Study on the Anchored Bearing Characteristics of Mooring Pile Foundations in Sandy Soil for Floating Wind Turbines

Abstract

As one of the mooring foundation types for floating wind turbine platforms, research on the anchor pullout bearing characteristics of mooring pile foundations remains insufficient, and the underlying mechanism of anchor pullout bearing capacity needs further investigation and clarification. This paper conducts a numerical study on the bearing characteristics of mooring pile foundations under tensile anchoring forces with loading angles ranging from 0° to 90° and loading point depths of 0.2L, 0.4L, 0.6L, and 0.8L (where L is the pile length). The research findings indicate that the anchor pullout bearing capacity decreases as the loading angle increases from 0° to 90°, and exhibits a trend of first increasing and then decreasing with the increase in loading point depth. For rigid pile-anchors, the maximum anchor pullout bearing capacity occurs at a loading point depth of 0.6–0.8L, while for flexible piles, it appears at 0.4–0.6L. Both the bending moment and shear force of the pile shaft show abrupt changes at the loading point, where their maximum values also occur. This implies that the structural design at the loading point of the mooring pile foundation requires reinforcement. Meanwhile, the bending moment and shear force of the pile shaft gradually decrease with the increase in the loading angle, which is attributed to the gradual reduction of the horizontal load component. The axial force of the pile shaft also undergoes an abrupt change at the loading point, presenting characteristics where the upper section of the pile is under compression, the lower section is in tension, and both the pile top and pile tip are subjected to zero axial force. The depth of the loading point significantly influences the movement mode of the pile shaft. Shallow loading (0.2–0.4L) induces clockwise rotation, and the soil pressure around the pile is concentrated in the counterclockwise direction (90–270°). In the case of deep loading, counterclockwise rotation or pure translation of the pile shaft results in a more uniform stress distribution in the surrounding foundation soil, with the maximum soil pressure concentrated near the loading point.

1. Introduction

Against the backdrop of the “dual carbon” goals, wind power generation has gradually become one of the globally high-profile new energy power generation methods [1]. As the development of nearshore wind power resources approaches saturation, floating offshore wind power has evolved into one of the key methods for utilizing offshore wind energy. Currently, coastal countries worldwide are vigorously advancing deep-sea floating wind power technologies. A floating wind turbine system mainly comprises a floating platform foundation, a mooring system, and an anchoring foundation, among which the anchoring foundation is a critical structure for maintaining the stability of the floating platform. The anchoring foundations for floating wind turbine platforms primarily include gravity foundations, suction bucket foundations, mooring pile foundations, and drag anchors. However, due to the influence of the gentle-slope continental shelf, the overall water depth in China’s sea areas is limited, and the marine geological conditions are complex, making mooring pile foundations one of the important forms of anchoring foundations for China’s floating wind power projects.

For floating wind turbines, the design experience of mooring pile foundations is relatively limited, mainly relying on the successful application experience of anchoring foundations in offshore oil and gas platforms. The mooring chains are usually connected to the anchoring foundation at a certain depth below the pile top, which results in significant differences in the mechanical characteristics between mooring pile foundations and traditional pile foundations loaded at the top. Mooring pile foundations not only need to bear the vertical load component of the mooring chains but also withstand horizontal forces and bending moments. Mohapatra et al. (2025) [2] studied the hydrodynamic response of large floating interconnected structures under the action of current and wind, and their research indicated that current speed is a key environmental factor affecting structural displacement. This conclusion is of reference value for the stability design of floating foundations in offshore wind power. With the growing demand for the development of floating offshore wind power, more and more scholars have focused on researching the bearing characteristics of mooring pile foundations.

Randolph, M. et al. (2015) [3] systematically elaborated on the difficulties faced in the bearing capacity analysis of pile foundations amid geotechnical engineering challenges in the offshore oil and gas sector. They also proposed that the maximum anchor pullout capacity of rigid anchoring foundations is achieved when the loading point is at a depth of 0.65 times the embedment length, a conclusion echoed by Andersen et al. (2005) [4]. Cerfontaine B. et al. (2023) [5] explored the bearing characteristics of mooring pile foundations for floating wind turbines under tensile anchoring forces. They suggested that the interaction between the mooring pile foundation and soil under the horizontal component of the anchor chain load is similar to that of traditional horizontally loaded piles. However, when the slenderness ratio of the anchor pile is large, failure usually occurs with one or two plastic hinges caused by pile bending, and these plastic hinges form at the location of the maximum bending moment below the mudline, which is consistent with the research conclusion of Mark Randolph (2017) [6]. Meanwhile, the soil tends to fail by forming a passive wedge near the ground surface or by flowing around the pile (Murff and Hamilton (1993) [7]). Wei et al. (2024) [8] conducted oblique tensile tests on model anchor piles in calcareous sand deposits. The study showed that the load–displacement curves are nonlinear, that dense sand can significantly restrain deformation and improve bearing capacity, and that the critical load inclination angle for the maximum uplift resistance is approximately 30°, providing a reference for the application of mooring pile foundations in calcareous sand foundations.

