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Integrated Research Programmeon Wind Energy

Project acronym: IRPWINDGrant agreement no 609795Collaborative projectStart date: 01st December 2013Duration: 4 years

D7.21 Report on Validation of design of grouted jointsWork Package 7.2

Lead Beneficiary: DTU Wind EnergyDelivery date:Dissemination level: PU

IRPWIND deliverable - project no. 609795

The research leading to these results has received funding from the European Union Seventh Framework Programme under the agreement 609795.

Author(s) information (alphabetical):Name Organisation EmailÁlvaro Rodríguez Ruiz

CTC [email protected]

Anand Natarajan DTU [email protected]ín Santos Varela


David Fernández Rucoba


John Dalsgaard Sørensen

AAU [email protected]

Tomas Gintautas AAU [email protected] Njomo Wandji

DTU [email protected]

Acknowledgements/Contributions:Name Name Name

Document InformationVersion Date Description

Prepared by

Reviewed by

Approved by

1.0 July 17 Authors Anand Natarajan

Definitions

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Table of Contents

Executive Summary....................................................................................11. Introduction..........................................................................................12. Design of Grouted Joints.......................................................................2

2.1 Limit States....................................................................................32.1.1 Case 1: Conical joint................................................................32.1.2 Case 2: Shear-keyed joints......................................................3

2.2 Reliability Assessment...................................................................53. 10 MW Offshore Wind Turbine on a Monopile.......................................6

3.1 Reference wind turbine and substructure dimensioning................63.2 Environmental Conditions and Load Assessment...........................73.3 Stress calculations.........................................................................93.4 Serviceability limit state...............................................................103.5 Ultimate limit state......................................................................103.6 Fatigue limit state........................................................................11

4. Material Models for Steel and Concrete..............................................124.1.1 Models for steel.....................................................................124.1.2 Models for fatigue strength of concrete in compression........134.1.2.1 fib Model Code 2010:..........................................................144.1.2.2 fib Model Code 1990...........................................................144.1.2.3 Eurocode 2..........................................................................144.1.3 Constitutive behavior and parameter values.........................15

5. Finite Element Based Design of Grouted Joints..................................185.1 Conical Connection......................................................................18

5.1.1 Structure geometry...............................................................185.1.2 Joint topology and dimensions...............................................185.1.3 Finite element model.............................................................195.1.4 Homogenization Methods......................................................20

5.2 Cylindrical Connection with Shear keys.......................................205.2.1 Geometry...............................................................................235.2.2 Time Series (Loads)...............................................................255.2.3 FE Model................................................................................265.2.4 Stresses (results)...................................................................295.2.5 Fatigue assessment...............................................................305.2.5.1 Module I description...........................................................325.2.5.2 Module II description..........................................................355.2.5.3 Module III description..........................................................365.2.6 Case study.............................................................................375.2.6.1 Geometry............................................................................375.2.6.2 Time Series.........................................................................415.2.6.3 FE Model.............................................................................415.2.6.4 Results................................................................................425.2.6.5 Fatigue assessment............................................................435.2.7 Fatigue reliability assessment...............................................45

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5.2.7.1 Stochastic model................................................................465.2.7.2 Stress range analysis..........................................................475.2.7.3 Results................................................................................48

6. Probabilistic Design Methods..............................................................506.1 Effect of Variation in Geometry and Material Parameters............50

6.1.1 Multivariate Interaction between the parameters.................506.1.2 Effect of conical angle............................................................536.1.3 Minimization of tensile crack.................................................53

6.2 Probabilistic model for concrete fatigue strength based on Data 536.2.1 Probabilistic model................................................................546.2.1.1 Model 1...............................................................................546.2.1.2 Model 2...............................................................................546.2.2 Results...................................................................................546.2.2.1 Results for high strength concrete – Model 1.....................566.2.2.2 TUD data – Model 1............................................................596.2.2.3 TUD and AAU data – Model 1..............................................626.2.2.4 Results for high strength concrete – Model 2.....................656.2.3 Summary – probabilistic model for fatigue of concrete.........68

7. Design Driving Fatigue Loads, Stress and Lifetime............................707.1 Conical Connection Design..........................................................70

7.1.1 Fatigue loads and stresses....................................................707.1.2 Fatigue damage.....................................................................717.1.3 Stiffness degradation.............................................................717.1.4 Vertical settlement and global stiffness.................................73

7.2 Effect of Corrosion on Steel..........................................................747.2.1 Corrosion model (methodology)............................................747.2.2 Case study considering corrosion loss...................................78

7.3 Fracture Mechanics based Approach...........................................807.3.1 Fracture mechanis based stochastic model for fatigue crack growth 807.3.2 Reliability assesment based on fracture mechanics model...83

8. Summary............................................................................................88

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LEANWIND deliverable - project no. 614020

Executive Summary

Grouted joints for offshore wind turbines forming the connection between the transition piece to the monopile and tower are one of the weakest links of the support structure. The grout being a reinforced concrete material is susceptible to cyclic loading comprising of tensile and compressive components. As offshore wind turbines reach 10 MW capacities, it is extremely important to determine the reliability of grouted joints and their design configurations so as to ensure integrity of the 10 MW support structure. This report investigates two types of grouted joint connections, the conventional cylindrical joint with shear keys and a conical joint without shear keys. In both cases, fully coupled load simulations are made to determine the fatigue resistance and ultimate load resistance of the joint. Key recommendations are made for the reliable design of grouted joints for 10 MW wind turbines on monopile substructures.

1. IntroductionThe connections between the transition piece and the monopile for wind turbine support structures are made by the means of grouted joints. Classically, the grouted joints for monopile substructures are built from the overlap of two cylindrical tubes: the transition piece and the pile, whose resulting annulus is filled with a high strength concrete. The grouted joints are efficient as they are easily constructible and they serve to correct the pile misalignment due to driving errors [1] as presented in Figure 1.

Figure 1: Grouted joint with plain cylindrical tubes [1].

A typical construction process follows few steps: (1) the transition piece is jacked up at the pile top edge using temporary brackets; (2) the concrete is poured in the annulus and left for curing; and (3) after the concrete has hardened, the jack-ups are removed and the transition piece holds due to the passive friction resistance at the interfaces between the layers.

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The passive friction resistance is made of two contributions. One is the chemical adhesive bond between the concrete and the steel, which has developed during the concreting process. The other is the mechanical interlock between the rough concrete surface and the undulations at the steel surfaces. In the case of the structure in hand (see later) and only considering the combination of these two contributions, one meter of the overlap length can bear 1.4 times the structure weight.

Moreover, during the loading operations the grout transfers the loads from the transition piece to the pile in the form of normal pressure and friction at the interfaces between the steel walls and the grout. Consequently, one contribution adds to the previous ones: it is the coulomb friction. However, after few cycles, gaps open between the grout and the steel walls at the connection top and bottom; the adhesive bond is deteriorated and cannot recover. It is rare to lose these bonds around the mid-height of the connections. Furthermore, the friction abrades the geometrical imperfections at the adjacent surfaces over the whole connection length. Very soon, the two initial contributions depreciate and leave the coulomb friction, which is only effective when the normal pressure is present. In case of insignificant normal pressure, the shear resistance may not support the structure weight anymore and the transition piece will progressively slide downwards till the temporary brackets touch the pile top edge: the connection fails.In order to constantly keep the shear resistance, two solutions were proposed as shown in Figure 2: the conical grouted joint and the shear-keyed grouted joints.

Figure 2: Conical grouted joint (left) and shear-keyed cylindrical grouted joint (DNV).

The conical grouted joint is derived from the convention grouted joint by imposing a small conical angle (1° to 3°) to the overlapping tubes. With the conical angle, the structure weight effect on the connection decomposes into a shear component along the interfaces and a normal component to the interfaces. The latter component generates a permanent coulomb friction resistance, which prevents the failure described above. The alternative solution adds shear keys to the inner faces of the steel walls close to the connection middle in order to enhance the mechanical interlock: the resulting friction resistance is said active. It is advisable to not put shear keys close to the connection edges as the gap openings will set them inefficient. In either solution, as the passive mechanical interlock and the adhesive bond are ephemeral, it is realistic to carry out analysis without accounting for their respective contributions.In the following sections, the design of both a conical grouted joint and a cylindrical grouted joint with shear keys are made for a 10 MW wind turbine mounted on a monopile. A grouted joint design for such a lrage turbine structure

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is challenging and requires invetsigations spanning material models, loads, structural deformations and material testing.

2. Design of Grouted Joints A reliability based design process is followed for the design of the grouted joint. The grouted joint consists of both steel and concrete material.

2.1 Limit States 2.1.1 Case 1: Conical joint

The most delicate component of the grouted connection is its grout. An adequate design should consider ultimate limit state, fatigue limit state [2], and serviceability limit state. The serviceability limit state should ensure that the relative sliding, δ h, of the transition piece with respect to the pile is low enough to keep a gap,h, between the pile top edge and the brackets (See Equation 1).Subjected to cyclic loadings, the connection engenders cyclic stresses that induce fatigue in the materials. The accumulated fatigue, D25, in the grout during the intended lifetime, calculated according to the Palmgren-Miner assumption should be lower than one (See Equation 2a). Moreover, the friction at the interfaces abrades the grout surfaces. The wear rate is function of shear stress, which is proportional to the normal pressure exerted from one layer to another. In order to limit the wear of the grout surface, the normal nominal stress, pnominal, acting at the steel-grout interfaces should be lower than 1.2 MPa [3] as presented by Equation 2b.

The shear stress, τ , due to friction between the steel wall and the grout surfaces should be lower than the shear strength, τ max, of the interface to prevent excessive sliding (Equation 3a). This limit state is evaluated for both sides of the grout. The Tresca stress, σ Tresca, generated in the grout material should be kept lower than the concrete strength, f c, as specified by Equation 3b.In Equations (1) and (3), the partial safety factors γm, γc, and γl are respective associated to the material uncertainties, to the consequences of failure of the component, and to the load uncertainties.Nielsen (2010) [4] pointed out the almost-inevitable formation of hairline cracks due to primary hoop stresses. Dallyn et al [5] recognized the effect of these cracks in the reduction of bending stiffness, but stating that the influence is limited (about 5%) as long as the lateral stresses are still transferred. Therefore, the same assumption made by Lee et al [2] is considered here: the grout material does not support significant tensile stress in the hoop direction; the grout is primarily in charge of transferring the pressure between the transition piece and the pile through shear friction, thus limiting the slide of the transition piece. Based on the above, the limit states governing the grouted joint design are given as follows.

Serviceability limit state

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γm γ c γl δ h≤h (1)Fatigue Limit state related to long term loading (also given in greater detail in Eq. 6 below)

D25≤1.00 (2a)

pnominal≤1.2[MPa] (2b)

Limit states related to short term loading

γm γ c γl τ ≤ τmax (3a)

γm γ c γlσTresca≤ f c (3b)

2.1.2 Case 2: Shear-keyed joints

For the case of cylindrical grouted connection with shear keys, the limit states for short and long term loading are described as follows:

The ultimate limit state for the grouted connection with shear key is:

FV 1Shk , d<FV 1Shk cap ,d -(4)

where:FV1Shk is the acting force per unit length along the circumference, owing to bending moment and vertical force and transferred to the shear key

Additionally, the following requirement for the maximum nominal radial contact pressure shall be fulfilled:

pnom ,d≤1.5 MPa -(5)

This requirement for the nominal radial contact pressure can be waived if a detailed FE analysis is performed

The cumulative damage D, due to fatigue, is calculated based on the long term distribution of the amplitude of the vertical downward dynamic load on the shear key and of the vertical upward dynamic load on the shear key:

D=DFF∑j=1

k

∑i=1

n0 n i

N i≤1 -(6)

where:

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n0 = total number of stresses blocks of constant-amplitude stressni = number of stress cycles in the ith stress blockk = number of lateral environmental load directionsNi = characteristic number of cycles to failure at the constant stress amplitude of stress block i

The S-N curve, which gives the number of cycles N to failure at a specified relative load level y, is represented as follows:

logN=5.400−8 y for y≥0.30logN=7.286−14.286 y for0.16< y<0.30

logN=13.000−50 y for y≤0.16

In which, for each load cycle, the relative load cycle is:

y=FV 1Shk γmFV 1Shk cap

where FV 1Shkcap is the characteristic shear key capacity, FV 1Shk is the shear key load of the load cycle in question, consisting of the static load plus the load amplitude of the load cycle in question, and γm is the material factor.

2.2 Reliability Assessment The probability of failure of a failure mode modeled by a limit state equation g(X) is

(7)where β is the reliability index and Φ is the standard Normal distribution function. The relationship between the reliability index and the probability of failure is shown in the table below.

Table 1 Relationship between reliability index and probability of failure.Pf 10-2 10-3 10-4 10-5 10-6 10-7

β 2.3 3.1 3.7 4.3 4.7 5.2

The target reliability level can be given in terms of a maximum annual probability of failures (i.e. reference time equal to 1 year) or a maximum lifetime probability of failure (i.e. for wind turbines a reference time equal to 20 – 25 years). For civil and structural engineering standards / codes of practice where failure can imply risk of loss of human lives target reliabilities are generally given based on annual probabilities. The optimal reliability level can be found by considering representative cost-benefit based optimization problems where the life-cycle expected cost of energy is minimized with appropriate constraints

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related to acceptable risks of loss of human lives, e.g. based on LQI (Life Quality Index) principles.

For wind turbines, the risk of loss of human lives in case of failure of a structural element is generally very small. Further, it can be assumed that wind turbines are systematically reconstructed in case of collapse or end of lifetime. The optimal reliability level can be found by considering representative cost-benefit based optimization problems where the life-cycle expected cost of energy is minimized. It is assumed that for wind turbines:

A systematic reconstruction policy is used (a new wind turbine is erected in case of failure or expiry of lifetime).

Consequences of a failure are only economic (no fatalities and no pollution).

Cost of energy is important which implies that the relative cost of safety measures can be considered large (material cost savings are important).

Wind turbines are designed to a certain wind turbine class, i.e. not all wind turbines are ‘designed to the limit’.

Based on these considerations the target reliability level corresponding to a minimum annual probability of failure is recommended to be P f =5x10-4, corresponding to an annual reliability index equal to 3.3. This reliability level corresponds to minor / moderate consequences of failure and moderate / high cost of safety measure. It is noted that this reliability level corresponds to the reliability level for offshore structures that are unmanned or evacuated in severe storms and where other consequences of failure are not very significant.

Specific failure functions for fatigue failure will be discussed in the appropriate sections where the reliability assessment is performed. But in general terms failure functions follow a general format:g(X )=∏ X R , iR−∏ X E ,i E (8)where R is a stochastic variable modelling the resistance (e.g. steel yield strength) with XR,I as stochastic variables representing modelling uncertainties related to resistance modelling; E represent the loading effect (e.g. loads or stresses in the component in question) with XE,I being stochastic variables representing modelling uncertainties related to load effect modelling. Such failure functions can be solved using FORM (First Order Reliability) or SORM (Second Order Reliability) methods and probabilities of failure (reliability indexes) can be obtained and compared to required reliably levels.

Strength or resistance variables are often modeled by Lognormal distributions. This avoids the possibility of negative realizations. In some cases it can be relevant also to consider Weibull distributions for material properties e.g. composite material. This is especially the case if the strength is governed by brittleness, size effects and material defects. The coefficient of variation varies with the material type considered. Typical values are 5% for strength of steel and reinforcement, 15% for the concrete compression strength and (~ 5-20%) for strength of composite materials. The characteristic value is generally chosen as the 5% quantile.

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Variable loads (wind and wave loads) can be modeled in different ways. The simplest model is to use a stochastic variable modeling the largest load within the reference period (often one year). This variable is typically modeled by an extreme distribution such as the Gumbel distribution or the Weibull distribution. The coefficient of variation is typically in the range 15-30% and the characteristic value is chosen as the 98% quantile in the distribution function for the annual maximum load.

