OWTs include FBWTs and FOWTs. FBWTs are usually operating in shallow water with a depth less than 60 m, and the foundations are inserted into the seabed. FBWTs are mainly subjected to environmental loads, such as wind and waves. Liu et al. (2010) considered that wind loads played a leading role in load combination for FBWTs’ tower. Different from FBWTs, FOWTs consist of a floating platform and restrained with various mooring systems that typically undergo displacement in the six degrees of freedom (Zou et al., 2021). Furthermore, they may undergo remarkable dynamic responses when operating in the hostile marine environment. FOWTs studied in this paper are the 5 MW OC4-DeepCWind semi-submersible wind turbine, as shown in Figure 2. The floater includes a centre column connecting the tower and three offset columns which are connected with the main column through a number of smaller pontoons and braces (details of the platform are given in Figure 2B). Three mooring lines are arranged symmetrically above the platform vertical axis with 120° between them. The radius to fairleads and anchors from the platform’s centreline is 40.868 m and 837.6 m, respectively. Each of the three lines has an unstretched length of 835.5 m with 0.0776 m diameter and an equivalent mass per unit length of 113.35 kg/m. The detailed layout and structural property are available in Robertson et al. (2014).

OWTs have to resist winds, waves, and currents during the operation stage. Therefore, the environmental loads should be estimated before calculating the dynamic responses of OWTs (Hu et al., 2020). All these environmental loads induce an aerodynamic and hydrodynamic impact on the structures. Ye and Ji (2019) investigated the effects of both hydrodynamic and aerodynamic excitations which include current, wave, and wind excitations, as well as buoyant forces, along with the dynamic interaction between the drive–train system and tower structure on the dynamic response of the spar-type floating platform under different sea conditions. Chen and Basu (2018) considered the effects of current and wave–current interactions in the fatigue analysis of FOWTs. Their results showed that the current and the wave–current interaction could have significant influences on FOWT cable responses. Philippe et al. (2013) performed a coupled dynamic analysis of a floating wind turbine system to investigate the effect of the wave direction relative to wind on the wind turbine system. They considered that the natural modes of the tower system are excited differently regarding the wave’s direction.

In this research, wind and wave loads are considered as primary environmental external forces. Despite that the current may also affect the FOWTs’ motions, especially on supporting the structures of an extensive draft, it mainly acts on the mooring systems and contributes less to fatigue damage on the towers (Zou et al., 2022). Therefore, the current force is not discussed in this paper.

The external loads on the ring flange connections are calculated, as shown in Figure 2C. The wind and wave spectra are set as stationary uniform and JONSWAP for both FOWTs and FBWTs, respectively. The significant wave height is set as 3 m, spectral peak period is set as 10 s, and horizontal wind speed is set as 11.4 m/s.

The coupled global dynamic analysis carried out the time domain using the module SIMA in software package SESAM. The SESAM-SIMA calculates the internal forces and moments in the cross sections of the FOWTs’ and FBWTs’ tower under the same operation condition. Figure 3 shows the time series of the axial force and the bending moment in a cross section of the tower. The results show that the ranges of fluctuations in axial force and those of bending moment of the FOWTs’ towers increase compared to FBWTs’ towers, and FBWTs’ towers bear a greater axial force and bending moment compared to FOWTs’ towers under operating conditions. It is clearly observed that FOWTs’ substructures undergo oscillating motions in six degree of freedoms (DOFs) with larger magnitudes compared to fixed-bottom wind turbines. Their compliant foundations can reduce the counterforce around the tower and lower the stress in the structural response. Moreover, the substructure’s motions may influence the aerodynamic condition of the rotor, which makes the aerodynamic loadings on FOWTs much more complicated than those on FBWTs. de VaalHansen and Moan (2012) studied the effect of a periodic surge motion on the integrated loads and induced velocity on a wind turbine rotor through numerical simulations. Among all motions of the six DOFs, surge and pitch are regarded as the most important ones affecting the FOWTs’ aerodynamics (Bayati et al., 2016; Fang et al., 2020; Fang et al., 2021). Once the aerodynamic conditions are affected by the substructures’ motions, the external forces on the wind tower are also changed. Hence, it is necessary to consider the impact of FOWTs’ motions in the fatigue assessment.

The FE analysis was performed based on linear material models. The materials were modelled considering the steel’s elastic properties with linear behaviour until yielding. According to EN 1993-1-1 (EN, 1993-1-1Eurocode 3, 2005), the defined material was steel with a modulus of elasticity of 210 GPa and Poisson’s coefficient of 0.3. The materials of OWTs’ flanges and bolts are Q345E and 42CrMo. Their yield strengths are 345 MPa and 940 MPa.

