Advances in Research for Mechanical Characteristics of Vertically Loaded Anchors for Offshore Platforms under Cyclic Loads

Abstract

Vertically loaded anchors (VLAs) are widely used as mooring foundations in marine environments. Their working conditions typically involve deep-sea seabed, frequently subjected to cyclic loads induced by wind, waves, and currents. Therefore, understanding the mechanical properties of VLAs under cyclic loading is essential for ensuring the safety of mooring systems. This paper summarizes the current research status on the mechanical properties of VLAs under cyclic loading, analyzing the mechanisms by which cyclic loads affect these properties. Additionally, it reviews and summarizes the research methods applied to studying VLAs under cyclic loading, discussing the issues inherent in various methodologies. Finally, it provides an outlook on future research into VLAs under cyclic loading, laying the groundwork for subsequent studies on the bearing mechanisms of novel VLAs, such as the double-plate vertically loaded anchor (DVLA), under cyclic loading.

1. Introduction

Advancements in energy extraction technology have prompted a shift from terrestrial to marine environments for the development of oil and gas resources. To facilitate these extraction activities, floating structural platforms are increasingly employed in marine settings. The positioning of offshore floating structures relies on the mooring system, which includes mooring foundations, mooring lines, and the moored floating structure. Among them, the catenary and taut mooring systems [1] are the primary technologies used for anchoring these offshore platforms, as shown in Figure 1; in catenary mooring systems, the cable is suspended from the sea surface with the bottom end of the cable embedded in the seabed, and in taut mooring systems, the cable is straightened and taut. Within these systems, the suction anchor, gravity anchor, suction embedded plate anchor, and gravity-penetrating anchor, depicted in Figure 2, are widely preferred [2]. Offshore structures are consistently exposed to natural forces such as wind, waves, and currents, which subject these anchors to cyclic loading. Therefore, a comprehensive analysis of the mechanical properties of VLAs under cyclic loading is crucial to ensure the stability of offshore floating platforms. This research is essential for advancing our understanding of structural dynamics in challenging marine environments.

Extensive research has been conducted by both domestic and international scholars on the mechanical performance of VLAs under cyclic loading. Through model tests, Li et al. [2], Datta et al. [3], Khatri et al. [4], and Singh et al. [5] have demonstrated the effects of static load ratio, cyclic load ratio, and other factors on the bearing capacity and deformation instability of VLAs. Additionally, Li et al. [6] and Andersen et al. [7] have employed theoretical analysis methods to elucidate the influence of soil properties on the bearing capacity of VLAs under cyclic loading. Their work also analyzes the combined effects of static and cyclic loads on the bearing capacity of anchors in soft soils. Furthermore, numerical simulations by Qiao et al. [8], Wang et al. [9], Liu et al. [10], Wang et al. [11], and Cheng et al. [12] have explored the impacts of burial depth, number of load cycles, and other variables on the ultimate uplift-bearing capacity and deformation instability of traditional drag anchors under cyclic loading. The aforementioned research methods each focus on specific aspects, lacking an integrated approach that integrates different methodologies. This limitation impedes the robust cross-validation of experimental, simulation, and theoretical data. Additionally, current studies on the mechanical performance of bearing anchors under cyclic loading predominantly concentrate on their load-bearing capacity, exhibiting a rather narrow research focus. This approach tends to overlook the impact of the complex working environment on the mechanical behavior of bearing anchors.

This paper reviews the research methodologies and key findings related to the mechanical properties of VLAs subjected to cyclic loading, emphasizing the shortcomings of current research approaches. Additionally, it offers a perspective on future research directions and topics concerning the mechanical behavior of VLAs under cyclic conditions. Moreover, this review establishes a foundation for subsequent studies on the mechanical performance of various types of VLAs [13] under cyclic loading.

2. Mechanical Characterization of VLAs under Cyclic Loading

For the investigation of the mechanical characteristics of VLAs under cyclic loading, the performance of these anchors often varies due to differences in anchor types, soil properties [14], and the nature of the cyclic loading [15]. This section offers a comprehensive review of current research methodologies, encompassing model testing, theoretical analysis, and numerical simulation.