Model uncertainties are in many cases modeled by a Lognormal distribution if they are introduced as multiplicative stochastic variables and by Normal distributions if they are modeled by additive stochastic variables. Typical values for the coefficient of variation for the model uncertainty are 3- 25% but should be chosen very carefully. The characteristic value is generally chosen as the 50% quantile.

3. 10 MW Offshore Wind Turbine on a Monopile

3.1 Reference wind turbine and substructure dimensioningThe study is based on the 10 MW reference wind turbine developed by the Technical University of Denmark (DTU 10 MW RWT) [6]. It is a variable-speed, pitch-controlled, direct drive machine. Its key design parameters are presented in Table 2. The DTU 10 MW RWT has a rotor speed varying between 6.0 rpm and 9.6 rpm. It follows that the allowable support structure soft-soft natural frequency domain ranges within [0.00 Hz 0.10 Hz], the soft-stiff domain ranges within [0.16 Hz 0.30 Hz], and the stiff-stiff domain within [0.48 Hz 0.60 Hz].

Table 2: Key parameters of the DTU 10 MW RWTParameters ValuesWind regime (see Table 3 and Table 4)Rotor type, orientation 3 bladed - Clockwise rotation – UpwindControl Variable speed – Collective pitchCut-in, rated, cut-out wind speed 4 m/s, 11.4 m/s, 25 m/sRated power 10 MWRotor, hub diameter 178.3 m, 5.6 mHub height 119.0 mDrivetrain Medium speed, Multiple-stage GearboxMinimum, maximum rotor speed 6.0 rpm, 9.6 rpmMaximum generator speed 480.0 rpmGearbox ratio 50Maximum tip speed 90.0 m/sHub overhang 7.1 mShaft tilt, coning angle 5.0°, -2.5°Blade prebend 3.3 mRotor mass including hub 227,962 kgNacelle mass 446,036 kgTower mass 628,442 kg

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In order to avoid the resonance, an iterative procedure leads to a substructure with reference dimensions of 8500 mm outer diameter for the transition piece and 9000 mm outer diameter for the pile. API RP2A WSD [7] recommends a minimum thickness to account for driving induced stresses tmin [mm ]=6.35+D [mm ]/100, which corresponds to about 96 mm. Survival to the limit states requires that the wall thickness of the pile range from 97 mm to 110 mm, and that of the transition piece be 80 mm. The penetration depth of the pile is set to 30 m.

3.2 Environmental Conditions and Load AssessmentThe environmental conditions used in this study have been adapted from [8]. The operational wind range is divided into 11 mean wind speed bins, which are each linked to a particular sea state characterized by an expected significant wave height and a peak spectral period, as shown in Table 3 and Table 4. The normal operational conditions have been modelled according to the IEC 61400-3 [9] design load case DLC 1.2, The wave height is modelled based on JONSWAP spectrum at the expected value of the sea state characteristics conditional on the mean wind speed. Misalignments of 0° or ±10° between the wind direction and the wave direction, yaw errors of 0° or ±10° between the wind direction and the rotor normal, and 6 seeds per mean wind speed have been simulated for a total of 594 time series of 10-minute duration.

Table 3: Sea state characteristics conditional on the mean wind speedWind speed [m/s]

Significant height, Hs [m]

Peak period, Tp [s]

Expected annual frequency [hrs/yr.]

5 1.14 5.82 933.757 1.245 5.715 1087.39 1.395 5.705 1129.0511 1.59 5.81 1106.7513 1.805 5.975 1006.415 2.05 6.22 820.1517 2.33 6.54 63319 2.615 6.85 418.6521 2.925 7.195 312.723 3.255 7.6 209.925 3.6 7.95 148.9650 9.4 13.7

For the design load case DLC 1.3 [9], which are operational conditions associated to normal wind, but with extreme turbulence, Table 3 and Table 4 present the metocean conditions. Wind and wave are collinearly directed along the rotor normal, with 6-seed wind box realizations. A total of 66 scenarios have been simulated.

Table 4: Wind conditionsWind speed [m/s] 5 7 9 11 13 15 17 19 21 23 25 50

Normal Turbulence Intensity [%]

18.95

16.75 15.6 14.9 14.4 14.0

513.7

5 13.5 13.35 13.2 13 11

Extreme Turbulence Intensity [%]

43.85 33.3 27.4

3 23.7 21.12

19.23

17.78

16.63

15.71

14.94 14.3 11

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DLCs 1.4 and 1.5 are associated to extreme coherent gust with wind direction change and extreme wind shear, respectively. For DLC 1.4, three scenarios related to 9 m/s, 11 m/s, and 13 m/s, respectively have been simulated. A total of four φ-parameter values have been considered for DLC 1.5. DLC 6.2a corresponds to turbulent extreme wind with loss of electrical power. Wind/wave misalignment of 0° or ±15° together with a rotational spread of 15° step of the wind direction around the support structure have been simulated. That is a total of 72 scenarios.

The soil conditions have been slightly modified from those in [8]. The foundation soil is mainly made of sandy layers whose properties are given in Table 5. The soil-structure interactions are modelled as Winkler elastic beam as proposed by DNV-OS-J101 [10].

Table 5: Soil conditionsDepth range [m] 0.0 – 7.0 0.7 – 15.0 15.0 –

20.020.0 – 22.5

22.5 – 90.0

Angle of internal friction [°]

29.5 35 35 35 35

Submerged unit weight [kN/m3]

9 9 10 10.5 11

The load assessment is carried out using the software package HAWC2 [11]. HAWC2 utilizes a multibody formulation, which couples different elastic bodies together using Timoshenko beam finite elements whereby their stiffness, mass, and damping are assembled into the governing equations of motion coupled to aerodynamic forces, whose aeroelastic solution is obtained using the Newmark-β method. The blade element momentum theory supplemented with Leishman Beddoes dynamic stall model and dynamic inflow is employed to represent the rotor unsteady aerodynamics.The Mann turbulence model is used in load case simulations to represent the random Gaussian turbulent wind realizations blowing over the rotor. Random wave kinematics are computed according to the linear Airy model with Wheeler stretching. The hydrodynamic forces are calculated based on the Morison equation (Equation (9)) [12] with corrected coefficient of inertia to account for diffraction phenomenon (Equation (10)) [13].

F=12ρw DCD (uw+uc−us )|uw+uc−us|+ρwCM

π D2

4 (u̇w−u̇s ) (9)

CM= 16

π k2D 2√ [J 1' ( kD /2 ) ]2+[Y 1

' (kD /2 ) ]2 (10)

where D [m] is the monopile’s outer diameter, uc [m/s] is the current speed, uw [m/s] is the wave particle speed normal to the monopile axis, us [m/s] is the moving monopile velocity, u̇w [m/s2] is the wave particle acceleration normal to the monopile axis, and u̇s [m/s2] is the moving monopile acceleration. ρw=1025 kg/m3 is the water mass density and CD=0.85 is the drag coefficient related to the pile cross section. J1

' and Y 1' are derivatives of Bessel function of

first and second kinds, respectively. k is the wave number defined as

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4 π 2=T p2 gk tanh (kh ), where g [m/s2] is the gravity acceleration and h [m] is the

water depth.Figure 3 illustrates a typical load time series generated from HAWC2 at the tower bottom at 11 m/s input mean wind speed.

Figure 3: Loads at tower bottom at 11 m/s. Top left: fore-aft (blue) and side-side (pink) forces. Top right: Vertical force. Bottom left: fore-aft (pink) and side-side (blue) moments. Bottom right: torsion.

3.3 Stress calculationsWith the loads assessed at various locations along the monopile axis, the nominal axial, shear, and hoop stresses are given by Equations (11), (12), and (13), respectively:

σ x=NA

+M1

I /Rsin θ−

M2

I /Rcosθ (11)

τ=| T2πt R2 −

2Q1

Asinθ+

2Q2

Acosθ| (12)

σ θ={ p ( y )4 πt [4− (π−2θ )sin θ ] ,∧soil part

0 ,∧ flooded water part(13)

whereN : axial forceM 1, M 2 : bending moments about axis 1 and 2, respectivelyT : torsional momentQ1 ,Q2 : shear forces along axis 1 and 2, respectivelyp( y ) : lateral force due to soil resistanceA : section’s areaI : section’s second moment of areaR : outer radiust : wall thicknessθ : circumferential co-ordinate, measured from axis 1

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The nominal stresses are magnified at the welds due to stress concentration. DNV RP C203 [14] recommends estimating stress concentration factor (SCF) for butt connections with same nominal diameter and thickness as in equation (14)

SCF=1+3δm

te−√ t /D (14)

where D and t are respectively the outer diameter and the wall thickness, δm=√δ t

2+δ r2 is the resultant imperfection measure, whose components may be

due to out of roundness or centre eccentricity. At butt welds where thicknesses change from a larger thickness T to a smaller thickness t, SCFs are calculated from Equation (15) [14]:

SCF=1+6 (0.5(T−t)+δm−δ 0 )

t (1+(Tt )β

)e−α

(15)

where

α=1.82L√Dt

1

1+( Tt)β ; β=1.5− 1.0

log(Dt )+ 3.0

[ log(Dt )]2 ; δ 0=0.1 t

3.4 Serviceability limit stateArany et al (2015) Error: Reference source not found pointed that the permanent deflection at the seafloor should not exceed 20 cm and permanent rotation should be lower than 0.25°, given that 0.25° is spared for possible pile verticality errors. Accumulated deflections are calculated along the method proposed by Lin and Liao (1999) [39]. Results given a deflection lower than about 3.16 cm and a permanent rotation of lower than about 0.17°.

3.5 Ultimate limit stateThe equivalent Von Mises stress at a particular point of the monopile shell is σ v=√ (SCF σ x)

2−SCF σx σθ+σ θ2+3 τ2. The utilisation factor is computed as

u1=γm γc γ lσ v / f y, where f y=235 MPa is the yield stress, the partial safety factor are taken from [16] and from [17]: γm=1.30, γc=1.10, and γl=1.35∨1.1 are associated to the material properties, to the component’s consequence of failure, and to the loads in normal or abnormal cases, respectively. It came out that DLC 6.2a utilizes material the most with a maximal factor of 70.95%, which is lower than 100% implying structure integrity.The structure has been checked with respect to global buckling and to local buckling. The respective utilization factors, which should be lower than one to ensure structural integrity, are given in DNV RP C202 [18]. The factors are all lower than 90%, which indicates the structural integrity of the monopile.Figure 4 depicts the distribution of the utilization factor associated to the ultimate limit state along the substructure axis.

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0 0.5 1Strength utilization ratio [-]

pile toe (56 m)

seabed (26 m)

mwl (0 m)

Interface (-26 m)A

ltitu

de [m

]

DLC13DLC14DLC15DLC62

0 0.2 0.4 0.6Local Buckling utilization ratio [-]

pile toe (56 m)

seabed (26 m)

mwl (0 m)

Interface (-26 m)


0 0.5 1Global Buckling utilization ratio [-]

seabed (26 m)

mwl (0 m)

Interface (-26 m)


Figure 4: Distribution of the strength utilisation factor along the substructure axis.

3.6 Fatigue limit stateThe design stresses are obtained at welded hotspots by σ d=γm γc γ lSCF σ x. The partial safety factors are taken from [16]: γm=1.25, γc=1.10, and γf=1.20 are associated to the material properties, to the component’s consequence of failure, and to the fatigue stress range counting, respectively. The cycles in the design stress time series are counted using Rainflow counting algorithm to obtain the number of occurrences n(∆σ ) of a given design stress amplitude ∆ σ. Using the design S-N curve of type C1 for seawater for free corrosion as per DNV RP C203 [14], the number of cycles till failure is obtained by:

log N (∆σ )=loga−m log [∆σ ( ttref )

k ] (16)

wherem and log a = are respectively the negative inverse slope of the S-N curve and

the intercept of log N axis. For seawater for free corrosion, (m=3, log a=11.972);

t ref= is the reference thickness equal to 25 mm;t = is the thickness through which the crack will most likely grow;

t=t ref if t<tref ;k = is the thickness exponent on fatigue strength. k=0.15.

Miner’s rule is used to aggregate the fatigue damage. During one year, the accumulated damage is expressed as:

D1=γFF∑i

ni(∆σ ) ti(∆σ )N i(∆σ )

(17)

where γFF=3.0 is the fatigue reserve factor and t i(∆σ ) is the occurence time of during one year. Added to the damage engendered during the construction, i.e equivalent to two years, the damage accumulated during the lifetime of the structure, i.e. 25 years, is DL=27D1, which should be lower than one. The maximum fatigue damage is seen just below the seafloor and is 98.70%.

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4. Material Models for Steel and Concrete 4.1.1 Models for steel

Steel is at present the main material considered for the construction of monopiles. Designs are mainly composed with steel plates of different steel compositions. Standards allow the design and use of different steels for support structures, and propose different model approaches that require parameters (for instance in fatigue, fatigue-corrosion or corrosion models) that vary for each steel or structural detail.

In the numerical models, different simplifications and assumptions are made to represent the stress-strain behaviour of metals. Figure shows different models of stress-strain curves, from elastic to different plastic theoretical curves. Furthermore, linear elastic behaviour of steel is very often applied by structural engineers as it is easy for FEM programmes to solve the models. In the former case, it is considered a valid structure while yield limit is not reached. In order to analyse yielding, the yield criteria frequently used for tri-axially loaded structures is Von Mises Yield Criteria Error: Reference source not found.

Figure 5: Theoretical models for stress-strain behaviour of steels, from left to right: linear elastic, rigid- perfectly plastic, perfectly plastic with an elastic

region and bi-linear elasto-plastic with strain hardening region

However, the most accurate model fitting for the real behaviour is the Ramberg-Osgood model and the Gurson-Tvergaard-Needleman damage model Error:Reference source not foundError: Reference source not found. Ramberg-Osgood model includes a linear elastic part for true stress-strain and the plastic part of the curve is fitted to a power law Error: Reference source not found. Ramberg-Osgood equation is usually described as:

ε= σE

σ ≤σY

ε= σE

+( σK )1 /n

σ>σY

where k and n are constants that depend on the material being considered.

14


There are differences between monotonic and cyclic stress-strain curves in metals. In cyclic stress-strain for fatigue analysis, several studies use Ramberg-Osgood to fit the stress-strain curve with hysteresis loops. Cyclic stress-strain curve according to Ramberg –Osgood model is described by Error: Referencesource not foundError: Reference source not found:

ε a=ε ael+εapl=σ a

E+( σa

K ' )1/n'

For the Ramberg-Osgood equation to be useful, values for the constants n and K must be known. The constants for this exponential equation are found by:

n=log( σ2

σ1)

log( ε2

ε1 )K=

σ 1

ε 1n

where (σ 1,ε 1) and (σ 2, ε 2) correspond to two points within the plastic region of the stress-strain curve. So, knowing two points within the plastic region the constants can be calculated. If the yield strength (Sty), ultimate strength (Stu), elastic modulus (E) and strain at break (εf) for a material are known, then two points within the plastic region can be determined (the yield and ultimate points), and from those points the plastic region curve can be calculated. Remember that the strain at break can be calculated from the percent elongation, eL, by ε f=eL/(100 % ). Luckily all of these properties are commonly known for a material.

It is important to note that the equation for the plastic region curve (σ=K ε pn ¿ is

dependent on the plastic strain, and so it will be needed to determine the values of plastic strain for the two points of interest. Plastic strain can be calculated from total strain using the following equation:

ε p=ε−ε e=ε− σE

¿

When determining the strain at the yield point, a plastic strain of 0.002 was assumed, consistent with the 0.2% offset method. This assumption is necessary in order to place the yield point within the plastic region of the curve. The coordinates in the stress-strain diagram of the yield point and ultimate point within the plastic region are given by:

Yield point (Sty, 0.002) Ultimate point (Stu, εf)

From the two points in the plastic region of the curve, the constants n and K for the Ramberg-Osgood equation can be calculated:

15


n=log ( Stu

Sty)

log ( εf0.002 )

K=S ty

0.002n

Now that the constants n and K have been determined, the equation for the total strain as a function of stress is known.