The geometrical model studied consists of an upper flange, lower flange, washers, and bolt joining both parts, and the details of the cross section of the bolted connection is shown in Figure 4.

A finite-element model should not only have a low computational requirement but also reflect the key characteristics, such as irregular geometries and large deformations. In this study, SOLID186-type finite elements are used for the flange. SOLID186 is a 3D element with 20 nodes, and three degrees of freedom can accurately simulate irregular geometries and structural phenomena, namely, plasticity, creep, and large deformations, among others (System, 2005). The mesh density has an effect on finite-element results. A good grid layout is one of the key factors to improve the reliability of simulation when using the finite-element method for structure simulation. The coarse mesh density can decrease the computation time, but it may lead to a larger finite-element stress result that is not consistent with the reality. On the contrary, fine finite elements are used to improve the accuracy of the finite-element results with more computation time. Li et al. (2009) put forward the concept of key areas, and it was concluded that the precision of the calculation result of the whole finite-element model was determined by the meshing level of all the key areas in the finite-element model. In this section, the mesh density to ESIZE is set as 6 in the mesh tool initially, and Figure 5 shows that the stress value of the flange is too high. With the further use of small mesh density, the tendency of the flange stress is clearly shown approaching a stable value indicating that the mesh density of 0–1 is reasonable. In this paper, the mesh size was chosen to be a minimum of 0.9 mm and a maximum of 16 mm, with a total of 107,242 nodes and 14,997 elements. Figure 6 (left) shows a localised fine mesh around the areas with high stress concentration, while a relatively coarser mesh size is adopted for other areas. In addition, a pretension element (PRETS179 element in ANSYS) is used to apply the preload force on the bolts. The pretension elements are located in the middle of the bolt shaft. Then, ANSYS internally cuts the bolt into two parts and translates the cut planes axially so that the sum of the nodal reaction forces is equal to the preload force.

The local model was created with the configuration of the contacts between elements and the application of boundary conditions, which consisted of a frictional contact between the surface of the upper and lower flanges, washers and flanges, inner surface of flanges and the bolt shank, and a bonded contact between the surface of nuts and washers and inner surface of nuts and the bolt head. The friction coefficient applied was 0.15, adopting an augmented Lagrangian equation (Simo and Laursen, 1992).

To assess the fatigue damage on OWTs’ tower flange, the calculation of the cyclic load amplitudes ΔF _b requires the approximation of the load transfer between the tower shell loads and the resulting bolt force inside the flange. According to the current design standards, this is performed using a load transfer function (LTF). Figure 7 (left) schematically shows the LTF F _b (Z), with the external load Z acting in the tower shell on the abscissa and the bolt load F _b on the ordinate. Due to the eccentric load introduction and the presence of the preload F _p of the bolts, the LTF is non-linear.

For the reduction of fatigue loads, bolt pretension F _p is necessary for structural integrity. The preload F _p is induced via either torque-controlled tightening or direct tensioning methods. With the broadly used torque-controlled tightening procedure, the bolt shall be preloaded up to the reduced nominal preload, F _p,c* = 0.7R _p0.2 ∙A _sp, where R _p0.2 is the material plastic strain limit and A _sp is the stress area of the bolt thread.

Under perfect geometric conditions, as the surface pressure between the upper and lower flange increases due to the tightening, a clamp solid emerges centrically around the longitudinal bolt axis as a counterpart of the preload, as shown in Figure 7 (middle). With the clamp solid distributed symmetrically around the bolt axis, external forces acting in the tower shell first diminish the resulting clamp force, which reduces cyclic bolt forces ΔF _b . However, under imperfect flatness divergence conditions, the flange contact surface is not ideally plane due to a flange inclination α _s, a flange opening length L _i , and a flange opening height h, which is shown in Figure 7 (right). The two flange parts may open, and the clamp solid may develop eccentrically from the bolt’s longitudinal axis.

The flange connections are mainly subjected to external loads, such as moments, pressure, and shear. The axial stress applied to the upper tower flange shell sections is calculated as follows (Eq. 1). The shear is neglected due to its minor contribution to fatigue damage. σ = Z A t = − 2 M y ⁡ cos ⁡ β R N + F a x i a l N / A t . (1)

Here, Z is the external load, β is the angle between the location of the bolt and the x-axis, F _axial is the maximum axial force (plotted in Figure 3), M _y is the y-axis bending moment (plotted in Figure 3) above the horizontal axis perpendicular to the wind direction, A _t is the area of the tower shell, R is the radius of the flange, and N is the number of high strength bolts installed in the flange (plotted in Figure 1).

A preload force of 510 KN is applied on the bolt in order to simulate the tightening of the bolt (Ajaei and Soyoz, 2020). A uniform tensile stress of 42.2 MPa and compressive stress of 43.5 MPa are applied to FOWTs’ tower shell sections, respectively. FBWTs’ tower shell sections are applied to the tensile stress of 92.1 MPa and the compressive stress of 94.3 MPa. All degrees of freedom at the bottom of the tower shell are fixed, and symmetric boundary conditions were applied.

