Investigation of Pullout Capacity Characteristics of Suction Anchors Under Inclined Loads in Layered Soil

Abstract

Suction anchors are widely used in marine engineering because of their easy installation, cost-effectiveness, and excellent load-bearing capacity. However, existing research on their bearing capacity has primarily focused on homogeneous soils, which fails to adequately reflect the actual bearing capacity of layered seabed soils. Therefore, this study conducted a series of numerical simulations to investigate the pullout bearing capacity of suction anchors subjected to inclined loads in upper-stiff–lower-soft layered clay. By considering the clay strength (S_um/kD) and soil layer thickness ratio (T_h/L, T_c/L), this study systematically explores the influence of the optimal centerline loading depth (Z_cl,opt), uniaxial ultimate bearing capacity (H_ult and V_ult), and the VH failure envelope of suction anchors. The results indicate that the layer thickness ratio T_h/L of lightly overconsolidated clay (LOC) is the key factor influencing the Z_cl,opt and ultimate bearing capacity H_ult and V_ult. An increase in T_h/L significantly enhances the pullout resistance of suction anchors, which primarily results from the combined enhancement effect of lateral friction resistance and end resistance at the anchor–soil interface. The layered clay has a distinct influence on the horizontal and vertical bearing capacities of suction anchors. Based on the results of parameter analysis, a conservative analytical expression for the lower bound of the VH failure envelope curve is further proposed. The research conclusions provide a theoretical basis and engineering practice guidance for the optimized design and safety assessment of suction anchors in layered soil.

1. Introduction

Suction anchors typically refer to cylindrical structures that are closed at the top and open at the bottom, commonly constructed of steel or concrete [1,2]. Its diameter is typically 3–7 m, with wall thickness ranging from 25 to 75 mm, and the L/D is typically between 1 and 10 [3]. Suction anchors are widely used in coastal floating platforms, offshore wind turbine foundations, and deepwater projects due to their rapid installation, low cost, high load-bearing capacity, and minimal disturbance to seabed soil layers [4,5]. During the installation of suction anchors, the anchors are initially driven into the seabed soil using their own weight. Subsequently, water is pumped out through the suction holes at the top of the anchor, which creates a pressure differential between the interior and exterior of the anchor. This pressure differential forces the anchor to continue driving into the soil. When the top cover of the suction anchor makes contact with the seabed soil, the anchor is considered fully penetrated [6,7].

In actual engineering environments, offshore structures inevitably experience the effects of waves, wind, and currents [8,9]. Since the load must be transmitted to the suction anchor via the suspension chain and mooring chain, the suction anchor is continuously subjected to inclined loads [10]. The bearing mechanism of suction anchors subjected to inclined pullout loads differs from that of suction anchor foundations bearing vertical loads at the top. The schematic diagram of the suction anchor mooring system is shown in Figure 1. The loading angle and padeye location alter the failure mode of suction anchors [11]. Keaveny et al. [12] conducted prototype tests on a series of suction anchors installed in clay and applied mooring forces to the padeyes of the anchors below the mud surface. The test results indicate that when the mooring force is applied at the midpoint below the mud surface of the suction anchor, the corresponding ultimate bearing capacity is twice that when applied at the mud surface. Newlin [13] suggested that when mooring forces are applied below the optimal padeye position, the top of the suction anchor tilts away from the mooring force direction upon failure. In this case, the failure mode is not pullout failure but rotation within the soil. The suction anchor can obtain its maximum bearing capacity only when the anchor undergoes translational displacement. Therefore, the loading angle and padeye are critical factors affecting suction anchors.

Figure 1. Schematic diagram of suction anchor mooring.

