17.1.1 Complexity of External Loading Conditions

OWTs are characterized by a unique set of dynamic loading conditions that is schematically depicted in Fig. 17.1. These include: (1) load produced by the turbulence in the wind, whose amplitude is function of the wind speed; (2) load caused by waves crashing against the substructure, whose magnitude depends on the height and period of waves; (3) load caused by mass and aerodynamic imbalances of the rotor, whose forcing frequency equals the rotational frequency of the rotor (referred to as 1P loading in the literature); (4) loads in the tower due to the vibrations caused by blade shadowing effect (referred to as 3P loading in the literature), which occurs as each blade passes through the shadow of the tower.

The loads imposed by wind and wave are random in both space and time, as a result these are better described statistically by using the Pierson–Moskowitz wave spectrum and Kaimal wind spectrum, as shown in Fig. 17.2. It is clear from the frequency content of the applied loads that the designer in order to avoid the resonance of the OWT has to select a design frequency that lies outside the ranges of forcing frequencies. Specifically, the Det Norske Veritas (DNV) code [1] recommends that the natural frequency of the wind turbine should be at least ±10% away from the main forcing frequencies introduced earlier. Depending on the design value of natural frequency, three design approaches are possible, namely, soft–soft (natural frequency <1P), soft–stiff (natural frequency between 1P and 3 P), and stiff–stiff (natural frequency >3P).

It is worth noting that the design procedure requires an accurate evaluation of the natural frequency, which is dependent on the support condition (i.e., the stiffness of the foundation) that in turn relies on the strength and stiffness of the surrounding soil. Furthermore, as the natural frequencies of OWTs are very close to the forcing frequencies, the dynamics pose multiple design challenges because of the tight tolerance of the target natural frequency, whereby the scale of the challenges will vary depending on turbine types and site characteristics. Typical values of vibration characteristics and site characteristics of operating wind turbines are listed in Table 17.1.

17.1.2 Design Challenges

There are two main aspects related to cyclic loading conditions, see Nikitas et al. [2], that have to be taken into account during design: (1) soil behavior due to nondynamic repeated loading, i.e., fatigue-type problem and this is mainly attributable to wind loading which has a very low frequency; (2) soil behavior due to dynamic loading which will cause dynamic amplification of the foundation response, i.e., the resonance-type problem. This is due mainly due to 1P and 3P loading but wave loading can also be dynamic for deeper waters and heavier turbines. A breakdown of the overall problem of soil–structure interaction into two types of soil shearing is schematically represented in Fig. 17.3. The current codes of practice (e.g., DNV [1], American Petroleum Institute, API [2,3], Institute of Electrical Engineers, IEC [4]) for the design of monopile foundations of OWTs recommend the application of the p–y curves primarily for the evaluation of lateral pile capacity in the ultimate limit state. The codes provide limited guidance in predicting the change of the foundation stiffness and consequent change of natural frequency, which are both design drivers for serviceability limit state requirements.

Furthermore, it is important to note that the vibration of the foundation will induce cyclic strains in the soil in its vicinity. Under moderate-to-high amplitudes of cyclic loading, most soils change their stiffness and strength. In order to study the changes in soil stiffness due to these cyclic strains, the developing strain in the soil around the shear zone must be taken into consideration. Soils in offshore sites can be fully saturated and therefore pore pressures are likely to develop as a result of these cyclic strains. The pore pressure developed may dissipate to the surrounding soil depending on factors including frequency of loading, permeability of the soil, and diameter of the pile. Pore water pressure may also develop in unsaturated soils under cyclic shearing. It should be noted that due to the nature of the external excitation, wave and wind-induced loads may impose either one-way or two-way cyclic loading on the monopile, whereby one-way loading develops more soil deformation and consequently more change in foundation stiffness.

OWTs are relatively new structures without any track record of long-term performance. Therefore, the uncertainties of their long-term response pose additional challenges to developers and designers of offshore wind farms. In fact, monitoring of a limited number of installed wind turbines has indicated a gradual departure of the overall system dynamics from the design requirements (e.g., the data from Lely wind farm data [5]), which may lead to amplification of the dynamic response of the turbines, leading to larger tower deflections and/or rotations beyond the allowable limits tolerated by manufacturer. The latter are often considered responsible for the damage observed in gearboxes and other electrical-rotating equipment.

