Abstractepubs.surrey.ac.uk/851802/1/SRI_Openaccess_Minimum... · Web viewIn the formulation, the jacket and wind turbine tower are modelled as Euler-Bernoulli beams and the foundations

To appear in the Journal of Soil Dynamics and Earthquake Engineering [SOILDYN_2018_1191]

Minimum foundation size and spacing for jacket supported offshore wind turbines considering dynamic design criteria

Saleh Jalbi1,2, Subhamoy Bhattacharya1

1University of Surrey, Guildford, United Kingdom2 Robert Bird Group, London, United Kingdom

Corresponding Author:Professor Subhamoy BhattacharyaChair in GeomechanicsUniversity of SurreyUnited KingdomEmail: [email protected]

Abstract Modes of vibrations play a dominant role in the design of WTG (Wind Turbine Generator) support structures. It is necessary to choose the overall system frequency such that the modes of vibration do not coincide with the rotor frequencies as well as the wave frequencies. WTG supported on multiple foundations (such as jacket or seabed frames) may exhibit rocking modes of vibration if the vertical stiffness of the foundation is not large enough which in turn may have serious implications on the fatigue performance of the overall structure. From the O&M (Operation and Maintenance) point of view, it is necessary to design the overall system to have sway-bending as the dominant mode of vibration. This paper develops a formulation for obtaining foundation (for both piles and shallow suction caissons) sizes and spacing such that rocking vibrations are prevented and sway-bending vibrations are achieved. Expressions for minimum vertical stiffness of foundations are proposed for different configurations: square base, symmetrical (equilateral) triangle, or asymmetrical (isosceles) triangle. Verification of the method is carried out through finite element analysis and a step-by-step solved example is taken to show the application of the formulation. It is hoped that the formulation will assist designers to optimize the foundation arrangement and provide preliminary sizing for tender design.

Keywords: Offshore Wind Turbines, Jacket, Piles, natural frequency, wave frequency, Suction Caisson

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mailto:[email protected]


Nomenclature

1P Operational frequency of the rotor3P Shadowing effects of the blade on the tower. The value of 3P is the 3 × 1P (For 3 bladed

turbines)Lp Pile LengthDp Pile DiameterLC Caisson LengthDC Caisson DiameterEIT-J Tower-Jacket StiffnessLbottom Lower jacket spacing/foundation spacinghJ Jacket HeighthT Tower Heighthtotal Height of tower-jacket systemGS Soil Shear Modulusνs Soil Poisson’s Ratiokv vertical stiffness of the foundationkv,SW Minimum sway-bending vertical stiffnesskv,SW vertical stiffness to initiate rockingf0 flexible natural frequency (including SSI)ffb fixed base natural frequencySB Square Base arrangement of the foundationST Symmetric Equilateral Triangle arrangement of the foundationAT Asymmetric Isosceles Triangle arrangement of the foundationα Foundation stiffness variability factor

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1.0 Introduction:Offshore Wind Turbines (OWTs) are steadily becoming one of the main pillars of energy production. Based on the experience and research over the past 20 years, future targets have been set by different governments to expand the output from clean sources with a low levelized cost of energy (LCOE) (Luther, et al., 2017). This is a challenging task that requires extensive research efforts to make the design and construction of offshore wind farms more viable. In addition to increasing capacity, windfarms will be sited further away from shore (up to 200 km) with water depths of more than 60m. Monopiles, which are currently the most utilized foundation systems for European Waters, are not economical for soft soils (see for example Chinese Seas) or seismic areas where such ground conditions would require longer piles with large diameters. Given that there are limited number of installation vessels, lifting cranes, and hydraulic hammers that can complete the installation of such structures, the day rate of such machinery would impose heavy cost implications on wind farm developers and raise the levelized cost of energy. Furthermore, driven monopiles are not environment-friendly solution to support large WTG (Wind Turbine Generator) due the challenges associated with transportation and installation which is known to produce high levels of noise during pile driving which has a negative impact on the surrounding marine life . As a result, other solutions such as jacket foundations and seabed frames are being used.

