2.3.1 Kaimal Spectrum

Some relevant details of Kaimal spectrum connected to foundation design are given in this section:

1. The power spectrum of turbulence can be modified by the landscape. If the inhomogeneity of the surface is high, the turbulence intensity increases. Another important aspect is whether the stratification is stable, unstable, or neutral. Neutral conditions rarely occur, but near‐neutral conditions are typical for medium and high wind speeds and are necessary for fatigue damage calculation.
2. The theoretical Kaimal spectrum for a fixed reference point in space in neutral stratification of the atmosphere S_uu(f ) as suggested by DNV can be written as:
   2.3

   where L_k is the integral length scale (formula available in the DNV code), f is frequency, is the mean wind speed (from site measurements), and σ_U is the standard deviation of wind speed. These can be estimated from measurements or calculated using Eq. ( 2.2), and turbulence intensity values may be obtained from standards IEC 61400‐1 and IEC 61400‐3.

Based on the DNV code, L_k = 5.67z for z < 60m and, L_k = 340.2m for z ≥ 60m where z denotes the height above sea level.

Figure 2.8 shows a comprehensive wind spectrum following van der Hoven where both long‐term variations of wind speed and turbulence effects are plotted. van der Hoven observed a significant four‐day synoptic peak and in some cases a small diurnal peak in the spectrum of the horizontal wind speed. The Kaimal spectrum describes wind turbulence on a short time scale (shown by a dotted line in Figure 2.8). This represents only the high‐frequency end of the spectrum, omitting the diurnal and synoptic peaks. Therefore, even though the Kaimal spectrum can be calculated for arbitrarily low frequency, its validity is limited to the high‐frequency variations. The lowest frequency that is typically considered corresponds to the time interval of 10 minutes, because the mean is taken over 10 minutes and therefore (T = 600 [s] → f = 1/600[Hz] ≈ 0.0017[Hz]).

A small local gust (say of 20 m diameter) passing through the rotor has little or no effect on distant parts of the rotor area. Referring to Figure 2.9, the wind speeds of points A and B are closely related, and they show a high coherence, while a distant point, such as C in the figure, has a low coherence with either A or B. In other words, low‐frequency variations affect a larger area of the rotor than high‐frequency variations. It should also be noted that through their rotary motion the blades experience a different spectrum from the Kaimal spectrum for a point in space. The blade will pass through any given eddy once in every revolution. In Figure 2.9, Blade I, for example, passes through Eddy 1 and Eddy 2 once in each revolution. Therefore, when rotational sampling is considered, that is, the wind speed ‘seen’ by the rotating blade is sampled, the PSD will show peaks at the rotational frequency f_1P and at higher harmonics . This effect is more important for blade load analysis; usually, only higher harmonics are transferred to the hub, as typically all blades pass through the same eddies.

Other available design wind spectra are Davenport (1961), Simiu and Leigh (1984), and Ochi and Shin (1988). For example, Ochi and Shin (1988) empirically derived a spectrum describing the wind over a sea based on offshore observations.

2.4.1 Method to Estimate Fetch

A method to estimate the fetch is to take the average of the distances to leeward shores (e.g. F_S, F_SSW, F_SW, etc.), adding weights to the distances based on the significance of the direction. For example, in Figure 2.10, the prevailing wind is blowing from south‐southwest (SSW) and southwest (SW); therefore, the weights of the distances F_SSW, F_SW will be the highest in the weighted average of the distances F_i.

2.4.2 Sea Characteristics for Walney Site

Figure 2.11 shows the significant wave height (Figure 2.11a) and the peak wave period (Figure 2.11b), as functions of the mean wind speed for Walney 1 wind farm location. Curves (1)–(5) represent the JONSWAP spectrum for increasing mean wind speed and for different fetch. On the other hand, curve (6) shows the Pierson‐Moskowitz spectrum. Curves (1)–(5) in Figure 2.12a show the JONSWAP spectrum for increasing mean wind speeds keeping the fetch constant at 60[km], while curves (1)–(5) in Figure 2.12b presents the JONSWAP spectrum for increasing fetch, keeping the mean wind speed constant at 10 [m s⁻¹].

2.4.3 Walney 1 Wind Farm Example

Figure 2.13 shows the main frequencies from a three‐bladed Siemens 3.6 MW wind turbine having a rotational operating interval of 5–13 RPM (lowest is 5RPM i.e. 0.083 Hz and rated is 13RPM i.e. 0.216 Hz). The site is characterised by a mean wind speed of 9 m s⁻¹ and has a peak wave frequency of 0.197 Hz. This example considers Kaimal spectrum for wind and JONSWAP spectra for wave. Details of the calculations are provided later in the chapter and in Chapter 6.