Alnmr et al. (2024) [9] carried out a parametric analysis on the performance of helical piles used for anchoring mooring cables. By setting load inclination angles (0°, 20°, 40°, and 60°) to simulate the action of mooring cable loads, they determined the optimal plate position ratio for maintaining bearing capacity and stability, thereby enriching the selection of mooring pile foundations for floating wind power. Currently, most studies on mooring pile foundations for floating platforms focus on the anchor pullout bearing characteristics of helical piles. Wang T, Zhao Y, Han W, et al. (2024) [10] studied the effects of inclination angle, burial depth, and anchoring specifications on the bearing performance of helical anchors. The study found that with a constant embedded length of the anchor rod, an increase in the inclination angle leads to a relative reduction in the embedded depth of the helical anchor, thereby decreasing its pullout resistance. In addition, there is a significant direct correlation between the pullout resistance of the helical anchor and its burial depth. It is worth noting that the change in burial depth has the least impact at the early stage of loading. However, as the load gradually increases, the force exerted on the anchor plate increases significantly with displacement, resulting in an increasingly greater impact of burial depth on the bearing capacity of the anchor. Jiang T, Liu C, Zhang X, et al. (2023) [11] investigated the soil deformation and bearing characteristics around multi-helical anchor piles under horizontal loads. The study found that the burial depth of the anchor plate has a significant impact on the influence range of soil displacement around the helical anchor pile as well as the distribution of active and passive zones. As the burial depth increases, the angle between the shear failure surface in the passive zone behind the pile and the vertical direction gradually decreases; the shear failure surface in the disturbed zone in front of the pile develops in the directions of lower right–vertically downward–lower left. Reape D, Naughton P. (2018) [12] studied the tensile strength of helical piles subjected to inclined loads in a geotechnical centrifuge. They found that there is no significant difference in tensile resistance between single-plate and double-plate helical piles, indicating that single-plate helical piles are the most effective type. When the loading angle is ≤45°, the horizontal deformation of the pile dominates, while when the loading angle is >45°, vertical deformation becomes dominant. Feng et al. (2025) [13] conducted numerical simulations on helical piles in composite foundations for transmission tower engineering, and the results showed that as the ratio of horizontal to vertical load increases, the axial bearing capacity of both single-helix and double-helix piles decreases bidirectionally. Through the analysis of incremental displacement contour lines of soil profiles, it was found that when the proportion of horizontal load increases, the soil sliding surfaces of both types of piles extend from the helical plates to the anchors, and this trend is more likely to occur in double-helix piles. In comparison, uplift load is more likely to expand the sliding surface than downward pressure load. In China, a total of four floating wind turbines have been successfully demonstrated, among which the “Haizhuang Fuyao” floating wind turbine adopts a mooring pile foundation, as shown in Figure 1.

According to the study by Cerfontaine B. et al. (2023) [5], the mechanical behavior of mooring pile foundations is basically similar to that of traditional pile foundations. The difference lies in the fact that the loading point of the tensile anchoring force is located at a certain depth of the pile shaft. At the loading point, the anchor chain load is decomposed into vertical and horizontal components, which causes the mooring pile foundation to bear uplift and horizontal actions. There have been numerous studies on the uplift bearing characteristics of pile foundations both domestically and internationally. Chen et al. [14] conducted model tests and found that the side friction of uplift piles develops from the upper part of the pile shaft and gradually transfers to the lower part. With the increase in test load, the side friction in the upper part of the pile shaft changes little, while the side friction in the middle and lower parts increases significantly compared with that in the upper part. Wang et al. (2025) [15] discovered through model tests and numerical simulations that excavation unloading in sandy strata has a significant impact on the bearing characteristics of anchor piles (uplift piles): the soil stress release caused by foundation pit excavation reduces the normal stress on the pile side, which in turn leads to the loss of pile side friction resistance. This is the core mechanism behind the attenuation of anchor pile bearing capacity. Bai et al. (2022) [16] summarized the core action mechanism of uplift piles: under the action of buoyancy, the pile transfers loads through interface friction with the surrounding soil. The soil around the pile moves upward with the pile, generating shear deformation, thereby forming uplift resistance. Equal-section uplift piles mainly rely on pile side friction resistance, while belled uplift piles provide additional end bearing capacity through the enlarged base, and their uplift resistance is more fully exerted. Sun [17] studied the uplift bearing characteristics of offshore platform foundations, focusing on the analysis of the influence of loading angle and pile length–diameter ratio on their ultimate bearing capacity, and obtained the envelope calculation equation for the ultimate bearing capacity of mooring pile foundations, which provides certain reference value for the research on deep-sea anchoring foundations. Yang B et al. [18,19,20] analyzed the uplift bearing characteristics of uplift piles under different soil conditions through on-site ultimate load tests and theoretical research. They obtained the relationship curves between pile top displacement and uplift load, and verified the model by comparing experimental and theoretical results to ensure its accuracy, thus providing theoretical support for research on uplift piles. Zheng et al. (2019) [21], based on the pile load test results of uplift bored piles in deep-buried underground substations, studied the uplift performance of under-reamed piles and post-grouted bored piles, and explored the load transfer characteristics and uplift bearing capacity improvement mechanism of these two types of uplift piles. The study showed that post-grouting can significantly improve the uplift bearing capacity of bored piles. After pile grouting, the pile–soil interface condition is improved, the pile side friction is significantly increased, and thus the uplift bearing capacity is enhanced. For long uplift piles, the uplift performance of post-grouted bored piles is better than that of under-reamed piles. Li et al. (2025) [22] proposed a new type of foundation structure—vertical-inclined composite high-pressure jet grouting piles, and studied their bearing performance and mechanical mechanism through model tests. The study found that for inclined piles with inclination angles of 10° and 20° in the vertical-inclined composite high-pressure jet grouting piles, their ultimate uplift bearing capacity increased by 16.29% and 60.31%, respectively, compared with the corresponding vertical piles. Moreover, after changing vertical piles to inclined piles, the vertical-inclined composite high-pressure jet grouting pile foundation can mobilize more soil to resist vertical loads, thereby improving the uplift bearing capacity.