To explore the ultimate bearing capacity of suction anchors under inclined loads, numerous studies have been conducted through theoretical analysis, numerical simulation, and physical testing. Current research primarily focuses on suction anchors in homogeneous soil. Wang et al. [14] conducted load-controlled model tests on the ultimate bearing capacity of suction anchors in soft clay and analyzed the effects of loading direction on failure modes and ultimate bearing capacity. The test results indicate that the bearing capacity of suction anchors is influenced by the loading direction. The reverse bearing capacity of the soil layer below the anchor base is a key factor affecting the ultimate bearing capacity of suction anchors. Zhang et al. [15] investigated the effect of cutting grooves on the ultimate bearing capacity of suction anchors in normally consolidated clay through numerical simulation methods. Kim et al. [16] investigated the behavior of suction anchor foundations installed in cohesionless soil under horizontal loading through numerical simulation. They conducted parametric studies on different length-to-diameter ratios and padeye positions of the suction anchors. The horizontal bearing capacity of the suction anchors was estimated, and soil stress distribution was analyzed under loading applied at the optimal padeye position. Existing studies on the bearing capacity of suction anchors have primarily focused on single homogeneous soil layers, which do not account for the actual layered characteristics of soil masses [17,18]. However, under the influence of geological movements and sedimentation processes, the actual seabed typically exhibits natural layering or anisotropic properties along the depth direction. The characteristics of such layered soil differ significantly from those of the current single-layer homogeneous soil layers studies [19,20]. In natural layered soils, a typical layered soil structure occurs where stronger soil layers overlie weaker layers [21]. For example, in the Bohai oil and gas fields off of China, the seabed exhibits a layered structure with upper-stiff–lower-soft layers depending on factors such as estuarine sediment transport patterns and tidal currents [22,23]. Additionally, in areas such as the Gulf of Guinea, the Bass Strait off southeastern Australia, and the Joa oil field in the North Sea, the seabed also contains hard soil layers with significantly greater strength than the underlying soil [24,25]. Furthermore, existing design guidelines for piles in layered soils primarily employ the equivalent lateral friction coefficient of the piles and the p–y curve method for lateral friction resistance. This approach is unsuitable for predicting the pullout resistance of suction anchors in layered soils. Existing guidelines, such as those from the American Petroleum Institute (API) [26] and DNV [27], typically assume homogeneous and uniform soil properties. Applying these existing guidelines to predict bearing capacity under layered soil conditions may be overly conservative. Therefore, it is important to fully consider the influence of layered soil properties to gain a deeper understanding of the pullout resistance capacity of suction anchors.

Based on the above-mentioned research status, this study aims to investigate the ultimate bearing capacity of suction anchors in upper-stiff–lower-soft layered clay. To analyze the bearing capacity of suction anchors under inclined loads, numerical simulation methods were employed. Considering variations in clay strength (S_um/kD) and layer thickness ratios (T_h/L, T_c/L, T_n/L), the ultimate bearing capacity of suction anchors subjected to inclined loads in layered clay (lightly overconsolidated clay (LOC, thickness = T_h), in normally consolidated clay (NC, thickness = T_c), and in low-strength normally consolidated clay (LNC, thickness = T_n)) was investigated. The primary research content includes (1) determining the optimal centerline loading depth Z_cl,opt in layered clay; (2) obtaining the corresponding uniaxial ultimate bearing capacities H_ult and V_ult; (3) quantifying the suction anchor VH failure envelope under inclined loading and deriving an analytical expression for its lower-bound solution.

2. Numerical Modeling

2.1. Geometry and Mesh

By referring the studies of Kim et al. [28] and Fu et al. [29], the numerical simulation model selected the suction anchor diameter D = 5 m and a depth of embedment of L = 7.5 m, with L/D = 1.5 and a thickness of t = 50 mm. The selected suction anchor dimensions are commonly adopted in engineering practice [30,31]. As shown in Figure 2a, the suction anchor is installed in layered clay. As the stiffness of suction anchors and soil differs significantly, suction anchors are typically treated as rigid bodies to improve computational efficiency. This method is widely applied in offshore geotechnical engineering [32,33]. The suction anchor is modeled using rigid materials with a density of ρ = 6800 kg/m³, an elastic modulus of E = 210 GPa, and a Poisson’s ratio of v = 0.3. An inclined load is applied by setting a reference point on the suction anchor.

Figure 2. Schematic diagram of the numerical model: (a) Model mesh partitioning; (b) Model constraint settings.

In this study, a three-dimensional finite element model was constructed using the commercial software ABAQUS 2020. The suction anchor and soil mass were modeled using three-dimensional eight-node solid elements (C3D8H). Due to load symmetry, only half of the soil mass was modeled to improve computational efficiency. The minimum mesh size for the model was 0.02 D. Based on existing research and the sensitivity analysis of mesh sizes, the selected minimum mesh size was reasonable [34,35]. The length and height of the soil were B_H = 10 D and B_V = 3 L, respectively, with the suction anchor positioned at the center of the soil model. The model dimensions were selected sufficiently large to eliminate the influence of boundary effects [18,36]. The relevant constraints on the soil are shown in Figure 2b.

2.2. Soil Parameters and Interface Properties

The clay in this study is treated as an elastoplastic material, adhering to the Tresca yield criterion and associated flow rules [26]. The Poisson’s ratio of the clay is v = 0.49, which is used to simulate undrained conditions where volume remains constant. The undrained shear strength of the clay is satisfied:

$$S_u=S_{um}+kz$$

(1)

where $S_{um}$ represents the undrained shear strength of the soil at the mud surface, $k$ represents the gradient of clay strength with depth, and $z$ represents the depth below the mud surface. The soil elastic modulus is taken as E = 500 S_u, and the normalized parameter S_um/kD is used to evaluate the influence of soil properties on bearing capacity. Based on relevant studies and geological exploration reports (S_um/kD = 0, 0.4, 0.67, and 1.0 [37,38,39,40]), the relevant parameters of the clay are shown in Table 1. The selection of clay parameters is based on the summary of idealized seabed profiles for offshore wind farms in numerous regions by Cerfontaine et al. [41]. The chosen clay strength encompasses both low-strength and high-strength clays. The numerical simulation tests for suction anchors are outlined in Table 2.

