Offshore wind turbine subjected to supershear earthquake ruptures

Abstract

Supershear earthquakes, analogous to supersonic speeds of sounds, show the presence of a Mach front in the top view. This feature was observed in several past earthquakes, including the 1999 Izmit earthquake, 2001 Kokoxili earthquake, to name a few. The ground motion from supershear ruptures can be destructive to structures due to dominant fault-parallel components. In this study, we demonstrate the effect of supershear ruptures on wind turbines by modelling them in OpenSees. Earthquake ruptures are simulated using SPECFEM3D, another open-source software. By considering arrays at different offsets along strike and away from the strike, the distance effect on serviceability limit states of wind turbines is studied using supershear and subshear earthquakes.

Keywords

wind farm wind turbine supershear earthquake fragility offshore structures

Introduction

With the double-digit growth rate, the offshore wind turbine (OWT) capacity already reached 29.1 GW in 2019 (Joyce et al., 2020). The popularity of OWT already crosses the seismically stable continent of Europe, predominantly in seismically active continents of Asia and North America. Hence the optimization and design of wind farms only for the wake losses, site location, wind farm layout, maintenance cost, and optimal usage of the control system is no more acceptable. Most of the research work on the seismic analysis of wind turbines focuses on the individual wind turbine structural performance. However, the focus on the influence of the earthquake on the micrositing of the wind turbine is limited. Hence this work presents the influence of the seismic source parameters on the OWT micrositing.

The literature shows the micrositing of wind turbines optimized for the direction and intensity of wind (Mosetti et al., 1994), minimizing wake losses (Kusiak and Song, 2010), turbine height (Chen et al., 2013), electrical system design (Hou et al., 2019), cost of energy, and the Levelized production cost (Elkinton et al., 2006), and economics, carbon emission(Wu et al., 2019) for several shapes of the wind farm. However, Katsanos et al., (2016) studied the seismic hazard aspect of wind turbines and firmly concluded that the seismic hazard has a profound role in the design and safety of wind turbine structures.

The performance of the OWT structure is evaluated for the combined effect of the earthquake and other environmental loads. Haciefendioǧlu (2012) performed the stochastic seismic analysis of 3 MW offshore wind turbine structure by considering the structure–seawater–soil interaction. The increased response is observed for the soft soil and is further affected by the seawater level and the presence of ice sheets. Kjørlaug and Kaynia, (2015) determined the effect of the vertical earthquake component on the performance of the OWT with soil-structure interaction (SSI). The work shows that the ground acceleration at the base amplifies a factor of two at the nacelle level. Zheng et al., (2015) performed an experimental study by considering the joint action of moderate sea waves condition and a strong earthquake motion on a monopile supported wind turbine. Their research concludes that ignoring the combined effect can lead to the underestimation of structural response. Sadowski et al., (2017) observed the catastrophic failure of a geometrically imperfect wind turbine tower under seismic forces. The tower wall imperfection notably reduces the spectral acceleration at failure. De Risi et al., (2018) performed the fragility analysis for the monopile-supported offshore wind turbines of capacity 2 MW and 5 MW by considering the unscaled earthquakes from crustal, in-slab, and interface earthquakes further found that earthquake vulnerability increases in soft soil. Ali et al., (2020) extended the work of De Risi et al., (2018) by considering pulse and non-pulse records. The 5MW turbine structure found more sensitivity to the near-fault crustal records PGV > 30 cm/s and vertical accelerations, irrespective of the pulse presence.

Kaynia, (2019) found that the effect of vertical earthquake excitation is crucial for structures with high natural frequencies in the vertical direction like an OWT. Zhao et al., (2020) used a response spectrum method to evaluate the OWT’s pile-water and pile-soil interactions, also pointed out that pile-water interaction significantly affects the structural displacement. In recent work, Kaynia, (2020) presented the effect of kinematic interaction through the numerical of monopole OWT. Higher kinetic interaction is noted for the stiff soil and medium-to-high frequency content. Meng et al., (2020) performed experimental work on a scaled model to determine the combined effect of wind and strong ground motions, the conclusion was that aerodynamic damping could reduce the seismic response of wind turbines. Previous studies have almost exclusively focused on either optimizing the wind farm layout without considering the seismic aspects or the performance of the individual wind turbine structure. Hence, an attempt is made to determine the influence of the micrositing of OWT with respect to the seismic source parameters. Performance of mono pile-supported offshore wind turbines is evaluated for various locations, the orientation of the turbine with respect to a fault, and different locations of earthquake nucleation that produces the subshear and supershear earthquakes.