In offshore engineering, such as offshore wind power, the vertical bearing characteristics of large-diameter extra-long steel pipe piles are crucial for the safety of foundations. However, traditional bearing capacity determination methods are difficult to adapt to their mechanical characteristics. Through on-site tests in an offshore wind power project in Shantou, Guangdong, Han et al. (2024) [23] found that such pile bodies exhibit significant deformation, and there are differences in the response laws between pile top settlement and pile bottom settlement. Relying solely on the pile top settlement curve is prone to misjudgment of the ultimate bearing capacity, and a comprehensive analysis that combines with pile bottom deformation is required. This provides a new idea for the bearing capacity evaluation of large-diameter piles. Research on the horizontal bearing characteristics of pile foundations is relatively well developed. For example, Zhu et al. (2021) [24] systematically carried out studies on the size effect and bearing capacity calculation theory of super-large diameter piles. Li et al. (2022–2024) [25,26] and Qin et al. (2023, 2025) [27] systematically revealed the pile–soil interaction mechanism and bearing response of large-diameter piles, and established a calculation method for the pile head stiffness of large-diameter horizontally loaded piles, which is convenient for quick calculation. Regarding the deformation characteristics of large-diameter piles under horizontal loading, Fan et al. (2025) [28] demonstrated through case studies that within the small deformation range (<10 mm), the results of the Euler–Winkler (E-W) model and the Timoshenko–Pasternak (T-P) model are relatively close. However, in the case of large deformations (>10 mm), the calculation results of the T-P model are more consistent with the measured values. In addition, the pile top displacement is positively correlated with the pile–soil relative shear ratio, and the influence of soil shear effects on lateral displacement is significantly greater than that of pile shaft shear deformation. This conclusion provides an important reference for the calculation of the horizontal bearing capacity of large-diameter piles. Qian et al. (2025) [29] found through field static load tests that the horizontal load–displacement curve of large-diameter single piles exhibits a significant “S”-shaped characteristic, which is highly consistent with the mathematical properties of the Usher curve. Based on this, a prediction model for the horizontal ultimate bearing capacity of large-diameter single piles was established using the Usher curve, enabling accurate prediction of the ultimate bearing capacity of undamaged piles. For the combined load action on pile foundations, Zhu et al. (2017) [30] and Liu et al. (2023) [31] proposed a coupled mechanical model and solved it using the transfer matrix method, providing methodological support for bearing capacity analysis and calculation, and revealing the influence law of the additional bending moment effect of vertical loads on the horizontal bearing characteristics of large-diameter piles.

Pan et al. [32] conducted indoor inclined loading tests on single piles, and the results showed that the ultimate bearing capacity of pile foundations first increases and then decreases with the decrease in loading angle; with the increase in pile burial depth, the ultimate bearing capacity of piles also increases, but the improvement of horizontal ultimate bearing capacity is more significant compared with that in the vertical direction. Miao et al. (2023) [33] conducted large-scale cyclic loading tests on marine double-layer soils. The results showed that under cyclic loading of millions of cycles, the ultimate bearing capacity of steel pipe piles follows a pattern of “first decreasing, then increasing, and finally stabilizing”. Moreover, the cumulative settlement at the pile top and the pile strain both increase significantly with the increase in the cyclic load ratio (CLR). Specifically, the influence of cyclic loading on settlement is far greater than that of static loading: when CLR increases by 0.2, the increase in cumulative settlement is more than 10 times that under the same increase in the static load ratio (SLR). These findings provide an important experimental basis for the optimal design and safety assessment of steel pipe pile foundations in offshore wind power projects. Zhong et al. [34] conducted research through indoor model tests, focusing on exploring the bearing characteristics of uplift batter piles. Their test results showed that the ultimate bearing capacity of inclined pile foundations increases with the increase in inclination angle when the loading angle is less than 30°, and decreases with the increase in inclination angle when the loading angle is greater than 30°. It was also found that for inclined pile foundations, horizontal load plays a dominant role when the loading angle is less than 45°, while vertical load becomes dominant when the loading angle is greater than 45°. Gao et al. (2024) [35] found through centrifuge model tests that cement–soil reinforcement can significantly improve the horizontal ultimate bearing capacity of single piles. When using reinforcement widths of 2.5D (where D is the pile diameter) and 3.0D, the ultimate bearing capacity of single piles increased by 5.45 times and 6.29 times, respectively, and the initial stiffness increased by 2.74 times and 2.61 times, respectively. This finding is of great significance for enhancing the ultimate bearing capacity of single piles.

