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Scientific Reports volume 16, Article number: 21979 (2026) Cite this article
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This study investigates the bearing behavior of a pile-bucket composite foundation in marine soft clay under combined vertical, horizontal, and moment (V-H-M) loading, with direct application to offshore photovoltaic systems deployed in shallow-water regions. Centrifuge tests and validated 3D finite element analyses employing the Nanshui constitutive model were conducted. The results indicate that the pile-bucket foundation exhibits a hybrid deformation mode, effectively integrating the deep rotational restraint of the pile with the shallow translational constraint of the bucket. Under combined V-H-M loading, the composite foundation demonstrates a significantly expanded failure envelope. Notably, the vertical load enhances the lateral capacity to a greater extent in the composite system compared to monopile or suction caisson foundations. Plastic strain analysis reveals a synergistic interaction, where the pile extends the plastic zone deeper while the bucket mobilizes a broader near-surface soil mass, leading to a more distributed and efficient load-transfer mechanism. The findings provide critical insights for the optimized design of innovative pile-bucket hybrid foundations in soft clay for offshore photovoltaic arrays.
With the global expansion of renewable energy development^1,2,3,4,5,6, offshore photovoltaic projects are progressively advancing into shallow-water regions underlain by extensive soft soil deposits (Fig. 1). The presence of soft seabeds, combined with wave, current, and operational loads, imposes significant challenges on conventional foundation systems^7,8,9,10. The pile-bucket composite foundation, which integrates a shallow bucket with an embedded pile, offers a promising solution by enhancing load distribution and adapting to soft soil conditions^11,12. Nevertheless, its bearing mechanism under combined vertical, horizontal, and moment (V-H-M) loading remains insufficiently understood, particularly in soft clay, limiting its optimized design for offshore PV applications.
Field implementation of offshore photovoltaic projects in China. (a) Installation process of photovoltaic panels, (b) soft foundation in coastal tidal flat areas.
The bearing capacity of foundations has long been a critical research topic in geotechnical and offshore engineering^{13,14,15,16,17}. For bucket foundations, Fan et al.¹⁸ employed advanced constitutive models to investigate failure envelopes. For monopiles, studies have focused on lateral response under combined loading. However, single pile or single bucket systems often suffer from either insufficient shallow restraint or limited deep rotational capacity. Recently, hybrid foundation systems have attracted increasing attention^{19,20,21,22,23}. Li et al.²⁴ experimentally and numerically studied hybrid pile-bucket foundations under lateral loading, finding that such foundations improve load distribution, reduce the accumulation of permanent plastic strain and soil stiffness degradation, and enhance overturning stability compared to monopiles, providing valuable insights for the design of offshore wind turbine foundations in soft soils. Yang et al.²⁵ conducted centrifuge tests to study the influence of pile spacing on the seismic response of piled raft foundations in soft clay, highlighting the importance of boundary effects and soil–structure interaction. Liu et al.²⁶ systematically investigated the bearing capacity of a novel pile-bucket composite jacket foundation through 1 g model tests and 3D finite element analysis. Their findings indicate that increasing pile diameter and length can significantly enhance the horizontal and bending moment capacities, while the composite structure effectively reduces plastic deformation within the bucket, shifts the rotation center downward, and expands the failure envelope under combined loading. These findings collectively emphasize the critical importance of enhancing and optimizing traditional pile or bucket foundations, particularly in scenarios where shallow soil layers are insufficient and the underlying strata consist of bedrock, stiff layers, or other difficult-to-penetrate soil types. While recent studies have highlighted the superior performance of hybrid foundation systems, systematic investigations focusing on the synergistic interaction between the pile and bucket components under realistic in-situ stress conditions are still limited. Specifically, the failure envelope under combined loading, the evolution of soil–structure interaction mechanisms, and the comparative performance against conventional single-pile or single-bucket systems in soft clays have not been thoroughly characterized through centrifuge modeling coupled with advanced constitutive numerical simulations.