4.1.2 Models for fatigue strength of concrete in compression

This section describes the characteristic SN-curves in fib Model Coce 2010 Error:Reference source not found, fib Model Code 1990 Error: Reference source notfound and Eurocode 2 Error: Reference source not found. The SN-curves give the number of load cycles to failure, N (og logN) as a function of the fatigue load represented by σc,max and σc,min being the maximum and minimum compressive stresses in one fatigue load cycle, i.e. the fatigue strength becomes dependent on the mean stress level = (σc,max + σc,min )/2.

4.1.2.1 fib Model Code 2010:

The following SN-curve is used in fib Model Code 2010 Error: Reference source not found:

For Log N ≤ 8.0log N=( 8

Y−1 )⋅(Sc ,max−1) (18)

For Log N > 8.0

log N=8+8⋅ln(10 )(Y−1 )

⋅(Y−Sc ,min )⋅log( Sc ,max−Sc ,min

Y−Sc ,min) (19)

whereY=

0 .45+1 .8⋅Sc ,min

1+1 .8⋅Sc ,min−0.3⋅Sc ,min2

Sc ,max=|σc ,max|/ f c, fat

Sc ,min=|σc ,min|/ f c ,fat

The fatigue compressive strength f c ,fat is estimated by

f c ,fat=f c (1−f c /400 )

where f c is the strength in MPa.

16


4.1.2.2 fib Model Code 1990

The following SN-curve is used in fib Model Code 1990 [Error: Reference source not found:

For Log N ≤ 6.0(20)

For Log N > 6.0(21)

whereSc ,max=|σc ,max|/ f c, fat Sc ,min=|σc ,min|/ f c ,fat

The fatigue compressive strength f c ,fat is estimated by:

where f c is the characteristic strength in MPa and = 10 MPa (reference strength).

4.1.2.3Eurocode 2

The following model in EN1992-2:2005 Error: Reference source not found is used to estimate the number of cycles, N to fatigue failure:

(22)

where the stress ratio, R is defined by:

(23)

and

; (24)

with

(25)

f c is the characteristic strength in MPa and k1 = 0.85.

17


4.1.3 Constitutive behavior and parameter valuesAs it has been ensured that the steel remains elastic in the monopile design process above, it is sufficient to model the steel stress-strain relationship as a linear curve.The grout is a high strength concrete of grade C120 Error: Reference source not found. Nielsen [4] proposed three candidates as constitutive formulations for the response for the grout. The most sophisticated alternative is the damaged plasticity model [28]. This formulation models strain hardening and softening, and thereby also cracking and crushing. Moreover, it captures the material damage along the loading cycles by altering the material stiffness, as well as it accounts for material recovery. Error: Reference source not found6 depicts the said formulation for the uniaxial load cycle path with the extreme cases of stiffness recovery factors, while the yield surfaces are illustrated in Error: Reference source not found. The basic relationships between the uniaxial parameters can be found in Model Code 2010 Error: Reference source not found.

Figure 6: Uniaxial load cycle (tension-compression-tension) [28].

Figure 7: Yield surfaces. Left: deviatoric plane. Right: plane stress [28].

The interface between the steel wall and the grout surfaces is modelled according to classic hard contact theory. This formulation assumes that the sticking contributions from geometric imperfections and chemical adhesion have already been lost. Therefore, only the Coulomb friction contributes to the stress

18


transfer between the various parts. With the absence of chemical adhesion (and geometric imperfections), the sliding parts can separate each other in the direction normal to interface. For a given normal pressure, the shear strength is proportional to the Coulomb friction coefficient, i.e. the shear resistance is equal to the product between the normal pressure and the Coulomb friction coefficient but does not exceed the shear strength, in which case sliding occurs after the sticking phase.Error: Reference source not found6 and Error: Reference source not found7 present the value of all the material parameters used in this study.

Table 6: Material parametersParameters Values Reference

Steel: Linear constitutive modelUnit mass, ρ s [kg/m3] 7850 Cremer and Heckl

Error: Reference source not found

Elastic modulus, E [MPa] 210×109 Cremer and Heckl Error: Reference source not found

Poisson’s ratio, ν [-] 0.3 Cremer and Heckl Error: Reference source not found

Yield stress, f y [MPa] 235×106 DNV-OS-J101 [10]Interface: Classic hard contact

Coulomb friction coefficient, μc [-]

0.47 Baltay and Gjelsvik Error: Reference source not found

Shear strength, τ [Pa] 1.05×105 Rabbat and Russel Error: Reference source not found

Concrete: damaged plasticity modelUnit mass, ρc [kg/m3] 2500 Model Code 2010

Error: Reference source not found

Characteristic strength, f ck [MPa]

120 Model Code 2010 Error: Reference source not found

Dilatation angle, ψ [⁰] 31 Tyau Error: Referencesource not found

Flow potential eccentricity, m [-]

0.1 Tyau Error: Referencesource not found

Initial biaxial/uniaxial ratio, σ co/σbo [-]


Shape parameter, K c [-] 2/3 Tyau Error: Referencesource not found

Viscosity parameter, μ [-] 0 Tyau Error: Referencesource not found

Compression recovery factor, w c [-]


Tension recovery factor, w t [-]


19


Table 7: Strain-damage relationship for compression and tension (adapted from Tyau Error: Reference source not found)CompressionInelastic strain 0.000

70.0014

0.0020

0.0054

0.0088

0.0122

0.0155

0.0189

0.0223

0.0257

0.0290

Damage 0.0000

0.0500

0.1000

0.1954

0.3500

0.4800

0.5964

0.7000

0.8000

0.8949

0.9500

TensionInelastic strain 0.000

00.0000

0.0001

0.0004

0.0007

0.0010

0.0013

0.0017

0.0020

0.0023

0.0026

Damage 0.0000

0.0000

0.0000

0.4064

0.6964

0.8100

0.8800

0.9204

0.9400

0.9600

0.9801

20


5. Finite Element Based Design of Grouted Joints

5.1 Conical Connection

5.1.1 Structure geometryThe finite element model (FEM) of the grouted joint is built on the Abaqus platform [28]. In order to effectively couple the aero-hydro-servo elastic simulations with soil boundary conditions, the FEM of the whole substructure has been prepared as presented on the right hand side of Figure 5. The loads at the tower bottom are input at the transition piece top. The distributed loads along the transition piece (aerodrag) and the monopile (sea loads) have been modelled as nodal loads at 10 locations spread along the axis above the seafloor. Bush and Manuel [32] have shown that the foundation model of apparent-fixity type and coupled-springs leads to similar behavior of the grouted joint than that of distributed-spring type. In this study, the distributed-spring foundation has been replaced by its equivalent apparent fixity model such that the mass and frequencies of the whole support structure is preserved.

Figure 5: Substructure modelling. Left: full structure. Middle: Substructure model in HAWC2. Right: Substructure model in Abaqus.

5.1.2 Joint topology and dimensionsThe conical joint is made of double co-axial frusto-conical overlapping each other whose annulus is filled with a concrete grout. The outer frustum is the transition piece (or sleeve) and the inner frustum is the pile. The relative position of the connection top with respect to the mean water level can also be considered as a design parameter. Figure presents the topology and the dimensions of a typical conical grouted joint and the description is given in Table 6.

21


Figure 9: Topology and dimensions of a typical conical grouted joint.

Table 6: Geometrical design parameters of a typical conical grouted jointSymbol Description

D Outer diameter of the cylindrical monopile, mα angle of the connection, degt p Wall thickness of the pile in the connection, mt s Wall thickness of the transition piece (sleeve) in the connection, mt g Grout thickness, mL Length of the connection, mLe Length of the pile/sleeve edges, mLt Length of the connection above the mean sea level, m

5.1.3 Finite element modelDNVGL-RP-0419 [33] recommends to use 1st order shell element for steel walls in conjunction with 1st order soild elements for the grout. This recommendation has been adopted for the finite element model prepared using the commercial software package Abaqus [28]. An aspect ratio equal to one has been used for all elements. For the steel wall, elements of type S4RS have been selected, which corresponds to 4-node doubly curved shell, reduced integration, hourglass

22


control, small membrane strains. For the grout, elements of type C3D8R are selected, which corresponds to 8-node linear brick, reduced integration, hourglass control. The relax stiffness method is used to control hourglass for the shell element and the stiffness method is used for the solid element. For details of these methods, reference is made to [28].The loads have been applied in two steps. First, the self-load of the structure is applied. The transition piece settles onto the grout. Second, the operational loads are then applied to the structure. Gradually applying the dead load and the operational loads at the same step would result in a resisting friction lower than the actual amount due by the total self-weight.With the setup described above, a convergence analysis has been conducted in order to find out the appropriate size of typical mesh element. Across the grout thickness, three elements have been used in accordance to DNVGL-RP-0419 [33]. Various analyses have been conducted with different meshing arrangements. Several structural responses have been monitored at some selected hotspots; the results at one of them are shown in Figure . It can be seen that above 21500 mesh elements for the grout part, the structural responses converge; this corresponds to a mesh size of 35 cm x 35 cm for the connection (both grout and steel wall).

Figure 10: Convergence analysis.

5.1.4 Homogenization MethodsHomogenization techniques belong to the family of multi-scale modeling. According to Babuska (1976) [35], the homogenization deals with macrobehaviour of engineering systems based on their microproperties. Practically, structural responses evaluated at mesh elements can be used to assign structural responses of homogenized topological domains (see e.g. [36], [37]). Actually, the whole grout is subdivided into homogenized topological domains and the equivalent structural responses of a given domain are obtained from the averaging of the structural responses of their elements. This averaging leads to robust response values and avoids conclusion on the structure based on a single element response.In this study, the grout has been subdivided into seven domains in the meridional direction, and six domains in the circumferential direction, which corresponds to rectangle of dimensions 2.43 m x 4.84 m. This subdivision is based on the knowledge acquired in the load transfer. Indeed, it is assumed [38] that the local pressure is exerted in a triangular shape on about the half height

23


of the grout. The meridional side of each triangle is subdivided in three domains. In the hoop direction, loads are transferred in various modes, which each modularly covers half of the circumference i.e. three domains.

5.2 Cylindrical Connection with Shear keys

A cylindrical grouted connection in a monopile can be constructed with the transition piece placed either outside or inside the foundation pile. Traditionally the transition piece is located outside the foundation pile. This is mainly to be able to mount accessories like boat landings and to paint the structure before load-out. Locating the transition piece inside the foundation pile may not protect the grout from wave action and associated wash-out during the curing of the grout. Full protection from wave action and associated washout during the curing of the grout will require fitting of a protective cover of the exposed grout at the top of the grouted connection. A cylindrical grouted connection with shear keys with the transition piece placed outside the foundation pile, as shown in Figure 6, has been studied and documented in this report.

Figure 6: Principle of cylindrical grouted connection in a monopile structure with the transition piece place outside

Grouted connections in monopiles may be made with or without shear keys. When the connection is to transfer axial force, the connection shall be conical or it shall be made with shear keys, but it should not combine a conical shape with shear keys. Tubular (cylindrical) grouted connections in monopiles which are to transfer axial force shall always be designed and constructed with shear keys. In general, the application of shear keys can improve the ultimate bearing capacity of a grouted connection significantly. Nevertheless, shear keys may reduce the fatigue strength of the tubular members and of the grout due to the stress concentrations around the shear keys. Depending on the flexibility of the grouted connection, shear keys used to transfer axial loads will also transfer part of an applied bending moment. This implies that in practice it may be difficult to

24


fully separate axial loads and bending moments when designing the shear keys [40]. The cylindrical grouted connection studied in this section has been made with shear keys. Figure shows in detail the main dimensions of a connection of this type:

Figure12: Definition of symbols for grouted connection with shear keys

The main issue of these types of connections is the fatigue and corrosion because wind turbines operate in a very aggressive environment. For this reason, these two degradation mechanisms will be evaluated in the grouted joint. Although fatigue is the most demanding loading condition, it is necessary to assess the maximum loads during storm conditions. Because of ultimate analysis is not a hot topic of research, only fatigue analysis will be explained in detail in this report.

Section 5.2 of this report describes the methodology followed by CTC to assess the fatigue damage of a cylindrical grouted connection with shear keys in a monopile able to support a 10 MW offshore wind turbine. Figure 7 illustrates this methodology:

25


Figure 73: Methodology followed to assess damage due to fatigue

This methodology describes how the geometry of the cylindrical grouted connection and the fatigue loads (time series) are the input of a parametric FE Model. This model runs all the fatigue time series for the given geometry and gives, as output, the stresses the model suffers. An assessment of these stresses is made for the design lifetime of the wind turbine, obtaining as final output the accumulated fatigue damage of the steel parts of the cylindrical grouted connection..

5.2.1 Geometry

The geometry of a cylindrical grouted connection with shear keys is formed by two concentric tubular sections made of metal, usually steel, where the annulus between the outer and the inner tubular is filled with grout. The inner tubular is generally the pile, which is the foundation of the connection. The outer is the transition piece. Shear keys are circumferential weld beads on the outside of the monopile and the inside of the transition piece in the grouted section. As it has been already mentioned, its purpose is to increase the sliding resistance between the grout and steel.

The parameters with fixed values provided are listed as follows:

PILE: Diameter (Dpile) Thickness (tpile) Length (Lpile)

26


TRANSITION PIECE: Thickness (tTP) Length (LTP)

Besides, two extra parameters have been defined to create the different geometries that are going to be evaluated with the parametric design methodology. First, the third dimension to totally define the geometry of the transition piece, its diameter, depends on the thickness of the grout (tg) and the diameter of the pile (Dpile). This parameter is one of the two parameters that has been defined to create the different geometries assessed in the parametric design methodology. The other parameter is the vertical centre-to-centre distance between shear keys (s), shown previously in Figure. Three different values have been assigned to this two parameters resulting in nine geometries.

If the values of the diameter of the pile and the thickness of the grout are known, the only dimension to define totally the grout is the effective length of the grout section (Lg). Lg is extended along all the length of the grouted section from the grout packers to the top of the pile (Loverlap) minus two times the grout thickness:

Lg=Loverlap−2∗t g (26)

It is recommended that the grout-length-to-pile-diameter ratio is kept within the following range:

1.5≤Lg

D p≤2.5

By this reason, there is a minimum and a maximum recommended value of Loverlap. The values of this parameter will be between this maximum and this minimum value:

Loverlapmax=Lg+2∗t g=(2.5∗Dpile )+2∗t g (27)

Loverlapmin=Lg+2∗t g=(1.5∗Dpile )+2∗t g (28)

Loverlapmean=

Loverlapmax+Loverlapmin

2(29)

Once the grout is defined, it is necessary to define the geometry of the shear keys and the vertical centre-to-centre distance between shear keys. There are three types of shear keys (see Figure 8) but only the weld bead type has been considered in this study [40].