Jackets and sea-bed frames are usually mounted on piles or suction caissons. Both 3-legged and 4-legged jackets have been installed in European waters: Beatrice wind farm consists of a 4-legged jacket on piles whilst the Aberdeen Offshore Windfarm consists of a 3-legged jacket on suction caissons (sometimes termed as Suction Bucket Jackets SBJs). Caisson foundations produce less noise during installation and provide inherent scour protection due to its geometry, see for example (Oh, et al., 2018) (Stroescu, et al., 2016). The process for installing such foundations consists of allowing the caisson to sink under its own weight and then achieving full depth of penetration by pumping out the trapped water by creating a pressure difference. This is an alternative to the use of impact hammers, and so arguably reducing noise pollution associated with the installation. Another advantage of suction caissons is the ease of decommissioning where the installation process may be easily reversed to remove the caissons from the seabed.

Studies carried out by Bhattacharya et al (2013) showed that the first Eigen frequency of vibration for OWTs supported on multiple shallow foundations (such as jackets on 3 or 4 suction caissons) correspond to low frequency rocking modes of vibration about the Principle Axes. The work is based on scaled model tests on 3 types of foundations: monopiles, tetrapods (4-legged jacket on caissons), and asymmetric tripods (3-legged seabed frame on caissons). It was further noted that the frequency of vibration changes with cycles of loading due to altering of soil stiffness around the foundation. It is shown that symmetric as well as asymmetric configuration exhibit closely spaced natural frequency due to the rocking modes of vibration. For Symmetric foundation arrangement, with cycles of loading, the closely spaced frequencies converge and this is due to uniformity in densification of the soil around the foundation. Rocking modes of vibration corresponds to vertical stiffness of the foundation. This is in contrast to the sway-bending modes of vibration typical of monopile structures or jacket on piles which effect of vertical stiffness of the foundation is negligible.

Rocking modes of vibration tends to have a lower frequency and may interfere with the 1P (rotor) frequency range and wave frequency, see (Arany, et al., 2016). This is particularly challenging for large turbines where the soft-stiff target frequency is shifting towards the wave frequency, see in Figure 1 . Furthermore, wave will have a higher energy of excitation and may impose serious fatigue

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damage to the structure if rocking modes are allowed. It is therefore advisable to avoid rocking modes for jacket supported on shallow foundations.

The above commentary is substantiated in the work presented in (Yu, et al., 2015) (Lombardi, et al., 2013) (Cox & Bhattacharya, 2011) (Bhattacharya, et al., 2012). It is shown that the natural frequency changes with the number of cycles. Typically, with increasing number of cycles, natural frequency of WTG structure increases for sandy soils due to densification and may decrease for clayey profiles. The increase in the frequency of the overall wind turbine system in cohesionless ground profiles is attributed to the densifying of sands under low amplitude and frequency of cyclic loads. On the other hand, the decrease of natural frequency in clayey grounds is attributed to the accumulation of pore pressure (fluidisation), change in clay microstructure which leads to a loss of stiffness of the ground. The change in soil stiffness can be estimated based on element tests such as simple cyclic simple shear apparatus shown in (Nikitas, et al., 2017) where strain levels experienced in OWT applications need to be applied. It is shown that in sands, the shear modulus increases with increasing number of cycles and then stabilizes which explains the merging of two closely spaced peaks for symmetric foundations.

It is evident that both foundation arrangement (square base, symmetric triangle, and asymmetric triangle) and the vertical stiffness of the foundation (be it a pile or a suction caissons) plays an important role on the dynamic performance of offshore wind turbines i.e. modes of vibration as well as change in natural frequency with cycles of loading. Thus, the aims of this paper are as follows:

(1) Establish criteria to differentiate two modes of vibration (rocking or sway-bending) for multiple foundation supported WTG. It is advisable to avoid rocking modes of vibration.

