Design Methods for Offshore Wind Turbines at Exposed Sites (OWTES)

Transcription

1 Design Methods for Offshore Wind Turbines at Exposed Sites (OWTES) Sensitivity Analysis for Foundations of Offshore Wind Turbines OWTES Task 4.1 OWEC Tools Task B.1 - B.2 Ir. M.B.Zaaijer (TUDelft, editor) 21 March, 2002 This contribution to the OWTES project has been carried under contract JOR3-CT awarded by the European Union. This work has been co-financed by NOVEM under contract SW Delft University of Technology, Section Wind Energy Stevinweg 1, 2628 CN, Delft, The Netherlands Phone , Fax

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3 Page i Summary An important aspect in the prediction of extreme- and fatigue loading of the support structure of an offshore wind energy converter (OWEC) is its dynamic response. In this study the first and second natural frequencies of the support structure are taken as the primary indicators of dynamic response. The work presented in this document focuses on the two following issues relating to the prediction of the natural frequency in wind turbine design codes: 1. Sensitivity of the predicted natural frequency to variations in input parameters and foundation models, 2. Comparison of predicted and measured natural frequencies. For the sensitivity study five different support structure concepts are selected, all designed for a 3 MW wind turbine. For the comparison of predicted and measured natural frequencies design data is collected for the wind farms Lely and Irene Vorrink in the Dutch IJsselmeer. It is emphasised here that many conclusions drawn from this study are only directly applicable to the reference cases considered and that interpretation of the results in a general perspective needs careful consideration of the assumed conditions. The parameter sensitivity shows that the uncertainty of the first natural frequency of the analysed support structures with pile foundations will be in the order of 4%. The sensitivity of the tripod and lattice tower was smaller than that of the tubular tower. The natural frequency of the tubular tower decreased by less than 5% for a scour hole of 2 times the pile diameter. The uncertainty of the first natural frequency of the analysed gravity base structures appears to be in the order of 20%. However, the analysis of the GBS is based on a rather simple foundation model and a conservatively large variation of soil parameters. The design process of gravity base structures will require a more thorough analysis of variations within a wind farm. Several foundation models were compared. Three of these models have a different basis: a finite element model based on stress-strain curves, a linear elastic model developed by Randolph and an effective fixity depth model. The finite element model and the linear elastic model give comparable results for the investigated nearly uniform soil. The uncertainty in the assumed effective fixity depth results in a large uncertainty in the predicted natural frequency. The use of the effective fixity depth model without a priori knowledge of the foundation is strongly discouraged for analysis beyond an initial guess of support structure behaviour. The first and second natural frequency obtained with a stiffness matrix with coupled lateral behaviour gives very good correspondence with the finite element foundation model. The use of uncoupled springs for lateral displacement, rotation and axial displacement is not recommended. For the tripod and lattice tower the lateral flexibility of the piles appeared to be much more important than the axial flexibility. The predicted natural frequencies of five turbines in the wind farm Irene Vorrink are within approximately 5% of the measured frequencies. The depth of the first stiff soil layer appears to be an important parameter. One of the turbines in the wind farm Lely showed a large difference of 9% between predicted and natural frequency. The other turbine showed an even much larger, inexplicable difference. Comparison of measurements of the current study with a previous study revealed no substantial change of natural frequency. This study has focussed on the influence of the foundation on the natural frequency. Further work must reveal the influence of the foundation on other aspects of dynamic response, in particular fatigue damage.

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5 Page 1 Foreword Results are reported for Task 4.1.A B of the project OWTES commissioned by the European Union and for Task B.1 - B.2 of the project OWEC Tools commissioned by NOVEM. The work can be characterised as an analysis of dynamics of support structures of offshore wind turbines, focussing on foundation influences. A working group consisting of the following persons has contributed to this work: TU Delft Michiel Zaaijer (editor), Toni Subroto Louis Speet Jan Vugts Ruud van Rooij FUGRO Engineers b.v. M. van der Kraan Steve Kay John Brown Hydrocarbons Limited Bernie Smith Ussam Mirza Paul Heywood The cooperation of NUON during the measurement activities at the wind farms Irene Vorrink and Lely and their provision of information are very much appreciated. The report has been published by TUDelft, Section Wind Energy. Delft, 12 March, 2003

6 Page 2 List of Symbols D diameter of circular gravity base structure or pile [m] D r soil relative density [-] E modulus of elasticity [N/m 2 ] E pile equivalent modulus of elasticity [N/m 2 ] p F lateral force on pile head [N] G shear modulus of elasticity [N/m 2 ] I second moment of inertia of pile cross-section [m 4 ] K coefficient of earth pressure at rest [-] 0 L c critical pile length [m] M moment on pile head [Nm] N bearing capacity coefficient [-] q c u undrained shear strength [N/m 2 ] k stiffness matrix m rate of change of soil shear modulus with depth [-] q cone penetration test tip resistance [N/m 2 ] 0 c r pile outer radius [m] s shape correction factor for bearing capacity [-] q u horizontal translation of pile head [m] z depth below the seabed [m] ϕ friction angle [ ] ν Poisson s ratio [-] ρ soil density [kg/m 3 ] σ v0 vertical effective soil pressure [N/m 2 ] θ rotation of pile head around horizontal axis [rad]

7 Page 3 Table of Contents 1 INTRODUCTION DESCRIPTION OF THE WIND FARMS LELY Site specification and Layout Turbines IRENE VORRINK Site specification and Layout Turbines TYPICAL NORTH SEA SITES AND TURBINES Site specifications Reference Turbine Other Turbines NUMERICAL MODELS FOR STRUCTURAL PROPERTIES SOIL PROPERTIES Shear Modulus of Elasticity Linearly Increasing Shear Modulus Scour Cone Penetration Tests STRUCTURE-SOIL INTERACTION Winkler Assumption and Stress-Strain Curves for Piles Rigid Gravity Base Foundations FOUNDATIONS Finite Element Models Effective Fixity Length Stiffness Matrix Uncoupled Springs at Seabed Level STRUCTURE Modelling approach Structural Elements ENVIRONMENT SENSITIVITY ANALYSIS OF NATURAL FREQUENCY PREDICTION INTRODUCTION Modelling Approach Types of Analyses PARAMETER SENSITIVITY Selected Parameter Variations Results DIFFERENT SITES LOADING CONDITIONS DIFFERENT MODELS VERIFICATION OF NATURAL FREQUENCY PREDICTION INTRODUCTION FINITE ELEMENT MODEL TO PREDICT NATURAL FREQUENCY MEASUREMENT SET-UP AT LELY AND IRENE VORRINK Instrumentation Data Processing RESULTS OF PREDICTIONS AND MEASUREMENTS ADDITIONAL MEASUREMENT RESULTS Soil aging effects Damping ratio CONCLUSIONS REFERENCES...44 APPENDIX A: SENSITIVITY OF THE 1 ST NATURAL FREQUENCY...45 APPENDIX B: NATURAL FREQUENCIES FOR DIFFERENT FOUNDATION MODELS...50

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9 Page 5 1 Introduction An important aspect in the prediction of extreme- and fatigue loading of the support structure of an offshore wind energy converter (OWEC) is its dynamic response. The predictability of this dynamic response differs in some important aspects from that of platforms for the offshore oil industry and of onshore wind energy converters. The natural frequency of an OWEC is wedged between different excitation frequencies, whereas the natural frequency of a fixed platform for the offshore oil industry is usually designed to be well above the wave excitation frequencies. The geometry and dimensions of offshore foundations differ from typical onshore solutions, resulting particularly in an expected larger influence of soil characteristics for the slender monopile foundation. The first and second natural frequencies of the support structure are taken as the primary indicators of dynamic response. The work presented in this document focuses on the two following issues relating to the prediction of the natural frequency in wind turbine design codes: 1. Sensitivity of the predicted natural frequency to variations in input parameters and foundation models, 2. Comparison of predicted and measured natural frequencies. The sensitivity of the system s natural frequency to variation of several parameters is studied in order to assess the accuracy of predictions of dynamic behaviour as well as variations between locations and during the OWEC lifetime. Also, different models of pile foundations are assessed. For the sensitivity study five different support structure concepts are selected, all designed for a 3 MW wind turbine. The five concepts are: 1. tubular tower on a monopile 2. tubular tower on a gravity base structure 3. tripod and tubular tower with piles 4. lattice tower with piles 5. lattice tower with a gravity base structure For the comparison of predicted and measured natural frequencies design data is collected for the wind farms Lely and Irene Vorrink in the Dutch IJsselmeer. Two wind turbines in the wind farm Lely and five wind turbines in the wind farm Irene Vorrink were equipped with accelerometers to collect data during normal operation and transients. FUGRO Engineers B.V. performed an introductory study that is reported in [6]. John Brown Hydrocarbons Limited (JBH) reviewed the work and performed additional studies that are reported in this document. Chapter 2 introduces the wind farms and support structures, followed by an overview of the applied modelling techniques in Chapter 3. The sensitivity analysis is presented in Chapter 4 and Chapter 5 gives the results of the predictions and measurements for the actual wind turbines. Conclusions are given in Chapter 6.