27


Figure 84: Types of shear keys: a) weld bead, b) steel block, c) round bar

The next step for defining the model is to select the distance between shear keys. The shear keys are placed in the central region of the grouted connection as indicated in Figure. The central region extends over half the effective grout length (Lg), is centered in the grouted connection midpoint and has a distance Lg/4 to either end of the effective part of the grout. The vertical centre-to-centre distance between shear keys (s) must fulfil the next requirement [41]:

s≥min{0.4 √Rpile ¿t pile0.4 √RTP ¿tTP

(30)

The relation between the height of the shear keys (h) and its width (w) (see Figure 8) needs to fulfil the following conditions [41]:

h≥5mm ; 1.5≤ wh≤3.0 ; hs ≤0.10 (31)

The parameter s is constant for the monopile and TP, being the number of shear keys on the TP the number of shear keys of the pile plus one. The number of shear keys in the pile and in the transition piece is given by the next expression:

Number of shear keys∈the transition piece(N ¿¿ shearkeysTP)=

Lg

2s

+1 ¿(32)

Number of s hear keys∈t h e pile(N s hearkeysP)=N s hearkeysTP−1 (33)With all the equations presented along this section, the geometry is totally defined. A summary of the parameters obtained with these equations is listed as follows:

Effective length of the grout section (Lg) Thickness of the grout (tgrout) Vertical centre-to-centre distance between shear keys (s) Height of the shear keys (h) Width of the shear keys (w) Number of shear keys in the transition piece (Nshearkeys_TP) Number of shear keys in the pile (Nshearkeys_P)

28


5.2.2 Time Series (Loads)

Once the geometry of the cylindrical grouted connection is created, the loads applied to this geometry will be defined. The life of a wind turbine can be represented by a set of design situations covering the most significant conditions that the wind turbine may experience. The load cases shall be determined from the combination of operational modes or other design situations, such as specific assembly, erection or maintenance conditions, with the external conditions. All relevant load cases with a reasonable probability of occurrence shall be considered, together with the behavior of the control and protection system. The design load cases used to verify the structural integrity of a wind turbine shall be calculated by combining:

Normal design situations and appropriate normal or extreme external conditions

Fault design situations and appropriate external conditions Transportation, installation and maintenance design situations and

appropriate external conditions

The time series for the 10 MW wind turbine at the monopile is based on the aero-elastic model of the 10MW DTU wind turbine. The time series are given at the interface between the transition piece and the tower. A list of the load cases considered in this report is shown in the following table:

Table 7: Description of DLCs consideredName Description Load PSF T(s)

DLC12 Power production in normal turbulence Fatigue 1 600

DLC13 Power production in extreme turbulence

Ultimate 1,35 600

DLC14Power production in extreme

coherent gust with wind direction change

Ultimate 1,35 100

DLC15 Power production in extreme wind shear

Ultimate 1,35 100

DLC62 Parked without grid connection in 50-year extreme wind

Ultimate 1,1 600

There are four load cases for ultimate limit state assessment and one load case for fatigue limit state assessment. Partial Safety Factor (PSF) increases the forces by a certain value, being applicable to the first four cases. Fatigue load case has a PSF equal to 1 because this case is affected by the Design Fatigue Factor (DFF). The design fatigue factor is a safety factor that reduces the fatigue life time, or what it is the same, fix the accumulated fatigue damage threshold below 1.

29


5.2.3 FE Model

CTC has developed and implemented a FE model of the cylindrical grouted joint in ANSYS. The model has been written in Ansys Parametric Design Language (APDL) in order to parametrize the geometry. The parameters of the geometry implemented in the FE model are listed as follows (rest of dimensions depend on these ones):

Diameter of the pile (Dpile) Thickness of the pile (tpile) Length of the pile (Lpile) Thickness of the transition piece (tTP) Length of the transition piece (LTP) Thickness of the grout (tgrout) Vertical centre-to-centre distance between shear keys (s) Height of the shear keys (h) Width of the shear keys (w)

Once all values of the parameters have been defined, the code automatically generates the geometry and the mesh. 3-D solid elements have been used in the pile, TP and grout and 3-D surfaced contacts have been set in the two interfaces: pile-grout and grout-TP.

The element and the type of contacts used in the FE model are explained below: SOLID185 has been used for meshing the geometry of the pile, grout and

transition piece. The number of elements depends on the value of the parameters because different geometries are created and the number of elements is not the same for all these geometries. SOLID185 is used for 3-D modeling of solid structures. It is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element has plasticity, hyperelasticity, stress stiffening, creep, large deflection, and large strain capabilities. It also has mixed formulation capability for simulating deformations of nearly incompressible elastoplastic materials, and fully incompressible hyperelastic materials. SOLID185 Structural Solid is suitable for modeling general 3-D solid structures. It allows for prism, tetrahedral, and pyramid degenerations when used in irregular regions, although for this FE model none of these degenerations have been used.

30


Figure 9: SOLID185 Structural Solid geometry

TARGE170 is the target part of all the contacts used in the model. Contact analysis are highly nonlinear and require significant computer resources to be solved. Two parts intervene in a contact: the target and the contact. Contact elements are constrained against penetrating the target surface. However, target elements can penetrate through the contact surface. TARGE170 is used to represent various 3-D target surfaces for the associated contact elements (CONTA173, CONTA174, CONTA175, CONTA176 and CONTA177). The contact elements themselves overlay the solid, shell, or line elements describing the boundary of a deformable body and are potentially in contact with the target surface, defined by TARGE170. Translational or rotational displacement, temperature, voltage, magnetic potential, pore pressure, and concentration on the target segment element can be imposed, as well as forces and moments on target elements. For rigid target surfaces, these elements can easily model complex target shapes. For flexible targets, these elements will overlay the solid, shell, or line elements describing the boundary of the deformable target body.

31


Figure 106: TARGE170 geometry

CONTA174 is the contact part of all the contacts between the grout and the pile and between the grout and the transition piece. The friction coefficient was assigned a value of 0.4 for both grout-steel interfaces. CONTA174 is used to represent contact and sliding between 3-D target surfaces and a deformable surface defined by this element. The element is applicable to 3-D structural and coupled-field contact analyses. It can be used for both pair-based contact and general contact. In the case of pair-based contact, the target surface is defined by the 3-D target element type, TARGE170. In the case of general contact, the target surface can be defined by CONTA174 elements (for deformable surfaces) or TARGE170 elements (for rigid bodies only). The element has the same geometric characteristics as the solid or shell element face with which it is connected. Contact occurs when the element surface penetrates an associated target surface. Coulomb friction, shear stress friction, user-defined friction and user-defined contact interaction are allowed. The element also allows separation of bonded contact to simulate interface delamination.

32


Figure 17: CONTA174 geometry

Figure 18 shows one of the 9 FE model created. The zone where the shear keys are placed has a higher mesh density (black area in Figure 18).

Figure 18: Mesh of the FE model

5.2.4 Stresses (results)

As it was indicated in Figure 7, the FE model has, as inputs, the geometry and the time series, to return, as output, the stresses generated by the time series in the geometry selected. As My is the most dominant load in all the fatigue load cases of the time series, the maximum stress will occur in the x-direction of the model. This assumption was also confirmed with the stresses obtained in the first load cases run, where the highest stress was in the indicated zone. By this

33


reason, only the stresses of the nodes located in two regions will be extracted for the later fatigue assessment. Considering angles from the positive part of the x-axis measured counterclockwise, these are the two regions mentioned:

from 330º to 30º (thirty degrees each side of the positive x-axis) from 150º to 210º (thirty degrees each side of the negative x-axis)

The following figure shows the elements whose nodes will be selected to extract stresses and run the fatigue assessment:

Figure 19: Elements whose nodes are selected to extract stresses

The stresses provided by the FE model for the steel parts, pile and transition piece, are Von Mises stresses. These results will be treated by CTC to run the fatigue assessment.The stresses considered for the grout design above are principal stresses.

5.2.5 Fatigue assessment

In order to carry out the fatigue assessment a methodology has been developed (see Figure ).

34


Fatigue Algorithm Module II

Fatigue Algorithm Module I

0

Design Load Cases (DLCs)DLC-1 DLC-2 DLC-i …

Load History (F-t)

Nodal Stress History(σ-t)

FE Model -Grouted Joint -ANSYS Mech.

S-N Curves-DNV: Hot Spot (D)Environments: • Air.• Seawater with CP.• Free corrosion.

Total Cumulative fatigue damage(20 yrs)PileandTP

Nodal Data Pre-processing

RainflowCycle Counting Method

Nodal DamageDLCi (MinerRule)

Corrosion Plate Thinning (yr-by-yr)

Fatigue Algorithm Module III:Data Post-processing: • RF Matrices / DLCi.• RF Matrix Combined 20yr.

Thickness correction

Annual DLC Occurrence

Environmental condition (yr-by-yr)

Figure 20: Methodology flowchart

This methodology is respectively composed by 3 modules. These modules have been developed in MATLAB programming language. The different modules and steps are listed below:

In Module I, the first step is to pre-process the information regarding the nodal stress. All the stress-time series for each DLC at the pile and transition piece (steel parts of the grouted joint) feed the module I of the methodology.

FE analyses of load-time series for 600 seconds of time span were performed dynamically in the FE model for each DLC, as described in previous sections using ANSYS [42]. Stress time history of each node for the grout, pile and transition piece limited by an angle of +/- 30 degrees from X-axis where the Von Mises equivalent stress was selected to analyse multiaxial fatigue stresses.

As a first step, data of all nodes is pre-processed in module I, therefore, nodes from pile and transition piece are classified. A value of 20 years for service life of the steel parts of the grouted joint is taken, according to the values often considered in normative [40].

35


For each node and DLC, cycles are counted using Rainflow cycle counting method (ASTM E1049 [45]). Rainflow method is usually recommended for fatigue assessment and known as very accurate [46]-[48]. Rainflow algorithm provides values of number of cycles corresponding to the same stress range and mean stress.

Until this point, corrosion has not been mentioned in section 5.2. Due to these grout connections are used in sea waters, corrosion must be taken into account as degradation mechanism. Along this section 5.2.5, plate thinning effect due to corrosion in this type of connections will be considered to create the methodology to assess fatigue. Otherwise, it is optional to include an annual stress-rising coefficient per year. In the case study developed in section 5.2.6 no corrosion will be considered in the fatigue assessment, while in the case study detailed in section 7.2.2, the effect of corrosion will be taken into account.

In the next step, the number of cycles to failure is obtained by means of S-N Curves. Before calculating cycles to failure with the S-N Curves, stress range must be corrected with thickness according to DNVGL-RP-0005 [49] because S-N Curves were originally tested for a limited range of thickness. Each S-N curve correspond to a detail. In this case, Curve D recommended for hot spots is used. Three environmental conditions are evaluated for S-N Curve for all the studied nodes and DLCs: in air, in seawater with cathodic protection and free corrosion.

In Module II, the previous results per DLC are collected and organized. Cumulated fatigue damage is estimated for the total service life of 20 years, considering the environmental effect in two ways: from modified S-N curve with environment and, in the corrosion plate thinning case, also by stress rising. The environmental effect is implemented in a year-by-year basis, including the selection of the S-N curve as summarized in Table 8, also based on the corrosion protection applied in agreement with Table . Palmgren-Miner Rule [50],[51] is used to estimate the accumulated fatigue damage. The cumulative damage D is obtained with a modified version of the equation described in section 6.6.3 in DNVGL-ST-0126 [40]

Table 8: S-N Curve selection related to corrosive environment (S-N curve D)

Designed life

(years)Pile

S-N Curve in Pile acc. to [40].Error:Referencesource not

found

Transition piece

S-N Curve in TP acc. to

[40].

0 - 5 Cathodic protection In seawater Coating In air

5 - 10 Free corrosion Free corrosion Coating In air

10 - 15 Free corrosion Free corrosion Free

corrosionFree

corrosion15 - 20 Free Free corrosion Free Free

36


corrosion corrosion corrosion

Finally, Module III is the last step in the methodology is to analyze and represent the results. By this reason, Rainflow matrices of each DLC are generated in module III for the most damaged node of both structural components, the pile and the transition piece. Furthermore, a combined matrix for the complete service-life (20 years) is defined and plotted for the nodes of the pile and transition piece.

A description of the three modules will be performed in the following sections:

5.2.5.1Module I description

The aim of the first module is to obtain the cumulated damages due to each DLC in all analyzed nodes, considering environmental effects.

The inputs of Module I are: Nodal stress history classified by DLC and component, both pile and

transition piece. Stresses are listed for Von Mises equivalent stress. List of DLC Cases. Service life in years. Mean thickness of the pile and transition piece. Yield limit of steel. Stress-rising coefficient per year due to corrosion plate thinning (optional). S-N Curve parameters according to DNVGL-RP-0005 [49] for air, seawater

with cathodic protection and free corrosion. Thickness correction exponent and reference thickness for S-N Curves

according to DNVGL-RP-0005 [49].

Output data given by this module are: Cumulative nodal damage per DLC and year for three environmental

conditions for pile and TP. Yield limit check for all stress histories. List of nodes classified by component: pile or TP.

Main steps executed by the algorithm module are:

1. Nodal data pre-processing (nodes are classified from DLC and component). Data is read from *.csv files of nodal results provided by FE model. Stress histories are listed with Von Mises equivalent stress.

2. Nodal stress history (equivalent stress vs. time) for the fatigue assessment is needed to arrange the fluctuating stress in cycles corresponding to a stress range and mean stress. The nodal stress history will be multiplied by a factor considering corrosion plate thinning before cycle counting, if is the case. As described in section 7.2.1, this coefficient is calculated as the inverse of the reduction in inertia moment due to corrosion ratio, assuming bending moment as main influence. To count the cycles related to a stress range and mean, the Rainflow Cycle Counting Method, documented in Section 5.4.4 of ASTM E1049 [45], has been applied. This method is a widely used approach for computing stress

37


cycles from a uniaxial stress histories [47],[52]. Rainflow counting received its name because the method resembles rain drops flowing off a pagoda roof as shown in Figure .

Figure 21: Rainflow counting illustration with beginnings and ends following the rainflow rules [52].

This algorithm is executed for each node and DLC year-by-year and when corrosion thinning is considered, stresses are increased with the stress-rising coefficient. Thus, this programmed function is called around 25 million times, which in turn needs a computational effort. For the studied case, a MATLAB programmed toolbox is used [53].

3. Once cycle counting is done, the number of cycles to failure can be obtained for Palmgren-Miner Rule. In order to do this, stress ranges are corrected considering thickness of the component. S-N Curves were obtained for a reference thickness; therefore, stress range must be modified according to DNVGL-RP-0005 [49], with the following equation:

Δ σmod=(Δ σRF ( ttref )

α

) (34)

where: t: component mean thickness. tref: reference thickness, tref= 25 mm for welded plates. α: thickness exponent, 0.20 for S-N Curve D.

The value of modified stress range is introduced in the S-N Curves associated to three environmental conditions: in air, in seawater with

38


cathodic protection and free corrosion. Logarithmic parameters of the Curve S-N are summarized in Table 9. Then, the number of cycles to failure is calculated. Each DLC for all the studied nodes is evaluated in a year-by-year basis.

Table 9: S-N Curve D parameters (hot spot) [49].

S-N Curve Environment

N ≤ Np cycles N > Np cycles Np

m1 log a1 m2 log a2

In air 3.0 12.164 5.0 15.606 107

In seawater with cathodic protection 3.0 11.764 5.0 15.60

6 106

Free corrosion 3.0 11.687 -- -- --

4. The number of cycles for each block allow to calculate the fatigue damage for each DLC and environmental condition in all nodes. Palmgren-Miner Rule modified as shown in the following equation for each DLC and node per year, as mentioned previously.

5. The cumulative nodal damage will serve as feed data for module II and this data is stored in Excel files classified by DLC short name.

5.2.5.2Module II description

This second module gathers all the cumulative nodal damage per DLC, providing total damage per DLC for the selected environmental conditions, considering the coating breakdown of transition piece and optionally, the annual corrosion rate in the inner and/or outer side of the pile and transition piece.

The inputs of module II are: Cumulative nodal damage per DLC and year for three environmental

conditions. List of nodes of pile and TP. Environmental condition by year in service. Service life in years. Annual occurrence of each DLC, expressed in percentage from total load

time of the year. Total load time per year (does not include calms). List of Design Load Cases (DLCs).

Main output data from module II include: Cumulative nodal damage for complete service life (20 years) considering

both effects of environment in S-N curves and optionally, corrosion plate thinning.

List of failed nodes in transition piece and pile (only if the case, for total damage > 1).

39


Number of failed nodes of both, transition piece and pile.

