## Abstract

This study investigates the seismic response of a horizontal axis wind turbine on two bottom-fixed support structures for transitional water depths (30–60 m), a tripod and a jacket, both resting on pile foundations. Fully coupled, nonlinear time-domain simulations on full system models are carried out under combined wind–wave–earthquake loadings, for different load cases, considering fixed and flexible foundation models. It is shown that earthquake loading may cause a significant increase of stress resultant demands, even for moderate peak ground accelerations, and that fully coupled nonlinear time-domain simulations on full system models are essential to capture relevant information on the moment demand in the rotor blades, which cannot be predicted by analyses on simplified models allowed by existing standards. A comparison with some typical design load cases substantiates the need for an accurate seismic assessment in sites at risk from earthquakes.

## 1. Introduction

While an increasing number of offshore wind farms are being planned worldwide to satisfy a growing energy demand, the design of offshore horizontal axis wind turbines (HAWTs) is facing novel and challenging tasks. In this context, seismic assessment has become crucial for bottom-fixed offshore HAWTs in seismically active areas, especially since evidence exists that earthquakes can damage the support structure of land-based HAWTs, as in the case of the 1986 North Palm Springs Earthquake [1]. Seismic assessment of offshore HAWTs is prescribed by recent international guidelines and standards [2–5]. In general, fully coupled nonlinear time-domain simulations [2–5] or response spectra methods [2–5] are suggested, on either simplified [2,5] or full system models [4]. Fully coupled nonlinear time-domain simulations compute the response to earthquake and environmental loads acting simultaneously, considering interactions of aerodynamic, hydrodynamic and seismic responses [2–5], while response spectra methods involve a linear superposition of separately computed responses to earthquake and environmental loads [2–5]. Simplified system models include the support structure only, with the rotor–nacelle assembly (RNA) modelled as a lumped mass at the tower top [2,5]. Full system models involve the support structure and the whole turbine, i.e. nacelle, rotor blades and, in general, turbine components such as power transmission inside the nacelle, pitch and speed control devices, with a different degree of accuracy depending on the specific modelling adopted [4]. Fundamental load cases reflect the possible scenarios for an earthquake strike and are generally chosen as (i) earthquake loads with operational loads, i.e. earthquake striking while the rotor is spinning; (ii) earthquake loads with emergency stop loads, i.e. earthquake triggering a shutdown; and (iii) earthquake loads with non-operational loads, i.e. earthquake striking when the turbine is parked (not operating) due to wind speeds exceeding the cut-off wind speed of the turbine.

As seismic assessment of offshore HAWTs has been included in international guidelines and standards, there is a great interest in assessing to which extent stress demands are increased by earthquake loads, and whether numerical results may be significantly affected by the method of analysis and system modelling adopted. Extensive research studies on these issues are not available yet. However, it is important to remark that earlier studies on land-based HAWTs have already addressed these issues, showing that accurate predictions of the seismic response can be obtained only by performing fully coupled nonlinear time-domain simulations, on full system models including support structure and the whole turbine [6–11]. The main reasons substantiating these conclusions can be summarized as follows. A full system model allows loads acting on all system components to be estimated, including those on the rotor blades, whose integrity is crucial to ensure a reliable power production over the design life of the HAWT. Further, higher rotor modes can be considered only in a full system model, and these modes may be important in the seismic response, as they may fall in the region of maxima spectral accelerations [8–10]. Nonlinear time-domain simulations can capture how tower top oscillations due to the earthquake ground motion affect rotor aerodynamics, in particular the relative wind speed at the blades, depending on which the aerodynamic loading, i.e. lift and drag forces on the blades, are calculated. Also, important sources of nonlinearity have been found in soil response, especially when HAWTs are installed on relatively soft soils or loose soils containing alluvial deposits [12]. Within this theoretical framework, Zhao *et al*. [6,7] and Prowell *et al*. [8–11] have investigated the seismic response of land-based HAWTs of different rated power, by fully coupled nonlinear time-domain simulations on full system models of the HAWT, based on a hybrid multi-body system approach [6,7] or a combined modal and multi-body dynamics formulation, as implemented in the FAST software package [8–11]. Zhao & Maißer [6] have found that force and bending moment at the tower base of a 1.5 MW HAWT are affected considerably by an earthquake striking in the operational state, especially in the lateral direction where there are no wind loads, even for a weak earthquake intensity. Prowell *et al*. have shown that, for the reference National Renewable Energy Laboratory (NREL) 5 MW HAWT [13], the bending moment demand at the tower base is significantly above the demand from extreme wind events. This result has been obtained for parked, operational and emergency stop simulations under a large set of ground motions [9,10], showing that earthquake loads may be a design driving for large turbines in regions of high seismic hazard.