The above studies provide substantial theoretical support for the research on mooring pile foundations of floating wind turbines. However, there are still many problems to be solved. Firstly, existing studies mainly focus on the ultimate bearing capacity of mooring pile foundations, with relatively few studies on the internal force analysis of pile anchors. Secondly, since the loading point is located at a certain depth of the pile shaft, whether the pressure distribution pattern around the pile is different from that of traditional horizontally loaded piles remains an unsolved problem.

Based on the limitations of existing research, this paper focuses on the pile-anchor foundation of floating wind turbines in sandy soil foundations. A three-dimensional numerical model is established using the finite element software ABAQUS (2022) to investigate the effects of anchor tension load angles (0–90°) and loading point depths (0.2L, 0.4L, 0.6L, and 0.8L, where L is the pile length) on the bearing characteristics of pile-anchor foundations. The study will systematically analyze the ultimate bearing capacity, load–displacement curve characteristics, and distribution laws of internal forces (bending moment, shear force, axial force) of rigid and flexible piles under different working conditions. It will reveal the mechanism by which loading parameters influence the pile movement mode (coupling effect of rotation and translation) and the stress diffusion characteristics of soil around the pile, and compare the differences in soil resistance distribution between piles with different stiffnesses to clarify the essential distinctions in pile–soil interaction under shallow and deep loading conditions. By addressing the gaps in existing research, such as insufficient analysis of internal pile forces and unclear distribution patterns of soil pressure around piles, this study aims to provide theoretical support and parameter references for the optimal design of mooring foundations for deep-sea floating wind turbines, contributing to enhancing the stability and safety of floating wind power structures under complex marine geological conditions in China.

2. Establishment of Numerical Model

2.1. Geometric Parameters

In numerical analysis, both the pile and soil are simulated as three-dimensional deformable bodies, and the Mohr–Coulomb constitutive model is adopted for soil plasticity. The pile-anchor foundation has a diameter of 3.75 m and a side wall thickness of 0.12 m. To analyze the influence of the relative stiffness between the pile and soil on the bearing characteristics of the mooring pile-anchor foundation, foundation models with pile lengths of 15 m and 60 m are established, corresponding to rigid piles and flexible piles, respectively. The stiffness of the rigid pile shaft is much greater than that of the surrounding soil. Under vertical loads, the overall deformation of the pile shaft is small, and the load is mainly transferred to the deep bearing layer through the pile end resistance, with the pile side friction playing a limited role. The stiffness of the flexible pile shaft is similar to that of the surrounding soil. Under vertical loads, the pile shaft undergoes significant flexural deformation, and the load is gradually transferred to the soil through the pile side friction, with the pile end resistance being small, see

Table 1. Material parameters.

Material Name	Elastic Modulus/MPa	Effective Unit Weight/kN·m−3	Cohesion/kPa	Internal Friction Angle/°	Poisson’s Ratio
Silty sand	33	20	2	33.7	0.3
Steel	210,000	78.5	-	-	0.3

.

2.2. Model Establishment

The meshing details of the components are shown in

Table 2. Meshing parameters.

	Total Number of Nodes	Total Number of Elements	Total Number of Soil Meshes	Global Size	Local Size
Rigid pile	858	384	37,893	0.5	0.5
Flexible pile	3198	1464	46,809	0.5	0.5

. Taking the flexible pile as an example, the horizontal range of the simulated soil is set to 15 times the diameter of the mooring pile anchor, and the vertical range of the soil is set to twice the pile length. The three-dimensional eight-node solid element C3D8 is used for meshing. To improve calculation efficiency while ensuring calculation accuracy, the foundation model is meshed as a whole with a global mesh edge length of approximately 0.5 m, resulting in 1464 mesh elements for the pile-anchor foundation model. The soil model adopts local refinement: the soil inside the pile is refined, and the soil outside the pile adopts a single-precision local refinement method, in which the closer to the mooring pile anchor, the smaller the soil mesh size and the higher the calculation accuracy. The total number of mesh elements for the foundation soil is 46,809. The contact surface between the mooring pile anchor and the foundation soil is set using the penalty function method. The tangential friction coefficient of the contact surface is taken as μ = tan(2/3φ), where φ is the internal friction angle of the soil, and the normal behavior of the contact surface is set to hard contact. A schematic diagram of the mesh division for the foundation and soil is shown in Figure 2.