The code is composed by the following 4 steps:

1. Files pre-processing and data reading, including the results of module I.2. Second part sums total damage of pile and transition piece nodes for the

complete service life for the selected environmental conditions, implicitly considering the coating breakdown of transition piece and, if it is the case, the annual corrosion rate in the inner and outer side of the pile and transition piece. The formula applied is:

Dtotal−node=∑k=1

yr

(∑j=1

m

f 0 , j · DDLC−node) (35)

where f 0 , j is calculated as f 0 , j=Time loadTimeseries

.Oc j /100

The annual time of load for all the DLCs is 7806.61 hours/year. The duration of the time series is 600 seconds. The occurrence percentage (Ocj) is the occurrence of each DLCj related to the total time of load, as it is shown in Table 9:

Table 9: Occurrence of DLCs.Load Case short name

Occurrence (h/yr) Ocj (%)

DLC12_1 933.75 11.961DLC12_10 1087.30 13.928DLC12_19 1129.05 14.463DLC12_28 1106.75 14.177DLC12_37 1006.40 12.892DLC12_46 820.15 10.506DLC12_55 633.00 8.109DLC12_64 418.65 5.363DLC12_73 312.70 4.006DLC12_82 209.90 2.689DLC12_91 148.96 1.908

3. In this part, all analyzed nodes have been checked against failure (Dtotal−node>1). Node indexes of failed nodes are archived in a file.

4. Total service-life damage is stored for each studied node in an Excel file.

40


5.2.5.3Module III description

The third module gives a post-processing analysis of results, providing Rainflow matrices of each DLC for more damaged nodes in steel parts. Also, it gives as result a combination of all matrices for full service life of the two nodes with maximum damage. Additionally, all the Rainflow matrices are shown graphically, plotting the cycles related to a mean stress and amplitude.

Main input data include: Nodal stress history classified by DLC and component, both pile and TP.

Stresses are listed for Von Mises equivalent stress. Only reads one node per component, the node with highest accumulated fatigue damage

List of Design Load Cases (DLCs). Service life in years. Cumulative nodal damage for complete service life (20 years). Annual occurrence of each DLC, expressed in percentage from total load

time of the year. Total load time per year (does not include calms).

The output data provided by module III: Rainflow matrices for each DLC in the more damaged node of both, pile

and TP. Combined Rainflow matrix for full service life of pile and TP, individually.

Considers full number of cycles and is capable to incorporate environmental and corrosion effects.

Blocks of number of cycles, with the related mean stress and stress amplitude for full service life in the more damaged node of both, pile and TP.

Contour and 3D mesh plots of Rainflow matrices generated.

Main programing parts of module III for both components are:

1. Nodal search of the nodes with higher cumulative damage.2. Rainflow matrices are generated in loop for each DLC for the most

fatigued node.3. Full assessment of fatigue of more damaged node to obtain the complete

range stress blocks for service life. Optionally, stress-rising coefficient due to corrosion may be applied yearly. Rainflow matrix combined generated from the calculated blocks of full service life (20 years).

4. Results are plotted in bar, 3D mesh and contour plots.5. Rainflow matrices generated are stored into excel files

5.2.6 Case study

In this section, a case study will be developed following the methodology explained in the previous sections (see Figure 7).

41


5.2.6.1GeometryFirst, the geometry of the connection will be defined. As it was explained in the section 5.2.1, some parameters were fixed whose values are listed as follows:

Diameter of the pile (Dpile) = 9m Thickness of the pile (tpile) = 97mm Length of the pile (Lpile) = 56m Thickness of the transition piece (tTP) = 80mm Length of the transition piece (LTP) = 26m

The pile and the transition piece are proposed to fulfill the following requirement according to [41]:

10≤Rp

t p≤30 ;9≤

RTP

tTP≤70 (36)

Both requirements are not fulfilled by the present values of the geometry.

The third dimension to define totally the geometry of the transition piece, its diameter, will depend on the thickness of the grout (tg). This parameter is one of the two parameters that will be modified to create the different geometries assessed. There will be three different values for the thickness of the grout: 70, 90 and 110mm. The three values fulfill the requirement to have a minimum grout thickness of 40 mm. The other parameter to be modified in the model is the vertical centre-to-centre distance between shear keys (s), shown previously in Figure. Three different values will be assigned to s too, resulting therefore nine different geometries.

The third dimension to define completely the grout is the effective length of the grout section (Lg):

Lg=Loverlap−2∗t grout (37)It is recommended that the grout-length-to-pile-diameter ratio is kept within the following range:

1.5≤ LgDp

≤2.5 (38)

By this reason, there is a minimum and a maximum recommended value of Loverlap. The values of the parametric model of this parameter will be between these two values, selecting finally a mean value of these two values:

Loverlapmax=Lg+2∗t g=(2.5∗Dpile )+2∗t g (39)

Loverlapmin=Lg+2∗t g=(1.5∗Dpile )+2∗t g (40)

Loverla pmean=Loverlapmax

+ Loverlapmin

2(41)

42


The mean value of Loverlap for the three values of tg is similar. Therefore, an unique value of Loverlap was considered by CTC for the three cases. The same occurs with Lg, so another unique value will be selected. The following table shows the values used for the parametric model:

Table 10: Values of Loverlap and Lg to be used in the modeltgrout (m) Loverlap

(m)Loverlap_used

(m) Lg (m) Lg_used (m)

0.07 17.1417.5

17.3617.30.09 17.18 17.32

0.11 17.22 17.28

The next step for defining the model is to select the vertical centre-to-centre distance between shear keys, that must fulfil the next requirement:

s≥min{0.4 √Rpile ¿t pile=0.26m0.4√RTP¿ tTP=0.22m

(42)

Therefore, three values of s are selected by CTC to assess the influence of this parameter in the structural behavior of the model: 0.5, 1 and 1.5m. Different values of height (h) and width (w) are considered attending the following requirement for the geometry of the shear keys:

h≥5mm ; 1.5≤ wh≤3.0 ; hs ≤0.10 (43)

Table shows how this requirement is fulfilled for the three values of s and their corresponding values of h and w.

Table 12: Fulfilled requirement for the three values of s

s (m) h (m) w (m) h≥5mm 1.5≤ wh≤3.0 h

s≤0.10

0.5 0.02 0.04 h=0.02; OK wh=2 ; OK h

s=0.04 ; OK

1.0 0.04 0.08 h=0.04; Ok wh=2 ; OK h

s=0.04 ; OK

1.5 0.06 0.12 h=0.06; OK wh=2 ; OK h

s=0.04 ; OK

To obtain the number of shear keys in each part of the connection, as Lg has been decided to have the same value (17.3m) for the three possible values of

43


the grout thickness, there will be a different number of shear keys for each value of s (see Table 11):

Table 1113: Number of shear keys in transition piece and piles (m) N shearkeysTP N shearkeys P

0.5 18 171.0 10 91.5 7 6

As three different values of s and three diferent values of tgruot have been considered, a total of nine geometries were studied (see Table ). One of these nine geometries will be selected, based on ULS analysis, to study its fatigue behavior.

Table 14: Geometries considered depending on s and tgrout

Geometry s (m) tgrout (m) h (m) N shearkeysTP N shearkeys P

10.5

0.070.02 18 172 0.09

3 0.114

1.00.07

0.04 10 95 0.096 0.117

1.50.07

0.06 7 68 0.099 0.11

Once all the parameters are fixed, the nine geometries were created in ANSYS. An ULS analysis was run for all of them to select the geometry that had the best structural behavior. This selected geometry has been used to run the fatigue assessment. The loads applied to the geometries were the maximum values of the static load cases of the time series. The load cases forultimate limit state are DLC13, DLC 14, DLC15 and DLC62. The values of the forces and moments of the highest load case are:

Fx = 2.943 e+06 N FY = 2.633 e+06 N Fz = -1.090 e+07 N Mx = -2.124 e+08 N·m My = 2.720 e+08 N·m Mz = 2.557 e+06 N·m

44


These loads were imposed into the FE models. Figure 11 shows an example of the calculations carried out by CTC in ANSYS.

Figure 112: Von Mises stresses for the highest load case of four of the nine geometries

Results of the static analysis concluded that geometry number 9 was the best option to run the fatigue analysis (bottom right corner of Figure 11). This geometry has 1.5m of distance between shear keys and 0.11m of grout thickness (see Table ).

5.2.6.2Time SeriesAfter selecting the most robust geometry, the fatigue load case will be described. As indicated in Table 7, this load case is DLC12. It simulates the power production of an offshore wind turbine without faults performed for wind speeds in the entire operational range with normal turbulence. The cut in wind speed is 4m/s and the cut out wind speed is 25m/s. There are time series for wind velocities from 5m/s to 25m/s (every 2m/s). 3 wave seeds are used in 3 different directions. Yaw errors during normal operation are set to +/- 10°. Several seeds per wind speed and yaw error are used. The wind and wave directions have misaligned combinations for each wind speed. As 11 wind speeds are considered and there are 3 values of wind direction and 3 values of wave direction for each wind speed, there is a total of 99 time series. All the time series have a length of 600 seconds.

45


Only the cases where the wind and wave direction are aligned have been simulated for each wind speed. The reason is the very high time-consuming these simulations are. Table 12 shows the time series used for the fatigue analysis.

Table 125: Time series used for the fatigue analysis (info from DTU)Time Series Short name

dlc12_wsp05_wdir000_wavdir000_s121001 DLC12_1











where: wspXX means that the wind speed has a value of XX. wdirYYY means that the wind direction has a direction of YYY degrees. wavdirZZZ means that the wave direction has a direction of ZZZ degrees.

5.2.6.3FE ModelThe elements and contacts used for the FE model were described previously in section 5.2.3. The model of the geometry selected has a total amount of 515.440 elements. For running the simulations, the properties of the materials of the connection need to be known. In the Table 13 these properties and their values are shown:

Table 136: Properties of the materials of the connection (information provided by DTU)

Property Grouted Joint

Pile and Transition piece

Young's Elasticity Modulus (Pa) 5 e+09 2.10 e+11

Poisson's ratio 0.20 0.3

46


Effective Density (kg/m3) 2350 7850

Figure 12 shows the FE model used for obtaining the stresses to run the fatigue assessment.

Figure 123: FE model used

5.2.6.4ResultsThe results of the simulations of the 11 load cases indicated in the Table 12 will be used for the fatigue assessment. It is important to point out that fatigue only will be assessed for the steel parts (pile and transition piece). As it was indicated in section 5.2.4, only one third part of the nodes have been considered to be evaluated from the fatigue point of view. A file with the Von Mises stress results has been generated for the third part of the joint, i.e. the 57.824 and 58.188 nodes for the pile and transition piece respectively. So, 116.012 files for each time series which makes a total of 1.276.132 files. Some examples of the results for certain instants of different time series are shown in Figure :

47


Figure 24: Examples of results of different FE analysis

5.2.6.5Fatigue assessment

In the present case study, only environmental effects that affect S-N Curves are considered. Two categories of S-N Curves have been studied herein. S-N Curve D is firstly analysed as is recommended for hot spot stresses according to DNVGL-RP-0005 [49]. S-N Curve C1 has also been selected with the objective of comparing with the methodology followed by DTU. Curve C1 corresponds to the detail of transverse splices in plates and rolled sections in Table A-5 according to DNVGL-RP-0005 [49]. Consequently, thickness exponent changes according to the S-N curve. While in air condition takes the value of 0.15, this value is 0.10 for the rest of environmental conditions. This assessment covers the pile and transition piece separately.

Following the methodology described in section 5.2.5, different results for fatigue assessment are obtained depending on the component and the selected S-N curve category. In the first case (with D-Curve), different results of damage are estimated for each component; while the pile is capable to resist 20 years’ service-life against fatigue failure, transition piece surpasses the level of admissible damage (D > 1) in 17 nodes. These failed nodes are located at the upper shear key in the model. In the second case (C1-Curve), both components resist fatigue damage for complete service life. Values of maximum

48


accumulated damage are shown below for the pile and the transition piece, classified by S-N curve classes (D and C1).

Table 17: Cumulative damage in pile and TP.

ComponentMax.

Damage with D-Curve

Nº failed nodes with

D-Curve

Max. Damage with C1-Curve

Nº failed nodes with C1-Curve

Pile 0.8433 0 0.2867 0Transition

piece 1.1361 17 0.4043 0

Figure 13 shows the fatigue damage of all the analyzed nodes separately for pile and transition piece with S-N Curve D, being 1 the threshold.

Figure 135: Cumulative fatigue in various FE nodes as estimated by algorithm; left side, pile and right side, TP (fatigue life limit marked with red line).

In the following graphs, plots of the combined Rainflow matrices are shown for the most fatigued node of the pile (see Figure ) and of the transition piece (see Figure 14). It is observed that transition piece node generally shows higher amplitudes compared to the counterpart node in transition piece. Rainflow matrices are often drawn to represent fatigue analyses [54].

49


Figure 6: Rainflow matrix plots (3-D mesh and contour) in pile.

X - ampl

Y -

mea

n

5 10 15 20 25

5

10

15

20

25

30

35

40

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

x 106

Figure 147: Rainflow matrix plots (3-D mesh and contour) in transition piece.

One reason that may explain the differences between the pile and the transition piece is the difference in the moment of inertia, lower in the case of transition piece,. It is also worth noting that the grout, as is less stiff (lower elastic modulus than steel, Table 13), may be acting like a damper, hence decreasing dynamic stresses downwards.

Figure 14 shows a dispersion of values in the up-right hand. These values came from only 3 load cases but have a strong impact in the fatigue life.

Several solutions are proposed to reach full service life in the case of transition piece:

Define an inspection program according to DNVGL for the transition piece, so DFF can be reduced to a value of 2.

Increase of lifetime of coating protection, assuring 20 years of duration. Wall thickness increase in the transition piece. Modified design of shear keys in grouted joint, with the aim of diminishing

notch effect and stress concentration in fatigued zones.

5.2.7 Fatigue reliability assessment

50


Fatigue reliability is assessed using SN-curve approach together with Miner’s rule, combined in the following limit state function:

g(X , t )=D cr−D ( t )≥0 (44)

g=Δ−∑i ,1

t ni(CSCF CW Δσ i( Tt ref )

k)m1

a1−∑

i, 2

t ni(C SCFCW Δσ i( Tt ref )

k

)m2

a2¿0

(45)

where CSCF and CLoad are model uncertainties related to stress concentration factors and fatigue load; Δ models model uncertainty related to Miner’s rule. a1 and a2 are stochastic variables modelling uncertainty related to the SN-curve; m1

and m2 are slopes of a bi-linear SN curve; k is the thickness exponent for a given SN curve; t is the time in years; T is the thickness of the element; tref is reference thickness (25mm); ni is the number of stress ranges Δσi.

5.2.7.1Stochastic model

SN curves from [49] are used in fatigue analysis (curve parameters are given in Table18). Curve D is applicable for the monopile nodes (curves for free corrosion in seawater and curves with cathodic protection). Curve E is applicable for transition piece nodes at shear keys, based on [10] section 9.3.5. A full description of the stochastic model for fatigue reliability assessment is given in Table18.

Table18: Parameters for probabilistic fatigue damage model.Variable Distributi

onExpected

valueStandard

deviation / COV

Comment

Curve D free corrosion in marine environmentm1 D 3 Slope SN curve

log a1 N 11.687+2x0.2 SD= 0.2 D curve in air DNVm2 D 3 Slope SN curve

log a2 N 11.687+2x0.2 SD= 0.2 D curve in air DNVk D 0.2 - Thickness exponent

Curve D with cathodic protection in marine environmentm1 D 3 Slope SN curve



Curve E “in air”m1 D 3 Slope SN curve



51


Model uncertaintiesΔ N 1 COV =

0.30Model uncertainty

Miner’s ruleCLOAD LN 1 COV=

0.22 (0.17)

Model uncertainty fatigue load

CSCF LN 1 COV= 0.1 (0.05)

Model uncertainty stress concentration

factorlog a1 and log a2 are fully correlated.Bracketed values are for monopile nodes (if different from transition piece).

Modelling uncertainties are not identical because the degree of uncertainty related to modelling wave loads (and stresses in consequence) in the splash zone (COVLOAD=0.22, for transition piece) and below splash zone (COVLOAD=0.17, for upper monopile nodes – down to 20m below MWL) is different according to [61] Table 10-3. Also, an increased uncertainty on load modelling for transition piece nodes next to shear keys stems from higher complexity of load transfer between steel (base material together with shear keys) and concrete within the grouted connection. Furthermore, there is also difference in stress concentration factor uncertainty– typical butt welds in the monopile are quite well understood and COVSCF=0.05 is recommended by [61]. However, for nodes located at shear keys in transition piece, the uncertainties are expected to be higher, due to more complex stress behavior, complex stress transfer between concrete and steel at shear keys, and the fact that “weld bead type” of shear key was used in the study, thus COVSCF=0.10 is used for such nodes.