It is apparent that the conclusions above, as drawn from the seismic analysis of land-based HAWTs, have general validity and shall be kept in mind also for seismic assessment of offshore HAWTs. On the other hand, it is important to remark that, in this case, nonlinearities arise also from the hydrodynamic loading and that, in general, interactions of aerodynamic, hydrodynamic and seismic responses shall be considered in fully coupled, nonlinear time-domain simulations.

Studies on the seismic response of offshore HAWTs are not as numerous as those on land-based HAWTs. They are quite recent and have been concerned with offshore HAWTs on monopiles. Haciefendioğlu [14] has investigated the seismic response of a 3 MW HAWT on a monopile, under a stochastic earthquake excitation occurring in the parked state. A simplified model of the HAWT has been used, with the RNA modelled as a lumped top mass and a full three-dimensional model of seawater and soil, and motion equations of the coupled system water–structure–soil have been derived upon enforcing continuity of displacements in the normal direction to the interfaces. Sensitivity of displacement and stress responses to seawater level, soil conditions and presence of a surrounding ice sheet has been investigated. Kim *et al*. [15] have studied the seismic response of the NREL 5 MW HAWT on a monopile, under real and artificial earthquake ground motions occurring in the parked state. A simplified model of the HAWT has been implemented, with the RNA modelled as a lumped top mass; nonlinear springs have been introduced along the pile length to model soil stiffness, considering also the variation of the earthquake ground motion through different soil layers. Important conclusions of this study are that fragility curves of the HAWT, built for a variety of peak ground accelerations (PGAs), can be predicted reasonably well by static pushover analyses and, also, that variation of earthquake ground motion through different soil layers plays an important role in the estimation of the fragility curves.

The purpose of this paper is to investigate the seismic behaviour of bottom-fixed offshore HAWTs in transitional water depths (30–60 m). This subject appears of particular interest considering that wind farms are being planned far from near shore shallow waters (less than 30 m) to minimize visual impact, and there are transitional water depth sites with high wind speed resources and medium-to-high seismic hazard. Typical examples in the USA can be found in the Hawaiian islands [16,17]. In particular, the study is carried out on the NREL 5 MW HAWT, as mounted on two typical steel support structures for transitional water depths, one with a tripod and one with a jacket, both resting on pile foundations. Wind and wave environmental states, water depth and soil profile are set in agreement with similar theoretical studies on offshore HAWTs [18,19]. Consistently with the approach followed for land-based HAWTs [9–11], the seismic response is investigated for a set of real earthquake records taken from existing databases [20,21], with different frequency content and intensity. Fully coupled nonlinear time-domain simulations are carried out on full system models including nonlinear soil stiffness, using the BLADED software package [22], certified by Germanischer Lloyd for design of wind turbines. Simulations are run for earthquake striking in operational and parked states, and earthquake triggering an emergency stop, comparing stress resultant demands to those when no earthquake loads are considered, for fixed and flexible foundation models (FMs). For a further insight into the importance of seismic assessment, a comparison with demands from some typical design load cases prescribed by IEC 61400-3 is also provided [3].

The paper is organized in six sections. Support structures and load cases are presented in §§2 and 3. Typical features of the response to an earthquake strike are illustrated in §4. Results of time-domain simulations with the full earthquake set are described in §5, while the comparison with some IEC 61400-3 load cases [3] is discussed in §6.

## 2. Tripod and jacket support structures

The turbine is the NREL 5 MW three-bladed turbine, whose details can be found in [13]. Two different steel support structures are considered, as shown in figure 1: one with a centre column tripod, and the other with a jacket quattropod, both resting on pile foundations. The two support structures are designed according to current practice; in particular, the one with the jacket quattropod is identical to that studied in [23]. Details on the structural members are given in figure 2. It is assumed that the water depth is 50 m, and the reference three-layer sandy soil of the OC3 project [18,19] is considered. In the following, the two support structures will be referred to as ‘Tripod’ and ‘Jacket’, for simplicity.

The full system is implemented in BLADED [22], modelling nacelle, blades, drive train, control system, as given in [13]. Beam elements with shear deformation are used for support structure structural members, piles and blades. Steel parameters are Young’s modulus = 210 GPa, Poisson coefficient = 0.3 and mass density = 7850 kg m^{−3}. Two different FMs are considered: the first is fixed (clamped base), the second is flexible with lateral and vertical springs along the piles at a 1-m spacing, and a vertical spring at the piles tip, modelling soil stiffness [18,19,24,25] (with respect to the reference system in figure 1, lateral springs are in *x*- and *y*-directions, vertical springs in *z*-direction). All springs are supposed to be uncoupled, with nonlinear force–displacement laws set based on the *p*−*y*, *t*−*z* and *Q*−*z* curves in the API code [26], using the parameters of the OC3 project three-layer sandy soil [18,19] and following the prescriptions for layered soils given in [19] (detailed examples can be found also at the NREL website: https://wind.nrel.gov/forum/wind/viewtopic.php?f=3&t=880&start=0). For completeness, *p*−*y* and *t*−*z* curves at various depths along the piles, and the *Q*−*z* curve at the piles tip, are reported in the electronic supplementary material attached to the paper.