(2) Develop formulation and practical method for obtaining minimum vertical stiffness of foundation (i.e. pile dimension or suction caisson dimensions) to achieve sway-bending modes of vibration.

(3) Verify the validity of the method using 3D finite element analysis.(4) Provide example comparisons between foundation size and spacing required for different

foundation arrangements (4-legged jackets, 3-legged symmetric triangle, 3-legged asymmetric triangle).

The formulations presented in this paper can be beneficial for concept design of jackets and to obtain preliminary dimensions of foundations without recourse to high fidelity calculation procedures. It will also be obvious that the analysis and design is multidisciplinary and complex which requires sound understanding of structural dynamics, geotechnical analysis and soil-structure interaction.

Figure 1: 1P/3P criteria for turbines of different sizes

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2.0 Dynamic criteria for jackets for rocking and sway-bendingFigure 2 shows a mechanical idealization of a jacket supported on multiple foundations following the work of (Jalbi & Bhattacharya, 2018) where closed form solution for natural frequency is obtained. In the formulation, the jacket and wind turbine tower are modelled as Euler-Bernoulli beams and the foundations are replaced with a set of springs. The global natural frequency of the whole system (f 0) is obtained by multiplying the fixed base frequency (ffb) by a flexibility coefficient (Cj) given by Equations 1 to 5. The fixed base frequency of the system (ffb) may be computed using Eq.1 and the readers are referred to the Jalbi and Bhattacharya (2018) for detailed derivation. The variation of the individual foundation stiffness due to variability of the ground or other reasons can be taken through the factor α.

(1)

where and the readers are referred to Figure 2 for definition of the terms.

Figure 2:Mechanical idealization of the system

The flexibility of the foundations is taken through the foundation flexibility coefficient C J as shown in Eq 2

(2)

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Where CJ is dependent on the equivalent rotational spring shown in Figure 2(d) and is computed using Eq.3 and Eq.4

C J=√ ττ+3 (3)

Such that τ is a function of the equivalent rotational stiffness kR

τ=k Rh totalEIT−J (4)

Using Castigialiano’s theorem, the rotational stiffness can be calculated from the vertical stiffness of the foundation. Assuming ideal conditions and a square configuration (α in Figure 2(b)=1)

(5)

Figure 3 plots the normalized natural frequency variation (f0/ffb) of the whole system as a function of normalised vertical foundation stiffness (kv/kt) where kt is the tower stiffness. In the plot, three zones are identified:

(a) lower value of (kv/kt) and (f0/ffb) which is characterised by rocking modes of vibration(b) high value of (kv/kt) and (f0/ffb) which is characterised by sway-bending modes of vibration(c) the intermediate zone which can be identified by initial slope of the curve and 0.9 (f0/ffb). The

use of 0.9 of fixed based frequency is explained in the next paragraph.

Arany et al (2016) analysed 15 operating monopile supported offshore wind turbines and found that the natural frequencies of these are closed to 90% of the fixed base frequencies. In other words, the foundations are very rigid and in comparison, the superstructure is flexible. Due to the good performance of these monopile-supported structures and in the absence of reported performance of jacket supported structures, 0.9 value is chosen. In other words, it is explicitly assumed that sway-bending mode of vibration is initiated at the vertical stiffness required to achieve 90% of the fixed base natural frequency. From the design point of view, a very high foundation stiffness (fixed base conditions) could result in excessive stresses in the top braces and a very low foundation stiffness could result in high stresses of the lower jacket legs (induced by rocking mode of vibration). Furthermore, the rocking mode of vibration (termed as rocking dominant zone) is defined as the intersection of the initial slope and 90% of the fixed base frequency. It is considered useful to define the foundation stiffness terms in Figure 3 as follows:

(a) kv,RCK is the minimum vertical stiffness of the foundation required to initiate the transition from the rocking dominant zone

(b) kv,SW is the minimum vertical stiffness of the foundation required to engineer a sway-bending mode of vibration.