To address these research gaps, this study conducts the centrifuge model test on a pile–bucket composite foundation embedded in marine soft clay. A corresponding three-dimensional finite element model is developed and validated against experimental results, employing an advanced double-yield-surface elastoplastic constitutive model to accurately capture the nonlinear soil behavior. The findings of this study are expected to provide theoretical insights and practical guidelines for the optimized design and application of pile–bucket composite foundations in offshore renewable energy infrastructure. It is important to clarify that the present investigation focuses on the ultimate bearing behavior under monotonic combined loading, which serves as the fundamental basis for understanding foundation capacity under extreme environmental events such as storm surges.
The stress state induced by soil self-weight is fundamental in geotechnical engineering, as soil mechanical properties are inherently stress-dependent. Small-scale physical model tests conducted under normal gravitational conditions often fail to satisfy stress similitude, resulting in poor representation of prototype behavior. The geotechnical centrifuge addresses this limitation by generating an enhanced gravitational field through centrifugal acceleration^27,28. This method effectively scales up soil stresses in a reduced-scale model, ensuring that stress levels correspond to those in the prototype^{29,30,31,32,33}. Consequently, the centrifuge enables accurate simulation of prototype mechanical response and failure mechanisms under representative in-situ stress conditions.
Experimental equipment in this study. (a) Geotechnical centrifuge, (b) consolidation instrument.
The centrifuge modelling tests in this study were conducted using the large-scale geotechnical centrifuge facility at the Nanjing Hydraulic Research Institute (NHRI). As illustrated in Fig. 2, the centrifuge is characterized by a maximum radius of 5.5 m and is capable of achieving a centrifugal acceleration of up to 200 g. At this acceleration level, the platform can carry a maximum payload of 2000 kg. The geometric scaling between the prototype and the model is characterized by the scale factor, defined as the ratio of the prototype dimension to the corresponding model dimension. The scale factors are presented in Table 1. In this study, a scaling factor of 80 was adopted. The model container used in the tests features a transparent acrylic side panel for visual observation, while the remaining sides, base, and cover are constructed from high-strength aluminium alloy to ensure structural integrity under elevated 80 g-levels. The internal dimensions of the model container are 700 mm (length) × 350 mm (width) × 450 mm (height).
The foundation soil was reconstituted using material analogous to that of the prototype site to preserve realistic strength characteristics. For modeling purposes, soil layers exhibiting comparable geotechnical properties were homogenized through weighted averaging of their shear strength and thickness, a validated approach routinely employed in centrifugal modeling of port and offshore engineering problems. The cohesive soil was prepared by air-drying, pulverizing, and subsequently remixing with controlled water content to achieve the target consistency. The soil was placed and compacted in successive lifts from the bottom of the model container upward. Consolidation of the soil model was conducted in consolidation instrument (Fig. 2b). The evolution of undrained shear strength during consolidation was monitored using a pocket penetrometer until the design strength—14 kPa in this case—was attained uniformly throughout the soil profile. It should be noted that natural soft clay deposits are often stratified. The homogenization approach, while necessary for centrifuge repeatability, may smooth out weak interlayers or drainage interfaces that could act as preferential failure planes (Table 2).
The pile-bucket foundation model in this study was fabricated from aluminum alloy. Since the structure is predominantly subjected to flexural loading under lateral forces, the model design follows the principle of equivalent bending stiffness. The scaling of bending stiffness follows the centrifuge similitude law. This ensures that the flexural deformation characteristics of the model under lateral loading faithfully represent those of the prototype, even under ultimate loading conditions where significant bending occurs. The wall thickness of the model components was determined using the following expression¹⁸:
where d_m and d_p represent the wall thicknesses of the model and prototype, respectively, E_m and E_p represent their modulus of elasticity, and N is the scale factor.
Following this conversion, the pile model has a diameter of 12.5 mm, a height of 100 mm, and bucket model has a diameter of 75 mm, a height of 50 mm, a wall thickness of 0.46 mm, as shown in Table 3.