2.6.1 Load Cases for Foundation Design

IEC codes (IEC 2005; IEC 2009a; IEC 2009b) as well as the DNV code (DNV 2014) describe hundreds of load cases that need to be analysed to ensure the safe operation of wind turbines throughout their lifetime of 20–30 years. However, in terms of foundation design, not all these cases are significant or relevant. The main design requirements for foundation design as will be explained in Chapter 3are ULS (Ultimate Limit State), FLS (Fatigue Limit State), and SLS (Serviceability Limit State). Five load cases important for simplified foundation design are identified and described in Table 2.1.

All design load cases are built as a combination of four wind and four sea states. The wind conditions are:

1. (U-1) Normal turbulence scenario. The mean wind speed is the rated wind speed (U_R) where the highest thrust force (Th) is expected, and the wind turbulence is modelled by the Normal Turbulence Model (NTM). The NTM standard deviation of wind speed is defined in IEC (2005).
2. (U-2) Extreme turbulence scenario. The mean wind speed is the rated wind speed (U_R), and the wind turbulence is very high. The extreme turbulence model (ETM) is used. The ETM standard deviation of wind speed is defined in IEC (2005).
3. (U-3) Extreme gust at rated wind speed scenario. The mean wind speed is the rated wind speed (U_R) and the 50‐year extreme operating gust (EOG) calculated at U_R hits the rotor. The EOG is a sudden change in the wind speed and is assumed to be so fast that the pitch control of the wind turbine has no time to alleviate the loading. This assumption is very conservative and is suggested to be used for simplified foundation design. The EOG speed is defined in IEC (2005).
4. (U-4) Extreme gust at cut‐out scenario. The mean wind speed is slightly below the cut‐out wind speed of the turbine (U_out) and the 50‐year EOG hits the rotor. Due to the sudden change in wind speed the turbine cannot shut down. Note that the EOG speed calculated at the cut‐out wind speed is different from that evaluated at the rated wind speed (IEC 2005).

The wave conditions are:

1. (W-1) One‐year extreme sea state (ESS). A wave with height equal to the 1‐year significant wave height H_{S, 1} acts on the substructure.
2. (W-2) One‐year extreme wave height (EWH). A wave with height equal to the 1‐year maximum wave height H_{m, 1} acts on the substructure.
3. (W-3) 50‐year ESS. A wave with height equal to the 50‐year significant wave height H_{S, 50} acts on the substructure.
4. (W-4) 50‐year EWH. A wave with height equal to the 50‐year maximum wave height H_{m, 50} acts on the substructure.

The one‐year ESS and EWH are used as a conservative overestimation of the normal wave height (NWH) prescribed in IEC (2009a). It is important to note here in relation to the ESS that the significant wave height and the maximum wave height have different meanings. The significant wave height H_S is the average of the highest one‐third of all waves in the three‐hour sea state, while the maximum wave height H_m is the single highest wave in the same three‐hour sea state.)

According to the relevant standards (IEC 2005; IEC 2009a; DNV 2014), in the probability envelope of environmental states the most severe states with a 50‐year return period has to be considered, and not 50‐year return conditions for wind and wave unconditionally (separately). Indeed, extreme waves and high wind speeds tend to occur at the same time; however, the highest load due to wind is not expected when the highest wind speeds occur. This is partly because the pitch control alleviates the loading above the rated wind speed, but also because turbines shut down at high wind speeds for safety reasons. Idle or shut‐down turbines, as well as turbines operating close to the cut‐out wind speed have a significantly reduced thrust force acting on them compared to the thrust force at the rated wind speed due to the reduced thrust coefficient, as shown in Figures 2.17 and 2.18.

The highest wind load is expected to be caused by scenario U‐3 and the highest wave load is due to scenario W‐4. In practice, the 50‐year extreme wind load and the 50‐year extreme wave load have a negligible probability to occur at the same time, and the DNV (2014) code also doesn't require these extreme load cases to be evaluated together. The designer has to find the most severe event with a 50‐year return period based on the joint probability of wind and wave loading. Therefore, for the ULS analysis (for details see Chapter 3), two combinations are suggested by Arany et al. (2017):

1. The ETM wind load at rated wind speed combined with the 50‐year EWH – the combination of wind scenario U‐2 and wave scenario W‐4. This will provide higher loads in deeper water with higher waves.
2. The 50‐year EOG wind load combined with the one‐year maximum wave height. This will provide higher loads in shallow water in sheltered locations where wind load dominates.

These scenarios are somewhat more conservative than those required by standards, and can be adopted for simplified analysis. From the point of view of SLS and FLS, the single largest loading on the foundation is not representative, because the structure is expected to experience this level of loading only once throughout the lifetime.

