Parametric Sensitivity Analysis of Mooring Chains of a Floating Offshore Wind Turbine in Shallow Water

Abstract

Floating offshore wind turbines (FOWTs) are severely restricted in numerous sea areas due to challenges from the strong nonlinear characteristics of mooring chains in shallow water (less than 50 m). Therefore, this paper introduces a design method of mooring chains of a FOWT at a water depth of 44 m and carries out a parametric sensitivity analysis on length, nominal diameter, and clump weights of mooring chains. The results of the study found that compared with the mooring chains in deep water, the mooring chains in shallow water show obvious nonlinear characteristics in mooring tension, the lying section of the mooring chain on the seabed, and the mooring chain spatial angle, which brings great risk to the safe operation of FOWTs. The change in the nominal diameter of the mooring chain has a certain impact on the dynamic characteristics of a FOWT, but it is not as significant as that from the change in the length of the mooring chain. In addition, a mooring chain in shallow water is prone to the slack–taut phenomenon; thus, this paper puts forward an optimization investigation using clump weights at the suspension section of the mooring chain, which improved the performance of the mooring chain significantly.

1. Introduction

Since the beginning of this century, with people’s attention on the climate and environmental pollution caused by fossil fuels, more and more new power sources have increasingly shifted toward clean and renewable energy. Among them, offshore wind power, as a renewable energy with good commercial potential, has been increasing in scale in the past decade. Nowadays, the development trajectory of offshore wind power is also like what the oil and gas industry has gone through, constantly moving from onshore to offshore. Hence, floating offshore wind turbines (FOWTs) have become one of the important means for offshore wind power in the future [1].

There are four types of FOWTs based on their hydrostatic stability, such as the spar type, semi-submersible type, tension-leg type, barge type, and hybrid types [2]. In 2009, the world’s first FOWT demo, Hywind, was installed in Norway [3]. In 2017, Statoil invested in the construction of the world’s first floating offshore wind farm on the northeast coast of Scotland with five spar-type FOWTs [4]. In 2020, the Windplus consortium invested in the construction of the world’s first semi-submersible floating offshore wind farm, WindFloat Atlantic, with a total installed capacity of 25 MW along the coast of Portugal [5]. At present, the construction of Hywind Tampen, a floating offshore wind farm with a total capacity of 95 MW, 140 km offshore in the Norwegian North Sea, is underway [6]. DNV GL (2020) [7] predicts that the global scale of floating wind power is expected to reach 260 GW by 2050. Although FOWTs have been demonstrated as a potentially huge market, it still faces a demand for cost reduction. According to some statistics [8], the mooring cost of floating wind farms accounts for more than 20% of the total construction cost of the entire floating offshore wind farm.

The mooring system is crucial for keeping a position of a FOWT within an admissible offset [9]. A mooring system consists of mooring lines, anchors, gravity and buoyancy accessories, etc. [10]. According to the spatial shape of the mooring lines [11], it can be roughly divided into catenary mooring lines, tensioned mooring lines, and tension-leg mooring lines. According to the materials used in mooring lines [12], it can be roughly divided into a mooring chain, steel rope, and high-polymer mooring lines. Due to the advantages of a low manufacturing cost, the ease of manufacturing, and high strength, the catenary mooring chain is the most popular used for FOWTs. In the marine environment, the mooring lines of a FOWT will withstand alternating tension for a long time during operation; thus, the design of FOWT mooring chains mainly focuses on the ultimate (ULS), accidental (ALS), and fatigue (FLS) limit state design criteria [13]. Masciola et al. [14] performed a comparison of simulations for a FOWT using both quasi-static and dynamic mooring line models and found that while the dynamics of the mooring lines have a minimal impact on the platform’s movements, it is significant for line tension and fatigue. Li et al. [15] used a fully nonlinear dynamic algorithm to conduct a fully coupled transient mooring lines breakage analysis on the OC3-Spar FOWT and found that the wind turbine will experience significant drift motion when the mooring lines breaks, and the tension of the remaining mooring lines will decrease subsequently. Bae et al. [16] studied the effects of different mooring lines’ breakage on the response of FOWTs and analyzed the effects of wind turbine operation and shutdown on the motion response after mooring line breakage. Sedghi and Kimlaei [17] conducted a fatigue sensitivity analysis of the design parameters of mooring lines of a FOWT using a dynamic mooring line simulation method.

FOWTs are often deployed in sea areas deeper than 100 m. However, due to poor geological conditions of the seabed, certain shallow water areas are unsuitable for the deployment of bottom-fixed offshore wind turbines when considering technical feasibility and economic viability. Therefore, the deployment of FOWTs in sea areas within 100 m or even 50 m has gradually attracted people’s attention [18]. In China, several floating wind turbine prototypes have been developed in shallow waters around 50 m, such as the “Three Gorges Pilot” semi-submersible floating wind turbine (30 m depth), the “Fu-Yao” semi-submersible floating wind turbine (65 m depth), the “Guoneng-Shared” semi-submersible floating wind turbine (35.7 m depth), and the “Mingyang Smart Energy” semi-submersible floating wind turbine (45 m depth). During the implementation of these projects, shallow water mooring chains pose significant challenges in design and result in higher costs. Xu et al. [19] found that the changes in mooring line tension and the stiffness of a FOWT in shallow water exhibit significant nonlinearity, and the mooring line tension sharply increases with the increase in the floating body displacement. Huang and Yang [20] conducted an investigation on the water depth variation impact on the catenary mooring of a FOWT in Taiwan western offshore areas, and the results show that the cost of mooring chains at the water depth of 50 m is the highest among the testing water depths from 50 to 100 m. Benassai et al. [21] conducted an analysis of the impact of both the quantity and type of mooring lines of a tri-floater semi-submersible FOWT over a water depth range of 50 to 300 m. Their findings indicated that the platform’s permissible offset and the configuration of the lines significantly affect the weight of the mooring system. Similarly, Campanile et al. [22] carried out a study on the design and selection of mooring systems for FOWTs in intermediate and deep water environments, examining the influence of line quantity, the permissible offset of the platform, line scope, etc.

Although the above research has to some extent revealed partial characteristics of mooring chains of a FOWT in shallow water, a detailed introduction to the design process, influencing factors, and optimization methods of the mooring chain of a FOWT in shallow water remain thin. This paper will conduct a sensitivity study on the design parameters of mooring chains of a 10 MW semi-submersible FOWT at a water depth of 44 m in the South China Sea. Thus, the impact of different chain lengths, nominal diameters, and counterweights on the tension, lying section, spatial shape, and dynamic responses of the 10 MW semi-submersible FOWT are assessed, which will provide relevant technical references for the mooring chain design of FOWTs in shallow water.