The embedded lengths of the pile and the bucket foundation below the mudline are 8 m and 4 m, respectively, in prototype scale. The centrifuge model test adopted a displacement-controlled loading scheme, with the loading point positioned 6 m above the mudline. This height represents the approximate resultant elevation of wind and wave loads on the PV support structure in shallow water. Horizontal displacement at the loading point and vertical displacement on the surface of the bucket foundation were monitored using reflective laser displacement sensors, as shown in Fig. 3. The sensors feature a measurement resolution of less than 0.01 mm, which satisfies the precision requirements of the experimental program.
Schematic of the centrifuge model cross-section and experimental setup photograph.
Figure 4 illustrates the horizontal load–displacement and horizontal load–rotation responses of the pile-bucket foundation. Both the horizontal displacement and the rotation of the foundation exhibit a positive correlation with the applied horizontal load. During the initial loading phase, the load–displacement and load–rotation relationships are approximately linear under relatively low load levels, indicating that the soil remains within the elastic deformation range. As the horizontal load exceeds 100 kN, the displacement and rotation increase nonlinearly with further loading. The slope of the curves gradually decreases in this regime, reflecting the progressive development of plastic deformation in the soil. The ultimate lateral capacity for foundation e is defined as the load at which the load-displacement curve reaches a horizontal asymptote, i.e. further displacement occurs without a significant increase in load, indicating fully developed plastic failure (as observed in the centrifuge test when the load reached 470 kN). In addition, the failure mode of the surrounding soil was also shown in Fig. 4, at the ultimate state, obvious soil heave occurred in front of the foundation, accompanied by a distinct gap forming behind the bucket.
Centrifugal test results of horizontal displacement and structural rotation angle.
A three-dimensional finite-element model was developed to simulate the lateral response of the pile–bucket composite foundation under monotonic horizontal loading, maintaining strict consistency with the geometric and material properties of the centrifuge test prototype. The three‑dimensional finite element analyses were performed using Abaqus³². The model consisted of two main components: the composite foundation structure (pile and bucket) and the surrounding saturated soft clay deposit, as shown in Fig. 5. To ensure that boundary effects did not artificially constrain the development of failure mechanisms, the soil domain was extended laterally to five times the diameter of the bucket and vertically to three times its embedded depth. Both structural and soil domains were discretized predominantly with eight‑node reduced‑integration hexahedral elements (C3D8R). A graded mesh was implemented to enhance computational efficiency and accuracy: the region surrounding the foundation and the near‑field soil were finely meshed to capture localized plasticity and interface behavior, while a gradually coarser mesh was used toward the far‑field boundaries. A mesh convergence study was conducted with three mesh densities. The difference in ultimate lateral capacity between the medium and fine meshes was less than 3%, while the coarse mesh showed a larger deviation. The medium mesh was therefore selected as providing a satisfactory balance between accuracy and computational cost.
Schematic diagram of the finite element model.
This paper employs the Mohr-Coulomb frictional contact model to simulate the interaction between the pile-bucket foundation and the soil. In mechanical analysis, face-to-face contact is commonly used, with the surface having a higher modulus of elasticity defined as the master face. Therefore, the pile-bucket foundation is set as the master face, and the soil is set as the slave face. The contact pair includes a normal behavior model and a tangential behavior model. The normal behavior uses a penalty function, while the divergent behavior adopts hard contact, allowing the pile-bucket foundation and soil to separate after contact, making the numerical model more realistic. The friction coefficient µ = 0.2 was selected based on interface shear tests on steel-soft clay interfaces reported in the literature³³. Geometric nonlinearity was activated throughout the analysis to account for finite rotations and displacements under progressively applied lateral loads.
This paper adopts the Nanshui constitutive model, an advanced double‑yield‑surface elastoplastic formulation grounded in generalized plasticity theory. Unlike single‑yield‑surface models (e.g., Modified Cam‑Clay), the Nanshui model separately describes volumetric hardening and shear hardening through two independent yield surfaces, making it particularly suitable for soft clays under combined loading.
