and the failure envelope of the tripod foundation under combined loading conditions (i.e., vertical, horizontal, and moment loading). Based on the finite element analysis results, closed-form expressions to describe the combined capacity envelope were proposed.

So far, the existing studies focus on the ultimate bearing capacity of the tripod foundation in one specific soil type. Whereas no literature is available on comparison studies of anti-overturning responses for tripod bucket foundations both in sand and clay. Moreover, the topsoil in the China Seas, especially the South China Sea, is dominated by soft clay with low strength [22,23]. The bucket may experience a large settlement under the downward force caused by the overturning load, which will adversely affect the application of the tripod bucket foundation in those areas. Hence, it is vital to understand the difference in anti-overturning characteristics for tripod foundations in both sand and soft clay, which could be used for reference in engineering design.

In the present study, the anti-overturning response of the tripod suction bucket foundation is explored by model tests and finite element analyses. The model tests with a scale ratio of 1:100 were carried out to investigate the load bearing behavior and failure mode of a laterally loaded tripod bucket foundation in medium-dense sands. Furthermore, a well-validated numerical model on an engineering scale was adopted to perform comparison studies of anti-overturning responses for tripod bucket foundations in both sand and soft clay.

2. Experimental Study

2.1. Experimental Test Introduction

The test model was designed with a scale ratio of 1:100 by referring to one prototype tripod bucket jacket foundation installed in the South China Sea. The model was made of 304 stainless steel with an elastic modulus of 200 GPa and a Poisson’s ratio of 0.3. As shown in Figure 2, the model consists of the jacket superstructure and the bucket substructure, which are connected by flanges and bolts. The height of the model jacket structure is 560 mm (56 m for the prototype), with a total weight of 7.36 kg (700 tons for the prototype). More details about the model’s dimensions are listed in

Table 2. The dimensions of model jacket structure main part.

Part	Diameter (mm)	Wall Thickness (mm)
Transition piece	70	2
Main leg	18	2
X brace	8	1

. The model bucket is arranged in a configuration of an equilateral triangle with a spacing of 285 mm (28.5 m for the prototype). Both the length of the bucket skirt L and the diameter of the top lid D are the same and equal to 135 mm (13.5 m for the prototype), leading to the aspect ratio L/D of 1. Considering the fabrication limitation and potential local buckling failure, the wall thickness of the bucket t was set to 2 mm, in contrast to 45 mm for the prototype. In addition, several stiffeners were welded radially on the top lid to improve its strength. The vent holes were drilled on the top lid of the bucket for convenience during installation.

Dry silica Fujian sand was used as the seabed ground in this study, and its basic physical properties are summarized in

Table 3. Physical properties of the Fujian sand.

Physical Parameters	Values
Specific gravity, $G_s$	2.62
Mass median diameter, $d_{50}$ (mm)	0.16
Maximum dry density, ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{y},\mathrm{m}\mathrm{a}\mathrm{x}}$ (g/cm3)	1.64
minimum dry density, ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{y},\mathrm{m}\mathrm{i}\mathrm{n}}$ (g/cm3)	1.35
Relative density, $D_r$ (%)	60
Dry density, ${\rho }_{\mathrm{d}\mathrm{r}\mathrm{y}}$ (g/cm3)	1.51
Critical internal friction angle, ${\phi }_{\mathrm{c}\mathrm{v}}$ (°)	39.0
Poisson’s ratio, $v$	0.21
Shear modulus, G (MPa)	15.8

. The test was conducted in a reinforced rectangular box with the dimensions of 1 m × 1 m × 0.8 m (length × width × height). To achieve a relative density of 60% (medium-dense sand), the sandy ground was generated layer by layer and compacted [24], with a thickness of each layer of 100 mm. The mass of each sand layer was calculated by multiplying the fill volume by the targeted density (${\rho }_{\mathrm{d}\mathrm{r}\mathrm{y}}=1.51$ g/cm³). As illustrated in Figure 3, the shear modulus G of sandy ground was estimated by utilizing the shear wave velocity method [25,26,27]:

$$v_s=\frac{l}{\mathsf{\Delta }t}$$

(1)

$$G=\rho v_s^2$$

(2)

where l is the distance between two accelerometers, $\mathsf{\Delta }t$ is the time interval between two sensors receiving shear wave signal, $v_s$ and ρ are shear wave velocity and soil density respectively.