10 Page 6 2 Description of the Wind Farms 2.1 Lely Site specification and Layout The wind farm Lely is situated in the IJsselmeer in the Netherlands off the coast near Medemblik. It consists of four wind turbines that are positioned parallel to the shoreline. The location and layout are shown in Figure 1. More information about the wind farm can be found in [7]. Figure 1 Location and layout of the wind farm Lely The average water depth at turbines A1, A3 and A4 is between 5 and 6 meters. At location A2 there is a depression in the seabed, due to dredging in the past. The average water depth at A2 is approximately 10 m. The typical soil profile at A1, A2 and A4 is given in Figure SOFT CLAY SAND [d] -19 STIFF CLAY SAND [vd] Figure 2 Typical soil profile for the wind farm Lely

11 Page 7 A dense sand is overlain with soft clay. The piles penetrate into the stiff clay layer, but do not reach the very dense sand. At location A2 the upper layer is also soft clay, so effectively the layer of dense sand is somewhat smaller than at the other locations Turbines The wind farm Lely consists of 4 turbines of type NW41, made by NedWind. The two bladed turbines have a rated power of 500 kw each, a rotor diameter of m and a constant rotational speed of 32 RPM. The turbines were commissioned on June 24, 1994 as the first offshore wind farm in the Netherlands. The turbines are mounted on conical tubular steel towers, with a cylindrical steel monopile foundation. The main dimensions of the support structures of turbine A2 and A3 are shown in Figure 3. The tower of turbine A2 has the same diameter as the monopile and is connected with a flange. To connect the tower of turbine A3 to its wider foundation pile the upper 1.5 m of the foundation pile was filled with concrete. Figure 4 shows a picture of the wind farm. 32,000 kg 32,000 kg 1.9 m x 12 mm 1.9 m x 12 mm 39.0 m 37.9 m Flange 20.4 m 39.0 m 37.9 m Flange 20.4 m 3.2 m x 12 mm 3.2 m x 12 mm 26 m 12.1 m 2.5 m Mean Sea Level 3.2 m x 35 mm 28 m 7.1 m 2.5 m Mean Sea Level 3.7 m x 35 mm Mudline Mudline Figure 3 Main dimensions of support structures - Left: A2 - Right: A3

12 Page 8 Figure 4 Wind farm Lely 2.2 Irene Vorrink Site specification and Layout The wind farm Irene Vorrink is situated in the IJsselmeer in the Netherlands off the coast near Dronten and Lelystad, as shown in Figure 5 and Figure 6. Figure 5 Location of the wind farm Irene Vorrink The first part of the wind farm consisted of 19 turbines parallel to the north coast. Later, 9 turbines were added at the west side, where the coast bends to the south. For the purpose of

13 Page 9 this study the turbines were renumbered, starting at the west side. Thus, the first 9 turbines have the numbers shown in Figure 6. For the remaining 19 turbines the number shown in Figure 6 must be raised with 9. As can be seen the turbines are located close to the shore. Each turbine is connected to the shore with a bridge for accessibility. Figure 6 Layout of the wind farm Irene Vorrink The average water depth at the turbine locations is approximately 5 m. A typical profile of the soil is shown in Figure 7. Layers of dense and very dense sand are overlain with soft clay and silt, at some locations containing a thin intermediate sand layer. At the location of turbine 3 the layer of soft clay is approximately 3 m thicker SILT SAND [d] SOFT CLAY SAND [d] SAND [vd] SAND [d] -22 STIFF CLAY -26 Figure 7 Typical soil profile for the wind farm Irene Vorrink Turbines The turbines in the wind farm Irene Vorrink are of type NTK 600, made by the Nordtank Energy Group. The turbines have a rated power of 600 kw each, a rotor diameter of 43 m and a constant rotational speed of 27 RPM. The first 19 turbines were commissioned in The turbines are mounted on conical tubular steel towers, with a cylindrical steel monopile foundation. The main dimensions of the support structures are shown in Figure 8. Figure 9 shows a picture of the wind farm.

14 Page 10 35,700 kg 1.7 m 8 mm 4.6 m 7 m 7 m 10 mm 12 mm 14 mm Flange 23.5 m 48.8 m 48.7 m 14 mm m m 2.2 m 3.5 m Mean Sea Level 3.5 m x 28 mm (tips 35 mm) Mudline Figure 8 Main dimensions of support structures

15 Page 11 Figure 9 The wind farm Irene Vorrink, seen from one of the turbines 2.3 Typical North Sea Sites and Turbines Site specifications FUGRO selected three sites in the North Sea with typical North Sea soil conditions [6]. These sites are indicated by R, IJ and A. The approximate locations and soil conditions of these sites are shown in Figure 10. The mean sea level at the sites is taken between 15 and 25 m, depending on the type of support structure that is analysed SAND [m] SAND [m] SAND [vd] SAND [d] SAND [vd] SOFT CLAY SAND [d] SOFT CLAY SAND [vd] SAND [d] -22 STIFF CLAY SAND [d] -26 SAND [vd] Location R Location IJ Location A Figure 10 Locations and soil profiles of reference sites

16 Page Reference Turbine The reference turbine for parametric studies is based on the design solution of the Opti-OWECS project [5]. The turbine has a rated power of 3 MW and is supported by a monopile foundation. The main dimensions of the support structure and the rotor-nacelle mass are defined in Figure 11. This turbine and support structure is considered to be a realistic option for application at North Sea sites. As shown, the water depth for this support structure is 21 m. 3.5m Rotor/nacelle mass 130,000 kg x m 4.6m 2800Ø x m 40.0m 5.0m 15.0m MSL Flange Tower Boat Landing 2800Ø x Ø x Ø x Ø x m 12.0m 12.0m 15.4m 5.0m 2500Ø x m 21.0m Pile Scour Protection J-Tube x Ø x m 37.0m (25.0m Penetration) Figure 11 Main dimensions of the support structure of the reference turbine Other Turbines Next to the reference turbine with a monopile foundation several other support structures are defined. Support structures are defined with the following concepts:

17 Page a cylindrical tubular steel tower with a monopile foundation (the reference turbine), 2. a cylindrical tubular steel tower with a gravity base structure foundation, 3. a tripod with a cylindrical tubular top section with a pile foundation, 4. a lattice tower with a pile foundation, 5. a lattice tower with a gravity base structure at each of its three legs. The definitions of these support structures are based on design studies and are therefore considered to be realistic and to show typical behaviour for each concept. Because the support structures are obtained from different design studies they are not designed for the same water depth and environmental conditions. However, it is also realistic that different concepts will be applied at different locations, e.g. monopiles in shallow water and lattice towers in deeper water. All support structures are designed for a turbine with a nominal power of 3 MW. Figure 12 illustrates the support structures that are defined. A description of each support structure is given below Figure 12 Schematic representation of concepts of support structures Ad 1: Tubular tower on a monopile This is the reference turbine that is described in the previous section. Ad 2: Tubular tower on a gravity base structure This support structure is designed in the Opti-OWECS project [5]. It is designed for the Baltic Sea, for a water depth of 15 m. The main dimensions are given in Table 1. Table 1 Main dimensions of tubular tower on a gravity base structure Gravity base structure Diameter 25 m Height 3.5 m Tubular tower Diameter 4 m - 3 m in steps Wall thickness m m in steps Height of rotor axis 54.5 m above MSL Water depth 15 m Rotor-nacelle mass kg Ad 3: Tripod and tubular tower with piles This support structure is designed by Heerema and was used in a study of the simulation of offshore wind turbines under stochastic loading [11]. It is designed for North Sea conditions, for a water depth of 25 m. The main dimensions are given in Table 2.

18 Page 14 Table 2 Main dimensions of tripod and tubular tower with piles Piles Diameter 1.2 m Wall thickness 0.02 m Penetration 50 m Tripod Central column 4.5 m x m Braces 1.75 m x m Foundation radius m Tubular tower Diameter 4 m - 3 m in steps Wall thickness m m in steps Height of rotor axis 69.2 m above MSL Water depth 25 m Rotor-nacelle mass kg Ad 4: Lattice tower with piles This support structure is designed in the Opti-OWECS project [5]. It is designed for North Sea conditions, for a water depth of 25 m. The original design is founded on three gravity bases, which are replaced by piles. The main dimensions are given in Table 3. Table 3 Main dimensions of lattice tower on piles Piles Diameter 1.2 m Wall thickness 0.02 m Penetration 50 m Lattice tower Base width 50 m (between leg centres) Height of rotor axis 61 m above MSL Water depth 25 m Rotor-nacelle mass kg Ad 5: Lattice tower with gravity base structures This support structure is designed in the Opti-OWECS project [5]. It is designed for North Sea conditions, for a water depth of 25 m. The main dimensions are given in Table 4. Table 4 Main dimensions of lattice tower on gravity base structures Gravity base structure Diameter 9 m Height 2 m Lattice tower Base width 50 m (between leg centres) Height of rotor axis 61 m above MSL Water depth 25 m Rotor-nacelle mass kg

