Design and Parametric Sensitivity Analysis of a Steel-Concrete Hybrid Semi-Submersible Foundation Supporting a 15 MW Wind Turbine

Abstract

With the rapidly growing global demand for clean energy, offshore wind power has become an important renewable energy source. To clarify how the principal dimensions affect the performance of a 15 MW-class floating wind turbine platform in 100 m water depth, this paper proposes a steel-concrete hybrid semi-submersible platform and systematically performs a parametric sensitivity analysis. The platform adopts a three-column configuration with heave tanks. The upper columns and cross braces are made of steel, while the lower hexagonal columns, pontoons, and heave tanks are constructed from concrete, significantly reducing steel consumption while satisfying structural and stability requirements. Focusing on three key design variables—draft, column spacing, and column diameter—this study establishes a unified normalized sensitivity analysis framework. It quantitatively evaluates their influence on platform mass, intact stability, natural periods, and fully coupled dynamic responses (including surge, heave, pitch motions, and mooring line tensions) under both operational and extreme conditions. The results reveal distinct roles of the principal dimensions in governing the platform dynamics: column spacing is the most sensitive parameter for tuning pitch response, restoring stiffness, and stability; increasing draft effectively suppresses heave and pitch responses but has only a limited effect on low-frequency surge motions; and column diameter strongly affects the natural periods of heave and pitch. Notably, dynamic responses exhibit significant nonlinear characteristics with variations in column diameter. When the diameter exceeds 110–120% of the baseline value, the peak pitch response under extreme sea states shows a deteriorating inflection point, accompanied by an accelerated surge in peak mooring loads. This indicates that excessive increases in column diameter may cause wave excitation forces to become dominant, thereby compromising the overall dynamic safety of the system. This paper identifies the governing geometric parameters for different motion modes and their control boundaries, providing a quantifiable and generalizable basis for the multi-objective collaborative design and cost reduction optimization of 15 MW steel-concrete hybrid semi-submersible floating wind turbine platforms.

1. Introduction

Amid the global transition towards a low-carbon energy structure [1,2], offshore wind power has become a strategic priority in the development of renewable energy [3,4,5,6]. In 2024, the global newly installed offshore wind capacity reached 8 GW, with China contributing 4 GW, accounting for 50% of the total [7]. Against this backdrop, the wind power industry is accelerating its expansion into deep and distant sea areas [8,9,10]. Compared to nearshore fixed-bottom wind turbines, floating wind turbines offer significant technical and economic feasibility in water depths exceeding 60 m [11,12]. However, as unit capacities advance towards 15 MW and even 20 MW, the aerodynamic loads on turbines increase dramatically, imposing higher demands on the load-bearing capacity, stability, and motion performance of floating foundations. The core bottleneck currently hindering the commercialization of floating wind power can be summarized as the need for “cost reduction and efficiency enhancement”: redundant floater designs lead to excessive steel consumption, suboptimal configurations induce excessive dynamic responses, and mooring system costs remain prohibitively high [13]. Therefore, pursuing low-cost design and performance optimization for high-power turbine floating foundations constitutes a critical scientific issue for promoting the industrialization of floating wind power [14,15,16].

Floating wind turbine foundations primarily include semi-submersible [17], tension leg platform (TLP) [18], and Spar [19] types. Spar platforms are constrained by their deep draft (typically >100 m), while TLPs face high tendon installation and maintenance costs. In contrast, semi-submersible platforms have become the most commercially promising configuration for deep-sea wind power due to their strong adaptability to various water depths, convenient wet-tow installation, and excellent dynamic characteristics [20]. In recent years, to accommodate very large 10 MW to 16 MW turbines, scholars have conducted in-depth research on the coupled dynamics of high-power semi-submersible platforms. As foundation configurations scale up, the accurate assessment of nonlinear hydrodynamic effects becomes particularly critical. A recent review by Amouzadrad et al. [21] provides a comprehensive overview of theoretical and numerical methods for sensitivity and uncertainty analysis in the hydrodynamic and hydroelastic behavior of floating offshore structures, highlighting the importance of parametric studies in optimizing design processes. Research by Zhang Lixian et al. [22] confirms that for large semi-submersible platforms, neglecting Morison drag forces leads to an overestimation of motion responses, and that second-order difference-frequency wave loads can readily induce low-frequency pitch resonance. Liu et al. [23] further revealed the detrimental effects of extreme sea states (e.g., rogue waves) and mooring line failures on the platform’s transient large deformations and system power output. Furthermore, research from the Norwegian University of Science and Technology (NTNU) has focused on the design of semi-submersible platforms [24,25,26]. Their findings indicate that the safety of the dynamic response of high-power semi-submersible platforms can be validated through a combination of rational frequency-domain and fully coupled time-domain analyses. In addition, beyond parametric optimization, Amouzadrad et al. [27] developed a numerical model for a moored articulated floating platform integrated with a vertical flap-type wave energy converter and a submerged interconnected structure, demonstrating that such hybrid multi-energy complementary systems can not only effectively reduce hydroelastic responses and enhance overall stability but also improve power output, offering valuable insights for the design of floating platforms.

However, traditional high-power semi-submersible platforms predominantly utilize all-steel structures. To meet the substantial stability demands of a 15 MW wind turbine, their principal dimensions must be significantly increased, leading to excessive steel consumption and high construction costs. Consequently, the use of low-cost materials to lower the center of gravity has emerged as an important design strategy. For instance, Deng Lu et al. [28] validated the feasibility of a steel-concrete hybrid semi-submersible platform concerning stability and hydrodynamics. Deng et al. adopted a symmetric four-column configuration with the tower centrally located. The columns and connecting members were constructed from reinforced concrete, while steel was used for the bottom plates. The wind turbine capacity was 5 MW, and the study primarily focused on validating the feasibility of the steel-concrete hybrid concept. Existing studies on steel-concrete hybrid platforms have primarily focused on feasibility validation, with limited attention given to larger turbine capacities, asymmetric mooring configurations, and systematic parametric investigations. In contrast, this study targets a 15 MW wind turbine integrated with an asymmetric mooring system under directional wave, wind, and current loads. A normalized sensitivity analysis framework is established to systematically evaluate the effects of key principal dimensions on platform performance. The objective is to derive design-oriented parametric patterns that can guide the practical design and optimization of steel-concrete hybrid semi-submersible platforms. While recent studies have developed systematic reliability assessment frameworks for complex integrated energy systems considering uncertainties in renewable energy generation and operational strategies [29], the present work establishes a parametric sensitivity analysis framework for a steel-concrete hybrid semi-submersible platform. The quantified influence patterns of principal dimensions on static and dynamic performance provide a quantitative basis for future reliability assessments of floating wind systems under uncertain environmental and operational conditions.

To achieve “cost reduction and efficiency enhancement” for a 15 MW-class floating wind turbine foundation in deep water, this paper proposes a novel steel-concrete hybrid semi-submersible platform. The design leverages the inherent advantages of the lower concrete structure—low cost, corrosion resistance, and substantial ballast mass—to ensure excellent hydrodynamic performance while significantly reducing equivalent steel consumption and construction costs. Based on this design, the paper establishes a unified parametric analysis framework covering static characteristics, modal behavior, and fully coupled dynamic responses. This framework systematically investigates the nonlinear effects of key principal dimensions (draft, column spacing, and column diameter) on the hybrid platform’s behavior. The study first quantifies the effects of each geometric parameter on mass redistribution, intact stability, and natural periods. It then investigates, under both operational and extreme survival sea states, how these parameters affect the platform’s six-degree-of-freedom motions and the ultimate mooring tensions. By integrating multi-dimensional static and dynamic analysis results, this paper precisely identifies the governing geometric parameters for different motion modes and their safety control boundaries, aiming to provide a robust theoretical basis and quantitative guidance for the multi-objective performance balance and low-cost optimization of next-generation very large hybrid floating wind turbine platforms. The innovations of this study lie in the following:

(1)

Proposing a novel steel-concrete hybrid semi-submersible platform concept;

(2)

Establishing a sensitivity analysis framework specifically applicable to steel-concrete hybrid platforms by means of a normalization strategy;

(3)

Quantifying the effects of principal dimension parameters on the static and dynamic performance of the steel-concrete hybrid platform, thereby providing a quantitative basis for principal-dimension optimization and multi-objective design of such platforms.

The framework of this paper is organized as follows: Section 1 introduces the research background and the main content of this study. Section 2 presents the theoretical models and calculation methods for offshore wind turbine loads. Section 3 details the design scheme of the novel 15 MW steel-concrete hybrid semi-submersible platform and the methodology for the parametric sensitivity analysis. Section 4 examines how perturbations in the principal dimensions affect the platform’s mass distribution, stability margin, and modal periods. Section 5 evaluates the effects of parametric variations on the platform’s coupled dynamic responses and peak mooring loads under multiple sea states. Finally, Section 6 summarizes the core findings of this paper and provides engineering design guidelines.