Li and Ren (2013) calculated the maximum stress of the 1.5 MW wind turbine tower under the operation condition, and the result showed that the maximum stress under the operating condition is 71 MPa. Ajaei and Soyoz (2020) calculated the external loads using TurbSim software and applied the vertical traction time series (the maximum traction is 44 MPa) to the upper edge of the tower wall and different bolt preloads in order to investigate the effect of a bolt preload level on fatigue damage in eccentrically loaded bolts of ring flange connections. Alonso-Martinez et al. (2019) applied a 519.91-KN preload force on the bolt, 32.57 KN compressive load, and 18.37 KN tensile load on the flange wall segment in order to study the behaviour of the flange and analyse the cause of the collapse.

Figure 9 shows that bolts’ and flanges’ stress concentrations occur at the bolt head under the perfect condition. Figure 10 shows that imperfect models’ stress concentration mainly occurs at the bolt head and the centre of the bolt shank. With the increase in opening length, the locations of stress concentrations are transferred from the bolt head to the centre of the bolt shank. For flanges with flange-sided gapping and tower-sided gapping (Figure 11 (1) (2)), stress concentrations initially occur at the bolt head and transfer to the opening gaps with the increase in opening length. For parallel gapping, a three-sector local finite-element model is established, as the contact surface between the two flange parts opens completely in the middle and the middle bolt loses its preload completely. Hence, the cyclic loadings on the FOWTs’ tower shells are mainly sustained by other two bolts, and the locations of stress concentrations occurring in the bolt head and gaps are shown in Figure 11 (3). These locations may play a critical role in fatigue assessments.

Figure 12 schematically shows the variation tendency of the bolt and flange stress increment under flatness divergence. It is evident that the magnitude of the bolt and flange stress increased considerably when the opening length increases. The main findings are drawn as follows:

1. When the tower shell is subjected to tensile stress, bolt and flange stresses significantly increase in flange-sided gapping compared to the other two types of flatness divergence. The maximum stress of bolts is 2763 MPa (Figure 10), where (1 with a maximum flange opening length, and the stress increases to 1787 MPa (Figure 12A) for flange-sided gapping compared to the perfect condition (Figure 9, right). The bolt stress increment is about 5% for tensile when the gap length is 49 mm (point A in Figure 8), and the bolt stress increment is about 183% for tensile when the gap length is 115 mm (point E in Figure 8) for flange-sided gapping. For flanges, the maximum stress is 9858 MPa [Figure 11 (1)] when the location of openings occurs in the centre of the bolt shank, i.e., point C (gap length 82 mm) in Figure 8, and the stress increases to 8610 MPa for flange-sided gapping (flange stress increment is about 690%) compared to the perfect condition (Figure 9, right).

Figures 9–11 show that the stress of both the bolt and the flange exceeds the materials’ yield strength. In the case of the model with flatness divergence, the structure is subjected to deformation or even destruction. The plastic deformation may occur at this bolt, and it will lose its resistance against external forces. The external force on this bolt will be transferred to the surrounding bolts. In this paper, the structure response after plastic deformation is not considered. Instead, the influence of the imperfections on the structural stress is mainly discussed. When using the finite-element method for meshing, improper meshing may lead to stress concentration. The non-convergence of stress can result in an extremely higher stress compared to the real structural stress (as shown in Figure 6). Therefore, the stress extrapolation method is generally used in finite-element calculation. Alonso-Martinez et al. (2019) applied a 520 KN preload force on the M36 bolt and calculated the maximum von Mises stress of local finite-element models of flange connections with the perfect model by ANSYS Workbench. The result showed that the maximum stress of the flange was about 4700 MPa. It also exceeds the yield strength of the materials. Ji et al., 2021 and Long et al. (2021) established three types of tower flange gap to discuss the effects of the flange gap on the bolts stress. The result revealed that the bolt stress was more sensitive to flange-sided gapping when the tower shell was subjected to tensile stress, and the bolt stress was more sensitive to tower-sided gapping when the tower shell was subjected to compressive stress. This result is consistent with the findings in Figure 12.

The stress difference of bolts is not significant between FOWTs and FBWTs at the beginning. When the location of openings occurs at the centre of the bolt shank, i.e., point C in Figure 8, the bolt stress of FBWTs is observed to be significantly affected by the tower-sided gapping and flange-sided gapping compared to FOWTs (as shown in Figure 13). This trend is due to external forces Z acting on the FBWTs’ tower shell larger than those on the FOWTs’ tower shell. This large external force Z leads to a higher bolt load F _b to some extent. With the openings becoming large until the flange contact surface completely opens, the bolts cannot exert an adequate clamping force to keep the joint together. Hence, parallel gapping has a weak influence in the middle bolt but has a greater impact on the neighbouring bolts for both FOWTs and FBWTs.