19 Page 15 3 Numerical Models for Structural Properties 3.1 Soil Properties Shear Modulus of Elasticity Relation between shear modulus of elasticity and modulus of elasticity The soil shear modulus is not given as input parameter in the soil profile data and has to be derived from other soil properties. The soil shear modulus, G, is related to the modulus of elasticity, E, using E G =, (1) 2 1+ν ( ) where ν is Poisson s ratio. This can be found in many textbooks, e.g. [17]. Relation between modulus of elasticity and vertical effective soil pressure Several suggestions are given in literature to express the modulus of elasticity in terms of the vertical effective soil pressure, σ v0. Based on work by Baldi et al. [2] FUGRO [6] proposed the approximation D 1+ 2 K e v0 r E σ, (2) 3 where D r is the soil relative density and 0 K is the coefficient of earth pressure at rest. Analysis of data in [3] gives a similar effect of the vertical effective soil pressure, being: 0.5 ~ G ~ v0 E σ. (3) Reanalysis of FUGRO s approach with a little less approximation resulted in the relation 0.8 E ~ σ v0. (4) Verruijt [18] suggests a linear relation between modulus of elasticity and vertical effective soil pressure according to: E ~ σ v0. (5) Relation between modulus of elasticity and friction angle According to FUGRO the modulus of elasticity depends linearly on the pile tip resistance, q. Verruijt [18] suggests the following relationship for the pile tip resistance: c q c ~ s N, (6) q q which can be related to the friction angle, ϕ, using

20 Page 16 s q N q = 1+ sinϕ 1+ sinϕ = e 1 sinϕ π tanϕ. (7) Using a curve fit of the above expressions the relation between modulus of elasticity and friction angle was approximated with 0.14 ϕ E ~ e. (8) Expression for soil shear modulus of elasticity used in this study Combining the previous relationships results in the following general semi-empirical formulation: C 2 σ v0 e G = C ϕ ( 1+ ν ). (9) In this study C 2 = 0.8 was used as an intermediate value. For C 1 the value 68 was used, based on numerical analyses of the shear modulus for gravity base structures for the tubular tower and lattice tower. For clay soils the shear modulus of elasticity is approximated as suggested by FUGRO with G = 100, (10) c u in which c u is the undrained shear strength Linearly Increasing Shear Modulus Randolph s method to analyse pile foundations as described in Section requires an equivalent linearly varying profile of the shear modulus expressed as G = m z, (11) where z is the depth below the seabed and m is the constant of proportionality. The actual shear modulus obtained from the soil profiles varies non-linearly with depth. In the study performed by FUGRO the actual shear modulus profile was approximated with a linearly varying profile according to L c 2 m = G( z) dz. (12) 2 L c o The critical pile length, L c, according to Randolph is given in Section m is solved iteratively, since its value is required in the determination of the critical pile length Scour The effect of scour is modelled as illustrated in Figure 13. The effect of local scour is a reduction of the vertical effective soil pressure that reduces linearly until the overburden reduction depth. Below the overburden reduction depth the effect of local scour vanishes. A typical value for the local scour depth is 1.5 times the pile diameter, although this depends on

21 Page 17 the local current and wave climate. A typical value for the overburden reduction depth is 6 times the pile diameter. Pile 0 Vertical effective soil pressure Seabed General scour depth Local scour depth No scour condition General scour only Local scour condition Overburden reduction depth Figure 13 Scour model Cone Penetration Tests The results of a cone penetration test (CPT) can be used to estimate properties of the soil. Generally, the CPT provides the cone resistance, shaft friction and friction ratio. Table 5 gives the soil type as a function of the friction ratio as proposed in [16]. In [1] a distinction is made between purely cohesive and purely cohesionless soils and this classification is also used throughout this study. The assumed classification is also given in Table 5. Table 5 Soil properties estimated from the friction ratio Friction ratio Soil type Category (-) No data Mud - 1 Sand Cohesionless 2 Loam Cohesive 3-5 Clay Cohesive 8-10 Peat Cohesive For a given soil type typical values of the submerged unit weight can be found in several handbooks. Brinch Hansen s formulation of the bearing capacity of the cone and the cone resistance measured in the CPT are used to obtain the friction angle of cohesionless soils and the undrained shear strength of cohesive soils. In the absence of other data the value 0.01 is used for the strain at 50% of the peak stress for cohesive soils. 3.2 Structure-Soil Interaction Winkler Assumption and Stress-Strain Curves for Piles The axial and lateral resistance of the soil against displacements of the pile is often modelled with non-linear springs. Commonly, three types of springs are considered as shown in Figure 14. The Winkler assumption states that each spring acts independently of the other springs and of pile displacements at other locations. The models for the spring behaviour of the soil that are used in this study are based on the recommendations of the API [1] and summarised below.

22 Page 18 Pile wall External shaft friction (t-z curves) Lateral resistance (p-y curves) Internal shaft friction (t-z curves) Pile plug resistance (Q-z curves) Pile point resistance (Q-z curves) Figure 14 Spring model of pile-soil interaction Lateral Resistance The stress-strain relation that represents the non-linear behaviour of the lateral resistance of the soil against pile displacements is called the p-y curve. For pile behaviour the pressure, p, is often expressed as a force per unit length, rather than as a real pressure. Several methods are proposed to obtain p-y curves from soil and foundation properties. The p-y curves vary for different types of soil, drained or un-drained conditions and cyclic or static loading. Generally, at higher displacements the p-y curves for cyclic loading drop off to lower resistance values than for static loading. The methods suggested by API for cyclic loading conditions correspond to the approach of Matlock [12] for soft clay and the approach of O Neil and Murchison [13] for sands. These methods are used for all types of sand and clay throughout this study. When required, additional information was used from [6] and [3]. Shaft Friction The stress-strain relation that represents the resistance of the soil against axial pile displacements is called the t-z curve and is generally also non-linear. The skin friction, t, is commonly expressed as a force per unit length. The approach recommended by the API uses tabulated values of the skin friction, made dimensionless with the maximum pile-soil adhesion. A different table is used for clays and sands. Pile Tip Resistance The tip resistance - displacement relation is called the Q-z curve and is also non-linear. In the model used in this study one spring is used for the pile plug and one for the circular steel pile tip. For each of these springs the tip resistance is multiplied with the associated area. As recommended by the API the same Q-z curves are used for both sands and clays Rigid Gravity Base Foundations Uncoupled springs, dashpots and inertia, as illustrated in Figure 15, often represent the soil-structure interaction of a gravity base foundation. The derivation of the values for these elements is usually obtained from elastic half-space models of the soil-structure interface that is assumed rigid. As a consequence, the resulting springs are also linear.

23 Page 19 Figure 15 Uncoupled springs, dashpots and inertia for gravity base structure behaviour In the elastic half-space models damping occurs because of radiation to infinity. Since the energy of this radiation is frequency dependent the spring and dashpot parameters are also frequency dependent. Although this frequency dependency is relevant to high frequency machinery, it is less important for the lower natural frequencies of a wind turbine support structure. Kühn [8] showed that the difference between frequency dependent and frequency independent models is small for a specific case of a gravity base foundation for a 3 MW turbine. In this study the frequency independent approach suggested by the API [1] was adopted for the springs. The values for the dashpots and inertia were obtained from the frequency independent approach of Barltrop [3]. The used equations are given in Table 6, where D is the diameter of the circular gravity base structure and ρ is the density of the soil. Table 6 Model parameters for gravity base foundations Spring stiffness Viscous damping Inertia Rocking Horizontal Vertical G D 3 3 ( 1 ν ) G D ( 1 ν ) ν 2G D 1 ν 4 D D D ρ G ( 1 ν ) ρ G ( 2 ν ) ρ G ( 1 ν ) ρ D ( 1 ν ) ρ D 3 ( 2 ν ) ρ D ( 1 ν ) 3.3 Foundations Finite Element Models A comprehensive finite element model to evaluate foundation behaviour is composed of structural elements for the foundation and soil elements for the environment. The boundary conditions at the soil-structure interface are used to formulate the constraints for the coupling of the soil elements and the structural elements. Since the extension of the soil is infinite, when compared to the structural dimensions, some kind of boundary elements must be defined. For static analysis the boundary elements can simply be soil elements connected to the rigid outside world. However, for dynamic analysis suppression of reflections of radiation at the soil boundary has to be considered.

24 Page 20 This type of model requires very many degrees of freedom, particularly for a reasonably accurate representation of the soil behaviour. Section 3.2 presented models to lump the properties of the soil-structure behaviour in spring, dashpot and inertia elements for piles and rigid gravity base foundations. These models greatly reduce the number of degrees of freedom, which make them much more practical for dynamic analysis. Therefore, the use of stress-strain curves under Winkler s assumption or the lumped properties for gravity base foundations are preferred, unless they are unsuitable. Examples of situations where the models proposed in Section 3.2 are expected to be unsuitable are the analysis of relatively flexible gravity base structures, geometrically complex foundations and foundations under combined loading outside the linear region of the stress-strain curves. Although finite element models with soil elements could be a good reference for other foundation models it is considered to be outside the scope of this study to implement these models. Whenever a reference is required in this study the finite element models using the lumping methods proposed in Section 3.2 will be used for this purpose Effective Fixity Length A simple model of the clamping effect of the soil is replacement of the soil by rigid clamping of the pile at an effective depth below the seabed, as shown in Figure 16. This model is sometimes used for (preliminary) dynamic analysis in the offshore industry, using tabulated values for the effective fixity length. The values proposed by Barltrop [3] are given in Table 7 as a function of the soil type and pile diameter D, along with values obtained from analysis of an offshore wind turbine support structure [10]. The great advantages of this model are its simplicity and the need of very little information about the soil properties. In the offshore industry the pile heads are often constrained by the space-frame structure, which is quite different from the unconstrained pile head of a monopile foundation. As a result the mode shape for which the effective fixity length model is used is very different for monopiles than for common piles in the offshore industry. Figure 16 Pile-soil model with effective fixity length Table 7 Suggestions for effective fixity length Effective fixity length Stiff clay 3.5 D D Very soft silt 7 D - 8 D General calculations 6 D From measurement of an offshore turbine (500 kw) 3.3 D D