Table 1 shows the frequencies of support structure modes and blades modes, in a parked state (no rotational speed) at 0° azimuth angle (one blade upward and two blade downward), for fixed and flexible FMs, the latter with force–displacement laws of the soil springs linearized to the initial tangent stiffness.

For the fixed FM, the frequencies of the first fore–aft (FA) and side-to-side (SS) support structure modes, as well as the frequencies of the blades modes, are almost the same for Tripod and Jacket, while a substantial difference exists in the second FA and SS support structure modes (FA and SS directions correspond to *x*- and *y*-directions in figure 1; ‘yaw’ and ‘pitch’ means that the blades modes are coupled with yaw and pitch motion of the rotor [7,18]). Shapes of first and second FA support structure modes are reported in figure 3; those in the SS direction are similar and are not reported for brevity.

As for the flexible FM, it can be observed that the frequencies of the first FA and SS support structure modes, and the frequencies of the blades modes, are practically identical to the corresponding ones for fixed FM, whereas the frequencies of the second FA and SS support structure modes are decreased. All these results are in agreement with findings of similar studies [24,27]. For design purposes, it is important to remark that the frequencies of the first FA and SS support structure modes are almost the same for Tripod and Jacket, even when foundation flexibility is accounted for. Shapes of the first and second FA and SS support structure modes are similar to those for fixed FM shown in figure 3 and are omitted for brevity.

Stiffness and mass parameters are reported in table 2, for fixed and flexible FMs, with nonlinear laws of soil springs linearized to the initial tangent stiffness.

## 3. Load cases

The earthquake set for seismic assessment includes 49 real records listed in table 3, taken from [20,21]. Each record has two horizontal components. Figure 4*a* shows the 5% damped acceleration response spectrum, computed as the maximum square root of the sum of the squares (SRSS) of the acceleration responses under the two horizontal components [10]. It can be seen that many frequencies of Tripod and Jacket, reported in table 1, fall within the range of significant spectral accelerations (for reference, figure 4*a* includes only the periods of the first and second FA support structure modes, for fixed FM: *T*_{1}=1/0.311=3.215, *T*_{2}=1/2.206=0.453 for the Tripod; *T*_{1}=1/0.317=3.155, *T*_{2}=1/1.219=0.820 for the Jacket).

Following the approach by Prowell *et al*. [9,10], who have extensively studied the seismic response of a land-based NREL 5 MW HAWT, seismic effects are investigated in different scenarios, considering three load cases:

LC1 = Earthquake loads and operational wind–wave loads, for a wind speed at hub height

*V*_{hub}=11.4 m s^{−1}, a wave period*T*_{p}=9.5 s and a significant wave height*H*_{s}=5.0 m.LC2 = Earthquake loads and emergency stop loads, for a wind speed at hub height

*V*_{hub}=11.4 m s^{−1}, a wave period*T*_{p}=9.5 s and a significant height*H*_{s}=5.0 m. It is assumed that the emergency stop is activated as the nacelle acceleration exceeds 1 m s^{−2}. This value is much higher than the nacelle accelerations due to the considered environmental state and is in agreement with the emergency stop nacelle acceleration used for land-based HAWTs [9,10].LC3 = Earthquake loads and wind–wave loads in a parked state, for a wind speed at hub height

*V*_{hub}=40 m s^{−1}, a wave period*T*_{p}=11.5 s and a significant wave height*H*_{s}=7.0 m.

Wind and wave parameters have been chosen based on the following criteria. In load cases LC1 and LC2, *V* _{hub}=11.4 m s^{−1} is the rated wind speed of the 5 MW turbine, i.e. the minimum wind speed at which the turbine generates its designated maximum power [2]; as turbines are generally designed to provide maximum power for wind speeds with high probability of occurrence at the site, *V* _{hub}=11.4 m s^{−1} can reasonably be assumed as a most likely operational wind speed. In load case LC3, *V* _{hub}=40 m s^{−1} is a very high wind speed, at which the turbine will certainly be parked, i.e. not operating. Consistently with similar studies [18], wave periods *T*_{p} and significant heights *H*_{s} have been chosen as those associated with the selected wind speeds *V* _{hub} in typical offshore environmental states, as for instance some encountered in the Pacific Ocean [28].