The geostress balance of the soil is divided into two analysis steps. Step 1: Deactivate the mooring pile foundation and perform geostress balance on the soil alone. The effect of this geostress balance is shown in Figure 3. Step 2: Deactivate the part of the soil where the mooring pile foundation is embedded, activate the foundation structure simultaneously, and then perform geostress balance again, as shown in Figure 4. The loading method adopts the reference point method: a reference point is set above the pile cap and coupled with the top surface of the pile cap, and the load is applied to the reference point during loading.

3. Analysis of Bearing Characteristics of Rigid Mooring Pile Foundations

3.1. Analysis on Bearing Capacity of Rigid Mooring Pile Foundations

To analyze the influence of different loading depths H on the bearing characteristics of mooring pile-anchor foundations, four loading depths are set in this numerical simulation: H = 0.2L, H = 0.4L, H = 0.6L, and H = 0.8L. By applying anchor loads at different angles for each of these four depths, the focus is placed on studying the bearing characteristics of the pile-anchor foundations under varying loading depths and angles.

The bearing capacity of rigid piles is closely related to the loading angle, as illustrated in Figure 5 and Figure 6 When the loading angle is 0° (pure horizontal load), the bearing capacity reaches its maximum value. As the loading angle increases, the bearing capacity gradually decreases, reaching its minimum at 90° (pure vertical load). The morphology of the load–displacement curve presents two typical patterns with changes in the loading angle: when the loading angle is ≤60°, the curve shows a gentle variation. In the initial stage, when the displacement is less than 0.05 m, the curve exhibits linear elastic deformation; subsequently, the stiffness gradually decreases with the increase in load, and the larger the loading angle, the more significant the stiffness attenuation. When the loading angle is >60°, the curve takes a steep form. After the initial elastic stage (with displacement less than 0.04 m), the bearing capacity drops rapidly and the displacement increases sharply; moreover, the larger the loading angle, the lower the foundation stiffness after the inflection point. This indicates that under the action of a large vertical load component, the pile–soil interaction undergoes a sudden change, resulting in the rapid pullout of the pile and a significant reduction in bearing capacity.

Analysis combined with Figure 5, Figure 6 and Figure 7 reveals that the bearing capacity of rigid piles is closely related to the loading angle, depth, and pile movement mode. When the loading angle is 0°, the pile movement mode is horizontal translation combined with rotation, resulting in the largest soil stress diffusion range and the highest bearing capacity. As the loading angle increases, the proportion of the vertical load component rises, and the pile movement gradually transforms into oblique upward translation with rotation, leading to a narrowed soil stress zone and reduced bearing capacity. In addition, the depth of the loading point has a significant impact on the bearing capacity: when the loading point depth is 0.2L, 0.4L, or 0.6L, the pile rotates clockwise, with the rotation amplitude decreasing as the depth increases, and the bearing capacity increasing accordingly. When the depth reaches 0.8L, the movement mode shifts to counterclockwise rotation, and the bearing capacity is slightly lower than that in the 0.6L case. The optimal loading point is between 0.6L and 0.8L, where the pile is dominated by horizontal translation with the weakest rotation effect, the soil stress distribution is more uniform, and the bearing capacity reaches its peak. This indicates that the pile movement mode (coupling effect of translation and rotation) and the characteristics of soil stress distribution are the key factors determining the bearing capacity.

3.2. Internal Force Analysis of Rigid Pile-Anchor Foundations

The internal force state of rigid piles directly reflects their mechanical response and stability under external loads. As the primary components of internal forces within piles, bending moments, shear forces, and axial forces each carry distinct physical meanings and engineering significance. Building upon the previous in-depth analysis of the relationships among the bearing capacity of rigid pile foundations, loading angles, and loading point depths, a further exploration of the variations in rigid pile internal forces holds great importance for aspects such as optimal design, construction control, and safety assessment.