This paper is organized as follows: the parameters of the FOWT and the design and analysis method are introduced in Section 2. Load case tests used for a parametric sensitivity analysis of the mooring chains are set in Section 3. The influence of the length of the mooring chains, the nominal diameter of the mooring chains, and the clump weight of the mooring lines (weight, position, quantities) on the static and dynamic characteristics of the FOWTs is investigated in Section 4. At the end of the paper, several important conclusions are drawn in Section 5.

2. Model and Methodology

2.1. Parameters of the Floating Offshore Wind Turbine

The OO-Star platform supporting the DTU-10 MW wind turbine was developed by Olav Olsen [23]. The floating foundation is a like a “Y”-shaped pontoon structure, with a central column and three side columns. This specific floating platform is shown in Figure 1, and the parameters are listed in

Table 1. Parameters of the OO-Star FOWT.

	Unit	Value
Mass of blades	kg	230,717
Mass of nacelle	kg	446,006
Mass of tower	kg	1.257 × 106
Height of tower	m	104.63
Mass of concrete platform (excl. tower and mooring systems)	kg	2.1709 × 107
Center of gravity	m	−15.225
Draft	m	22.0
Displacement	m3	2.3509 × 104

. The original mooring system of the OO-Star FOWT at a water depth of 130 m with three catenary chains at an angle of 120° [23] is shown in Figure 2. The nominal diameter of the mooring chain is 137 mm and the length of the mooring chain is 703 m, with a 50 t clump weight at a distance of 118 m from the fairlead along the chain.

2.2. Design of Mooring Chains in Shallow Water

The mooring chains mentioned above should be redesigned to work at a water depth of 44 m in the shallow water area of the South China Sea. The design process of the mooring system can be drawn as shown in Figure 3. The design goal of the mooring system was to meet the requirements of the horizontal offset limit of the floating platform and the strength of mooring lines at a reasonable cost. Therefore, in the design process of the mooring system, it was necessary to ensure that the maximum tension of the mooring chain was less than the breaking load with a certain safety margin. In addition [13], it was necessary to ensure that the anchor point did not bear the uplift force from the mooring chain, that is, to ensure there was a sufficient length of the lying section of the mooring chains on the seabed. Finally, if all requirements were met, the fatigue analysis of the mooring system was carried out to check whether the fatigue damage exceeded the requirements of the relevant specifications. Due to the limitation of the length of the paper, the mooring chain fatigue is not discussed here.

According to the specification DNVGL-OS-E302 [13], the proof load, breaking load, and the weight per unit length of a mooring chain in different grades class were calculated, and the results are listed in

Table 2. Proof load, breaking load, and weight of mooring chains [13].

Iterm	Grade R3	Grade R3S	Grade R4	Grade R4S	Grade R5
Proof load, stud link (kN)	0.0156D2 (44-0.08D)	0.0180D2 (44-0.08D)	0.0216D2 (44-0.08D)	0.0240D2 (44-0.08D)	0.0251D2 (44-0.08D)
Proof load, studless (kN)	0.0156D2 (44-0.08D)	0.0174D2 (44-0.08D)	0.0192D2 (44-0.08D)	0.0213D2 (44-0.08D)	0.0223D2 (44-0.08D)
Breaking load (kN)	0.0223D2 (44-0.08D)	0.0249D2 (44-0.08D)	0.0274D2 (44-0.08D)	0.0304D2 (44-0.08D)	0.0320D2 (44-0.08D)
Weight, stud link (kg/m)	0.0219D2
Five-link length (mm)	Minimum 22D and Maximum 22.55D

Note: D is the chain nominal diameter.

. Referring to the original mooring design [23], the R4 grade chain was selected and the nominal diameter of the mooring chain was tested at 137 mm, 127 mm, and 117 mm, respectively.

According to the DNVGL-OS-E301, the effective elastic modulus should not be less than 5.6 × 10¹⁰ N/m² for grade R3/R4/R5 stepped mooring chains. Therefore, the elastic modulus of the mooring chain is taken as 5.6 × 10¹⁰ N/m² in the study. The parameters of mooring chains with different nominal diameters calculated are listed in

Table 3. Testing parameters of mooring chains in shallow water.

Item	Unit	Chain I	Chain II	Chain III
Nominal diameter	m	0.137	0.127	0.117
Mass of chains per unit length (in air)	kg/m	411.041	353.225	299.789
Weight of chains per unit length (in water)	N/m	3505.4	3012.4	2556.6
Equivalent hydro-diameter	m	0.257	0.239	0.220
Axial stiffness (EA)	N	1.6510 × 109	1.4188 × 109	1.2041 × 109
Proof load	kN	1.3395 × 104	1.1789 × 104	1.0242 × 104
Breaking load	kN	1.6992 × 104	1.4955 × 104	1.2993 × 104

.

The length and anchor position of the mooring chain is calculated based on the formula according to reference [23], and the mooring configuration is shown in Figure 2.

$$L_i=h\sqrt{2{\displaystyle \frac{T_{\max }}{\omega h}}-1}$$

(1)

$$x={\displaystyle \frac{T_{\max }-\omega h}{\omega }}ar\cos \mathrm{h} \left[1+h\left({\displaystyle \frac{\omega }{T_{\max }-\omega h}}\right)\right]$$

(2)

where $L_i$ is the length of a mooring chain; x is the horizontal distance from the anchor to the fairlead point (the fairlead is located on the deck of the floating platform, with a distance of 9.5 m above the still water surface); and h represents the vertical distance from the fairlead points to the seabed. The water depth is set to 44 m, so the vertical height h = 44 + 9.5 = 53.5 m; $\omega$ represents the wet weight per unit length of the chain and the maximum tension $T_{max}$ can be taken as proof load of the mooring chain. Referring to the original mooring chains with a section diameter of 137 mm (Chain I in Table 3), by substituting $T_{max}$ = 1.6992 × 10⁷ N and $\omega =3505.4 \mathrm{N}/\mathrm{m}$ into Equations (1) and (2), the length of the mooring chain and the position of the anchor point can be calculated. The other design parameters of the mooring chains at the water depth of 44 m are listed in

Table 4. Preliminary design parameters of the mooring chains.

Item	Values
Quantity of mooring lines	3
Angle between adjacent mooring chains	120°
Vertical distance from fairlead to water surface (m)	9.5
Radius of fairlead from centerline of floating body (m)	44
Vertical distance between anchor point and water surface z (m)	−44
Horizontal distance between anchor point and fairlead x (m)	634.184
Radius from anchor point to center line of floating body (m)	678.18
Length of unextended mooring chain (m)	637
Seabed stiffness (Pa/m)	3.0 × 106
Seabed damping (PaS/m)	3.0 × 105

.

