Bucket foundations are considered to be environmentally friendly foundations. Their stiffness determines the resonant frequencies and fatigue life of the supported offshore wind turbines. This study proposes a rigorous three-dimensional (3D) elastic solution for the stiffness of laterally loaded bucket foundations in different soil profiles. The lumped spring stiffness acting on the top of the bucket and the exact distribution of the distributed soil spring stiffness along the bucket are first obtained from the analytical model. Closed-form formulae for the lumped spring stiffness are then fitted and verified with the existing studies. To facilitate the engineering application, the distributed soil spring stiffness is then averaged to a uniform distribution using the equivalent work method. Two types of simplified Winkler models are finally proposed and calibrated: one in which the spring stiffness is uniformly distributed along the bucket, and the other in which the distributed Winkler springs are divided into two parts bounded by the centre of rotation. The non-dimensional Winkler springs are mainly related to the bucket aspect ratio, the soil Poisson's ratio and the loading height. It is shown that the lateral soil springs alone, asp-y springs for piles, are not sufficient for bucket foundations. The combined two-part p-y springs and uniform rotational springs are suggested to obtain accurate bucket foundation responses.

As a newly emerged solution for supporting the new generation of offshore wind turbines (OWTs), the pile-bucket foundation has received wide attention. However, little attention has been paid to the grouted connection that connects the monopile and bucket foundation. As the loadtransferring, yet vulnerable component, the fatigue mechanism of the grouted connection and its influence on the cyclic laterally-loaded response of OWT foundation are still not clear. In this study, a sophisticated three-dimensional (3D) finite element (FE) model of the pile-bucket foundation with grouted connection is constructed, which incorporates a hypoplastic clay model and the concrete damage plasticity (CDP) to consider the cyclic load effect on both soil and grout material. A modal analysis is first performed to verify the rationality of the proposed model. Then the influence of cyclic load frequency, load amplitude and stiffener arrangement on the accumulation of pile head displacement, stress distribution and crack development of the grouted connection is systematically analyzed. Results indicate that as load frequency approaches the eigen-frequency, the OWT structure tends to vibrate more intensively, leading to stress concentration and fatigue damage of the grouted material and rapid accumulation of the pile-head displacement. The influence of load amplitude on grout damage seems to be limited in the contact area in the simulated cases. Meanwhile, the installation of stiffeners slightly mitigates the pile head displacement accumulation, but also raises the risk of stress concentration and fatigue damage of the grouted connection. The numerical results reveal the load-transferring function and fatigue damage of the grouted connection, which could provide some reference for an optimized structure and dynamic design for the pile-bucket foundation under cyclic load.

Each individual bucket of multi-bucket foundations sustains mainly the vertical upward and downward cyclic load during its lifetime. It is evidenced from centrifuge test and engineering experience that the behaviour of individual bucket under upward and downward load is not identical - usually the capacity and stiffness of downward direction is stronger than the upward. This anisotropic behaviour is mainly due to the different failure mechanism and soil strengths mobilized. In this paper, a macro element model is established to reproduce the anisotropic behaviour of individual bucket under vertical cyclic loading, expanded from previous study of the cyclic-softening macro element model. The model is formulated based on multi-surface plasticity and a combined isotropic and kinematic hardening rule. The anisotropy is implemented by establishing the oval yield surfaces and non-symmetrical hysteresis loops. The parameters of the macro element model are calibrated by a small amount of FE analyses, where an anisotropic soil constitutive model and an attached or separated soil plug are adopted to highlight the anisotropy. The performance of the model is demonstrated by a series of numerical cases and is compared to parallel FE analyses. The new macro element model is capable of capturing the anisotropic load-displacement loops real-timely during a cyclic load sequence, with high computational efficiency and reasonable accuracy.

Offshore wind turbines (OWTs) are gaining prominence worldwide, and the hybrid pile-bucket foundation, which combines a monopole and a bucket, has emerged as a noteworthy development. In this study, a 3-D numerical model for the 5-MW OWT was constructed utilizing the OpenSees platform. The dynamic characteristics of the sand was modeled with the PDMY02 constitutive model and the soil was discretized using brick up elements. To investigate the dynamic behavior of the OWT in an actual marine environment, the coupled model was subjected to dynamic loadings, encompassing waves, wind, and earthquake. Two seismic motions with different frequency components were considered, respectively. The study focused on exploring the impacts of key influencing factors on the OWT rotation, tower-top acceleration development and spatiotemporal distribution of excess pore water pressure ratio (EPWPR). These factors include dynamic load combinations, earthquake intensity, soil relative density, wind speed, angle between load directions, and pile length. It is revealed that the inclination angle of offshore wind turbines (OWTs) may exceed the allowable threshold under specific conditions of load combinations, seismic motion inputs, and seabed conditions. Thus, it is suggested to appropriately consider the effects of wind and wave actions in the seismic analysis of OWTS.