2. Theoretical Methodology

An offshore floating wind turbine is a coupled system composed of a wind turbine, a floating foundation, and a mooring system, and it is subjected to the combined effects of wind, waves, currents, and other marine environmental loads. The wind turbine is mainly subjected to wind loads, while the floating foundation and the lower mooring system are mainly affected by wave loads and current loads. The theoretical models used to calculate aerodynamic loads, wave loads, and mooring forces are introduced below. These models form the basis of the fully coupled wind turbine model used to predict the dynamic responses accurately.

2.1. Blade Element Momentum (BEM) Method

The calculation of aerodynamic loads on wind turbine blades constitutes a critical aspect in wind turbine design, directly impacting blade structural integrity, stability, and overall performance. Currently, the primary methods for computing these aerodynamic loads include Blade Element Momentum (BEM) theory and Computational Fluid Dynamics (CFD) approaches. Due to its computational efficiency and simplicity, the BEM method has been widely used in engineering practice [19].

The BEM theory discretizes the rotor blade into multiple independent blade elements along the spanwise direction. The aerodynamic forces on each element are computed individually based on local inflow conditions. The thrust dT and torque dQ generated by a single blade element are given by the following equations:

$$dT={\displaystyle \frac{1}{2}}{\rho }_{air}c{u}_{rel}^2\left(C_L\cos \theta +C_D\sin \theta \right)dr$$

(1)

$$dQ={\displaystyle \frac{1}{2}}{\rho }_{air}c{u}_{rel}^2\left(C_L\sin \theta -C_D\cos \theta \right)dr$$

(2)

where ρ_air is the air density, c is the airfoil chord length, u_rel is the relative inflow velocity at the blade element, θ represents the inflow angle, C_L is the lift coefficient, and C_D is the drag coefficient. By integrating the thrust and torque contributions from all blade elements along the span, the total aerodynamic loads acting on the entire blade can be obtained. These integrated loads subsequently yield the complete rotor’s thrust and torque characteristics.

2.2. Hydrodynamics

2.2.1. Morison’s Equation

The hydrodynamic loads F on slender structural members consist primarily of drag and inertia force components, which are calculated using Morison’s equation as follows [22]:

$$F=F_D+F_I={\displaystyle \frac{1}{2}}{C}_D\rho D{U}^2(t)+C_M\rho {\displaystyle \frac{\pi D^2}{4}}{\displaystyle \frac{\partial U\left(t\right)}{\partial t}}$$

(3)

where F_D is the drag force, F_I is the inertia force, C_D is the drag force coefficient, ρ is the fluid density, D is the member diameter, U(t) is the flow velocity, C_M is the inertia coefficient, C_M = 1 + C_m, and C_m is the added mass coefficient.

2.2.2. Potential Flow Theory

For large-scale floating bodies, where significant wave diffraction and radiation phenomena occur during wave-structure interaction, the hydrodynamic coefficients and wave forces must be computed using three-dimensional potential flow theory based on diffraction and radiation analysis. Potential flow theory assumes the fluid is inviscid, incompressible and irrotational. The fluid velocity potential satisfies Laplace’s equation, expressed as [28]:

$${\nabla }^2\Phi \left(\mathrm{x},y,z,t\right)={\displaystyle \frac{{\partial }^2\Phi }{\partial x^2}}+{\displaystyle \frac{{\partial }^2\Phi }{\partial y^2}}+{\displaystyle \frac{{\partial }^2\Phi }{\partial z^2}}=0$$

(4)

The linear solution under steady-state conditions with incoming wave frequency ω can be expressed by:

$$\Phi \left(x,y,z,t\right)=\mathrm{Re}\left[\varphi \left(x,y,z\right){\mathrm{e}}^{-i\omega t}\right]$$

(5)

Considering the radiation and diffraction problem of floating bodies, velocity potential can be decomposed into the incident potential ϕ_I, diffraction potential ϕ_D, and radiation potential ϕ_R:

$$\varphi \left(x,y,z\right)={\varphi }_I\left(x,y,z\right)+{\varphi }_D\left(x,y,z\right)+{\varphi }_R\left(x,y,z\right)$$

(6)

in which the radiation potential can be expressed as the linear superposition of the six motion components as follows:

$${\varphi }_R\left(x,y,z\right)={\displaystyle \sum _{k=1}^6{x}_k}{\varphi }_{Rk}\left(x,y,z\right)={\displaystyle \sum _{k=1}^6{x}_k}\left\{\left.\mathrm{Re}\left[{\varphi }_{Rk}\left(x,y,z\right)\right]+i\mathrm{Im}\left[{\varphi }_{Rk}\left(x,y,z\right)\right]\right\}\right.$$

(7)

Wave forces F(t) acting on the floating body can be obtained by integrating hydro-pressure over the wetted surface of the structure, and based on the potentials, forces can be further expressed as follows:

$$F\left(t\right)=\mathrm{Re}\left[\left\{\left.F_K\left(\omega \right)+F_D\left(\omega \right)+F_R\left(\omega \right)\right\}\right.e^{-i\omega t}\right]$$

(8)

$$F_K\left(\omega \right)=-{\displaystyle \underset{S}{\iint }i\omega \rho {\varphi }_I\left(x,y,z\right)ndS}$$

(9)

$$F_D\left(\omega \right)=-{\displaystyle \underset{S}{\iint }i\omega \rho {\varphi }_D\left(x,y,z\right)ndS}$$

(10)

$$F_R\left(\omega \right)=-{\displaystyle \underset{S}{\iint }i\omega \rho {\varphi }_R\left(x,y,z\right)ndS}$$

(11)

where S is the wetted surface of the floating body; n is the outward normal vector at a point on the floating body surface; F_K is the Froude-Krylov force (F-K force); F_D is the wave diffraction force; and F_R represents the wave radiation force.

The radiation force can be further decomposed into the added mass coefficient and the radiation damping coefficient of the floating body, expressed by Equations (12) and (13):

$$A_k\left(\omega \right)={\displaystyle \frac{\rho }{\omega }}{\displaystyle \underset{S}{\int }\mathrm{Im}\left[{\varphi }_{Rk}\left(x,y,z\right)\right]ndS}$$

(12)

$$B_k\left(\omega \right)=-\rho {\displaystyle \underset{S}{\int }\mathrm{Re}\left[{\varphi }_{Rk}\left(x,y,z\right)\right]ndS}$$

(13)

2.3. Current Load Calculation Theory

In engineering calculations, the current velocity is typically assumed to be constant at the same water depth. When considering only current effects, the current load F_C on the platform is calculated with reference to the drag force term in the Morison equation, expressed as:

$$F_C={\displaystyle \frac{1}{2}}\rho C_D{A}_C{V}_C^2$$

(14)

where ρ is the fluid density, C_D is the drag coefficient, A_C is the projected area of the structural member perpendicular to the current direction, and V_C is the current velocity.

2.4. Theory of Mooring System

The simulation of mooring systems is based on the catenary theory using finite element methods to obtain mooring restoring forces, mooring configuration, and mooring tension. The actual mooring line is first simplified as slender rod elements, then discretized in space through the finite element method to establish the dynamic response equation of the mooring line [30]:

$$R^I(r,\ddot{r},t)+R^D(r,\dot{r},t)+R^S(r,t)=R^E(r,\dot{r},t)$$

(15)

where R^I represents generalized inertial forces, such as hydrodynamic inertial forces acting on the mooring line; R^D denotes generalized damping forces, including fluid damping and structural damping; R^S stands for structural reaction forces, such as interactions between the mooring line and seabed; R^E is the external force vector, including gravity and buoyancy; r, $\dot{r}$ and $\ddot{r}$ are the nodal displacement, velocity, and acceleration vectors of the structure, respectively. By solving Equation (15) using the Newton-Raphson iteration method, the kinematic physical quantities of nodes along the mooring line are obtained, from which the mooring tension at the fairlead can be determined. Since this method directly performs time-stepping iterative solutions of Equation (15) without linear simplification, nonlinear hydrodynamic forces on the mooring line, material and geometric nonlinearities of the mooring line, and seabed interactions are all considered in the mooring load calculation.

2.5. Equations of Motion

2.5.1. Frequency Domain Equations of Motion

Under hydrodynamic actions, frequency domain calculations of floating bodies can quickly obtain various hydrodynamic parameters and preliminarily evaluate the linear motion response of the floating body. The frequency domain motion equation for floating foundations of offshore wind turbines is expressed as:

$$\left[-{\omega }^2\left(M+A\left(\omega \right)\right)+\mathrm{i}\omega \left(B{\left(\omega \right)}_p+B_v\right)+C+C_e\right]X\left(\omega ,\beta \right)=F\left(\omega ,\beta \right)$$

(16)

where ω represents the incident wave angular frequency; β denotes the incident wave propagation direction; M is the floating body mass matrix; A(ω) is the added mass matrix of the floating body at wave frequency ω; B(ω)_p is the radiation damping matrix of the floating body at wave frequency ω; B_v is the linear damping matrix; C is the hydrostatic restoring matrix; C_e is the restoring matrix of the mooring system; X(ω,β) is the floating body motion matrix; and F(ω,β) is the wave excitation force matrix. During the preliminary design stage, the mooring system effects are not considered.