The load cases in Table 2.1 are considered to be representative of typical foundation loads in a conservative manner and may serve as the basis for conceptual design of foundations. However, detailed analysis for design optimization and the final design may require addressing other load cases as well. These analyses require detailed data about the site (wind, wave, current, geological, geotechnical, bathymetry data, etc.) and also the turbine (blade profiles, twist and chord distributions, lift and drag coefficient distributions, control parameters and algorithms, drive train characteristics, generator characteristics, tower geometry, etc.).

2.6.2 Wind Load

The thrust force (Th) on a wind turbine rotor due to wind can be estimated in a simplified manner as

2.6

where ρ_a is the density of air, A_R is the rotor swept area, C_T is the thrust coefficient, and U is the wind speed. The wind speed can range from cut‐in to cut‐out, with the appropriate thrust coefficient. The thrust coefficient can be approximated in the operational range of the turbine using three different sections (as shown in Figures 2.16 and 2.17):

1. Between cut‐in (U_in) and rated wind speed (U_R), the method of Frohboese and Schmuck (2010) is recommended following Arany et al. (2017)
   2.7
2. After rated wind speed, when the pitch control is active, the power is assumed to be kept constant, and thus the thrust coefficient is expressed as
   2.8
3. The thrust coefficient is assumed not to exceed 1; therefore, in the low‐wind‐speed regime where the formula of Frohboese and Schmuck (2010) overestimates the thrust coefficient, the value is capped at 1.

When the wind speed is changing slowly, the thrust force follows the mean thrust curve as the pitch control follows the change in wind speed. However, when a sudden gust hits the rotor, the pitch control's time constant might be too high to follow the sudden change. If this is the case, then the thrust coefficient is ‘locked’ at its previous value while the wind speed in Eq. (2.11) changes to the increased wind speed due to the gust.

Assuming a quasi‐static load calculation method, the wind speed can be divided into two parts, a mean wind speed , and a turbulent wind speed u component. For each load case, the mean wind speed and the turbulent wind speed component u are defined separately, and the total wind speed is expressed as

2.9

Using this assumption, the wind load can be separated into a mean thrust force (or static force) and a turbulent thrust force (or dynamic force).

2.10

In this equation, the thrust coefficient C_T is calculated as shown in Eq. ( 2.11).

2.6.2.1 Comparisons with Measured Data

Figure 2.17 plots the measured mean mudline‐bending moment for a Vestas V80 wind turbine at the Horns Rev offshore wind farm obtained from Hald et al. (2009) and compares it with the approximation based on Eq. (2.10). This is based on the measured thrust force acting at the hub level, and the corresponding thrust coefficient is shown in Figure 2.18.

The maximum thrust force occurs around the rated wind speed (or, more specifically, before the pitch control activates). In reality, the pitch control activates somewhat below the rated wind speed (as can be seen in Figures 2.17 and 2.18). This is to ensure a smooth transition between the section where the power is proportional to the cube of the wind speed and the pitch controlled region where the power is kept constant to avoid repeated switching around the rated wind speed (Burton et al. 2001).

Therefore, in the measured scenario the maximum of the thrust force (and thus the bending moment) occurs at around 11[m s⁻¹], as opposed to the theoretical approximation, in which the maximum is at U_R = 14[m/s]. Taking the maximum to be at U_R is, however, conservative due to the formula used for the approximation. If the value of 11[m s⁻¹] is substituted into the formula in Eq. ( 2.10), one still arrives at a conservative approximation for the mean thrust force, and therefore this value (at which pitch control activates) may also be used. It should be noted, however, that typically the nature of the pitch control mechanism and the thrust coefficient curve of the turbine are not available in the early design phases. Consequently, the use of U_R is suggested, which is typically available and produces a conservative approximation.

Wind scenario U‐1: Normal Turbulence (NTM) at Rated Wind Speed (U_R)

This scenario is typical for normal operation of the turbine. The standard deviation of wind speed in normal turbulence following IEC (2005) can be written as

2.11

where I_ref is the reference turbulence intensity (expected value at U = 15 [m/s]).

For the calculation of the maximum turbulent wind speed component u_NTM, the time constant of the pitch control is assumed to be the same as the time period of the rotation of the rotor. In other words, it is assumed that the pitch control can follow changes in the wind speed that occur at a lower frequency than the rotational speed of the turbine. Then u_NTM may be determined by calculating the contribution of variations in the wind speed with a higher frequency than f_{1P, max} to the total standard deviation of wind speed. From the Kaimal spectrum used for the wind turbulence process, this can be calculated using Eq. (2.16).

2.12

The turbulent wind speed encountered in normal operation in normal turbulence conditions is found by assuming normal distribution of the turbulent wind speed component and taking the 90% confidence level value. This is substituted into the quasi‐static equation used in Eq. (2.14). Equation (2.15) shows expressions for the corresponding mudline moment.