2.2. Test Procedure

Figure 4 demonstrates the setup of the model test. All model tests were carried out under 1 g conditions. The tripod bucket model was pressed into the ground at a slow rate to avoid unexpected disturbances to the model sand [14]. The horizontal force, generated by a pulley system and the dead weight, was applied at the top of the model jacket structure (560 mm above the ground surface) to create the overturning moment. A batch of laser displacement transducers was placed properly to monitor the vertical displacement of buckets and the horizontal displacement of jacket structure during the loading process. The rotation of the whole model was recorded by an inclinometer attached to the top of the jacket structure.

Considering the plane symmetry of the tripod bucket foundation, the horizontal force was loaded in two opposite directions as shown in Figure 4c, corresponding to two different loading conditions, namely, one bucket in tension (OBT) and two buckets in tension (TBT). The horizontal force was loaded in 5 N increments and maintained for 10 min. The loading procedure was terminated when the overturning failure of the model was observed.

2.3. Experimental Test Results

2.3.1. Overturning Moment-Rotation Response

Figure 5 gives a comparison of moment versus rotation for the tripod foundation under OBT and TBT loading conditions. The bearing capacity curve in sandy soil is obviously composed of two sections with a yield point. When the loading force reaches a certain threshold, the rotational displacement of the structure suddenly increases, which implies a brittle response. A similar phenomenon was observed in the monotonic loading test carried out by Wang et al. [11] and Faizi et al. [14].

To quantitatively compare the ultimate anti-overturning bearing capacity of the tripod foundation in two loading directions, the tangent intersection method proposed by Villalobos [28] was used to determine the yield point on the moment-rotation curve. The ultimate capacity of the foundation is 54.2 Nm under TBT and 39.2 Nm under OBT, respectively. It indicates that the anti-overturning capacity of the tripod foundation in sand is much higher when two buckets are in tension. Despite the varied bearing capacity, the yielding rotation of TBT (0.56°) is slightly higher than that of OBT (i.e., 0.54°).

2.3.2. Overturning Movement Response

Figure 6 shows the vertical displacement of the #1 and #2 buckets measured in tests. During the loading process, the vertical displacement of the downward bucket is relatively small, with a maximum value of less than 2 mm. The vertical displacement of the upward bucket is close to that of the downward bucket at the initial stage of loading, but suddenly increases after reaching the yield point. The vertical displacement of the upward bucket is around 8 times that of the downward bucket when the failure occurs. It implies that the failure of the laterally loaded tripod bucket foundation is mainly caused by the pull-out of the upward bucket, resulting in the overall rotation of the foundation.

As shown in Figure 7, the position of the instantaneous rotation center for the tested model can be estimated from two vertical displacement measurements at the top lid and one horizontal displacement measurement at the jacket transition piece. The coordinate system is defined with the geometric center of the foundation on the ground surface as its origin. The horizontal and vertical coordinates of the rotation center can be calculated by Equations (3) and (4), based on the first-order approximation obtained for the small displacement of buckets:

$$x_0=\frac{v_1{l}_2-v_2{l}_1}{v_1+v_2}$$

(3)

$$z_0=\frac{\left(l_1+l_2\right)h}{v_1+v_2}-H$$

(4)

where $x_0$ and $z_0$ are the horizontal and vertical coordinates of the rotation center; $l_1$ and $l_2$ are the horizontal distances between the vertical displacement measurement point and the central axis of the jacket model; $v_1$ ($v_1>0$, upward) and $v_2$ ($v_2>0$, downward) are the measured vertical displacements of two buckets, respectively. H is the distance from the horizontal displacement measurement point to the ground surface; h is the horizontal displacement measurement of the loading point. The details of the coordinate system and notations are presented in Figure 7.