It is assumed that wind and waves both act in the *x*-direction (figure 1). Samples are generated in BLADED based on pertinent power spectra [22]. The Kaimal spectrum is used for the wind process [2,29]
3.1
where *f* is the frequency (Hz), *k* is the index referring to the velocity component (1=*x*-direction, 2=*y*-direction and 3=*z*-direction), *σ*_{k} is the standard deviation and *L*_{k} is the integral scale parameter of each velocity component. Assuming medium turbulence characteristics [27], all parameters in equation (3.1) are set according to IEC 61400-1 prescriptions for a normal turbulence model [2]. The JONSWAP spectrum is used for the wave process [30]
3.2
where *f*_{p}=1/*T*_{p} and *γ* is the JONSWAP peakedness parameter [3]
3.3
and
3.4
The Kaimal and JONSWAP spectra for the considered environmental states are reported in figure 4*b*, along with the rotor frequency band (1P) and blade passing frequency band (3P) of the 5 MW HAWT [31]. It can be observed that the frequencies of the first FA support structure modes of both Tripod and Jacket fall within the interval 1P–3P, corresponding to a typical soft–stiff design.

Fully coupled nonlinear time-domain simulations are carried out in BLADED by numerical integration of motion equations built by a combined multi-body dynamics and modal approach [22], considering interactions of aerodynamic, hydrodynamic and seismic responses, and including nonlinear soil stiffness as modelled in §2. While the aerodynamic loading on the spinning rotor is generated based on classical concepts of combined blade element and momentum theory [32], the hydrodynamic loading on the structural members is computed based on Morison’s equation [33], with drag and inertia coefficients set according to DNV recommendations [5]. Wind loads acting along the tower are included. For both Tripod and Jacket, modal damping ratios are set equal to 10^{−2} for support structure modes, and 4.775×10^{−3} for the blades modes [13]. The simulation length is 800 s, with the earthquake ground motion starting 400 s into the simulation, to ensure that the earthquake occurs as the structural response has already attained a steady state [9,10].

## 4. Response to a single earthquake record

To gain a preliminary insight into the response of Tripod and Jacket under combined wind, wave and earthquake loading, the response to a single earthquake is discussed. Specifically, the Northridge earthquake is considered (ID no. 44 in table 3) a 40 s duration near fault ground motion [21]. Results are obtained assuming that the fault normal and fault parallel components act in the *x*- and *y*-directions, respectively (figure 1).

The response is computed for load cases LC1, LC2 and LC3 in §3. For each load case, one sample of the wind process and one sample of the wave process are generated based on the spectra given in equations (3.1) and (3.2). For load case LC3, 0° and 180° azimuth angles are considered for the parked rotor (180°=two blades upward and one blade downward). Tower top deflection and maxima accelerations along the support structures are given in figures 5 and 6, for fixed and flexible FMs.

### (a) Response for fixed foundation model

Figures 5*a*,*b* and 6*a*,*b* show the tower top deflection in *x*- and *y*-directions, for fixed FM. For both Tripod and Jacket, it is observed that

(1) If the earthquake occurs in the operational state, the tower top deflection increases significantly starting from the earthquake strike (time history above

*t*=400 s), reducing progressively to the operational deflection once the earthquake has expired (time history above*t*=440 s).(2) As a result of an emergency stop triggered at a 1 m s

^{−2}nacelle acceleration, the tower top deflection deviates from the operational deflection and, after a transient, attains a parked state, where the deflection is due only to wave loads, and wind loads acting on the parked rotor and along the tower.(3) If the earthquake occurs in a parked state, the tower top deflection increases starting from the earthquake strike reducing progressively to the parked deflection. Differences between 0° and 180° parked states are not notable. It can be argued that, although the geometry of the two rotor positions is different, the difference in terms of mass distributions along the height is relatively small, with a consequent relatively small effect on the seismic response. Note that, once the earthquake has expired, the final parked deflections in load cases LC2 and LC3 are different, due to the fact that load case LC2 and load case LC3 involve different wind speeds

*V*_{hub}, wave periods*T*_{p}and significant wave heights*H*_{s}.

Figures 5*c* and 6*c* show the maxima accelerations along the support structures, in *x*- and *y*-directions. The acceleration profile in the *x*-direction shows that combined wind–wave–earthquake loadings activate first and second FA support structure modes, in both Tripod and Jacket, in all three load cases under investigation. The same observation can be made based on the acceleration profile in the *y*-direction. The activation of the second FA and SS support structure modes is confirmed by the fact that the acceleration profiles exhibit significant values at approximately 2/3 of the support structure height, and this result is consistent with analogous results for land-based HAWTs under earthquake loading [11].

### (b) Response for flexible foundation model

Figures 5*d*–*f* and 6*d*–*f* show the tower top deflection and maxima accelerations along the support structures, in *x*- and *y*-directions, for flexible FM. Results appear in agreement with the corresponding ones for fixed FM. That is, the tower top deflection is significantly affected by the earthquake strike, with a considerable increase with respect to the operational deflection in load case LC1, a deviation from the operational deflection and subsequent transient in load case LC2, an increase with respect to the parked deflection in load case LC3, with no notable differences between 0° and 180° parked states. The acceleration profiles show contributions from first and second support structure modes. Also, it is seen that deflections and accelerations of the tower top are slightly larger, in most cases, than those for fixed FM.