2.3. Analysis Method

A parametric sensitivity analysis of the mooring chains of the FOWT in shallow water was studied using static and dynamic methods, as presented in Figure 4. In the static analysis method, the mooring chains of the FOWT were simulated using SIMA V3.5 software [24] with the bar element model. The mass and stiffness characteristics of the element were input according to the parameters described in Table 4. For the specific mooring chain, the shape and tension load of the mooring chain were studied with different horizontal offsets of the floating platform in a static analysis. The results were then processed by the MATLAB program to investigate the impact of the mooring changes from different design parameters. On the other hand, the dynamic analysis was conducted using the wind turbine’s numerical simulation software FAST V8, developed by the Renewable Energy Laboratory [25]. The testing load cases were set up for an investigation on the dynamic characteristics of the mooring chains according to the hydrometeorological data in the South China Sea. First, a finite element model of the floating platform was established by SESAM-GeniE V8.4 software [26] and relevant frequency–domain hydrodynamic transfer functions of the floating platform were solved by SESAM-HydroD V4.10, which was used as the input files in the hydrodynamic module of the FAST V8 software. Then, the mooring chains were simulated using the MoorDyn module [27]. Finally, a sensitivity analysis of the dynamic responses of the FOWT was conducted according to different mooring chain parameters. After all that, the design scheme of the mooring system was determined.

3. Testing Cases Setting

In this study, several testing cases were selected for the following time domain numerical simulations of the FOWT with the mooring chains: still water, rated operations, and an extreme shutdown condition, respectively. The corresponding environmental parameters of the above conditions are shown in

Table 5. Testing cases setting.

Load Cases	Still Water	Rated Operation	Extreme Shutdown
	(DLC. 1)	(DLC. 2)	(DLC. 3)
Direction (deg)	0.0	0.0	90.0
Wind speed (m/s)	0.0	11.4	56.2
Wind shear index	0.0	0.067	0.096
Significant wave height (m)	0.0	1.75	11.53
Wave period (s)	0.0	7.5	14.93
Peak elevation parameter	0.0	3.3	3.3
Current speed (m/s)	0.0	0.46	1.19

. As listed in the table, the still water condition is used to check the initial static state of the mooring chains when the FOWT stays in equilibrium position. The rated operation sea state corresponds to the normal operation conditions of the FOWT at rated wind speed. Under extreme conditions, according to the design load case recommended in the LIFES50+ report [23], the extreme wind speed in a 50-year period (10 min average wind speed) at the hub height, the maximum significant wave height, and the peak period in a 50-year return period are selected. In order to fully understand the dynamic characteristics of the mooring system, two incident directions of 0° and 90° are selected for the conditions.

$$V_{\mathrm{w}}=V_{\mathrm{H}}·{\left({\displaystyle \frac{h}{H_{ref}}}\right)}^{\alpha }$$

(3)

where $H_{ref}$ is the reference height at the hub of 119 m and $V_{\mathrm{H}}$ and $\alpha$, respectively, represent the horizontal wind speed and wind shear index at $H_{ref}$, according to Table 5.

The irregular wave is defined by the JONSWAP spectrum, in which the significant wave height and spectral peak period are defined in Table 5. The sea current flow profile is defined as

$$U_{SS}\left(Z\right)=U_{0_{SS}}·{\left({\displaystyle \frac{Z+d}{d}}\right)}^{1/7}$$

(4)

where Z represents the submergence distance under the surface of the water; d represents the water depth of the sea area, which is 44 m; and the representative surface current speed $U_{0_{SS}}$ is determined according to the values in Table 5.

4. Results and Discussion

4.1. Length of Mooring Chains

4.1.1. Static Characteristics Analysis

Figure 5 compares the tension results of mooring chains with the same nominal diameter of 137 mm but different chain lengths. It can be found that the pre-tension of the mooring chains in shallow water (44 m) is less than that of the original mooring chain at a water depth of 130 m, except for the 637 m long one. The pre-tension of the original mooring chain at the water depth of 130 m is 1.647 × 10⁶ N. In contrast, the pre-tension of the D137L637 mooring chain is 5.319 × 10⁶ N, the pre-tension of the D137L647 mooring chain is 8.406 × 10⁵ N, the pre-tension of the D137L652 mooring chain at the water depth of 44 m is 5.127 × 10⁵ N, and the pre-tension of the D137L657 mooring chain at the water depth of 44 m is 3.689 × 10⁵ N (where D represents the nominal diameter of the chain and L represents the length of the chain). Although the shorter mooring chain has a larger pre-tension, the tension of the mooring chain increases more significantly with the same offset of the FOWT with more obvious nonlinear characteristics, which is not conducive to mooring safety.

According to Figure 6, the design schemes of D137L652 and D137L657 in shallow water are close to the stiffness of the original mooring system at the water depth of 130 m within the horizontal offset from −15 m to 15 m. However, with the increase in offset displacement, the restoring force of the mooring system increases significantly, which is one of the most important characteristics of the mooring system in shallow waters. In general, a conclusion can be drawn that the length of a mooring chain in shallow water has a great impact on the mooring chain stiffness characteristic.

The spatial shape of a mooring chain with different lengths is compared in Figure 7. Although there was a certain length of the lying section on the seabed in the initial state, with the increase in the horizontal offset of the FOWT, all the mooring chains that were 637 m (Figure 7a) or in 647 m (Figure 7b) long were lifted up completely, which cannot meet the design requirements of keeping a sufficient length of the lying section on the seabed. According to Figure 7d, if the length of the mooring chain is too large (i.e., L = 657 m), although a sufficient length of the lying section is ensured within the testing horizontal offset, the mooring chain is in a very loose state and cannot provide sufficient restoring force (see Figure 5). It can be seen from Figure 7c that the mooring chain with a length of 652 m has a sufficient length of the lying section on the seabed with the change in the offset displacement and has good mooring restoring stiffness at the same time (see Figure 6).

As shown in Figure 8, it can be found that when the horizontal offset of the FOWT exceeds 5 m, although the surge motion of the FOWT increases by only a few meters, the mooring chain will be lifted up by tens of meters or even more. Taking the D137L652 mooring chain as an example, when the offset of the FOWT increases from 10 m to 15 m, the length of the lying section of the mooring chain decreases from 433.8 m to 274.3 m, that is, the lying section of the chain on the seabed is lifted up by 159.5 m. In contrast, the chain is only lifted up by 32 m under the same offset of the FOWT with the original mooring chains at the water depth of 130 m. This is also a significant difference in mooring chains between deep water and shallow water. Therefore, for the mooring chains in shallow water, special attention should be paid to the length of the mooring chain lying on the seabed, so as to prevent the chain from being lifted up completely when the FOWT has a large displacement.