25 Page Stiffness Matrix For pile foundations a stiffness matrix can express the stiffness of the pile-soil system at the seabed. The stiffness matrix gives the forces, F, and moments, M, for displacements and rotations of the pile head. The relevant degrees of freedom of a laterally loaded pile are the horizontal translation, u, in the plane of interest and the rotation, θ, about the horizontal axis perpendicular to this plane. For this case the stiffness matrix, k, is defined by: F k = M k xx θx k k xθ θθ u. (13) θ The advantage of this model is the condensation of foundation properties in a single matrix. This facilitates the exchange of information from the foundation engineer to the system engineer. Both FUGRO and JBH adopted this approach to transfer information from their foundation analysis to TUDelft, who performed the natural frequency calculations for the system. Two methods to obtain the values for the stiffness matrix are given below. Load displacement analysis with p-y curves Equation 13 contains three unknowns in the stiffness matrix, since the off-diagonal elements must be equal. Substitution of the results of a load case analysis into Equation 13 yields two equations. Two more equations are obtained from a second load case analysis. Only one of the last two equations needs to be used to solve the three unknowns. The second load case must be sufficiently different from the first one to give independent results. The analysis can be performed with a pile foundation model with p-y curves. Since the p-y curves are non-linear, the stiffness matrix elements depend on the loading conditions. If the loading conditions of two load cases are similar it is assumed that the stiffness matrix elements are the same for these conditions and the suggested method can be applied. The loading conditions must be representative for the conditions for which the stiffness matrix will be applied. Note that the solution of the load case depends on the order in which the loads are applied, because of the non-linearity. A discussion of this is given in [19]. In FUGRO s study the load cases are defined by the force and moment at extreme loading conditions, with variations of 1% between the two load cases. Randolph elastic continuum model When the pile displacements are small the soil-structure interaction is linear with respect to the stresses. As a consequence, the pile head behaviour is linear with respect to applied loading for small displacements. This can be expressed in a stiffness matrix. Randolph performed dimension analysis and finite element analysis of piles in an elastic continuum to obtain an expression for the pile head flexibility [15]. This resulted in parameterised flexibility matrices for piles in an elastic continuum with a constant soil shear modulus and with a linearly increasing soil shear modulus. The latter is the preferred model for sandy soil, where the soil shear modulus varies with depth and generally increases due to increasing effective vertical soil pressure. The stiffness matrix for Randolph s approach is the inverse of the flexibility matrix he obtained and is given by the following expressions:

26 Page 22 k xx = 4.52 m * 2 ro E p * m r o E * p k xθ = kθ x = 2.40 m ro *, (14) m ro E * p kθθ = 2.16 m ro. * m ro where EI E p = 1, (15) D 4 π 64 * 3 m = m 1 + ν (16) 4 and E is the modulus of elasticity of the pile material, I is the second moment of inertia of the pile cross-section and r 0 is the pile outer radius. The pile penetration depth is not parameterised in Randolph s model. The model has been derived for piles longer that the critical pile length given by 2 9 E p L 2 0 * c = r. (17) m r0 Below the critical pile length pile deflections are negligible and therefore the actual pile length is irrelevant when piles are longer than that. Section describes how the coefficient m, defining the linearly increasing soil shear modulus, was obtained by FUGRO. When a scoured pile is analysed Randolph s model must be applied at the base of the scour pit. To obtain the stiffness matrix at the seabed the pile between the base of the scour pit and the seabed must be considered Uncoupled Springs at Seabed Level The stiffness matrix model of the previous section can be simplified to uncoupled stiffness represented by springs for the relevant degrees of freedom. For a laterally loaded pile this model is shown in Figure 17 with two springs at the seabed. Figure 17 Pile model with uncoupled lateral and rotational spring at seabed To obtain the stiffness of the spring elements the two approaches illustrated in Figure 18 can be applied.

27 Page 23 Applied force/moment F M θ u Forced displacement/rotation u θ F M Ignore θ Ignore u Ignore M Ignore F Figure 18 Two methods to obtain uncoupled lateral and rotational springs for piles In the first approach on the left-hand side the stiffness is obtained by application of a force or moment, without constraining the response. The response will consist of a rotation and a translation of the pile head, but only the corresponding degree of freedom will be considered. This method will be referred to as the Force method. In the second approach on the right-hand side a deflection is applied to the pile head and the corresponding required force is used. The force corresponding to the other degree of freedom is ignored. This method will be referred to as the Displacement method. The resulting stiffness is equivalent to the diagonal terms of the stiffness matrix for the same load conditions. 3.4 Structure Modelling approach Throughout this study a finite element model of the support structure is used to analyse the natural frequencies. The finite element model of the structure above the seabed can be combined with any of the foundation models given in Section 3.3. FUGRO applied an analytical model called ANAMOL, which gives the natural frequencies of the first two bending modes for a cantilever beam with a rotational spring and a top mass. This model gives fairly good results compared with a finite element model of the same configuration, but it is insufficient for the more complicated geometry of the actual structure. Furthermore, ANAMOL is only developed for a rotational spring as foundation model Structural Elements In the finite element model the following types of elements have been used: cylindrical pipe, submerged cylindrical pipe, dot mass, non-linear spring, symmetric stiffness matrix, symmetric damping matrix.

28 Page 24 The cylindrical pipes are beam elements that model the load carrying parts of the support structure. The submerged pipes incorporate the possibility to apply hydrodynamic loading and to account for the effects of the water surrounding the pipe, as discussed in Section 3.5. The dot mass is an element with mass and moment of inertia for 6 degrees of freedom. It is used for the rotor-nacelle assembly, fittings and the mass effect of the gravity base structure-soil interaction. A larger density of the cylindrical pipes models the mass of cables and ladders. The non-linear springs are used for the pile-soil interaction. For a modal analysis these springs are linearised about their neutral position. The stiffness and damping matrices are used for the lumped characteristics of the gravity base structure-soil interaction. 3.5 Environment The hydrodynamic force per unit length on a cylinder in motion according to Morison [4] is given by the equation π 2 π 2 1 f = CM ρ D aw CM D & x c + CD D vw x& c vw x&, 1 ρ ρ,, c ( ) ( ) where x c is the lateral coordinate of the pile (most other symbols in this expression are not relevant for the discussion below and therefore not explained). The second term on the right-hand side of this expression is proportional to the acceleration of the cylinder. The proportionality factor is referred to as the water added mass, because mathematically this force is equivalent to that of an additional mass attached to the cylinder. For a circular cylinder the water added mass theoretically equals the mass of the water displaced by the cylinder. This corresponds with C M = 2, which is a commonly applied value. In the finite element model the water added mass is included with the structural mass for the parts of the structure between the seabed and the still water line. Water may enter the submerged part of the support structure during installation, through the soil or through holes in the structure. For flooded members the entrained water is treated as an additional mass in the model. Damping and pressure effects of the water are not modelled. Due to marine growth the outer diameter of the submerged parts increases and extra mass is added to the structure. Marine growth is modelled as an insulation layer without stiffness or damping with a density of 2200 kg/m 3. Thus, the effect of the diameter increase on the water added mass, the mass increase and the hydrodynamic force on the cylinder are included in the model.

29 Page 25 4 Sensitivity Analysis of Natural Frequency Prediction 4.1 Introduction Modelling Approach In the sensitivity analysis the support structures that are described in Section are modelled according to Section 3.4. Pile foundations were modelled according to Section and 3.3.1, unless specified otherwise. The soil-structure interaction of gravity base structures is modelled as described in Section The soil profiles that are shown in Section are used and unknown soil properties were obtained using the relations of Section 3.1. For the submerged parts of the structures the water added mass is taken into consideration. Only for the piled monotower the submerged part is assumed to be flooded and the entrained water is included in the model. In the reference situation no marine growth is assumed. The support structures with a pile foundation have a pile length of 50 m below the seabed. The length of the piles is based on a pre-analysis of the effect of pile length on dynamic behaviour. This effect is shown in Figure 19, for the first and second bending mode Relative natural frequency (-) Lattice tower Tripod tower Mono tower 1st Bending mode 2nd Bending mode Pile penetration length (m) Figure 19 Variation of natural frequency with pile penetration length The smallest pile lengths that are plotted in the graphs of Figure 19 are required to obtain sufficient lateral and axial bearing capacity for static loading (without safety margins!). For increasing pile lengths the natural frequencies increase, as the foundation gets stiffer. Somewhere, the natural frequencies reach a limit. At this point increasing the pile length no longer influences the dynamic behaviour, as the lower section of the pile is not moving. Piles with 50 m penetration are assumed to have the same dynamic behaviour as infinitely long piles, even for reduced soil-structure stiffness. As a consequence, the sensitivities that are assessed in the next sections cannot be avoided by using longer piles and are the minimum sensitivities that need to be anticipated.