Figure 8 gives a comparison of the trajectory of the instantaneous rotation center for the foundation under two loading conditions (namely, OBT and TBT). The variation of the rotation center in two opposite loading directions obeys a similar evolution law. At the early stage of loading, the rotation center is located below the bottom of the foundation and close to the windward bucket. The rotation center gradually moves towards the leeward bucket along the loading direction with the increase in lateral load, and its vertical position is also closer to the ground surface. It shows that the foundation experiences a rotational displacement accompanied by a forward translational movement. At the end of the loading stage, the center of rotation is transferred into the front bucket, with a failure of the foundation witnessed.

2.3.3. Foundation Failure Mode

Furthermore, to determine the failure mode of a tripod foundation in sandy soil, the contributions of both the rotational and the translational components to the horizontal displacement of the loading point when failure happens are estimated by displacement measurements. As summarized in

Table 4. Sharing of rotational component and translational component in measured structure displacement.

Loading Condition	Measured Displacement (mm)	Rotational Component (mm)	Translational Component (mm)	Contribution of Rotation
TBT	22.5	20.14	2.36	89.51%
OBT	23.9	20.79	3.11	86.99%

, the horizontal displacement of the loading point caused by rotational movement is significantly greater than that caused by translational movement. The sharing percentage of rotational components is more than 85% despite varied loading directions, which indicates that the structure rotation caused by the lateral load is the major contributor to the horizontal displacement of the foundation. Therefore, the failure mode of the tripod bucket foundation under lateral load is the overall rotation rather than translation.

Figure 9 illustrates the failure mode and soil displacement pattern of the test model after loading. An overall rotation with a rotation axis located at the leeward bucket was observed when the foundation failure occurred. The windward bucket was pulled out of the ground, resulting in a significant upward vertical displacement. The soil at the front of the bucket was heaved due to the rotation of the foundation, while soil subsidence at the rear side was created. Therefore, the failure mode of the tripod bucket foundation in sand is the overall rotation of the foundation caused by the pull-out of the windward bucket.

3. Numerical Modeling

3.1. Numerical Model

In this study, three-dimensional finite element (FE) models of tripod bucket foundations were established using ABAQUS [29] and utilized for a further comparison study on an engineering scale. For the sake of reducing computation, only half of the finite model was adopted due to the symmetry of both geometrical and loading conditions. Eight-node brick C3D8 elements were applied to model both the soil and the bucket. To avoid unexpected boundary effects, the soil domain has a diameter of 7.5 D and a depth of 3 L. Both mesh sensitivity tests and domain tests were conducted in order to balance both sufficient accuracy of simulation results and saving computation time. It was observed that the variation in moment-rotation response by doubling the soil domain and mesh densities is less than 5%. The lateral and bottom boundaries of the soil domain were constrained in both horizontal and vertical directions. The tangential interactions between buckets and soil were simulated following the classical Coulomb’s model with a friction angle of two-thirds of the internal friction angle [30]. For the sake of modeling simplification, the superstructure was reduced to a reference point (RP) rigidly coupled with two model buckets and located at the geometric center of the tripod bucket foundation [18,20]. A typical model mesh and its dimensions are presented in Figure 10.

The buckets were prescribed as the rigid body by assigning a high elasticity modulus. The wall thickness t of the bucket was taken as 45 mm for both the top lid and skirt. In an effort to investigate the influence of changing D and L on the overturning capacity of the tripod foundation, three numerical models with different L/D were established. The dimensions of the bucket are listed in

Table 5. Dimensional properties for bucket in comparison study.