Supershear earthquakes

The ground motion features exhibited during fault rupture depends on source parameters like stress drop, rupture area, and shear wave velocity. One such important parameter which influences the characteristics of ground motions and the radiation pattern of seismic waves is the rupture velocity of an earthquake. Rupture velocity can be defined as the speed at which the rupture front moves along the fault surface during an earthquake. The condition of supershear happens if the rupture velocity propagates with a specific velocity.

A few parameters that influence the rupture velocity are S-parameter, K-parameter, transition length, fault width, and stress heterogeneity. S-parameter depends on the ratio of difference of static and initial stress and the difference of initial and dynamic stress. According to the study by Andrews, (1976), conditions for S parameter < 1.77 (in 2-D) and also based on the study by Dunham, (2007) S parameter < 1.19 (in 3-D). K-parameter is a measure of energy at the crack tip, and for the condition in the case of a supershear earthquake, the value k > 1.3kc, where kc depends on initial stress conditions, friction coefficient, and length parameter. For rupture to propagate at any instant of time, k should always be greater than kc. Transition length is the length where rupture transformation from sub shear to supershear takes place. Dunham, (2007) presented the conditions on transition length for an earthquake to propagate at supershear speeds in 3D.

Earthquakes in the past which exhibited supershear phenomena include 1906 San Francisco (Mw = 7.9) (Song et al., 2008), 1979 Imperial Valley, CA (Mw = 6.5) (Archuleta, 1984), 1999 Izmit, Turkey (Mw = .6) (Bouchon et al., 2001), 1999 Duzce, Turkey (Mw = 7.6) (Bouin et al., 2004), 2001 Kunlunshan, Tibet (Mw = 7.8) (Bouchon and Vallée, 2003), Denali, 2002 Alaska (Mw = 7.9) (Dunham and Archuleta, 2004) and 2009 L’Aquila, Italy (Mw = 6.3) (Ellsworth and Chiaraluce, 2009). The characteristics of the ground motions exhibited during these earthquakes are when rupture travels at supershear velocities, due to the interference of S-waves Mach cone is formed. Mach cone induces very high stresses near the fault plane, causing enhanced off-fault damage(Bhat et al., 2007) and amplifying ground motions. S-wave displacement field in case of supershear rupture does not have an attenuation factor, so strong ground motions are carried to longer distances unattenuated when compared to subshear ruptures (Mello et al., 2010). Another characteristic of a supershear earthquake is that the Fault-Parallel (FP) component of ground motion is more than Fault-Normal (FN) components (Mello et al., 2010).

Earthquake simulations

Dynamic rupture is more advanced modelling, than kinematic ruptures for earthquake simulation coupling fracture mechanics with the contact-friction laws between the crustal rock interfaces. In this study, a vertical strike-slip fault is considered of dimensions 30 km × 15 km, which is typical of a magnitude Mw 7 scaling laws (Wells and Coppersmith, 1994). This fault is embedded in a 2670 kg/m³ homogenous medium with 6 km/s P-wave velocity and 3.464 km/s S-wave velocity. Earthquake is triggered by artificially perturbing the shear traction at the hypocentre (in this case assumed to be at the centre of the fault, along strike as well as along dip) beyond the static friction levels. Once triggered, the rupture propagates spontaneously in a self-sustained manner (assuming that the size of nucleation asperity at the hypocentre is sufficiently large enough) until it hits a barrier. The fault reaches the free surface, and assuming that the origin is at the centre of the free surface intersection of the fault, we have set a barrier at 15 km on either side along strike, and at 15 km depth, in the down-dip direction.

