wave run-up on monopiles. an engineering model

Wave Run-Up on Monopiles.

An engineering model

<Erik Asp Hansen><2009-09-16

© Det Norske Veritas AS. All rights reserved Slide 218 April 2023

Wave Run-up Field Experience


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)


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 theorya) H2% b) The Peak Period Tpc) The Water Depth

%2max,

2%2

%2 2

g

umRu


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.


AUC Model Tests 2006(completed after De Vos et al. 2007 tests)

AUC, Horns Rev II, 2-D Model TestsWave 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)


Results of experiments: AUC Model Tests 2006

Max Run-Up

2% Run-Up


Effect of wave Steepness, AUC Model Tests 2006

AUC, Horns Rev II, 2-D Model TestsWave Run-Up on Pile. 2006(Downloaded from the internet)

%2max,

2%2

%2 2

g

umRu


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

g

umRu

2

2%2

%2max,%2


Measurements carried out at DHI. With Focussing waves. (copy from EOW 2007)

D=0.164 m

Water depth =0.4 m.


Run-up height versus distance from foundation to the focus point. (copy from EOW 2007)

Wave Dir


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


New Run-Up model

The maximum run-up for breaking waves is here assumed to be described as

Stream function wave inputHmax

Peak Period Tp

Water Depth

)2

(2

max g

cRu crest

C

Breaking Waves: Crest velocity =Phase velocity C


Theory Vs AUC Measurements

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.1 0.2 0.3 0.4 0.5Run-Up(m) Measurements

Ru

n-U

p(m

) T

heo

ry

Line of perfect agreementh/D=2h/D=3h/D=4+-20%


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

)2

(*2.12

max g

cRu crest


http://www.dnv.com/

wave run-up on monopiles. an engineering model

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wave runup

engineering model