Table 1. Clay parameters.

Parameter	Clay A	Clay B	Clay C	Clay D
Sum (kPa)	0.1	3	5	10
K (kPa/m)	1.25	1.5	1.5	2
γ′ (kN/m3)	6	6	6	7.2
Sum/kD	0	0.4	0.67	1

Table 2. The experimental setup for the suction anchor numerical simulation test.

Group	Sum/kD (Th)	Sum/kD (Tc)	Th/L	Tc/L	Tn/L
Group A	—	—	—	—	—	Model validation
Group B	1	0.4, 0.67, 1	0.5, 0.75, 1.25	0.5, 0.75, 1.25	(3 L − Th − Tc)/L	To determine the optimum centerline loading depth Zcl,opt
Group C	1	0.4, 0.67, 1	0.5, 0.75, 1.25	0.5, 0.75, 1.25		To calculate the uniaxial ultimate bearing capacity (Hult and Vult)
Group D	1	0.4, 0.67, 1	0.5, 0.75, 1.25	0.5, 0.75, 1.25		To calculate the VH failure envelopes

To investigate the bearing capacity of suction anchors in upper-stiff–lower-soft layered clay under inclined loading, the soil in this study was divided into three layers. The first layer consisted of LOC with S_um/kD = 1.0 and layer thickness ratios T_h/L = 0.5, 0.75 and 1.25. The second layer comprised either NC or LOC, with S_um/kD values of 0.4, 0.67, and 1.0, and layer thickness ratios T_c/L = 0.5, 0.75, and 1.25. The third layer consisted of LNC, with S_um/kD = 0 and a soil layer thickness ratio T_n/L = (3 L − T_h − T_c)/L. The relevant parameters were obtained by referring to related research and geological exploration reports. Regarding the bearing capacity of suction anchors in clay, due to the low permeability coefficient of clay, numerous studies have assumed the soil to be in undrained conditions [42,43,44].

2.3. Details of Analysis and Loading Methods

The finite element modeling process includes the following steps:

(1)

The model construction and meshing stage: A finite element model of the suction anchor and soil was constructed and meshed. The mesh size for the suction anchor was set to 0.02 D, with a C3D8H mesh type. The soil mesh size was progressively refined, with smaller mesh sizes closer to the suction anchor, and the minimum mesh size was 0.02 D.

(2)

The initial geostress equilibrium stage: The finite element model was assembled, and the geostress equilibrium and loading analysis steps were set up. The geostress equilibrium analysis was performed first. In this stage, only the soil mass was subjected to geostress equilibrium analysis, and the suction anchor was treated as void space. In the initial geostress equilibrium stage, the anchor–soil interface contact was not activated.

(3)

The contact activation stage: After the soil stress equilibrium is established, the anchor–soil interface contact is activated. This means the penetration process of the suction anchor is disregarded, and the suction anchor is considered to be in the “in-place” state.

(4)

The load application stage: A reference point, RP, is established at the suction anchor to apply the inclined load. The inclined pullout load is applied under displacement control, with a maximum allowable displacement of 0.2 D.

The tangent method was employed to determine the uniaxial bearing load capacity, based on the study of Long et al. [45], for which no distinct yield value was observed when the load-displacement curve reached its maximum displacement. When the suction anchor moves horizontally or vertically without rotation, the uniaxial bearing capacity is equivalent to the uniaxial ultimate bearing capacity H_ult and V_ult. The complete VH failure envelopes for the suction anchor can be obtained through sweep analysis, reverse sweep analysis, and probe analysis, which have been widely applied [46,47,48].

As shown in Figure 3, when the suction anchor moves horizontally under inclined loading without rotation, the inclined load can be simplified into a horizontal force H, a vertical force V, a constraining moment M, and mooring angle $\theta$. By applying the principle of moment equilibrium, the optimal padeye depth Z_pad,opt at the corresponding angle and the optimal centerline loading depth Z_cl,opt can be obtained, which satisfy the equation:

$$Z_{cl,opt}={\displaystyle \frac{M}{H}}$$

(2)

$$Z_{cl,opt}=Z_{pad,opt}+{\displaystyle \frac{D}{2}}\times \tan \theta$$

(3)

Figure 3. The schematic diagram of the optimum centerline loading depth for the suction anchor.

By displacement control the inclined load was applied at the reference point set at the top center of the suction anchor, and the accuracy of the test results has been extensively validated [49]. The ultimate bearing capacity of suction anchors was defined as the load capacity corresponding to translational motion without rotation. Therefore, a reference point “PR” was established at the top center of the suction anchor to restrict rotation. By applying the corresponding inclined load, the corresponding ultimate bearing capacity was obtained.