2.1. Model Test Method

Experimental studies conducted on the mechanical performance of VLAs subjected to cyclic loading offer crucial insights into the intricate soil movement patterns and failure instability states [16,17]. These investigations are instrumental in identifying influential factors and lay the groundwork for practical engineering applications. Therefore, numerous domestic and international scholars have embarked on experimental endeavors to assess the bearing capabilities of these anchors.

The bearing capacity of traditional drag anchors is notably influenced by the amplitude and frequency of cyclic loading. In this context, Datta et al. [3], Khatri et al. [4], Singh et al. [5], and Yu et al. [18] have conducted scaled model tests to scrutinize the movement behavior of traditional drag anchors under cyclic loading. Their observations reveal that high-frequency cyclic loading [19] leads to significant displacements in drag anchors. Furthermore, as the cyclic loading level intensifies, there is a growing tendency towards cyclic failure of the VLAs.

The study of normal bearing anchors has been explored by various scholars, who have developed a unidirectional cyclic loading device using displacement sensor, force sensor, guide cylinder, and water tanks (as indicated in Figure 3a,b). Subsequent small-scale model tests were conducted to investigate the failure criteria and deformation instability mechanisms under combined static and cyclic loading. For instance, Li et al. [2] and Cheng et al. [20] utilized a unidirectional cyclic loading device to measure the cumulative displacement of the bearing anchor and the forces on the anchor plate under cyclic loading. They further validated and extended the unidirectional cyclic loading conditions using a directional cyclic loading device, enabling scaled experiments on bearing anchors under 1 g conditions. Their research revealed the bearing mechanism of normal bearing anchors under cyclic loading, established the relationship between displacement failure and anchor plate embedment depth, and clarified that under consistent loading conditions, higher cyclic loading frequencies are more likely to cause anchor failure. These studies also found that the combination of static and cyclic loading results in increased cumulative displacement with the number of cycles, which is another primary cause of deformation instability.

Furthermore, changes in the number of cycles can alter the ultimate pullout resistance of the VLAs [21,22,23,24,25]. Liu et al. [10] investigated the bearing mechanisms of suction anchors under combined static and cyclic loading in taut mooring systems. Through model tests, they concluded that the failure mode of suction anchors subjected to monotonic inclined static loads at the optimal mooring point depends on the friction between the anchor sidewall and the soil layer, the self-weight of the anchor, the weight of the soil plug, and the properties of the soil layer below the anchor base. Additionally, the characteristics of cyclic loading can alter the instability and failure modes of suction anchors. For example, Wang et al. [11] analyzed the deformation and failure processes of suction anchor foundations under different static load ratios and cyclic load ratios through model tests. Their research indicated that the primary cause of instability and failure of suction anchor foundations is the increase in cumulative displacement due to cyclic loading.

The double-plate vertically loaded anchor (DPVLA) is a novel offshore platform-anchoring foundation. Through scaled experiments, Xing et al. [26] investigated the differences in bearing performance between the new anchor and traditional drag anchors. Their research revealed that the overall bearing capacity of the new DPVLA surpasses that of traditional drag anchors. Furthermore, in ultimate loading tests, increasing the angle between the plates significantly enhances the bearing capacity of the DPVLA, with the optimal plate angle being 30°.

For the existing cyclic loading experiments, the direction of the applied cyclic load is predominantly aligned with the direction of the cable. This method of loading does not accurately replicate the actual conditions experienced by VLAs. For instance, in model tests of VLAs, cyclic loads are applied along the direction of the mooring line on the anchor plate’s surface. However, in marine environments, the cable is subjected to cyclic loads not only along its length but also perpendicular to the mooring line, as illustrated in Figure 4, Therefore, it is essential to design an experimental apparatus that accounts for the cyclic loading effects perpendicular to the mooring line.

2.2. Theoretical Analysis Method

In the theoretical study of structural anchor mechanics under cyclic loading, Andersen et al. [7] first proposed a failure mode for suction anchors subjected to inclined loads at optimal mooring points, as depicted in Figure 5. In this failure mode, the anchor experiences pure translation without rotation.