This study simulates two types of earthquakes from the dynamic rupture principles (1) subshear and (2) supershear. The former has rupture propagating at speeds less than the shear-wave speed of the medium, while in the latter case, rupture propagates faster than the shear waves. Earthquakes are mixed-mode fractures (mode II & mode III) based on fracture mechanics, and supershear is observed in mode II depending on certaining favourable conditions (S-parameter < 1.19) between background shear stress and the dynamic friction levels at the rock interfaces. The static friction coefficient is assumed to be 0.677, and the friction coefficient drops to a dynamic level of 0.525 linearly as slip (relative displacement on either side of the fault) increases from 0 to 0.4 m. This linear slip-weakening law was initially proposed by (Ida, 1972) and featured again in (Andrews, 1976) to demonstrate spontaneous earthquake rupture propagation.

The background normal stress is assumed to be 120 MPa compression for both subshear and supershear cases. However, the background shear stress is 70 MPa for the subshear case, while 80 MPa for the supershear case. Note that the shear traction to the normal traction ratio is very close to the static friction levels in the supershear case. The most important distinguishing feature of subshear and supershear earthquakes is the difference in Fault-Parallel (FP) and Fault-Normal (FN) components of ground motion, the acceleration time histories and response spectra of which are shown in subsequent section by consideration arrays of stations at certain offsets away from the strike, and at distances along strike.

Receiver locations

Receivers considered in this study are assumed to be arranged in two different fashions (i) parallel array (ii) perpendicular array. In each array, four different distances are also considered. There are 4 parallel arrays (a) Y = 1 km away from the fault (b) Y = 2 km away from the fault (c) Y = 5 km away from the fault (d) Y = 10 km away from the fault, and 4 perpendicular arrays (a) X = 0 km along strike from the epicentre (b) X = 7 km along strike from the epicentre (c) X = 15 km along strike from the epicentre (d) X = 22 km along strike from the epicentre. In each case, seven stations are considered, as shown in Figure 1. The earthquake data for perpendicular and parallel arrays is shown in Figure 2 and Figure 3. For each of these cases, Incremental Dynamic Analysis (IDA) is carried out of the wind turbine model, and fragility is computed for SLS associated with pile top ration at mud level and tower top rotation at nacelle.

Figure 1.

Station locations where earthquake shaking is considered. The fault line is shown in red color, and the epicentre is shown by a star symbol. Origin is at the epicentre. Circles indicate parallel arrays at certain offsets from the fault, while triangles indicate the perpendicular arrays.

Figure 2.

Acceleration time histories for the subshear and supershear cases. Parallel array and perpendicular arrays are shown separately. For each of these cases, Fault-Parallel (FP) and Fault-Normal (FN) components of ground motion are also shown separately.

Figure 3.

Response spectra for the subshear and supershear cases. Parallel array and perpendicular arrays are shown separately. For each of these cases, Fault-Parallel (FP) and Fault-Normal (FN) components of ground motion are also shown separately.

Offshore wind turbine model

The wind turbine model on a monopile foundation immersed into water is considered to have three parts (Figure 4) (i) the monopile part below the seabed, (ii) the transition piece surrounded by water (iii) the main of the superstructure. A 5 MW capacity model is common and mostly referred to in literature (Ali et al., 2020; Katsanos et al., 2016; Kaynia, 2019; Zhao et al., 2020; Zuo et al., 2018, 2020). Hence, in this study, the NREL offshore 5MW baseline wind turbine is used. The tributary mass of soil is applied on the monopile, and the tributary mass of water is applied at the transition piece. Only 80% of the cylindrically shaped water column is considered for the transition piece nodal mass. The tower joints are locations of structural mass idealization. Rotor vibration-related dynamic loads are neglected in this study.

Figure 4.

Schematic diagram and numerical idealization of OWT model. (Chaudhari and Somala, 2021)

Wind and wave loads are considered in this study, apart from earthquake loading. Wave loads are applied assuming stationary sea conditions at the nodal masses of the transition piece. The static loads due to wind are calculated as suggested in ASCE/SEI 07-10 (ASCE/SEI 7-10, 2013) and IEC (IEC, 2009). The power law is used to determine the wind speed profile along with the tower (IEC, 2009). The equation-1 is used to estimate the wind speed v(z) at height z above the sea level in terms of v_Hub is the wind speed at the hub level, h_Hub is the hub centre’s height from the sea level, and the κ is the power-law (or wind shear) exponent. The horizontal force due to wind is calculated by equation-2, where A(z) is the tributary area of the structure at height z.

