April 12, 2012

Vermelding onderdeel organisatie

1

Chapter 10: Wave-structure interaction

ct5308 Breakwaters and Closure Dams

H.J. Verhagen

Faculty of Civil Engineering and GeosciencesSection Hydraulic Engineering

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overview of interactions

• Wave (pressure) penetration• Wave reflection• Wave run-up• Wave overtopping• Wave transmission

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waves and pressures (1)measurements at the Zeebrugge breakwater

storm of 4 November 1999

15 min wave recordWR = waverider, 150 m awayLR = laser at toe 385,386, 388, 384 = pressure sensors on one level

Data from Peter Troch, Ghent University, PIANC bull 108, sept 2001

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Zeebrugge

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waves and pressures (2)

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waves and pressures (3)

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waves and pressures (4)

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wave reflection

• The problem is the determination of the reflection coefficient

• Two proposals made by Postma

• In this equation P is the Notional Permeability as defined by Van der Meer

• This equation has a very strict validity

( )

0.730

0.780.14 0.440

0.140

0.081 cot

r p

pr

K

K P s

ξ

α −− −

=

=

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definition of wave run-up

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correction factors for run-up

Structure γSmooth, impermeable (like asphalt or closely pitched concrete blocks)

1.0

Open stone asphalt etc. 0.95 Grass 0.9 – 1.0 Concrete blocks 0.9 Quarry stone blocks (granite, basalt) 0.85 – 0.9 Rough concrete 0.85

Structure γ One layer of stone on an impermeable base 0.55 – 0.6 Gravel, Gabion mattresses 0.7 Rip-rap rock, layer thickness n > 2 0.5 – 0.55

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wave run-up on a smooth permeable slope

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run-up specific for breakwaters

%

%

1.5

1.5

um m

s

cumm

s

za for

Hz

b forH

ξ ξ

ξ ξ

= <

= >

%u

s

z dH

=

For non-permeable breakwaters (P=0.1)

For permeable breakwaters

(P=0.4)

run-up level u (%)

a b c d

0.1 1.12 1.34 0.55 2.58 1 1.01 1.24 0.48 2.15 2 0.96 1.17 0.46 1.97 5 0.86 1.05 0.44 1.68 10 0.77 0.94 0.42 1.45 Sign. 0.72 0.88 0.41 1.35 Mean 0.47 0.6 0.34 0.82

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Relative 2% run-up on rock slopes

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Example

n1,2 = 1.5B=0gamma =0.5

p (5,95), z

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typical wave overtopping

Models available from Bradbury (textbook), Van derMeer and Besley.

Bradbury is only valid for “normal” slopes (1:1.5)

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Equations of Bradbury

*

3 2om

s

sQQg H π

=

2*

2c om

s

R sRH π

⎛ ⎞= ⎜ ⎟⎝ ⎠

* *( ) bQ a R −=

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Overtopping (1)

• Basically same type of equations as for run-up• Usually wave overtopping is expressed in a discharge q

However, this is a time-averaged discharge

exp

( ) 0.06, 5.2, 0.550.2, 2.6, 0.35

b

b

RQ a b

forbreaking plunging a bfor non breaking a b

γσσ

⎛ ⎞= ⎜ ⎟

⎝ ⎠= = =

− = = =

Q is dimensionless overtoppingR is dimensionless freeboard

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Overtopping (2)

03

/tan

1s

k

s

h LqQgH

hRH

α

ξ

=

=

In which:q = average overtopping (m3/s per meter)hk = crest freeboard (m)

In case of non-breaking, this root should be 1

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Measured overtopping (breaking)

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Measured overtopping (non-breaking)

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Overtopping (3)

• Reduction coefficients are equal to Run-up• However:

correction for angle of incidence:γb = 1- 0.0033 β

run demo Cress

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Elements in overtopping

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Top view of the model

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Dimensionless results

Q*d

perc

enta

ge o

f ov

erto

ppin

g

decreasing crest width

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A real case (H= 3 m, T=7 sec, 1 l/s per m)

3.3 m4.7 m

4 m

20 m

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Overtopping vs. Run-up

• For design inner slope overtopping is more relevant than run-up

• In the past overtopping could not be computed• In modern design, apply overtopping rules

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overtopping discharges and their effects

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Allowable overtopping

• Dutch dikes:• any slope q < 0.1 l/s• normal slope q < 1.0 l/s• high quality slope q < 10 l/s

• For breakwaters much higher values can be applied• For safe passages of cars q< 0.001 l/s• For safe passage of pedestrians q< .005 l/s• For no damage to buildings q< .001 l/s• For acceptable damage to buildings q< .02 l/s

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overtopped rock structures with low crown walls

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wave transmission for a vertical breakwater

3exp( )c

ss

Rq a bHgH γ

= −

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typical wave transmission

50

ct

n

RK a bD

= +

50

0.031 0.24i

n

HaD

= −1.84

50 50

5.42 0.0323 0.0017 0.51iop

n n

H Bb sD D

⎛ ⎞= − + − +⎜ ⎟

⎝ ⎠

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wave transmission for low crested structures

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