Andersen et al. [7] explored the stability of offshore platform foundations under cyclic loading conditions and introduced the cyclic strength of the soil as a criterion for soil deformation failure. Specifically, when a soil element meets the deformation failure criterion after a certain number of cycles, the combined initial static stress and cyclic stress on the shear failure plane is defined as the cyclic strength failure criterion of the soil (as denoted in Equation (1)). Utilizing this failure criterion, they developed a pseudo-static limit equilibrium analysis method. This method estimates the ultimate bearing capacity of the soil, offering a reference framework for the failure and instability criteria of VLAs. Nevertheless, in practical engineering applications, the soil experiences significant deformations upon reaching its ultimate bearing capacity, suggesting that additional experimental validation is needed to confirm the accuracy of this method.

$${\sigma }_{f,d}={({\sigma }_f+{\sigma }_d)}_f$$

(1)

where σ_f,d represents cycle strength of soil, σ_f denotes axial static deviatoric stress, and σ_d is axial cyclic stress.

In theoretical analyses, the unconsolidated undrained cyclic shear strength of soil is a critical determinant of the bearing capacity of anchors. Li et al. [6] examined this parameter specifically for saturated soft soil, employing the limit equilibrium analysis method to evaluate the bearing capacity of taut suction anchors under combined cyclic loads. Their study introduced two approaches for determining the average shear stress within different failure zones of the soil, which were subsequently used to define the undrained cyclic strength of soft clay. Utilizing these methods, the cyclic bearing capacity of suction anchors was calculated through the limit equilibrium analysis, with the relevant formulas provided in Equations (2)–(5).

Based on the proposed methods for determining the average shear stress in different failure zones, the normalized cyclic shear strength of suction anchors in saturated soft soil was established. It was found that the cyclic bearing capacity of suction anchors decreases to varying degrees under different numbers of combined cyclic load cycles.

$$H=H_{\mathit{passive}}-H_{\mathit{active}}+H_{\mathit{passive},\mathit{side}}+H_{\mathit{active},\mathit{side}}+H_{\mathit{anchor},\mathit{side}}+H_{\mathit{anchor},\mathit{deep}}+H_{\mathit{anchor},\mathit{tip}}$$

(2)

where H_passive denotes the passive earth pressure in the horizontal direction, H_active represents the active earth pressure in the horizontal direction, H_passive,side is the backward horizontal shear resistance, H_active,side denotes the forward horizontal shear resistance, H_anchor,side is the horizontal shear force acting on the upper portion of the suction anchor, H_anchor,deep represents the horizontal force acting on the anchor, and H_anchor,tip is the horizontal shear force at the bottom of the suction anchor.

$$V=T_{\mathit{active}}-T_{\mathit{passive}}+T_{\mathit{anchor},\mathit{side}}+T_{\mathit{anchor},\mathit{deep}}+V_{\mathit{anchor},\mathit{tip}}$$

(3)

where T_active is the vertical shear force in the soil of the active zone, T_passive denotes the vertical shear force in the soil of the passive zone, T_anchor,side represents the vertical downward force acting on the front and back faces of the suction anchor, T_anchor,deep denotes that the suction anchor is subjected to vertical downward forces from all around, and V_anchor,tip is the reverse bearing capacity acting on the bottom of the suction anchor.

When the anchor is in a state of limit equilibrium considering vertical cracks, the total horizontal resistance H and total vertical resistance V are as follows:

$$H=H_{\mathit{passive}}+H_{\mathit{passive},\mathit{side}}+H_{\mathit{anchor},\mathit{side}}+H_{\mathit{anchor},\mathit{deep}}+H_{\mathit{anchor},\mathit{tip}}$$

(4)

$$V=T_{\mathit{anchor},\mathit{side}}+T_{\mathit{anchor},\mathit{deep}}+V_{\mathit{anchor},\mathit{tip}}-T_{\mathit{passive}}$$

(5)

In real-world settings, VLAs are subjected to the combined effects of oceanic cyclic loads and static loads, resulting in a complex stress state. Liu et al. [10] explored the bearing capacity of taut suction anchors under these combined loads by integrating the plastic upper-bound analysis method with the pseudo-static analysis method. The determination of the bearing capacity of suction anchors under combined cyclic loads was based on the cyclic strength of the soil layer, following a systematic approach: First, the undrained static shear strength of the surface layer of soft clay was utilized to calculate the static ultimate bearing capacity of the anchor using the plastic upper-bound analysis method. Next, the horizontal and vertical bearing capacity coefficients of the soil around the anchor’s sidewall at the limit state were defined and determined based on established formulas, facilitating the calculation of the average load on the soil. These formulas were then integrated to determine the normalized average shear stress ratio of the soil surrounding and beneath the anchor. By combining the experimentally obtained static strength of the soil with these calculation methods, the ultimate bearing capacity of the anchor under the combined action of static and cyclic loads, referred to as the cyclic bearing capacity, was derived. The calculation formulas are provided in Equations (6)–(9).