The yield surface equation is as follows:
Here, p denotes the spherical stress, q is the deviatoric stress, and s and r are parameters that define the shape and size of the yield surface.
The elastoplastic stress–strain relationship of the soil can be expressed as follows:
where A₁ and A₂ are the plastic multipliers corresponding to the yield surfaces f₁ and f₂, respectively, and [D] is the elastic stiffness matrix.
Under triaxial test conditions:
Substituting these expressions into the above equation:
According to the Duncan–Chang formulation of the elastic modulus, the tangent modulus and tangent bulk modulus are defined as follows:
Substituting these relationships into the above expression:
where G is the shear modulus, B is the bulk modulus, and η denotes the stress ratio.
The tangent modulus E_t is defined according to the Duncan–Chang model as follows:
where R_f denotes the failure ratio; K is a dimensionless coefficient; n is a dimensionless exponent; p_a denotes the standard atmospheric pressure; c is the cohesion; and φ is the internal friction angle.
The tangent bulk modulus can be expressed as follows:
where R_s denotes the stress level; R_d represents the ratio of the deviatoric stress (σ₁−σ₃)_d at the point of maximum volumetric contraction to the ultimate deviatoric stress (σ₁−σ₃)_ult; d is a dimensionless exponent; and c_d is the maximum contractive volumetric strain corresponding to a confining pressure of the standard atmospheric pressure.
The Nanshui model was implemented in Abaqus via a user‑defined material (UMAT) subroutine¹⁸. The calibrated parameters of the Nanshui model for the soft clay foundation are summarized in Table 4, which were calibrated against a series of triaxial compression tests. As shown in Fig. 6, the Nanshui model predictions agree well with the measured stress–strain responses under different confining pressures, confirming the validity of the calibrated parameters. The pile-bucket foundation was simulated as a linear-elastic material with an elastic modulus of 210 GPa, a density of 7850 kg/m³, and a Poisson’s ratio of 0.3.
Validation of the Nanshui constitutive model. (a) Indoor test results, (b) prediction of constitutive model.
Figure 7(a) compares the horizontal load–displacement responses of the pile-bucket foundation obtained from centrifuge model testing and numerical simulation. As shown in the figure, the two load–displacement curves exhibit consistent trends and demonstrate close agreement, with a difference of only 2.6% in the ultimate lateral load, thereby validating the accuracy of the numerical model. In addition to horizontal displacement, the foundation rotation at the loading point was also compared⁴. As shown in Fig. 7(b), the numerical model accurately reproduces the rotation–load relationship observed in the centrifuge test, with a difference of less than 5% at the ultimate state. This additional metric further strengthens the validation basis. The observed agreement between the experimental and simulated results confirms the reliability of the modeling methodology, including the constitutive models, contact formulations, and boundary conditions employed. Moreover, this consistency supports the use of the calibrated numerical model for subsequent parametric analyses under more complex loading scenarios that are challenging to replicate in physical testing.
Comparison of response of the foundation between centrifuge test and numerical simulation. (a) load–displacement response, (b) load–rotation response.
To systematically evaluate the bearing mechanism of the pile-bucket composite foundation, two reference models—a single pile foundation and a single suction caisson foundation—were established for comparative analysis. Figure 8 illustrates the three-dimensional finite element models of the single pile and the single caisson used in this study. The single pile model and bucket model retains the geometric and material properties of the pile component and bucket component from the composite system, respectively. The soil domain, constitutive model (Nanshui model), boundary conditions, and interface properties are identical to those used in the pile-bucket composite foundation simulation, ensuring a consistent basis for comparison. It should be specifically noted that, to ensure consistency in the comparative testing conditions, the loading point for all control models (single pile and single bucket) was set at the same elevation as that of the pile-bucket foundation, i.e., 6 m above the mudline.
Numerical simulation model of comparative models. (a) Pile foundation, (b) bucket foundation.