## 5. Response to an earthquake set

Next, the seismic response of Tripod and Jacket is investigated using the full earthquake set in table 3, for load cases LC1–LC2–LC3 introduced in §3. In particular, considering that the results of load case LC3 do not seem affected by the rotor position, a 0° parked state is assumed. For a given load case, two simulations are carried out for each earthquake, in agreement with the studies by Prowell *et al*. [9,10] on land-based HAWTs. The two simulations differ as the two horizontal components of the earthquake are rotated 90°, in order to reduce bias from the orientation of the earthquake components relative to the wind direction [9,10]. Therefore, each load case involves 98=49×2 simulations.

For each simulation, some results of particular interest are considered as measures of the earthquake demand: maximum resultant bending moment at the tower base (=maximum SRSS of the bending moments in *x*- and *y*-directions); maximum axial force at the pile head, for pile #1^{′} of the Tripod and pile #3′′ of the Jacket (figure 1); maximum resultant bending moment at the blade root (=maximum SRSS of the bending moments in orthogonal planes of the blade local coordinate system); maximum resultant acceleration at the tower top (=maximum SRSS of the accelerations in *x*- and *y*-directions). It is noted that pile #1^{′} of the Tripod and pile #3′′ of the Jacket are selected since, according to the simulation results, they undergo slightly higher demands with respect to the other piles. However, variability of results is very limited and, from an engineering point of view, demands in all piles can be considered within the same range, in all load cases LC1–LC2–LC3. For completeness, results for all piles are reported in the electronic supplementary material attached to the paper.

Results are reported in figures 7 and 8 assuming the PGA as earthquake intensity measure, for fixed and flexible FMs. In total, 588=2×3×98 simulations have been run for each structure.

## 6. Stress resultant and tower top acceleration demands for fixedfoundation model

In figures 7 and 8, stress resultant and tower top acceleration demands for fixed FM are denoted by symbol ‘×’. Black vertical lines indicate the corresponding demands due to wind and wave loads only, i.e. without earthquake loads, for the environmental states considered in load cases LC1–LC2–LC3 (see §3).

Firstly, some relevant comments are in order on the stress resultant demands at the tower base and pile head. For both Tripod and Jacket, it can be seen that, as a result of the earthquake strike, stress resultant demands increase significantly, in all load cases LC1–LC2–LC3. In particular, considering that, in both Tripod and Jacket, the maxima stress resultant demands without earthquake loads are attained in the operational state (black vertical lines in load case LC1 of figures 7 and 8), maxima stress resultant demands due to earthquake loads increase by a factor of 2–3 at the tower base and by a factor of 8–9 at the pile head of the Tripod (figure 7), by a factor of 3–4 at the tower base and by a factor of 4–5 at the pile head of the Jacket (figure 8). Further important observations are that significant stress resultant demands are encountered not only for high, but also for moderate PGA, and that stress resultant demands in load cases LC1–LC2–LC3 can be considered to be practically within the same range (100–400 MNm at the tower base and 10–80 MN at the pile head of the Tripod; 50–400 MNm at the tower base and 15–80 MN at the pile head of the Jacket). In this regard, it is worth noting that stress resultant demands in the parked state (load case LC3) falling within the same range of stress resultant demands in the operational state (load case LC1) have been observed also in the seismic response of land-based HAWTs [8–10]. This result can be explained considering that, when the turbine is parked, the only damping is the structural damping of the support structure, usually low in steel structures, whereas in the operational state the structural response experiences an additional aerodynamic damping, whose source is essentially the spinning rotor aerodynamics, and that depends on the oscillations of the tower top due to earthquake loading [34,35]. It is also worth noting that the significant stress resultant demands found in case of an emergency stop (load case LC2), shown in figures 7 and 8, mean that triggering a shutdown does not provide substantial benefits and that, therefore, load case LC2 shall generally be considered in the seismic assessment. In this context, it is pointed out that in all simulations of load case LC2, earthquake loads do trigger an emergency stop, i.e. the nacelle acceleration exceeds 1 m s^{−2}.

Comments on stress resultant demands at the tower base and pile head hold also for the tower top accelerations. Figures 7 and 8 show indeed that the tower top acceleration demands are significantly higher than the corresponding values without earthquake loads, in all load cases LC1–LC2–LC3.