3. Model Validation

To validate the accuracy of the constructed numerical model, the numerical simulation results of suction anchors under inclined loading were compared with existing experimental results, as shown in Figure 4. It can be seen from Figure 4a that for NC with S_u = 1.25 z and L/D = 1.5, the numerical simulation results show excellent consistency with test results from Supachawarote [50] and the experimental results from the Norwegian Geotechnical Institute (NGI), the Offshore Technology Research Center (OTRC), and the Center for Offshore Foundation Systems (COFSs) [30,51]. The VH envelope obtained from the numerical model closely matches their findings, which indicates that the numerical model developed in this study can effectively reproduce the pullout behavior of suction anchors in clay.

Figure 4. Model validation results: (a) Validation results for clay [50]; (b) Validation results for silty sand [28].

Furthermore, the accuracy of the constructed numerical simulation model was further validated by referencing centrifuge test data and finite element modeling results for non-cohesive soils from Kim et al. [28]. The loads were applied at the top of the suction anchor and below the mud surface at Z_pad = 2/3 L, with cu = 7 kPa, the internal friction angle φ = 32°, and the dilation angle ψ = 8°. The selection of relevant parameters strictly followed those used in the centrifuge tests and the finite element model. The corresponding comparison results are shown in Figure 4b, which shows that the constructed numerical model can effectively characterize the bearing capacity of the suction anchor.

4. Results of Numerical Analyses

4.1. Optimum Centerline Loading Depth Z_cl,opt

The optimal centerline loading depth Z_cl,opt is the key factor determining whether the suction anchor undergoes translational or rotational motion under inclined loading. When the inclined load vector applied to the suction anchors padeye passes through Z_cl,opt, the suction anchors move horizontally under the inclined load without rotation. At this point, the inclined load corresponds to the maximum pullout force at the given mooring angle. When the inclined load vector applied to the anchor padeye deviates from Z_cl,opt, the suction anchor will rotate forward or backward during the pullout process, correspondingly reducing the pullout resistance of the suction anchor. Therefore, Z_cl,opt is an indicator reflecting the pullout resistance capacity and failure mode of the suction anchor under corresponding soil parameter conditions. In engineering design, the location of Z_cl,opt must be prioritized for determination.

Figure 5 shows the influence of different soil mechanical parameters and layer thickness on the optimal centerline loading depth Z_cl,opt for layered clay. It can be seen that the LOC thickness ratio T_h/L is the key factor controlling Z_cl,opt. Taking S_um/kD = 0.4 as an example, when T_h/L = 0.5, half of the suction anchor is embedded in the LOC layer, with Z_cl,opt = 0.65. With the increase in T_h/L to 0.75 and 1.25, the upper portion of the suction anchor contributes more lateral friction resistance due to the increased thickness of the LOC layer. To balance the moments, the suction anchors Z_cl,opt shift downward, with the corresponding values Z_cl,opt being 0.67 and 0.71, respectively. When T_h/L > 1, the suction anchor is fully embedded in the LOC layer. The values of Z_cl,opt remain nearly unchanged for different S_um/kD and T_c/L, as the high strength of the LOC soil dominates the pullout resistance. When T_h/L = 0.5 and T_c/L = 0.5, the suction anchor end is located between the NC layer and the LNC layer interface. It can be observed that the variation of Z_cl,opt at this point is still influenced by the higher-strength clay within the suction anchor, which means that the impact of high-strength clay on Z_cl,opt is significantly greater than that of low-strength clay.

Figure 5. The effect of layered soil thickness on the optimal centerline loading depth Z_cl,opt.

4.2. Uniaxial Ultimate Bearing Capacity (H_ult and V_ult)

The uniaxial ultimate bearing capacity (H_ult and V_ult) represents the pullout resistance of the suction anchors when subjected to horizontal or vertical pullout forces without rotation. In numerical simulations, the uniaxial ultimate bearing capacity equals the integral of the ultimate lateral friction resistance along the anchorage depth. Based on the above principles, the effects of suction anchor relative positions (T_h/L and T_c/L) and soil strength (S_um/kD) on uniaxial ultimate bearing capacity were quantified. The uniaxial ultimate bearing capacities H_ult and V_ult of suction anchors under different conditions are shown in Table 3, Table 4 and Table 5.

Table 3. Uniaxial ultimate bearing capacity H_ult and V_ult (S_um/kD = 0.4).

Th/L	Tc/L	Hult (kN)	Vult (kN)
0.5	0.5	3990.1	4195.2
	0.75	4009.95	4400.57
	1.25	4010.13	4686.89
0.75	0.5	4479.21	4849.38
	0.75	4480.61	5148.21
	1.25	4480.6	5251.78
1.25	0.5	5097.45	6402.32
	0.75	5097.48	6456.7
	1.25	5098.36	6490.71

Table 4. Uniaxial ultimate bearing capacity H_ult and V_ult (S_um/kD = 0.67).