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Figure 3: Variation of the natural frequency

The paper suggests that designers, in order to avoid rocking mode of vibration, need to provide adequate vertical stiffness of the foundation and the expression for the minimum stiffness is provided in Section 3. Expressions for vertical stiffness of different types of foundations are is provided in the Appendix A for ready reference.

3.0 Expression for minimum vertical stiffness of foundation (kv,SW) to avoid rocking modes of vibration

Based on the discussion provided in the earlier section and Figure 3, Eq.2 can be re-written as Eq.6

(6)

Hence, cancelling ffb from both sides of the equation results in Eq7

(7)

Using Eq.4, the following equality can be derived

(8)

Which means the value of τ is as per Eq 9

(9)

Equating Eq.9 with Eq.4 results in the following

(10)

Where kv is solved for as shown in Eq11

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(11)

The above expression is developed for the 2D idealisation and therefore the minimum vertical stiffness of a single foundation to achieve sway-bending modes of vibration ksw is given by Eq 12.

(12)

The above method can be repeated for symmetric and asymmetric triangles and few derivations are provided in Appendix B. Table 1 provides a summary of different arrangements.

Table 1: Summary Table for minimum vertical single foundation stiffness to avoid rocking

Foundation arrangement Threshold Vertical foundation stiffness Square Base (SB)

Symmetric Equilateral Triangle (ST)

Asymmetric Isosceles Triangle (AT)

It is important to note that designers may use the stiffness values in Table 1 keeping in mind the recommendations concerning safety factors in current standards. For instance, the (DNVGL-ST-0126,2016) recommends that the natural frequency should have a safety factor margin of 10% on the maximum and minimum rotor speeds (soft-stiff design region). Similarly, the recommended values should also consider the ground material stiffness values when performing natural frequency analysis (nfa). Typically, the characteristic soil conditions (material safety factor=1) are used for natural frequency analysis as shown in (De Vries, et al., 2011) , however projects with complex ground profiles or limited data might consider other safety factors.

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kv

kv kv

Lbottom

Lbottom

Lbottom

LbottomLbottom

kv

Lbottom

kvkv

kv

Lbottom

kv

kv kv


4.0 Dimensions of foundations to avoid rocking modes of vibrationsThe formulation developed in the earlier section can be applied to jackets as well as seabed frames. Typically, foundations used are either suction caissons or piles. This section of the paper provides simple expressions for choosing pile dimensions as well as suction caissons and a verification of the method is provided using finite element analysis

4.1 Pile dimensions to achieve sway-bending vertical stiffness (kv,SW):The (API-RP2A-WSD, 2014) and (DNVGL-RP-C212, 2017) codes provide “Winkler” type foundations in the form of q-z and t-z curve to represent the load-placement relationships of axially loaded piles. As the natural frequency is concerned with very small amplitude vibrations, the deformations will be small and the initial foundation stiffness would suffice (Arany, et al., 2017). (Mylonakis, 2001) and (Anoyatis & Mylonakis, 2012) provided formulations for the static and dynamic Winkler moduli in homogeneous elastic soils. Using charts provided in (Anoyatis & Mylonakis, 2012), it can be demonstrated that the static stiffness of piles can be used for preliminary sizing as the cyclic and dynamic loads applied on offshore wind turbines (wave, 1P,3P) have a very low frequency. Dynamic stiffness is applicable for OWTs sited in seismic areas such as Taiwan, India, and some areas of the United States. Eq.13 shows the Winkler modulus for the static case

(13)

The formulations for Winkler type foundations can then be used to obtain the “Pile head” stiffness which represents the foundation with a single spring at the mudline as shown in Figure 2 (a-c) using standard t-z,q-z software. Alternatively, there are solutions available in literature for the load-displacement relationships at the pile head which can be used to obtain the vertical stiffness such as the ones recommended by (Poulos & Davis, 1968) (Randolph & Wroth, 1978) , (Poulos & Davis,1980) (Randolph, 1981), (El Sharnouby & Novak, 1990), (Fleming, et al., 1992), and (Shama & ElNaggar, 2015). These formulations typically depend on the pile stiffness (function of Lp, Dp E,p, and Ip) and the soil shear modulus.