30 Page Types of Analyses The following types of analyses were performed: 1. Parameter sensitivity 2. Site dependency 3. Loading conditions 4. Different models These analyses are described briefly below. The results of the analyses are given in the next sections. Ad 1: Parameter sensitivity The designer of a support structure for an OWEC has to consider many variations to parameters that influence the system s natural frequencies. The causes of the variations that are assessed in this study are: Uncertainty: Spread in a parameter due to uncertainty in its determination. Lifetime: Change of several parameters during the lifetime of the OWEC. Location: Variation of e.g. soil parameters and water depth within a wind farm. The sensitivity analysis has been performed with one-dimensional parameter variations, with all other parameters at their reference value. Each variation consisted of 5 steps, including the extreme values of the parameter range and its reference value. Ad 2: Site dependency The variations of parameters within one wind farm are assessed in the parameter sensitivity analysis. The variations between different sites or in a highly non-uniform site may be too large to use this approach. Typical variations of the natural frequencies for different sites in the North Sea are assessed from the differences between the three sites of Section Very large variations in environmental conditions, water depth or morphology may require adaptation of the support structure designs. This has not been considered in this study. Ad 3: Loading conditions The structure-soil interaction of pile foundations is non-linear. As a result, the stiffness of the pile head depends on the loading conditions. In this study the secant stiffness is assessed and the difference with the tangent stiffness is illustrated in Figure 20. To analyse the effect of the variation in secant stiffness on the natural frequency FUGRO determined the pile head stiffness matrix for several loading conditions. The lateral load and bending moment were increased simultaneously in steps of 10% up to the extreme loading conditions of the wind turbine. The pile head stiffness matrices are used as a foundation model according to Section to obtain the natural frequencies. Load case Stress Tangent linearisation Secant linearisation Strain Figure 20 Difference between secant and tangent linearisation

31 Page 27 Ad 4: Different models The community of soil mechanics has produced a large variety of models for piled and gravity base foundations. Which model can be used best depends on many things, such as the application, the environment and the properties that are investigated. Particularly in early phases of the design it is desirable to use simple models with few degrees-of-freedom and little information of soil conditions. Furthermore, it is practical to know whether accurate models for foundation behaviour are required. Therefore, the foundation models presented in Section 3.3 are compared. This analysis is only performed for pile foundations. The model that has been implemented for the gravity base structure is fairly simple and analysis of more complex models is outside the scope of this project. However, the large sensitivity of the GBS to soil parameters suggests that accurate soil measurements and more detailed models may be required for good predictions of dynamic behaviour. 4.2 Parameter Sensitivity Selected Parameter Variations The selected parameters, their variation and reference value are given in Table 8. The values are obtained from a brief literature survey and are merely indicative. For an actual project more precise values can and must be obtained, based on geophysical, geotechnical, turbine and support structure data. Some environmental and structural parameters are selected as well, to provide insight in the relative importance of the foundation sensitivities. Some selected parameters are irrelevant to some support structure concepts. Note that pile penetration is not selected as a parameter, since the influence of pile length on the natural frequency was studied separately and the pile length was chosen to have negligible influence (see Section 4.1.1).

32 Page 28 Table 8 Parameter variations and reference values Uncertainty Location variation Lifetime variation Reference value Soil (cohesionless) Effective soil unit weight ± 10% ± 10% Location IJ Friction angle ± 10% ± 10% Location IJ Coefficient of lateral earth pressure Poisson s ratio Shear modulus of elasticity factor 5 factor 10 factor 1-5 Section Initial modulus of subgrade reaction factor 2 factor 2 Related to friction angle [1] Position of characteristic soil ± 1 m ± 5 m Location IJ layer transition General scour -2 m - 0 m 0 Local scour depth 0-2D 0 Depth of postholing gap 0-3D 0 Foundation Pile diameter ± 0.1% Section Pile wall thickness ± 0.5% Section GBS radius ± 0.1% Section GBS mass ± 0.1% Section Environment Marine growth 0-50 mm 0 Sea level ± 3 m (tide) Section Water depth at installation ± 3 m - Section (MSL) Topside Rotor/nacelle mass ± 0.1% ± 10% ± 10% Section Fittings mass (boat landing, access platform, etc.) ± 0.1% 1000 kg 15 m above MSL Cable and ladder mass ± 0.1% 100 kg/m Diameter ± 0.1% Section Wall thickness ± 0.5% (Corrosion) Section System Vertical position alignment ± 0.1 m Section Results As an example, the sensitivity of the natural frequency of a tubular tower on a monopile for the friction angle of the soil is shown in Figure 21. Typically, the natural frequency is not linearly dependent on soil parameters. The kink at the left is caused by the assumption that the friction angle will not be below 29. Also typically, the first natural frequency is least sensitive and the second natural frequency is most sensitive to the foundation behaviour. This is caused by the relatively small deflections of the foundation for the first mode shape and the relatively high deflections for the second mode shape.

33 Page Sensitivity (%) 0-5 Fore-aft bending mode: Deviation of friction angle (% of maximum uncertainty) Figure 21 Natural frequency sensitivity for friction angle Tubular tower on monopile 3 6 Appendix A tabulates the effect of parameter variation on the first natural frequency. The most important sensitivities of the different support structure concepts are given below. Tubular tower on a monopile The natural frequency of the first bending mode of the tubular tower on a monopile was found to be Hz in the reference situation. The main sensitivities of this natural frequency are presented in Table 9. Table 9 Most important natural frequency sensitivities for tubular tower on a monopile Uncertainty Location (in farm) Lifetime Soil 4% 4% 6% Foundation 0.06% - - Environment - 0.1% 0.1% Structure 0.02% 4% 4% The friction angle of the soil causes the largest uncertainty and variation within the farm. The largest variation during the lifetime is caused by the post-holing gap. The relatively large sensitivity to structural parameters is caused by the assumed large variation in rotor/nacelle mass. Avoiding differences in the configurations of the turbine(s) can reduce this sensitivity, since possible variation of components from different suppliers has led to the assumed mass variation of 10%. Tubular tower on a gravity base structure The natural frequency of the first bending mode of the tubular tower on a gravity base structure was found to be Hz in the reference situation. This natural frequency is higher than that of the tubular tower on a monopile. This difference is mainly caused by the smaller water depth and the different tower design, rather than by the different foundation. The main sensitivities of the natural frequency are presented in Table 10.

34 Page 30 Table 10 Most important natural frequency sensitivities for tubular tower on a gravity base structure Uncertainty Location (in farm) Lifetime Soil 19% 35% 4% Foundation 0.01% - - Environment % 0.03% Structure 0.2% 4% 4% The sensitivity to soil parameters is caused by the shear modulus of elasticity and is very large. Using more detailed models and more detailed and precise information about the soil may reduce the uncertainty. However, the variation between several locations within the wind farm demonstrates that the gravity base is inherently more sensitive to soil parameters. As in the case of the tubular tower on a monopile the sensitivity of structural parameters is caused by the variation of rotor/nacelle mass. Tripod with piles The natural frequency of the first bending mode of the tripod with piles was found to be Hz in the reference situation. The main sensitivities of this natural frequency are presented in Table 11. Table 11 Most important natural frequency sensitivities for tripod with piles Uncertainty Location (in farm) Lifetime Soil 0.9% 0.9% 0.7% Foundation <0.01% - - Environment % 0.01% Structure 0.1% 3.2% 3.2% This case is relatively insensitive to variations. The uncertainty and variation of the friction angle within the farm are dominant, but less than 1%. This case is also insensitive to variation of the general scour, which is the dominant factor during the lifetime of the support structure. The largest variation of the natural frequency is caused by the variation in the rotor/nacelle mass. This can be reduced, as discussed for the tubular tower on a monopile. Lattice tower with piles The natural frequency of the first bending mode of the lattice tower with piles was found to be Hz in the reference situation. The main sensitivities of this natural frequency are presented in Table 12. Table 12 Most important natural frequency sensitivities for lattice tower with piles Uncertainty Location (in farm) Lifetime Soil 3% 3% 3% Foundation 0.01% - - Environment % 0.04% Structure 0.04% 4% 4% This lattice tower has a moderate influence of the uncertainty and variation of the friction angle within the farm, as well as of the general scour depth. Again, the largest structural influence is caused by the rotor/nacelle mass.

35 Page 31 Lattice tower with a gravity base structure The natural frequency of the first bending mode of the lattice tower with a gravity base structure was found to be Hz in the reference situation. The main sensitivities of this natural frequency are presented in Table 13. Table 13 Most important natural frequency sensitivities for lattice tower with a gravity base structure Uncertainty Location (in farm) Lifetime Soil 23% 38% 7.8% Foundation 0.01% - - Environment % 0.02% Structure 0.04% 4% 4% As for the tubular tower with a gravity base structure the shear modulus of elasticity dominates the sensitivity for soil parameters. The variations are even larger in this case, whereas the variations of the lattice tower with piles were smaller than those of the tubular tower on a monopile. Natural frequency of second bending mode The sensitivity of the second natural frequency to soil parameters is 10%-20% for pile foundations and larger than 50% for GBS foundations. The sensitivity to environmental parameters is up to 3.5%, but this will generally be negligible compared with the sensitivity to soil parameters. The sensitivity to foundation and structure parameters is less than 0.1%. 4.3 Different Sites At sites with similar environmental conditions and water depth the same support structure design could be used, provided that its natural frequencies are insensitive to the morphological differences between the sites. Because the variation in soil conditions between different sites is too large to obtain useful results from the one-dimensional parameter sensitivity analysis, the natural frequencies of the support structures have been determined for location R and A of Section It has been checked that the foundations need no modification to provide sufficient bearing capacity and lateral resistance in these soil conditions. The variation of the first natural frequency between different sites is given in Table 14. Table 14 Variation of natural frequency between 3 North Sea sites of Section IJ (reference) A R Hz % Hz % Hz % Tubular tower on monopile Tubular tower on GBS Tripod on piles Lattice tower on piles Lattice tower on GBS The natural frequencies of the support structures with GBS foundation are identical for the reference site and the site with the weak soil. The model for GBS-soil interaction only incorporates the topsoil, which is identical for these two sites up to 12 meters depth. The pile foundations have nearly the same natural frequency at the weaker site, because the upper part of the pile soil interaction is most significant for the first bending mode.

