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.