The variation in the mooring chain angle for different lengths of mooring chains is compared in Figure 9. It can be seen that the angle between the mooring chain and the horizontal plane increases significantly as the length of the mooring chain increases. This is because increasing the length of the chain will make the mooring chain more slack, which is closer to the state of vertical suspension, thus leading to the increase in the angle between the mooring chain and the horizontal plane. By comparing the mooring chains in shallow water and that at a 130 m water depth, it can be found that the mooring chain angle in shallow water changes dramatically with the same offset of the FOWT. Taking the D137L652 mooring chain as an example, during the displacement of the FOWT from 0 m to 20 m, the mooring angle decreases from 51.4° to 9.7°; however, the mooring angle only decreased from 57.8° to 42.9° for the mooring chain at a deep water depth. The restoring force of the mooring system is determined by the mooring chain tension and the mooring angle, so the change in the mooring angle will affect the stiffness characteristics of the mooring system. When the mooring angle between the chain and the horizontal plane changes greatly, the stiffness performance of the mooring system will also change dramatically.

From the above results, it can be clearly seen that the mooring chains in shallow water show significant differences and stronger nonlinearities in the stiffness performance, length of the lying section, and the mooring chain angle when compared to the original mooring chain at the water depth of 130 m, which increases the design difficulty of the mooring chain system in shallow water.

4.1.2. Dynamic Characteristics Analysis

The static analysis is investigated above for the mooring chain with a diameter of 137 mm and different lengths of chains; then, the dynamic response analysis in the time domain will be carried out in accordance with the testing load cases in Table 5 so as to analyze the impact of different design lengths of the mooring chain on the dynamic responses of the FOWT.

(1) Rated operation condition

The load case DLC. 2 is carried out and the statistical results of surge motion are compared in Figure 10. The mean, maximum, and minimum of surge motion increase with the increase in the length of the mooring chain, which is due to the fact that the longer the mooring chain is, the more slack and less tense the chain is, thus giving rise to the horizontal motion of the FOWT under the rated operation condition.

The time-series of the tension force at fairlead#1 (labeled in Figure 2) under the rated operation condition (DLC. 2) is shown in Figure 11, and the statistical results are shown in Figure 12. According to the results, the mean, maximum, and minimum tension decrease with the length of the mooring chain, which is consistent with the result shown in the static analysis aforementioned. The maximum tensions of the mooring chains with a length of 647 m, 652 m, and 657 m under the rated operation condition are 2.232 × 10⁶ N, 1.985 × 10⁶ N, and 1.900 × 10⁶ N, respectively; the corresponding safety factors are 7.613, 8.560, and 8.943, respectively.

(2) Extreme conditions

In the extreme condition (DLC. 3), the wind turbine is parked under the extreme condition for a 50-year return period. The statistical results of the sway motion of the FOWT are shown in Figure 13. It can be seen that the mean, maximum, and minimum values of the sway motion increase with the length of the mooring chain. In addition, it is found that the sway motion of the FOWT for the D137L657 design scheme reaches more than 30 m, which is very likely to cause damage to the transmission cable of the FOWT [23].

The time-series of tension at fairlead#3 (labeled in Figure 2) under the extreme condition is shown in Figure 14, and the statistical results are shown in Figure 15. As can be seen, the tension force generally decreases with the increase in the length of the mooring chain under the extreme condition. The maximum tensions of the mooring chain at 647 m, 652 m, and 657 m long are 1.075 × 10⁷ N, 1.040 × 10⁷ N, and 1.027 × 10⁷ N, respectively, and the corresponding safety factors are 1.58, 1.63, and 1.65, respectively, which cannot meet the requirements. In addition, as shown in Figure 14, the minimum tension of the mooring chain is close to zero (in slack state) but the maximum tension reaches the order of 10⁶ N and the range of tension variation is large, which are “slack-taut effects”. The resulting snap load is not conducive to the safe use of the mooring chain; thus, it should be improved by adding clump weights later.

In general, the change in the length of the mooring chain has a great impact on the horizontal motion (surge/sway) of the FOWT, and the mean and maximum values of the horizontal motion increase with the length of the mooring chain, especially in the extreme sea state, in which the displacement limitation of the FOWT needs to be taken into full consideration and the length of the mooring chain must be chosen reasonably. However, the length of the mooring chain should not be too short, otherwise it will lead to excessive tension of the mooring chain and cannot meet the safety requirements as well. By comprehensively analyzing the dynamic characteristics of different mooring chain lengths in the testing cases, the length of 652 m was deemed appropriate to ensure the limiting requirements of the tension of the mooring chains of the FOWT.

4.2. Nominal Diameter of Mooring Chains

The effect of the length of the mooring chain has been analyzed above, and the chain with a length of 652 m has been screened to meet the design requirements preliminarily. In the following section, the static and dynamic characteristics of the mooring system are investigated by varying the nominal diameter of the mooring chain as 137 mm, 127 mm, and 117 mm, respectively, and the results are compared with the original mooring chain at the water depth of 130 m.

4.2.1. Static Characteristics Analysis

Figure 16 compares the results of the mooring chain tension with different nominal diameters, and Figure 17 shows the horizontal stiffness curves of the mooring system. The black dashed lines in the figures represent the original mooring system at the water depth of 130 m. As can be seen from Figure 16, the difference in the trend of the tension curves of the mooring chain with different nominal diameters is not obvious. In comparison, the larger the nominal diameter of the mooring chain, the larger the tension of the mooring chain at the same offset. This is due to the fact that the mooring chain with a larger nominal diameter has a greater weight per unit length. However, the effect of the change in nominal diameter on the mooring chain tension is not as great as the effect of the change in mooring chain length mentioned above. In addition, it can be found that the pre-tension of the mooring chains in shallow water is less than that of the original mooring chain at the 130 m water depth. The pre-tension of the original mooring chain is 1.647 × 10⁶ N, and those of the shallow water mooring chain with diameters of 137 mm, 127 mm, and 117 mm are 5.127 × 10⁵ N, 4.40 × 10⁵ N, and 3.733 × 10⁵ N, respectively. A too small pre-tension of the mooring chain may lead to excessive slack in the mooring line, which is not conducive to the station-keeping of a FOWT.

The spatial shape of the mooring chain with different nominal diameters is compared in Figure 18. The curves in Figure 18 exhibit a high degree of agreement in their spatial shapes and patterns of variation. In addition, Figure 19 presents that the change in the nominal diameter of the mooring chain has little effect on the length of the lying section of the mooring chain on the seabed. The change in the angle between the mooring chain and the horizontal plane at the fairlead with different nominal diameters is shown in Figure 20. In general, the change in the nominal diameter of the mooring chain has little effect on the mooring chain angle.