36 Page Loading Conditions The p-y curves have a nearly linear region for small lateral displacements of the pile, but get increasingly non-linear for larger displacement. As a consequence, the stiffness matrix for the pile head is a function of the loading conditions. FUGRO determined the pile head stiffness matrix for the monopile of the tubular tower for increasing moment and lateral force. The moment and force are increased simultaneously in steps of 10% of the maximum of Nm and N, respectively. The maximum moment and force are considered to be an overestimation of the extreme loading condition. The approach adopted by FUGRO to calculate the stiffness matrices effectively uses the secant stiffness of the p-y curves, rather than the tangent stiffness. The stiffness matrices calculated by FUGRO are used as the foundation model for the tubular tower, according to Section The resulting sensitivity of the natural frequency to the loading conditions is given in Table 15. Table 15 Sensitivity of natural frequency to load-level on pile top Load-level 1 st Bending mode 2 nd Bending mode Hz % Hz % Different Models Several foundation models are described in Section 3.3. The foundations of the tubular tower, tripod and lattice tower on piles are modelled with these different approaches for location IJ, resulting in the following models: finite element model based on stress-strain curves and Winkler s assumption, clamping, for several effective fixity depths, stiffness matrix, based on the finite element model in the linear region of the p-y curves and on Randolph s elastic model, uncoupled lateral and rotational springs, both force- and displacement method, based on the finite element model. For the tripod and lattice tower the springs and stiffness matrix based on the finite element model include an uncoupled spring for axial pile behaviour. This model is also split into a purely axial and a purely lateral flexibility to assess the relative importance of axial and lateral behaviour of the piles. Note that only the Randolph stiffness matrix and the effective fixity depth model are independent of the finite element model. The predictions of natural frequencies with these foundation models are compared in Figure 22 and Figure 23. The absolute values are given in Appendix B.

37 Page st natural frequency (normalised) Tubular tower Tripod Lattice tower Winkler FEM (reference) 8D 6D 4D 2D (Seabed) 0D Effective fixity depth FEM-based Randolph Stiffness matrix Force method Displacement method Springs Only axial springs Only lateral stiffness matrix Figure 22 Predicted first natural frequency for several foundation models The Winkler assumption and stress-strain relations for pile-soil interaction are used as a reference. However, note that this model tends to underestimate the stiffness of the soil-pile interaction and results in lower predictions of the natural frequency than obtained from measurements.

38 Page 34 2nd natural frequency (normalised) Tubular tower Tripod Lattice tower Winkler FEM (reference) 8D 6D 4D 2D (Seabed) 0D Effective fixity depth FEM-based Randolph Stiffness matrix Force method Displacement method Springs Only axial springs Only lateral stiffness matrix Figure 23 Predicted second natural frequency for several foundation models Several observations from Figure 22 and Figure 23 are highlighted below: Effective fixity depth Both first and second natural frequency of the tripod and lattice tower correspond with the reference value for an effective fixity depth of approximately 6 times the pile diameter. This is in agreement with the suggested value for general calculations for offshore platforms. This can be expected, since the vibration shape and pile diameter are similar to that of fixed space frame type offshore structures. The effective fixity depth of the tubular tower gives better results for lower values, in the order of 4 times the pile diameter. This is in agreement with earlier studies of monopile behaviour. In [10] this discrepancy is attributed to the larger diameter of the pile, but the different mode shape of the vibration is probably also an important aspect. The results of this model are very sensitive to the selected effective fixity depth, particularly for the tubular tower. The tabulated values of the effective fixity depth as shown in Table 7, Section 3.3.2, show a large variation as a function of soil conditions. Therefore, large inaccuracies of natural frequency must be anticipated for a priori assumed fixity depths. Randolph s linear elastic model The first natural frequencies obtained with Randolph s model correspond within 2.5% with the finite element model. Similar results were found in [6] for location R and A. It must be noted that Randolph s model assumes that the piles are longer than a critical pile length and thus have the same behaviour as infinitely long piles. The lengths of the piles used in this study are also selected to show the same behaviour as infinitely long piles. When the pile length is below the critical pile length the decrease of the natural frequency shown in Figure 19 will not be revealed by Randolph s model.

39 Page 35 Furthermore, the natural frequency with the finite element foundation model is obtained for the linear region of the stress-strain curves. When large deflections are expected the non-linear effect shown in Section 4.4 will not be revealed with Randolph s model, since this is a linear model. Note that part of the error made with Randolph s model for the tripod and lattice tower is caused by the omission of axial pile flexibility. Uncoupled lateral and rotational springs For the tubular tower the springs determined with the force method give closer correspondence of the first natural frequency than those obtained with the displacement method. This can be expected, since the shapes of the pile deflections of the first approach are close to the mode shape of the vibration, whereas those of the second approach are very different. For a similar reason the displacement method gives better results for the first natural frequency of the tripod and lattice tower. For higher natural frequencies the mode shapes of the vibration tend to deviate from the static deflection shapes and give worse results. Axial and lateral behaviour The stiffness matrix that represents the lateral behaviour of the foundation gives less deviation than the model with only axial springs. The close correspondence of the first model with the finite element model indicates that the natural frequencies of the tripod and lattice tower are dominated by the lateral behaviour of the piles. Due to the lateral flexibility of the piles, which is at least an order of magnitude higher than the axial flexibility, the horizontal translation of the tower is a more important contribution to the vibration than its rotation.

40 Page 36 5 Verification of Natural Frequency Prediction 5.1 Introduction The natural frequencies of the support structures of 5 wind turbines in the wind farm Irene Vorrink and 2 wind turbines in the wind farm Lely are measured and estimated from finite element model analysis. The analysed wind turbines in the wind farm Irene Vorrink are: 3, 7, 12, 23 and 28. The analysed wind turbines in the wind farm Lely are: A2 and A3. The wind farms and turbines are described in Section 2.1 and Section Finite element model to predict natural frequency For the analysed wind turbines cone penetration test data was available. This data was used to determine the soil properties and foundation model according to Section 3.1.4, and The model of the structure is made according to Section 3.4. For the submerged parts of the structure the water added mass is taken into consideration and the mass of the entrained water up to the still water line is included. No marine growth has been assumed. The concrete in the upper 1.5 m of the pile of turbine A3 in the wind farm Lely was not modelled. 5.3 Measurement set-up at Lely and Irene Vorrink Instrumentation The movement of the top of the tower was measured by accelerometers in the nacelle, in order to determine the lowest resonance frequencies of the bending mode of the tower. The coordinate system used is the nacelle reference system defined in [14], with the exception that it is fixed in space. The x-axis is the direction of the rotor axis; positive direction is from the rotor to the transmission. The z-axis is the centreline of the tower; positive direction is upwards. The y-axis is according to a right-handed coordinate system. The origin is at the centre of the yaw-bearing system. The coordinate system is illustrated in Figure 24. Figure 24 Coordinate system for the measurements To measure the translation of the nacelle two accelerometers were situated at the bottom of the nacelle, at the same position. In the turbines of the Lely wind farm, the (x, y) coordinates of the accelerometers are (-1.1, 1.0) m. For the accelerometers in the turbines of the Irene Vorrink wind farm the (x, y) coordinates are (0.8, 0) m. The measuring directions are the x

41 Page 37 and the y-directions. To measure the rotation of the nacelle a third accelerometer was placed at the outmost rear side of the nacelle, measuring in the y-direction. The accelerometers are type QA700 of Sundstrand. The sensitivity is 1.3 V/(m/s 2 ) and the frequency range is Hz. The output signals of the accelerometers are filtered with low pass filters with a cut-off frequency of 13 Hz. The output signals of these filters were measured with a 16 bits A/D-converter and a notebook. The sample frequency was 100 Hz. The data acquisition program was written using the program 'Testpoint'. The resolution of this measurement set up is high enough to measure movements of the nacelle, even at very low wind velocities. The following measurements were carried out: To determine the resonance frequencies of the bending mode of the tower, monitoring was done during periods of one hour, with the turbine parked and in production at various wind velocities. To determine the damping ratio of the tower, transient translation movements were measured after a stop. To determine the rotational resonance frequencies transient rotational movements of the nacelle were measured after yaw movement Data Processing Natural frequencies of bending modes from monitoring data Resonance frequencies were determined with a high accuracy from the monitoring measurements. The power spectra of the accelerations were determined. Small frequency steps were obtained by using acceleration data from long measurement periods. The accuracy of each spectrum is increased by taking the average of a high number of spectra. Typically, measurement periods of s are used and 703 spectra are used for averaging. An example of a measured power spectrum is given in Figure 25. Figure 25 Power spectrum of acceleration in y-direction (Irene Vorrink, Turbine 12) To further increase the accuracy of the resonance frequency of the first bending mode of the tower, a general spline interpolation was used between 7 values of the spectrum around the peak value, as illustrated in Figure 26. This results in a frequency resolution of Hz.