3.2.1. Bending Moment Results for Rigid Pile-Anchor

Under different conditions of loading point depths and angles, the distribution of bending moments along the pile shaft exhibits significant regular variations, as shown in Figure 8. When the loading point depth is 0.2L, the bending moment distribution characteristics above the loading point are basically consistent: the bending moment at the pile top is zero and increases with depth, reaching a maximum value near the loading point, among which the bending moment is the largest under the 30° loading condition. The bending moment distribution below the loading point is closely related to the angle: under loading angles of 0–75°, the bending moment first decreases to zero and then increases in the opposite direction, reaching a maximum value at 0.6–0.8L. The smaller the angle, the faster the change rate, and the minimum bending moments under 0° and 10° loading even exceed the maximum bending moment at the loading point. Under 80° and 90° loading, the bending moment gradually decreases with depth until it reaches zero at the pile end. When the loading depth is 0.4L, the bending moment distribution gradually transitions from one-sided bending to bilateral symmetric bending. The bending moment reaches its peak under 20° loading and is the smallest under 90° loading. At a loading depth of 0.6L, under small-angle (0–30°) loading, the bending moment shows an approximately centrally symmetric distribution, and the maximum bending moment is significantly higher than that in other working conditions, which is consistent with the conclusion that the bearing capacity is the highest at this depth. Under large-angle (70–90°) loading, the bending moment distribution tends to be more symmetric, and the amplitude decreases. When the loading depth is 0.8L, the bending moment distribution undergoes a directional change, showing a special distribution pattern of first negative then positive below the pile top. This is because with the change in the loading point, the rotation direction of the pile after being subjected to a horizontal load changes, and the direction of the passive earth pressure on the pile top side changes from the opposite direction to the same direction as the horizontal external load.

Comprehensive analysis shows that the loading depth and angle jointly determine the distribution pattern and amplitude characteristics of the bending moment. Among them, the bending moment effect is the most significant when the loading depth is 0.6L combined with small-angle loading.

3.2.2. Shear Force Results for Rigid Pile-Anchor

As shown in Figure 9, under all working conditions, the shear force at the pile top is zero. With the increase in depth, the shear force along the pile first increases in the negative direction, reaching a negative minimum value above the loading point. Then, a sudden change occurs at the loading point, where it quickly converts to a positive maximum value (i.e., the maximum shear force of the pile), and gradually attenuates with increasing depth, eventually returning to zero at the pile end. When the loading point depth is 0.2L and the loading angle ranges from 0° to 70°, a secondary negative shear force zone appears in the lower part of the pile, and the amplitude of this reverse zone increases as the angle decreases. However, this phenomenon disappears when the loading depth H ≥ 0.4L, and the shear force no longer rebounds after attenuating to zero. When the loading point depth is 0.6L, the overall shear force level of the pile reaches the maximum value. For example, the positive extreme value is approximately 20% higher than that when H = 0.2L. When the loading point depth H = 0.8L, the shear force distribution is similar to that at H = 0.6L, but the overall amplitude decreases.

In summary, the shear force effect is most significant when the loading depth is H = 0.6L combined with small-angle loading (0–30°), which corresponds to the previous conclusions.

3.2.3. Axial Force Results for Rigid Pile-Anchor

As shown in Figure 10, within the loading range of 0–90°, the axial force along the pile shaft presents a three-stage distribution with depth. The pile shaft above the loading point is in compression; the axial force at the pile top is always zero, and increases with depth until reaching the first extreme value. Among them, the negative axial force at this point is the largest when the loading angle is 60°. Subsequently, a sudden change occurs at the loading point, where the axial force rapidly converts to a positive peak value (i.e., the maximum axial force of the pile shaft), and gradually attenuates with increasing depth until it reduces to zero at the pile end. There always exists a critical optimal loading angle for the axial force peak at the loading point: this angle is 30° when the loading point depth is 0.2L, 0.4L, or 0.6L, and 45° when the loading point depth is 0.8L. When the loading point depth is 0.2L and the loading angle ranges from 0° to 80°, the axial force above the loading point increases positively with the increase in embedment depth, and the increase is more significant as the loading angle decreases. For loading point depths of 0.4L, 0.6L, and 0.8L, except for the brief tension in the pile shaft under 0–30° loading when H = 0.4L, the pile shaft is entirely in compression under other loading angles, and the compression amplitude increases significantly with depth. For example, the compression amplitude at H = 0.6L is approximately 40% higher than that at H = 0.4L.

4. Analysis of the Bearing Characteristics of Flexible Pile-Anchor Foundations

4.1. Analysis of the Bearing Capacity of Flexible Pile-Anchor Foundations

As shown in Figure 11, Figure 12 and Figure 13, the bearing capacity of flexible piles is closely related to the loading angle and the depth of the loading point. When the displacement is less than 0.2 m, the bearing capacity under large-angle loading (60–90°) is relatively high and similar, while the bearing capacity under small-angle loading (0–20°) is lower, and the smaller the angle, the lower the bearing capacity. At this time, the flexible pile is dominated by vertical loads (self-weight + lateral frictional resistance). When the displacement exceeds 0.2 m, the stiffness under large-angle loading decreases sharply, and the larger the angle, the more obvious the attenuation, while the stiffness under small-angle loading remains basically unchanged. In addition, the bearing capacity first increases and then decreases with the depth of the loading point, reaching a peak at a depth of 0.6L, where the bearing capacity under small-angle loading is higher. When the depth of the loading point is 0.2L or 0.4L, the pile exhibits clockwise rotation + horizontal translation; when the depth is 0.6L or 0.8L, the pile exhibits counterclockwise rotation + horizontal translation, with the weakest rotational effect at a depth of 0.6L.