Bucket Parameters	Foundation 1	Foundation 2	Foundation 3
Diameter, D (m)	17.7	13.5	13.5
Skirt length, L (m)	13.5	13.5	16.9
Wall thickness, t (mm)	45	45	45
Aspect ratio, L/D	0.75	1.00	1.25

.

To gain further insight into the anti-overturning response of the tripod foundation in varied soil scenarios, two kinds of soil (i.e., medium-dense sand and soft clay) were considered in this study. A Mohr-Coulomb material model with an assumption of soil having elasto-plastic behavior was exploited to model the sandy soil’s mechanical property. The Young’s modulus of sand (E), varying with mean principal stress, was implemented to simulate non-linear soil stiffness [31,32]:

$$E=\kappa p_a{\left(\frac{{\sigma }_m}{p_a}\right)}^{\lambda }$$

(5)

where $p_a$ = 100 kPa is the atmospheric pressure; $\kappa$ = 400 and $\lambda$ = 0.6 are stiffness constants for medium-dense sand [33]; ${\sigma }_m$ is the mean principal stress. The internal friction angle $\phi$ for sand was estimated by [34]:

$$\phi =16D_r^2+0.17D_r+28.4$$

(6)

where $D_r$ denotes relative density, taken as 60% for medium-dense sand with buoyant unit weight ${\gamma }^{\prime }$ = 9 kN/m³ simulated in this study. As for foundations in soft clay, the undrained shear behavior of clay obeys the Tresca failure criterion. The undrained shear strength of clay $s_u$ was assumed to vary linearly with soil depth z [35]:

$$s_u=s_{um}+kz$$

(7)

where $s_{um}$ is the undrained shear strength at the mudline; and k is the gradient of undrained strength in terms of depth. The $s_{um}$ was fixed as 1.25 kPa to avoid convergence problems as well as to consider the non-homogeneity of clay by setting k = 1.25 [36]. Young’s modulus of soft clay with ${\gamma }^{\prime }$= 6 kN/m³ was set as ${400s}_u$ [17].

Poisson’s ratio ν was chosen to be 0.3 for sand in a drained condition and 0.495 for normally consolidated clay in an undrained condition, respectively. In numerical analysis, three steps were adopted to simulate the overturning bearing behaviors of tripod bucket foundations. The initial geo-stress field was generated first. Then, the tripod bucket foundation was installed as “wished-in-place” by ignoring the installation effects, and the soil-bucket contact pairs were also activated simultaneously. Subsequently, external forces or displacements were imposed at the RP.

3.2. Validation of Numerical Model

3.2.1. Validation by Model Test

Firstly, the developed numerical model is verified by the model test carried out in this paper under the 1 g condition. Figure 11 shows the comparison of the moment-rotation curves from the test results and the FE results under two loading conditions. It can be observed that the numerical model is capable of capturing the rotational bearing behavior of the tripod bucket foundation under overturning loading.

3.2.2. Validation by Field Test

Given the scarcity of large-scale field tests for the tripod bucket foundation in literature, the field tests of monopod bucket foundations conducted in Frederikshavn [37] and Sandy Haven [7] were utilized to verify the accuracy of the numerical model on an engineering scale. The suction bucket tested in Frederikshavn [37] was installed in dense sand, with a diameter of 2 m, a height of 2 m, and a wall thickness of 12 mm. The foundation was subjected to a horizontal force at 17.4 m above the ground, and the vertical force remained at 37.3 kN during the loading process. For the field test carried out at Sandy Haven [7], the bucket installed in medium-dense sand had a diameter of 4 m, a skirt length of 2 m, and a wall thickness of 20 mm. A horizontal force with an eccentricity of 14.5 m was applied to the model bucket. The soil properties reported in [38] were used for the second validation in this study. As shown in Figure 12, the overturning response estimated by the FE model agrees well with the results measured from field tests, which gives confidence for the further comparison study conducted on an engineering scale.