2.5.2. Equations of Motion in Time Domain

Offshore floating wind turbines are subjected to complex loads with multi-physics characteristics, requiring consideration of aero-hydro-servo-structural coupling effects. The aerodynamic loads on the wind turbine and complex control strategies exhibit strong nonlinear characteristics, while the viscous effects of hydrodynamic loads on the floating body and nonlinear restoring effects of mooring systems cannot be neglected. Therefore, frequency domain dynamic models, due to their linear nature, cannot account for these nonlinear loads, necessitating integrated time-domain simulation calculations. In time-domain analysis, frequency-domain hydrodynamic parameters can be transformed into the time domain using the Cummins equation [31], further considering time-domain aerodynamic loads, hydrodynamic loads, current loads, mooring loads, and control strategies. The coupled motion equation can be expressed as:

$$\left(M+M\left(\infty \right)\right)\ddot{x}\left(t\right)+{\displaystyle {\int }_0^{t}R\left(t-\tau \right)}\dot{x}\left(\tau \right)d\tau +Cx\left(t\right)=F_{wind}\left(t\right)+F_{wave}\left(t\right)+F_{current}\left(t\right)+F_{mooring}\left(t\right)$$

(17)

where M(∞) represents the platform added mass at infinite wave frequency; R(t − τ) is the retardation function, which quantifies the wave memory effects; C is the hydrostatic restoring matrix; x, $\dot{x}$ and $\ddot{x}$ are the displacement, velocity and acceleration of the floating wind turbine system, respectively; F_wind is the wind load; F_wave is the wave load, including first-order and second-order wave forces; F_current is the current load; and F_mooring is the mooring load.

3. Design Scheme and Parametric Sensitivity Analysis

3.1. Configuration and Mass Redistribution Design of the 15 MW Hybrid Semi-Submersible Platform

The floating foundation designed to support a 15 MW wind turbine rotor (see

Table 1. Design parameters of the 15 MW wind turbine.

Parameter	Value
Tower mass (t)	1265.77
Tower COG-z (m)	75.97
Nacelle and wind rotor mass (t)	759.58
Nacelle and rotor COG-z (m)	150.00

) is subjected to large overturning moments induced by the substantial hub height (150 m) and nacelle mass (759.58 t). To overcome the significant increase in principal dimensions and construction costs that traditional all-steel platforms incur to maintain stability, this paper innovatively proposes a “steel-concrete hybrid” semi-submersible platform configuration featuring three columns with heave tanks, designed for a water depth of 100 m.

As shown in Figure 1, the novel platform adopts an asymmetric arrangement with the wind turbine positioned atop a single column. Regarding the spatial distribution of materials, the platform strictly adheres to a “steel above, concrete below” structural design principle. The main bodies of the three columns and the connecting cross braces are constructed from high-strength steel. This choice aims to provide sufficient buoyancy with a minimal cross-sectional area while efficiently transmitting and resisting the complex, high-frequency dynamic loads transmitted down from the wind turbine assembly. The lower hexagonal columns, the pontoons, and the bottom heave tanks are entirely constructed from poured concrete. This material topology not only enhances the structure’s corrosion resistance but also achieves an excellent mass redistribution of the system mechanically. The high-density concrete acts as an extremely efficient solid ballast at the base, significantly lowering the overall center of gravity of the platform system to Z = −15.96 m (see

Table 2. Parameters of the new floating platform.

Parameter	Value	Parameter	Value
Column height (m)	30	Platform mass (t)	18,995.4
Column diameter (m)	15	Platform COG-z (m)	−15.96
Hexagonal prism side length (m)	12	Overall COG-x (m)	4.63
Hexagonal prism height (m)	6	Overall COG-y (m)	0
Float height (m)	6	Overall COG-z (m)	−4.58
Float length (m)	59	Mass moments of inertia Ixx (kg·m2)	1.68 × 1010
Heave tank diameter (m)	30	Mass moments of inertia Iyy (kg·m2)	1.68 × 1010
Platform draft (m)	15	Mass moments of inertia Izz (kg·m2)	3.07 × 1010

). This drastically extends the restoring moment arm, providing ample intact stability margin to resist the thrust forces of the 15 MW turbine. Furthermore, the large-diameter concrete heave tanks at the bottom substantially increase the vertical added mass and viscous damping, effectively shifting the heave natural period away from the dominant wave energy frequency band.

In terms of economic indicators, the proposed hybrid design demonstrates significant potential for cost reduction. As shown in Table 2, the total displaced mass of the platform is 18,995.4 t. Of this, the lower concrete structure accounts for 16,502.1 t, while the mass of the upper steel structure is controlled to 2493.3 t. Based on current industry benchmark costs (approximately 4000 yuan per ton for steel structure and 250 yuan per ton for concrete structure), this design optimizes the key performance metric of equivalent steel consumption per MW for the 15 MW wind turbine to 235 t/MW. Assuming the same total mass, the proposed steel-concrete hybrid design achieves a reduction of approximately 81.4% in structural material cost compared to an equivalent all-steel platform. When compared to the Kincardine project (315 t/MW), the FuYao project (677 t/MW), and the CNOOC Guanlan (552 t/MW), the platform designed in this study demonstrates a significant reduction in projected equivalent steel consumption per megawatt, exhibiting superior economic benefits. This metric confirms the substantial economic advantage of this hybrid platform for large-scale commercial development in deep-sea areas. A diagram illustrating the overall global coordinate system of the floating platform (origin at the center of the still water surface, Z-axis vertically upward) and the definitions of its principal dimensions is provided in Figure 2.

3.2. Asymmetric Catenary Mooring System Design and Restoring Characteristics

To counteract the substantial and highly directional aerodynamic thrust generated by the 15 MW high-power wind turbine under both rated and extreme conditions, this paper breaks through the limitations of traditional symmetric mooring by designing an asymmetric pure catenary mooring system composed of seven anchor chains (as shown in Figure 3). This system strictly adheres to the national “Mooring Chain” specification [32] and aims to efficiently resist the platform’s mean drift in the wind direction and suppress low-frequency slow-drift motions through a differentiated spatial distribution of stiffness. Regarding the mooring topology layout, to provide strong directional restoring stiffness against turbine thrust, three 585 m long R4-142 studless anchor chains (R4 denotes the chain grade) are concentrated on the turbine-side column, with the angle between adjacent chains optimized to 3° to form a high-stiffness restraint on the windward side. To enhance the system’s yaw restoring stiffness, two 581 m long R4-152 studless anchor chains are arranged on each of the two non-turbine-side columns, with the adjacent angle set at 4°. The entire system adopts a pure catenary configuration without incorporating clump weights or buoys, relying on the nonlinear geometric restoring stiffness generated by the lifting and bottoming effects of the heavy anchor chains’ submerged weight (see

Table 3. Mooring line cross-sectional parameters.

Parameter	R4-142	R4-152
Diameter (m)	0.142	0.152
Dry weight (kg/m)	407.31	466.7
Wet weight (kg/m)	354.1	405.7
Axial stiffness (N)	1.6138 × 109	1.8400 × 109
Breaking strength (MN)	18.034	20.157

) on the seabed. The mooring lines are intended to ensure sufficient geometric restoring force at a water depth of 100 m. Integrated simulation analyses under operational and extreme conditions resulted in a maximum mooring tension of 10.49 MN, with a safety factor (maximum mooring tension/minimum breaking load) greater than 1.67, meeting the design requirements.

Furthermore, concerning the critical interface design, all seven fairleads are uniformly positioned 5 m below the platform’s waterline (Z = −5 m). This design offers two distinct advantages: first, by lowering the point of tension application, it effectively reduces the moment arm of the mooring system’s horizontal restoring forces relative to the platform’s center of gravity, thereby significantly decoupling the additional overturning moment on pitch induced by mooring tension; second, it ensures the fairlead area avoids direct slamming loads from wave action in the splash zone. The specific cross-sectional mechanical properties of the mooring lines and the three-dimensional spatial coordinates of the fairleads and anchor points are detailed in Table 3 and

Table 4. Mooring point coordinates.