(Poulos & Davis, 1968) presented Eq.14 to find the percentage of the load taken by the pile base

(14)

Pile aspect ratios (Lp/Dp) in the range of 15-25 are expected for jacket piles supporting offshore wind turbines as the loads are mainly resisted in the axial direction. This results in a percentage of 4-6% contribution of the base to the vertical stiffness of the piles. Thus, for preliminary sizing, it is assumed that the shaft is the only parameter contributing to the vertical stiffness of the pile making the formulations less dependent on the diameter. Moreover, this will facilitate the computation as the pile stiffness will be the same for both tension and compression, assuming the stiffness in tension and compression have the same safety factors. (Fleming, et al., 1992) proposed the following formulation for the elastic settlement of rigid embedded piles due to shaft friction

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where is the average shear modulus (15)

ζ is between 3 and 5 and an average value of 4 has been suggested by (Baguelin & Frank, 1979)

The average shear modulus (Gs) expressed by (Fleming, et al., 1992) is a simplification of the effect of confining pressure on the stiffness of soils. For instance, OC clays typically have a linear variation

of stiffness with depth and in this case, the recommended value of the shear modulus is the average between the top and bottom of the pile. Moreover, this relation assumes an elastic stiffness which is acceptable at the concept design stage since the natural frequency is by definition small amplitude vibration. However, designers are required to consider the effect of plastic shear strains on the stiffness of the soil in the detailed design stage.

For a Square Base (SB) foundation, substituting Eq.15 in Eq.12 the, length of the pile required to avoid rocking is as per Eq.16

(16)

Hence the length of the pile required to control rocking is a function of

The structural stiffness of the tower-jacket system EIT-J

The total height of the structure (which also affects the structural stiffness) The square of the bottom spacing of the foundations (also affects the structural stiffness) The inverse of the ground stiffness

Similarly a minimum pile length can be calculated for symmetric and asymmetric triangles

(17)

(18)

It is considered useful to take an example and the 4-legged jacket provided in (Alati, et al., 2015) is taken and shown in Figure 4. The bottom spacing of the foundation Lbottom is 12.5m and the total height (htotal) is approximately 140m. The stiffness of the tower-jacket structure EIT-J (see Figure 1b,c,d) is calculated as 1.635x1012 Nm2, see (Jalbi & Bhattacharya, 2018). Taking ζ as 4 in Eq.16, the variation of the minimum pile length (to achieve sway-bending) with soil stiffness G S is plotted in Figure 5.

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Figure 4: Reference Jacket Dimensions

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Figure 5: Variation of pile length with soil stiffness

As shown in Figure 5, a shear modulus of 25 MPa (which is expected in a medium dense sand) returns a value of 26 m of pile length, whilst a change in the shear modulus to 30 MPa results in a 21m pile length which is indicative of the high sensitivity of the foundation dimensions to the soil stiffness. Keeping in mind that the soil shear modulus varies with cyclic load, it is important to provide adequate length such that rocking is avoided throughout the service life of the wind turbine

