## Abstract

Three forms of the mooring system in 60 m water depth are proposed for semi-submersible with partially inclined columns (SPIC) concept floating wind turbine (FWT). One is a simple form with only catenary lines, and the other two are hybrid forms including clump weights. The clumps are attached to the suspended section for Hybrid form1 and the bottom section for Hybrid form2. Hybrid form2 achieves the smallest line length and chain weight. Three alternative proposals can be evaluated through mooring line characteristics, dynamic responses, utilization factors, and simple cost analysis. Hybrid form2 allows for smallest pretension, and largest stiffness and nonlinearity only at large offsets. Under operational conditions, the mean surge for Hybrid form1 and Hybrid form2 is similar, but the fairlead tension is significantly smaller for Hybrid form2. Under the survival condition, the clumps of Hybrid form2 are lifted up and put down, leading to small mean offsets of FWT but large wave-frequency components of line tension. Among the three forms of the mooring system, the Hybrid form2 can limit the FWT to the smallest offset range while also controlling the mean mooring line tension to a level similar to the other two forms. Under normal working conditions and accidental conditions with single line broken, the maximal surge motions of FWT under the restraint of three mooring systems all meet the design requirements. The mooring line strength of the three mooring systems meets the requirements in ultimate limit state (ULS) and accidental limit state (ALS) analyses. Among them, the utilization coefficient of Hybrid form2 is closest to 1, demonstrating its best economic performance.

## 1 Introduction

Compared with onshore wind resources, offshore wind is superior in terms of resource stability, regional utilization, construction scale, visual and auditory environment, and public acceptance [1]. Offshore wind turbine is therefore developing rapidly. In general, offshore wind turbines are supported by fixed or floating foundations. For fixed foundations, the maximum applicable water depth is limited to 15 m for gravity type and 30 m for monopile type [2], for instance. However, offshore wind resources in many countries, like China, are found in intermediate water depths between 40 m and 60 m [3], where bottom-fixed wind turbines become prohibitively expensive [4]. Therefore, floating wind turbines (FWTs) are more attractive aiming at a lower levelised cost of energy in intermediate waters [5]. The continental shelves of China sea have extremely mild slopes [6]. For example, the water depth of 40 km away from the coastline of Fujian Province is about 40 m. Besides, China sea is characterized with frequent typhoons and complicated seabed condition. It is of great significance to develop a new wind turbine concept and mooring line concept suitable for the intermediate waters.

When the wind turbine deviates from the equilibrium position due to environmental forces such as wave, wind, and current loads, the mooring system provides restoring force to keep the FWT in position [7,8]. Excellent design of the FWT mooring system is important. Compared with deep water mooring systems, the structural characteristics and design philosophies are quite different in shallower water [9]. In intermediate water depth, the effective water depth from the fairlead to the seabed becomes very limited, which makes the design of the mooring system more challenging than the design of the deep water mooring system. A large number of parameters related to the design and analysis of the mooring systems need to be considered when water depth changes [10]. Some researchers analyzed and studied the performance of the mooring systems in intermediate water depths. A numerical tool was developed by Brommundt et al. [11] to optimize the length and angle of the mooring lines for the mooring system used in the water depth of 75 m. Benassai et al. [12–14] considered the influence of the mooring line pattern on the motion performance of the Dutch Tri-floater wind turbine under 50 m water depth. Campanile et al. [15] focused on the design and selection of the mooring systems for FWTs in intermediate water depth ranging from 50 m to 80 m, based on ultimate, accidental, and fatigue limit state (FLS) design conditions. Li et al. [16] put forward several design suggestions for the mooring configuration of FWTs in intermediate waters in China. The design parameters considered by Li et al. [16] contained the inclination angle, the position of the fairlead point, the length of the mooring line, and the direction of the environmental load. In addition, in the past few years, various rules and guidelines provided by the American Bureau of Shipping (ABS) [17], Bureau Veritas [18], and Det Norske Veritas (DNV) [3] have also proved that there is growing interest in offshore wind resources in intermediate water depth.

Some methods can be used to improve the mooring performance, including using clump weight and changing the location of fairlead. A clump is a concentrated weight which can be incorporated with smaller size mooring lines to achieve the same required geometric stiffness. Vicente et al. [19] compared mooring configurations composed of chain with or without clumps. Relative to the mooring line tension, the horizontal motion and output power are less sensitive to the clump configuration. Yuan et al. [20] proposed a hybrid mooring concept for deep water semi-submersible platforms, including clump weights and buoys connected to the lower and upper end of the line, respectively. Liu et al. [21] verified the effect of clump weights on the performance of the platform under three regular waves and three irregular waves. Clumps of one-tenth of the total mooring line mass can effectively reduce wave-induced response. As the depth of the position of clump weights increases, the performance of the platform is significantly improved. Barbanti et al. [22] showed that the platform response is almost insensitive to the geometry of the mooring line, while the use of clumps can reduce fatigue loads and optimize the overall system response. Bruschi et al. [23] added clump weights to the mooring system of a spar-type FWT, and considered the optimal position and weight of the clumps under different sea conditions to minimize platform response. The results show that for the degree-of-freedom of surge, the influence of the weight of the clumps is not as great as the influence of the position of the clumps. Xu et al. [24] designed seven mooring concepts for a 5 MW semi-submersible wind turbine in a water depth of 50 m, and compared them to determine a structurally reliable and economically attractive solution. The performances of the seven mooring concepts were compared from the aspects of mooring line characteristics, motion response amplitude operator, utilization factor, and cost. As mentioned above, another way to improve the mooring performance is to change the fairlead location. Two cooperative research projects, INNWIND.EU [25] and LIFES50+ [26], moved the fairlead from below to above the surface, in order to increase the effective water depth.

Previous studies have paid attention to the influence of water depth on the design parameters of FWT mooring systems, but no detailed FWT mooring system design has been carried out for specific water depth of the Chinese coast. The previous research on mooring design in intermediate water depth was composed of pure chain, while the hybrid mooring concept composed of clumps and chain was mainly designed for deep water, and the application in intermediate water depth was not considered. Regarding the FWT mooring system, there is a lack of detailed comparison between several proposals for industry guidance. In order to further enhance the applicability of FWTs in intermediate water depth, this paper focuses on the design challenges and design methodologies of the FWT mooring system in 60 m water depth. In order to evaluate the benefits of adding additional clumps, design concepts of hybrid mooring systems with heavy clumps were compared with the simple form mooring system with pure chain. At the same time, two hybrid mooring concepts with clumps attached to different positions were proposed to demonstrate the influence of the position of the clump weights. Therefore, by comparing and studying different mooring system concept proposals, a rational design can be proposed for FWTs in intermediate water depth for industrial guidance.

## 2 Methodology of Mooring System Design

In intermediate water depth ranging from 40 m to 60 m, semi-submersible type floating structures are proposed to support large multi-megawatt wind turbines. Therefore, the present study focuses on the design methodology of the catenary mooring systems, which are most common for semi-submersible floating wind turbines.

