1. Mudline MSL Fixed BaseCoupled SpringsDistributed SpringsApparent Fixity Foundation Models for Offshore Wind Turbines Erica Bush and Lance Manuel University of Texas at Austin

2. Problem Overview Characteristic loads for reliability-based design of offshore wind turbines can be derived from time- domain aeroelastic-hydrodynamic response simulations Design load = Load Factor × Characteristic Load Accuracy of derived characteristic loads depends on number of simulations run accuracy of critical sea state selection (when using Inverse FORM) accuracy of the simulation models used Objective Compare loads derived from alternative foundation model using simulations

3. 5 MW baseline offshore wind turbine developed at the National Renewable Energy Laboratory (NREL) 11.5 m/s rated wind speed FAST is used to simulate waves and turbine response; TurbSim is used to simulate wind 126 m 90 m 20 m 36 m Mudline Hub MSL Tapers linearly upward Outer diameter = 3.87 m Wall thickness = 1.9 cm Outer diameter = 6 m Wall thickness = 2.7 cm Outer diameter = 6 m Wall thickness = 6 cm not to scale Wind Turbine Model

4. Mudline MSL Fixed BaseCoupled SpringsDistributed SpringsApparent Fixity Foundation Models Different properties and dimensions need to be specified for each model These properties and dimensions depend on the sea state considered We discuss how they are computed and then used in FAST

5. STEP 1STEP 2 STEP 3 36 m AFL, EI M F F M Ѳ ww Ѳ M F Apparent Fixity Model From a fixed base simulation, obtain shear, F, and moment, M, values at the mudline in the fore-aft direction

6. STEP 1STEP 2 STEP 3 36 m AFL, EI M F F M Ѳ ww Ѳ M F Apparent Fixity Model Determine the corresponding deflection, w, and rotation, Ѳ, for the real pile

7. STEP 1STEP 2 STEP 3 36 m AFL, EI M F F M Ѳ ww Ѳ M F Apparent Fixity Model Calculate the length and stiffness of a cantilever that would produce the same deflection and rotation for the given shear and moment

8. For each sea state, 50 contemporaneous shear (F) and moment (M) pairs at the tower base in the fore-aft direction are randomly selected from a single fixed base simulation  idea: to calibrate flexible foundation model for anticipated loads from what’s above the mudline Are 50 random pairs selected from one fixed-base simulation representative? Step 1: Shear and Moment Values Sea State 1 Simulation ASimulation B μ F (kN) μ M (kN-m) ρ F,M μ F (kN) μ M (kN-m) ρ F,M 50 Random Pairs555632100.86615643740.73 Time Series576648090.80572647090.78 Sea State 2 Simulation ASimulation B μ F (kN) μ M (kN-m) ρ F,M μ F (kN) μ M (kN-m) ρ F,M 50 Random Pairs315334480.80157330410.92 Time Series306346520.88322355670.88

9. We use LPILE to perform lateral pile analysis (with p-y curves) in order to determine the deflections and rotations of the real pile based on each of the shear and moment pairs The p-y curves for the lateral force- displacement relationships are based on API guidelines A pile length of 36 m below the mudline and this sand profile were chosen based on previous work (Passon, 2006; Jonkman et al., 2007) γ = 10 kN/m 3 Ф ’ = 38.5° k = 35288 kN/m 3 22 m Sand 1 γ = 10 kN/m 3 Ф’ = 33° k = 16287 kN/m 3 5 m Sand 2 γ = 10 kN/m 3 Ф ’ = 35° k = 24430 kN/m 3 9 m Sand 3 Soil Profile Considered Step 2: Deflections and Rotations

10. F M L, EI L = AFL EI = Stiffness Step 3: Equivalent Length and Stiffness L and EI are calculated for each of the 50 randomly selected shear and moment pairs The average L and EI is then used in the model

11. Coupled Springs Model Spring stiffnesses are calculated from the AFL and EI Flexibility MatrixStiffness Matrix

12. Coupled Springs Model Note that the AFL and EI were calculated from shear and moment in the fore-aft direction But the translational and rotational springs will be attached in both horizontal directions (totaling four coupled springs) Heave and yaw DOF are turned off FAST must be recompiled with this platform stiffness matrix surge roll yawpitch heave sway wind

13. The sea state must be represented by a single shear and moment pair The shear and moment pair that has an AFL closest to the average AFL is selected from the 50 contemporaneous pairs Distributed Springs Model ShearMomentDeflectionRotation AFLEI FMw θ (kN)(kN-m)(cm) × 10 -3 (rad) (m)(kN-m 2 ) 11417691701.160.00125517.631.15E+09 261.7548600.720.00084816.971.11E+09 ::::::: 8298.3468900.660.00075617.131.12E+09 ::::::: 48850.5871001.300.00146217.401.12E+09 49739.4706401.060.00118517.341.13E+09 50-413439900.500.00061916.491.08E+09 Average17.131.12E+09 Note: V = 12 m/s is shown in table......