Moreover for a given location (i.e. water depth, wind speed, and wave speed), a 3-legged jacket and a 4-legged jacket are expected to have the same structural stiffness (EIT-J) and strength as they have to resist the same loads at the Ultimate Limit State (they both must have similar utilization ratios) and satisfy the same serviceability criteria (allowable deformations and natural frequency). Having the same stiffness does not necessarily mean that both arrangements (3-legged vs 4-legged) will have the same mass, nevertheless it is shown in (Jalbi & Bhattacharya, 2018) that the mass of the jacket does not have a great contribution on the first natural frequency of the structure. While it is difficult to carry out a generalized comparison between 3-legged and 4-legged jacket, it is of interest to make some conclusions regarding the effect of foundation arrangement on the foundation size. Thus, for the sake of argument the value of EIT-J the symmetric and asymmetric 3-legged jackets is also taken as 1.635x1012 Nm2 and the variation of the pile dimensions for these 2 additional arrangements is also shown in Figure 5. It can be seen that a symmetric 3-legged arrangements require double the pile length of a square arrangement to maintain the same natural frequency, whilst an asymmetric triangle would require triple the pile length. If for instance one wants to maintain the pile length at a certain level, an alternative solution would be to increase the foundation spacing (Lbottom). This solution is useful for ground profiles with complex layering and sharps shifts in stiffness or in ground profiles that have a shallow bedrock which requires shorter piles.

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Through equating Eq.17 and 18 to Eq.15 would result in Eq.19 and Eq.20

√2Lbottom , SB=Lbottom , ST (19)

√3 Lbottom, SB=Lbottom , AT (20)

Thus, in order to have the same natural frequency, the spacing of the foundation must be widened by a factor √2 or √3 to maintain the pile length as a square base arrangement.

Thus, judging from Eqs provided in Table 1 and Eq.19-20, it is evident that that asymmetrical arrangements seem to require larger dimensions than the corresponding symmetric ones. This may imply longer piles or wider spacing and is useful at the conceptual/optimization stages of the design.

It is important to note that the equations provided in this section are dependent on the foundation stiffness formulation suggested by (Fleming, et al., 1992), however the same methodology can be used for other stiffness formulation or through site specific solutions obtained from advanced Finite Element Analysis. Moreover, the provided solutions assume equal stiffness values under each foundation, whereas offshore foundations usually have varying stiffness values due to the change in the soil stratigraphy below the structure. Thus, the α in Eq.5 must be changed and L p calculated accordingly. Finally, it may be reminded that this is the minimum required stiffness and further checks on the dimensions should be made regarding the ultimate capacity, allowable deformations, and fatigue life.

4.2 Suction Caisson size to achieve sway-bending:Similarly, solutions for the vertical stiffness of shallow foundations are provided in provided in the API and DNV as shown by Eq.21

k v=4GSR1−υs (1+1 .28 RH )(1+ D2R )×[1+(0 .85−0.28DR )

DH

1−DH ](21)

DR<2

DH

<12

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Figure 6: Figures defining the terms in Eq.20

Other stiffness formulae can be found (Gazetas, 1991) and (Wolf & Deeks, 2004) where the following expression for the vertical stiffness of shallow embedded foundations in an elastic half space is provided

(22)

where Dc and Lc in this paper are the caisson diameter and length respectively as shown in Figure 7

Figure 7: Caisson dimensions

Similar to Section 4.1, the minimum length required can be achieved by equating Eq.22 to Eq.12

(23)

As shown in Eq.23, in the case of shallow foundations, the diameter plays an integral role and cannot be excluded and the solutions can be further simplified by assuming typical aspect ratios of the suction caisson (Lc/Dc). The solutions for aspect ratios of 0.5 and 2 as shown in Eq.24-25

For LC/DC=2

(24)

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For LC/DC=0.5

(25)

Similar solutions can be derived for 3-legged arrangements. Eq 24 and 25 can also assist in the preliminary stages of design to assist engineers in the selection of piles or suction caisson as support structures. The final section shows a step-by-step example of the method.

5.0 Verification using Finite Element Analysis (FEA):Natural frequency analysis (nfa) was performed using geotechnical 3D finite element package PLAXIS 3D. The analysis is performed in order to verify the proposed method and the same 4-legged jacket shown in Figure 4 was modelled (see Figure 8). For the verification, two cases have been considered:

Jacket supported on Lp=26m long piles with soil shear modulus Gs=25 MPa Jacket supported on Lp=21m long piles with soil shear modulus Gs=30 MPa, where both cases

have been analysed using the proposed methods and shown in Figure 5.