To elucidate the mechanical advantages of the pile-bucket composite foundation under lateral loading, this section presents a systematic comparison of its behavior against that of single pile and single caisson foundations subjected to pure horizontal force. The evaluation encompasses both global load-displacement responses and detailed displacement field characteristics. As illustrated in Fig. 9, all three foundations exhibit hyperbolic load–displacement curves under lateral loading, with distinct differences in stiffness and ultimate capacity. The pile-bucket composite foundation demonstrates the highest lateral capacity, approximately 490 kN, along with the greatest initial stiffness. The bucket foundation follows, with an ultimate lateral capacity of about 300 kN and intermediate stiffness, while the single pile foundation shows the lowest capacity, around 175 kN, and the smallest stiffness. These results clearly highlight the superior load–bearing and deformation‑resisting performance of the pile–bucket composite system under lateral loading.
Comparison of load displacement relationship curves.
Figure 10 illustrates the displacement contours of the three foundation types at comparable load levels. The single pile foundation undergoes a characteristic deep-seated flexural deformation. Displacement is concentrated primarily at the pile head, with progressively smaller displacements along the embedded shaft, indicating a rotational mechanism constrained by the deeper soil. The single bucket, in contrast, exhibits a more rigid-body translational mechanism, characterized by nearly uniform lateral displacement along its embedded depth and a distinct separation gap forming behind the foundation at the mudline.
Comparison of displacement fields (Units: m). (a) Pile foundation, (b) bucket foundation, (c) pile-bucket composite foundation.
The pile-bucket composite foundation demonstrates a fundamentally different displacement pattern. The bucket component restricts shallow translation and rotation, while the embedded pile provides deep rotational restraint. This interaction results in a more uniform displacement field with reduced lateral movement at the mudline and enhanced deformation control throughout the soil profile. The combined system effectively transforms the failure mechanism from a localized deep rotation (pile) or shallow translation (bucket) into a composite mode that engages both shallow and deep soil layers simultaneously.
In the context of offshore renewable energy infrastructure, such as photovoltaic arrays or wind turbines, foundations are subjected to complex environmental loads that are fundamentally multi-directional and dynamic. These include persistent vertical dead loads from the superstructure, horizontal forces induced by waves and currents, and significant overturning moments generated by wind and eccentric loading. This combined vertical (V), horizontal (H), and moment (M) loading regime critically governs the stability, serviceability, and long-term performance of the support structure. Understanding the bearing behavior under such multi‑component loading is essential for the safe and economical design of foundations, as the interaction between different load components can significantly influence the overall bearing capacity and failure mechanism.
Figure 11 presents the bearing capacity envelopes of the single pile, single bucket, and pile-bucket composite foundations in the V-H, H-M, and V-M loading planes, respectively. Herein, V_ult, H_ult, and M_ult represent the ultimate bearing capacities of the foundation under pure vertical, pure horizontal, and pure moment loading, respectively.
Comparison of V-H-M bearing capacity. (a) H-V load plane, (b) H-M load plane, (c) M-V load plane.
As can be seen from the figure, despite the differences in geometric configuration and load transfer mechanisms among the single pile, single bucket, and pile-bucket composite foundations, their normalized bearing capacity envelopes in the V-H, H-M, and V-M combined loading spaces exhibit remarkably similar patterns. Specifically, In the V-H and V-M planes, the influence of vertical load on horizontal and moment capacities demonstrates a clear nonlinear coupling characteristic: at low vertical load levels, an increase in vertical load significantly enhances the system’s lateral and moment capacities by improving the lateral confinement of the foundation soil and increasing base friction. However, when the vertical load continues to increase beyond a critical threshold, the resulting excessive vertical stress induces punching shear or deep-seated yielding in the soil, thereby degrading the system’s lateral and flexural performance. This leads to the typical “rise-then-fall” shape of the envelope. This coupling behavior is consistent with classical V‑H interaction theories for undrained clay³⁴ where the failure envelope expands under moderate vertical load and contracts as the vertical load approaches the pure vertical capacity due to soil punching. In the H-M plane, the capacity envelopes of all three foundations can be approximated as straight lines passing through the origin, with their slopes representing a stable proportionality between the system’s flexural and lateral resistances. This phenomenon indicates that, although the overall stiffness and embedment depth vary among different foundations, their internal force distribution and failure mechanisms under combined horizontal force and moment share an inherent consistency. In other words, horizontal load and moment exhibit a similar driving effect on the bearing behavior of these foundation types.