The mono-column composite bucket foundation (MCCBF) is a new offshore wind turbine foundation suitable for shallow overburden geology. There are few studies on the bearing capacity and deformation of the new subdivided structure 's all-steel MCCBF in layered soil under cyclic loading. This article conducts cyclic bearing characteristics tests on MCCBF in layered soil and shallow overburden layers and studies the ultimate bearing capacity, cumulative rotation angle development rules, and stiffness evolution mechanism. Combined with the finite element analysis results, a calculation method for the ultimate bearing capacity under layered soil is established. The results show that under bidirectional and multidirectional cyclic loading, the ultimate bearing capacity of pure sand changes little, but the strength of clay is reduced, and the ultimate bearing performance decreases. In the clay overlying sand, under high -amplitude cyclic loading, the strength of the sand at the bottom increases, which increases the cumulative angle stiffness and ultimate bearing capacity of the MCCBF. After cyclic loading, the shallow overburden layer will prevent the load from transferring to the deeper soil layer. The foundation will drive the soil in the compartment to slide on the surface of the shallow overburden layer, resulting in a decrease in the load-bearing performance. The initial stiffness of the foundation is increased so that the stiffness change during the cycle is not apparent. Finally, the accuracy of the calculation formula for the ultimate bearing capacity of MCCBF under layered soil is proposed and verified.

The soil surrounding bucket foundations that are subjected to vertical cyclic loading would become softened but not consolidated. This would reduce the uplift resistance and even cause foundation failure. The paper firstly investigates the development, especially the dissipation of excess pore pressure and base suction (the suction between the bucket lid and soil) under vertical cyclic loading through 1 g model tests. The test results demonstrate that although base suction can bear 54 % of the uplift resistance of the bucket foundation at the beginning, the upward movement of foundation causes cracks at the soil surface, which accelerates excess pore pressure dissipation and leads to faster foundation failure. Therefore, the base suction should not be considered in the foundation design under long-term cyclic uplift loading. Then, an amended kinematic hardening model that can consider the strain softening effect of soil is employed to obtain the uplift resistance under vertical monotonic and cyclic loadings for various soil softening parameters and cyclic load level (the ratio of cyclic mean load to the monotonic ultimate uplift resistance). Through extensive fatigue analyzes with tens of thousands or even hundreds of thousands of cyclic loadings in each analysis, it is concluded that the fatigue cyclic number increases as the cyclic load level decreases or softening parameters (xi 95 and delta rem) increase. A prediction formula of fatigue curve of bucket foundation is proposed and verified to predict the fatigue cyclic number. The prediction error is within 10 %, and the formula can provide a convenient reference for the design of bucket foundation.

Traditional suction bucket foundations incur high maintenance costs and are susceptible to corrosion, resulting in a diminished bearing capacity over prolonged service. The suction bucket foundation, constructed with a glass fibre -reinforced polymer (GFRP), introduces a novel approach to iteratively optimise conventional steel bucket foundations. In this study, three-dimensional finite element models of the GFRP bucket -soil interaction were established using the VUMAT subroutine, which incorporates the stress -strain damage relationship of GFRP materials. The mechanical response during installation was analyzed for different fibre -laying angles( A ) and wall thicknesses( t ) of the GFRP bucket, and the results were compared with those of a steel bucket. The results indicated increased circumferential stress, radial deformation, and out -of -roundness of the GFRP bucket as the fibre laying angle increased. Deformation and stress of the bucket skirt remained low at A of 0 - 45 degrees . When A >= 60 degrees , the matrix ' s damage area significantly increases, with the minimum damage occurring at 45 degrees . For A <= 30 degrees , it approaches the maximum radial deformation of an equivalent -sized steel suction bucket. As the wall thickness increased, the circumferential stress, radial deformation, and out -of -roundness of the GFRP bucket skirt gradually decreased. When the GFRP bucket t was four times that of the steel bucket, its radial deformation was approximately equal.

The foundation of offshore wind turbines is an important factor that determines their bearing capacity and service life. A theoretical analysis and model test of the bucket foundation with and without bulkheads at a scale of 1:150 are conducted in this study. The frequency-domain impedances of the two models were obtained and compared via cyclic loading tests at different frequencies. When the loading frequency was low, the absolute values of the real and imaginary impedances of the foundation model without a bulkhead in the frequency domain were higher than those of the foundation model with a bulkhead. Based on the analysis of the variation in soil pressure at the top of the bucket, it was found that the variation in soil pressure almost alternated with the cyclic load. The adsorption force is beneficial for the bearing capacity of a composite bucket foundation, making the structure safer. The impedance matrix of the foundation is determined by the size and shape of the foundation, mechanical parameters of the foundation medium, and frequency of the forced vibration. Wolf's lumpedparameter model was evaluated for applicability to analyse the bucket foundations with bulkheads.