4. Comparison Study in Engineering Scale

4.1. Anti-Overturning Bearing Capacity

Figure 13a displays the overturning moment-rotation curve of the tripod bucket foundation with different L/D in sand. The tripod foundations with different aspect ratios have similar initial stiffness in two opposite loading directions, which agrees with the observation obtained from Figure 7 and the literature [14]. The bearing capacity of the foundation with two buckets in tension is higher than the scenario where one bucket is in tension. Based on the results, it is evident that the main loading direction of the environmental loads should be fully considered to align with that of making two buckets in tension for the plane layout design of the tripod bucket foundation in a sandy seabed.

The ultimate anti-overturning bearing capacity of a tripod foundation was determined by the tangent intersection method mentioned above (see Figure 5), as illustrated in Figure 13b. The anti-overturning bearing capacity of the foundation in sandy soil can be greatly improved by increasing D and L. For the foundation with L/D = 1.25, the ultimate capacity increased by 44.1% (OBT) and 51.9% (TBT) in two loading directions, respectively. Extending the skirt length can significantly improve the anti-overturning performance of the tripod foundation in sand, as opposed to increasing the bucket diameter.

Likewise, the overturning moment-rotation curves of the foundation with varied aspect ratios in the soft clay are compared in Figure 14a. Different from the scenario in sand, the bearing capacity of the foundation in soft clay under OBT is greater than that under TBT. It indicates that the unfavorable loading direction of the foundation in clay should be carefully confirmed with the avoidance of overlapping between the main wind/wave direction and the TBT. This finding is consistent with the engineering experience obtained from the application of tripod bucket jacket foundations in the South China Sea [39].

It can be seen from Figure 14b that the ultimate bearing capacity of the foundation with L/D = 1.25 under TBT and OBT is 6.6% and 13.7% higher than that with L/D = 1. A significant increment of 36.9% and 46.6% is witnessed for the ultimate capacity of a foundation with L/D = 0.75 in soft clay. As a result, enlarging the bucket diameter has a bigger effect on strengthening the performance of the tripod foundation to prevent overturning in soft clay.

4.2. Variation of Bucket Displacement

The vertical displacement at the center of the top lid of the #1 bucket and the #2 bucket is extracted from the numerical results and shown in Figure 15. A positive overturning moment represents an OBT condition, while a negative one indicates a TBT condition. Figure 15a presents the vertical bucket displacement of the foundation in sand. The vertical movement of the #1 bucket is significantly greater than that of the #2 bucket when one bucket is in tension. Because of the identical skirt length, the vertical displacement of the #1 bucket for foundations with an aspect ratio of 0.75 and 1 varied with the overturning moment at a similar rate. After increasing L (that is, varying L/D from 1 to 1.25), the vertical displacement of the #1 bucket decreases dramatically due to the increase in vertical soil friction applied on the inner and outer skirts of the uplift bucket, leading to an increase in the anti-overturning bearing capacity of the foundation. Although only a single bucket bears the pressure generated by the overturning moment under the TBT condition, the vertical displacement of the downward bucket is similar to that under the OBT condition owing to the large compression modulus and compactness of the sandy soil.

Figure 15b shows the vertical displacement of the bucket in soft clay. Given the low bearing capacity of soft clay, when the #1 bucket bears the downward pressure alone under TBT conditions, its vertical displacement is remarkably increased compared with that in sandy soil. It is obvious that expanding the diameter of the bucket is more conducive to extending the contact area between the soil and the top lid, thus improving the vertical bearing capacity of the bucket and reducing its settlement on the compression side of the tripod foundation. The above discussion also explains the conclusion drawn from Figure 14 in principle, that is, increasing D is more beneficial to enhance the anti-overturning bearing capacity of the tripod foundation in soft clay.