5.2.7.2Stress range analysis

The hot spot stress ranges were obtained from the data (a limited set of Von Mises stress time series, covering the full operational range of the wind turbine) by applying Rainflow counting algorithm. The extracted hot spot stress ranges subsequently are combined into equivalent damage stress range Δσeq in order to identify the most critical nodes in the using the following equation:

Δσ eq=[∑i=1

n

N i Δσ im

∑i=1

n

N i ]1/m

(46)

Here Ni is number Δσi of stress ranges, m is chosen as 3 (assuming a linear SN curve, with slope m=3). The following figures show the equivalent stress ranges for transition piece and monopile nodes (upper figures) and the most critical cross section (lower figures).

52


a bFigure 28: Equivalent stress ranges, pile – a, Transition piece – b.

It is clear that for the pile the most critical cross section is in the bottom part, where the transition piece ends (for location reference see Figure 11). For the transition piece, data indicates that the most critical cross-section lies next to the first level of shear keys, with stresses significantly reduced at the second level of shear keys. These two critical cross sections were selected for more detailed analysis, the following Figure29 shows the stress amplitude distribution contours for critical cross sections in the monopile and transition piece (all nodes circumferentially).

a bFigure29: Stress amplitude distributions for most critical cross-sections, pile –

a, Transition piece – b.

Further, for detailed analysis only most critical nodes in the cross-section are selected (1 node for pile and for transition piece) and further used in probabilistic modelling of fatigue crack growth, since the most likely crack propagation can be considered to originate from the location where the most critical loading is expected. Furthermore, for crack growth in transition piece, it is very likely that cracks would initiate at the edges of “weld bead” shear keys due to micro-cracks originating from the welding process. Therefore, the following Figure shows the stress range distributions for the two selected nodes, these distributions will be used in further analysis as input to SN and facture mechanics based fatigue crack growth models.

53


a bFigure 0: Stress range distributions for most critical nodes, pile – a, Transition

piece – b.

5.2.7.3Results

Using the stress range distributions for both critical nodes, FORM estimates of annual reliability index are calculated using FERUM 4.1 (Matlab toolbox for structural reliability, [64]) and presented in the following Figure and Figure 15.

Figure 21: Annual reliability index for most critical pile node.

It is seen that at year 16 the annual reliability index becomes smaller than the limit of 3.3 and thus the monopile can be considered “not safe/in failure”. However, it should be noted that a high uncertainty level was considered due to limited loading information available (COVLOAD=0.17). With increased confidence in loading it would be possible to achieve annual reliability index at least or higher than 3.3 at service year 20. Another option could be to implement corrosion protection measures for a part or all lifetime (or coating) – orange curve in the figure above shows results when cathodic protection is active throughout the lifetime. Finally, it could also be investigated if it is possible to perform inspections.

54


Figure 15: Annual reliability index for most critical transition piece node.

The transition piece seems to satisfy the annual reliability requirements when the correct SN curve E is used to estimate the annual reliability index (blue curve in Figure 152). The scenario when the fatigue crack is initiated on the inside of the transition piece (at shear keys) is highly likely due to initial imperfections from welding of the shear keys, thus the use of “In air” SN curve is justified. In a scenario where a fatigue crack is initiated on the outside surface of the transition piece, corrosion protection or coating is necessary to achieve sufficient annual reliability level at service year 20 (yellow curve in2), since the when SN curve for free corrosion in marine environment is used (orange curve), the minimum annual reliability index requirement is violated by year 5.

Figure 163: SN model sensitivity.

However, it should be noted that above reliability estimates are sensitive to choice of magnitude of load and stress concentration factor uncertainties (COVLOAD and COVSCF), as can be seen in Figure . Furthermore, the following Figure17 shows the change in annual reliability index with respect to changing COV LOAD and COVSCF throughout the lifetime of the wind turbine. It is clear that change of either uncertainty effects the annual reliability index significantly. Thus, care must be taken when choosing these parameters and further investigation is necessary to identify and minimize the most influential uncertainties, which is beyond the scope of this deliverable, but will be investigated in D7.42 in more detail.

55


Figure 174: SN model sensitivity to change of Load and Stress concentration factor

uncertainties.

6. Probabilistic Design Methods

6.1 Effect of Variation in Geometry and Material Parameters 6.1.1 Multivariate Interaction between the parameters

The investigation of the effect of geometry and material parameters has been carried out on the conical joint model using static loads resulted from DLC 1.3. The geometry parameters included in the analysis are shown in Table 19 and with the considered range. Table 14 presents the probability distributions of the material parameters. A total of 750 points has been uniformly sampled from the parameter space using the Latin hypercube sampling (LHS) technique. Material parameters are taken between the 0.5 and 99.5 percentiles.

Table 19: Geometry parameters and the considered rangesParameters Nominal Values Lower bounds Upper bounds

LayersPile wall thickness, T p [m] 0.10 0.05 0.15Transition wall thickness, T s [m]

0.08 0.05 0.15

56


Grout thickness, T g [m] 0.15 0.10 0.90Connection

Length, L [m] 18.00 4.00 26.00Conical angle, α [deg] 3.00 0.10 4.00Length of wall ends, Le [m]

0.50 0.10 1.00

Table 140: Material parameters and their probability distributions

Parameters ValuesBias

Mean CoV DistributionSteel

Unit mass, ρ s [kg/m3] 7850 DeterministicElastic modulus, E [MPa] 210 x 109 1.00 0.03 LNPoisson’s ratio, ν [-] 0.3 1.00 0.03 LNYield stress, f y [MPa] 235 x 106 1.05 0.07 LN

InterfaceCoulomb friction coefficient, μc [-]

0.47 1.00 0.15 NShear strength, τ [Pa] 1.05 x 105 1.00 0.05 N

ConcreteUnit mass, ρc [kg/m3] 2500.00 DeterministicCharacteristic strength, f ck [MPa] 120.00 1.00 0.06 LNPoisson’s ratio, ν [-] 0.20 1.00 0.05 LN

As results of the simulations, structural responses related to the limit states presented above were monitored: equivalent stress in the grout, nominal pressure in the grout surface from each of transition and pile sides, shear stress in the interface from both sides, and the relative displacement or sliding between the transition piece and the pile. Two linearized methods were selected to measure the sensitivity of the structural responses with respect to the independent parameters. One is the Input / Output correlation and the other is the standard regression coefficients. Both methods yield to matching results; hence only results from the first method are presented. Figure presents the Pearson product-moment correlation coefficient (denoted linear) and the Spearman's rank correlation coefficient (denoted Rank). The latter is more robust than the former in the presence of strongly nonlinear dependence between variables. The Pearson product-moment correlation coefficient between

the input X i and the output Y j is computed as ρ (X i , Y j )=E [ ( X i−μi ) (Y j−μ j ) ]

σ iσ j

; where

μi and μ j are the means of X i and Y j, respectively; σ i and σ j are the standard deviations of X i and Y j, respectively; and E [ ∙ ] is the expected value operator. The Spearman's rank correlation coefficient is computed as the Pearson product-moment correlation coefficient by substituting the input / output actual value by their corresponding rank-transformed equivalents Ri and R j: ρ s ( X i , X j )= ρ (Ri , R j ).

57

<Stress>

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Figure 35: Input / Output correlation coefficients. ‘Linear’ denoted the Pearson product-moment correlation coefficient and the ’Rank’ Spearman's rank correlation coefficient.

The results show that: The maximal equivalent stress is not significantly linearly correlated to the

parameters. The nominal pressure at the interface is linearly correlated to the length of

the connection: about -80 % correlation coefficient. This means that the longer the connection is, the smaller will be the nominal pressure. As the nominal pressure is robustly measured around the mid-height of the connection, it is not very sensitive to the edge conditions.

Similarly, the maximal shear stress in the interface is highly linearly dependent on the shear strength with a correlation coefficient of about 80 % for the transition side and 70 % for the pile side. This means that the maximal shear stress increases with the shear strength, which is physically meaningful as the maximal shear stress value grows up and is only limited by the shear strength or a fraction of local pressure, and will stay moderate for smaller values of shear strength. The edge length is found to be linearly correlated to the maximum shear stress for the pile side. This can be explained by the fact the load transfer mainly operates at the top edge. For a zero length edge, gap openings at the pile leading meridian will decrease the local pressure and then the maximal shear stress at that location. Conversely, for longer edges, pile ovalization has little effect to the interface as higher shear stress values can occur.

58


The maximum relative sliding of the transition piece with respect to the pile mainly depends on the connection length and the conical angle. Indeed, the relative vertical displacement primarily depends on the tangential component of the structure weight to the interface, whose amplitude depends on the conical angle and the connection length. The necessary reduction of this displacement requires the increase of the conical angle and the connection length.

6.1.2 Effect of conical angleIn particular, the influence of the conical angle on the vertical displacement of the interface is studied. The structural dimensions are set as their nominal values (see Table 19) but the conical angle is varied. A typical loading set is applied on the structure during 600 s and the displacement of the interface is monitored. The results are shown in Figure . They show that with a conical angle of one degree, the transition piece continuously settles down, while with three degrees cone angle, the settlement is stabilized at about 17 mm. This demonstrates the failures observed for near cylindrical joints without shear keys and indicates the necessity to choose a conical angle large enough to guarantee the grouted joint vertical settlement stability.

0 100 200 300 400 500 600Time [s]

-120

-100

-80

-60

-40

-20

0

Dis

plac

emen

t [m

m]

Interface vertical displacement

= 3° = 1°

Figure 36: Influence of the conical angle on the vertical displacement of the interface.

6.1.3 Minimization of tensile crack.Though the apparition of tensile damage on the grout component is acceptable, its amount should be minimized to ensure that the grout continues to play its role. That is why a perturbation analysis has been carried out in order to determine which grout dimensions lead to acceptable level of tensile damage.With the other joint dimensions kept at their nominal values, the grout thickness and height are varied. For a given loading set, the maximum tensile damage is recorded for each grout dimension pair. The results presented in Table shows that marginal tensile damage is obtained with a design of 10 cm grout thickness and 18 m connection length.

Table 21: Perturbation analysis for tensile damage minimizationCase 1 Case 2 Case 3 Case 5

59


Grout thickness [cm] 15 20 15 10Connection length [m] 15 15 18 15Maximum Tensile damage [-]

0.9801 0.1809 0.0732 0.9801

6.2 Probabilistic model for concrete fatigue strength based on Data

This section describes a probabilistic model for fatigue strength of grout / concrete in compression. In section 3.1.2 is presented the characteristic SN-curves used in fib Model Code 1990 and 2010 and in the Eurocode for concrete bridges. These models are used as basis for formulating a probabilistic model for the fatigue strength. Two probabilistic models are proposed, see section 5.2.1. Next, using the Maximum Likelihood Methods (MLM), see section 5.2.2 and data available from different sources the parameters in the probabilistic model are calibrated. In section 5.2.3 the results are summarized and a recommendation for a hierarchical stochastic model is presented. This model can be used in reliability analyses.

6.2.1 Probabilistic modelTwo probabilistic models are considered taking basis in the model in Model Code 2010.

6.2.1.1Model 1Fatigue test data is only available for log N ≤ 8.0, see below. Therefore basis is taken in the SN-curve for log N ≤ 8.0 which is rewritten:

(47)whereA parameter

parameterε error tern assumed to be Normal distributed with expected value = 0 and standard deviation = σ ε .

A , and σ ε are estimated from data available using the Maximum Likelihood Method for data sets of:

N Sc ,min Sc ,max Failure/Run-out...

where it is accounted for if the fatigue test results in failure or non-failure (run-out), see below.

6.2.1.2Model 2Fatigue test data is only available for log N ≤ 8.0, see below. Therefore basis is taken in the SN-curve for log N ≤ 8.0 which is rewritten:

60


(48)whereA parameter ε error tern assumed to be Normal distributed with expected value = 0 and

standard deviation = σ ε .

A and σ ε are estimated from data available using the Maximum Likelihood Method for data sets of:

N Sc ,min Sc ,max Failure/Run-out

In the following sections, model fits to measured data for S-N curves for concrete are presented.

6.2.2 Results The statistical parameters (in Model 1 A , and σ ε ) are estimated using the Maximum Likelihood Method for data sets available of (Ni, Sc,min,i and Sc,max,i). The likelihood function is written:

(49)

where is the number of tests where failure occurs, and is the number of tests where failure did not occur (run-outs). The total number of tests is n= +

.

A , and σ ε are obtained from the optimization problem (50)

or using the log-likelihood function(21)

which can be solved using a standard nonlinear optimizer (e.g. NLPQL algorithm, see Schittkowski [58].

Because the parameters A , and σ ε are determined using a limited amount of data; they are subject to statistical uncertainty. Since the parameters are estimated by the maximum-likelihood method, they become asymptotically (number of data should be > 25 – 30) normally distributed stochastic variables

61


with expected values equal to the maximum-likelihood estimators and covariance matrix equal to, see e.g. Lindley [59].

(52)

is the Hessian matrix with second-order derivatives of the log-likelihood function. , and denote the standard deviations of A , and σ ε , respectively, and e.g., is the correlation coefficient between A and .

The statistical parameters in Model 2 A and σ ε are estimated similarly.

Data for fatigue strength of concrete in compression has been avaiable from the following two reports:

Lantsoght, E.O.L.: Fatigue of concrete under compression - Database and proposal for high strength concrete. Delft University of Technology, Report nr. 25.5-14-04, 2014. [55]

Slot, R.M.M. and Andersen, T.: Fatigue behavior and reliability of high strength concrete. MSc thesis, Aalborg University, Denmark, 2014. [56]

In these reports data from several tests have been collected including test results mentioned in Lohaus et al. [57].

The data has been divided in three groups: High strength concrete (larger than 90 MPa) – number of data = 226 All data from TUD (Lantsoght [55]) – number of data = 371 All data from TUD (Lantsoght [55]) and AAU (Slot and Andersen [56]) –

number of data = 469

6.2.2.1Results for high strength concrete – Model 1Statistical analysis by the Maximum Likelihood Method gives the following results:

Table 152: Statistical results for high strength concrete data.Mean Standard

deviationsCorrelation coefficients

A 5,78 0,28 1 0,02 -0,960,90 0,043 0,02 1 -0,01

σ ε1,13 0,016 -0,96 -0,01 1

Figure 187 to Figure 201 show for Sc ,min = 0,05, 0,10, 0,20, 0,30 and 0,40 the measurement data the mean (best) fit / SN-curve

62


the characteristic SN-curve obtained using the 5% quantile of Model Code 2010 Model Code 1990 Eurocode 2

0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9

1data Smin=0,05meanmean - 2 std.dev.MC 2010MC 1990EC 2

log N

Smax

Figure 187: Fitted SN-curve for high strength concrete for Sc,min = 0,05.

0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9


log N

Smax


63


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0.9


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Smax


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64


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Smax


6.2.2.2TUD data – Model 1Statistical analysis by the Maximum Likelihood Method gives the following results:

Table 163: Statistical results for TUD data.

Mean Standard deviations

Correlation coefficients

A 5,77 0,25 1 0,01 -0,951.04 0,039 0,01 1 -0,01

σ ε1,10 0,013 -0,95 -0,01 1

Figure 212 to 46 show for Sc ,min = 0,05, 0,10, 0,20, 0,30 and 0,40 the measurement data the mean (best) fit / SN-curve the characteristic SN-curve obtained using the 5% quantile of Model Code 2010 Model Code 1990 Eurocode 2

65


0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9


log N

Smax

Figure 212: Fitted SN-curve using TUD data for Sc,min = 0,05.

0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

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0.9


log N

Smax


66


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0.9


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Smax


0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9


log N

Smax

Figure45: Fitted SN-curve using TUD data for Sc,min Sc ,min = 0,30.