For a mooring chain in catenary form, its restoring force depends on the relationship between the weight of the suspended portion of the chain and the floating platform’s offset. A larger nominal diameter results in a heavier unit length of the suspended chain, thereby influencing the stiffness of the catenary chain. However, the shape of the catenary chain is primarily determined by the positions of its two endpoints and the length of the chain. Therefore, changes in the chain nominal diameter have minimal impact on the spatial configuration.

4.2.2. Dynamic Characteristics Analysis

(1) Rated Operation Condition

The statistical results of surge motion under the rated operation condition are shown in Figure 21. It can be seen that the mean, maximum, and minimum values of surge motion decrease with the increase in the nominal diameter of the mooring chain. This is due to the fact that a larger nominal diameter of mooring chains gives rise to greater tension in the mooring chain, thereby better limiting the movement of the FOWT. Therefore, it is recommended to select the larger-diameter mooring chains to limit the movement of the FOWT, but that means a higher cost.

The time history curve of the tension force at fairlead#1 under the rated operation condition is shown in Figure 22, and the statistical results are shown in Figure 23. It can be seen that the mean, maximum, and minimum values of the tension force at the fairlead increase with the nominal diameter of the mooring chain. Under the rated operation condition, the maximum tensions of the mooring chains with nominal diameters of 137 mm, 127 mm, and 117 mm are 1.775 × 10⁶ N, 1.935 × 10⁶ N, and 1.907 × 10⁶ N, respectively, with corresponding safety factors of 9.573, 7.729, and 6.813, respectively. It can be seen that the mooring chain with a nominal diameter of 137 mm has the largest safety margin.

(2) Extreme Conditions

The statistical results of the sway motion are shown in Figure 24. It can be seen that the mean, maximum, and minimum of the sway motion decrease with the increase in the mooring chain nominal diameter. The maximum sway motion of the FOWT in all three design schemes exceeds 25 m (half of the water depth); the one with the 117 mm diameter has the largest sway motion.

The time history curve of the tension force at fairlead#3 under the extreme shutdown conditions (DLC. 3) is shown in Figure 25. It can be seen that the mean, maximum, and minimum values of the mooring chain tension force at the fairlead with different nominal diameters do not vary significantly. Moreover, the maximum tensions of the mooring chain with 137 mm, 127 mm, and 117 mm diameters are 1.040 × 10⁷ N, 1.001 × 10⁷ N, and 9.552 × 10⁶ N, respectively, with corresponding safety factors of 1.63, 1.49, and 1.36, respectively, as shown in Figure 26.

In general, the change in the nominal diameter of the mooring chain has a certain impact on the dynamic characteristics of a FOWT, but it is not as significant as that in the length of the mooring chain. As the nominal diameter of the mooring chain increases, the mean and maximum values of the horizontal movement decrease as well. This is mainly due to the fact that the larger nominal diameter of the mooring chain gives rise to a larger weight per unit length, which provides a large horizontal restoring force and can limit the movement of the FOWT at the same time. Moreover, it was found that the safety factors of mooring chains with nominal diameters of 117 mm and 127 mm were too small to ensure the safe use of the mooring system. Therefore, it is recommended to choose the mooring chain with a nominal diameter of 137 mm to ensure that the mooring tension meets the design requirements among the optional scope of the test.

4.3. Clump Weights of Mooring Chains

4.3.1. Static Characteristics Analysis

(1) Weight of a clump weight

From the above analysis, it can be seen that the mooring chain in shallow water exhibits a “slack-taut effect” under the extreme sea conditions due to its insufficient pre-tension. Therefore, it is necessary to add clump weights to increase the pre-tension of the mooring chain to mitigate the “slack-taut effect”. Taking the mooring chain with a nominal diameter of 137 mm and a length of 652 m as an example, 60 t, 50 t, and 40 t clump weights are set up at 60 m from the fairlead to investigate the influence of different weights of clump weights on the mooring chains.

The tension curve of a single mooring chain with different clump weights is compared in Figure 27. It can be seen that the pre-tension of the mooring chain has increased after adding the clump weight but is still less than the original design at the water depth of 130 m (1.647 × 10⁶ N). In comparison, the pre-tension of the D137L652 mooring chain is 5.127 × 10⁵ N; the pre-tension of the D137L652 mooring chain with a 40 t clump weight is 1.086 × 10⁶ N; the pre-tension of the D137L652 mooring chain with a 50 t clump weight is 1.225 × 10⁶ N; and the pre-tension of the D137L652 mooring chain with a 60 t clump weight is 1.362 × 10⁶ N. Compared with Figure 5 mentioned above, adding clump weights is more effective than shortening the length of the mooring chain in increasing the pre-tension.

Comparing the tension curve of the D137L652 pure mooring chain with that with added clump weights, it can be found that the tension curve of the mooring chains with clump weights shifts upward by a certain distance during a small offset in Figure 27, but the overall trend in the tension–offset relationship remains unchanged. That is, the addition of clump weights increases the tension of the mooring chain, but it hardly changes the stiffness characteristics of a mooring chain. When the displacement of the FOWT is large, the stiffness curve of the D137L652 pure mooring chain changes very significantly, which is not conducive to the safety of the mooring system, while the stiffness curve of the mooring chain with clump weights changes relatively smoothly.

It can be seen in Figure 28, the influence of different weights of the clump weight on the stiffness curve under a small offset is compared. It can be obtained from the figure that the horizontal restoring force provided by the original deep water mooring system is 2.421 × 10⁵ N when the displacement of the FOWT is 5 m. The horizontal restoring force provided by the D137L652 pure mooring chain in shallow water is 4.154 × 10⁵ N; the horizontal restoring force provided by the D137L652 mooring chain with a 40 t clump weight is 5.885 × 10⁵ N, which is 41.7% greater than that of the pure mooring chains; the horizontal restoring force provided by the D137L652 mooring chain with a 50 t clump weight is 6.301 × 10⁵ N, which is 51.7% greater than that of the pure mooring chain; and the horizontal restoring force provided by the D137L656 mooring chain with a 60 t clump weight is 6.706 × 10⁵ N, which is 61.4% greater than that of pure mooring chain. It can be seen that increasing the weight of clump weights can greatly improve the horizontal restoring force of the mooring system, which is beneficial to the station-keeping of the mooring system.

In summary, it can be concluded that increasing the clump weights and shortening the length of the mooring chain can both increase the pre-tension of the mooring chain, but shortening the length of the mooring chain will give rise to more dramatic changes in the restoring stiffness of the mooring chain. In contrast, increasing the clump weights can not only significantly increase the pre-tension of the mooring chain but also maintain the restoring stiffness of mooring chains, keeping it almost unchanged or even slightly slowed down. Therefore, it is recommended to use the design scheme of D137L652 with clump weights to improve the stiffness characteristics of a mooring system under extreme sea conditions. However, as the weight of the clump weights increases, the cost of the mooring chain increases accordingly. Therefore, it is recommended to consider the results of dynamic analysis and cost factors comprehensively for selection.