Mooring Line	Fairlead (m)	Anchor (m)	Mooring Line Type
Line 1_1	(53.49, −2.80, −5.00)	(602.74, −31.59, −106.00)	R4-142
Line 1_2	(53.56, 0.00, −5.00)	(603.56, 0.00, −106.00)	R4-142
Line 1_3	(53.49, 2.80, −5.00)	(602.74, 31.59, −106.00)	R4-142
Line 2_1	(−25.15, 47.30, −5.00)	(−283.36, 532.92, −113.00)	R4-152
Line 2_2	(−28.38, 45.43, −5.00)	(−319.84, 511.85, −113.00)	R4-152
Line 3_1	(−28.38, −45.43, −5.00)	(−319.84, −511.85, −106.00)	R4-152
Line 3_2	(−25.15, −47.30, −5.00)	(−283.36, −532.92, −106.00)	R4-152

, respectively.

3.3. Parametric Sensitivity Analysis Scheme

To systematically evaluate the nonlinear effects of key parameters on the 15 MW steel-concrete hybrid semi-submersible platform under complex marine conditions, this paper establishes a normalized parametric sensitivity analysis framework constrained by stability boundaries. The core principal dimensions governing the platform’s hydrodynamic profile and mass distribution—namely draft, column spacing, and column diameter (geometric definitions are provided in Figure 4)—are selected as the research variables. Using the original model as a baseline, and keeping all other principal dimensions unchanged, each of these three variables is individually increased or decreased in increments of ±5%. This process generates a total of 24 derivative configurations, with the specific parameters detailed in

Table 5. Parameters of all models.

Model	Draft	Column Spacing	Column Diameter	Model	Draft	Column Spacing	Column Diameter
Baseline model	100% (22 m)	100% (80 m)	100% (15 m)	J1.15	100%	115%	100%
D0.8	80%	100%	100%	J1.2	100%	120%	100%
D0.85	85%	100%	100%	J1.25	100%	125%	100%
D0.9	90%	100%	100%	J1.3	100%	130%	100%
D0.95	95%	100%	100%	R0.9	100%	100%	90%
D1.05	105%	100%	100%	R0.95	100%	100%	95%
D1.1	110%	100%	100%	R1.05	100%	100%	105%
D1.15	115%	100%	100%	R1.1	100%	100%	110%
D1.2	120%	100%	100%	R1.15	100%	100%	115%
J0.9	100%	90%	100%	R1.2	100%	100%	120%
J0.95	100%	95%	100%	R1.25	100%	100%	125%
J1.05	100%	105%	100%	R1.3	100%	100%	130%
J1.1	100%	110%	100%

. The sensitivity of each performance indicator to a principal-dimension parameter is defined as the relative percentage deviation from the baseline value. For a given parameter X and a given indicator Y, the sensitivity is computed as S = (Y(X) − Y(X₀))/Y(X₀) × 100%, where X₀ denotes the baseline design. This normalization enables direct comparison of the effects of different geometric parameters across diverse physical quantities (e.g., mass, period, tension).

If a principal dimension is set too small, it may compromise the stability requirements; conversely, if it is set too large, it may lead to excessive material costs and reduced economic viability. Accordingly, the minimum draft ratio relative to the baseline model is set to 80% and the maximum ratio to 120%. For column spacing and column diameter, the minimum ratio is set to 90% and the maximum ratio to 130%. The adjustment method for each parameter is as follows. Draft is adjusted by varying the column height, during which the freeboard height and other parameters are kept constant. Column spacing is adjusted by varying the pontoon length. Column diameter is adjusted by directly changing its geometric dimension. To facilitate a quantitative analysis of the impact of principal dimension variations on economic efficiency,

Table 6. Influence of a 1 m reduction in each parameter on platform mass.

Parameter	Per 1 m Reduction in Draft	Per 1 m Reduction in Column Spacing	Per 1 m Reduction in Column Diameter
Change in steel mass (t)	−55.30	−7.70	−129.63
Change in concrete mass (t)	0	−103.20	0
Change in total mass (t)	−55.30	−110.90	−129.63

lists the change in platform mass corresponding to a 1 m reduction for each parameter. Integrated simulation analyses are performed on all models. The resulting multi-dimensional measurement data—encompassing mass distribution, stability margins, natural periods, and dynamic responses under multiple operating conditions—are non-dimensionalized. By extracting the percentage change relative to the baseline model, a global sensitivity evolution map for each parameter is visualized intuitively, thereby providing a quantitative basis for the multi-objective optimization of the foundation configuration.

Based on limit state design criteria, this paper defines two typical service scenarios for the complex dynamic load environment of deep-sea locations. The first is the operational condition, which employs combined wind-wave-current actions at the rated wind speed to evaluate the platform’s motion stability during normal power generation. The second is the extreme condition, which introduces a 50-year return period combination of extreme wind, wave, and current events to rigorously test the platform’s nonlinear transient response and the maximum bearing capacity of its mooring system under extreme environmental loads. For environmental field modeling, random waves are reproduced in the time domain using the three-parameter JONSWAP spectrum. Ocean currents are modeled considering a depth-shear gradient that accounts for marine boundary layer effects. Current velocities, designated Uc1, Uc2, and Uc3, are discretely specified at the still water surface (0 m), mid-depth (−50 m), and near the seabed (−100 m) to accurately approximate the realistic nonlinear hydrodynamic pressure distribution. For a conservative assessment, all environmental excitations are applied collinearly at 0° (i.e., along the positive X-axis, as shown in Figure 5) to induce the most unfavorable longitudinal coupled response of the system. The total duration for the time-domain solution is set to 4000 s. In the post-processing of data, the initial transient hysteresis effects during the first 400 s of system start-up are strictly excluded. The subsequent 3600 s interval (equivalent to 1 h) is extracted for statistical convergence analysis of low-frequency slow-drift motions and steady-state extreme values. This time-domain coupled model incorporates a modified hydrostatic stiffness matrix to account for restoring force variations induced by the wind turbine [33,34]. Only the second-order mean drift forces are included, which are calculated using the near-field method. The slow-drift motions are then evaluated based on Pinkster’s formula. Second-order difference-frequency QTF loads are not explicitly considered. The viscous effects of the floating turbine structure are modeled using 4% of the critical damping ratio [35,36]. The environmental parameters for each scenario are detailed in

Table 7. Environmental condition parameters.

Condition	Hs (m)	Tp (s)	Wind Speed (m/s)	Uc1 (m/s)	Uc2 (m/s)	Uc3 (m/s)	State
LC1	3	7	12	1.6	1.0	0.1	Operating
LC2	11.7	14.6	52	2.4	2.0	0.8	Shutdown

.

Figure 6 presents the wind spectra and wave spectra for both the operational and extreme conditions. The turbulence intensity of the wind is 11%. As shown in Figure 6a,c, the energy density of the wind spectra calculated by TurbSim V1.21 is primarily concentrated in the low-frequency range, which aligns with the inherent characteristics of wind spectra. As shown in Figure 6b, the energy density of the wave spectrum is mainly concentrated around 0.9 rad/s, corresponding to the designated peak period of 7 s. As shown in Figure 6d, the energy density of the wave spectrum is mainly concentrated around 0.43 rad/s, corresponding to the designated peak period of 14.6 s.

3.4. Hydrodynamic Performance

Frequency-domain analysis is a widely used approach for evaluating structural motion responses in waves. It efficiently solves the linear motion responses and first-order wave forces of floating platforms under both regular and irregular wave conditions, while also providing theoretical support for subsequent time-domain analyses. In this study, frequency-domain hydrodynamic analysis is performed using the HydroD V4.10 module of SESAM software to obtain the hydrodynamic coefficients of the semi-submersible wind turbine foundation, including added mass, potential damping, and first-order wave force transfer functions.

Surge, heave, and pitch are the primary motion modes affecting the motion performance of floating offshore wind turbines; therefore, this study focuses on the added mass and potential damping characteristics in these three degrees of freedom.

As shown in Figure 7, within the wave energy concentration range of 5–20 s, the added mass and potential damping in surge, heave, and pitch remain at relatively high levels. This enhances the platform’s wave resistance in this frequency band and indicates favorable energy dissipation capacity, enabling effective resistance to wave loads and reduction in motion responses.

Figure 8 presents the results of the first-order wave force transfer functions under four wave directions (0°, 30°, 60°, and 90°), corresponding to the surge, heave, and pitch motions. The selected wave directions are chosen because 0° represents the head-sea condition (wind turbine facing the incoming flow), 90° represents the beam-sea condition, and 30° and 60° serve as intermediate angles to capture the influence of varying wave incidence angles on hydrodynamic loads.

According to the results shown in Figure 8, the peak values of the first-order wave force transfer functions in surge, heave, and pitch all occur within the wave energy concentration range of 5–20 s, indicating that the proposed novel semi-submersible wind turbine foundation will experience significant first-order wave loads in this frequency band. Among them, surge and pitch are more sensitive to changes in wave direction, while heave is largely unaffected by wave direction.