67


0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9

1 data Smin=0,40meanmean - 2 std.dev.MC 2010MC 1990EC 2

log N

Smax


6.2.2.3TUD and AAU data – Model 1Statistical analysis by the Maximum Likelihood Method gives the following results:

Table 4: Statistical results for TUD + AAU data.

Mean Standard deviations

Correlation coefficients

A 5,79 0,21 1 0,04 -0,950,95 0,032 0,04 1 -0,03

σ ε1,10 0,011 -0,95 -0,03 1

Figure 47 to 51 show for Sc ,min = 0,05, 0,10, 0,20, 0,30 and 0,40 the measurement data the mean (best) fit / SN-curve the characteristic SN-curve obtained using the 5% quantile of Model Code 2010 Model Code 1990 Eurocode 2

68


0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9


log N

Smax

Figure 227: Fitted SN-curve using TUD+AAU data for Sc,min = 0,05.

0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9


log N

Smax

Figure48: Fitted SN-curve using TUD+AAU data for Sc,min = 0,10.

69


0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9


log N

Smax


0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9


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Smax

Figure 50: Fitted SN-curve using TUD+AAU data for Sc,min = 0,30.

70


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0.6

0.7

0.8

0.9


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71


6.2.2.4Results for high strength concrete – Model 2Statistical analysis by the Maximum Likelihood Method gives the following results:



A 8,91 0,16 1 0,01

σ ε1,17 0,056 0,01 1

2 to Figure 6 show for Sc ,min = 0,05, 0,10, 0,20, 0,30 and 0,40 the measured data the mean (best) fit / SN-curve the characteristic SN-curve obtained using the 5% quantile of Model Code 2010 Model Code 1990 Eurocode 2

0 2 4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9

1 data Smin=0,05meanmean - 2 std.dev.MC 2010MC 1990EC 2

log N

Smax

Figure 232: Fitted SN-curve for high strength concrete for Sc,min = 0,05 – Model 2.

72


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73


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74


6.2.3 Summary – probabilistic model for fatigue of concreteThe statistical analyses described in section 5.2.3 show that the best fit generally is obtained using Model 1 and that only minor differences between the estimated statistical parameters are obtained. Therefore an appropriate hierarchical stochastic model for grout / high strength concrete can be established based on model 1 with statistical parameters obtained from the high strength fatigue data. 5 stochastic variables are introduced in the probabilistic model:

uncertainty in SN-curveA parameter in SN-curve

parameter in SN-curveσ ε standard deviation of

compression strength of concrete

I.e. the following model for the number of cycles to fatigue failure is used(53)

whereA parameter

parameterε error tern assumed to be Normal distributed with expected value = 0 and

standard deviation = σ ε .Y=

0 .45+1 .8⋅Sc ,min

1+1 .8⋅Sc ,min−0.3⋅Sc ,min2

Sc ,max=|σc ,max|/ f c, fat Sc ,min=|σc ,min|/ f c ,fat

The fatigue compressive strength f c ,fat is estimated by

f c ,fat=f c (1− f c /400 )

where f c is the strength in MPa.

A , and σ ε are Normal distributed with the mean values, standard deviations and correlation coefficients in the following table.



A 5,78 0,28 1 0,02 -0,960,90 0,043 0,02 1 -0,01

σ ε1,13 0,016 -0,96 -0,01 1

75


Further, the compression strength of concrete, is modelled as lognormal distributed with a coefficient of variation approximately equal to 0,12, following the recommendations of JCSS [60].

This probabilistic model for the fatigue strength of concrete can be used together with Miner’s rule, a Markov matrix with fatigue load and a probabilistic model for the fatigue load to estimate the reliability as a function of time for fatigue critical details in e.g. grouted connections.

76


7. Design Driving Fatigue Loads, Stress and Lifetime

7.1 Conical Connection Design

7.1.1 Fatigue loads and stressesThe fatigue loads are those resulting from simulations under DLC 1.2. Some load samples are shown in Figure 3. More load samples at the interface resulting from wind speed of 19 m/s are presented in Figure 277.

Figure 277: Load time series at the interface for mean wind speed 19 m/s.

Dynamic analyses carried out with this loading set result in stresses in the grout material. For fatigue assessment, the influence of multiaxial stress states is generally accepted insignificant. That is why focus is given on principal stresses as illustrated in Figure 58for few selected hotspots and during a turbulent wind with mean speed of 19 m/s. In this figure the positive sign refers to the compression. The maximum principal stresses are of compressive type and vary between 0.0 and 9.0 MPa, whereas the minimum principal stresses are tensile and are between 0.0 and – 6.0 MPa.

77

Figure 58: Principal stress time series for mean wind speed 19 m/s.

7.1.2 Fatigue damageFatigue damage accumulates over lifetime due to cyclic stresses presented above. DNVGL-ST-0126 (2016) [33] proposes an algorithm to estimate the total damage. The characteristic number of cycles to failure is calculated from:

log N={ Y ,∧Y <XY (1+0.2 (Y−X ) ) ,∧Y ≥ X

(54)

Y=C1(1− σmax

0.8 f cn/γm )/(1− σ min

0.8 f cn /γm ); X=C1/(1−σmin

0.8 f cnγm

+0.1C1); f cn=f ck(1−

f ck600 )

Whereσ max, σ min = are respectively the largest value of the maximum principal

compressive stress during a stress cycle within the stress block and the smallest compressive stress in the same direction during this stress cycle. They are to be individually set to zero if they belong to the tensile range;

γm= 1.5 is the safety factor associated to the grout material;f ck is the characteristic grout cylinder strength measured in MPa;C1 = calibration factor. For structures in water, C1=10.0 for

compression-compression range and C1=8.0 for compression-tension range.

The damage accumulated over one year is linearly aggregated using Equation (6); and the lifetime is calculated as Lf=D1

−1. Figure presents the distribution of the fatigue damage accumulated over 25 years on an unrolled grout. As the grout has been meshed in three layers across its thickness, the respective fatigue damage levels of the different layers are shown in Fig. 59. The mid-layer and the outer layer show fatigue damage levels lower that one at all points, whereas a minimal region of the inner layer has a damage level of 1.12. As this fatigue damage does not affect the whole thickness and is circumscribed at a

78


marginal zone, the grout can be considered safe. The average across the whole thickness of the damage levels is also depicted.In general, it can be noticed that fatigue primarily affects the top edge of the grout. On the transition layer, the fatigue damage along the meridian at 0⁰ suggests the nascence of a hairline crack.

060

0.5

Pile face

1

0

Fatig

ue d

amag

e [-]

1.5

Height [m]Circumference [°]

5020040400

060

0.1

0.2

Mid-thickness

0.3

0

0.4


5020040400

060

0.005

0.01

Transition face

0.015

0.02

0

0.025


5020040400

060

0.1

0.2

Average across the thickness

0.3

0

0.4


5020040400

Figure 59: Fatigue damage on unrolled grout over 25 years.

7.1.3 Stiffness degradationFollowing the concrete damaged plasticity model [28], the occurrences of plastic strain generate the apparition of triaxial damage either of compressive (dc) or of tensile (d t) types in the grout material. The equivalent degradation (d), which combines the effect of the compressive and of the tensile damages, alters the elastic stiffness of the concrete: Del|t+∆t=( 1−d|t+∆t )D el|t, where Del is the material stiffness matrix. The scalar degradation variable, d, is computed based on the tensile and compressive damage variables: (1−d )=(1−s tdc ) (1−sc dt ) . dc and d t are taken as the maxima between their respective previous state values and the present state values obtained by interpolation in Error: Reference source not found. st=1−wt r (σ̂ ) and sc=1−w c(1−r ( σ̂ )). w t and w c are the recovery factor

indicated in Error: Reference source not found. r (σ̂ )=∑i=1

3

⟨σ̂ i ⟩ /∑i=1

3

|σ̂ i| is a stress

weight factor equal to one if all principal stress components σ̂ i ,(i=1,2 ,3) are positive or zero if they are negative. ⟨ ∙ ⟩ is the Macaulay bracket.Figure 60 presents the results related to material degradation over a 600 s simulation with wind speed of 19 m/s. On the left, the history data of the compressive damage at some selected hotspots are shown. Similar data are shown for the tensile damage on the center of the figure. These two quantities monotonically increase over time. On the right, the time series of equivalent degradation variable is presented. Due to the material recovery phenomenon, the degradation variable can reduce. The plots show that the tensile damage mainly contributes to the degradation variable compared to the compressive damage. This was expected as the plastic tensile stresses appear earlier in the grout.

79


Figure 60: Typical spatial distribution of the degradation variable. Left: 3-D representation. Right: 2-D representation.

In Table ,the typical distribution of the degradation variable is illustrated. It shows that tensile degradation initiates before the compressive one. Once more, the locus of degradation insinuates future apparition of hairline cracks in the meridional direction and high material damage at the top edge of the grout. These observations are in line with previous experimental or numerical studies [2], [4], [5].

Table 27: Visual history of the compressive, tensile, and equivalent degradation variables

Time [s] 0 50 200 500 600 Legend

Com

pres

sive

dam

age

Tens

ile

dam

age

Degr

adat

ion

varia

ble

7.1.4 Vertical settlement and global stiffnessWith the progressive deterioration of the grout, the transition piece continuously settles down. Schaumann et al [1] observed a similar behavior on a cylindrical connection without shear keys where passive shear resistance was due to coulomb friction and chemical adhesion. They explained the vertical

80


displacement as due to the reduction of coulomb friction when the transition piece approaches its neutral position where the operational loads are small. For the specific case of conical grout where the shear resistance is only due to coulomb friction and the initial settlement has already been undergone, the long term vertical displacement may be due to the combination of two main phenomena: (1) the relative sliding of the transition piece with respect to the pile; and (2) the increase in flexibility of the support structure, which forces it to bend more.

For simulation of 600 s duration, the relationship between the grout degradation and the increase in vertical settlement can be observed in Figure 28. Indeed, as the damage increases in the grout, the vertical settlement increases but tends to stabilize notwithstanding the apparition of cracks when the cone angle is at least 3 degrees.

Furthermore, the estimations of the support structure global stiffness at different damage levels have shown insignificant deterioration within the simulation duration.A quasi-static load has been applied on the interface after 0 s, 50 s, 200 s, 500 s, and 600 s and the displacement have been measured. The various time stamps shown in Table 7, represent various damage levels. Prior to the application of the quasi-static load, the support structure has been set to its neutral position in order to annul all strains pertaining to the dynamic simulation (the vertical load representing the dead weight has been kept on the structure). Results show no significant change in the displacement. e.

These observations are in line with the assumption that the hairline cracks do not significantly deter load transfer. However, 600 s simulations are not long enough to confirm the long term behavior of the connection. It can be hypothesized that if the top edge is damaged, the grout capacity will significantly decrease. This suggests modeling the grout material more adequately with the possibility of conversion to particles or element deletion in case of excessive deterioration.

81


Figure 281: Displacement history of the interface centre node.

7.2 Effect of Corrosion on Steel As in section 5.2, the methodology will be described first and then, a case study where this methodology is developed will be presented.

7.2.1 Corrosion model (methodology)

Corrosion is one of the most critical degradation mechanisms that threat the structural integrity of offshore structures. As the pile and the transition piece are made of steel and are in contact continuously with seawater, it is extremely important to take into consideration effect of corrosion on the steel when the fatigue assessment is carried out. By this reason, the methodology described in section 5.2 and summarized in Figure 7, needs to be modified to take into account the effect of corrosion in the components made of steel. This effect will be included as an input of the FE model as is shown in Figure622. Only the effect of corrosion on the steel will be considered..

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Figure62: Methodology followed to assess damage due to fatigue including effect of corrosion

There are two main forms of corrosion that have big impact in offshore applications: general or uniform corrosion and pitting corrosion. The first directly influences structural strength. The second causes very localized and relatively severe penetration of the metal. Corrosion loss models, both empirical or theoretical models have one important exception, they fail to capture longer-term corrosion behavior. The typical models are able to describe only what might be expected to occur the first two or three years. This is clearly not applicable for offshore wind turbines due to they have to operate for longer than 20 years. Figure 29 shows a collection of data of recorded corrosion losses for steel coupons exposed in marine tidal conditions [40]. The losses have been converted from measured loss in coupon mass over time to the equivalent loss of metal from one side.

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Figure 293: Collected data for tidal corrosion losses to 1994. The mean trend is shown together with the 10 percentile curves

Two observations can be made after observing carefully the figure 63:I. The amount of corrosion decreases slowly with time. This means that in

practice there is no such thing as a ‘corrosion rate’ (constant rate of loss of material with time).

II. There is a high degree of scatter in the data and that this scatter increases considerably with time. This suggests, immediately, that there are factors at play that are not explicit in Figure 293.

Due to the high degree of scatter, and, although corrosion is not uniform along time, a corrosion rate for the whole operating life of the pile and transition piece will be considered to include the effect of corrosion on the steel in the fatigue assessment. Recommended practice [41] defines a corrosion rate of 0.3mm/year for external surfaces and 0.1mm/year for internal surfaces (see Table 19).

Table 19: Minimum values for design corrosion rate (Vcorr) on primary structural parts in splash zone

RegionVcorr

(External Surface)[mm/yr]

Vcorr(Internal Surface)[mm/yr]

Temperate climate (annual mean surface

temperature of seawater ≤ 12°C)

0.3 0.1

Subtropical and tropical climate 0.4 0.2

In the case described in this report, it will be considered that the transition piece only has its external surface in contact with seawater and the pile has its internal surface, and the external surface which is not in contact with the grout. The protection used against corrosion in each part is indicated in the Table :

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Table 29: Corrosion protection for pile and transition piece along the design life

Designed life (years) Pile Transition piece

0 - 5 Cathodic protection Coating

5 – 10 Free corrosion Coating10 – 15 Free corrosion Free corrosion15 - 20 Free corrosion Free corrosion

The offshore wind turbine was designed for an operational life of 20 years. It has been supposed that the cathodic protection in the pile works properly only the five first years, the rest of the life this part will suffer free corrosion. It means that from the fifth year on, the corrosion rate will be of 0.3mm/year for external surfaces and 0.1mm/year for internal surfaces. The transition piece has been assumed to be coated, working properly for 10 years. After that, free corrosion will take place in the external surface of the transition piece (0.3mm/year). The effect of corrosion in the structural behavior of the pile and transition piece is listed in Table 0.

Table 30: Stress-rising coefficient in pile and transition piece.Service

year Ksr pile Ksr TP

1 ÷ 5 1.00000

1.00000

6 1.00220

1.00000

7 1.00441

1.00000

8 1.00663

1.00000

9 1.00886

1.00000

10 1.01110

1.00000

11 1.01335

1.00386

12 1.01561

1.00775

13 1.01787

1.01167

14 1.02015

1.01562

15 1.02243

1.01960

16 1.02473

1.02362

17 1.0270 1.0276

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4 618 1.0293

51.0317

319 1.0316

81.0358

420 1.0340

11.0399

7

The highest rising in stresses is observed in the transition piece, around a value of 4% of increase.

7.2.2 Case study considering corrosion loss

The effect of considering the effect of corrosion is to increase the stress ranges. Consequently, this stress rising promotes lower number of cycles to failure and higher fatigue damage. Therefore, it is coherently observed that transition piece exceeds fatigue life limit of 1 in more nodes compared to the case without considering corrosion plate thinning with S-N Curve D. On the other hand, the pile doesn’t exceed value of 1, showing that the pile is strong enough to withstand all the loads defined for 20 years of operational life. The fatigue assessment considering S-N Curve C1 shows fatigue damage values below than 1 in all points of both components, pile and transition piece. Results considering both S-N Curve types (D and C1) are summarized in Table 201.

Table 201: Cumulative damage in pile and TP.

Component Max. Damage with D-Curve

Nº failed nodes with D-

CurveMax. Damage with C1-Curve

Nº failed nodes with C1-Curve

Pile 0.8883 0 0.3109 0Transition

piece 1.2060 20 0.4299 0

The two graphs below show the fatigue damage of all the analyzed nodes separately for pile and transition piece with S-N Curve D (Figure 304). In this case study, the failed nodes with corrosion thinning also include those failed without considering corrosion thinning effect.