### 2.1 Design Challenges of Catenary Mooring Systems for Intermediate Water Depth.

For catenary mooring systems, the weight and pretension of the mooring lines are the main sources of restoring forces for surge, sway, and yaw motions of floating structures. The design of catenary mooring systems is a complicated iterative process. It is necessary to consider both the motion of the floating platform and the tension of the mooring lines. On the one hand, the mooring system should have sufficient stiffness to limit the offset of the floating platform under wind, wave, and current loads. On the other hand, it should have sufficient compliance to allow the wave-frequency motion and avoid the large mooring line tension caused by environmental loads. These characteristics are challenging to achieve in intermediate water depth (40–60 m). There are four main challenges:

The vertical span from fairlead to seabed in intermediate water depth is much smaller than that in deep waters, which directly shortens the length of the suspended section of the mooring line that could provide pretension. In order to achieve the same pretension as in deep water, the wet weight of the mooring line must be increased when used in intermediate water depth.

When the offset increment is identical, more of the catenary line will be lifted up in the intermediate water depth, compared with in the deep water depth. Xu et al. [5] conducted a comparative study on the performance of a catenary mooring system used for water depth of 50 m, compared with mooring systems used for water depths of 100 m and 200 m. From Fig. 1, it can be seen that the mooring line tension in all three water depths increases nonlinearly with horizontal displacement, and the nonlinear characteristics of mooring line tension become more significant when the water depth decreases. On the basis of the same pretension, the stiffness of the mooring system in intermediate water depth increases faster than that in deep water when the offsets increase. The sudden increase of mooring line tension could cause potential line breaking.

- The horizontal stiffness
*k*_{G}of a catenary mooring system can be expressed as [27]where(1)$KG=\u2202TH\u2202x=w[\u221221+2(TH/wh)+cosh\u22121(1+whTH)]\u22121$*T*_{H}and*x*are the tension and offset in the horizontal direction, respectively.*w*is the unit wet weight of mooring line, and*h*is the water depth. Given the same*T*_{H}, the horizontal stiffness*K*_{G}would increase with the decrease of water depth. A mooring system with larger horizontal stiffness results in a higher natural frequency of horizontal motion. This makes the FWT more susceptible to the excitation of wave-frequency loads in extreme conditions or difference frequency wave loads in other conditions. The angle

*α*between the mooring line and the vertical axis, and the angle*β*between the mooring line and the horizontal axis can be used to indicate the catenary shape of the mooring line, as shown in Fig. 2. To obtain a horizontal pretension equivalent to that in deep water,*α*should be increased. This will lead to the elimination of the catenary shape to some extent, resulting in a fully stretched mooring line. As the water depth decreases, the rate of change of*α*with increasing offset tends to increase, which means that the mooring lines in intermediate water depth are more likely to lose the catenary shape, compared with those in deep waters. When the mooring line becomes taut, there would be a vertical force applied to the anchor, which leads to challenges in the design and selection of anchors. In order to prevent the anchor from being subjected to vertical forces, catenary lines in intermediate water depths usually need to provide a sufficiently long bottom section, which requires a large footprint and is not conducive to the wind field layout.

### 2.2 Design Criteria of Mooring Systems.

The design of a mooring system is affected by restrictions and requirements from, e.g., the safety of the power transmission cable, the motion performance of the floating platform, and the structural characteristics of the mooring lines. Generally speaking, according to the API-RP-2SK standard [28], the design criteria for a mooring systems in intermediate water depth include the following aspects:

Its offset should be limited to a reasonable range to avoid excessive curvature or tension in the power cable.

- All mooring lines must have sufficient strength to withstand the loads under all operational environmental conditions (ECs). It should also be ensured that the mooring system has sufficient capacity to withstand the mooring line tension under accidental conditions of a certain mooring line is broken. The maximum mooring tension
*T*_{max}cannot exceed the breaking strength (MBS) of the chain with the consideration of the safety factor*γ*:(2)$Tmax<MBS\gamma $ The bottom section of the mooring line should be long enough to avoid being pulled up completely during use. The stretching of the line will cause large line tension, and the anchor should not sustain upward vertical loads under any circumstances.

### 2.3 Design Procedure of Mooring Systems.

Considering the aforementioned design challenges and design criteria, a general design procedure for the FWT mooring systems is summarized in Fig. 3. In the initial stage of the mooring system design, it is necessary to clarify the preliminary design of the whole FWT system (step 1.1), and the environmental data and design conditions at the site where the floating wind turbine will be positioned (step 1.2). Then, the environmental forces acting on the FWT could be estimated (step 2). Based on location specifics and environmental loads, the preliminary layout of the mooring system could be decided according to experience (step 3). For catenary mooring systems, a mooring line may consist of several segments that are made of chain, steel wire rope, polyester rope, etc. Attachments like buoys and clumps can also be considered during the design process. After the dimensions of the mooring lines, buoys and clump weights are initially chosen (step 4), the stiffness of the mooring system and the natural frequency of the FWT can be calculated (steps 5 and 6), and the dynamic responses of the FWT under ultimate limit state (ULS) and accidental limit state (ALS) can be analyzed (step 7). The ULS required that any individual mooring line of an intact mooring system has adequate strength to withstand the load effects imposed by design load cases and survival load cases. The ALS ensures that any individual mooring line has adequate capacity to withstand the failure of one mooring line. Using the fully coupled aero-hydro-servo-elastic-mooring method mentioned in Sec. 4.1, the FWT offsets, the mooring line tensions, and the vertical forces on the anchors were detected under both normal conditions and accidental conditions (step 8). If these results did not fulfill the requirements from the design standards listed in Sec. 2.2, the dimensions of the mooring systems would be reselected. If the requirements were fulfilled through the iteration process, the design check could be proceeded for FLS analysis (step 9). However, the FLS design check was not the focus of the present study. In general, through the general design process shown in Fig. 3, the proposals of the mooring system concept could be obtained (step 10).

#### 2.3.1 Simple Form Mooring System.

The simple form mooring system indicates the mooring system with only catenary mooring chains, which is illustrated in Fig. 4(a). The restoring forces for both vertical and horizontal motions are influenced by the submerged weight of the suspended part for the catenary chain. For the preliminary design of the simple form catenary mooring system, only linear static analysis was performed and the effect of elasticity of mooring line was neglected, simplifying the problem into the classic catenary equations [27]. According to the targeted surge natural frequency, the restoring coefficient *C*_{11} could be assumed. After initially arranging the layout of the mooring system, the linear restoring coefficient *k*_{i} for one mooring line could be obtained. Wet weight *w* is a function of *k*_{i}, water depth *h*, and pretension *T*_{H}. Once wet weight *w* was known, the mooring line properties, including chain grade, nominal diameter, stiffness, and breaking strength could be obtained according to design standards, such as DNV-OS-E302 [29]. Then, step 5 to step 8 in Fig. 3 could be repeated until the design fulfilled the requirements of the standard.

#### 2.3.2 Hybrid Form Mooring System.

The simple form mooring system with pure chain should be quite heavy in order to achieve reasonable pretension. In addition, the mooring line should be long enough to achieve adequate restoring force under severe environmental conditions. Therefore, the addition of the clump weights was considered, constituting the hybrid mooring system. The locations of the clump weights on the mooring lines can be chosen according to different principles and purposes.

*Hybrid form1: The clump weights are attached to the suspended section (Fig. 4(b)).*

Clump weights in a catenary mooring system could provide a larger reaction to the floating platform displacements, and provide a reduction of the mooring line length by adding additional masses in specific zones of the mooring system. In this case, a clump weight system based on several units spread along a section of the mooring line near the fairlead is the most suitable solution.

Attaching the clump weights on the suspended section directly increases the pretension of the mooring line. The number, position, weight, and volume of the clump weights were chosen, and steps 5–8 as shown in Fig. 3 were then repeated until the design fulfilled the requirements of the standard. For hybrid form1 mooring system, the property parameters of the chains were not modified, with only the mooring line length and anchor positions were changed. Therefore, the stiffness slope of the whole mooring system was not varied, with only pretension increased.