2.13

2.14

2.15

Wind scenario U‐2: Extreme Turbulence (ETM) at Rated Wind Speed ()

The ETM is used to calculate the standard deviation of wind speed at the rated wind speed, and from that the maximum wind load under normal operation in extreme turbulence conditions. The standard deviation of wind speed in ETM is given in IEC (2005) as

2.16

where U_avg is the long‐term average wind speed at the site. The maximum turbulent wind speed component u_ETM is determined similarly to the previous case.

2.17

The turbulent wind speed encountered in normal operation in extreme turbulence conditions, which is used for cyclic/dynamic load analysis, is found by assuming normal distribution of the turbulent wind speed component. As opposed to the normal turbulence situations, the 95% confidence level value is taken. This is substituted into the quasi‐static equation used in Eq. ( 2.14). Equation (2.20) shows the expression for mudline moments.

2.18

2.19

2.20

Wind Scenario U‐3: Extreme Operating Gust (EOG) at Rated Wind Speed ()

The maximum force is assumed to occur when the maximum mean thrust force acts and the 50‐year EOG hits the rotor. Due to this sudden gust, the wind speed is assumed to change so fast that the pitch control doesn't have time to adjust the blade pitch angles. This assumption is very conservative as the pitch control in reality has a time constant that would allow for some adjustment of the blade pitch.

The methodology for the calculation of the magnitude of the 50‐year extreme gust is described in DNV (2014). This methodology builds on the long‐term distribution of 10‐minutes mean wind speeds at the site, which is typically represented by a Weibull distribution. The cumulative distribution function (CDF) can be written in the following form:

2.21

where K and s are the Weibull scale and shape parameters, respectively. From this the CDF of 1‐year wind speeds can be obtained using

2.22

where the number 52596 represents the number of 10‐minutes intervals in a year (52596 = 365.25[days/year]·24[hours/day]·6[10 min intervals/hour]).

From this, the 50‐year extreme wind speed, which is typically used in wind turbine design for extreme wind conditions, can be determined by the wind speed at which the CDF is 0.98 (i.e. 1‐year 10‐minutes mean wind speed that has 2% probability).

2.23

The extreme gust speed is then calculated at the rated wind speed from

2.24

where D is the rotor diameter, Λ₁ = L_k/8 with L_k being the integral length scale, σ_{U, c} = 0.11U_{10, 1 − year} is the characteristic standard deviation of wind speed, U_{10, 1 − year} = 0.8U_{10, 50 − year}. Using this, the total wind load is estimated as

2.25

and using the water depth S and the hub height above sea level z_hub, the mudline bending moment (without the load factor γ_L) is given as

2.26

Wind Scenario U‐4: Extreme Operating Gust (EOG) at the Cut‐Out Wind Speed (U_out)

This load case is examined here because intuitively it may seem natural to expect the highest loads when the turbine is operating at the highest operational wind speed, however, this is not the case. Wind load caused by the EOG at the highest operational wind speed (the cut‐out wind speed U_out) is calculated taking into consideration that the thrust coefficient expression of Frohboese and Schmuck (2010) is no longer valid. The thrust coefficient is determined from the assumption that the pitch control keeps the power constant. This means that the thrust force is inversely proportional to the wind speed above rated wind speed U_R and the thrust coefficient is inversely proportional to the cube of the wind speed.

2.27

The EOG speed at cut‐out wind speed is determined as given (note that this differs for different mean wind speeds, i.e. the value is not the same at U_R and at U_out). The thrust force and moment are then given by:

2.28

2.29

2.6.2.2 Spectral Density of Mudline Bending Moment

The spectral density of the turbulent thrust force on the rotor S_{FF, wind}(f ) can be written as:

2.30

where D is the diameter of the rotor, S_uu(f ) is the Kaimal spectrum, is the normalised Kaimal spectrum, ρ_a is the density of air, C_T is the thrust coefficient, I is the turbulence intensity, and σ_U is the standard deviation of wind speed. The fore‐aft bending moment at the mudline is simply given by:

2.31

where H is the hub height above mean sea level and S is the mean sea depth (see Figure 2.6).

Similarly, the load can be reduced to any other cross section, such as the transition piece (TP). The mudline moment spectrum associated with wind speed fluctuations can be expressed as:

2.32

2.6.3 Wave Load

In simplified load calculation methodologies, to determine the wave loading, simple linear waves are assumed. Higher‐order theories like Stokes waves or Dean's stream function theory would provide better estimates, especially in shallow waters. However, the linear theory allows for simpler load calculation and its application is justified for foundation design loads.