To benchmark the hydrodynamic performance of the present steel-concrete hybrid platform, we have compared the computed motions and mooring tensions with those of the OC4 DeepCwind semi-submersible platform reported in the literature [37]. Although the two platforms differ in structural shape and mass distribution, both belong to the semi-submersible category. The comparison shows that the present platform exhibits similar trends in motion responses and mooring tensions under the same environmental conditions. Furthermore, the frequency-domain RAOs of the present platform show good agreement with the steady-state response amplitudes extracted from time-domain simulations. This consistency confirms the reliability of the numerical model and the expected hydrodynamic behavior.

4. Influence of Principal Dimension Variations on the Hydrostatic Characteristics and Modal Evolution of the Hybrid Platform

For a 15 MW steel-concrete hybrid semi-submersible platform, variations in core geometric dimensions not only alter its hydrodynamic profile but also necessitate nonlinear adjustments in ballasting, consequently modifying the platform’s static and dynamic characteristics. Based on the parametric scheme established in Section 3.3, this chapter systematically investigates the influence patterns of draft, column spacing, and column diameter on the platform’s hydrostatic performance and modal characteristics. The analysis focuses on the following three aspects: first, mass redistribution, quantifying the impact of geometric scale variations on platform mass and analyzing its correlation with the system’s center of gravity and construction costs; second, stability evolution, analyzing the changes in the center of buoyancy, center of gravity, and waterplane area moment of inertia induced by geometric parameter variations, and evaluating the contribution of each parameter to the righting moment area ratio and initial metacentric height; third, frequency-domain response, analyzing the effects of changes in mass, added mass, and restoring stiffness caused by geometric perturbations on the natural periods of heave, surge, and pitch motions. This analysis aims to prevent resonance between the turbine’s very low-frequency thrust and the wave spectrum during the design phase. Employing a single-factor non-dimensionalization method, the sensitivity of the aforementioned static and modal indicators to different geometric variables is analyzed. The results of this analysis can serve as a theoretical basis for the principal dimension optimization of the 15 MW hybrid foundation and provide support for the subsequent analysis of nonlinear characteristics in fully coupled dynamic responses under multiple operational scenarios.

4.1. Influence of Draft Variation on Platform Static Performance and Natural Periods

In the design of floating foundations, the selection of draft directly determines the system’s waterplane area, the vertical position of the center of gravity, and the integration interval of wave excitation forces along the water depth. To analyze the influence patterns of draft variation on the hydrostatic performance and modal characteristics of this steel-concrete hybrid platform, this section takes the initial draft of 22 m as a baseline. Nine derivative configurations (sequentially labeled D0.8 to D1.2) are generated within a range of ±20% at 5% intervals. During the parameter adjustment process, the column spacing and column diameter are kept fixed, and ballast is adjusted to ensure that each configuration satisfies the hydrostatic equilibrium condition.

4.1.1. Mass Analysis Results

Changes in draft directly alter the platform’s displaced volume. Under hydrostatic equilibrium conditions, to balance the increment in buoyancy resulting from an increased draft, the ballast within the bottom concrete compartments must be adjusted accordingly. This ballast adjustment process not only determines the total mass of the platform but also leads to nonlinear changes in the system’s mass distribution and the vertical position of its center of gravity, consequently influencing the platform’s initial stability and motion inertia characteristics. The mass calculation results for each derivative model are non-dimensionalized using the baseline model as a reference and are presented as percentages, as shown in Figure 9.

Figure 9 reveals a key feature: the total platform mass increases almost linearly with draft, but the growth rate remains relatively small. Specifically, for every 5% increase in draft, the corresponding increase in the platform’s total mass is only 0.31%. This marked difference reflects the geometric advantage of the proposed semi-submersible platform, namely its large-volume lower section and small-cross-section upper section. Because the platform’s displaced volume is primarily contributed by the lower concrete pontoons and heave tanks, while the waterplane area of the three steel columns piercing the free surface is relatively minimal, the incremental increase in displaced volume resulting from a draft increase is consequently very limited. This unique mass redistribution mechanism indicates that by moderately increasing the draft, additional ballast can be deployed within the bottom pontoons with almost no increase in total material cost (total mass increase of only 0.31%). This produces a pronounced center-of-gravity lowering effect with increasing draft, thereby enhancing the overturning resistance of the platform.

4.1.2. Stability Analysis Results

Changes in draft alter the platform’s displaced volume and its hydrostatic equilibrium state. The ballast adjustments necessary to restore equilibrium lead to variations in the platform’s mass distribution and the vertical position of its center of gravity, consequently affecting its righting moment characteristics and intact stability. To systematically evaluate the impact of draft adjustments on platform stability, the area ratio of the righting moment to the wind heeling moment was extracted for each derivative model. These results were non-dimensionalized using the baseline model as a reference, and the calculated outcomes are presented in Figure 10.

Figure 10 shows that the platform’s intact stability index increases monotonically with draft. Within the draft variation range of 80% to 120%, each 5% increase in draft yields an average increase of 1.13% in the righting moment to wind heeling moment area ratio, with the increment showing a nonlinear increasing trend. These results reveal that for this type of “steel above, concrete below” semi-submersible platform, moderately increasing the draft is an effective technical approach to enhance its overturning resistance and stability margin.

4.1.3. Natural Period Analysis Results

The modal natural periods of a floating foundation are key parameters for determining whether coupled resonance with wave-frequency or low-frequency excitation forces may occur. Variations in draft influence the natural periods of each platform’s degree of freedom by altering the system’s mass distribution, added mass, and hydrostatic restoring stiffness. To quantify this effect, free decay numerical simulations were conducted for each draft configuration. The normalized calculation results for the surge, heave, and pitch natural periods are presented in Figure 11 and

Table 8. Natural period calculation results for different drafts.

Draft	Surge Natural Period (s)	Heave Natural Period (s)	Pitch Natural Period (s)
80%	106.2	26.6	32.5
85%	107.5	26.6	32.5
90%	109.2	26.6	32.5
95%	110.8	26.4	32.3
105%	113.8	26.6	32.3
110%	114.8	26.6	32.0
115%	116.3	26.6	31.8
120%	117.3	26.8	31.8

.

Figure 11 and Table 8 reveal the differentiated influence mechanisms of draft variation on the platform’s motion periods across degrees of freedom. The surge period is primarily governed by inertial effects (simultaneous increase in structural mass and added mass), exhibiting a linear increase of approximately 10%. The heave period remains relatively stable because the waterplane area remains constant and the increase in system mass is small, resulting in a nearly unchanged inertia-to-stiffness ratio. The overall reduction in the pitch period is relatively modest (decreasing from 100.6% to 98.5%), yet its evolution exhibits significant nonlinear characteristics. This slight shift toward higher frequencies fundamentally results from the coupling between two competing effects: “increased rotational inertia” and “enhanced restoring stiffness”. On one hand, increasing draft enlarges both the rotational inertia and added inertia (tending to prolong the period). On the other hand, ballast redistribution lowers the center of gravity, thereby enhancing the restoring moment (tending to shorten the period). Beyond the baseline draft, the effect of stiffness enhancement begins to outweigh the influence of increased inertia, causing the pitch period to exhibit a nonlinearly accelerating decreasing trend.

4.2. Influence of Column Spacing Variation on Platform Static Performance and Natural Periods

To resist the substantial overturning moment generated by the offset 15 MW wind turbine, increasing the column spacing is a key geometric design measure to enhance the platform’s restoring moment arm and improve its anti-overturning capacity. To analyze the influence of this parameter on the platform’s static performance and modal periods, this section takes the baseline column center spacing of 80 m and generates nine derivative configurations (sequentially labeled J0.9 to J1.3) within the range of 90% to 130% at 5% increments. During the parametric variation, the draft and column diameter are kept fixed to eliminate interference from changes in local hydrodynamic cross-sectional area on the results. Simultaneously, ballast is adjusted to maintain mechanical equivalence in the hydrostatic state for each configuration.

4.2.1. Mass Analysis Results

Variations in column spacing not only affect the platform’s net weight and construction costs but also influence its stability restoration capability and the inertial characteristics of motions across degrees of freedom by altering the moment of inertia and center of gravity position. To quantify this effect, the mass of each model corresponding to different column spacings was calculated in this section. To facilitate analysis of the variation trends, the mass calculation results for all derivative models were non-dimensionalized relative to the baseline model and are presented as percentages, as shown in Figure 12.

Figure 12 presents the mass calculation results, which indicate that the total mass of the platform exhibits a highly linear positive correlation with column spacing. Within the parametric variation range of 90% to 130%, each 5% increase in column spacing corresponds to an average increase of approximately 2.44% in total platform mass, with the growth trend remaining stable. Compared to the mass response induced by draft variation (where each 5% increase in draft yields only a 0.31% increase in total platform mass), the mass change rate resulting from column spacing adjustments is significantly higher.

4.2.2. Stability Analysis Results

Figure 13 presents the calculation results for the intact stability index (i.e., the area ratio of the righting moment curve to the wind heeling moment curve) for configurations with different column spacings, non-dimensionalized with respect to the baseline model. Variations in column spacing alter the distribution characteristics of the platform’s waterplane area, thereby influencing its capacity to resist wind-induced overturning.