v (z) = v_{Hub} \cdot {(\frac{z}{h_{Hub}})}^{k}

(1)

F (z) = \frac{ρ_{Air} \cdot v {(z)}^{2} \cdot A (z)}{2}

(2)

The wind thrust (F_Hub) on RNA is calculated using equation-3 (Arany et al., 2017), where ρ_Air is the air density typically assumed as 1.25 kg/m³. The v_Hub is the wind velocity at hub height, and the d_rot is the diameter of the rotor, C_t is the coefficient of the thrust. The coefficient of thrust is calculated as by equation (4) (Arany et al., 2017; Frohboese and Schmuck, 2010). Here, the rated velocity v_r corresponds to the steady turbine output and the hub’s velocity, and both are assumed to be 15 m/s.

F_{Hub} = \frac{ρ_{Air} \cdot v_{Hub}^{2} \cdot π d_{rot}^{2} \cdot C_{t}}{8}

(3)

where

C_{t} = \frac{(7 v_{r}^{2} + 8.75 v_{r}^{2})}{v_{Hub}^{3}}

(4)

Earthquake loading is modeled in the dynamic regime. The wind turbine model is created in an open-source software OpenSees (McKenna et al., 2000), accounting for soil-structure interaction (SSI). Fully constrained fixed nodes and partially constrained (only for rotation) slave nodes are used to model SSI. Displacement-based nonlinear non-prismatic distributed plasticity elements are used for the tower. The monopile is modelled as a beam on a Winkler foundation. The foundation is zero-length Q-z, t-z springs to capture pile tip and shaft action. Zero-length P-y springs oriented horizontally are also included in the modelling according to API 1987. Steel02 material, following Giuffre-Menegotto-Pinto(Marco Pinto, 1973), is used to capture the nonlinear material properties of the substructure and superstructure nodes.

A 0.5 m discretization is used between nodes for the fibre section model of OpenSees, with 1000 fibres along the circumference and four fibres along the radial direction, with three integration points per element. The OWT structure’s total damping force is contributed by the structural damping, hydrodynamic forces, and soil. Valamanesh and Myers, (2014) computed the aerodynamic damping high as up to 5% in the fore-aft direction for operational conditions and 0.6% for the park condition. Based on the first and third model natural frequencies, rayleigh damping is set to 3%[13,14] of the damping ratio. Newmark’s average acceleration is used for time integration with a stable timestep of 2 milliseconds. The system of nonlinear equations is solved using the Newton-Raphson algorithm. The wind turbine model’s detailed dimensions and material properties are given in Tables 1 and 2, respectively. The first four-time periods are 3.89 s, 0.727 s, 0.3 s, and 0.133 s, respectively.

Table 1.

Wind turbine model parameters.

SrNo	Parameter	Symbol	Rating	Unit
1	RNA Mass	m_rna	386.80	ton
2	Diameter of rotor	d_rot	126.00	m
3	Height of tower	h_Towr	77.60	m
4	External diameter at tower top	d_TowrT	3.87	m
5	External diameter at tower Bottom	d_TowrB	6.00	m
6	Wall Thickness at tower top	t_TowrT	19.00	mm
7	Wall Thickness at tower Bottom	t_TowrB	27.00	mm
8	Height of transition piece (above seabed)	h_Trap	30.00	m
9	External diameter of transition piece (Uniform)	d_Trap	6.00	m
10	Wall Thickness of transition piece (Uniform)	t_Trap	60.00	mm
11	Embedded length of monopile (below the seabed)	h_Monp	30.00	m
12	External diameter of monopile (Uniform)	d_Monp	6.00	m
13	Wall Thickness of monopile (Uniform)	t_Monp	60.00	mm
14	Depth of water	d_Water	20	m

Table 2.

Input parameter for material modelling.