Th/L	Tc/L	Hult (kN)	Vult (kN)
0.5	0.5	4182.01	4457.01
	0.75	4218.84	4712.71
	1.25	4218.67	5167.98
0.75	0.5	4597.07	5056.31
	0.75	4600.14	5460.85
	1.25	4600.27	5615.79
1.25	0.5	5096.61	6566.56
	0.75	5096.65	6632.6
	1.25	5097.61	6670.71

Table 5. Uniaxial ultimate bearing capacity H_ult and V_ult (S_um/kD = 1).

Th/L	Tc/L	Hult (kN)	Vult (kN)
0.5	0.5	5017.5	5341.32
	0.75	5095.87	5810.55
	1.25	5085.19	7211.5
0.75	0.5	5095.87	5810.55
	0.75	5086.97	6739.91
	1.25	5083.68	7285.91
1.25	0.5	5085.19	7211.5
	0.75	5083.68	7285.91
	1.25	5085.34	7314.39

As shown in Table 3, Table 4 and Table 5, the LOC thickness ratio T_h/L is the core factor determining the uniaxial ultimate bearing capacity. Specifically, the undrained shear strength of LOC is significantly higher than that of NC and LNC. As the embedment length of the suction anchor into the LOC increases, the combined effect of lateral friction resistance and end resistance at the anchor–soil interface becomes more pronounced. Taking S_um/kD = 0.67 and T_c/L = 0.5 as examples, when T_h/L increases from 0.5 to 1.25, the corresponding horizontal ultimate bearing capacity H_ult of the suction anchor rises from 4182.01 kN to 5096.61 kN, representing an increase of approximately 21.9%. The vertical ultimate bearing capacity V_ult increases from 4457.01 kN to 6566.56 kN, representing an increase of approximately 47.3%. This supports the findings of Zhou et al. [18,45], which concluded that the pullout resistance of suction anchors in layered soils is positively correlated with the thickness of the anchor embedded in the higher undrained strength clay layer. As the anchor embedment depth in the higher undrained strength clay layer increases, both lateral friction resistance and end resistance enhance during the anchor–soil interface interaction under pullout forces.

The corresponding displacement contour map (Figure 6) also shows that as T_h/L increases from 0.5 to 1.25, the suction anchors experience passive earth pressure on the external wall under horizontal loading, which results in the formation of a passive earth pressure zone. The extent of this passive earth pressure zone is primarily influenced by the length L of the suction anchor. When the suction anchor length remains constant, the horizontal ultimate bearing capacity is primarily influenced by the strength of the clay surrounding the anchor.

Figure 6. The displacement contour plots of suction anchors under horizontal/vertical loads (S_um/kD = 0.67,T_c/L = 0.5): (a,b) T_h/L = 0.5; (c,d) T_h/L = 0.75; (e,f) T_h/L = 1.25; the units in the figures are meters.

When subjected to vertical loads, the pullout resistance of suction anchors is primarily composed of the anchor–soil lateral friction resistance and end resistance. As the thickness ratio T_h/L of the LOC soil layer increases, Figure 6 shows that the end-resistance influence zone expands. By combining the results in Table 3, Table 4 and Table 5, it can be seen that as T_h/L increases, the bearing capacity of the suction anchor improves. Based on the definition of lateral friction resistance, the lateral friction resistance of the suction anchor remains unchanged at this stage. This means that the contribution of end resistance to the vertical bearing capacity of the suction anchor increases, and consequently, the corresponding vertical ultimate bearing capacity V_ult increases. The vertical ultimate bearing capacity is primarily influenced by the thickness ratios T_h/L and T_c/L.

The layered clay makes the soil strength along the clay surface exhibit non-uniformity. The increase in S_um/kD enhances the uniaxial bearing capacity of layered clay. Taking T_h/L = 0.5 and T_c/L = 0.5 as examples, when S_um/kD increases from 0.4 to 1.0, H_ult rises from 3990.1 kN to 5017.5 kN, an increase of approximately 25.7%; V_ult increases from 4195.2 kN to 5341.32 kN, an increase of approximately 27.3%. The higher the S_um/kD, the greater the overall shear strength of the layered soil, and both the friction resistance and end resistance at the anchor–soil interface increase simultaneously. The soil strength S_um/kD is positively correlated with bearing capacity: the higher the soil strength, the greater the corresponding bearing resistance. The thickness of the LNC soil layer has no significant effect on H_ult and V_ult. The displacement vector contour plots for layered soil subjected to horizontal/vertical loads are shown in Figure 7.