The results shown in Figure 13 indicate that the platform’s intact stability exhibits a significant nonlinear positive correlation with column spacing. As the column spacing increases from 90% to 130% of the baseline value, the area ratio of the righting moment to the wind heeling moment rises from 71.1% to 192.8%. Within the parametric variation range of 90% to 130%, each 5% increase in spacing yields an average increase of 12.1% in the area ratio, with the increment showing an increasing trend as spacing grows. This stability enhancement effect originates from the parallel axis theorem: the waterplane area moment of inertia is proportional to the square of the distance from the column centroid to the platform’s rotation center. Consequently, a moderate increase in column spacing can significantly enhance the system’s restoring stiffness. These results indicate that column spacing is a geometric parameter with high sensitivity concerning the stability of this 15 MW steel-concrete hybrid platform, providing a basis for anti-overturning design under extreme sea conditions.

4.2.3. Natural Period Analysis Results

To quantitatively assess the influence of column spacing on modal characteristics, free decay simulations were conducted for models with different column spacings in this section to obtain their natural periods for surge, heave, and pitch motions. All results are presented as percentages, normalized by the natural period values calculated for the baseline model. The natural period calculation results for surge, heave, and pitch motions of the platform under different column spacings are shown in Figure 14 and

Table 9. Natural period calculation results for different column spacings.

Column Spacing	Surge Natural Period (s)	Heave Natural Period (s)	Pitch Natural Period (s)
90%	109.7	25.6	35.0
95%	109.2	26.0	34.3
105%	109.2	27.0	31.8
110%	113.8	27.6	30.5
115%	114.5	27.8	30.0
120%	114.8	28.2	29.8
125%	115.2	28.6	29.2
130%	115.7	28.8	29.0

.

Figure 14 and Table 9 present results indicating that the influence mechanisms of column spacing variation on the platform’s modal periods across degrees of freedom exhibit significant differences. The surge period is primarily influenced by the increase in inertial terms (mass and added mass) resulting from the extension of the bottom pontoons, showing an increasing trend. The heave period, under the condition of constant waterplane area, is driven by the combined increase in vertical added mass and structural mass, exhibiting an increase exceeding 12%. The pitch period demonstrates a significant attenuation of 17.2%. The physical mechanism underlying this is that while expanding the column spacing shifts mass outward and increases rotational inertia, the resulting increase in the waterplane area moment of inertia (proportional to the square of the column spacing) is more pronounced, leading to a substantial enhancement of the restoring stiffness and, consequently, shortening the period.

4.3. Influence of Column Diameter Variation on Platform Static Performance and Natural Periods

In the hydrodynamic design of semi-submersible platforms, column diameter is a critical geometric parameter: it not only determines the system’s hydrostatic restoring stiffness at the free surface (proportional to the square of the diameter) but also directly influences the first-order wave excitation forces and second-order nonlinear fluid loads acting on the platform. To analyze the influence of this parameter on the platform’s static and dynamic characteristics, this section takes the baseline column diameter of 15 m and generates nine derivative configurations (sequentially labeled R0.9 to R1.3) within the range of 90% to 130% at 5% increments. During the parametric adjustment process, the draft (22 m) and column center spacing (80 m) are kept fixed. Ballast is adjusted to compensate for the change in displaced volume caused by the diameter variation, ensuring that each configuration satisfies the hydrostatic equilibrium condition.

4.3.1. Mass Analysis Results

Variations in column diameter not only affect the platform’s net weight and material consumption but also influence its stability restoration capability and motion inertial characteristics by altering the mass moment and moment of inertia. To quantify this effect, the mass of each model corresponding to different column diameters was calculated in this section. To facilitate analysis of the variation trends, the mass calculation results for all derivative models were non-dimensionalized relative to the baseline model and are presented as percentages, as shown in Figure 15.

Figure 15 presents the calculation results, which indicate that the total mass of the platform exhibits a highly linear positive correlation with column diameter. Within the parametric variation range of 90% to 130%, each 5% increase in column diameter corresponds to an average increase of approximately 0.62% in total platform mass. Increasing the column diameter also leads to a quadratic growth in the waterplane area. This characteristic will have two implications for subsequent stability and natural period analyses: on one hand, the restoring stiffness will be correspondingly enhanced; on the other hand, the nonlinear wave excitation forces acting on the platform may also increase accordingly.

4.3.2. Stability Analysis Results

Column diameter determines the sectional characteristics of the floating structure as it penetrates the free surface and is a key geometric parameter influencing the system’s initial metacentric height and wind resistance capacity. To quantify the influence of diameter variation on platform stability, the area ratio of the righting moment curve to the wind heeling moment curve for configurations with different column diameters was extracted in this section. These results were non-dimensionalized using the baseline model as a reference, and the calculated outcomes are presented in Figure 16.

The stability calculation results shown in Figure 16 indicate that the intact stability index exhibits a significant nonlinear positive correlation with column diameter. As the column diameter increases from 90% to 130% of the baseline value, the area ratio of the righting moment to the wind heeling moment rises from 64.3% to 230.6%. Within the parametric variation range of 90% to 130%, each 5% increase in diameter yields an average increase of 19.2% in the area ratio, with the increment showing an increasing trend as diameter grows. Combined with the conclusions from Section 4.3.1, a 5% increase in column diameter only increases the total platform mass by 0.62% while causing a quadratic increase in waterplane area. This characteristic provides the platform with significant hydrostatic restoring stiffness. These results indicate that column diameter is a key geometric parameter with high sensitivity in the stability optimization design of this 15 MW steel-concrete hybrid platform.

4.3.3. Natural Period Analysis Results

Variations in column diameter not only affect the hydrostatic restoring stiffness but also cause a quadratic increase in the loaded cross-sectional area for wave radiation and diffraction, consequently altering the system’s mass distribution and stiffness characteristics. Free decay numerical simulations were conducted for each diameter derivative configuration in this section. The normalized calculation results for the surge, heave, and pitch natural periods are presented in Figure 17 and

Table 10. Natural period calculation results for different column diameters.

Column Diameter	Surge Natural Period (s)	Heave Natural Period (s)	Pitch Natural Period (s)
90%	109.0	29.6	38.7
95%	110.7	28.0	35.0
105%	114.8	25.5	30.0
110%	115.5	24.2	27.8
115%	117.2	23.2	26.0
120%	119.5	22.3	24.5
125%	122.8	21.5	23.2
130%	124.0	21.0	23.2

.

Figure 17 and Table 10 present results indicating that the influence of column diameter variation on the platform’s modal periods across degrees of freedom exhibits significant differences. The surge period is primarily governed by the increase in horizontal added mass, showing an increasing trend. In contrast, the heave and pitch periods experience a marked decrease due to the substantial increase in waterplane area and moment of inertia (proportional to the square of the diameter) caused by enlarging the column diameter, which significantly enhances the hydrostatic restoring stiffness. Specifically, the heave period decreases by 32.4%, while the pitch period decreases by 48.0%. This phenomenon reveals an inherent trade-off between stability enhancement and resonance risk. Although the significant shortening of the pitch period is beneficial for improving the platform’s static stability, it may also shift its natural frequency into the high-energy wave frequency band, potentially increasing the risk of resonance under extreme sea conditions. The analysis above suggests that there may exist an optimal range for the column diameter of this platform type, requiring a comprehensive balance between stability benefits and dynamic response characteristics.

5. Influence of Principal Dimensions on Dynamic Response

The global dynamic response of a semi-submersible platform serves as a crucial indicator for evaluating its operational capability and power generation performance in random ocean environments. Based on the parametric static characteristics and modal analysis results established in Section 4, this section places the platform physical model within a fully coupled aero-hydro-servo-mooring time-domain framework to analyze the dynamic response characteristics under environmental loads for variations in draft, column spacing, and column diameter. The study selects typical operational conditions and extreme survival conditions, extracting transient and steady-state responses for the platform’s surge, heave, and pitch degrees of freedom. The primary load-bearing mooring line on the windward side (Line 2-2) is selected to evaluate peak mooring loads. Through statistical processing of time-domain results and frequency-domain power spectral density (PSD) analysis, the energy distribution characteristics of low-frequency slow-drift components and wave-frequency components are identified, aiming to provide a dynamic reference basis for the principal dimension optimization of the 15 MW steel-concrete hybrid platform.

5.1. Draft Sensitivity Analysis

For both operational and extreme conditions, this section extracts the six-degree-of-freedom motion time histories and the tension response of the primary load-bearing mooring line on the windward side (Line 2-2) for each draft derivative configuration. To analyze the frequency components of excitation forces under different environmental conditions, fast Fourier transform (FFT) is applied to the time-domain signals to obtain their power spectral density distributions. Simultaneously, the steady-state extreme values and mean values for each configuration are non-dimensionalized relative to the baseline model (D1.0) and presented as percentages.