As for the moment demands at the blade root, figures 7 and 8 show, that in both Tripod and Jacket, they are not affected by an earthquake strike in the operational state (load case LC1) and in case of an emergency stop (load case LC2), while increments are experienced in the parked state (load case LC3); considering that the maxima moment demands without earthquake loads are attained in the operational state (black vertical lines in load case LC1), maxima moment demands increase by a factor of 1.2 in the Tripod (figure 7), and by a factor of 2 in the Jacket (figure 8). This result is evidence that seismic-induced blade vibrations are damped by aerodynamic damping in the operational state, but become significant in the parked state due to very low structural damping of the blades, in agreement with similar findings for land-based HAWTs [10]. For completeness, a comment is in order on the ‘×’ symbols on the left of the vertical lines in load case LC2, that correspond to simulations in which the maximum blade root bending moment after the start of earthquake shaking is found to be smaller than the maximum due to the considered operational wind–wave loads. This may happen considering that (i) on one hand, the emergency stop may be activated just a few seconds after the start of earthquake shaking, i.e. when not enough time has elapsed for earthquake loads to cause moments higher than the maximum moment due to the operational wind–wave loads; (ii) on the other hand, after the activation of the emergency stop, the moments caused by the combined earthquake loads + emergency stop loads may not exceed the maximum moment due to the operational wind–wave loads. However, there are also simulations in load case LC2 (‘×’ symbols on the right of the vertical lines) in which after the start of earthquake shaking, either before or after the activation of the emergency stop, the maximum moment slightly exceeds the maximum due to the operational wind–wave loads, especially for high PGAs. As for load case LC2, recognize that moment demands smaller than the corresponding value without earthquake loads are encountered also at the tower base, for some simulations (‘×’ symbols on the left of the vertical lines).

Comparing the responses of Tripod and Jacket, it is worth recalling that the frequencies of the first FA and SS support structure modes, as well as the frequencies of the blades modes (table 1), are almost identical for the two structures; stress resultant demands at the tower base and pile head are found approximately within the same range, but moment demands at the blade root are generally higher in the Jacket, with a maximum demand nearly equal to 40 MNm (figure 8) versus 20 MNm in the Tripod (figure 7). It is evident that these differences shall be attributed to dissimilar stiffness and mass distributions along the two support structures (table 2) and, also, to the activation of the second FA and SS support structure modes, whose frequencies are substantially different in the Tripod and Jacket (table 1).

A final important comment is that, as shown in figures 7 and 8, stress resultant and tower top acceleration demands generally increase with the PGA, thus meaning that the PGA can be taken as an acceptable indicator of demand for the structures under study. Because the PGA is typically related to the short-period energy content of the earthquake, this result reflects the fact that the rotor modes and second support structure modes (table 1) play an important role in the seismic response, as shown in figure 4*a* (periods of the rotor modes and second support structure modes fall in the region of maxima spectral accelerations) and figures 5 and 6 (activation of the second support structure modes), in agreement with similar findings for land-based HAWTs [8–10].

### (a) Stress resultant and tower top acceleration demands for flexible foundation model

In figures 7 and 8, stress resultant and tower top acceleration demands for flexible FM are denoted by symbol ‘Δ’, while grey vertical lines indicate the corresponding demands due to wind and wave loads only, for the environmental states in load cases LC1–LC2–LC3 (see §3).

At the tower base and pile head, in both Tripod and Jacket, stress resultant demands do not change significantly with respect to the corresponding demands for fixed FM, in all load cases LC1–LC2–LC3. This result may be explained considering that the frequencies of the first FA and SS support structure modes, as well as the frequencies of the blades modes, hold almost the same values for fixed and flexible FMs (table 1), while the frequencies of second FA and SS support structure modes, although being reduced by the foundation flexibility (table 1), still correspond to periods falling within the range of high-spectral accelerations, as shown in figure 4*a* (for instance, for the second FA support structure modes: *T*_{2}=1/1.277=0.783 s in the Tripod, and *T*_{2}=1/0.984=1.016 s in the Jacket). The same observations can be made for the stress resultant demands at the tower base and pile head without earthquake loads (grey vertical lines in load cases LC1–LC2–LC3), which appear almost identical to the corresponding demands for fixed FM (black vertical lines), showing that frequencies of the second FA and SS support structure modes, although being reduced by the foundation flexibility, shift within a frequency range that is still relatively far from the excitation frequencies of wind and wave processes (figure 4*b*).

Figures 7 and 8 also show that, unlike the stress resultant demands at the tower base and pile head, moment demands at the blade root in the parked state (load case LC3) increase with respect to the corresponding demands for fixed FM, in both Tripod and Jacket. In particular, the maximum moment demand in the Tripod is found to be 60 MNm (versus 20 MNm for fixed FM), whereas that in the Jacket is 90 MNm (versus 40 MNm for fixed FM). It is interesting to remark that, as shown in figures 7 and 8, such an increase of maximum moment demand at the blade root mirrors an increase of maximum tower top acceleration demand in the parked state (load case LC3) with respect to the corresponding maximum acceleration demand for fixed FM, and shall be considered, in this case, as a result of the additional flexibility introduced by the flexible FM [36].

Comparing Tripod and Jacket responses, it is observed that stress resultant demands at the tower base and pile head fall approximately within the same range, whereas the maximum moment demand at the blade root is encountered in the Jacket (90 MNm). In these respects, results appear in a substantial agreement with those for fixed FM.