Analysis of the soil stress contour maps for flexible piles under different loading angles at varying depths reveals that for large loading angles (60–90°), soil stress is concentrated in the upper part of the pile, exhibiting a distinct vertical pulling effect. This results in a stress concentration zone near the pile top. When the displacement exceeds 0.2 m, abrupt stress changes and a sudden drop in bearing capacity occur in the soil surrounding the pile. In contrast, small loading angles (0–20°) lead to a horizontally uniform stress distribution along the pile shaft, forming a stable passive earth pressure zone with progressive failure characteristics. At loading depths of 0.2L and 0.4L, stress is concentrated in the upper-middle part of the pile, accompanied by an asymmetric stress distribution due to clockwise rotation. At depths of 0.6L and 0.8L, stress shifts toward the middle-lower part, with the most uniform stress distribution and the highest bearing capacity observed at 0.6L.

Comprehensive comparisons indicate that the optimal loading point for flexible piles lies between 0.4L and 0.6L. Applying a horizontal load at this position ensures pure horizontal translation without rotation, thereby achieving optimal bearing performance.

4.2. Internal Force Analysis of Flexible Pile-Anchor Foundations

4.2.1. Bending Moment Results for Flexible Pile-Anchor

As shown in Figure 14, changes in loading depth and angle significantly affect the bending moment distribution patterns and extreme value characteristics of flexible piles. The research results indicate that: when the loading depth is 0.2L, the bending moment distribution pattern is similar to that of rigid piles, with the bending moment peak appearing at the loading point, and the extreme value of bending moment shifts from negative to positive under small-angle loading; when the loading depth increases to 0.4L, as the loading angle increases from 0° to 90°, the bending moment distribution along the pile shaft undergoes a transition from unilateral bending (showing an obvious asymmetric distribution under 0° loading) to bilateral symmetric bending (showing a centrally symmetric distribution under 90° loading). Among them, the bending moment reaches its maximum under 30° loading, and its minimum under 90° loading; when the loading depth is 0.6L, the bending moment distribution characteristics are similar to those at the loading depth of 0.8L. From 0° to 90°, the bending moment distribution along the pile shaft gradually changes from asymmetric to a more uniform bidirectional distribution; when the loading angle is 90°, the positive bending moment reaches its maximum. This phenomenon is consistent with the special movement mode of flexible piles at a depth of 0.6L obtained in previous studies.

4.2.2. Shear Force Results for Rigid Flexible Pile-Anchor

As shown in Figure 15, changes in loading depth and angle significantly affect the position and magnitude of the extreme values of shear force along the pile shaft. An analysis of the shear force distribution characteristics of flexible piles under different loading depths (0.2–0.8L) and angles (0–90°) reveals obvious regular patterns in the shear force distribution along the pile: the shear force at the pile top is always zero. As the burial depth increases, the shear force first increases in the negative direction, reaching a negative minimum value above the loading point; the growth amplitude of this negative shear force increases as the loading angle decreases. Then, a positive abrupt change occurs at the loading point, where the shear force shifts from negative to positive and reaches a positive maximum value, and this extreme value decreases as the loading angle increases. Subsequently, the shear force attenuates rapidly with increasing depth until it decreases to zero at the pile end. Notably, when the loading point depth is 0.2L and the loading angle ranges from 0° to 70°, after attenuating to zero, the shear force experiences a brief negative increase again, forming a second minimum value, and then gradually returns to zero. When the loading point depth is 0.4L, the shear force distribution exhibits central symmetry. Based on the shear force distribution curves at loading depths of 0.6L and 0.8L, it can be seen that the positive shear force extreme value corresponds to a loading angle of 30° in all cases, while the negative shear force minimum value corresponds to a loading angle of 0° in all cases. When the loading angle is 90°, the fluctuation of shear force along the depth is relatively small.

4.2.3. Axial Force Results for Rigid Flexible Pile-Anchor

As shown in Figure 16, the pile shaft above the loading point is in a compressed state. The axial force at the pile top is zero; as the burial depth increases, the axial force increases in the negative direction (compression) and reaches a negative minimum value above the loading point. This axial force value gradually increases as the loading point depth increases. A sudden change in axial force occurs at the loading point, where the pile shaft transitions from compression to tension. Beyond this point, the axial force gradually decreases with increasing depth, and the rate of decrease accelerates as the loading angle decreases. When the loading point depth is 0.2L, 0.4L, or 0.6L, the maximum axial force is positive; when the depth is 0.8L, the maximum axial force is negative. Additionally, a comparison of axial force diagrams for different loading points shows that under the same loading angle, the axial force difference between the upper and lower parts of the loading point remains constant and is unaffected by the loading point depth.