17.1.3 Technical Review/Appraisal of New Types of Foundations

Foundations typically cost 25%–35% of an overall offshore wind farm project and in order to reduce the LCOE, new innovative foundations are being proposed. However, before any new type of foundation can actually be used in a project, a thorough technology review is often carried out to de-risk it. European Commission defines this through TRL (Technology Readiness Level) numbering starting from 1 to 9; see Table 17.2 for different stages of the process. One of the early works that needs to be carried out is technology validation in the laboratory environment (TRL-4). In this context of foundations, it would mean carrying out tests to verify the long-term performance. It must be realized that it is very expensive and operationally challenging to validate in a relevant environment and therefore laboratory-based evaluation has to be robust so as to justify the next stages of investment. This is another motivation for scaled model testing.

17.1.4 Physical Modeling for Prediction of Prototype Response

Experimental investigations on physical wind turbine models can provide valuable information for understanding the dynamic behavior and long-term performance of OWTs. While physical modeling at normal gravity (often known as 1 g testing) can be used for modeling different loading conditions experienced by structures, its application in tackling soil–structure interaction needs additional consideration. In such cases, geotechnical centrifuge facilities are often used where 1:N scale model can be subjected to N g (N times earth gravity) to replicate the prototype stresses. However, OWTs are very complex structure involving aerodynamics (wind turbulence at the blades), hydrodynamics (wave slamming the tower and the part of the tower under water), cyclic, and dynamic soil–structure interaction. Ideally, a wind tunnel and a wave tank onboard a geotechnical centrifuge is suitable which seems to be unlikely with the current technology development. For such problems involving many interactions, where overall system dynamics and long-term performance needs to be studied, centrifuge is not well suited due to the unwanted parasitic vibration of geotechnical centrifuge and the lack of stable platform. Another important limitation of centrifuge facilities is the limited number of cycles that can reasonably be applied when compared with the expected number of cycles that a typical OWT experiences over its life span of 25 years, which is in the range 10⁷–10⁸. This calls for alternative modeling techniques where a problem will be studied through a set of nondimensional groups and is explained in the next section.

17.2.1 Dimensional Analysis

Dimensional analysis refers to a method of great generality and mathematical simplicity that can be conveniently used for studying phenomena that at first appear to be very complex but which can be qualitatively analyzed and described in more simplified terms [9]. Although the basis of dimensional analysis was set in the 19th century by Fourier in his work on the theory of the heat flow, only in the 20th century the method has been extensively used in different fields of physics and engineering. The approach is based on the concept of similarity, which in physical terms implies that that any phenomenon can be studied through a finite number of independent quantities expressed in a nondimensional form, i.e., unit-free. In this context, the aim of dimensional analysis is to determine these nondimensional quantities, which constitutes the first step in an experimental study.

17.2.2 Definition of Scaling Laws for Investigating OWTs

As discussed earlier, OWTs are dynamically sensitive structures because of the multiple frequencies that contribute to the complexity of the interaction of the foundation with the supporting soil. To study the dynamics and predict the long-term performance of OWTs, the following phenomena have to be considered and correctly replicated in the model tests, namely:

Based on the above discussion, the following physical mechanisms are considered for the derivation of the nondimensional groups:

17.3.1 Monopile Foundation

Most of the OWTs currently in operation are supported on monopiles. Monopiles consist of tubular steel tubes having diameter in the range 3.5–10 m. The choice of monopiles results from their simplicity of installation and the proven success of conventional piles—characterized by smaller diameters, i.e., 1.5–3.0 m, in supporting offshore oil and gas infrastructures.

17.3.2 Strain Field in the Soil Around the Laterally Loaded Pile

Repeated shear strain may reduce the stiffness of saturated soils. Assuming that the changes in soil stiffness drive the long-term performance, the average strain next to a pile is a governing criterion and must be preserved in order to ensure similar stiffness degradation in both model and prototype. The relevant nondimensional group can be derived by considering that the average shear strain field around a laterally moving pile is a function of pile head deflection (δ) and pile outer diameter (D), mathematically expressed by:

${\epsilon }_{\mathrm{s}}\propto \frac{\delta }{D}$ (17.1)

(17.1)