42 Page 38 Figure 26 Spline interpolation around resonance frequency of first bending mode (Irene Vorrink, Turbine 12) Damping ratio of first bending mode from transient after a stop During the transient following a stop the decaying accelerations of the translation of the nacelle are measured. The decaying translations are used to determine the damping ratio of the first bending mode. The above-described method to determine resonance frequencies for the bending modes cannot be used for this transient measurement, because the total time of the phenomenon is too short. This can be seen from the power spectrum in the y-direction shown in Figure 27, which has very wide peaks. Figure 27 Power spectrum of the decaying acceleration in y-direction (Irene Vorrink, Turbine 28) The damping ratio of the first bending mode of the tower is determined from the decaying acceleration of the nacelle. The slowly rotating rotor has been stopped by using the mechanical brake. This initiates a bending of the tower in the y-direction. The decay of the acceleration relates mainly to the first bending mode. The decay can be determined from the amplitude of the combination of the accelerations in the x- and y-directions. When the acceleration in the y-direction is significantly greater than in the x-direction during the whole measuring time the decay is determined from the range of the acceleration. In this context the range is defined as the absolute difference between the successive maxima and minima. The decay of the acceleration continues until a stationary situation is reached caused by wind excitation. From this point, there is no decay any more and the damping ratio cannot be determined. The transient measurements were performed at wind velocities of at least 8 m/s and therefore the amplitude of the acceleration in the stationary situation is rather high. Only the first part of the decay can be used for determination of the damping ratio. An example of the decay of the acceleration and the damping ratio are given in Figure 28 and Figure 29.

43 Page 39 Figure 28 Decay of the acceleration - top: y-direction - bottom: x-direction (Irene Vorrink, Turbine 3) Figure 29 Damping ratio as function of time (Irene Vorrink, Turbine 3) Natural frequencies of torsion modes from transient after yaw movement The rotation of the nacelle has been measured with a third accelerometer at the rear side of the nacelle, with the sensitive direction along the y-coordinate. This direction relates to the torsion of the tower. By subtracting the two accelerations in the y-direction the translation of the nacelle can be eliminated resulting in the rotation only. The rotation is excited by stopping the yaw movement. The decay of the acceleration is fast and the spectrum must be calculated from a period of 10 seconds. An example of the spectrum of the rotation, from which the resonance frequencies can be determined, is shown in Figure 30.

44 Page 40 Figure 30 The linear spectrum of the decaying rotational acceleration of the nacelle (Lely, Turbine 2) 5.4 Results of predictions and measurements Table 16 and Table 17 present the predicted and measured natural frequencies for the wind farm Irene Vorrink and Lely, respectively. The differences are given as a percentage of the measured frequency. Table 16 Predicted and measured frequencies of turbines in wind farm Irene Vorrink Turbine 1 st Bending mode (Hz) 2 nd Bending mode (Hz) Predicted Measured Difference Predicted Measured Difference % % % % % % % % % % Table 17 Predicted and measured frequencies of turbines in wind farm Lely Turbine 1 st Bending mode (Hz) 2 nd Bending mode (Hz) Predicted Measured Difference Predicted Measured Difference A % % A % % Except for turbine 7 in the wind farm Irene Vorrink all predicted natural frequencies are below the measured frequencies. This is consistent with the notion that p-y curves tend to underestimate the stiffness of the soil-structure interaction. Wind farm Irene Vorrink The results for Irene Vorrink are consistent with the results of the parameter sensitivity study in Section 4.2, where an uncertainty in the order of 4% was found for a tubular tower. However, it must be noted that the parameter sensitivity study was performed for a different support structure at a different location and that the systematic underestimation of soil-structure stiffness was not included. The difference in the wind farm Irene Vorrink is largest for turbine 3. According to the cone penetration test at this site the stiffer sandy soil starts approximately 3 meter lower than at the other sites.

45 Page 41 The differences in the second natural frequencies are larger than in the first natural frequencies. This is consistent with the results of the parameter sensitivity study in Section 4.2 and can be contributed to the relatively larger deflections of the pile for this vibration. The differences for the turbines in the wind farm Irene Vorrink are of similar magnitude as the uncertainty found in the sensitivity study for the tubular tower. However, the results for the second natural frequency must be considered carefully, since the higher frequencies are more difficult to identify. It is possible that some of the identified second natural frequencies of the tower are actually natural frequencies of the rotor or blades. Wind farm Lely The differences for the natural frequencies of the turbines in the wind farm Lely are very high, particularly for turbine A2. This was found earlier in a comparison of a finite element model prediction with measurements performed by ECN ([9] and [20]). The results of that study are given in Table 18, along with the current results. Table 18 Frequencies of wind farm Lely compared with earlier study Turbine Design Earlier study [9] Current study value (Hz) Predicted (Hz) Measured (Hz) Predicted (Hz) Measured (Hz) A A No explanation has been found for the large difference for turbine A2. A sensitivity study was performed in [9], but the resulting variations in the natural frequency were much lower. Since the measurements of the two independent studies agree it is expected that there is a difference between the structural or foundation model of this turbine and the actual situation, although this could not be found within the timescale and scope of this study. 5.5 Additional Measurement Results Soil aging effects Table 18 in the previous Section showed the results of measurements performed in 1995 and in The first measurements are performed approximately one year after installation of the turbines. The second measurements, 6 years later, give a slightly higher natural frequency, but this may be within measurement accuracy Damping ratio The damping ratio of turbines 12, 23 and 28 of the wind farm Irene Vorrink were determined from the decaying acceleration. For three all turbines a damping ratio of 0.9% is found. The small magnitude of the damping coefficient justifies the negligence of damping in the models used to predict the natural frequencies.

46 Page 42 6 Conclusions This report presents a variety of information relating to the prediction of dynamic behaviour of the support structure of offshore wind turbines. The report focuses on the foundation, particularly the sensitivity of the natural frequency to soil parameters, the differences between several foundation models and the comparison of predictions and measurements. It is emphasised here that many conclusions drawn from this study are only directly applicable to the reference cases considered and that interpretation of the results in a general perspective needs careful consideration of the assumed conditions. Particularly, the pile foundations have the same behaviour as infinitely long piles. Shorter piles will probably be more sensitive to parameter variations and some foundation models do not reflect variation of pile length. Parameter sensitivity Soil parameters dominate the uncertainty of the natural frequency and its variation within a wind farm and during the lifetime of the support structure. Although the sensitivity to soil parameters needs consideration for piled structures, it is within practicable margins, even for the (large) monopile. The first natural frequency of the monopile showed a sensitivity of approximately 4% to variation in the friction angle of the soil. The natural frequency decreased by less than 5% for a scour hole of 2 times the pile diameter. Increase of loading condition caused a decrease of natural frequency of 3%, due to the non-linear soil behaviour. Typical variations of the natural frequencies of the tripod and lattice tower with pile foundations are 1% and 3%, respectively, for the cases analysed in this study. The sensitivity of gravity base structures appears to be much larger. However, the analysis of the GBS is based on a rather simple foundation model and a conservatively large variation of soil parameters. An uncertainty of approximately 20% was found. The natural frequency may vary to a large extent between different locations within the wind farm. Therefore, it is possible that the design of the gravity base cannot be uniform within the wind farm. Furthermore, to perform design and validation calculations for different locations within the wind farm detailed knowledge of local soil conditions will be required. Rotor-nacelle mass causes a relatively large variation in natural frequency, under the assumption that up to 10% variation in total mass can occur when components from different suppliers are used. However, strict configuration management can avoid this. Other parameter variations relating to the structure caused a variation of the natural frequency of less than 0.2%. Foundation models Several foundation models were compared. Three of these models have a different basis: a finite element model based on stress-strain curves, a linear elastic model developed by Randolph and an effective fixity depth model. The finite element model and the linear elastic model give comparable results, within 2% for the first natural frequency and 6% for the second natural frequency. However, note that the soil of this case study is nearly uniform. Randolph s method will not reveal the influence of pile length and loading conditions and is therefore less suitable for piles with a penetration less than a critical pile length and for deflections outside the linear region of the soil-structure interaction. Suitable values for the effective fixity depth for a monopile and for the tripod and lattice tower differ, probably due to the different mode shapes of the vibration. Besides, the appropriate value of the fixity depth depends on both pile stiffness and soil properties and this