The plastic upper-bound analysis method and the pseudo-static method examine the soil–anchor interaction from a mechanical standpoint, facilitating a precise determination of the ultimate bearing capacity of suction anchors under cyclic loads. Nevertheless, in real marine environments, cyclic loads can induce soil softening, leading to a reduction in the actual cyclic bearing capacity of the anchor compared to the theoretical value. Consequently, further experimental investigations or finite element analyses are necessary to quantitatively assess the extent of soil softening under cyclic loading conditions.

The horizontal component of the static ultimate bearing capacity is as follows:

$$F_{f,H}=F_f\mathit{cos}\theta =N_H{\displaystyle \underset{L_f}{\int }{\mathit{DS}}_{u1}\mathit{dz}}$$

(6)

where F_f,H denotes the horizontal component of the static ultimate bearing capacity, θ is the angle between the loading direction and the horizontal direction, N_H represents the horizontal bearing capacity factor of the soil, D is the internal energy dissipation rate of the soil, S_u1 represents the undrained shear strength of the soil, and L_f is the penetration depth of the anchor.

The vertical component of the static ultimate bearing capacity is as follows:

$$F_{f,V}=F_f\mathit{sin}\theta =N_V{\displaystyle \underset{L_f}{\int }D\alpha S_{u1}\mathit{dz}+V_b}$$

(7)

where F_f,V is the vertical component of the static ultimate bearing capacity, F_f denotes the static ultimate bearing capacity of the anchor, N_V represents the vertical bearing capacity factor of the soil, α is the friction coefficient, and V_b is the reverse bearing capacity of the anchor.

The horizontal component of the average load is as follows:

$$F_{a,H}=F_a\mathit{cos}\theta =N_H{\displaystyle \underset{L_f}{\int }D{\tau }_{a1}\mathit{dz}}$$

(8)

where F_a,H represents the horizontal component of the average load, F_a is average load, and τ_a1 denotes the equivalent average shear stress of the anchor.

The vertical component of the average load is as follows:

$$F_{a,V}=F_a\mathit{sin}\theta =N_V{\displaystyle \underset{L_f}{\int }D\alpha {\tau }_{a1}\mathit{dz}+V_{b,a}}$$

(9)

where F_a,V is the vertical component of the average load, and V_b,a denotes the reverse bearing capacity of the anchor.

Under long-term oceanic cyclic loads, soft clay undergoes stiffness softening, leading to a reduction in soil strength. As the number of cycles increases, the cyclic deformation of the soil gradually increases, resulting in changes to the soil’s elastic modulus. To investigate the relationship between the bearing performance of anchors and the soil’s elastic modulus, Cheng et al. [12] introduced a modulus softening coefficient ζ, to calculate the maximum elastoplastic modulus during the Nth cycle, with the calculation formula provided in Equation (10). The introduction of the modulus-softening parameter for soft clay makes the calculation results closer to the observed data from actual engineering projects. However, its applicability is limited, and further validation is needed to determine whether it is suitable for other types of soils.

The maximum elastoplastic modulus of the soil during the Nth cycle is as follows:

$$H_{\mathit{max}}^N={\zeta H}_{\mathit{max}}^1$$

(10)

where $H_{\mathit{max}}^N$ represents the maximum elastoplastic modulus corresponding to the Nth cycle, and $H_{max}^1$ is the maximum elastoplastic modulus on the initial loading path.