Klar [10] suggested a value of 2.6 for the coefficient of proportionality between the average strain in the soil and the ratio of head deflection and pile diameter. However, there is a lack of consensus in the literature on this proportionality coefficient. The pile head deflection is a function of the external load (P), the shear modulus of the soil (G), and the pile diameter. Therefore, the average strain field in the soil around a pile can be expressed as a function of only three parameters (Fig. 17.5A):

${\epsilon }_{\mathrm{s}}=f\left(P,D,G\right)$ (17.2)

(17.2)

The parameters in Eq. (17.2) can be used to obtain a dimensionless group as follows:

${\epsilon }_{\mathrm{s}}=f\left(\frac{P}{G{D}^2}\right)\frac{\left[F\right]}{\left[F{L}^{-2}\right]{\left[L\right]}^2}$ (17.3)

(17.3)

Eq. (17.3) describes the nondimensional group that takes into account the strain field in the soil generated by a lateral loaded pile. Eq. (17.3) shows that the strain in the soil is directly proportional to the horizontal load applied at the pile head, inversely proportional to the soil stiffness and inversely proportional to the square of the pile diameter.

17.3.3 CSR in the Soil in the Shear Zone

In geotechnical earthquake engineering, it is well established that degradation of a soil due to liquefaction-type failure is a function of CSR which is defined as the ratio of the shear stress to the effective vertical stress at a particular depth, defined in Eq. (17.4) [11]. The CSR can be expressed in Eq. (17.4):

$\mathrm{CSR}=\frac{{\tau }_{\mathrm{cyc}}}{{\sigma \prime }_{\mathrm{v}}}$ (17.4)

(17.4)

${\tau }_{\mathrm{cyc}}\propto \frac{P}{D^2}\frac{\left[F\right]}{{\left[L\right]}^2}$ (17.5)

(17.5)

where ${\tau }_{\mathrm{cyc}}$ is the cyclic shear stress imposed by the pile on the soil at a particular depth and ${\sigma \prime }_{\mathrm{v}}$ is the effective vertical stress on the soil at the same depth.

The vertical effective stress can be related to the shear modulus of the soil:

${\sigma \prime }_{\mathrm{v}}\propto G\frac{\left[F\right]}{{\left[L\right]}^2}$ (17.6)

(17.6)

It is usually found that G is proportional to ${\sigma \prime }_{\mathrm{v}}^n$, where the exponent n is a function of the type of soil, varying from 0.435 to 0.765 for sandy soil, although a value of 0.5 is commonly used in practice. For clayey soil, the value of n is generally larger and usually taken as 1 [12].

Combining Eqs. (17.4)– (17.6), one can see that the nondimensional group expressed in Eq. (17.3) can also guarantee similarity of CSR. This leads us to a nondimensional group, expressed in Eq. (17.7a,b), that must be satisfied.

${\left(\frac{P}{G{D}^2}\right)}_{\mathrm{model}}={\left(\frac{P}{G{D}^2}\right)}_{\mathrm{prototype}}$ (17.7a)

(17.7a)

It is interesting to note that using two different approaches based on average strain in the soil, and on the CSR, dimensional analysis leads to a unique nondimensional group given in Eq. (17.7a). It can be easily shown that considering the overturning moment (M) at the head of the foundation, i.e., pile head for example, the group in Eq. (17.7b) can equally be used.

${\left(\frac{M}{G{D}^3}\right)}_{\mathrm{model}}={\left(\frac{M}{G{D}^3}\right)}_{\mathrm{prototype}}$ (17.7b)

(17.7b)

17.3.4 Rate of Soil Loading

Pore pressure generation and subsequent dissipation is a function of the frequency of loading exerted on the soil. The time (t) in which the pore pressure dissipates will be directly proportional to the soil permeability (k_h) and inversely proportional to characteristic length, e.g., monopile diameter:

$t\propto \frac{k_{\mathrm{h}}}{D}$ (17.8)

(17.8)

Considering the variables in Eq. (17.8), one can obtain the only possible dimensionless group:

$\left(\frac{k_{\mathrm{h}}t}{D}\right)\frac{\left[L{T}^{-1}\right]\left[T\right]}{\left[L\right]}$ (17.9)

(17.9)

Replacing time by forcing frequency (f_f), the pore pressure dissipation is therefore correctly modeled when:

${\left(\frac{k_{\mathrm{h}}}{f_{\mathrm{f}}D}\right)}_{\mathrm{mod}\mathrm{el}}={\left(\frac{k_{\mathrm{h}}}{f_{\mathrm{f}}D}\right)}_{\mathrm{prototype}}$ (17.10)