Sr No	Parameter	Symbol	Rating	Unit
1	Unit weight of steel	γ _steel	78.60	kN/m³
2	Young’s modulus of steel	E_steel	210.00	GPa
3	Shear modulus of steel	G_steel	80.80	GPa
4	Poisson’s ratio of steel	ν _steel	0.3	—
5	Strain hardening ratio	b_steel	1	%
6	Unit weight of soil	γ _soil	10	mm
7	Shear modulus of soil	G_soil	250	kg/m3
8	Internal friction angle	Φ	35	^o

Analysis setup

The modal analysis is performed to find the vibration modes used to determine the Rayleigh damping coefficients and to validate the model. Simultaneously, the nonlinear dynamic analysis is performed to produce IDA curves (Vamvatsikos and Allin Cornell, 2002). The peak ground acceleration is used to define the ground motion level as a scalar Intensity Measure (IM). The increment of 0.1 is used to scale the ground motions. The dynamic instability is considered as a collapsed state (Vamvatsikos and Allin Cornell, 2002). The damage-based assessment is assumed as limit-state is exceeded if the Damage Measure (DM) is greater than or equal to the capacity. For this study, the performance of the OWT structure is checked for Serviceability Limit State (SLS). For the SLS, the monopile head rotation at the mud level is considered as a demand. The allowable rotation of ±0.50 is considered as capacity. This criterion is adopted from the guideline given in DNV-OS-J10 (Veritas Det Norske, 2014). Though, there are no explicit guidelines given for the rotation of the tower top. However, in the literature, ±0.50 tower top rotation is assumed to be the capacity for which the turbine is switched off(Ali et al., 2020; Bisoi and Haldar, 2014; De Risi et al., 2018). The Fragility curves are developed for the probability of the structure’s failure in terms of IM. The structural failure or the damage state (Y) is defined when demand (D) reaches the capacity (C). The fragility function is expressed as the lognormal cumulative distribution function (equation (5)) (Baker, 2015).

P [DS | IM = d] = Φ [\frac{ln (d / θ)}{β}]

(5)

where

P[DS|IM = d]: The probability of structural failure

Φ(): The standard normal cumulative distribution function;

θ: The median of the fragility function

β: The standard deviation

The θ and β are assessed for ln(IM), which are obtained from IDA curves.

Results and discussion

Figure 5 shows the IDA and fragility curves plotted for offset distance of parallel array from the fault for the case of sub-shear rupture. The IDA curves are plotted with IM as PGA versus normalized DM. The values are normalized with the SLS capacity and represented here with the black dotted line. The first two columns of figures are for the SLS associated with the pile top rotation, whereas the latter two are for tower top rotation. The first and third column is plotted for the FP components, while the second and fourth column is for FN components. Since the ground motions are applied in the direction of the fore-aft direction of the wind turbine structure, the parallel and normal component also indicates the orientation of the wind turbine. The top four rows are IDA curves for parallel array location at Y= 1 km, 2 km, 5 km, and 10 km, respectively, where the bottommost row indicates the related fragility curves. To develop these curves, the structural response is assessed at all seven stations on each parallel array for X = −3 km to +3 km (Figure 1).

Figure 5.

Fault-Parallel (FP) and Fault-Normal (FN) component for the sub-shear scenarios at all FP arrays.

From Figure 5(q)-(t), it can be observed that the turbine structure is more sensitive to the ground motion at a 10 km parallel array for the considered earthquake scenario. The FP component also indicates the fore-aft axis parallel to a fault and thereby orientation of OWT. The fragility curve for the parallel component at the 10 km array (Figure 5q) attained the 50% and 100% probability of exceedance for the IM of 0.38 g and 0.70 g, respectively, whereas, for normal components (Figure 5r), it is 0.48 g and 0.9 g, which indicates that orienting the OWT-facing fault will be more advantageous. For the FP component OWT at 1 km away from the fault is least vulnerable for SLS of pile top rotation, while for the FN component OWT at 5 km showed a lesser response. The median values of least vulnerable cases in Figure 5(q & r) for parallel and normal components have shifted by 60% and 40%, with respect to the most vulnerable case of 10 km. Figure 5(s & t) shows that for all the parallel array locations, both 50% and 100% probability failure of tower top rotation has reached a smaller value of IM than the pile top rotation. The median value of IM for the 10 km array is 0.045 g for both the components, while for the least vulnerable case of the 1 km array, it is 0.17 g and 0.09 g for parallel and normal components, respectively.