14. LPILE is run with the chosen shear and moment pair We discretize the embedded pile at 252 points; LPILE gives the distributed lateral resistance and deflection at each point The lateral spring stiffness is calculated at each point by dividing the distributed resistance (kN/m) by the deflection (m) and, then, multiplying by the tributary length (m) for that point  result: spring stiffness for each point in kN/m We reduce the number of springs to 37 at 1-meter spacing by adding stiffnesses at points within the tributary length of each discrete spring FAST is recompiled with these spring stiffnesses for each simulation with the distributed springs model Distributed Springs Model......

15. Random wind loading 3-D Inflow turbulence random field over a 2-D rotor plane uses Kaimal power spectrum and exponential coherence spectrum Random wave loading Irregular long-crested waves are simulated using a JONSWAP spectrum, Airy wave kinematics, and Morison’s equation Structural response Combine modal and multi-body dynamics formulation (includes control systems) Wind load Wave load u v w Loading Models

16. Rosenblatt Transformation  = Reliability index  (-  ) = P T = Target Failure Probability  U2U2 U1U1 V (m/s)H s (m)T p (s) 105.55.8 126.2 146.96.5 167.56.8 188.17.1 208.67.3 229.07.5 Selecting Critical Sea States 20-year return period considered (T = 20 yrs) P T = 1/(20 × 365.25 × 24 × 6) = 9.51 × 10 -7 (load exceedance probability in 10 mins)   = 4.76 2D Inverse FORM (Environmental Contour Method)

17. V (m/s) Mean (MN-m) Std. Dev. (MN-m) Max (MN-m) 1266.016.2119.2 2234.818.7105.5 % Inc. 12-22 m/s -4715-11 PF (max) SkewnessKurtosis Upcrossing Rate (s -1 ) 3.270.012.890.29 3.780.033.250.36 16n/a1224 Mean + (Std. Dev.)(PF) = Max + x = Fore-Aft Tower Bending Moment at the Mudline for Fixed Base Model (150 sims) Summary Statistics ( V = 12 vs. 22 m/s) V (m/s) Mean (MN-m) Std. Dev. (MN-m) Max (MN-m) 1266.719.5130.1 2235.223.1112.9 % Inc. 12-22 m/s -4719-13 PF (max) SkewnessKurtosis Upcrossing Rate (s -1 ) 3.250.022.930.21 3.36-0.073.100.22 3n/a63 Fore-Aft Tower Bending Moment at the Mudline for Apparent Fixity Model (150 sims) Going from 12 to 22 m/s (with either fixed base or AF model)

18. V (m/s) Mean (MN-m) Std. Dev. (MN-m) Max (MN-m) 1266.016.2119.2 2234.818.7105.5 PF (max) SkewnessKurtosis Upcrossing Rate (s -1 ) 3.270.012.890.29 3.780.033.250.36 Fore-Aft Tower Bending Moment at the Mudline for Fixed Base Model (150 sims) Summary Statistics (Fixed vs. Flexible) V (m/s) Mean (MN-m) Std. Dev. (MN-m) Max (MN-m) 1266.719.5130.1 2235.223.1112.9 PF (max) SkewnessKurtosis Upcrossing Rate (s -1 ) 3.250.022.930.21 3.36-0.073.100.22 Fore-Aft Tower Bending Moment at the Mudline for Apparent Fixity Model (150 sims) Consider 12 m/s sea state only With change from fixed-base to flexible model  Mean is unchanged; SD increases by ~20%, PF is unchanged; hence max increases but by only ~10% [since max = mean + SD × PF]

19. Max = Mean + (Std. Dev.)(PF) Summary Statistics Model Mean (MN-m) Std. Dev. (MN-m) Max (MN-m) Fixed 66.016.2119.2 AF 66.719.5130.1 CS 64.622.4138.7 DS 64.520.1132.6 PF (max) SkewnessKurtosis Upcrossing Rate (s -1 ) 3.270.012.890.29 3.250.022.930.21 3.300.042.920.20 3.380.032.910.26 Fore-Aft Tower Bending Moment at the Mudline for V = 12 m/s (150 sims) Mean trend matches control system’s dependence on mean wind speed All models are seeing the same wind and wave time series; so, control system behaves the same way as far as mean load goes Only about 3% difference between largest and smallest mean (among models)