(1)

Operational conditions

Figure 18 and Figure 19 present the time-domain statistical and spectral analysis results, indicating that under operational conditions, the influence mechanisms of draft variation on the platform’s three-degree-of-freedom motions exhibit significant differences. Surge response is primarily governed by the turbine’s low-frequency aerodynamic thrust and second-order wave drift forces, showing insensitivity to draft changes. The extreme heave response demonstrates a decreasing trend with increasing draft (decreasing from 127.0% to 81.0% of the baseline value), attributed to the attenuation of wave dynamic pressure amplitude with water depth, which reduces the wave excitation forces acting on the bottom heave tanks at increased drafts. The pitch response amplitude also decreases with increasing draft, as the ballast adjustment resulting from increased draft elevates the platform’s initial metacentric height and pitch-restoring stiffness, thereby enhancing its capacity to resist the turbine’s aerodynamic overturning moment.

The mooring line tension results and spectral analysis are presented below:

Figure 20 and Figure 21 demonstrate that under sustained thrust at rated wind speed, the mean mooring tension of the system is minimally affected by draft variation (decreasing from 100.7% to 99.8% of the baseline value). This occurs because the mean tension primarily balances the turbine’s aerodynamic thrust and the second-order mean wave drift force, both of which are essentially unaffected by draft changes. However, regarding dynamic response, increasing draft leads to a decreasing trend in extreme mooring tension (maximum tension decreasing from 104.8% to 98.3%). Combined with the spectral analysis, this reduction in dynamic tension correlates with the aforementioned attenuation of heave and pitch motions. The decreased motion response of the platform in the wave frequency band reduces the velocity and geometric displacement at the fairlead, consequently diminishing the dynamic tension amplitude in the mooring lines.

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Extreme conditions

Figure 22 and Figure 23 present results indicating that under extreme survival sea states, increasing draft has a significant mitigating effect on the platform’s dynamic response. Surge response remains primarily governed by low-frequency second-order wave drift forces and is insensitive to draft variations. The extreme heave response exhibits a substantial decreasing trend with increasing draft (a reduction of nearly 30%), attributed to the attenuation of wave dynamic pressure with water depth, which significantly reduces the wave excitation forces acting on the bottom heave tanks at increased drafts. The extreme pitch response also decreases notably with increasing draft, as the ballast adjustment resulting from increased draft significantly elevates the platform’s initial metacentric height and pitch-restoring stiffness, thereby effectively enhancing its capacity to resist extreme wave overturning moments under conditions where the turbine’s aerodynamic damping is absent.

The mooring line tension results and spectral analysis are presented below:

Figure 24 and Figure 25 demonstrate that under extreme conditions, increasing draft has a minimal effect on mean mooring tension (decreasing from 101.8% to 99.0% of the baseline value) but significantly reduces the maximum transient tension. As the draft increases from 80% to 120% of the baseline value, the maximum tension of mooring line 2-2 on the windward side decreases from 111.1% to 93.8% (each 5% increase in draft corresponds to approximately a 2.2% reduction in extreme tension). Frequency-domain energy spectral analysis indicates that the increase in mooring tension under extreme sea states primarily results from the superposition of low-frequency slow-drift motions and wave-frequency motions. Therefore, the reduction in peak mooring loads directly correlates with the aforementioned attenuation of extreme heave and pitch motions: the reduced motion amplitude of the platform at the fairlead locations consequently diminishes the dynamic tension in the mooring lines. By increasing draft to reduce the platform’s attitude variations, severe chain lifting and bottoming-out phenomena in the mooring lines can be effectively avoided, thereby enhancing the platform’s survivability under extreme sea conditions.

5.2. Column Spacing Sensitivity Analysis

(1)

Operational conditions

Figure 26 and Figure 27 present time-domain statistical and spectral analysis results, indicating that the influence mechanisms of column spacing variation on the platform’s three-degree-of-freedom motions exhibit significant differences. Surge response is primarily governed by the turbine’s aerodynamic thrust, and the loaded cross-sectional area in the horizontal direction remains essentially unchanged, making it insensitive to column spacing variations. Heave response is influenced by wave phase interference effects, exhibiting non-monotonic variations whose fluctuation characteristics correlate with the ratio between column spacing and incident wavelength. Pitch response shows a substantial decreasing trend with increasing column spacing (extreme values decreasing from 148.4% to 43.0% of the baseline value). This occurs because outward column expansion significantly increases the waterplane area moment of inertia (proportional to the square of the spacing), thereby substantially enhancing the platform’s pitch-restoring stiffness and effectively strengthening its capacity to resist wind-wave overturning moments. These results indicate that column spacing is a critical geometric parameter for suppressing platform pitch motion.

The mooring line tension results and spectral analysis are presented below:

Figure 28 and Figure 29 demonstrate that under operational conditions, the response of mooring tension to column spacing variation exhibits differential characteristics. Mean tension is primarily governed by the turbine’s aerodynamic thrust and remains insensitive to column spacing variations, with values remaining essentially stable. Maximum tension, however, shows a slight increasing trend with greater column spacing. This phenomenon indicates that while outward column expansion significantly enhances pitch-restoring stiffness, it also reduces the platform’s compliance capacity to accommodate wave-induced motions, causing some dynamic loads to be more directly transmitted to the mooring system. However, from a multi-objective optimization perspective, the substantial attenuation of pitch response (a reduction exceeding 100%) is achieved at the cost of less than a 5% increase in extreme mooring tension, demonstrating the high efficiency of this geometric adjustment in suppressing platform motions.

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Extreme conditions

Figure 30 and Figure 31 present time-domain statistical and spectral analysis results, indicating that under extreme conditions, the influence of column spacing variation on the platform’s limit motions exhibits differentiated characteristics. After the turbine’s aerodynamic thrust diminishes, surge response is primarily governed by low-frequency second-order wave drift forces and remains insensitive to column spacing variations. The mean heave displacement shows a decreasing trend with increasing column spacing, while its extreme response exhibits non-monotonic fluctuation characteristics, potentially related to long-wave interference and nonlinear wave effects. The extreme pitch response demonstrates a substantial decreasing trend with increasing column spacing (extreme and mean values decreasing to 85.6% and 57.1% of the baseline value, respectively). This occurs because outward column expansion significantly increases the waterplane area moment of inertia (proportional to the square of the spacing), thereby substantially enhancing the platform’s pitch-restoring stiffness under extreme sea states and strengthening its capacity to resist wave overturning moments. These results indicate that column spacing is a critical geometric parameter for improving platform survivability under extreme sea conditions.

The mooring line tension results and spectral analysis are presented below:

Figure 32 and Figure 33 demonstrate that under extreme conditions, extreme mooring tension values exhibit a decreasing trend with increasing column spacing (maximum tension decreasing from 104.2% to 92.3% of the baseline value). This trend contrasts with the slight increase in tension observed with increasing spacing under operational conditions, with the difference attributed to changes in the physical mechanisms governing mooring loads under different sea states. Under extreme conditions, extreme mooring tension is primarily influenced by geometric nonlinear deformation at the fairlead caused by large platform motions (particularly pitch) rather than rigid transmission of high-frequency displacements. Therefore, the attenuation of pitch motion achieved through outward column expansion effectively reduces the dynamic displacement amplitude at the fairlead, consequently decreasing the extreme loads generated during chain lifting and tensioning processes. These analysis results can provide a reference basis for mooring system design of high-power floating wind turbine foundations under extreme sea conditions.

5.3. Column Diameter Sensitivity Analysis

(1)

Operational conditions

Figure 34 and Figure 35 present time-domain statistical and spectral analysis results, indicating that under operational conditions, the influence of column diameter variation on the platform’s three-degree-of-freedom motions exhibits significant differences. Surge response shows an increasing trend with larger diameters (extreme values rising to 105.5% of the baseline value), attributed to the increase in horizontal wave excitation forces and viscous drag forces accompanying the enlarged loaded cross-sectional area. Heave and pitch responses, however, demonstrate decreasing trends with increasing diameter (heave extreme values decrease from 110.5% to 73.7%; pitch extreme values decrease from 140.0% to 59.0% of the baseline value). This occurs because increasing column diameter causes the waterplane area and moment of inertia to increase quadratically, thereby significantly enhancing the system’s hydrostatic restoring stiffness. Although wave-frequency excitation forces are also amplified, the enhancement of restoring stiffness dominates, ultimately resulting in attenuated heave and pitch motions. These results indicate that column diameter is a critical geometric parameter influencing platform stability and wave-frequency response under operational conditions.