*Hybrid form2: The clump weights are attached to the bottom section (Fig. 4(c)).*

If the purpose is to limit excessive line tension in order to avoid breakages, and to limit vertical loads on the anchors, a system with heavier clump weights positioned on the bottom section of the mooring line seems to be more efficient.

Attaching the clump weights on the bottom section restricts the floating platform offsets under severe environmental conditions. The mooring line length could then be shortened on this basis to save mooring system footprint. For the hybrid form2 mooring system, lighter chain was used to decrease the pretension. At the same time, the stiffness slope of the whole mooring system was changed. The number, position, weight, and volume of the clump weights were chosen, and steps 5–8 as shown in Fig. 3 were then repeated until the design fulfilled the requirements of the standard.

## 3 Floating Wind Turbine and Mooring System Concept

### 3.1 Floating Wind Turbine Concept.

In this study, a 10 MW semi-submersible FWT concept named semi-submersible with partially inclined columns (SPIC) [30], proposed for China’s seas, was used to compare different mooring system proposals at an intermediate water depth of 60 m. This FWT system, as shown in Fig. 5, consists of the Technical University of Denmark (DTU) 10 MW reference wind turbine [31], a redesigned tower [32], and a self-designed semi-submersible platform with partially inclined side columns. The dimensions and main parameters of the SPIC concept FWT system are briefly listed in Table 1 and described in detail in Ref. [33].

Parameter | Value | Unit |
---|---|---|

Rated power | 10 | MW |

Cut-in, rated, cut-out wind speed | 4.0, 11.4, 25.0 | m/s |

Minimum and maximum rotor speed | 6.0, 9.6 | rpm |

Gearbox ratio | 50 | – |

Rotor diameter | 178.3 | m |

Hub height above water line | 119.0 | m |

Height of central column and pontoons | 46.0, 7.0 | m |

Height of upper and lower side columns | 18.0, 20.0 | m |

Diameter of central column | 8.3 | m |

Side length of side columns and pontoons | 9.0, 9.0 | m |

Distance between central and upper side columns | 50.0 | m |

Draft | 30.0 | m |

Displacement | 1.64 E7 | kg |

Center of gravity below mean waterline (MWL) | 9.79 | m |

Parameter | Value | Unit |
---|---|---|

Rated power | 10 | MW |

Cut-in, rated, cut-out wind speed | 4.0, 11.4, 25.0 | m/s |

Minimum and maximum rotor speed | 6.0, 9.6 | rpm |

Gearbox ratio | 50 | – |

Rotor diameter | 178.3 | m |

Hub height above water line | 119.0 | m |

Height of central column and pontoons | 46.0, 7.0 | m |

Height of upper and lower side columns | 18.0, 20.0 | m |

Diameter of central column | 8.3 | m |

Side length of side columns and pontoons | 9.0, 9.0 | m |

Distance between central and upper side columns | 50.0 | m |

Draft | 30.0 | m |

Displacement | 1.64 E7 | kg |

Center of gravity below mean waterline (MWL) | 9.79 | m |

### 3.2 Mooring System Proposals.

The 10 MW semi-submersible FWT concept named SPIC was designed for the China South Sea, with the representative environmental conditions listed in Table 2. The environmental conditions contain the operational conditions (EC1–EC3) and survival condition (EC4). In this study, according to the design criteria given in Sec. 2.2, it is assumed that:

Based on our communication with researchers and developers of China’s floating wind turbine prototype, the extreme values of the offsets under given environmental conditions should be limited to 50% of the water depth.

The maximum mooring tension

*T*_{max}cannot exceed the breaking strength MBS of the chain with the consideration of the safety factor*γ*. The required safety factors of the chain are given in the ABS rule [17]. For ULS analysis, safety factors are defined as 2.25 and 1.67 in design and survival load cases, respectively. For ALS analysis, safety factors are defined as 1.22 and 1.05 in design and survival load cases, respectively.The anchor is not subjected to vertical force under any condition, that is, the bottom section is not completely lifted at any time.

Wave | Wind | Current | |||||
---|---|---|---|---|---|---|---|

EC | $Hs$ (m) | $Tp$ (s) | Shape factor | Wind type | Mean speed (m/s) | Turbulence intensity (TI) (%) | Mean speed (m/s) |

EC1 | 3.8 | 8.3 | 2.4 | − | − | − | − |

EC2 | − | − | − | Turbulent | 11.4 | 14.6 | − |

EC3 | 3.8 | 8.3 | 2.4 | Turbulent | 11.4 | 14.6 | 0.6 |

EC4 | 10.3 | 14.1 | 2.0 | Turbulent | 50 | 12.3 | 1.3 |

Wave | Wind | Current | |||||
---|---|---|---|---|---|---|---|

EC | $Hs$ (m) | $Tp$ (s) | Shape factor | Wind type | Mean speed (m/s) | Turbulence intensity (TI) (%) | Mean speed (m/s) |

EC1 | 3.8 | 8.3 | 2.4 | − | − | − | − |

EC2 | − | − | − | Turbulent | 11.4 | 14.6 | − |

EC3 | 3.8 | 8.3 | 2.4 | Turbulent | 11.4 | 14.6 | 0.6 |

EC4 | 10.3 | 14.1 | 2.0 | Turbulent | 50 | 12.3 | 1.3 |

On this basis, this research proposes three forms of mooring systems according to the methodology mentioned in Sec. 2. All of three mooring systems contain six mooring lines, and the plan view is shown in Fig. 6. The mooring lines are divided into three groups which spread 120-deg-symmetrically about the center of the platform. Each group consists of two chains spaced 5 deg apart. Lines #3–#6 are positioned upwind, and lines#1–#2 are positioned inline. In this study, all three forms use two mooring lines in one direction, thus the system could remain safe when a certain mooring line is broken. Among three alternative mooring systems, one is a pure-catenary form (simple form, as seen in Fig. 4(a)), and the other two are hybrid forms consisting of catenary lines and clumps (hybrid form, as seen in Figs. 4(b) and 4(c)). All three mooring systems are catenary, and the fairlead points of these forms are identical, but there are many differences in parameters, as shown in Table 3. Compared with the simple form, hybrid forms have smaller footprint areas and shorter bottom section lengths. The biggest difference between the two hybrid forms lies in the position of clumps. For Hybrid form1, the clumps are installed at the suspension section of the catenary line, while for Hybrid form2, the clumps are mounted at the bottom section of the catenary line. The clump weight in Hybrid form2 is larger. However, the length, outer diameter, wet weight, and elastic modulus times area (EA) of the chain in Hybrid form2 are significantly reduced. The parameters of the chain are selected according to offshore standard DNV-OS-E302 [29].