A simplified approach to wave load estimation is Morison's (or MOJS) equation (Morison et al. 1950). In these equations, the diameter of the substructure is taken as D_S = D_P + 2t_TP + 2t_G[m] to account for the transition piece (TP) and the grout (t_G) thickness. The circular substructure area A_S is also calculated from this diameter. The methodology in this paper builds on linear (Airy) wave theory, which gives the surface elevation η, horizontal particle velocity w, and the horizontal particle acceleration as

2.33

2.34

2.35

where x is the horizontal coordinate in the along‐wind direction (x = 0 at the turbine, see Figure 2.19) and the wave number k is obtained from the dispersion relation

2.36

The force on a unit length strip of the substructure is the sum of the drag force F_D and the inertia force F_I:

2.37

where C_D is the drag coefficient, C_m is the inertia coefficient, and ρ_w is the density of seawater. The total horizontal force and bending moment at the mudline is then given by integration as

2.38

2.39

The peak load of the drag and inertia loads occur at different time instants, and therefore the maxima are evaluated separately. The maximum of the inertia load occurs at the time instant t = 0 when η = 0 and the maximum of the drag load occurs when t = T_S/4 and η = H_m/2. The maximum load is then obtained by carrying out the integrations:

2.40

2.41

2.42

2.43

2.44

2.45

2.46

2.47

In the simplified method for obtaining foundation loads, it can be conservatively assumed that the sum of the maxima of drag and inertia loads is the design wave load. This assumption is conservative, because the maxima of the drag load and inertia load occur at different time instants. All wave scenarios (W‐1)–(W‐4) are evaluated with the same procedure, using different values of wave height H and wave period T.

2.6.4 1P Loading

A wind turbine is subjected to cyclic loading with the rotational frequency, and the source of this load is mainly the rotor mass imbalance and aerodynamic imbalance (due to differences in the pitch of individual blades). The amplitude of this forcing depends on the extent of the imbalances, and typical values can be used based on the literature. A simple method is shown to estimate the fore‐aft bending moment at the mudline caused by the mass imbalance; however, the calculation of the effect of blade pitch misalignment requires more input information and more sophisticated methods. The mass imbalance can be modelled as an added lumped mass on the rotor at θ azimuthal angle from Blade I. and at R distance from the centre of the hub, as shown in Figure 2.20. Here the imbalance is assumed to be on Blade I (θ = 0).

2.52

where I_m is the mass imbalance with units of [kg·m], m is a lumped mass, and R is the radial distance from the centre of the hub along Blade I. The centrifugal force at any time can be calculated from the centrifugal acceleration a = RΩ² with Ω being the angular frequency and f = Ω/(2π) the frequency of rotation. The lever arm of the centrifugal force F_cf is called the rotor overhang b (see Figure 2.20), with which the bending moment is expressed:

2.53

It is to be noted here that the centrifugal force also produces torsion in the tower (around the x‐axis), as well as moments in side‐to‐side direction (around the z‐axis), as shown in Figure 2.20. The bending moment in the side−side direction caused by the centrifugal force is much higher than the fore−aft moment because the arm of the force is H + MSL instead of b. The effect of the gravity force acting on the mass imbalance can be considered negligible.

2.6.5 Blade Passage Loads (2P/3P)

The wind produces drag force on the tower, which can be considered constant at a given mean wind speed, ignoring buffeting and vortex shedding on the tower and also without the effect of the rotating. When a blade passes in front of the tower, it disturbs the flow downwind and decreases the load on the tower. The frequency of this load loss is three times the rotational frequency of the turbine 3P (2P in case of two‐bladed designs). In a simplified method, the magnitude is estimated by a simple geometric consideration: the upper part of the face area of the tower is partly covered by the blade when the blade is in a downward pointing position (ϕ = π). The drag force on the covered part of the tower is taken to be zero and the blade causes a load loss on the tower. When the blade is in the downward direction, it covers the tower from z = H − L to z = H. The total moment of drag force on this upper section without the effect of blade passage:

2.57

where H is the hub height from mean sea level, L is the length of the blades, ρ_a is the density of air, C_D is the drag coefficient, D(z) is the diameter of the tower at z (assuming the diameter linearly decreases between the bottom and top diameters), z is the vertical coordinate (zero at mean sea level), S is the mean sea depth, and U(z) is the power law velocity profile using the exponential wind profile with β = 1/7 ≈ 0.143. If the ratio of the face area of the blade and the area of the top part of the tower (see Figure 2.16) is R_A, then the 3P moment amplitude can be written:

2.58

2.6.6 Vertical (Deadweight) Load

The total vertical load on the foundation is calculated as

2.60

where m is the total mass of the structure

2.61

where m_RNA is the total mass of the rotor‐nacelle assembly, m_T = ρ_TD_Tπt_TL_T is the total weight of the tower, m_TP = ρ_TP(D_P + 2t_G + t_TP)πt_TPL_TP is the mass of the transition piece, and m_P = ρ_PD_Pπt_P(L_P + L_S) is the mass of the pile.