The advantage of the FEA is the ability to model the soil as a continuum and the piles as plates, which provides a better idealization of the soil-structure interaction of the system. As only the vibrations with very small amplitudes are considered (in the linear range), the dynamic analysis was run using linear elastic soil properties and by providing viscous boundary conditions. Without these boundary conditions, the waves propagating in the soil due to vibration of the foundations would reflect causing inaccuracies in the analysis. The jacket and tower were constructed using beam elements, while the transition piece was modelled using plate elements. As the soil material model was linear elastic (no strength was specified) no slip or gapping between the soil and the pile plate elements was allowed and a rigid contact is maintained between them. These assumptions were implemented as the main aim of the analysis is to verify the validity of the pile lengths obtained using the simplified equations provided in Table 1. Finally, as the two cases of undamped free vibration are compared, neither soil nor structural damping were not taken into account.

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Figure 8: Description of the 3D finite element model. Note: Pile diameter is 2.082m with 60mm wall thickness based on (Alati, et al., 2015)

After building the geometry, the lumped mass is given a small perturbation at rotor level (tower tip) and the structure is allowed to vibrate freely. The natural frequency is then obtained from the inverse of the period of the free vibration. The method described above to perform nfa is based on a similar example provided in the PLAXIS 3D tutorial manual (PLAXIS, 2017) and the readers are referred to the guidance for a step-by-step methodology.

Table 2 summarizes the results obtained from both analyses, and it is shown that the proposed method matches well with PLAXIS 3D since both cases have f 0/ffb in close proximity to 0.9. A number of possible explanations can be given to the slight discrepancies in the results, for instance the pile diameter effect in piles was ignored in section 4 but included in the FEA. In addition, the slight difference in the tension and compression vertical stiffness of the piles which is also captured in the FEA analysis. However, considering the comparative cost and computational time of each method, the simplified method can be a powerful tool in the concept design stage of jacket foundations for offshore wind farms.

Table 2: Summary of the finite element analysis

Foundation Natural Frequency (Hz) f0/ffb

Fixed Base 0.302 1Gs=30 MPa, Lp=21m 0.264 0.87Gs=25 MPa, Lp=26m 0.267 0.88

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6.0 Solved Example:

This section takes an example of a pile supported jacket of square configuration supporting a 4 MW turbine proposed to be used in Fujian Pintang Dalian island in the Chinese sea. The details of the turbine and the tower is given in Table 2. The jacket consists of a square base of 26m x 26m at the base and it tapers to 14m x 14m at the top. Each of the legs of the jacket is supported on 3m diameter piles 50m long. Figure 9,Table 3, and Table 4 provide information about the tower and jacket used in this example

Table 3: Wind turbine specifications

Tower Bottom Diameter (m) 5.042Tower Top Diameter (m) 3.083Tower Thickness (mm) 24-30Tower Height (m) 72Tower Mass (Tons) 176Mass of RNA (Tons) 240Mass of TP (Tons) 200

Table 4: Jacket dimensions

Lbottom (m) 26Ltop(m) 14Jacket Height(m) 40Jacket Leg Section Outer diameter 1600 mm, 32 mm wall thicknessJacket Brace Section Outer diameter 900mm, 25 mm wall thickness (3 layers)

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Figure 9: Schematic of the example

Step 1: Obtain the jacket stiffness:

For vibration along the main axis

EIJ=EI top⋅f (m)

Step 2: Obtain the tower Stiffness:

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EIT=EItop⋅f (q )

Step 3: Obtain the Tower-Jacket stiffness:

Step 3: Obtain the minimum foundation dimensions:

From Eq.16, the minimum pile length may be obtained

Hence depending on the shear modulus of the soil at the location of the pile, one can obtain the range of sizes expected as shown in Figure 10.