Parameter | Unit | Simple form | Hybrid form1 | Hybrid form2 |
---|---|---|---|---|

Number of mooring lines | − | 6 | 6 | 6 |

Angle between each group of lines | deg | 120 | 120 | 120 |

Angle between adjacent lines | deg | 5 | 5 | 5 |

Fairlead above MWL | m | 15 | 15 | 15 |

Anchor below MWL | m | 60 | 60 | 60 |

Radius from platform center to fairleads | m | 54.5 | 54.5 | 54.5 |

Radius from platform center to anchors | m | 830.0 | 530.0 | 498.0 |

Length of mooring line | m | 800.0 | 500.0 | 465.0 |

Outer diameter of mooring line | m | 0.120 | 0.120 | 0.095 |

Mass of mooring line in water | t/m | 0.303 | 0.303 | 0.190 |

EA of mooring line | kN | 1.243 × 10^{6} | 1.243 × 10^{6} | 7.788 × 10^{5} |

The number of clumps on each line | − | − | 10 | 10 |

Each clump weight in air | t | – | 2.8 | 3.8 |

Clump position from fairlead | m | − | 40 − 2 − 58 | 180 − 15 − 315 |

Length of bottom segment | m | 645.0 | 330.0 | 285.0 |

Pretension | kN | 621.2 | 973.5 | 478.2 |

Breaking strength | kN | 11,047 | 11,047 | 8180 |

Parameter | Unit | Simple form | Hybrid form1 | Hybrid form2 |
---|---|---|---|---|

Number of mooring lines | − | 6 | 6 | 6 |

Angle between each group of lines | deg | 120 | 120 | 120 |

Angle between adjacent lines | deg | 5 | 5 | 5 |

Fairlead above MWL | m | 15 | 15 | 15 |

Anchor below MWL | m | 60 | 60 | 60 |

Radius from platform center to fairleads | m | 54.5 | 54.5 | 54.5 |

Radius from platform center to anchors | m | 830.0 | 530.0 | 498.0 |

Length of mooring line | m | 800.0 | 500.0 | 465.0 |

Outer diameter of mooring line | m | 0.120 | 0.120 | 0.095 |

Mass of mooring line in water | t/m | 0.303 | 0.303 | 0.190 |

EA of mooring line | kN | 1.243 × 10^{6} | 1.243 × 10^{6} | 7.788 × 10^{5} |

The number of clumps on each line | − | − | 10 | 10 |

Each clump weight in air | t | – | 2.8 | 3.8 |

Clump position from fairlead | m | − | 40 − 2 − 58 | 180 − 15 − 315 |

Length of bottom segment | m | 645.0 | 330.0 | 285.0 |

Pretension | kN | 621.2 | 973.5 | 478.2 |

Breaking strength | kN | 11,047 | 11,047 | 8180 |

## 4 Numerical Model Establishment and Validation

### 4.1 Fully Coupled Numerical Model.

The coupled aero-hydro-servo-elastic-mooring time domain simulations were conducted for the full-scale SPIC concept floating wind turbine, using fast v8 [34] developed by the National Renewable Energy Laboratory (NREL). An overview of fast integrated with several modules is illustrated in Fig. 7.

Various external environmental conditions were introduced and input into the numerical model, including irregular wave time series, turbulent wind time series, constant current, etc. The hydrodynamic calculations of the platform were based on the combination of potential flow theory and Morison’s equation in HydroDyn module. The hydrodynamic coefficients, including the added mass, potential damping, first-order and second-order wave force transfer functions, were first calculated in the frequency domain, and then applied in the time domain by convolution technique. The drag coefficients for calculating the viscous drag force were selected according to the Reynolds (Re) and Keulegan–Carpenter number. The two-dimensional drag forces were applied as distributed line forces on the columns and pontoons. The establishment and calibration of the numerical damping model based on slender Morison elements was conducted through trial and error. When the viscous damping coefficient in the numerical model was tuned, the results of free decay tests can be used for preliminary verification. The viscous damping coefficients were obtained through the following steps:

A rough range of drag coefficients of the cross sections with different geometry was determined according to the recommended practice DNV-RP-C205 [35], as shown in Table 4.

The decay test in the heave direction was used to calibrate the

*C*_{d}-coefficient of the rectangular shaped pontoons. It was then assumed that the drag coefficient for the pontoon was identical in horizontal and vertical directions.The decay test in the surge direction was then utilized to obtain the damping coefficients for the central column and side columns.

Finally, a check was made by comparing the pitch decay curves and yaw decay curves between numerical and experimental tests.

Description | Cross-sectional geometry | L/D | R/D | Cd |
---|---|---|---|---|

Central column | Ellipse | 1.0 | − | 1.0 |

Side columns (surge direction) | Rectangle with rounded corners | 1.0 | 0.07 | [1.2–2.0] |

Pontoons (heave direction) | Rectangle with rounded corners | 0.78 | 0.07 | [2.2–2.5] |

Description | Cross-sectional geometry | L/D | R/D | Cd |
---|---|---|---|---|

Central column | Ellipse | 1.0 | − | 1.0 |

Side columns (surge direction) | Rectangle with rounded corners | 1.0 | 0.07 | [1.2–2.0] |

Pontoons (heave direction) | Rectangle with rounded corners | 0.78 | 0.07 | [2.2–2.5] |

The drag coefficients obtained through the calibration of decay tests are summarized in Table 5.

Description | Cd |
---|---|

Central column | 1.0 |

Side column | 1.2 |

Pontoon | 2.4 |

Description | Cd |
---|---|

Central column | 1.0 |

Side column | 1.2 |

Pontoon | 2.4 |

The AeroDyn module was used to calculate the loads on blades through blade element momentum theory. The structural dynamic characteristics of the wind turbine, tower, and the supporting platform were calculated by the ElastoDyn module. The Reference OpenSource Controller (ROSCO) [36] developed by Delft University of Technology was selected for ServoDyn module. On this basis, the proportional gains *K*_{P} and integral gains *K*_{I} were modified to reduce the natural frequency of the pitch controller from 0.38 rad/s (land-based) to 0.13 rad/s, such that blade pitch controller natural frequency is lower than the platform pitch frequency (0.24 rad/s).

The catenary mooring system was modeled by the MoorDyn module [37], which is based on the lumped-mass mooring line model. Each mooring line was made up of a series of evenly distributed segments; each segment was divided into two parts and the mass of each part was lumped to the two adjacent nodes. The segments were replaced by damper spring systems. The model considers the axial stiffness, damping, weight, buoyancy, and hydrodynamic forces from Morison’s equation, and vertical spring-damper forces from the contact with the seabed. In the simulation, the properties of steel mooring lines including the diameter, mass density, and EAs were given in detail in line type section. The coordinates of the fairlead, clumps, and anchor on line #1 of Hybrid form1 and Hybrid form 2 mooring systems are provided in Table 6, and the coordinates of the clumps on lines #2–#6 could be obtained through calculation. The connection properties section defines the connection node points to which mooring lines can be connected, including “Fixed,” “Vessel,” and “Connected.” The anchor is defined as “Fixed,” the fairlead is defined as “Vessel,” and the place of clumps is defined as “Connection.” The clump weight can be given as the node mass of “Connected” node.

