Current Efforts towards Reliability-based Design of Wind Turbine Foundations

1. Current Efforts towards Reliability-based Design of Wind Turbine Foundations Jomaa Ben Hassine, PE, ing., P.Eng., M.ASCE Engineering Specialist, RES Americas, Broomfield, CO PhD Candidate, Colorado School of Mines, Golden, CO Workshop on Uncertainty and Risk Assessment in the Design Process for Wind NREL NWTC, July 12-13, 2016

2. Presentation Outline • Introduction - Design Checks • Introduction - Design Methods • Introduction - Reliability Concepts • Design Practice – State-of-the-Art • Direct Reliability Based Design (d-RBD) • Random Fields & RFEM • Publications

3. Foundation Design - What must be verified? • Global Stability Checks • Overturning • Sliding • Capacity Checks (ULS) • Concrete design • Reinforced concrete flexure • Concrete shear • Concrete bearing • Geotechnical design • Bearing capacity • Other materials (grout, steel inserts, anchor bolts) • Operational Performance (SLS) • Concrete cracking • Settlement & tilt • Foundation stiffness • Fatigue Life of various components (concrete, grout, reinforcement, anchor bolts, etc.)

4. Traditional Global Factor of Safety – Non-probabilistic approach • Lumps all uncertainty into one global factor • If resistance and loads are random variables, FOS is also random. Design reliability is thus unknown. • FOS values are selected based on historical performance.

5. Partial Safety Factor – Semi-probabilistic Approach • Resistance factors, load factors and other factors obtained through code calibration to achieve pre-defined reliability levels. • Any changes to assumptions invalidate the factors • There is an infinite number of factor combinations that can result in the same reliability levels.

6. Fully-probabilistic Methods • Calculate probability of failure directly • No factors needed • Used mostly in studies and code calibrations, not as a design tool • First Order Reliability Methods (FORM) • Hasofer Lind Method • First Order Second Moment Methods (FOSM) • Taylor Series Method • Point Estimate Method (PEM) • Monte Carlo Simulation Methods: • Random Finite Element Method (RFEM) • Direct Reliability Based Design Method (d-RBD)

7. Progression of Design Philosophies Most Design Codes Today

8. Reliability Concepts – Limit State Function • Performance function, or limit state function, for any of the design checks: • Alternate forms:

9. Reliability Concepts – Probability of Failure

10. Reliability Concepts – Reliability Index • On a PDF graph of the performance function, reliability index is the distance in standard deviations, from the mean value.

11. Reliability Concepts – β, pf and FOS • There is a unique, one-to-one relationship between pf and β. • This is not the case for the relationship between FOS and β or pf.

12. Typical Reliability Implied in Design Codes • For 50 year reference period.

13. Design Practice – State-of-the-Art • IEC61400-01 supplies partial load factors with the assumption that appropriate resistance factors are applied on the resistance side. • Resistance factors left up to national practice • Material resistance factors are well established for structural design, but not for geotechnical design. • A new international standard under development: IEC61400-06: Wind Turbines: Tower and Foundation Design – currently in Committee Draft status.

14. IEC61400-6 Status • The primary achievement of the first edition is to harmonize and document current practice around the world. • The apparent goal is to match reliability of common structures as implied in design codes. • However, this cannot be confirmed without in depth calibration studies. • The industry stands to gain from rigorous reliability-based assessments. • It will take several PhD dissertations to investigate the various limit states.

15. Recent Publications of Interest • ISO 2394:2015, particularly Annex D dedicated to resistance variability for geotechnical design. • Nadim, F., Choi, Y.J., Lacasse, S. and Liu, Z. (2015). Calibration of Partial Safety Factors for Offshore Foundation Design. Inter. J. Reliability & Safety, 9(1), pp. 51-69. • Ben-Hassine, J. and Griffiths, D.V. (2012). Reliability Based Design of Shallow Foundations Subjected to Combined Loading with Application to Wind Turbine Foundations. CIMENICS 2012 - 11th International Congress on Numerical Methods in Engineering and Scientific Applications, Isla de Margarita, March 26-28, 2012.

16. d-RBD: What is it? • Evaluate a performance function in a MCS process assuming predefined variable distributions and cross-correlations. • Analyze CMS statistics to arrive at an optimal design for a predefined target reliability index.

17. d-RBD as a Practical Design Tool:

18. d-RBD: Advantages & Limitations • Advantages • Simple and quick (within minutes on an ordinary laptop) • Easy to code using readily available tools (EXCEL, MatLab, Mathcad, etc.) • Flexibility to set target reliability • Can be used to investigate variable cross-correlations • Very useful for sensitivity analysis so that attention is focused on driving variable uncertainty • Amenable to performance based design • Limitations: • Does not allow modeling of spatial variability (but few other methods do) • Due care must be exercised for model uncertainty (same applies for any other method)

19. Random Fields – Theory & Implementation • Rigorous mathematical approach to simulate random processes: • Point variability • Spatial variability • Random variable values are generated and mapped onto Finite Element models (each element or integration point is assigned a different value) • Random variables can be cross-correlated

20. Random Fields – Theory & Implementation • Inputs needed to generate random fields: • PDF’s of random processes (variables) • Scales of fluctuation • Cross-correlation between variables

21. Random Fields – Theory & Implementation • Point variability • Reflection of repeatability statistics of a measurement taken over a localized finite area or volume. • Spatial variability: • Measured using scale of fluctuation (or auto-correlation distance) • Larger distance = lower spatial variability (“longer wavelengths”) • Shorter distance = choppier field • Mean is unchanged

22. Random Fields – Scale of Fluctuation

23. Random Fields – Scale of Fluctuation

24. Random Fields – Scale of Fluctuation

25. Random Field Concepts

26. Random Fields – Scale of Fluctuation

27. Random Fields – Scale of Fluctuation

28. RFEM – RCOMB2D Program