Breakwaters and closure dams 10
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Transcript of Breakwaters and closure dams 10
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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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