Proposal | Hybrid form1 | Hybrid form2 | ||||
---|---|---|---|---|---|---|

coordinates | x (m) | y (m) | z (m) | x (m) | y (m) | z (m) |

Fairlead | 54.45 | −2.38 | 15.00 | 54.45 | −2.38 | 15.00 |

Clump1 | 80.13 | −3.50 | −15.67 | 212.73 | −9.29 | −60.00 |

Clump2 | 81.51 | −3.56 | −17.12 | 227.72 | −9.94 | −60.00 |

Clump3 | 82.92 | −3.62 | −18.53 | 242.71 | −10.60 | −60.00 |

Clump4 | 84.38 | −3.68 | −19.91 | 257.70 | −11.25 | −60.00 |

Clump5 | 85.86 | −3.75 | −21.25 | 272.70 | −11.91 | −60.00 |

Clump6 | 87.39 | −3.82 | −22.54 | 287.69 | −12.56 | −60.00 |

Clump7 | 88.96 | −3.88 | −23.78 | 302.60 | −13.22 | −60.00 |

Clump8 | 90.56 | −3.95 | −24.98 | 317.65 | −13.87 | −60.00 |

Clump9 | 92.20 | −4.03 | −26.12 | 332.64 | −14.52 | −60.00 |

Clump10 | 93.88 | −4.10 | −27.20 | 347.63 | −15.18 | −60.00 |

Anchor | 529.50 | −23.12 | −60.00 | 797.24 | −34.81 | −60.00 |

Proposal | Hybrid form1 | Hybrid form2 | ||||
---|---|---|---|---|---|---|

coordinates | x (m) | y (m) | z (m) | x (m) | y (m) | z (m) |

Fairlead | 54.45 | −2.38 | 15.00 | 54.45 | −2.38 | 15.00 |

Clump1 | 80.13 | −3.50 | −15.67 | 212.73 | −9.29 | −60.00 |

Clump2 | 81.51 | −3.56 | −17.12 | 227.72 | −9.94 | −60.00 |

Clump3 | 82.92 | −3.62 | −18.53 | 242.71 | −10.60 | −60.00 |

Clump4 | 84.38 | −3.68 | −19.91 | 257.70 | −11.25 | −60.00 |

Clump5 | 85.86 | −3.75 | −21.25 | 272.70 | −11.91 | −60.00 |

Clump6 | 87.39 | −3.82 | −22.54 | 287.69 | −12.56 | −60.00 |

Clump7 | 88.96 | −3.88 | −23.78 | 302.60 | −13.22 | −60.00 |

Clump8 | 90.56 | −3.95 | −24.98 | 317.65 | −13.87 | −60.00 |

Clump9 | 92.20 | −4.03 | −26.12 | 332.64 | −14.52 | −60.00 |

Clump10 | 93.88 | −4.10 | −27.20 | 347.63 | −15.18 | −60.00 |

Anchor | 529.50 | −23.12 | −60.00 | 797.24 | −34.81 | −60.00 |

### 4.2 Experimental Model.

Experimental methods were used to explore the dynamic responses of the SPIC concept FWT with the Hybrid form2 mooring system. The model test was conducted at the Deep water Offshore Basin in Shanghai Jiao Tong University, with a Froude ratio of 1:64 and a basin water depth of 0.94 m (60 m in full scale). The basin plan view of the model tests is illustrated in Fig. 8. The FWT model was anchored in the middle of the basin by the mooring system. All six mooring lines can be fully positioned in the basin without truncation. The targeted wind conditions were generated by the wind generation system placed 5.2 m in front of the FWT model, and the wave and current conditions could also be generated according to requirements. All of these environmental conditions were calibrated and recorded before the formal basin model tests.

In the model test, thrust-matched blades were used to obtain the Froude-scale rotor thrust. A motor was installed in the nacelle to imitate the rotor speed accurately, and the blade pitch angle could be adjusted manually before each test case, while the angle cannot be tuned in real time during the test. A stiffness-matched tower model was used to ensure the first-order natural frequency and deformation of the tower model structure. A geometry-matched platform model was established in order to correctly obtain the hydrodynamic force applying to the model. The model scaling method of each part of the wind turbine system and the simulation of environmental conditions at the model scale have been introduced [32].

The present research focuses on the analysis of the mooring system, so the model scaling method of the mooring line is given in detail. A produced mooring line model is shown in Fig. 9. Iron chain and lead wire were used to tune the weight of the mooring line. A homogeneous iron chain was selected with the length of geometrical similarity. The lead wires were placed in certain places with the same interval, so that the wet weights of model-scaled mooring line correspond to that of the prototype one. The experiment did not scale the outer diameter of each line directly, thus the drag force was not imitated accurately. Lead wires were also arranged at each required position to correctly simulate the wet weight of the clump weight. The stiffness of the mooring line was adjusted by a spring, and a tensile test was conducted to ensure that the axial stiffness (EA) of the model-scale mooring line is correctly modeled. In addition, the positions of fairleads and anchors of the mooring system were all obtained by a direct scale of 1:64 from real values.

During the model test, series of dynamic responses of FWT model were recorded by different instruments. A noncontact optical motion capture system was used to measure the 6DOF motions of the FWT. The global *X*-axis is toward the downwind direction of the wind turbine. As seen in Fig. 8, the mooring line #1 and line #2 are arranged in the inline direction of the environmental loads, and mooring line #4 to line #6 are arranged toward the upwind direction. Therefore, the tension of line #4 and line #1 are worth studying as examples. The fairlead tension of each mooring line could be measured through the single-component load cell. In the following study, the pitch motion, surge motion, and fairlead tension of line #4 are compared.

### 4.3 Validation of the Numerical Model.

Before comparing the three mooring systems through numerical simulation, the numerical model of the SPIC concept FWT with Hybrid form2 mooring system was calibrated and validated by comparison against model test results. The experimental and numerical FWT responses in a horizontal restoring stiffness test, free decay test, and survival condition test were compared. Cao et al. [38] provided a more detailed validation of the numerical model.

To calibrate the numerical model of Hybrid form2 mooring system, the relationship between the horizontal forces and offsets in positive *X*-direction were compared between the experimental and numerical simulations. The force–displacement relationships obtained from model tests and fast software were compared in Fig. 10. The numerical results are in good agreement with the experimental results.

The natural periods and damping coefficients of FWT motions in horizontal plane are greatly influenced by the mooring system. Decay tests in calm water can initially give insight into the viscous damping of the floating platform, and the process for tuning the damping coefficient in the numerical model was described in detail by Cao et al. [38]. It can be seen in Table 7 that the experimental and numerical natural periods and nondimensional damping coefficients match well.

Exp | Num | Exp | Num | |
---|---|---|---|---|

Item | period (s) | period (s) | damping (–) | damping (–) |

Heave | 21.40 | 21.22 | 0.033 | 0.031 |

Surge | 107.52 | 107.79 | 0.108 | 0.106 |

Pitch | 26.79 | 26.63 | 0.062 | 0.059 |

Yaw | 98.99 | 98.21 | 0.088 | 0.086 |

Exp | Num | Exp | Num | |
---|---|---|---|---|

Item | period (s) | period (s) | damping (–) | damping (–) |

Heave | 21.40 | 21.22 | 0.033 | 0.031 |

Surge | 107.52 | 107.79 | 0.108 | 0.106 |

Pitch | 26.79 | 26.63 | 0.062 | 0.059 |

Yaw | 98.99 | 98.21 | 0.088 | 0.086 |

The dynamic responses under survival condition EC4 mentioned in Table 2 were simulated through experimental and numerical methods. The irregular wave, turbulent wind, and constant current were measured during the model test, and the recorded time series for measured wave and wind were input into the numerical models. The time series and power spectral densities (PSDs) of surge motion are compared between model test and numerical simulation in Fig. 11. The mean values of the responses, which are mainly decided by the current forces, were simulated accurately by the numerical model. For PSD results, the low-frequency components at surge natural frequency and the wave-frequency components caused by the clump weights motion matched well between experimental and numerical results.