In general, the vertical displacement of the upward bucket is larger than that of the downward bucket for sandy soil under the OBT condition. Accordingly, the most unfavorable loading direction of the tripod bucket foundation is the direction that puts one bucket in tension, with a failure mode of pull-out of the windward bucket. Whereas, for a tripod foundation in soft clay, the vertical displacement of the downward bucket, corresponding to the condition of two buckets in tension (namely, the single bucket in compression), is greater than that of the upward bucket. Hence, the most unfavorable loading direction is the TBT, with a failure mode of foundation rotation caused by the settlement of the leeward bucket.

To further understand the horizontal movement characteristic of the tripod foundation subjected to the overturning moment, horizontal displacement curves at the reference point are exhibited in Figure 16. Considering that each bucket of the tripod foundation is rigidly connected to the reference point located at the geometric center of the foundation, the horizontal displacement at the top lid of each bucket is the same as that of the reference point. Compared with Figure 15, it can be found that the horizontal displacement of the bucket in both sandy soil and soft clay is obviously less than the vertical one under the application of an identical overturning moment.

4.3. Variation of Rotation Center

According to the presented results of vertical and horizontal displacement of buckets shown in Figure 15 and Figure 16, the trajectory of the instantaneous rotation center for the tripod bucket foundation in both sand and soft clay during the overturning procedure is estimated by Equations (3) and (4) and given in Figure 17. To facilitate the comparison of foundations with varied L/D, the horizontal coordinate of the rotation center x was normalized by the bucket diameter (D), while the vertical coordinate z was normalized by the skirt length (L). The figure reveals that with the increase of the overturning moment, the rotation center of the tripod foundation subsequently moves along the loading direction. As far as the tripod foundation in sand is concerned, given that the upward displacement of the windward bucket is greater than the settlement of the leeward bucket, the rotation center is gradually transferred from the rear bucket into the front one. Whereas, as pointed out in the preceding section, the rotation center of the tripod foundation in soft clay does not move to the inside of the front bucket due to a great settlement of the leeward bucket. Both aspect ratio and loading direction have little influence on the distribution range of the loci of the rotation center. In sandy soil, the rotation center of the tripod bucket foundation is mainly located at 0.8–0.9 L below the ground surface with little dependence on the magnitude of the overturning moment. The position of the rotation center is relatively shallow when it comes to the tripod foundation in soft clay, with vertical coordinates lying between 0.6 L and 0.7 L of the bucket height.

4.4. Contribution of Rotational Soil Resistance to Anti-Overturning Bearing Capacity

As discussed in the prior section, the displacement pattern of the tripod bucket foundation under the overturning moment is mainly composed of the vertical and rotational movement of the buckets. As a result, the overturning moment will be resisted by a combination of vertical and rotational soil resistance generated by the movement of buckets [40], as presented in Figure 18. To date, no academic research has been conducted to investigate the sharing factor of rotational soil resistance in the anti-overturning bearing capacity of tripod foundations. In view of this, the internal moment of each bucket was extracted from FE models and added together to determine the rotational soil resistance.

Figure 19a compares the contribution of the rotational resistance of the foundation with varied L/D to the total anti-overturning bearing capacity of the foundation in sandy soil. It can be observed from the figure that, at the initial stage of loading, the proportion of the rotational component in the load bearing capacity is relatively large. However, with the increase of the loading moment, the sharing factor of the rotational soil resistance in sand decreases rapidly and remains constant, with little dependence on loading direction and aspect ratio. A similar trend can also be observed in Figure 19b for the tripod bucket a foundation in soft clay. In contrast to sandy soil, the rotational resistance has a substantially higher sharing factor for the tripod foundation in soft clay. It implies that the rotating soil resistance brought on by the rotational movement of buckets is what primarily contributes to the anti-overturning bearing capability of the foundation in soft clay. As shown in Figure 19, despite the varied load cases adopted in this paper, the sharing percentage of the bearing capacity of the rotational soil resistance is always less than 50%. This demonstrates that the anti-overturning bearing capacity of a laterally loaded tripod foundation is mainly provided by the vertical soil resistance caused by the vertical movement of both windward and leeward buckets.