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Figure 304: Cumulative fatigue in nodes as estimated by algorithm with S-N Curve D; left side, pile and right side, TP (cumulative fatigue limit drawn with

a red line).

Figure 315 represents the fatigue damage of all the analyzed nodes separately for pile and transition piece with S-N Curve C1. It can be observed that none of the nodes fail, where cumulated damage does not exceed 1.

0 1 2 3 4 5 6

x 104

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6

x 104

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Figure 315: Cumulative fatigue in nodes as estimated by algorithm with S-N Curve C1; left side, pile and right side, transition piece

(cumulative fatigue limit drawn with a red line).

In the following graphs, plots of the combined Rainflow matrices are shown for the most fatigued node of the pile (see Figure 326) and of the transition piece (see Figure 33). It is observed that transition piece node generally shows higher amplitudes compared to the counterpart in the pile as it was mentioned for the case without plate thinning in section 5.2.6.5.

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Figure 326: Rainflow matrix plots (3-D mesh and contour) in pile

Figure 337: Rainflow matrix plots (3-D mesh and contour) in transition piece.

As mentioned previously, one reason that may explain the differences between the pile and the transition piece is the moment of inertia, lower in the case of transition piece, as can be seen in Table . Thickness loss due to corrosion only broadens the difference. Bending moment caused by wind loading is assumed to be the main factor of fatigue usage. Compared to results without plate thinning, Rainflow matrices obtained show less scattering and more cycles with higher amplitudes. In the case of the pile, the number of cycles in the highest peak point (Figure 3266) exceeds 7 million cycles, which increases compared to the same peak in the case without corrosion plate thinning (Figure 66).

With respect to corrosion protection only some additional solutions to section 5.2.6.5 are presented herein to reach full service life in the case of transition piece:

An accurate measurement of corrosion rate in splash and submerged zones related to site condition could reduce plate thinning, both inner and outer sides.

Prepare a cathodic protection program for transition piece, avoiding free corrosion conditions for full service life.

Thickness increase in the transition piece, including corrosion allowance, if needed.

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7.3 Fracture Mechanics based Approach Probabilistic models for fatigue failure are in general established using the SN-approach together with the Miner rule of linear fatigue damage accumulation. SN-test results are used to model the uncertainty related to the SN-curves. However, the probabilistic model based on SN-curves cannot be used investigate the effect of inspections on the reliability levels. Therefore, a probabilistic fracture mechanics approach is needed where an explicit measure of the fatigue crack is represented. Traditionally in reliability- and risk-based inspection planning (RBI) the probabilistic fracture mechanics model is calibrated to give the same reliability as function of time as obtained by the SN-approach. This approach is also used in the following sections.

7.3.1 Fracture mechanis based stochastic model for fatigue crack growth

The fatigue crack growth model (based on fracture mechanics) is bi-linear and growth is considered in both ‘c’ and ‘a’ (depth and width) directions, see Figure, right side. The model is generally based on [65] with crack growth parameters adopted from [62] where necessary. The crack growth is typically described by the following coupled differential equations:63

dadN

=Aa(ΔK a )m a(N0 )=a0 (55

dcdN

=Ac(ΔK c)m c (N0 )=c0

(56)

here Aa, Ac and m are material parameters, a0 and c0 describe the crack depth a and crack length c, respectively, after N1 cycles and where the stress intensity ranges are ΔKa(Δσ) and ΔKa(Δσ).

Failure is considered when a crack grows through the thickness of the monopile/transition piece steel and can be summarized in the following limit state function:

g(X , t )=acr−a( t )≥0 (57)

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Figure68: Weld geometry parameters for crack growth model, [64].

Where t is time in the interval between 0 and service life TL. Crack dimensions at any given time within turbines service life can be calculated using following equations:

a ( t )=(∑i ,1 N i ,1 A1 (CSIF ΔK a ,i ,2)m1+∑i ,1

N i , 2 A2 (CSIF ΔK a ,i , 2)m2) (58)

c ( t )=∑i ,1

N i ,1 A1 (CSIF ΔK c , i ,2 )m1+∑i ,1

N i ,2 A2 (CSIF ΔKc , i ,2 )m2 (39)

ΔK i , a=M kma MmaC LoadCSCF Δσ i√πai (40)

ΔK i , c=M kmcMmcC LoadCSCF Δσ i√πai (61)

M kma=f 1( aT , ac )+ f 2( aT ,θ)+f 2 ( aT ,θ , L

T ) (62)

M kmc=f 1( aT , ca, LT ) f 2( aT , a

c,θ) f 2( aT , a

c,θ , L

T ) (63)

Mma(c )=[M 1+M 2( ac )2+M 3( ac )

4 ] g⋅f Θ/Φ(64)

Here Ni is number of stress ranges Δσi within considered lifetime window; A1, A2 m1 and m2 are material parameters based on crack growth environment for bi-linear crack growth curves; CSIF is model uncertainty related to stress intensity magnification factors (Mkma(c) and Mma(c)); CLOAD models uncertainty related to load (stress) modelling and CSCF models uncertainty related to stress concentration factor calculation.

Stress intensity magnification factors based on weld and crack geometry (see Figure68) are calculated based on [61], [62] and [63] using f1, f2, f3, M1, M2, g, fΘ

geometrical coefficients. θ is weld angle in Figure on the left and Θ is the crack growth direction angle in Figure68 on the right (90 for growth in depth direction “a” and 0 for growth in width direction “c”). It should be noted here that only “membrane loading” was considered, and thus only M(k)ma(c) stress magnification factors are used (M(k)ba(c) magnification factors are considered for “bending” loading and most applicable for tubular members in jacket structures).

The following Table 212 summarizes all the parameters used for this analysis. It should be noted that while most parameters are identical for considered nodes in transition piece and monopile, differing parameters are shown in brackets for monopile nodes.

Table 212: Parameters for Crack growth (Fracture mechanics) probabilistic model

Variable Distribution

Expected value

Standard deviation /

COV

Comment

90


a0 LN Fitted to match SN

results

COV= 0.66

Initial crack depth

c0 LN a0/0.62 COV= 0.40

Initial crack width

acr D 80 mm(97 mm)

- Critical crack depth, thickens of the steel.

In marine environment without Cathodic protectionlog(A1) N -13.27 SD= 0.253 FM curve parameterlog(A2) N -6.246 SD= 0.06 FM curve parameter

1m D 3.42 - Slope FM curve2m D 2.67 - Slope FM curve

ΔKTrans D 1098 N/mm3/2 - FM curve slope change point

In marine environment with Cathodic protection at -850mV (Ag/AgCl)log(A1) N -17.32 SD= 0.32 FM curve parameterlog(A2) N -11.22 SD= 0.264 FM curve parameter



In marine environment with Cathodic protection at -1100mV (Ag/AgCl)log(A1) N -17.32 SD= 0.32 FM curve parameterlog(A2) N -11.28 SD= 0.144 FM curve parameter



In Airlog(A1) N -17.32 SD= 0.32 FM curve parameterlog(A2) N -12.23 SD= 0.171 FM curve parameter



Model uncertaintiesCLOAD LN 1 COV=

0.22 (0.17)

Global stress analysis/load uncertainty

CSCF LN 1 COV= 0.1 (0.05)

Stress concentration

CSIF LN 1 COV= 0.07

Stress intensity factors

Bracketed values are for monopile nodes (if different from transition piece), e.g. (97mm steel thickness for TP).

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Here again it should be noted that modelling uncertainties are not identical for monopile and transition piece nodes, as it was described in section 5.2.7 Fatigue reliability assessment. General procedure of crack growth modelling using differential equations given in the beginning of this section is summarized in Figure69.

a bFigure69: Procedure for crack growth calculation (a) [64] and Paris law sketch (b) [65].

Based on recommendations in [64] and [65] the following additional geometrical parameters for transition piece nodes at shear keys and monopile are assumed:

LTPweld=1 . 5⋅T TP=1. 5⋅80=120mm

θTPweld=450

LPILEweld=0 . 5⋅T TP=0 .5⋅97=48 .5mm

θPILEweld=150

7.3.2 Reliability assesment based on fracture mechanics model

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The fracture mechanics based crack growth model (FM model) needs to be calibrated to appropriate SN curve results throughout the lifetime, thus the following Figure 34 shows the results of such calibration. Here “in air” SN curve E as recommended by [61] and [45] together with “in air” parameters from Table 21. Calibration parameter, as indicated in Table 21 is initial crack depth a0.

Figure 340: Results of FM model calibration for most critical Transition Piece node.

Relatively good match can be observed in the figure above, however it should be noted that required maximum average initial crack at shear keys should not exceed 0.02mm. This might not be feasible for “weld bead” shear keys because it would imply very high welding quality requirements that could be excessive and too costly. However, it should be kept in mind that both SN and FM models are highly sensitive to uncertainties related to load and stress concentration factor modelling (CLOAD and CSCF), see Figure 35. Furthermore, FM model also incorporates uncertainties related to stress intensity magnification factor calculation (CSIF). It could be argued here that by reducing the aforementioned uncertainties would be beneficial towards allowing higher initial cracks in transition piece steel close to shear keys. This claim can also be supported by the fact that initial crack size a0 is significantly less important (has very low alpha value in Figure 351) when compared to other variables implying that higher gains in annual reliability would be achieve by reducing the CLOAD and CSCF, CSIF uncertainties, rather than trying to control the initial crack size.

Figure 351: Fracture mechanics based crack growth model sensitivity, Transition piece node.

93


When it comes to most critical monopile node, the FM model was calibrated using results with SN curve D “with cathodic protection”, since it was established in section 5.2.7 that cathodic protection is necessary to ensure safe operation throughout the lifetime of the turbine. Parameters for crack growth model are given in Table 2132. The following Figure 4072 shows the results from calibrated fatigue crack growth model compared to identical situation using SN curve D.

Figure 3672: Results of FM model calibration for most critical Pile node in marine environment without cathodic protection.

A good match is achieved between SN and Fracture mechanics models for the last 10 years of turbines service life – both models predict “non-safe” monopile condition after service year 16 (annual reliability index falls below 3.3). However, it should be noted that calibration parameter – initial average crack depth a0– reaches 2.8mm for this particular case, implying relatively large initial cracks at monopile butt welds. It could be argued that good weld quality control would be implemented during manufacturing and initial cracks could be expected to be smaller than 2.8mm in depth, thus increasing the annual reliability index throughout the lifetime. The following Figure 373 shows an increase of annual reliability index to 3.3 at service year 20 (“safe” monopile condition throughout the service life) by limiting the average initial crack size to 2.0mm.

Figure 373: Results of FM model calibration for most critical Pile node in marine environment without cathodic protection, βannual (year = 20) = 3.3.

94


Assuming a lognormal distribution for initial crack sizes, a 2.0mm average initial crack depth limitation would translate to 0.62mm limitation on characteristic maximum allowable crack depth (assuming a characteristic value defined by 5% quantile of the initial crack size distribution). Such relatively large initial crack sizes are a consequence of monopile operating within “Stage A” of the Paris law parameter space, where crack growth increments da/dN are small (5.37·10 -14), see Figure (b) (low values of ΔK, coming from relatively low values of Δσ for monopile nodes). The following Figure 38 shows the sensitivity coefficients of crack growth model, when no corrosion protection is assumed in marine environment.

Figure 384: Fracture mechanics based crack growth model sensitivity, Pile node in seawater without cathodic protection.

High sensitivity coefficients α for initial crack size a0 and crack growth constant A1 can be observed in figure above. Near 0 sensitivity coefficient for crack growth constant A2 again indicates that, given the input stress range distribution from Figure (a), the monopile nodes operate in “Stage A” of Paris law parameter space, where A1 and initial crack size are the most influential parameters.

When cathodic protection is assumed to be active throughout the lifetime of the structure, the reliability index increases substantially, see Figure 395 and Figure406 for different levels of aggressive marine environment.

95


Figure 395: Results of FM model calibration for most critical Pile node,cathodic protection in marine environment at -850mV (Ag/AgCl).

It is obvious that a good match was achieved, however, as it was also for the transition piece node, maximum allowable average initial crack size is only ~0.64mm (0.2mm, assuming a characteristic value defined by 5% quantile of the initial crack size log-normal distribution). This again implies high welding quality requirements for monopile butt welds. It should be noted here that it is easier to achieve very small initial cracks in monopile butt welds when compared to “weld bead” shear keys, by grinding the welded surfaces and using advanced welding techniques and thus 0.64mm maximum average initial crack size could be feasible and realistic.

Figure 406: Results of FM model calibration for most critical Pile node, cathodic protection in marine environment at -1100mV (Ag/AgCl).

When a more aggressive marine environment is assumed (Figure 406), maximum allowable average initial crack size is reduced to ~0.22mm (0.06mm, assuming a characteristic value defined by 5% quantile of the initial crack size log-normal distribution), thus requiring even higher weld quality control during manufacturing of the monopile.

96


Figure 417: Fracture mechanics based crack growth model sensitivity, Pile node in marine environment with cathodic protection.

Figure 417 above shows crack growth model sensitivity when cathodic protection is used in different levels of aggressive marine environment. As expected, the FM model sensitivity for monopile modes is quite similar to that of transition piece nodes - CLOAD being the most influential parameter for both locations. However, for the monopile stress intensity magnification factor uncertainty CSIF is more influential than stress concentration factor uncertainty CSCF. Previous claim that more benefit, in terms of increased annual reliability index, would be achieved by decreasing the CLOAD and CSIF uncertainties rather than implementing very strict weld quality control (to reduce initial crack sizes) still holds.

It should be noted that all results presented in this section are derived using limited dataset of fatigue load time series, as indicated in section 5.2.6.2. The simulated load cases, described in Table 125, constitute only ~10% of the total required dataset. Therefore, it is recommended to perform a full fatigue analysis, comprising of at least all the load cases described in section 5.2.6.2, to verify the results in this section and reduce the uncertainties related to load (stress) modelling.

8. SummaryAbout fatigue assessment in steel components of grouted joints with shear keys, the following conclusions have been observed:

1. The effect of corrosion in fatigue due to plate thinning is necessary to be accounted, otherwise unconservative results are obtained.

2. In the case of a monopile, where a large thickness is used, the effect of corrosion in fatigue due to plate thinning is not really important.

3. A reduction of dynamic stresses is observed in the studied grouted joint between transition piece and pile as shown in the rainflow matrices. Two main reasons have been identified: the first one is a higher moment of inertia of the tubular section for the pile compared to the transition piece and the second one is the lower stiffness of the grout that may act as a damper for dynamic loads.

97


4. S-N Curve selection is a very sensitive factor for fatigue damage assessment. Considering S-N Curve D the pile is safe, however a very small area of the transition piece exceeds fatigue life limit of 1. Considering S-N Curve C1 in both components, pile and transition piece withstand to the experienced loads for all service life (20 years).

With respect to the assessment of the conical grouted joint, the following conclusions are observed:1. The fatigue model recommended by the DNV GL standards predicts a

satisfactory fatigue lifetime of the grouted connection, equivalent to the intended lifetime of the structure (25 years)

2. In order to study the grout material stiffness deterioration overtime, the damage plasticity model for concrete reveals the appearance of hairline cracks in line with previous experiments. As it could be expected, the tensile deterioration pattern drives the overall deterioration process of the grout and defines the apperance of the cracks.

3. It is challenging to forecast the evolution of the material deterioration process over long time period due to expensive computations. Therefore it will be necessary to develop a model to predict the material deterioration over long time period based on short time simulation results. Nevertheless, the influence of the material deterioration on the support structure stiffness has been studied.

4. In particular, the vertical settlement of the transition piece can be significantly reduced and stabilized when increasing the conical angle from 1⁰ to 3⁰. Though stabilization is noticed during the 600 s simulation, the evolution of the grout deterioration can disrupt this stability.

5. The local deterioration of the top edge suggests a more sophisticated modeling of the grout material that accounts for the possibility of conversion to particles or element deletion in case of excessive deterioration.

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