Figure 6 illustrates the influence of the sub-shear earthquake on FN arrays of OWT at strike distances of 0 km, 7 km, 15 km, and 22 km from the epicentre. From Figure 6(q), it can be observed that the OWT on the normal array at X = 0 km and 22 km has reached the 100% probability of failure at the 1.0 g of IM, whereas, for less than 70% probability of exceedance, OWT at fault tip (X = 15 km) arrays are more vulnerable with the median value of 0.45 g. The OWT on the X = 7 km showed the least vulnerability. For the normal component of the ground motion in Figure 6(r), it is found at 1.2 g value of IM, OWT except at X = 0 km has reached 100% probability of failure. For this case, the OWT at 15 km array with the median value of 0.47 g was observed as crucial. For the normal component, the fragility curve at X = 0 km has reached the maximum 80% probability for considered maximum IM of 1.5g. In the case of the SLS of the tower, top rotation X = 22 km and X = 0 km are most crucial to the FP and normal components, respectively. For both, the component of ground motion OWT at X = 7 km has a median value of IE of 0.09 g as the least vulnerable condition.

Figure 6.

Fault-Parallel (P) and Fault-Normal (FN) component for the sub-shear scenarios at all FN arrays.

Figure 7 shows the plot of the IDA and fragility curves for the performance of the OWT structure on the FP array for the supershear earthquake scenario. Figure 7(q) all fragility curves of SLS of pile top ration and FP component reached the 100% probability of exceedance between the IM value of 0.27g and 0.65 g, contrary to sub-shear here OWT at Y = 1 km found most vulnerable with the median value of 0.23 g. Further, it can be observed that a slight difference in the IM value at 0%, 50%, and 100% probability of exceedance indicates the lesser standard deviation. The fragility curve for the 5 km parallel array has a negligible probability of exceedance, with the median value shifted to the right by more than 100% with respect to the median value of the most crucial case of Y = 1 km. From this, it can be said that a supershear earthquake has accumulated damaging energy. For the normal component of ground motion in Figure 7(r), the Y = 10 km fragility curve has a high probability of failure with the median value of 0.48g and reached 100% probability at IM of 0.85 g. The median value of 0.58 g for the fragility curve of Y =1 km and Y = 2 km has coincided, though only for the Y =1 km curve has reached the100% probability of exceedance for the considered maximum IM value of 1.2 g. Figure 7(s) for the parallel component of the ground motion has strongly excited the tower top of the OWT more at the array Y = 5 km and 10 km, while the tower top has low sensitivity at Y = 1 & 2 km. The experiment conducted by (Mello et al., 2016) showed the FP component of velocity field dominant in the case of the supershear earthquakes. Hence more severe damage was observed for the parallel component of ground motion. For FN ground motion components with lesser damaging energy typically showed more sensitivity to the array far from the fault.

Figure 7.

Fault-Parallel (FP) and Fault-Normal (FN) component for the supershear scenarios at all FP arrays.

The effect of supershear earthquake for FN arrays is as follows. The performance of the OWTs is evaluated for four arrays at a strike distance of 0 km, 7 km, 15 km, and 22 km from the epicentre (Figure 1). Figure 8(q) shows the probability of exceedance of the pile top rotation, wherein it can be noted that the OWT on the FN array near the epicentre is more susceptible with the median value of IM 0.35 g. The reason can be understood in terms of the secondary trailing sub-Rayleigh rupture phenomena of the supershear (Mello et al., 2016). As the rupture propagates up to X = 15 km, the critical FP velocity wavefront must be diminishing by 22 km. Hence least response of OWT was observed on the normal array at X = 22 km with the median value of IM equal to 0.53 g. Figure 8(r) shows that the ground motion’s normal component has excited more to the OWT at X = 7 km and 15 km with the median value of 0.45g. The OWT at the X = 0 km showed the minor response to the ground motion’s FN component with the median value of IM 0.57 g. The FP component of the ground motion at X = 22 km becomes the most crucial for tower top rotation (Figure 8(s)), whereas, at X = 15 km, OWT is the least sensitive.

Figure 8.

Fault-Parallel (FP) and Fault-Normal (FN) component for the supershear scenarios at all FN arrays.