The spatial shape of the D137L652 mooring chain with different clump weights is compared in Figure 29. In the initial state, the clump weights are roughly located at a depth of 32 m underwater. All design schemes have a sufficient length of the lying section on the seabed even if the FOWT moves at a horizontal offset of 20 m. It can be found in Figure 29 that changing the weight of clump weights has little effect on the spatial shape of the mooring chain. Comparing Figure 29 with Figure 18c, which shows the comparison of the configuration of mooring chains with or without clump weights, it can be found that when there is a negative offset, that is, when the mooring chain is in a slack state, the clump weights have a significant impact on the spatial shape of the mooring chain; when there is positive offset of the FOWT, that is, when the mooring chain is stretched, the impact of the clump weights on the spatial shape of the mooring chain is relatively small.

When the FOWT undergoes horizontal displacement, the change in the lying section of the mooring chain with different clump weights is compared in Figure 30. It can be seen that when the horizontal offset of the FOWT remains unchanged, the length of the lying section of the D137L652 pure mooring chain is greater than that of the D137L652 mooring chain with clump weights. However, as the displacement of the FOWT increases, the gap between the mooring chains with different clump weights gradually decreases. In addition, it can be found that the length of the lying section of the mooring chain with a 40 t clump weight is the largest and that with the 60 t clump weight is the smallest under the same offset of the FOWT. Therefore, it can be found that the larger the weight of the clump weight, the smaller the length of the lying section of the mooring chain under the same displacement. From the perspective of ensuring a sufficient length of the lying chain, the smaller clump weight scheme should be selected as much as possible. However, the difference is not significant, generally within 10 m within the scope of testing, which means that the change in clump weight has little impact on the length of the lying section of the mooring chain.

When the FOWT undergoes horizontal displacement, the angle between the mooring chain and the horizontal plane with different clump weights is compared in Figure 31. It can be observed from the figure that after adding the clump weights, the angle between the mooring chain and the horizontal plane changes more gently as the FOWT moves. After adding the clump weights, the initial angle between the mooring chain and the horizontal plane decreases, and the smaller the clump weight, the smaller the angle. Comparing the results of different clump weights, it can be observed that the angle between the mooring chain and the horizontal plane decreases as the weight of clump weights increases when the FOWT displacement is small. However, when the FOWT displacement is large, the angle between the mooring chain and the horizontal plane increases as the clump weight increases. However, overall, the change in clump weights has little effect on the size of the angle, only within a few degrees.

(2) Position of a clump weight

The previous sections analyzed the impact of different weights of the clump weights on the stiffness of the mooring system, the length of the lying section on the seabed, and the mooring chain angle. By comprehensive consideration, the design scheme of the mooring chain with a 60 t clump weight is the best choice in the preliminary analysis. Next, the impact of a 60 t clump weights at different positions on a mooring chain is investigated by placing 60 t clump weights at 40 m, 50 m, and 60 m along the mooring chain from the fairlead to the anchor position.

The tension curve of the D137L652 mooring chain with a 60 t clump weight at different locations is shown in Figure 32. It can be seen that the change in the position of the clump weights has little effect on the tension of a single mooring chain. In addition, the pre-tension is 1.362 × 10⁵ N with the clump weights at the 60 m position; the pre-tension is 1.324 × 10⁵ N with the clump weights at the 50 m position; and the pre-tension is 1.269 × 10⁵ N with the clump weights at the 40 m position. It can be seen that as the clump weights move downward, the pre-tension of the mooring chain slightly increases, but the change in the tension curve trend is not significant.

Figure 33 shows the horizontal restoring stiffness curve of the mooring system after changing the position of the clump weight. It can be seen that the change in the position of the clump weight has little effect on the horizontal restoring force of the mooring system, which is consistent with the results of the tension curve of a single mooring chain. When the displacement of a FOWT is 5 m, the horizontal restoring force provided by the original mooring system at a 130 m water depth is 2.421 × 10⁵ N. The horizontal restoring force provided by the D137L652 pure mooring chain in shallow water is 4.154 × 10⁵ N; the horizontal restoring force provided by the mooring system with a 60 t clump weight located at 60 m is 6.706 × 10⁵ N, which is 61.4% higher than the pure mooring chain; when the clump weight is located at 50 m, the horizontal restoring force provided is 6.501 × 10⁵ N, which is 56.5% higher than the pure mooring chain; and when the clump weight is located at 40 m, the horizontal restoring force provided is 6.314 × 10⁵ N, which is 52.0% higher than the pure mooring chain.

It can be concluded that the restoring stiffness of the mooring system is increased for a clump weight placed as close to the seabed as possible. In addition, if the clump weight is placed too close to the water surface, it will be rising up and falling down from the water surface frequently and accelerating corrosion. Therefore, it is recommended to place the clump weight close to the seabed in the suspended section, taking into account the influence of the range of heave motion so that the clump weight will not repeatedly touch the seabed frequently.

(3) Quantities of clump weights

The impact of the weight and position of a clump weight to the mooring chain have been analyzed above. The following analysis will focus on the influence of quantities of clump weights. The scheme of a mooring chain with two clump weights will be compared with that of a mooring chain with a clump weight or the pure mooring chain in order to investigate the impact of the number of clump weights on the mooring chain.

Using a mooring chain with a nominal diameter of 137 mm and a length of 652 m, the following design schemes are set up: no clump weight (D137L652); a 50 t clump weight attached at the length of 60 m of the mooring chain (D137L652 + 50 t); a 60 t clump weight attached at the same position (D137L652 + 60 t); a 50 t clump weight attached at the length of 60 m of the mooring chain and an additional 10 t weight attached close to the tangent point between the mooring chain and the seabed (D137L652 + 50 t + 10 t); and a 60 t clump weight attached at the length of 60 m of the mooring chain and an additional 10 t clump weight attached at the tangent point between the mooring chain and the seabed (D137L652 + 60 t + 10 t).

The tension curve of the mooring chain with different numbers of clump weights is compared in Figure 34, and the horizontal restoring force curve provided by the mooring system is compared in Figure 35. From the result in Figure 34, it can be seen that the pre-tension of the mooring chain (corresponding to zero offset) is the same with the same weight of the clump weights in the suspended section, that is, only the clump weight in the suspended section will affect the pre-tension, and the clump weight arranged in the lying section has almost no effect on the pre-tension.