Figure 7. The displacement vector plots of suction anchors under horizontal/vertical loads (T_h/L, T_c/L = 0.5): (a,b) S_um/kD = 0.4; (c,d) S_um/kD = 0.67; (e,f) S_um/kD = 1; the units in the figures are meters.

It can be observed that when the thickness ratios T_h/L and T_c/L remain unchanged, the corresponding horizontal/vertical load-displacement vector plots show little variation. This indicates that at this point, the bearing capacity of the suction anchor is primarily influenced by the friction resistance at the anchor–soil interface.

The thickness ratio T_c/L of the NC soil layer has little effect on the horizontal ultimate bearing capacity H_ult but significantly affects the vertical ultimate bearing capacity V_ult. For example, when S_um/kD = 1.0 and T_h/L = 0.5, as T_c/L increases from 0.5 to 1.25, H_ult changes little, rising only from 5017.5 kN to 5085.19 kN. Meanwhile, V_ult increases from 5341.32 kN to 7211.5 kN, representing an increase of approximately 35.0%. Combining Figure 6 and Figure 7 with the studies by Supachawarote [50], vertical bearing capacity relies more on the accumulated effect of friction resistance at the anchor–soil interface (the accumulation of lateral friction and end resistance). As the strength of the clay in the suction anchorage zone increases, the friction resistance becomes more pronounced. In contrast, horizontal bearing capacity is dominated by the distribution pattern of lateral resistance. The influence of T_c/L on H_ult is smaller than that of T_h/L and S_um/kD, which leads to a relatively minor overall change in H_ult.

When T_h/L > 1, which corresponded to the suction anchor being fully embedded in the LOC layer, the horizontal ultimate bearing capacity H_ult tended toward stability. Meanwhile, the vertical ultimate bearing capacity V_ult still shows a slight increase, which suggests that the vertical bearing capacity is more complexly affected by the coupling of multiple soil layers. The lower soil layers (NC, LNC) still contribute to the end resistance. As the end resistance represents the force between the suction anchor end and the soil it contacts, it can also be seen from Figure 6 that an end-resistance influence zone exists. This means that the end resistance of the suction anchor is related to the strength of the soil within a certain area around the end of the suction anchor.

4.3. The VH Failure Envelopes

The VH failure envelopes for layered soil are shown in Figure 8. By dimensionless processing of horizontal and vertical bearing capacities using H₀/γ′D and V₀/γ′D, respectively, the effects of parameters such as suction anchor dimensions and soil weight are eliminated.

Figure 8. The results of VH failure envelopes: (a–c) S_um/kD = 0.4, T_h/L = 0.5, 0.75, 1.25; (d–f) S_um/kD = 0.67, T_h/L = 0.5, 0.75, 1.25; (g–i) S_um/kD = 1, T_h/L = 0.5, 0.75, 1.25.

As shown in Figure 8, with the increase in the LOC layer thickness ratio T_h/L (from 0.5 to 1.25), the horizontal bearing capacity of the VH failure envelopes significantly increases under the same vertical load. This indicates that the total area of the VH failure envelopes expands, which means that the corresponding combined uniaxial bearing capacity improves. The LOC soil layer exhibits relatively high strength. As the thickness ratio T_h/L increases, the contact area between the suction anchor and the high-strength clay expands. This allows the anchor–soil interface to provide more uniform and substantial lateral friction resistance. Consequently, when horizontal loads increase, the attenuation of vertical loads becomes more gradual. The research findings align with the conclusions of Zhao et al. [52], indicating that the embedment length of suction anchors in high-strength soil layers is positively correlated with the combined bearing capacity.

The VH failure envelopes in layered clay exhibit asymmetry, which indicates that layered clay has a distinct influence on the horizontal and vertical bearing capacities of suction anchors. The horizontal friction resistance of the suction anchors dominates when horizontal loads dominate, with the thickness of the LOC layer determining the horizontal bearing capacity. When vertical loads dominate, the friction resistance at the anchor–soil interface and the end resistance play key roles, while the vertical bearing capacity is influenced by both the LOC and the underlying NC and LNC layers. By combining the results with Figure 8c,f,i, it can also be observed that when T_h/L = 1.25, the suction anchor is fully embedded in the LOC layer. As the strength of the NC and LNC layers varies, the horizontal pullout bearing capacity of the suction anchor remains nearly constant, while the corresponding vertical pullout bearing capacity slightly increases with the increase in the strength of the NC and LNC layers.