## 5 Performance Comparison of Mooring System Proposals for the Floating Wind Turbine

### 5.1 Mooring Line Characteristics

#### 5.1.1 Horizontal Force.

The horizontal restoring stiffness curves in *X*-direction are compared among the three different mooring forms through numerical simulations, as shown in Fig. 12. A series of initial offsets were applied to the wind turbine in positive *X*-direction and negative *X*-direction. At small *X*-offsets, the stiffness characteristics of simple form and Hybrid form2 do not show obvious differences no matter in positive or negative directions, while Hybrid form1 looks more stiff. However, when the offset is larger than 15 m in positive *X*-direction, or larger than 5 m in negative *X*-direction, the stiffness of Hybrid form2 increases significantly, unlike the other two.

#### 5.1.2 Fairlead Tension.

The mooring line characteristics also consider the relationship between the fairlead tensions of a certain mooring line and offsets in inline direction. Mooring lines #1 and #2 are arranged in line with the environmental loads (*X*-direction). When the wind turbine moves in the negative direction, these two lines are stretched. A series of initial offsets were applied to the wind turbine in positive *X*-direction and negative *X*-direction through numerical simulations. The fairlead tensions of line #1 were recorded under different offsets to show inline offset characteristics.

In Fig. 13, pretensions of three mooring systems can be compared first. The pretension is influenced by the submerged weight of the suspended part for the chain. The pretension for Hybrid form2 is smaller than the other two forms because the size of the catenary for Hybrid2 is smaller and there is no clump attached to its suspended part. It can also be seen that tension varies linearly when the offsets are positive, while the variation becomes nonlinear at large *X*-offsets in negative direction. This is a typical characteristic for the catenary mooring system and it is more significant for this intermediate water depth. Simple form and Hybrid form1 have identical chain characteristics and the clump weight for Hybrid form1 only changes the pretension, compared with the simple form. Among these three concepts, the nonlinear variation of Hybrid form2 is the most noticeable due to large clump weight on the bottom section. The dotted lines and numbers in Fig. 13 indicate that when the negative offset is 3 m, 9 m, and 12.5 m, there will be one, five, and ten clumps on the bottom section of Hybrid form2 lifted up, respectively.

### 5.2 Response Amplitude Operator and Quadratic Transfer Function.

It is necessary to investigate the effect of mooring system stiffness on the first-order motion response amplitude operators (RAOs) and second-order wave load transfer functions. The stiffnesses of three mooring system forms differ, and each mooring system provides different stiffness at different offsets, as shown in Fig. 12. The restoring matrix used in frequency domain analysis in hydrod software should be distinguished for different mooring forms and offsets. For each mooring system form, three models with different mooring system stiffness caused by different offsets were considered (Hybrid form2 is taken as an example):

*Model 1*: No mooring system stiffness (zero)*Model 2*: Mooring system stiffness based on zero offset (1.06 × 10^{5}N/m for Hybrid2)*Model 3*: Mooring system stiffness based on the maximum mean offset under extreme condition (3.11 × 10^{5}N/m for Hybrid2)

These three models have same critical damping but different restoring matrix. The RAOs of surge and pitch motions in the range of 0–2 rad/s were first compared in Fig. 14. Large differences can be observed in the low-frequency range. The natural frequency and the magnitude of the RAO differ among the three models. However, they do not influence the second-order wave load calculation when the wave is in wave-frequency range, and they only influence the low-frequency motion responses. For extremely low wave frequencies, like less than 0.25 rad/s, the corresponding wave period is 25+ s. There would be no such first-order wave, so the difference of RAOs at extremely low-frequency range would not affect the low-frequency motion responses obtained by three models. However, the second-order wave load will affect the low-frequency surge and pitch response. For the hydrodynamic calculation of the full quadratic transfer functions (QTFs) in frequency domain, the solutions of the first-order motion RAOs are used as the boundary conditions. What matters for calculating the second-order wave loads for a given irregular wave condition is the motion RAOs in the wave frequency range (from 0.4 rad/s to 1.4 rad/s). It can be observed from Fig. 14 that the RAOs at wave frequency are basically the same among three models for both surge and pitch motions.

The transfer functions of F1 (wave force in the surge direction) and F5 (wave force in the pitch direction) of the FWT with Hybrid2 mooring system and model 3 mooring system stiffness are shown as an example in Figs. 15(a) and 15(b), respectively. The frequency range is from 0.4 rad/s to 1.4 rad/s, corresponding to the incident wave frequency range. The black dotted line represents that the difference frequency is equal to the corresponding natural frequency. In order to see the difference of the QTFs among three models, the second-order transfer functions at the diagonal line and the dotted line are illustrated in Fig. 16. The values at the diagonal line represent the transfer functions of mean drift forces, and the values at the dotted line represent the second-order transfer functions at surge or pitch natural frequency. The mean drift force and QTF at natural frequency in the pitch direction are basically identical among three models, which means the QTF for F5 is not greatly affected by the mooring stiffness. However, for F1, the QTFs of model 2 and model 3 indeed show differences in relatively larger frequency ranges. For the environmental conditions used in this study, the incident frequency of irregular waves is concentrated in the lower part of the wave-frequency range. Therefore, the same QTF results were used for calculating dynamic responses of FWT with three different mooring systems.

### 5.3 Dynamic Responses of Floating Wind Turbine Under Operational and Survival Conditions.

The environmental parameters of the operational conditions (EC1–EC3) and survival condition (EC4) are given in Table 2. Some essential dynamic responses concerning the mooring system, including the pitch motion, surge motion, fairlead tension of mooring line #4, etc., were simulated through numerical methods. These responses under four environmental conditions were compared among three mooring system cases.

#### 5.3.1 Wave-Only Condition.

The results of the wave-only test (EC1) are compared first. The mean values and power spectra of pitch motion, surge motion, and fairlead tension of line #4 with three different mooring systems under wave-only condition EC1 are compared in Table 8 and Fig. 17, respectively. Under wave-only conditions, the mean surge motion and pitch motion are basically same among three cases. This is because the mean drift force are very small, and the stiffness of each mooring system is very similar within the small offset range. In the PSD, significant spectral peaks appear at the natural frequencies of the pitch and surge motions. The low-frequency components excited by the surge and pitch resonant motion show some differences among three cases. Hybrid form2 shows larger low-frequency motions because of the smaller mass of the suspended part of mooring line. However, the difference is not obvious. The mean fairlead tension of line #4 differs among three cases. The average tension of Hybrid form1 is even twice that of the Hybrid form2. In addition, the wave-frequency tension component of Hybrid form1 is obviously larger than those of the other two cases. During the small motion of the wind turbine, the clumps attached to the suspended part move violently, leading to large fluctuation of the fairlead tension of Hybrid form1. For wave-only condition with small offsets, the Hybrid form2 is a better choice for small and stable fairlead tension.