20. fff wind structure TBM Summary Statistics Model Mean (MN-m) Std. Dev. (MN-m) Max (MN-m) Fixed 66.016.2119.2 AF 66.719.5130.1 CS 64.622.4138.7 DS 64.520.1132.6 PF (max) SkewnessKurtosis Upcrossing Rate (s -1 ) 3.270.012.890.29 3.250.022.930.21 3.300.042.920.20 3.380.032.910.26 Fore-Aft Tower Bending Moment at the Mudline for V = 12 m/s (150 sims) Max = Mean + (Std. Dev.)(PF)

21. Summary Statistics Model Mean (MN-m) Std. Dev. (MN-m) Max (MN-m) Fixed 66.016.2119.2 AF 66.719.5130.1 CS 64.622.4138.7 DS 64.520.1132.6 PF (max) SkewnessKurtosis Upcrossing Rate (s -1 ) 3.270.012.890.29 3.250.022.930.21 3.300.042.920.20 3.380.032.910.26 Fore-Aft Tower Bending Moment at the Mudline for V = 12 m/s (150 sims) Max = Mean + (Std. Dev.)(PF) PF = f (exposure time, asymmetry, tails, upcrossing rate) Only about 4% difference between flexible foundation models

22. Summary Statistics PF (max) SkewnessKurtosis Upcrossing Rate (s -1 ) 3.270.012.890.29 3.250.022.930.21 3.300.042.920.20 3.380.032.910.26 Fore-Aft Tower Bending Moment at the Mudline for V = 12 m/s (150 sims) Max = Mean + (Std. Dev.)(PF) The variability in maxima for the four models mostly depends on std. dev. As std. dev. increases, the max increases Model Mean (MN-m) Std. Dev. (MN-m) Max (MN-m) Fixed 66.016.2119.2 AF 66.719.5130.1 CS 64.622.4138.7 DS 64.520.1132.6

23. High frequency peaks shift left as the upcrossing rate for the model decreases AF and CS have very similar behavior because they tell FAST effectively the same information However, the AF model has more inertia by design AF has slightly less power than CS as seen in the smaller std. dev. Power Spectra

24. Exceedance Plots Median of 10-min. extreme can be taken as 20-year characteristic value (Inverse FORM) 20-year loads for the flexible models differ by less than 6% (from each other) All four models have 90% confidence interval < 4 MN-m (on 20-year load) based on bootstrap estimation 150 simulations are sufficient for 2D Inverse FORM Tails will be more important for 3D Inverse FORM Then, more simulations will be necessary FixedAFCSDS 119.0 129.6137.2132.3 Median of 10-min. Extremes (MN-m)

25. Medians of 10-min. extremes for this sea state are not associated with 20- year load because they are not the largest on the environmental contour Medians for the three flexible models differ by less than 1% (from each other) Statistics and power spectra have similar trends to the 12 m/s case FixedAFCSDS 103.9 110.5 109.6 Median of 10-min. Extremes (MN-m) Another Sea State Fore-Aft Tower Bending Moment at the Mudline for V = 22 m/s (150 sims)

26. Recipe for Use of Flexible Foundation Models Each sea state requires the following steps: STEP 1 Run one fixed base simulation, and select 50 random shear and moment pairs from the time series. STEP 2 Run LPILE for all 50 load pairs, and calculate the AFL and EI for each pair. STEP 3 AF model Use the average AFL and EI. CS model Use the average AFL and EI to calculate the coupled spring constants. DS model Choose the shear and moment pair that produces an AFL and EI closest to the average. Run LPILE for this pair, and calculate distributed spring constants from the output. STEP 4 Run N simulations per model, and extract N 10-min extremes. (N = 150 was used here  apply Inverse FORM to get long-term load)

27. The three flexible models yield 20-year loads that are within 6% of each other when using 2D Inverse FORM to evaluate critical sea states The three flexible models seem fairly interchangeable, but AF may be the easiest to implement because FAST does not need to be recompiled Conclusions The AF and CS models do not have same mass as the original structure Evaluate alternative inertia distributions for these Verify whether 50 random (F, M) pairs from a single FB simulation are sufficient Perform 3D Inverse FORM (a more accurate approach to sea state selection) Well-behaved tails are required for acceptable confidence in 20-year loads More simulations are necessary to produce well behaved tails Study other soil profiles to evaluate flexible foundation models Future Work

28. Dr. Jason Jonkman of the National Renewable Energy Laboratory Dr. Puneet Agarwal, former student of Dr. Lance Manuel Dr. Shin Tower Wang of Ensoft, Inc. National Science Foundation Grant No. CMMI-0449128 (CAREER) Grant No. CMMI-0727989 Acknowledgments