To visually represent the relative shape of the VH failure envelope, the results can be normalized based on the uniaxial bearing capacity H₀ and V₀. Extensive research indicates that the only lower bound solution of the VH failure envelope can be observed through relevant processing, which shows that the normalized VH failure envelope is independent of soil layer thickness and soil properties [53,54]. This conservative solution method allows the yield envelope in the VH envelope to be obtained simply by scaling H₀ and V₀. Based on previous research findings and regression analysis, the lower bound of the VH failure envelope, as shown in Figure 9, and can be expressed as follows:

$${\displaystyle \frac{H_0}{H_{ult}}}={\left\{1-{\left({\displaystyle \frac{V_0}{V_{ult}}}\right)}^3\right\}}^{1/0.85}$$

(4)

where ${\displaystyle \frac{V_0}{V_{ult}}}$ represents the normalized vertical bearing capacity and ${\displaystyle \frac{H_0}{H_{ult}}}$ represents the normalized horizontal bearing capacity. The exponent 1/0.85 indicates that the vertical bearing capacity reduces the capacity of the horizontal bearing capacity. Meanwhile, the ultimate bearing capacity of the suction anchors installed in layered clay can be obtained by multiplying the corresponding ultimate bearing capacities H_ult and V_ult by Equation (4).

Figure 9. The normalized VH failure envelope.

5. Discussion

In this paper, the bearing capacity of suction anchors subjected to inclined loads in upper-stiff–lower-soft layered clay is systematically investigated. The numerical simulation results indicate that the clay strength S_um/kD and the thickness ratio T/L are the core factors determining the bearing capacity of layered clay. To investigate the difference in bearing capacity of suction anchors in layered clay and homogeneous clay under inclined loading, the same numerical model shown in Figure 1 was employed to analyze the pullout bearing capacity of suction anchors for different clay strengths S_um/kD (Clay A to Clay D), as listed in Table 1. The optimum centerline loading depth, uniaxial ultimate load capacity, and VH failure envelopes under the corresponding operating conditions were investigated.

It can be seen from Figure 10 that for homogeneous clay with varying S_um/kD, as the clay strength increases, Z_cl,opt decreases from 0.71 to 0.69. The increase in S_um/kD indicates a higher proportion of shear strength near the mud surface, shifting the center of gravity of the anchor shear strength upward. According to the principle of moment equilibrium, to prevent anchor rotation, Z_cl,opt shifts slightly upward. Overall, Z_cl,opt exhibited little change.

Figure 10. Optimal centerline loading depth Z_cl,opt for suction anchors in homogeneous clay.

Compared with the results in Section 4.1, it can be observed that the homogeneous clay Zcl,opt is solely influenced by S_um/kD, which has a more stable variation pattern. For layered clays, Z_cl,opt is primarily affected by the LOC layer, while the influence of the NC and LNC layers on Zcl,opt is masked by the high-strength LOC layer. This indicates that layered soils differ from homogeneous soils in their single correlation of ‘S_um/kD-Z_cl,opt,’ with the thickness of high-strength soil layers being the core variable controlling Z_cl,opt. By comparing with the findings of Fu et al. [29] for homogeneous clay Z_cl,opt, the accuracy of the constructed numerical model can be further validated.

In combination with Figure 11, it can be observed that, as S_um/kD increases, the uniaxial ultimate bearing capacity grows synchronously. However, the rate of increase varies: when S_um/kD rises from 0.4 to 1.0, the horizontal ultimate bearing capacity H_ult increases from 2915.65 kN to 5095.8 kN (an increase of approximately 74.8%), whereas the vertical ultimate bearing capacity V_ult increases from 3976.02 kN to 7317.5 kN (an increase of approximately 84.0%). The increase in H_ult is more pronounced. This difference stems from the distinct mechanisms governing bearing capacity. Horizontal bearing capacity relies on the uniform mobilization of lateral friction resistance throughout the entire anchor length; as S_um/kD increases, lateral friction resistance at all anchor depths rises synchronously. In contrast, because the vertical bearing capacity is simultaneously influenced by end resistance, this also results in a greater increase in the vertical ultimate bearing capacity than in the horizontal ultimate bearing capacity.

Figure 11. Uniaxial ultimate bearing capacity H_ult and V_ult for homogeneous clay.

In comparison with Section 4.2, it is evident that H_ult in layered clay is largely unaffected by the thicknesses of the NC and LNC layers. When T_c/L increases from 0.5 to 1.25, H_ult remains nearly constant, being controlled solely by the LOC layer thickness T_h/L, whereas V_ult is influenced by both T_h/L and T_c/L. When T_c/L increases to 1.25, V_ult increases by approximately 35%. This contrasts with the behavior in homogeneous clay, where both H_ult and V_ult are governed by a single S_um/kD. Horizontal bearing capacity is more sensitive to the upper high-strength soil layer, while vertical bearing capacity is influenced by the coupled effects of multiple soil layers.

The VH failure envelopes for homogeneous clay are shown in Figure 12. By comparing with Section 4.3, it can be observed that the VH envelopes of layered clay exhibit distinct differences from those of homogeneous clay. Specifically, when the horizontal bearing capacity is high, the envelope retains relatively high vertical bearing capacity, with the LOC layer providing significant lateral friction resistance. Conversely, when the vertical bearing capacity is high, the envelope corresponds to a decrease in bearing capacity, where the anchor tip may be located in the NC or LNC layer, resulting in reduced end resistance.