In order to have an indicator of nonlinearity of the soil response, the maxima lateral *x*- and *y*-deflections obtained from all simulations of the earthquake set, at various depths along the piles, are reported in figure 9 for load cases LC1–LC2–LC3. Here, the maximum deflection is intended as the maximum deviation from the initial vertical configuration of the pile and, as such, may be encountered in either the positive or the negative direction of *x*- and *y*-axes. In particular, it has been found that the maxima lateral deflections at all depths are attained in the same simulation, and at the same time instant of the simulation, specifically as the pile head attains its maximum deflection. For example, in pile #1^{′} of the Tripod, the maxima *x*-deflections at all depths are found in the simulation with the Northridge earthquake (ID no. 43 in table 3), when its fault normal component acts in the *x*-direction, in all load cases LC1–LC2–LC3. It is observed that the profiles in figure 9, with positive and negative deflections (the latter are slightly visible, for instance, in pile #1^{′} of the Tripod), are in accordance with typical deflection profiles of flexible piles constrained by lateral springs and supporting structures under dynamic lateral loads [37]. For comparison, figure 9 also includes (i) the maxima lateral deflections due to wind–wave loads only (no earthquake loads), for the environmental states considered in load cases LC1–LC2–LC3; (ii) the lateral deflections at which the soil resistance forces attain, with a tolerance of 10^{−2}, the maxima asymptotic values given by the *p*−*y* API curves [26] for the considered sandy soil [18,19], at various depths along the piles; note that these lateral deflections can be taken as indicators of a significant nonlinear soil response, because *p*−*y* curves deviate from linearity also for relatively small soil displacements [26]. Figure 9 shows that earthquake loads cause a considerable increase of lateral deflections with respect to corresponding values without earthquake loads. It is also seen that nonlinear effects are significant, especially in the Tripod, where maxima lateral deflections are well above the lateral deflections corresponding to maxima soil resistance forces, over about one-fourth of the total pile length. These results suggest that using linearized *p*−*y* curves, as for instance in simplified fatigue analysis of offshore HAWTs on bottom-fixed support structures [38], may not be appropriate for seismic assessment.

## 7. Comparison with IEC 61400-3 load cases

In order to assess whether earthquake loads are design driving for the Tripod and Jacket under study, a full set of design load cases should be considered, as for instance those prescribed by IEC 61400-3 [3]. Analyses should be carried out for site-specific conditions, based on accurate joint statistics of wind and wave states, sea currents and water level, and on a proper description of local seismicity, as required by IEC 61400-3 [3].

Here, it is of interest to compare the earthquake demands in figures 7 and 8, obtained for earthquake loads combined with wind–wave loads in a typical operational state and a typical parked state, with demands from some IEC 61400-3 design load cases [3]. For this purpose, the load cases in table 4 are selected as representative of operational and parked states [3], assuming environmental parameters that can reasonably be expected in offshore sites for wind turbines, in accordance with those in §3 (more details on the environmental parameters in table 4 are reported in the electronic supplementary material attached to the paper). Bearing in mind that a definitive answer as to whether earthquake loads are design driving can be given only for site-specific conditions, that the environmental parameters in table 4 may not reflect particularly unfavourable site conditions and that only a few environmental states are selected in table 4 (e.g. DLC 1.3 and DLC 1.6 would require discrete values of the wind speed at the hub, *V* _{hub}, ranging from the cut-in speed *V* _{in}=3.0 m s^{−1} and the cut-out speed *V* _{out}=25 m s^{−1} of the 5 MW turbine [13] with intervals of 2 m s^{−1} [3]), it is believed that the load cases in table 4 can provide at least a reasonable order of magnitude of typical operational and parked state demands as prescribed by IEC 61400-3 [3], for comparison with the earthquake demands in figures 7 and 8.

For each load case, six simulations are implemented in BLADED [22], with either 10 min or 1 h length [3]. Maxima stress resultants at the tower base, pile head (pile #1^{′} of the Tripod and pile #3′′ of the Jacket) and blade root are reported in tables 5 and 6. Maxima axial forces in the other piles are found within the range of those in tables 5 and 6 and, for completeness, are reported as the electronic supplementary material attached to the paper.

Hence, according to IEC 61400-3 [3], the demands in tables 5 and 6 should be multiplied by a load safety factor equal to 1.35 and, for the operational load cases involving a wind speed range (Section 7.5.4 in [3]), a second multiplicative factor should be considered to extrapolate appropriate long-term characteristic demands, based on a site-specific joint probability distribution of wind and wave states. Although different approaches exist to compute such extrapolation factor, indicative values of 1.2÷1.3 may be derived from land-based HAWTs (see [9,10] or Annex F in [2] for the characteristic moment at the blade root). Therefore, multiplying the values in tables 5 and 6 by a 1.35 load safety factor and also by a 1.3 extrapolation factor for the operational load cases, it can readily be observed that the derived demands would be smaller than the earthquake demands obtained for the highest levels of PGA, as reported in figures 7 and 8. It is also worth noting that, at the pile head and blade root of the Tripod, earthquake demands would be higher also for moderate levels of PGA. In particular, at the blade root, this holds true for the flexible FM (figure 7).