2.7.1 Application of Estimations of 1P Loading

To determine the 1P moment spectrum, one needs a typical value of the mass imbalance of the rotor. Some values are available for a somewhat smaller wind turbine studied in the literature. For the 2 MW Vestas V80 turbine, mass imbalance values of about 350–500 [kgm] were applied in these studies. The imbalance value is estimated for the 3.6 MW Siemens wind turbine by assuming that the imbalance is proportional to the mass of the rotor and also to the diameter of the turbine. The mass ratio and the diameter ratio of the rotors are calculated and the imbalance is scaled up by both ratios.

The mass of the rotor of the Vestas turbine is 37.5 tonnes, while that of the Siemens turbine is 95 tonnes. The diameter of the rotor of Vestas turbine is 80 m and that of the Siemens is 107 m. Therefore, the estimated imbalance value for the Siemens SWT‐107‐3.6 turbine is estimated as follows:

2.62

The original imbalance value of V80 is a value typical for an average operational wind turbine. As an upper bound estimate, one may consider I_m = 2000 [kgm]. The distance between the axis of the tower and the centre of the hub (i.e. the rotor overhang) is estimated as b = 4 [m]. (For clarity, see Figure 2.20 for rotor overhang.) This way the maximum of the fore−aft bending moment caused by the imbalance can be written as:

2.63

The maximum bending moment occurs at the highest rotational speed of Ω = 13 [rpm], that is f = 0.2167 [Hz], its value is M_1P = 0.015 [MNm].

Table 2.2 shows an example for this case study based on Arany et al. (2015a) and the readers are referred to this publication for further details.

Mean wind speed at hub height	Rotational speed Ω [rpm]	Fore−aft DAF [−]	1P fore−aft mudline bending moment M1P[MNm]/(with DAF)	Side‐to‐side DAF [−]	1P side‐to‐side mudline bending moment M1P, side − to − side[MNm]/(with DAF)
5	5.8	1.09	0.002/(0.002)	1.09	0.077/(0.084)
9	9	1.25	0.007/(0.009)	1.25	0.187/(0.234)
15	13	1.71	0.015/(0.025)	1.72	0.389/(0.669)
20	13	1.71	0.015/(0.025)	1.72	0.389/(0.669)

The readers are also referred to Example 6.7 of Chapter 6and Arany et al. (2015a) for further details.

2.7.2 Calculation for 3P Loading

The 3P moment can be determined by estimating the total drag moment on the top part of the tower, which is covered by the downward‐pointing blade, and then reducing this moment by the ratio of the face area of the blade and the face area of the top part of the tower. The drag moment is estimated by the method presented in Section 2.3. The density of air is ρ_a = 1.225 [kg/m³], the drag coefficient of the tubular tower at high Reynolds number is C_D ≈ 0.5 [−], and the linearly decreasing diameter of the tower can be written as:

2.64

with the z coordinate running from mean sea level along the length of the tower, D_b and D_t are the bottom and top diameters of the tower, respectively. Using the exponential wind profile and the water depth S = 21.5 [m], the moment can be written as:

2.65

which gives M_drag ≈ 0.326[MNm] for . Both the area of the blade and the area of the top part of the tower are approximated as trapezoids, the areas are calculated as:

2.11

The magnitude of the load loss is then approximated as written in Eq. (2.45).

2.67

The drag load on the tower is calculated by integrating along the whole tower:

2.68

The 3P forces and moments are estimated in Table 2.3 for several values of the mean wind speed. Note that in the vicinity of 6.125 m s⁻¹ (∼6.7 rpm rotational speed), the DAF gets very high and the 3P moment is an order of magnitude higher than without DAF.

Wind speed	Total drag force on the tower [MN]	Total drag moment on the tower [MNm]	3P freq. [Hz]	DAF [−]	3P force F3P[MN]/(with DAF)	3P moment M3P[MNm]/(with DAF)
5	0.0019	0.176	0.29	3.77	0.001/(0.003)	0.069/(0.262)
9	0.0062	0.570	0.45	1.23	0.003/(0.004	0.225/(0.275)
15	0.0173	1.584	0.65	0.36	0.008/(0.003)	0.625/(0.225)
20	0.0308	2.816	0.65	0.36	0.014/(0.005)	1.111/(0.401)
6.125 (resonance)	0.0289	0.189	0.335	10	0.001/(0.013)	0.104/(1.042)

2.7.3 Typical Moment on a Monopile Foundation for Different‐Rated Power Turbines

Based on the method described in the chapter and developed in Arany et al. (2015a,b, 2017), Table 2.4 shows typical values of thrust due to the wind load acting at the hub level for five turbines ranging from 3.6 to 8 MW. The thrust load depends on the rotor diameter, wind speed, controlling mechanism, and turbulence at the site. The mean and maximum mudline bending moment on a monopile is also listed. Wave loads strongly depend on the pile diameter and the water depth and it is therefore difficult to provide a general value. Table 2.4 contains a relatively severe case of 30 m water depth and a maximum wave height of 12 m.