47 Page 43 dependency is not rigorously represented in tabulated values. Due to the large sensitivity of the predicted natural frequency to the effective fixity depth this model is strongly discouraged as an a priori model for analysis beyond an initial guess of support structure behaviour. An effective fixity depth could be determined from a reference model or from measurements to reduce complexity of the foundation model. However, a sensitivity study is always recommended when this model is applied. The other investigated models are derived models and in this study they are based on the finite element model. The first and second natural frequency obtained with a stiffness matrix with coupled lateral behaviour gives very good correspondence with the finite element foundation model. The observed difference is far less than expected uncertainties in foundation behaviour. This stiffness matrix has far less degrees-of-freedom than the comprehensive finite element model and will therefore reduce computations in dynamic analyses. The uncoupled springs for lateral displacement, rotation and axial displacement give larger errors and do not give a significant reduction of degrees-of-freedom. Therefore, the use of uncoupled springs is not recommended. For the tripod and lattice tower the lateral flexibility of the piles appeared to be much more important than the axial flexibility. However, the relative importance of lateral and axial foundation behaviour depends mainly on lateral and axial foundation stiffness, spacing between the piles and the mass distribution of the tower and turbine. It requires further analysis to assess if the conclusions for these cases are generally valid. Comparison of predictions with measurements The predicted first natural frequencies of five turbines in the wind farm Irene Vorrink are within expectable deviations from the measured frequencies. The largest deviation was 5.3%. The soil profile at the site of this turbine differs slightly from that of the other turbines, which show a difference of less than 3.5% between prediction and measurement. This indicates that site-specific information of soil profiles is important, especially in case variability in the depth of the first stiff soil layer can be expected. One of the turbines in the wind farm Lely showed a large difference of 9% between predicted and measured first natural frequency. An earlier study for the same turbine resulted in a slightly smaller difference, but this could not be reproduced. Moreover, the current prediction is close to the design value, which is a prediction without a posteriori knowledge. For the other turbine in the wind farm Lely the predictions of the natural frequency of this study, an earlier study and the design study all deviated more than 30% from the measured value. The earlier study has investigated this difference extensively, without success. The difference can also not be explained by the results of the parameter sensitivity study. A comprehensive re-assessment of the structural parameters and soil data for the support structure to model the actual situation would be required to get new insights. A comparison of two measurement campaigns at the turbines in the wind farm Lely with an interval of 6 years showed no substantial change of natural frequency. Changes in the soil have been negligible or reversible or have taken place in the first year, between installation and the first measurements. Other future work This study has focussed on the influence of the foundation on the natural frequency. Further work must reveal the influence of the foundation on other aspects of dynamic response, in particular fatigue damage.

48 Page 44 7 References [1] API, RP 2A-LRFD: API Recommended Practices for Planning, Designing and Constructing Fixed Offshore Platforms Load and Resistance Factor Design, First Edition, July 1, [2] Baldi, G.; Bellottini, R.; Ghoinna, V.N.; Jamoilkowski, M.; Lo Presti, D.C.F., Modulus of Sands from CPT s and DMT s, In: Proceedings of the Twelfth International Conference on Soil Mechanics and Foundation Engineering, Vol 1, pp , [3] Barltrop, N.D.P., Adams, A.J., Dynamics of Fixed Marine Structures, Butterworth-Heinemann Ltd, Oxford, [4] Chakrabarti, S.K., Hydrodynamics of Offshore Structures, WIT Press, Southampton, [5] Ferguson, M.C. (editor); Kühn, M.; Bussel, G.J.W. van; Bierbooms, W.A.A.M.; Cockerill, T.T.; Göransson, B.; Harland, L.A.; Vugts, J.H.; Hes, R., Opti-OWECS Final Report Vol. 4: A Typical Design Solution for an Offshore Wind Energy Conversion System, Institute for Wind Energy, Delft, [6] Kay, S.; Kraan, M. van der, Geotechnical Data and Analysis - Stage 1, Offshore Wind Turbines at Exposed Sites, North Sea, Fugro Engineers B.V., Leidschendam, October [7] Kouwenhoven, H.J.; Topper, A.M.; Sande, A.M.C. van de, Windfarm Lely, the First Off-shore Windfarm in the Netherlands, In: Proceedings of the 5 th European Wind Energy Association Conference and Exhibition, Held in Thessaloniki, Greece, October [8] Kühn, M., Dynamics and Design Optimisation of Offshore Wind Wind Energy Conversion Systems, PhD thesis, Delft University of Technology, Delft, [9] Kühn, M., Modal Analysis of the Nedwind 40 Tower - Comparison of Measurements and Calculations for the Sites Oostburg and Lely (IJsselmeer), Institute for Wind Energy, Delft, November 1995, (Confidential). [10] Kühn, M., Overall Dynamics of Offshore Wind Energy Converters, Opti-OWECS Final Report Vol. 2: Methods Assisting the Design of Offshore Wind Energy Conversion Systems, Part D, Institute for Wind Energy, Delft, [11] Kühn, M., Simulation of Offshore Wind Turbines Under Stochastic Loading, In: Proceedings of the 5 th European Wind Energy Association Conference and Exhibition, Held in Thessaloniki, Greece, October [12] Matlock, H., Correlations for Design of Laterally Loaded Piles in Soft Clay, Paper number OTC 1204, In: Proceedings second annual Offshore Technology Conference, Houston, Texas, USA, Vol. 1, pp , [13] O Neill, M.W.; Murchison, J.M., An Evaluation of p-y Relationships in Sands, Report to American Petroleum Institute, University of Texas at Austin, May [14] Rooij, R. van, et. al., Terminology, Reference Systems and Conventions, DUWIND , Delft University of Technology, Delft, October [15] Randolph, M.F., The Response of Flexible Piles to Lateral Loading, Géotechnique, Vol. 31, no. 2, pp , [16] Tol, A.F. van, Funderingstechnieken, (in Dutch), Delft University of Technology, Delft, [17] Verruijt, A., Grondmechanica, (in Dutch), Delftse Universitaire Pers, Delft, [18] Verruijt, A., Offshore Soil Mechanics, Delft University of Technology, Delft, August [19] Vugts, J.H., Offshore ground conditions and foundations, In: Technology of Offshore Wind Energy, Course Notes, Delft University of Technology, Delft, October [20] Wekken, A.J.P. van der, Frequency Measurements Nedwind 40 Wind Turbines of Wind Farm Lely, ECN, Petten, October 1995, (Confidential).

49 Page 45 Appendix A: Sensitivity of the 1 st Natural Frequency This appendix presents the minimum and maximum natural frequencies in Hz that have been found for the first bending moment for the parameter variations given in Table 8, Section 4.2. Tubular tower on a monopile Reference natural frequency: Hz. Uncertainty Location variation Lifetime variation Soil (cohesionless) Effective soil weight Friction angle Lateral earth pressure - - Poisson s ratio - - Shear modulus Subgrade reaction Soil layer transition General scour Local scour depth Postholing gap Foundation Pile diameter Pile wall thickness GBS radius - GBS mass - Environment Marine growth Sea level Water depth (MSL) Topside Rotor/nacelle mass Fittings mass Cable and ladder mass Diameter Wall thickness System Vertical position

50 Page 46 Tubular tower on a gravity base structure Reference natural frequency: Hz. Uncertainty Location variation Lifetime variation Soil (cohesionless) Effective soil weight - - Friction angle Lateral earth pressure - - Poisson s ratio Shear modulus Subgrade reaction - Soil layer transition - - General scour - Local scour depth - Postholing gap - Foundation Pile diameter - Pile wall thickness - GBS radius GBS mass Environment Marine growth Sea level Water depth (MSL) Topside Rotor/nacelle mass Fittings mass Cable and ladder mass Diameter Wall thickness System Vertical position

51 Page 47 Tripod and tubular tower with piles Reference natural frequency: Hz. Uncertainty Location variation Lifetime variation Soil (cohesionless) Effective soil weight Friction angle Lateral earth pressure Poisson s ratio - - Shear modulus Subgrade reaction Soil layer transition General scour Local scour depth Postholing gap Foundation Pile diameter Pile wall thickness GBS radius - GBS mass - Environment Marine growth Sea level Water depth (MSL) Topside Rotor/nacelle mass Fittings mass Cable and ladder mass Diameter Wall thickness System Vertical position

52 Page 48 Lattice tower with piles Reference natural frequency: Hz. Uncertainty Location variation Lifetime variation Soil (cohesionless) Effective soil weight Friction angle Lateral earth pressure Poisson s ratio - - Shear modulus Subgrade reaction Soil layer transition General scour Local scour depth Postholing gap Foundation Pile diameter Pile wall thickness GBS radius - GBS mass - Environment Marine growth Sea level Water depth (MSL) Topside Rotor/nacelle mass Fittings mass Cable and ladder mass Diameter Wall thickness System Vertical position

53 Page 49 Lattice tower with gravity base structures Reference natural frequency: Hz. Uncertainty Location variation Lifetime variation Soil (cohesionless) Effective soil weight - - Friction angle Lateral earth pressure - - Poisson s ratio Shear modulus Subgrade reaction - - Soil layer transition - - General scour - Local scour depth - Postholing gap - Foundation Pile diameter - Pile wall thickness - GBS radius GBS mass Environment Marine growth Sea level Water depth (MSL) Topside Rotor/nacelle mass Fittings mass Cable and ladder mass Diameter Wall thickness System Vertical position

54 Page 50 Appendix B: Natural Frequencies for different Foundation Models This appendix presents the values of the natural frequencies in Hz predicted with different foundation models. The natural frequencies are shown graphically in Figure 22 and Figure 23 of Section 4.5. Tubular tower on monopile Tripod on piles Lattice tower on piles 1 st 2 nd 1 st 2 nd 1 st 2 nd FEM (Reference) Effective 8D fixity 6D D D (mudline) 0.01D Stiffness FEM-based matrix Randolph Uncoupled Force method springs Displacement method Only axial springs Only lateral stiffness matrix Tubular tower on monopile Tripod on piles Lattice tower on piles 1 st (%) 2 nd (%) 1 st (%) 2 nd (%) 1 st (%) 2 nd (%) FEM (Reference) Effective 8D fixity 6D D D (mudline) 0.01D Stiffness FEM-based matrix Randolph Uncoupled Force method springs Displacement method Only axial springs Only lateral stiffness matrix