1. Wave Run-Up on Monopiles. An engineering model <2009-09-16

2. © Det Norske Veritas AS. All rights reserved Slide 215 May 2015 Wave Run-up Field Experience

3. © Det Norske Veritas AS. All rights reserved Slide 315 May 2015 Numerical & Physical Models Numerical simulation using DHI refined flow code, NS3, of wave run-up on a circular wind turbine, with a scour protection ( copy from Offshore Center Denmark Annual report) DHI Wave Run-up Test ( EOW(2007)

4. © Det Norske Veritas AS. All rights reserved Slide 415 May 2015 Run-Up Formula by De Vos et al 2007 Based on experiments carried out at AUC DE Vos et all have made a run-up formula for irregular waves: The 2% highest run-up can be determined as For monopile fundations:m=2.72 For cone fundations: m=4.45 Crest velocity and crest elevation from second wave order theory a)H2% b)The Peak Period Tp c)The Water Depth

5. © Det Norske Veritas AS. All rights reserved Slide 515 May 2015 Run-Up Tests by De Vos et al. 2007 Water depth=0.35m-0.5m pile diameter=0.12m Bed Slope in front of pile 1:100 Non-dimensional Properties Water depth to pile diameter ratio (h/D = 3 and 4). Significant Wave height to water depth ratio (Hs / h =0.23-0.39). Wave steepness (s0p = 0.018 - 0.06) Both regular and irregular tests.

6. © Det Norske Veritas AS. All rights reserved Slide 615 May 2015 AUC Model Tests 2006 ( completed after De Vos et al. 2007 tests) AUC, Horns Rev II, 2-D Model Tests Wave Run-Up on Pile. 2006 (Downloaded from the internet from AUC homepage) Water depth=0.2m 0.3m and 0.4m Pile diameter=0.1m Bed Slope in front of pile 1:100 Water depth to pile diameter ratio (h/D = 2,3 and 4). Wave height to water depth ratio (Hs / h = 0.35, 0.40, 0.43 and 0.46). Deep water wave steepness (s0p = 0.02 and 0.035)

7. © Det Norske Veritas AS. All rights reserved Slide 715 May 2015 Results of experiments: AUC Model Tests 2006 Max Run-Up 2% Run-Up

8. © Det Norske Veritas AS. All rights reserved Slide 815 May 2015 Effect of wave Steepness, AUC Model Tests 2006 AUC, Horns Rev II, 2-D Model Tests Wave Run-Up on Pile. 2006(Downloaded from the internet)

9. © Det Norske Veritas AS. All rights reserved Slide 915 May 2015 Results of experiments: AUC Model Tests 2006 Wave slope= 0.02:m=4 Wave slope=0.035: m=3 Crest velocity and crest elevation and are calculated by stream function waves theory based on a) H2% b) the Peak Period Tp and c) the Water Depth

10. © Det Norske Veritas AS. All rights reserved Slide 1015 May 2015 Measurements carried out at DHI. With Focussing waves. (copy from EOW 2007) D=0.164 m Water depth =0.4 m.

11. © Det Norske Veritas AS. All rights reserved Slide 1115 May 2015 Run-up height versus distance from foundation to the focus point. (copy from EOW 2007) Wave Dir

12. © Det Norske Veritas AS. All rights reserved Slide 1215 May 2015 Motivation for Re-analyze The m factor used in De Vos et al. Formula is based on Second Order wave theory, not valid for High waves. The 2% highest run-up is calculated from 2% highest wave. (The run-up heights should be the extreme as they are used for ULS design of secondary structures) The run-up heights are highly influenced by possible Wave-Breaking (conclusions made from the DHI model tests and Numerical Simulations ) The crest velocity for breaking waves are equal to the wave celerity

13. © Det Norske Veritas AS. All rights reserved Slide 1315 May 2015 New Run-Up model The maximum run-up for breaking waves is here assumed to be described as Stream function wave input Hmax Peak Period Tp Water Depth C Breaking Waves: Crest velocity =Phase velocity C

14. © Det Norske Veritas AS. All rights reserved Slide 1415 May 2015

15. © Det Norske Veritas AS. All rights reserved Slide 1515 May 2015 Summary A conservative estimate for maximum run-up on monopiles for breaking waves is suggested Stream function waves theory input Hmax Peak Period Tp Water Depth Current can be included

16. © Det Norske Veritas AS. All rights reserved Slide 1615 May 2015