Item | Form | EC1 | EC2 | EC3 | EC4 |
---|---|---|---|---|---|

Simple | 0.010 | 3.604 | 2.779 | −1.871 | |

Pitch (deg) | Hybrid1 | 0.012 | 3.780 | 3.047 | −1.639 |

Hybrid2 | 0.008 | 3.597 | 2.756 | −2.052 | |

Simple | 0.583 | 6.560 | 9.830 | 23.056 | |

Surge (m) | Hybrid1 | 0.498 | 5.971 | 8.454 | 21.488 |

Hybrid2 | 0.685 | 6.483 | 8.765 | 17.687 | |

Simple | 0.772 × 10^{3} | 1.032 × 10^{3} | 1.205 × 10^{3} | 2.159 × 10^{3} | |

Tension #4 (kN) | Hybrid1 | 1.111 × 10^{3} | 1.303 × 10^{3} | 1.457 × 10^{3} | 2.291 × 10^{3} |

Hybrid2 | 0.554 × 10^{3} | 0.929 × 10^{3} | 1.152 × 10^{3} | 2.168 × 10^{3} |

Item | Form | EC1 | EC2 | EC3 | EC4 |
---|---|---|---|---|---|

Simple | 0.010 | 3.604 | 2.779 | −1.871 | |

Pitch (deg) | Hybrid1 | 0.012 | 3.780 | 3.047 | −1.639 |

Hybrid2 | 0.008 | 3.597 | 2.756 | −2.052 | |

Simple | 0.583 | 6.560 | 9.830 | 23.056 | |

Surge (m) | Hybrid1 | 0.498 | 5.971 | 8.454 | 21.488 |

Hybrid2 | 0.685 | 6.483 | 8.765 | 17.687 | |

Simple | 0.772 × 10^{3} | 1.032 × 10^{3} | 1.205 × 10^{3} | 2.159 × 10^{3} | |

Tension #4 (kN) | Hybrid1 | 1.111 × 10^{3} | 1.303 × 10^{3} | 1.457 × 10^{3} | 2.291 × 10^{3} |

Hybrid2 | 0.554 × 10^{3} | 0.929 × 10^{3} | 1.152 × 10^{3} | 2.168 × 10^{3} |

#### 5.3.2 Wind-Only Condition.

The mean values and power spectra of pitch motion, surge motion, and fairlead tension of line #4 with three different mooring systems under the wind-only condition EC2 are compared in Table 8 and Fig. 18, respectively. Under the wind-only condition, the offset of the wind turbine is significantly increased compared with that under the wave-only condition. However, the mean offsets of three cases are still less than 7 m, at which offset the stiffness of three mooring systems is also similar. The fluctuation of surge and pitch motion at low-frequency range is extremely similar among three cases. However, the mean fairlead tensions of simple form and Hybrid form2 are smaller than the mean value of the Hybrid form1. For giving a slightly larger surge offsets over 5 m, the clump on the bottom section of Hybrid form2 is lifted up from the bottom. Therefore, the low-frequency component of the fairlead tension for Hybrid form2. Under this wind-only condition, the performances of three mooring forms are similar.

#### 5.3.3 Combined Wave-Wind-Current Condition.

The mean values and power spectra of pitch motion, surge motion, and fairlead tension of line #4 with three different mooring systems under operational wind-wave-current combined condition EC3 are compared in Table 8 and Fig. 19, respectively. When the wave-wind-current loads are combined, the mean pitch motion is slightly decreased and mean surge motion is obviously enlarged compared with those under wind-only conditions, as seen in Table 8. When the current is applied, the low-frequency spectral peak of surge spectrum is significantly suppressed. However, the frequency corresponding to the spectral peak slightly increases, because the surge natural frequency of the floating wind turbine due to the nonlinear stiffness of the mooring system due to the large mean offset. The surge resonant frequency moves away from the low-frequency range of the inflow turbulent wind, such that the responses are less excited by the wind load.

In Table 8, it can be seen that the pitch motion is almost not influenced by the mooring system. However, the three average surge motions are different. For larger offsets, the stiffness of Hybrid form1 is largest and the stiffness of simple form is smallest, leading to the smallest mean surge value of Hybrid form1 and largest mean surge value of simple form. The mean surge motion of Hybrid form2 is slightly larger than that of Hybrid form1, but the mean fairlead tension of Hybrid form2 is significantly smaller than that of Hybrid form1. This proves the excellent properties of Hybrid form2 under this wind-wave-current combined condition. The low-frequency component of the fairlead tension is slightly larger for Hybrid form2 because some clumps on bottom section were lifted up.

#### 5.3.4 Survival Condition.

An survival condition EC4 with severe wave, wind, and current given in Table 2 was also simulated. The wind turbine was shut down and blades feathered. The mean values and power spectra of pitch motion, surge motion, and fairlead tension of line #4 with three different mooring systems under survival wind-wave-current combined condition EC4 are compared in Table 8 and Fig. 20, respectively. Compared to EC3, the mean surge motion and fairlead tension of line #4 under EC4 are significantly larger, and the mean pitch motion under EC4 is smaller. The dominant mean force comes from current but not wind.

The pitch motion is not impacted by the different mooring systems. The mean surge motion increases to 17 m for Hybrid form2 and to over 23 m for Hybrid form1 and simple form. This is a very large displacement, so Hybrid form2 exhibits the greatest stiffness of the three mooring systems. The low-frequency and wave-frequency fluctuations of surge motion and pitch motion differ slightly among three cases. For fairlead tension of line #4, the clumps attached to the bottom section are lifted up under this condition to provide large constraining force. The mean fairlead tensions of line #4 in three mooring forms are similar. However, the wave-frequency component of PSD for Hybrid form2 is significantly larger than those of the other two forms. The mean surge motion increases to 17 m which is a very large displacement. The clumps attached to the bottom section are lifted up under this condition to provide large restoring force. The clumps are lifted up and put down, leading to large wave-frequency components in the line tension. Throughout the whole process, the anchors were not lifted. In this survival condition, the analysis of tension at the positions of fairlead and ten clump weights was conducted for the Hybrid form2 mooring system. All of the ten clump weights were lifted up under the mean loads for this condition. Figure 21 gives the mean values and standard deviations (STDs) of the tensions under this extreme wind-wave-current combined condition. The mean and dynamic fairlead tension are larger than the tensions at clump weights.

The Hybrid form2 mooring system can limit the FWT in a more reasonable offset, and controls the mean mooring line force similar to the other two forms at the same time, which shows better performance under this kind of survival condition.

### 5.4 Ultimate Limit State and Accidental Limit State Design Check for Three Alternative Mooring System Proposals.

The performance of the FWT with three alternative mooring systems shall be verified according to design criteria in terms of ULS and ALS, as mentioned in Sec. 3.2. This section analyzes the FWT motions and mooring line tensions of three alternative mooring systems under both normal conditions and accidental conditions.

*Y*(

*t*) in the interval

*T*is expressed as

*M*(

*T*), then the extreme value distribution of

*M*(

*T*) is described as

*v*

^{+}(

*y*;

*t*) indicates the up-crossing rate corresponding to level

*y*. The probability of

*M*(

*T*) exceeding the defined level

*y*is then expressed as

*y*can be obtained through

*T*, the number of up-crossing of level

*y*is defined as

*n*

^{+}(

*y*;

*T*). Then for

*k*time series of interval

*T*, the sample mean up-crossing rate is

*y*by the

*j*th of

*k*time series. The 95% confidence interval (CI) of the series number

*k*is

*y*≥

*y*

_{0}).

*q*(

*y*) is slowly varying and

*a*,

*b*,

*c*are all constant values.

In this research, the maximum values are obtained using five 1 h realizations, and extrapolated with an up-crossing rate of 10^{−4} Hz. As expressed in Eq. (4), at a given period of 1 h, the up-crossing rate of 10^{−4} Hz corresponds to a probability of exceedance of approximately 30%.

#### 5.4.1 Extreme Responses for Normal Condition.

The maximum values of the surge motion and fairlead tension of line #4 with three mooring system forms under operating condition (EC3) and survival condition (EC4) are demonstrated in Fig. 22. Compared with simple form and Hybrid form1, Hybrid form2 has relatively smaller maximum values of surge motion and fairlead tension under operational condition. In the survival condition, the Hybrid form2 limited the maximum surge motion to 23 m, while the FWT with the other two mooring forms reached a maximum surge motion of more than 26 m. In general, the maximum offsets of FWT with three mooring systems are all within reasonable ranges in design requirements. On this basis, the mooring line of Hybrid form2 withstands a maximum tension of 4170 kN, which is larger than the maximal tensions of simple form and Hybrid form1.