Figure 12. The VH failure envelopes for homogeneous clay.

A comprehensive analysis reveals significant differences in the pullout resistance of suction anchors in homogeneous clay and layered clay. While extensive research has focused on the bearing capacity of suction anchors in homogeneous clay, it is essential to investigate their pullout resistance in layered clay.

6. Limitations

This study conducted a series of pullout bearing capacity analyses for suction anchors with a commonly used L/D = 1.5 in engineering applications, specifically within upper-stiff–lower-soft clay. It systematically investigated the effects of upper-stiff–lower-soft layered clay on the optimal centerline loading depth Z_cl,opt, uniaxial ultimate bearing capacity H_ult and V_ult, and VH failure envelopes of suction anchors. The findings provide a theoretical basis and practical guidance for optimizing the design and safety assessment of suction anchor foundations in layered clay. However, certain limitations remain.

(1)

This paper investigates the pullout bearing capacity of suction anchors subjected to inclined loads in layered clay with upper-stiff–lower-soft. In practical engineering, layered clay exhibits diverse characteristics, such as upper-stiff–lower-soft, upper-soft–lower-hard, soft–hard–soft, and hard–soft–hard, etc. Therefore, based on existing research, a systematic investigation into the bearing capacity of suction anchors in layered clay is necessary.

(2)

This paper investigates the pullout bearing capacity of suction anchors with a L/D = 1.5 in layered clay. In practical engineering applications, the L/D of suction anchors varies according to project design (ranging from L/D = 1 to 10). Therefore, further research is required to study the pullout bearing capacity in layered clay under a wide range of L/D.

(3)

This paper only systematically analyzes the pullout capacity of suction anchors and does not examine in detail how pullout capacity varies with different padeyes. Further research is needed to analyze the pullout capacity of suction anchors at different padeyes under inclined loads.

Therefore, subsequent research should systematically investigate the bearing capacity of suction anchors under different layered soils (upper-stiff–lower-soft, upper-soft–lower hard, soft–hard–soft, and hard–soft–hard, etc.), varying L/D, and different padeyes locations. By normalizing relevant data, the pullout resistance capacity of suction anchors in different layered soils should be evaluated, and the corresponding design framework based on numerical analysis should be proposed.

7. Conclusions

In this paper, finite element numerical simulations were conducted to investigate the pullout capacity of suction anchors under inclined loading. This study examined the effects of varying soil parameters S_um/kD and layer thickness ratios T_h/L and T_c/L on the optimum centerline loading depth Z_cl,opt, uniaxial ultimate bearing capacity (H_ult and V_ult), and VH failure envelope of suction anchors. The main conclusions are as follows.

(1)

The layer thickness ratio Th/L of the LOC is the core factor controlling Z_cl,opt. When the suction anchor partially embeds into the LOC layer, as the LOC layer thickness increases, the upper portion of the suction anchor contributes more lateral friction resistance. To balance the moments, the suction anchors Z_cl,opt shifts downward. When the suction anchor is fully embedded in the LOC soil layer, Z_cl,opt depends solely on the parameters of the LOC soil mass.

(2)

The thickness ratio T_h/L of the LOC soil layer is the core factor determining the uniaxial ultimate bearing capacity, as the undrained shear strength of the LOC layer is significantly higher than that of the NC layer. As the length of the suction anchor embedded into the LOC layer increases, the combined effect of lateral friction resistance and end resistance at the anchor–soil interface becomes more pronounced. The layered soil makes the soil strength along the clay surface exhibit non-uniformity. The increase in S_um/kD enhances the uniaxial bearing capacity of layered clay. The thickness of the NC layer T_c/L, has little effect on the horizontal ultimate bearing capacity H_ult but significantly influences the vertical ultimate bearing capacity V_ult.

(3)

The strength of the LOC soil is relatively high. As the thickness ratio T_h/L increases, the contact area between the suction anchor and the high-strength clay expands, providing more uniform and greater lateral friction at the anchor–soil interface. When the horizontal bearing capacity increases, the decrease in vertical bearing capacity becomes more gradual. The lower bound solution for the VH failure envelope of the corresponding layered soil has been obtained.

(4)

A comparative analysis of the pullout bearing capacity of suction anchors under inclined loads in layered clay and homogeneous clay reveals that soil layering significantly affects the bearing capacity of suction anchors. In homogeneous clay, the pullout bearing capacity of suction anchors is solely influenced by the soil strength S_um/kD. In contrast, the pullout bearing capacity in layered clay is affected by factors including the soil strength S_um/kD and the soil layer thickness ratio T/L.