The similarity in normalized envelope shapes can be explained by the normalization procedure itself. The ultimate capacities V_ult, H_ult, and M_ult inherently incorporate geometric information such as foundation width, embedment depth, and contact area. Normalizing by these values removes geometry-dependent scaling, yielding dimensionless coordinates that represent the intrinsic failure envelope of the soil-foundation system. Classical plasticity solutions for undrained clay^18,35 demonstrate that demonstrate that for various foundation types, the normalized failure envelope in V-H space follows a consistent shape. Once geometric effects are normalized, the dimensionless collapse mechanism converges to a similar form. This theoretical expectation is confirmed by the present numerical results: despite distinct deformation modes (deep rotation for the pile, shallow translation for the bucket, and hybrid for the composite foundation), their normalized V-H-M envelopes collapse onto a nearly unique surface, indicating that the envelope is a fundamental property of the clay–foundation interface under combined loading.
Meanwhile, differences in the responses of different foundations under combined loading are also evident, particularly in the enhancing effect of vertical load on lateral capacity and its optimal coupling ratio. As noted previously, the presence of moderate vertical load mobilizes additional lateral soil resistance through increased confining pressure and interface friction. The data further reveal that the effectiveness of this coupling is foundation-dependent. Specifically, the single pile, single bucket, and pile-bucket composite foundations reach their peak lateral capacities when the vertical load reaches 0.35, 0.50, and 0.55 times their respective ultimate vertical capacities (V_ult), with the corresponding peak values being 1.18, 1.59, and 1.84 times their ultimate horizontal capacities (H_ult), respectively. This gradation suggests that the composite foundation benefits from a more extended and efficient load-transfer mechanism: the bucket engages shallow soil to provide initial confinement, while the pile distributes vertical load to deeper strata, thereby delaying the onset of soil yield and allowing a higher vertical load to be applied before the coupling benefit diminishes. Consequently, the pile-bucket composite foundation not only achieves the highest absolute lateral capacity but also exhibits the most significant synergistic enhancement under its optimal vertical load, underscoring its superior performance in combined loading scenarios.
Figure 12 presents a comparative visualization of the plastic strain contours developed in the soil surrounding the single pile, single caisson, and pile-bucket composite foundation under identical monotonic loading. The distribution and extent of the plastic zones reveal fundamental differences in their failure mechanisms and load-transfer efficiency.
In the single pile foundation, the plastic zone is primarily localized around the pile shaft at a certain depth, forming an asymmetric bulb-shaped region that indicates a deep-seated rotational failure mechanism. The soil near the mudline remains largely elastic, underscoring the pile’s reliance on deeper soil resistance for moment capacity. For the single caisson foundation, significant plastic strains develop along the outer skirt and beneath the caisson base. The failure mechanism is dominated by a shallower translational movement, with pronounced soil yielding near the leading edge and a distinct gap forming on the trailing side. The plastic zone spreads laterally rather than extending deeply into the soil profile.
In contrast, the pile-bucket composite foundation exhibits a synergistic and integrated plastic zone that encompasses both the embedded pile and the periphery of the bucket. The pile extends plastic deformation deeper into the soil, while the bucket engages a broader volume of near-surface soil and enhances lateral confinement. This results in a composite failure mechanism that is more spatially distributed, effectively mobilizing a larger soil mass and providing a more efficient load-transfer path than either system acting independently.
Comparison of plastic zones. (a) Pile foundation, (b) bucket foundation, (c) pile-bucket composite foundation.
The overlapping and interacting plastic regions demonstrate a clear mechanical interaction between the pile and bucket components. This integrated failure mechanism corresponds directly to the expanded VHM failure envelope observed earlier, confirming that the enhanced bearing capacity of the composite foundation stems from a fundamentally optimized soil-structure interaction.