Although the considered operational and parked states are certainly not exhaustive, and other important loads shall be considered in design analyses, such as fatigue loads, the results discussed above substantiate the need for an accurate seismic assessment of offshore HAWTs, also in recognition of the fact that no load safety factor has been applied to earthquake demands when compared with the demands from the IEC 61400-3 load cases. Analogous conclusions have been drawn in studies on a land-based NREL 5 MW HAWT [9,10], showing that earthquake demands may be design driving in regions of high seismic hazard.

## 8. Concluding remarks

The seismic behaviour of the NREL 5 MW HAWT [13], mounted on a Tripod and a Jacket in transitional water depths, has been investigated by fully coupled nonlinear time-domain simulations on full system models implemented in BLADED [22], for fixed and flexible FMs. Some typical scenarios, i.e. earthquake striking in the operational state (load case LC1) or parked state (load case LC3), and earthquake triggering an emergency stop (load case LC2) have been considered, selecting two typical wind–wave states for operational and parked states. The main results can be summarized as follows.

(1) For the fixed FM, in both Tripod and Jacket, moment demand at the tower base and axial force demand at the pile head in load cases LC1–LC2–LC3, as well as moment demand at the blade root in load case LC3, increase significantly with respect to the corresponding demands without earthquake loads, even for moderate PGA.

(2) For the flexible FM, in both Tripod and Jacket, moment demand at the tower base and axial force demand at the pile head in load cases LC1–LC2–LC3 do not change significantly with respect to the corresponding demands for fixed FM, whereas maxima moment demands at the blade root in load case LC3 increase significantly. This is consistent with the fact that, as a result of the foundation flexibility, maxima tower top acceleration demands increase with respect to corresponding maxima for fixed FM [35], whereas, in contrast, the natural frequencies are not significantly reduced.

(3) For both fixed and flexible FMs, demands at the tower base and pile head of both Tripod and Jacket fall approximately within the same range, whereas maxima moment demands at the blade root are always encountered in the Jacket. These results are evidence that different mass and stiffness distributions, as well as activation of second FA and SS support structure modes, play a crucial role in the seismic response of the two structures.

The results of load cases LC1–LC2–LC3 suggest that fully coupled nonlinear time-domain simulations on full system models, i.e. including support structure, rotor blades and nacelle, as those implementable in BLADED [22] or similar software, are highly recommended for the seismic assessment of offshore HAWTs, while simplified models allowed by standards and guidelines [3,6], that involve only the support structure and a lumped mass modelling the RNA at the tower top, would fail to capture relevant data. These conclusions can be drawn especially considering that simplified models could not provide any prediction on the response of the rotor blades, whereas the simulations run in this study have revealed that, at the blade root, moment demands are significantly increased by earthquake loads, with maxima very sensitive to foundation flexibility, and that relevant differences may exist between maxima moment demands when different support structures are used, such as the Tripod and Jacket in figure 2. Because rotor blades are key components of the turbine, all these data are of crucial importance in the seismic assessment of offshore HAWTs. It is also recommended that full system models account for nonlinear soil response, in recognition of the significant nonlinear effects shown in figure 9.

Further, this study has shown that the stress resultant demands in load cases LC1–LC2–LC3 may be higher than demands from some typical design loads prescribed by IEC 61400-3 [3], in general for the highest levels of PGA. Although a definitive answer as to whether earthquake loads are design driving for the two structures under study can be given only considering site-specific conditions, these results substantiate the need for an accurate seismic assessment when installing offshore HAWTs in seismically active areas. In this context, refined seismic analyses should be carried out, considering vertical ground motion, variation of earthquake acceleration through soil layers [15], potential misalignment between wind and wave loads during earthquake shaking, and other important issues such as sensitivity to different models of *p*−*y* curves [37] and potential uncertainties in soil properties [39], alterations of the foundation stiffness due to strain-hardening or strain-softening soil behaviour [40,41]. Related effects shall accurately be investigated considering site-specific conditions.

## Acknowledgements

The authors wish to thank Prof. M. Di Paola, University of Palermo, Italy, and Prof. D. Porcino, University of Reggio Calabria, Italy, for fruitful discussions on this work. The financial support of PON01_01869: Tecnologie e Materiali Innovativi per la Difesa del Territorio e la Tutela dell’Ambiente (TEMA DI TUTELA) is gratefully acknowledged.

## Footnotes

One contribution of 17 to a theme issue ‘New perspectives in offshore wind energy’.

- © 2015 The Author(s) Published by the Royal Society. All rights reserved.