The mooring line tension results and spectral analysis are presented below:

Figure 36 and Figure 37 demonstrate that under operational conditions, changes in mooring tension reflect the comprehensive influence of increased column diameter within the multi-field coupled system. The extreme tension of the windward mooring line shows a continuous increasing trend with increasing diameter (rising from 98.1% to 104.6% of the baseline value). This increase arises, on one hand, from the enlarged second-order mean wave drift force resulting from the increased loaded cross-sectional area. On the other hand, the significant enhancement of heave and pitch stiffness accompanying increased column diameter, while suppressing platform motion amplitudes, also reduces the platform’s capacity to dissipate wave energy through rocking motions, thereby causing some dynamic loads to be more directly transmitted to the mooring system. This characteristic—achieving platform attitude stability at the cost of a modest increase in extreme mooring tension—is feasible under operational conditions. However, attention must also be paid to the uncertainties in platform dynamic response under extreme sea states as nonlinear wave loads intensify.

(2)

Extreme conditions

Figure 38 and Figure 39 present time-domain statistical and spectral analysis results, indicating that under extreme conditions, the influence of column diameter variation on the platform’s extreme motion response follows certain patterns. Surge response exhibits relatively low sensitivity to diameter variations (extreme values ranging from 99.2% to 103.7% of the baseline value), indicating that horizontal low-frequency drift forces remain the dominant factor under extreme sea states. The mean heave response shows a decreasing trend with increasing diameter, while its extreme values stabilize after the diameter exceeds 115% (remaining within the 90–93% range), suggesting a balance is achieved between enhanced hydrostatic stiffness and nonlinear wave forces induced by the enlarged cross-section. The extreme pitch response exhibits an initial decrease followed by an increase with increasing diameter. As the diameter increases from 90% to 120% of the baseline value, the extreme pitch decreases to 60.4%. However, when the diameter further increases to 125–130%, the extreme pitch rebounds to 67.3%. This variation indicates that when the diameter is relatively small, the enhancement of restoring stiffness dominates, leading to motion convergence. When the diameter becomes excessively large, wave diffraction effects intensify significantly, causing the increase in first-order wave excitation forces and nonlinear moments to outweigh the benefits of increased restoring stiffness, resulting in a rebound in motion response. These results suggest that for this platform type, there exists an optimal diameter range for withstanding extreme sea states (approximately 115–125% of the baseline value).

The mooring line tension results and spectral analysis are presented below:

Figure 40 and Figure 41 demonstrate that under extreme conditions, mooring tension increases significantly with increasing column diameter. Unlike the nonlinear variation characteristics observed in platform motion response, the maximum mooring tension exhibits a monotonically increasing trend with increasing diameter (rising from 98.5% to 111.8% of the baseline value, with the increment expanding as diameter increases). Regarding mean tension, the increased frontal area resulting from larger column diameters enhances the second-order mean wave drift force, thereby elevating the mean tension baseline (rising to 103.4% of the baseline value). For maximum tension, the amplification of wave excitation forces caused by larger diameter sections, combined with the rebound in pitch response beyond a certain diameter range, collectively results in wave energy being less effectively dissipated through platform motion and, consequently, transmitted more directly to the fairleads and mooring chains. These results indicate that under extreme sea conditions, solely increasing column diameter to enhance hydrostatic stability may lead to a significant increase in the extreme loads borne by the mooring system, underscoring the necessity for multi-parameter collaborative optimization in deep-sea platform design.

Based on the results and analysis, we could provide the recommended parameter ranges of the platform draft, column diameter, and spacings, as shown in

Table 11. Recommended design ranges for principal dimensions.

Parameter	Recommended Range	Key Performance Implications
Draft	100–110%	Reduce extreme heave and pitch motions and significantly decrease extreme mooring tensions
Column spacing	105–120%	Significantly enhance platform stability and substantially reduce extreme pitch response
Column diameter	115–125%	Significantly enhance platform stability and reduce extreme pitch response

, for future design references.

6. Conclusions

As global demand for clean energy continues to grow, offshore wind power has attracted increasing attention as a significant form of renewable energy. This study conducts a parametric sensitivity analysis on three key principal dimensions—draft, column spacing, and column diameter—for a semi-submersible floating platform supporting a 15 MW wind turbine. Through the establishment of theoretical models and systematic parametric investigations, the influence patterns of these parameters on the platform’s static performance (including total mass, stability, and natural periods) and dynamic response characteristics (including surge, heave, and pitch motions, as well as mooring tension) are analyzed. The main research conclusions are as follows:

(1)

The influence of principal dimension parameters on the platform’s hydrostatic characteristics exhibits significant differences. The total platform mass and intact stability (characterized by the area ratio of the righting moment to the wind heeling moment) show varying sensitivity to different geometric parameters. Among these, adjustments to column diameter demonstrate high “mass-stiffness efficiency”: increasing column diameter causes the waterplane area moment of inertia to increase quadratically, significantly enhancing the platform’s overturning resistance while incurring only a modest increase in platform mass (approximately 0.62% mass increase per 5% diameter increase). This indicates that column diameter is a critical geometric parameter influencing the platform’s initial stability.

(2)

Column diameter and draft have a relatively significant impact on material cost, with each 5% increase leading to a total mass increase of 0.62% and 0.31%, respectively, both contributed entirely by the steel structure. In contrast, a 5% increase in column spacing results in a 2.44% increase in total mass, which is primarily attributed to the concrete structure. When converted to an equivalent steel mass based on the cost ratio, this corresponds to only a 0.15% increase in steel-equivalent mass, indicating a limited effect on material cost. Therefore, a moderate increase in column spacing can significantly enhance platform performance while incurring only a modest cost increase, offering favorable cost-effectiveness.

(3)

Variations in principal dimension parameters exert significantly different effects on the platform’s modal periods. Due to the distinct influences of each parameter on the hydrodynamic inertia matrix and hydrostatic stiffness matrix, the natural periods of different degrees of freedom exhibit differentiated characteristics. The surge period shows an increasing trend, primarily influenced by the increase in horizontal added mass. The heave and pitch periods, however, demonstrate decreasing trends, attributed to the significant enhancement of restoring stiffness resulting from increased waterplane area and moment of inertia. Notably, increases in column spacing and diameter substantially shorten the pitch natural period. While this alteration enhances the platform’s hydrostatic stability, it simultaneously modifies the relative positioning between the platform’s natural frequencies and the concentrated energy bands of the wave spectrum.

(4)

Under extreme sea conditions, the influence mechanisms of principal dimension parameters on the platform’s dynamic response exhibit distinct characteristics. Increasing draft reduces wave excitation forces on bottom components (wave dynamic pressure attenuates with increasing water depth), thereby effectively suppressing extreme heave responses. Simultaneously, the increase in initial metacentric height and pitch-restoring stiffness resulting from greater draft also reduces pitch response. Increasing both column spacing and diameter can significantly suppress pitch response. However, it should be noted that column diameter exhibits a critical range under extreme conditions: when the diameter is less than 120% of the baseline value, the enhancement of restoring stiffness dominates, and pitch response decreases with increasing diameter; when the diameter exceeds 125–130%, wave diffraction effects intensify significantly, causing the increase in first-order wave excitation forces and nonlinear moments to outweigh the benefits of increased restoring stiffness, resulting in a rebound in pitch response. These findings indicate that for this platform type, there exists an optimal diameter range for resisting extreme sea states.

(5)

The extreme tension response of the mooring system exhibits different characteristics with variations in principal dimension parameters. Under extreme conditions, increasing draft and column spacing significantly suppresses platform pitch motion, reducing displacement amplitudes at the fairleads, thereby decreasing chain bottoming out and tensile impact loads and achieving effective control of extreme mooring tensions. Conversely, a continuous increase in column diameter substantially enhances the platform’s restoring stiffness, reducing to some extent the platform’s capacity to dissipate wave energy through rocking motions. This causes some dynamic loads to be more directly transmitted to the mooring system, consequently leading to increased extreme mooring tensions.

(6)

The recommended parameter ranges are as follows: draft between 100% and 110% of the baseline value, column spacing between 105% and 120% of the baseline value, and column diameter between 115% and 125% of the baseline value.

In summary, this study analyzes the influence patterns of principal dimension parameters on the static and dynamic characteristics of a 15 MW semi-submersible floating wind turbine platform. The research results indicate that in floating foundation design, excessively increasing column diameter or spacing solely for the purpose of enhancing hydrostatic stability may lead to intensified wave excitation forces and increased extreme mooring loads under extreme sea conditions. The principal dimension influence patterns, nonlinear response characteristics, and optimized parameter ranges obtained in this study can provide a reference basis for multi-parameter collaborative optimization design of high-power floating wind turbine platforms in deep-sea areas.

It should be noted that the principal dimension adjustments in this study are primarily based on hydrodynamic performance considerations, and the current parametric analysis does not incorporate a detailed structural model and therefore involves certain uncertainties. Consequently, the results should not be regarded as the final structural design scheme. In addition, the influence of other design variables, such as heaving plate configurations, mooring line stiffness, turbine controller settings, etc., is not considered in the current work and can be considered in the future.