Typical values of wave loading ranges between 2 and 10 MN acting at about three‐fourths of the water depth above the mudline, which must be added to the wind thrust. Typical peak wave periods are around 10 seconds. The pattern of overturning moment on the monopile is schematically visualised in Figure 2.21. In the figure, a typical value of the peak period of wind turbulence is taken and can be obtained from wind spectrum data.

Note. It may be noted that only wind and wave moments are considered in the Figure 2.21. 1P and 3P moments are ignored, as they are about three orders of magnitude lower.

2.11.1 Seismic Hazard Analysis (SHA)

A detailed SSA can be divided into three parts: (i) Estimation of seismic hazard by carrying out deterministic seismic hazard analysis (DSHA) and probabilistic seismic hazard analysis (PSHA); (ii) evaluation of local site effects by carrying out nonlinear ground response analysis; and (iii) preparation of hazards maps and response spectra.

Two approaches, probabilistic (PSHA) and deterministic (DSHA), are commonly adopted for seismic hazard assessment. In DSHA, a particular earthquake scenario is assumed based on earthquake data and tectonic setup of the study area. The hazard is estimated on the basis of attenuation characteristics of the region. For a worst‐case scenario, DSHA is more useful. Hazard is evaluated considering the closest distance between the source and the site of interest as well as the maximum magnitude for the fault.

To evaluate seismic hazard deterministically for a particular site or region, all possible sources of seismic activity are identified and their potential for generating strong ground motion is evaluated. It is used widely for nuclear power plants, large dams, large bridges, hazardous waste containment facilities, and also as a ‘cap’ for PSHA. On the contrary, in probabilistic method (PSHA), the uncertainties in earthquake size, location, and time of occurrence are explicitly considered, see Figure 2.26 for the steps.

The procedure followed in carrying out the SHA is as follows:

1. Consider an area covering 300–500 km radius around point of interest as seismic study area.
2. Collect all the tectonic information such as location, magnitude, and depth of earthquakes occurred, and satellite imageries of the fault lines for the seismic study area.
3. All this information has to be merged to prepare a single map (seismotectonic map), which represents tectonic setting of the seismic study area.
4. Prepare an earthquake catalogue for the study region, which includes all recordings from pre‐instrumental and instrumental period. Try to collect data from all the possible sources. Check the catalogue for duplicity of events, clustering of events, and completeness.
5. Determine Gutenberg‐Richter seismicity parameters a and b for the estimation of rate of occurrence of different magnitudes of earthquake and return periods. For DSHA, this step can be avoided.
6. Identify the tectonic features likely to generate significant ground motions in the study area. Also assign maximum observed magnitude (Mobs) to each source.
7. Calculate the maximum magnitude potential (M_max) for all the seismogenic sources present in the study area. For PSHA, it is important to consider uncertainty in size of earthquake.
8. Consider a suitable grid on the area of interest for e.g. 0.2° × 0.2° for a country, 0.1° × 0.1° for a state, and 0.005° × 0.005° for a city.
9. Compute shortest distance of grid points to each seismogenic source. For PSHA, it is important to consider uncertainty in the location of earthquake.
10. Select a suitable ground motion prediction equation (GMPE), which accurately represents the tectonic setup of the study area. In case of nonavailability of regional GMPEs, GMPEs developed for other regions can also be used, provided their source and site characteristics are similar to the study area. For PSHA, it is necessary to handle epistemic uncertainty in the GMPEs. This can be handled by adopting logic tree approach.
11. For the computation of hazard at a grid point, compute ground motion parameters with respect to various seismogenic sources and identify the source causing maximum ground motion at the point of interest. For that grid point, consider the maximum magnitude potential of that seismogenic source as the controlling earthquake.
12. Site amplification factors can be estimated by carrying out linear, equivalent linear, or nonlinear ground response analysis.

2.11.2 Criteria for Selection of Earthquake Records

Ground motion records to be used in analysis should represent the potential earthquake hazards at the site i.e. consideration of magnitude, distance, site conditions, source mechanism, directivity, and other effects obtained from SSA. In this regard, the appendix of ISO 19901‐2 states that a minimum of four records should be used for analysis, and that each record should be selected according to the following criteria:

Given the magnitude and distance of events dominating extreme level earthquake (ELE) ground motions, the earthquake records for time history analysis can be selected from a catalogue of historical events. Each earthquake record consists of three sets of tri‐axial time histories representing two orthogonal horizontal components and one vertical component of motion. In selecting earthquake records, the tectonic setting (e.g. faulting style) and the site conditions (e.g. hardness of underlying rock) of the historical records should be matched with those of the structure's site.