5. Distribution of Soil Resistance in Mooring Pile Foundations

Analysis of Figure 17 and Figure 18 reveals that the loading depth has a decisive influence on the distribution pattern of soil resistance. When the loading depth is 0.2L, the pile rotates clockwise, causing the soil pressure in the upper section (<13 m) to be symmetrically distributed in the load-facing direction (45° to −45°) with the maximum value at 0°. In contrast, the soil pressure in the lower section (>13 m) is mainly concentrated in the load-back direction (90–270°) and reaches a peak at 180°, which is attributed to the dominant negative displacement at the pile bottom. At a loading depth of 0.4L, the maximum soil pressure shifts to the vicinity of the loading point (6.5 m) and decreases with depth. At this point, the dominant positive displacement significantly reduces the soil pressure at the pile bottom. When the loading depth increases to 0.6L, the maximum soil pressure remains at the loading point, but stress concentration occurs at the pile bottom, causing a sudden increase in soil pressure within the range of 60° to −60°. At a loading point depth of 0.8L, the soil pressure at the pile bottom exceeds that at the loading point (12 m), becoming the most stressed area.

The results indicate that the loading depth, by altering the pile’s rotation center and displacement field distribution, not only affects the spatial distribution characteristics of soil pressure but also changes the location at which the maximum soil pressure acts. Notably, the rotation effect under shallow loading (0.2L) and the stress concentration at the pile bottom under deep loading (0.8L) are particularly significant.

6. Conclusions

This paper systematically analyzes the bearing characteristics of rigid piles through numerical simulation methods, investigating the influences of different loading angles and loading point depths on the bearing capacity, internal force distribution, and soil stress diffusion characteristics of mooring pile foundations. The main conclusions are as follows:

(1)

The bearing capacity of pile foundations with different stiffnesses shows a significant negative correlation with the loading angle: the bearing capacity is maximum under 0° loading and gradually decreases as the angle increases (up to 90°). The load–displacement curve of rigid piles shows a steep drop (an abrupt increase in displacement) when the loading angle is greater than 60°. For flexible piles, when the loading angle is greater than 60°, the bearing capacity decreases significantly with increasing displacement; under small-angle loading (≤20°), the curve shows a gentle variation.

(2)

The optimal loading point depth for rigid piles is 0.6–0.8L, within which their bearing capacity is significantly higher than that at other loading point depths: the bearing capacity is increased by approximately 20–30% compared with a loading point depth of 0.2L, by about 10–15% compared with 0.4L, and still 5–8% higher than that at a loading point depth of 0.8L. At this depth, the pile is mainly subjected to horizontal translation without obvious rotation, and the soil stress diffusion zone forms a symmetric arch-shaped distribution, resulting in the best bearing performance. The optimal loading point depth for flexible piles is 0.4–0.6L, and their bearing capacity improvement shows the following characteristics: it is increased by about 25–35% compared with a loading point depth of 0.2L, by approximately 15–20% compared with 0.8L, and by around 5–10% compared with the adjacent depth of 0.4L. The bearing capacity of flexible piles is significantly affected by the combined action of pile self-weight and side friction resistance. Under small-angle loading conditions, the rotation amplitude is obviously reduced, which further optimizes the bearing efficiency.

(3)

The movement mode of the pile after loading (rotation + translation or pure translation) directly affects the soil stress distribution. Rotation causes stress at the loading point to concentrate on the side with smaller displacement, reducing the bearing capacity; pure translation enhances the symmetry of stress diffusion and improves the bearing capacity. When the loading point depth is shallow (0.2–0.4L), the pile mainly rotates clockwise, and stress is concentrated in the lower part of the pile; when the loading point depth increases (0.6–0.8L), the movement mode changes to counterclockwise rotation or pure translation, resulting in more uniform stress diffusion.

(4)

The maximum bending moment is concentrated near the loading point. Under small-angle loading, the bending moment distribution shows asymmetric one-sided bending; under large-angle loading, it gradually transitions to a symmetric distribution. The extreme shear force occurs at the loading point and decreases with increasing loading angle; the axial force changes abruptly from compression to tension at the loading point, significantly affected by the vertical load component.

(5)

The distribution of soil resistance is closely related to the depth of the loading point: under shallow loading, the pile bottom soil pressure is concentrated in the counterclockwise direction (90–270°); under deep loading, the stress diffusion range expands, and the maximum soil pressure is concentrated near the loading point.

(6)

In practical engineering, it is recommended to select 0.6–0.8L as the loading point position for rigid piles and control the loading angle between 30° and 60°. For flexible piles, the pile stiffness and soil conditions should be comprehensively considered to avoid a sudden drop in bearing capacity caused by large-angle loading.

In the finite element simulation of the connection between anchor chains and pile-anchor foundations, this study simplified the process by directly applying loads at the pile surface, ignoring the local structural reinforcement at the loading point. This simplification may lead to excessive local stress in the pile body at the direct load application point. Therefore, it is recommended to conduct a refined finite element analysis of the local structure during the pile design phase.