This paper conducted a centrifuge model test and advanced numerical simulations to investigate the bearing characteristics and synergistic mechanisms of a pile–bucket composite foundation in marine soft clay under complex loading conditions. The primary conclusions are as follows:
The centrifuge tests and validated FE model demonstrate that the pile–bucket composite foundation effectively combines the mechanical advantages of both components. Under lateral loading, it exhibits a hybrid deformation mode, restraining shallow translation through the bucket and providing deep rotational restraint via the pile, resulting in a more uniform displacement field and enhanced deformation control compared to single-pile or single-bucket foundations.
Under combined V–H–M loading, all three foundation types exhibit similar normalized envelope shapes, characterized by a “rise-then-fall” response in the V–H and V–M planes and a linear relationship in the H–M plane. However, the composite foundation achieves the most significant expansion of the failure envelope, indicating superior load-carrying integration.
The composite foundation benefits the most from vertical load coupling. It reaches its peak lateral capacity (1.84 H_ult) at a higher vertical load ratio (0.55 V_ult) than the single pile (1.18 H_ult at 0.35 V_ult) and single bucket (1.59 H_ult at 0.50 V_ult). This is attributed to its more efficient load-transfer mechanism, where the bucket mobilizes shallow confinement and the pile distributes load to deeper strata, delaying soil yield.
Analysis of plastic strain contours confirms a synergistic soil–structure interaction. The composite system develops an integrated plastic zone that engages both shallow and deep soil masses simultaneously, leading to a more spatially distributed failure mechanism and a more efficient load-transfer path than either component acting alone.
This study provides a technical foundation for the design of pile-bucket composite foundations in soft clay for offshore photovoltaic applications. It should be acknowledged that offshore foundations are subjected to long-term cyclic loads, whereas the present study is limited to monotonic loading. Under cyclic conditions, accumulated rotation, stiffness degradation, and soil remoulding may reduce the effective bearing capacity compared to the monotonic envelope. Nevertheless, the monotonic failure envelope established herein provides an essential upper-bound reference and a basis for subsequent cyclic analyses. Future research will include centrifuge cyclic loading tests and advanced numerical simulations to quantify the effects of cyclic loading on the pile-bucket composite foundation.
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.
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This study was funded by the National Natural Science Foundation of China (52501347 and 52401336) and Basic Research Program of Jiangsu (BK20250285) and China Postdoctoral Science Foundation (2025M773225) and Central Public-Interest Scientific Institution Basal Research Fund (Yj326005).
Department of Geotechnical Engineering, Nanjing Hydraulic Research Institute, Nanjing, 210024, China
Guanghui Yu, Kaifang Fan, Changsheng Gao & Xun Zhu
East China Branch Construction Department, China Resources Power Investment Co., Ltd, Nanjing, 210024, China
Guanghui Yu
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Conceptualization, G.Y. and K.F.; Methodology, G.Y. and K.F.; Software, G.Y., K.F. and C.Gao; Validation, G.Y. and X.Z.; Formal analysis, X.Z.; Investigation, X.Z.; Resources, C.Gao.; Data curation, G.Y., K.F. and C.Gao.; Writing—original draft, G.Y.; Writing—review & editing, K.F., C.Gao. and X.Z.; Visualization, C.Gao. and X.Z.; Supervision, K.F.; Project administration, K.F.; Funding acquisition, K.F. and X.Z. All authors have read and agreed to the published version of the manuscript.
Correspondence to Kaifang Fan.
The authors declare no competing interests.
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Yu, G., Fan, K., Gao, C. et al. Bearing mechanism of innovative pile-bucket foundations for offshore photovoltaic systems in soft clay under combined loading. Sci Rep 16, 21979 (2026). https://doi.org/10.1038/s41598-026-53057-7
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Received: 10 February 2026
Accepted: 11 May 2026
Published: 13 May 2026
Version of record: 14 July 2026
DOI: https://doi.org/10.1038/s41598-026-53057-7
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