4.5. Evolution of Foundation Rotational Stiffness

It should be noted that the support structure of OWTs is dynamic sensitive, and as a result, evaluating the influence of foundation stiffness on the dynamic characteristics (for instance, the natural frequency) of the whole structure is one of the key design considerations. The tripod bucket jacket foundation is one of the shallow foundations, with an embedment smaller than that of the traditional pile foundation, leading to a relatively low vertical stiffness of the bucket foundation. Jalbi et al. [41,42] proposed that the free vibration mode of the jacket foundation supported on multi-buckets under lateral excitation may be represented as the rocking mode, and the suction bucket below the ground surface can be simplified as a spring with a rotational stiffness $K_r$, as illustrated in Figure 20. Therefore, the rotational stiffness directly affects the dynamic characteristics of the tripod jacket foundation.

Figure 21 shows the degradation of rotational stiffness with foundation rotation for tripod bucket foundations in sand and soft clay. The dimensionless rotational stiffness was estimated by adopting $M/{\gamma }^{\prime }{D}^4$ in sand and $M/AD{s}_u$ (where, A denotes the projected area of the tripod foundation) in soft clay, respectively. It can be seen from Figure 21 that the rotational stiffness of the tripod foundation with varied L/D basically follows a similar degradation pattern. The rotational stiffness of the foundation in sand decreases dramatically with the growth of the rotation angle, while the rate of decline of that in soft clay is relatively slow. Quantitatively, the rotational stiffness of the foundation in sand and soft clay drops to around 50% and 80% of their initial values, respectively, when the rotation angle of the foundation reaches 0.25° (that is, the maximum allowable inclination of the OWT support structure [9]). This observation is similar to that reported by Wang et al. [11]. It is clear that modal analysis using initial stiffness may overestimate the natural frequency of the OWTs, which can be estimated based on the analytic expression reported in Refs. [5,42]. Subsequently, it may mislead the dynamic and fatigue analysis of the OWT support structure under environmental excitation.

5. Conclusions

In this paper, the anti-overturning response of the tripod bucket foundation at a scale ratio of 1:100 was studied by performing model tests. Furthermore, the effects of aspect ratio, loading direction, and soil type on the bearing characteristics of the tripod foundation are numerically investigated. The key conclusions can be drawn as follows:

(1)

The failure mode of the tripod bucket foundation under an overturning moment is the foundation rotation caused by the vertical movement of the buckets. The rotation center of the foundation moves toward the leeward bucket along the loading direction. In sandy soil, the failure mode is mainly manifested as the pull-out of the windward bucket. While a large settlement of the leeward bucket is observed when foundation failure occurs due to the relatively small compression modulus of the soft clay.

(2)

Given the varied failure mechanisms of the tripod foundation in sandy soil and soft clay, the most unfavorable loading direction is different accordingly. The anti-overturning bearing capacity of the foundation in sand under two buckets in tension is greater than that under one bucket in tension. Whereas the unfavorable loading direction is the direction that puts one bucket in tension for a foundation in soft clay.

(3)

The aspect ratio has a prominent impact on the overturning bearing capacity of the foundation. Extending the skirt length will lead to greater vertical soil friction borne by the upward movement, thus significantly improving the anti-overturning bearing capacity of the foundation in sand. In contrast, enlarging the bucket diameter is more beneficial to improve the bearing capacity in soft clay.

(4)

The anti-overturning bearing capacity of the foundation is dominated by the vertical soil resistance generated by the vertical movement of the buckets. The sharing factor of the rotational reaction in soft clay is significantly higher than that in sandy soil.

(5)

The rotational stiffness of the tripod foundation decreases with the growth of the rotation. This suggests that adopting the initial stiffness of the foundation in the dynamic analysis will overestimate the natural frequency of the OWT, which may have adverse effects on the evaluation of both structural dynamic response and fatigue life.