Figure 9 plotted to compare the OWT’s response near the FP array. From Figure 9(i) of the SLS of pile top, it can be clearly understood that the supershear earthquake is more crucial for the FP component of ground motion. The median value of the sub-shear shifts to the right by 170% with respect to the median value associated with the supershear earthquake. As mentioned in the literature, the velocity predominantly results in the FP direction for a supershear earthquake. For the FN component, both fragility curves are coinciding. Even for the tower top rotation, a similar observation can be made for the parallel component of the ground motion. The OWT is more sensitive to the supershear earthquake ground motion for the FN component of ground motion.

Figure 9.

Fault-Parallel (FP) and Fault-normal (FN) component for the sub-shear and supershear earthquake scenarios for parallel array near to the fault.

Figure 10 compares the performance OWT for the sub shear and super shear earthquake for the FN arrangement of the OWT structure. InFigure 10(i), for the FP component of ground motion, the median value of sub shear has shifted to the right by 47% with respect to the median value of 0.34g for the super shear earthquake. This shift is much lesser than the previous case (Figure 9(i)), indicating that influence of the super shear diminishing with the distance from the fault. Here for the FN component of the ground motion, the fragility curves coincide around the median value. For higher probability, the super shear case becomes more vulnerable. For SLS of the tower top rotation, both the components of the subshear earthquake ground motion are more vulnerable than the super shear case Figure 10(m & l).

Figure 10.

Fault-Parallel (FP) and Fault-Normal (FN) component for the sub-shear and supershear earthquake scenarios for normal array near to the epicentre.

Conclusion

This work presents the influence of sub shear and super shear earthquakes on the micrositing of the offshore wind turbine. The subshear and supershear scenario earthquakes are simulated using SPECFEM3D software by varying the background shear stresses. To determine the influence on micrositing of OWT, the FP and FN arrays are considered. For each scenario, the OWT performance is evaluated for FP and normal components, indicating OWT orientation. The incremental dynamic analysis is performed using the OpenSees package, and fragility curves are plotted for serviceability limit state associated pile and tower top rotation at mudline and nacelle level, respectively. FN and FP array influence is presented; OWT performance is also compared for supershear and subshear earthquakes. The following conclusions are made.

For the subshear earthquakes with OWT on the FP array, the probability of exceedance for all considered SLS structures far from the fault are more vulnerable than the structure close to the fault. For the FP array, the OWT pile top rotation at the mudline is found more sensitive at the fault tip. Whereas the tower top rotation OWT is more sensitive far from the epicentre for FP-ground motion, inversely, the FN component of ground motion near the epicentre is more vulnerable. For sure, SLS associated with pile top rotation is more crucial than the tower top rotation. Hence said that vulnerability of OWT increases with distance from both the fault and epicentre. Further, it is found that orienting the OWT normal to the fault has lightly more advantageous for sub-shear earthquakes.

OWT in the vicinity of the super shear rupture behaved opposite to that of subshear rupture. For super shear OWT near the fault and epicentre showed high sensitivity. Hence the wind turbine structure sitting near the fault and epicentre are more vulnerable. For both FP and normal arrays, orienting the OWT parallel to the fault (fore-aft axis parallel to the fault line) would be more vulnerable. Hence orienting the OWT parallel to fault can lead to severe damage during the earthquake event. Further, it is noted that the standard deviation is either very small or high for the super shear type of earthquake because of accumulated damaging energy.

When compared to the performance of OWT for subshear and supershear earthquakes near the earthquake source, the OWT fault is highly sensitive to the super shear; however, the effect gets diminishing with distance for the earthquake source.

It is essential to highlight that, in this numerical model, inertial eccentricities of RNA, the effect of local buckling, the ultimate limit state associated with the material failure, and the tower imperfections are ignored, considering these aspects may lead to further structural failure. Further, the results are presented for the numerically simulated single scenario of the subshear and supershear earthquakes; a more detailed investigation is required with real and more earthquakes data sets.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

Funding from the Ministry of Earth Sciences, India through grant MoES/P.O. (Seismo)/1(304)/2016 is acknowledged.

ORCID iD

Vasudeo Chaudhari

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