Figure 36 shows that the clump weight arranged in the lying section is gradually lifted up as the FOWT moves horizontally. When the horizontal offset of the FOWT is in the range of 0 m~5 m, the tension of D137L652 + 60 t is larger than that of D137L652 + 50 t + 10 t, but the horizontal restoring force of the one-clump weight scheme is less than that of the two-clump weight scheme. As the horizontal movement of the FOWT increases, the tension and horizontal restoring force of the mooring chains in the D137L652 + 50 t + 10 t design scheme are greater than those in the D137L652 + 60 t design scheme. In addition, the D137L652 + 60 t + 10 t design scheme provides the largest horizontal restoring force. Therefore, it can be found that changing the distribution of the clump weights has little effect on the stiffness characteristics of the mooring chain, but the change in the weight of clump weights will have a greater effect.

In summary, it is clear that only the clump weight arranged in the overhanging section of a mooring chain has a significant effect on its pre-tension. If the weight of the clump weight is specified, the mooring chains with multiple clump weights provide a greater horizontal restoring force than a single clump weight scheme under the same total weight of the clump weights, which is consistent with the conclusions obtained in the clump weight position analysis. In addition, the use of a decentralized arrangement scheme allows the stiffness profile of the mooring system to be flatter at small displacements and provides sufficient horizontal restoring force at large displacements.

For the D137L652 mooring chain scheme, the static spatial shape of the mooring chain with different numbers of clump weights under different offsets is shown in Figure 36. Comparing Figure 19a,b, the static spatial shape of the mooring chain is almost identical in the initial state, i.e., when the horizontal offset of the FOWT is zero and the same weight of clump weight is hung on the suspended section. When the FOWT moves horizontally, the clump weight lying on the seabed is gradually lifted up. When the horizontal offset of the FOWT is 5 m, the 10 t clump weight is starting to be lifted up. At this time, the spatial shape of the mooring chain shows like a folded line instead of the “catenary” form. Therefore, in the previous section, we can see that the tension curve of the mooring chain with a 10 t clump weight at the lying section changes gently from 0 m to 5 m but increases rapidly from 5 m to 10 m. Combined with the results in Figure 36, it can be found that the tension curve of the design schemes D137L652 + 50 t + 10 t and D137L652 + 60 t almost coincide with each other after the clump weight is lifted up completely.

Figure 37 shows the length of the lying section of the mooring chain on the seabed with different numbers of clump weights. From Figure 37, it can be seen that the change in the number of clump weight has a certain effect on the length of the lying section of the mooring chain within a localized offset about from 0 m to 10 m. When the FOWT moves at the negative offset with the mooring chains in a slack state, the length of the lying section of the mooring chain on the seabed is exactly the same for different design schemes.

The angle between the mooring chain and the horizontal plane is plotted in Figure 38 for design schemes with varying numbers of clump weights when the FOWT undergoes horizontal displacement. The result reveals that altering the number of clump weights has a negligible impact on the mooring angle. Nevertheless, the difference is very small, being within 2 degrees.

According to the analysis above, it is evident that the design scheme with two clump weights can enhance the restoring stiffness of the mooring system compared to that with a single clump weight or the pure mooring chain. However, it does not noticeably increase the tension of the mooring chain when the clump weight is of the same weight. Considering that the arrangement of 60 t and 10 t clump weights will increase the average mooring chain tension and construction cost, it is advisable to opt for the design scheme of D137L652 + 50 t + 10 t.

4.3.2. Dynamic Characteristics Analysis

(1) Rated operating conditions

Figure 39 displays the time-series of tension at fairlead#1 under the rated operation condition, and the statistical results are depicted in Figure 40. The results indicate that the mean, maximum, and minimum values of the mooring chain tension increase with the weight of clump weights in the hanging section. The maximum tension values under the rated operation condition with clump weights of 40 t, 50 t, and 60 t are 2.496 × 10⁶ N, 2.626 × 10⁶ N, and 2.758 × 10⁶ N, respectively. This is because increasing the clump weight enhances the pre-tension of the mooring chain, increases the restoring stiffness of the mooring system, and proportionally decreases the tension margin of mooring chains. In addition, the mooring chain tensions for the D137L652 + 50 t + 10 t scheme and the D137L652 + 60 t scheme reach a maximum of 2.664 × 10⁶ N and 2.798 × 10⁶ N, respectively. The maximum tension value for the D137L652 + 50 t + 10 t design is lower than that of the D137L652 + 60 t design scheme in the rated condition.

(2) Extreme shutdown conditions

The time history of tension at fairlead#3 during the extreme sea state is illustrated in Figure 41, and the statistical results are presented in Figure 42. According to the results, it is evident that as the weight of clump weight increases, the mean, maximum, and minimum tension values at fairlead#3 also increase. Conversely, the variation range of the tension force decreases with an increase in the clump weight. The maximum tensions exhibited by the mooring chain with 40 t, 50 t, 60 t, 50 t + 10 t, and 60 t + 10 t clump weights are 9.077 × 10⁶ N, 8.808 × 10⁶ N, 8.560 × 10⁶ N, 8.535 × 10⁶ N, and 8.311 × 10⁶ N, corresponding to safety factors of 1.87, 1.93, 1.99, 2.00, and 2.04, respectively. Increasing the clump weight could substantially decrease the maximum tension of the mooring chain, enhance the safety, and concurrently lower the variation range of the dynamic response of the mooring chain of the FOWT.

In conclusion, it was discovered that positioning the clump weight as far down as possible in the hanging section can enhance the restoring force of the mooring chain system without significantly increasing the tension of the mooring chain. Increasing the weight of the clump weight can effectively enhance the pre-tension of the mooring chain, putting the mooring chain in a tensioned state, which is beneficial for keeping the positioning of FOWTs. The dynamic analysis results demonstrate that all clump weight schemes mentioned above satisfies the design requirements of mooring chains during the rated operation condition. The horizontal movement of the FOWT is also within acceptable limits during the extreme sea state. Increasing the weight of a clump weight can appropriately diminish the horizontal movement of the FOWT, while the length of the mooring chain remains an influential factor. The primary effect of the clump weight is to enhance the pre-tension of the mooring chain, thus alleviating the “slack-taut effect” issue in the mooring chain. Based on the analysis of mooring chain tension in the extreme sea state, increasing the weight of the clump weight can lower the maximum tension and enhance the safety coefficient. However, it can also elevate the average tension value, so we should aim for a clump weight with a greater weight within a reasonable range. In addition, the number of clump weights was also investigated. The static analysis results indicate that using two clump weights can increase the restoring stiffness of the mooring system compared to that using a single clump weight with the same weight. However, it does not cause a significant increase in the tension of the mooring chain. The dynamic analysis results indicate that the displacement of a FOWT falls within a reasonable range for both the rated and extreme sea states with the use of the two-clump weight schemes. In comparison with the pure mooring chain scenario, the tension of the mooring chain with two clump weights is significantly decreased, leading to improved safety of the mooring chains. Considering that the scheme combining 60 t and 10 t clump weights will raise the mean value of the mooring chain tension and increase construction costs, it is advisable to select the D137L652 + 50 t + 10 t design scheme as a preferred solution for the mooring chains in the study.