The double-plate vertically loaded anchor (DPVLA), as a novel type of normal bearing anchor, renders traditional bearing capacity formulas inapplicable for its load-bearing calculations. In response to this, Xing et al. [27] proposed an improved bearing capacity formula for the DPVLA model, based on the empirical formula of the VLA model. The calculation formula is provided in Equation (11). Using this improved formula, the bearing capacity coefficients of the DPVLA under shallow and deep embedding conditions were found to be 5.013 and 4.106, respectively. Furthermore, Li et al. [28,29] validated the applicability of the bearing capacity calculation formula by investigating the embedding performance of the DPVLA. Although the improved calculation formula provides specific bearing capacities, the reliability of these results requires further verification through full-scale model tests and centrifuge model tests.

$$UPC=1.866.N_c.A.s_u$$

(11)

where UPC denotes ultimate bearing capacity of the DPVLA, N_c is bearing capacity coefficient, A represents anchor plate area of the DPVLA, and s_u is undrained shear strength of the soil.

The theoretical investigations into the mechanical performance of VLAs under cyclic loading have predominantly concentrated on the calculation of bearing capacity [30]. These studies have comprehensively examined the influence of soil properties on the bearing capacity of anchors, offering significant reference points for further research. However, the bearing capacity calculations in these studies involve numerous assumed parameters and neglect critical factors such as anchor weight, mooring line weight, and the direction of cyclic loads. Consequently, the existing bearing capacity calculation formulas require further derivation and validation using actual engineering data.

2.3. Numerical Simulation Method

Numerical simulation methods, in comparison to other analytical approaches, provide significant advantages, including broad applicability, rapid solving speed, substantial data processing capacity, safety, and cost-effectiveness, which have led to their extensive use in various experimental studies. Among these methods, the finite element method (FEM) [31] stands out as an effective numerical simulation technique for analyzing the stress distribution and deformation characteristics within complex structures. As a result, an increasing number of scholars are employing finite element analysis to investigate the mechanical performance of VLAs.

The current research employing finite element software to simulate the mechanical behavior of VLAs under cyclic loading primarily emphasizes the constitutive relationships of the soil. For instance, Cheng et al. [12] utilized finite element software to characterize the cyclic stress–strain response of soft clay. By leveraging the bounding surface theory, they developed an elastoplastic-bounding surface model for soft clay and examined the influence of embedment depth on the bearing performance of suction anchors under combined cyclic loads. Similarly, Li et al. [2] devised models for both shallowly and deeply embedded VLAs. Their findings revealed that variations in the embedment depth of the anchor plate lead to soil compaction along the mooring line direction and substantial displacement of the anchor plate. Additionally, a cavity forms as the bottom of the anchor plate detaches from the soil. Under shallow embedment conditions, significant soil surface heaving is observed (as shown in Figure 6a), whereas deep embedment conditions do not produce noticeable surface failure (as depicted in Figure 6b).

For the finite element analysis, there is no universally accepted criterion for determining the embedment depth boundary of VLAs. For instance, Ruinen et al. [32] define the boundary between shallow and deep embedment failure as three times the width of the anchor plate, while DNV et al. [33] suggest a boundary of 4.5 times the anchor plate width. Varying embedment depths significantly increase the computational workload in finite element analysis. Furthermore, under deep embedment conditions, the nonlinear behavior of both soil and anchor becomes more pronounced, necessitating more refined nonlinear analysis methods to accurately capture these behaviors, thereby further increasing computational complexity. Consequently, establishing a reasonable criterion for determining the embedment depth boundary of VLAs is imperative.

When investigating the bearing performance of plate anchors under cyclic loading, Yu et al. [34,35] utilized finite element analysis software to quantify the strain-softening parameters of soft clay under these conditions. The research findings indicate that under low-stress conditions, repeated cyclic loading induces the formation of a cavity beneath the anchor plate, significantly reducing the residual bearing capacity of the anchor (as illustrated in Figure 7). Conversely, under high-stress conditions, as the number of cycles increases, the strain-softening behavior of the clay leads to an increase in plastic shear strain, resulting in a decrease in the bearing capacity of the anchor (as shown in Figure 8). By quantifying the strain-softening parameters, the study more accurately simulated the mechanical behavior of soft clay under cyclic loading, thereby enhancing the credibility of the simulation results. However, the finite element model employed in the experiment simplified actual working conditions and did not fully account for the complex interactions between the soil and the anchor plate, which may result in discrepancies between the simulation outcomes and real-world conditions. Furthermore, the study primarily focused on low- and high-stress conditions, without thoroughly investigating the bearing performance under intermediate stress levels, potentially limiting the generalizability of the study’s conclusions.