For the tower-sided gapping condition, the maximum stress of FBWTs’ bolts is about 1200 MPa and the maximum stress of FOWTs’ bolts is about 1800 MPa when the tower shell is applied with tensile stress. In addition, when the tower shell is subjected to compressive stress, the maximum stress of FBWTs’ bolts is about 4300 MPa and the maximum stress of FOWTs’ bolts is about 3300 MPa. For the flange-sided gapping condition, the maximum stress of FBWTs’ bolts is about 3000 MPa and the maximum stress of FOWTs’ bolts is about 2700 MPa when the tower shell is applied with tensile stress. When the tower shell is subjected to compressive stress, the maximum stress of FBWTs’ bolts is about 2200 MPa and the maximum stress of FOWTs’ bolts is about 2400 MPa.

In this section, a global–local methodology of the fatigue assessment procedure is utilized. This method emphasises the theoretical concepts associated with the modal superposition and fatigue analysis. A workflow for the global–local fatigue assessment methodology is shown in Figure 14. It introduces two different phases of analysis from the global to the local scale with increasing details of geometrical, material, and contact properties. The two phases of fatigue analysis are systematized as follows. In the first phase, a global approach based on the accumulation of damage computed with nominal stresses and S–N curves is introduced. The adopted global numerical model should be accurate enough to obtain nominal stresses to be used as input loading for the linear damage accumulation method. Since the available S–N curves with nominal stress may not properly reflect the local geometrical and material characteristics of critical details, a conservative S–N curve for the fatigue resistance is, thus, considered. Based on the fatigue analysis result, the critical details should be identified, which require a more refined assessment by implementing local scale models. Then, in the second phase, submodelling techniques leveraged by modal superposition concepts are used to accurately evaluate local fatigue damage.

For an offshore structure design, fatigue damage is usually calculated based on the S–N curve approach. The fatigue resistance is represented by S–N curves (Gao et al., 2021). S–N curves define the relationships between the stress ranges and the numbers of cycles to failure in those stress ranges. GL 2010 (Wind guideline, 2010) provides S–N curves for different structural materials, including a bolt with a diameter larger than 30 mm (M36 bolts) used in the bolted connection, which is considered in this paper. The basic design of the S–N curve is given as log ⁡ N = log ⁡ a − m ⁡ log    S , (2) where

N = predicted number of cycles to failure for stress range

S = stress range with unit MPa

Miner’s rule for damage summation described in DNVGL-RP-0005: 2014-06 (DNVGL-RP-0005:2014-06, 2014) and given in Eq. 3 is used in this paper to estimate fatigue damage. D = ∑ i = 1 k n i N i ≤ 1 , (3) where n _i is the number of the existing stress cycles in each range and N _i is the number of stress cycles in each range, which can cause fatigue failure. It is usually assumed that failure occurs when the damage index D reaches 1.0.

Figure 15A shows the fatigue damage on FOWTs’ and FBWTs’ bolts with a maximum flange opening length within 20 years. It is observed that the existence of flatness divergence in bolted flange connection increases the fatigue damage severely. Moreover, it makes a significant impact to consider the different types of flatness divergence in fatigue assessments, especially under tower-sided gapping and flange-sided gapping conditions. On the contrary, the fatigue damage of the middle bolt appears not so sensitive to parallel gapping which may significantly affect the neighbouring bolts. Compared to FOWTs, FBWTs’ bolts are more vulnerable to fatigue damage due to higher external loads and stress range (the stress range of bolts is calculated by stress extrapolation method), as shown in Figure 15B. The flexible foundations of FOWTs can reduce the counterforce around the tower against the environmental loads and result in lower structural responses. The fatigue damage of FBWTs’ bolts is 0.86, which is about 1% larger than that of FOWTs, which is 0.85, when the tower is subjected to tensile stress and the fatigue damage of FOWTs’ bolts is 0.65, which is about 2% larger than that of FBWTs, which is 0.63, when the tower shell is subjected to compressive stress for flange-sided gapping. Furthermore, the fatigue damage of FOWTs’ bolts is 0.5, which is about 2% larger than that of FBWTs, which is 0.48, when the tower shell section is subjected to tensile stress and the fatigue damage of FBWTs’ bolts is 1.16, which is about 18% larger than that of FOWTs, which is 0.98, when the tower shell is subjected to compressive stress for tower-sided gapping. Hence, more attention to FBWTs’ bolts with tower-sided gapping under the compressive stress is necessary during the design process for safe operation.