According to Myhr’s mooring cost statistics [28] on the Hywind II and the WindFloat floating offshore wind turbine projects, the unit cost of mooring chains is approximately EUR 1976/ton. For mooring chains with nominal diameters of 137 mm, 127 mm, and 117mm, the unit length weights are approximately 0.411 tons/m, 0.353 tons/m, and 0.299 tons/m, respectively. The unit cost of clump weights is approximately EUR 1270/ton. For the preferred clump weight combination in this study, totaling 60 tons, the cost is approximately EUR 76,200. Taking the Stevshark MK5 anchor as an example, the cost of each anchor is approximately EUR 113,900. Therefore, the cost statistics for single mooring chain with different chain lengths and nominal diameters are listed in

Table 6. Cost statistics of single mooring chain.

	L(m)	637	647	652	657
D (mm)
117		EUR 377,310	EUR 383,234	EUR 386,195	EUR 389,157
127		EUR 444,564	EUR 451,543	EUR 455,033	EUR 458,522
137		EUR 517,331	EUR 525,452	EUR 529,513	EUR 533,573

Cost of 60-ton clump weights: EUR 76,200; cost of a Stevshark MK5 anchor: EUR 341,700.

. Since the mooring system consists of three chains and three anchors, the total cost of the mooring system of the FOWT is approximately three times the values listed in Table 6.

The findings from the above study indicate that increasing the nominal diameter of the mooring chain and increasing the weight of the clump weights both enhance the mooring stiffness, with minimal impact on the spatial shape of the anchor line. Therefore, other combinations that meet the design requirements, such as a smaller diameter and larger clump weights, may also be feasible. However, a smaller mooring diameter typically implies lower breaking load limits, reduced corrosion allowance, and shorter fatigue life. Thus, these factors need to be considered comprehensively. This paper only provides a design methodology and flow, and other potential schemes will be considered in future research.

5. Conclusions

This paper introduces the design method of mooring chains of a FOWT in shallow water of a 44 m depth and carries out a parametric sensitivity analysis on the length, nominal diameter, and clump weights of mooring chains in shallow water compared to that in deep water of 130 m in depth. In general, the mooring chains in shallow water show stronger nonlinearities in the stiffness characteristics, length of the lying section on the seabed, the mooring chain angle, and even the motion responses of the FOWT when compared to the original mooring chain in deep water, which increases the design challenge of mooring chains in shallow water. The effects of changes in chain length, size, and various clump weight systems on the static and dynamic characteristics of shallow water mooring chains are summarized in

Table 7. Summary of design factor characteristics.

Design Factors	Static Characteristics	Dynamic Characteristics
Length	Mooring chains in shallow water show significant nonlinearities in the stiffness performance and spatial shape. The shorter chain has a larger pre-tension, but the tension of the mooring chain increases more significantly.	The horizontal motion of a FOWT is strongly affected by the length of the mooring chain. A too long mooring chain causes a significant offset of the FOWT, while a too short mooring chain quickly increases the tension of the mooring chain.
Nominal diameter	Mooring chains with a larger nominal diameter have a greater tension force under the same platform offset, but the spatial shape differences are minimal.	As the nominal diameter of the mooring chain increases, the mean and maximum values of the horizontal movement of the FOWT will decrease, but it is not as significant as the impact of the change in the chain length.
Clump weights	Increasing the weight of clump weights improves the pre-tension of the mooring chain and results in a shorter lying section. Positioning the clump weights as close to the touchdown point on the seabed as possible can improve the restoring force of the mooring system.	Increasing the weight of a clump weight can appropriately diminish the horizontal movement of the FOWT. Increasing the weight of a clump weight can enhance the pre-tension and lower the maximum dynamic tension of the mooring chain, thus alleviating the “slack-taut effect” issue in the mooring chain.

, and the main contributions of the paper can be summarized as follows:

(1)

A shorter mooring chain has a larger pre-tension, but the tension of the mooring chain increases more significantly with the same offset of the FOWT with more obvious nonlinear characteristics, which is not conducive to mooring safety. In addition, it is found that the horizontal motion of a FOWT is strongly affected by the length of the mooring chain. A too long mooring chain causes a significant offset of the FOWT, while a too short mooring chain quickly increases the tension of the mooring chain. Therefore, it is crucial to design the appropriate length of the mooring chains to ensure the operation and safety of FOWTs.

(2)

The mooring chain with the larger nominal diameter has larger tension force under the same platform offset, but the spatial shape of the mooring chains with different nominal diameters is almost the same. The change in the nominal diameter of the mooring chain has a certain impact on the dynamic responses of the FOWT. As the nominal diameter of the mooring chain increases, the mean and maximum values of the horizontal movement of the FOWT will decrease, but it is not as significant as the impact from the change in the mooring chain length.

(3)

By analyzing the weight and position of the clump weights, it is evident that increasing the weight of clump weights improves the pre-tension of the mooring chain. Additionally, a heavier clump weight results in a shorter lying section under the same displacement of the FOWT. When the weight of the clump weight remains unchanged, positioning the clump weights as close to the touchdown point on the seabed as possible can improve the restoring force of the mooring system. Additionally, the horizontal restoring force provided by a design scheme with multiple counterweights is greater than that with only a single counterweight. Moreover, a reasonable layout of clump weights attached to mooring chains can effectively restrain the “slack-taut” effect of mooring chains in shallow water. This article only explores the influence of some key mooring chain parameters, such as mooring chain length, nominal diameter, and suspension clump weights, to reveal the nonlinear characteristics of mooring chains of a FOWT in shallow water. Within a limited range of design parameters, a suitable design scheme was selected, providing a certain reference for mooring chain design in shallow water. In addition, as a matter of fact, wave nonlinearity becomes more pronounced as the water depth decreases. According to DNV-RP-C205 [29], the Stokes waves may be more appropriate for describing the extreme wave conditions in the study rather than linear wave models.

Future research can consider integrating multi-objective optimization algorithms for the design of mooring chains in shallow water; Additionally, surrogate models can be used to predict mooring tension, thereby considering the effects of mooring fatigue in the design optimization process; a nonlinear wave model should be adopted to fully account for the characteristics of nonlinear wave loads in shallow water.