(17.10)

17.3.5 System Dynamics

In order to correctly simulate the system dynamics resulting from the interaction between the external loads (i.e., forcing frequency) and the wind turbine (i.e., natural frequency), the ratio between the forcing frequency and the natural frequency of the turbine should be of the same order in the physical model and prototype. The main forcing frequencies are (see also Fig. 17.2):

From Fig. 17.2 it may be noted that for any of the three design approaches possible (i.e., soft–soft, soft–stiff, and stiff–stiff), the ratio between the forcing and the natural frequency is close to 1. This aspect must be preserved also in the physical model. Therefore the nondimensional groups for the correct modeling of the dynamics of the system can be expressed as a ratio between the forcing and natural frequency:

${\left(\frac{f_{\mathrm{f}}}{f_{\mathrm{n}}}\right)}_{\mathrm{model}}={\left(\frac{f_{\mathrm{f}}}{f_{\mathrm{n}}}\right)}_{\mathrm{prototype}}$ (17.11)

(17.11)

Lombardi et al. [8] pointed out that the two groups for “rate of soil loading,” given in Eq. (17.10), and “system dynamics,” given in Eq. (17.11), cannot be simultaneously satisfied with same pore fluid in model and prototype. It is obvious that both coefficient of permeability and diameter of the monopile affect the drainage condition. Modeling both the nondimensional groups together can be conveniently accommodated through the use of a different pore fluid such as silicone oil or methyl cellulose solution for the model tests.

17.3.6 Bending Strain in the Monopile

The strain in the monopile is a function of its mechanical properties and the characteristics of the external loads. As shown in Fig. 17.1, the external loads due to the wind and the waves can be conveniently modeled as a horizontal force acting at the distance y above the foundation level—see Figs. 17.3 and 17.5A. Making the assumption that the monopiles remains elastic, the strain in the pile wall will be a function given in Eq. (17.12).

${\epsilon }_{\mathrm{p}}=f\left(P,y,D,E,t_{\mathrm{w}}\right)$ (17.12)

(17.12)

where t_w is the pile wall thickness and E is the Young’s modulus of the pile.

The parameters in Eq. (17.12) can be combined to obtain a dimensionless group:

${\epsilon }_{\mathrm{p}}=f\left(\frac{Py}{E{D}^2{t}_{\mathrm{w}}}\right)\frac{\left[F\right]\left[L\right]}{\left[F{L}^{-2}\right]{\left[L\right]}^2\left[L\right]}$ (17.13)

(17.13)

In order to correctly model the material nonlinearity of the pile, the nondimensional group expressed in Eq. (17.14) must be preserved in the model and the prototype:

${\left(\frac{Py}{E{D}^2{t}_{\mathrm{w}}}\right)}_{\mathrm{model}}={\left(\frac{Py}{E{D}^2{t}_{\mathrm{w}}}\right)}_{\mathrm{prototype}}$ (17.14)

(17.14)

17.3.7 Fatigue in the Monopile

The stress in the monopile can be an important parameter influencing the fatigue phenomena. Fatigue relates to the degradation of the material after a large number of load cycles (>10⁷ cycles). The design of an OWT must ensure that the fatigue limit state is satisfied. The fatigue in the monopile can be expressed as a function of the external load, pile diameter, pile wall thickness, vertical distance between the application point of the load P and the pile head, and the yield stress of the material (${\sigma }_{\mathrm{y}}$):

$f\left(P,D,t_{\mathrm{w}},y,{\sigma }_{\mathrm{y}}\right)$ (17.15)

(17.15)

The parameters in Eq. (17.15) can be combined to obtain a dimensionless group:

$f\left(\frac{Py}{{\sigma }_{\mathrm{y}}{D}^2{t}_{\mathrm{w}}}\right)\frac{\left[F\right]\left[L\right]}{\left[F{L}^{-2}\right]{\left[L\right]}^2\left[L\right]}$ (17.16)

(17.16)

Eq. (17.16) represents the nondimensional group required to take account of the fatigue phenomenon. This can be correctly modeled when Eq. (17.17) is satisfied:

${\left(\frac{Py}{{\sigma }_{\mathrm{y}}{D}^2{t}_{\mathrm{w}}}\right)}_{\mathrm{mod}\mathrm{el}}={\left(\frac{Py}{{\sigma }_{\mathrm{y}}{D}^2{t}_{\mathrm{w}}}\right)}_{\mathrm{prototype}}$ (17.17)

(17.17)

To explore the usefulness of these dimensionless groups derived so far, the next section of the paper describes typical results obtained from high-quality small-scale experiments.