#### 5.4.2 Extreme Results for Accidental Condition.

If any mooring line in a mooring system is broken and the remaining part of the FWT meets the ALS criterion, then the initial undamaged mooring system is said to be redundant. All of the three mooring systems in this study contained six mooring lines. As seen in Fig. 6, line #3–line #6 which are positioned upwind withstand relatively greater environmental loads than line #1–line #2. Assuming line#3 is broken, the line #4 bears the tension that originally two lines should bear. This accidental case was simulated under the design load case EC3 and the survival load case EC4. The fairlead tension of line #4 would be used to check the performance of the mooring system for ALS analysis. The maximum values of the surge motion and fairlead tension of line #4 under accidental conditions with line #3 broken are given in Fig. 23. For accidental condition with one line broken, the maximum values of mooring line tension are significantly larger than those of intact mooring systems. Besides, the maximum values under survival conditions are more severe than those under operational conditions. For survival condition EC4, the maximum offsets of FWT with three mooring systems are all within reasonable ranges in design requirements. On this basis, the mooring lines of Hybrid form2 can still withstand the maximum tension among three mooring systems.

#### 5.4.3 Utilization Factor.

*η*of a mooring system can be obtained by dividing the maximum mooring line tension

*T*

_{max}to the allowable mooring line tension. When

*η*reaches 1, it means the mooring system fails. The allowable tension of the mooring system is defined as dividing the minimum breaking strength (MBS) by the safety factor

*γ*

_{S}. Therefore, the utilization factor can be calculated as follows:

The required safety factors of the chain are given in the ABS rule [17]. For ULS analysis, safety factors are defined as 2.25 and 1.67 in design and survival load cases, respectively. For ALS analysis, safety factors are defined as 1.22 and 1.05 in design and survival load cases, respectively. The breaking loads of chains in three different intact mooring forms are given in Table 3. The extreme fairlead tensions of line #4 under normal conditions and accidental conditions are shown in Figs. 22 and 23, respectively. Then the utilization factors of mooring lines in three forms are calculated and listed in Table 9. The utilization factors of all three mooring systems are smaller than 1, which means that the strength of the mooring lines are enough for both ULS and ALS design checks. Moreover, among all three forms, the utilization factor of Hybrid form2 is closest to 1, while the other two forms have significant redundancy in utilization.

Analysis condition | Load condition | Simple | Hybrid1 | Hybrid2 |
---|---|---|---|---|

Normal (intact) | Design load case | 0.363 | 0.394 | 0.518 |

Survival load case | 0.567 | 0.611 | 0.950 | |

Accidental (one line failure) | Design load case | 0.296 | 0.315 | 0.434 |

Survival load case | 0.564 | 0.622 | 0.909 |

Analysis condition | Load condition | Simple | Hybrid1 | Hybrid2 |
---|---|---|---|---|

Normal (intact) | Design load case | 0.363 | 0.394 | 0.518 |

Survival load case | 0.567 | 0.611 | 0.950 | |

Accidental (one line failure) | Design load case | 0.296 | 0.315 | 0.434 |

Survival load case | 0.564 | 0.622 | 0.909 |

### 5.5 Economic Cost.

*Price*represents the price of chain material per kilogram. The clumps used in hybrid form can be seen as heavy chain, so the price for the clump weights can also be estimated using Eq. (10). The cost for mooring lines in three mooring systems is given in Table 10. The cost for mooring lines in Hybrid form2 is the lowest, which is nearly half of the cost for simple form. Therefore, the Hybrid form2 mooring system shows the best economic performance.

Form | Line | Clump | Total |
---|---|---|---|

Simple | 315.4 × 800 × 6 × price | 0 | 1513.9 × 10^{3} × price |

Hybrid1 | 315.4 × 500 × 6 × price | 2800 × 10 × 6 × price | 1114.2 × 10^{3} × price |

Hybrid2 | 197.6 × 465 × 6 × price | 3800 × 10 × 6 × price | 779.3 × 10^{3} × price |

Form | Line | Clump | Total |
---|---|---|---|

Simple | 315.4 × 800 × 6 × price | 0 | 1513.9 × 10^{3} × price |

Hybrid1 | 315.4 × 500 × 6 × price | 2800 × 10 × 6 × price | 1114.2 × 10^{3} × price |

Hybrid2 | 197.6 × 465 × 6 × price | 3800 × 10 × 6 × price | 779.3 × 10^{3} × price |

## 6 Conclusions

Mooring system design is quite challenging for intermediate transition water depths. This paper proposed three forms of the mooring system for SPIC concept FWT which can be applied to a water depth of 60 m. One is a simple form with only catenary lines, and the other two are hybrid forms consisting of clump weights and catenary lines. The biggest difference between the two hybrid forms lies in the position of clumps at suspension section and bottom section, respectively. Hybrid form2 has smaller footprint area and shorter bottom section length. Also, the length, outer diameter, wet weight, and EA of Hybrid form2 can be significantly reduced. Three alternative mooring system proposals were evaluated through mooring line characteristics, natural period and damping coefficient, dynamic responses, and simple cost analysis.

The inclusion of the clump weight could help the mooring system achieve a larger stiffness. Attaching the clump weights on the bottom section allows for less pretension and makes the mooring line exhibit relatively significant nonlinearity only at large offsets. The first-order motion RAOs and second-order wave load transfer functions can be considered the same for all three proposals. Under operational conditions, the surge motion of FWT with the Hybrid form1 mooring system is smaller, while the mooring line tension is extraordinarily larger compared with other two forms. Especially for the combined wind-wave-current condition EC3, the surge motion for Hybrid form1 and Hybrid form2 is similar, but the fairlead tension is significantly smaller for Hybrid form2. Under survival condition, the clumps of Hybrid form2 were lifted up and put down, leading to small mean offsets of FWT but large wave-frequency components of mooring line tension. For Hybrid form2, the mean value and STD of fairlead tension are still larger compared with the tensions at clump weights. Among the three forms of the mooring system, the Hybrid form2 can limit the FWT to the smallest offset range while also controlling the mean mooring line tension to a level similar to the other two forms. Under normal working conditions and accidental conditions with single line broken, the maximal surge motions of FWT under the restraint of three mooring systems all meet the design requirements. The mooring line strength of the three mooring systems meets the requirements in ULS and ALS analyses and there are no vertical forces acting on the anchors. Among them, the utilization coefficient of Hybrid form2 is closest to 1, demonstrating its best economic performance. From the cost analysis, the utilization coefficient of Hybrid form2 is closest to 1, demonstrating its best economic performance. Therefore, the Hybrid form2 mooring system with better performance and competitive cost is recommended for future application.

## Acknowledgment

The authors would like to thank the 2022 OMAE Best Paper Award issued by the ASME OMAE Awards Committee. The authors are grateful for the careful instructions and guidance from Erin E. Bachynski-Polić from Norwegian University of Science and Technology and Zhen Gao from Shanghai Jiao Tong University. The authors would like to thank the support from the National Natural Science Foundation of China (Grant Nos. 42176210, 52031006, and 52201330) and the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University (Grant No. SL2021PT203).

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.