Three approaches are often used, and all these methods have their advantages and disadvantages and are discussed later in this section through an example.

2.11.2.3 Method 3: Intelligent Scaling or Code Specified Spectrum Compatible Motion

Traditionally, seismic hazard at a site for design purposes has been represented by design spectra. Thus, all seismic design codes and guidelines require scaling of selected ground motion time histories so that they match or exceed the controlling design spectrum within a period range of interest. Figure 2.27 shows the response spectra of IS: 1893 (2002) for hard soil or rock together with a Chi‐Chi (Taiwan) earthquake motion and spectrally matched motion. Several methods of scaling time histories are available that involve rigorous mathematics.

Essentially, in all these methods, an input motion is selected from a strong motion database, and the motion is manipulated in such a way so as to obtain a motion that matches the target design spectra. The manipulation can be carried out in frequency‐domain where the time‐frequency content of the recorded ground motions is manipulated in order to obtain a good match. Mathematically, this can be expressed as follows, following Alexander et al. (2014): a process that can transform a known signal or input motion x(t) into a similar input motion y(t) that matches the spectrum. The additional aim is that transformed signal y(t) should maintain very similar nonstationary characteristics such as general envelope, time location of large pulses, and variation of frequency content with time. In other words, the aim signal y(t) should look, for all intents and purposes, like a real earthquake.

Figure 2.28 shows the response spectra for different types of earthquake that can also be used to estimate the inertia forces on the structure. For example, for a three‐second period wind turbine structure, the spectral acceleration will be function of the location and can be read off the ordinate (y‐axis).

2.11.3 Site Response Analysis (SRA)

Once the bedrock motion is obtained, the vertically propagating shear waves are convoluted through the soil depth using a SRA to obtain the site effects. Figure 2.29 shows a schematic diagram of the methodology. Various software exist in performing this particular function such as SHAKE 91, DEEPSOIL, DMOD, EERA, Cyclic 1D. For liquefiable deposits, Cyclic 1D can be used to perform the SRA, as it uses an advanced constitutive model for the liquefied soil developed by Parra (1996) and Yang (1999) in its analysis. Literature can be found on the use of various site response analysis programs, which capture various nonlinear aspects of the soil in Hashash et al. (2010).

2.11.4 Liquefaction

Apart from site response analysis, it is necessary to predict if the subsurface will liquefy. The part of the foundation in liquefiable soil needs to be considered as laterally unsupported. Therefore, the length of the tower will effectively increase leading to elongation of natural period. From the point of analysis, liquefaction may be assumed to progress along the depth of the soil layer in top‐down fashion. A modal analysis can be carried out to study the variation of depth of liquefaction (DL) with the first natural period of the soil‐pile system. The results are plotted in Figure 2.30, which is a graphical representation of normalised elongation of period for various depths of liquefaction. In Figure 2.30, DL represents depth of liquefaction, L is the embedded length of the pile, T is the time period, and T_initial is the initial time period of the structure. However, this is momentary, and as the earthquake stops, the ground resolidifies and most of the ground stiffness is regained. Three cases are considered in the study:

1. Post liquefaction, the American Petroleum Institute (API) prescribed soil spring stiffness is degraded 92% using a p‐multiplier as per Brandenberg (2005).
2. Zero initial stiffness and strength are provided to the p‐y spring for the liquefied soil as per RTRI (1999).
3. Hyperelastic p‐y spring for liquefiable soils (Lombardi et al. (2017).

As the eigenvalue analysis is linear, only the initial stiffness of the p‐y curves (reduced API, hyperelasticity, zero strength API) is used in the model to compute the natural frequencies of the soil‐pile system.

2.11.5 Analysis of the Foundation

Analysis of foundations is usually carried out using beams on nonlinear Winkler foundation approach as shown in Figure 2.31. Various details of modelling are discussed in Dash et al. (2010). Once the DL is estimated, it is important to use the Winkler or p‐y springs of appropriate shape as shown in the figure. The shape of non‐liquefied and liquefied p‐y curves are very different. The seismic forces, H_Pre (pre‐liquefaction) and H_Post (post‐liquefaction), depend on the time period of the whole structure and can be estimated based on the response spectra of the site.

The aim of this section is to further the discussion carried out in Section 1.1 of Chapter 1 on the good performance of a near‐shore wind farm. Calculations were carried out based on the available information of the ground profile and the turbine characteristics. In the absence of data, engineering judgements were used to carry out the analysis in order to draw broad conclusions. The focus of the investigation is the behaviour during the 2011 Tohoku earthquake seismic shaking and during the tsunami run‐up, discussed in the following examples.