17.3.8 Example of Experimental Investigation for Studying Long-Term Response of 1–100 Scale OWT

This section describes an example of experimental investigation carried out on a small-scale OWT. The experimental apparatus is shown in Fig. 17.5B, however, more details regarding the experimental arrangement can be found in Lombardi et al. [8]. As it can be seen from the figure, modeling of the environmental dynamic loads can be achieved by using an electrodynamic actuator fixed to the laboratory strong wall and connected to the tower. The blades are rotated by a DC electric motor to model the 1P loading, which also give some aerodynamic damping to the system. An alternative cyclic loading system is proposed by Nikitas et al. [2]. This consists of two identical interlocking gears where masses can be attached (see Fig. 17.4). The working principle of this cyclic loading device is based on the unbalanced rotation of eccentric masses and is presented schematically in Fig. 17.6. This counter-rotating eccentric mass of equal magnitude is able to produce a unidirectional cyclic load in Y axis only as the net force in X axis is zero due to cancelation of the equal and opposite forces. In the case when the two masses mounted on the interlocking gears are not equal, there will be a sinusoidal loading along two perpendicular directions (X and Y axes). The force resultants in X and Y axes for two cases when the masses are equal and unequal are presented in Fig. 17.7.

It may be noted that the excitation force produced by this device is dependent on three variables: mass of the weights attached to the gears (m), the radius of the gears (r), and the angular velocity of the gears (ω). The frequency (Hz) of the cyclic loading depends mainly on the angular velocity which can be easily controlled by the voltage (V) of the power supply. In order to control the force in Y axis, the appropriate masses should be attached to the rotating gears, considering the fact that the radius remains the same. Also it is possible to change the frequency and the amplitude by just replacing the type and the diameter of the gears. Once the amplitude and the frequency of the cyclic loads are defined, the device is mounted on the tower to simulate the desired overturning moment at the level of the foundation.

In a typical offshore project, the largest contribution toward the overturning moment is due to the wind and the wave loads having different magnitude of overturning moment, frequency, and also the number of cycles. A way to address this loading complexity in a scaled model tests is by attaching two of these eccentric mass actuators, one to represent each load (frequency and amplitude) and placing them at the correct height in order to produce the desired scaled bending moment at the base of the model. The result of such an arrangement would provide realistic results of the foundation’s long-term performance. Such a configuration is presented schematically in Fig. 17.8, where the wind and the wave are both acting along the same direction, i.e., collinear. There can be loading scenarios, when the wind and the wave may not be aligned and Fig. 17.9 shows a possible configuration that can be used for simulation.

Typical results presented by Lombardi et al. [8] highlighted that the long-term behavior of OWTs supported on monopiles is strongly affected by the level of strain generated in the soil adjacent the foundation (given in Eq. 17.3), whereby larger strains result in higher variation in foundation stiffness and natural frequency of the system. Evidently, the potential change in vibration characteristics has to be appropriately taken into account in design and prediction of the long-term performance of OWTs.

17.4.1 Typical Experimental Setups and Results

A series of tests were carried by Bhattacharya et al. [13] to investigate the dynamics and long-term performance of small-scale OWTs models supported on multipod foundations (Fig. 17.11). Fig. 17.12 shows the asymmetric model arrangement in a typical setup. The results showed that the multipod foundations (symmetric or asymmetric) exhibit two closely spaced natural frequencies corresponding to the rocking modes of vibration in two principle axes. Furthermore, the corresponding two spectral peaks change with repeated cycles of loading and they converge for symmetric tetrapods but not for asymmetric tripods. From the fatigue design point of view, the two spectral peaks for multipod foundations broaden the range of frequencies that can be excited by the broadband nature of the environmental loading (wind and wave) thereby impacting the extent of motions. Thus the system life span (number of cycles to failure) may effectively increase for symmetric foundations as the two peaks will tend to converge. However, for asymmetric foundations, the system life may continue to be affected adversely as the two peaks will not converge. In this sense, designers should prefer symmetric foundations to asymmetric foundations.