To further explore the influence of soil-constitutive relationships on the mechanical performance of VLAs under cyclic loading, some researchers have employed interface subroutines within finite element software to develop the necessary material constitutive models. For example, Wang et al. [11] created a subroutine utilizing finite element software to simulate the stress–strain response of soft clay under unconsolidated undrained conditions. This effort resulted in the formulation of an incremental elastoplastic finite element method capable of tracking cyclic load history to analyze the deformation of saturated soft clay under combined cyclic loads. By applying this method, they were able to analyze and predict the deformation behavior of suction anchors subjected to cyclic loading. The research findings indicate that during vertical failure, the suction anchor is extracted from the soil layer, causing slight soil heaving (as shown in Figure 9a). In contrast, during horizontal failure, the vertical deformation of the suction anchor is minimal, but significant horizontal deformation occurs, accompanied by noticeable soil heaving and cracking (illustrated in Figure 9b). Developing constitutive models for ideal materials facilitates a clear analysis and prediction of certain mechanical behaviors of VLAs. However, the parameters within the soil-constitutive model significantly influence the analysis results; minor variations in these parameters can lead to substantial fluctuations in the outcomes, thereby increasing uncertainty. Consequently, it is essential to comprehensively consider multiple factors to enhance the reliability and accuracy of the analysis.

Li et al. [6] proposed a quasi-dynamic viscoelastic–plastic finite element method to analyze the cyclic deformation instability process of suction anchors under cyclic combined loads. By setting the initial cyclic shear model and damping ratio, an equivalent viscoelastic analysis step calculation was performed under the combined action of static load and cyclic load at the i-th stage. The flowchart for calculating the cyclic deformation and cumulative deformation of the suction anchor is shown in Figure 10. The established quasi-dynamic viscoelastic–plastic-constitutive model successfully predicted the model test results of the stress–strain relationship of soil elements under the combined action of cyclic loads. Additionally, using the quasi-static elastoplastic finite element method, the cyclic bearing performance of tensioned suction anchors under cyclic combined loads was also successfully predicted.

Considering the dynamic response of soil during vibration, Feng et al. [36] introduced a pseudo-dynamic algorithm to model the deformation process of suction anchors in soft soil under cyclic loading. This algorithm effectively predicts the cumulative deformation of the soil subjected to both static and cyclic loads without the need to track detailed stresses within the soil elements, thereby successfully forecasting the deformation of suction anchors. On the other hand, Wang et al. [9] proposed a pseudo-static algorithm to assess the variation in bearing capacity of suction anchors in soft soil under cyclic loading. This method leverages the undrained strength of soft soil and employs elastoplastic finite element analysis to generate load–displacement curves and determine the cyclic bearing capacity of anchors based on displacement failure criteria. Additionally, they examined the impact of load cycles and failure modes on the cyclic bearing capacity of anchors using this approach. The research findings suggest that under normalized static load conditions, factors such as loading direction, geometric anchor dimensions, and the friction coefficient of the anchor’s outer wall have a negligible effect on the relationship between normalized cyclic load capacity and load cycle failure times. The normalized cyclic load capacity curve is predominantly influenced by the normalized static load, as demonstrated in Figure 11. When suction anchors experience vertical and lateral failure, the cyclic bearing capacity of the anchors shows a decreasing trend with the increase in the number of load cycles. This trend is observed across different embedment depths, load angles, and static load ratio conditions. Furthermore, the predictive results obtained from the quasi-static finite element method are slightly lower than the model test results, with an average deviation not exceeding 10%.

The pseudo-dynamic and pseudo-static viscoelastic–plastic finite element methods provide a detailed simulation of soil–anchor interactions under cyclic loading, presenting an innovative analytical approach. However, the efficacy of these methods heavily depends on the selection of appropriate parameters and precise model calibration, both of which necessitate substantial experimental data. Inaccurate parameter selection can significantly compromise the reliability of the computational outcomes.

When analyzing the mechanical properties of VLAs subjected to cyclic loading through numerical simulation methods, it is feasible to comprehensively account for the influences of soil-constitutive relationships, the characteristics of cyclic loads, and the material properties of the anchor plate [35,37,38,39]. This methodology effectively compensates for the constraints of certain experimental conditions and broadens the applicability of model tests. Nevertheless, simplifications in boundary conditions and material properties inherent in numerical analysis can lead to variations in accuracy and introduce both subjective and objective errors. Hence, it is imperative to judiciously integrate numerical simulation methods with experimental and theoretical approaches to mitigate the limitations associated with each analytical method.