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Figure 10: Variation of the pile length with soil shear modulus

It is evident in this figure that the factor of safety imposed on the ground profile stiffness plays a big effect on the pile size. If the soil shear modulus is between 2-5 MPa, an onerous safety factor of safety must be obtained compared when the shear modulus is more than 6 MPa. Clearly other factors should be taken into account such as the overall deformation of the structure and the shift with cyclic loads.

Similarly, if the same 4-legged jacket is supported on suction caissons with an aspect ratio L C/DC of 0.5 and assuming a Poisson’s ratio of 0.25, using Eq.25

Hence, the caisson dimension variation with depth is shown in Figure 11

Figure 11: Jacket supported on suction caissons (LC/DC=0.5)

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A similar trend to piles is obtained due to the inverse nature of the function with the soil shear modulus. If the site is consistent of a soil with a shear modulus of 4MPa, the minimum caisson size required with an aspect ratio of 0.5 is 6.8m in diameter and 3.4m in penetration length (See Figure11)

7.0 Conclusion:Offshore Wind Turbine (OWT) structures are dynamically sensitive due to heavy rotating mass at the hub level. Often, OWT structures are supported on jackets or seabed frames where multiple foundations (piles or suction caissons) are used. Modes of vibration of these structures are an important design consideration as it affects not only the Soil-Structure Interaction (SSI) but also the fatigue issues. Jacket or seabed frame supported on multiple foundation may exhibit rocking mode of vibration or sway-bending mode and it depends on the vertical stiffness of the foundation elements. It is advisable to avoid rocking modes of vibration for OWT structures as rocking modes are typically low frequencies which is in the vicinity of the rotor frequency for and sometimes wave frequency. This paper provides formulations for sizing of foundations to avoid rocking modes. The following conclusions can also be drawn from the studies:

(a) The modes of vibration of WTG system (i.e. rocking vs sway-bending) plays an important role in the size, type and configuration of the foundations

(b) For a given structural stiffness and foundation spacing, the foundation depth will increase by double or even triple if a triangular arrangement is used instead of a square base arrangement.

(c) For jacket supported on piles, similar pile lengths can be achieved by increasing the spacing of the foundations by √2 or √3 depending symmetric or asymmetric arrangements.

(d) Asymmetrical foundation arrangements require larger foundations than symmetrical arrangements

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Appendix A: Obtaining kv,RCKA parameter β is introduced to simplify algebraic calculations as shown in A.1

(A.1)

The first derivative of Eq.2 can then be taken as shown in A.2

(A.2)

Hence, equation of the line of the slope is calculated as shown in A.3

where kv,1 is the point on the curve on which the tangent lies. The initial point may be taken as 0 (A.3)

Hence Eq A.2 can be substituted in A.3

(A.4)

Substituting f0 with ffb equation A.4 can be written as

(A.5)

Cancelling ffb from both sides and solving for kv

(A.6)

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Appendix B: Minimum vertical stiffness kv,SW for symmetric and Asymmetric triangles

For symmetric triangle (ST):

In a similar manner to Eq.9 of τ is taken as

(B.1)

For the vibrations about the x-x’ plane and sing Castigialiano’s theorem, the rotational stiffness can be calculated from the vertical stiffness of the foundation.

(B.2)

(B.3)

(B.4)

Since it is symmetric, solving for the vibration in the orthogonal direction (y-y’_ will yield the same result

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For asymmetric triangle (AT)

For the vibration about the x-x’

(B.5)

(B.6)

For the vibration about the y-y’

(B.7)

(B.8)

Clearly we must satisfy the larger requirement in Eq. B.6

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Abstractepubs.surrey.ac.uk/851802/1/SRI_Openaccess_Minimum... · Web viewIn the formulation, the jacket and wind turbine tower are modelled as Euler-Bernoulli beams and the foundations