3. Conclusions

This paper synthesizes the model tests, theoretical analyses, and numerical simulations employed in existing studies on the mechanical performance of VLAs under cyclic loading, serving as a reference for investigating the mechanical behavior of other types of VLAs under similar conditions. By addressing the limitations inherent in current research methodologies, it outlines prospects for future studies on the mechanical properties of anchored foundations subjected to cyclic loading. The following aspects are recommended for further discussion and exploration:

(1) Existing research primarily addresses the mechanical properties of VLAs under unidirectional cyclic loading, typically considering cyclic forces aligned with the mooring line direction. However, the effects of cyclic loads perpendicular to the mooring line axis, which are pertinent to real-world engineering applications, remain insufficiently explored. To comprehensively understand the mechanical behavior of VLAs under realistic conditions, further investigation into their response to multi-directional cyclic loading is essential.

(2) Theoretical analysis methods for calculating the bearing capacity of anchors under cyclic loading often involve numerous assumptions and empirical parameters, leading to discrepancies with actual conditions. Although the limit equilibrium analysis and upper bound plasticity analysis methods are well-established, incorporating soil-softening parameters into these calculations could reduce reliance on empirical parameters and enhance the accuracy of bearing-capacity predictions. This approach could also be applicable to the study of other novel anchor systems.

(3) In practical applications, VLAs are embedded in the seabed and subjected to cyclic loads. These loads can cause the attached mooring lines to cut through the embedded soil layers, disturbing the soil and consequently affecting its shear strength. Considering soil disturbance as a critical factor may offer a novel perspective for analyzing the mechanical properties of VLAs under cyclic loading.

(4) The bearing capacity is the most critical indicator for evaluating the performance of anchor bearings. However, different research methods can result in significant discrepancies in the estimated bearing capacity. Model testing is the most direct approach to investigating the bearing performance of anchor bearings under cyclic loading, providing relatively reliable results through various experimental conditions. Numerical simulations can serve as an auxiliary method to validate the conclusions drawn from model experiments. However, due to the complex motion behaviors induced by the characteristics of cyclic loading, numerical simulations often fail to accurately calculate the bearing capacity of anchor bearings, leading to deviations in the results. Theoretical analysis simplifies the force processes involved in calculating the bearing capacity under cyclic loading and introduces numerous parameters, many of which are empirically derived. These parameters offer significant reference values for calculating the bearing capacity of the same type of anchor bearings. In summary, to ensure the reliability of experimental data, it is essential to integrate all three research methods for a comprehensive evaluation of the bearing performance of anchor bearings under cyclic loading.

Numerous studies, both domestically and internationally, have extensively investigated the mechanical properties of VLAs in cohesive soils subjected to cyclic loading. However, the understanding of bearing mechanisms in sandy soils remains limited. Furthermore, under the influence of marine loads, sandy soils are susceptible to liquefaction, resulting in decreased soil density and loosening, which negatively impact the performance of VLAs. Consequently, targeted engineering tests are essential to explore the effects of soil liquefaction on the mechanical properties of VLAs. In addition, research on a novel type of bearing anchor—double-plate vertically loaded anchor—has demonstrated that its ultimate uplift capacity surpasses that of traditional bearing anchors under the same soil conditions. Currently, studies on double-plate vertically loaded anchors have primarily focused on predicting drag trajectories and static loading experiments. However, there remains a significant gap in systematic theoretical analysis and experimental validation of their mechanical behavior under cyclic loading. Therefore, future research should prioritize the following areas: First, it is recommended to conduct cyclic loading experiments on double-plate vertically loaded anchors to thoroughly investigate their deformation characteristics and failure mechanisms under long-term loading conditions. Second, based on experimental results, corresponding numerical models should be developed to simulate the response behavior of double-plate vertically loaded anchors under varying soil conditions and load frequencies, thereby providing more reliable theoretical support for their application. Finally, combined with field tests, the adaptability and long-term performance of double-plate vertically loaded anchor in practical engineering applications should be assessed.