March 29, 2012

Vermelding onderdeel organisatie

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Chapter 9: Stability of monolithic breakwaters

ct5308 Breakwaters and Closure Dams

H.J. Verhagen

Faculty of Civil Engineering and GeosciencesSection Hydraulic Engineering

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important aspects of caisson walls

• Quasi static load• Impact forces

• sliding• turning

• placing on a mound

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historical development of breakwater in Japan

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historical development of breakwater in Japan(2)

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historical development of breakwater in Japan(3)

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schematic pressure distribution for non-breaking waves

( )11

22 coshigHrph

L

ρπ

+⎛ ⎞= ⎜ ⎟⎝ ⎠

wd = ρgh

??

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load and equilibrium diagram

o

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example of a pressure record

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changes to incoming wave front induced by high mound breakwater

H=γh

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Risk of local impact forces

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Brighton Marina, UK

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Parapet damage

Damage due to typhoon Tokage (Oct 2004)Muroto Kochi, Japan

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Sketch of upright breakwater for stability analysis

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wave pressure distribution

Hiroi

Sainflou

Minikin

p = 1.5 w0H( )

( )

01 02

0

02

20

cosh/ coth

Hp p w hh H

w Hp

khH L kh

δδ

δ π

+= +

+ +

=

=

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Design wave for Goda’s method

• Wave heightcomplicated method (formula of a magician)

• Wave periodTmax = T1/3

• Angle of incidence βAssume an approach of 15 degrees to the normal

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Design wave height according to Goda

( ){ }1/3 0

max * ' * * '0 0 1 max 0 1/3 0

1.8 : / 0.2

min , ,1.8 : / 0.2

H h LH

H h H H h Lβ β β

≥⎧⎪=⎨ + <⎪⎩

( ){ }'0 0

1/3 ' ' '0 0 1 max 0 0 0

: / 0.2

min , , : / 0.2

s

s

K H h LH

H h H K H h Lβ β β

⎧ ≥⎪=⎨+ <⎪⎩

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Goda’s coefficients

( )( )

{ } ( )

0.38'1.50

00

10.29'

0max

0

0.028 exp 20tan

0.52exp 4.2tan

max 0.92,0.32 exp 2.4tan

HL

HL

β θ

β θ

β θ

−

−

⎛ ⎞= ⎜ ⎟

⎝ ⎠=

⎛ ⎞= ⎜ ⎟

⎝ ⎠

( )( )

{ } ( )

0.38'* 1.500

0

*1

0.29'* 0max

0

0.052 exp 20tan

0.63exp 3.8tan

max 1.65,0.53 exp 2.4tan

HL

HL

β θ

β θ

β θ

−

−

⎛ ⎞= ⎜ ⎟

⎝ ⎠

=

⎛ ⎞= ⎜ ⎟

⎝ ⎠

θ is the inclination of the seabed

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Nonlinear shoaling coefficient

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surface elevation

rise of the water above the caisson:η* = 0.75 (1+cosβ) Hmax

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wave pressure with Goda’s formula

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pressure values according to Goda

21 1 2 0 max

12

3 3 1

0.5(1 cos )( cos )

cosh

p w Hpp kh

p p

β α α β

α

= + + +

=

=

2

1

2max

2max

3

20.6 0.5sinh2

2min ,3

' 11 1cosh

b

b

khkh

h d H dh d H

hh kh

α

α

α

⎛ ⎞= + ⎜ ⎟⎝ ⎠

⎧ ⎫− ⎛ ⎞⎪ ⎪= ⎨ ⎬⎜ ⎟⎝ ⎠⎪ ⎪⎩ ⎭

⎛ ⎞⎛ ⎞= − −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

hb is waterdepth at 5 H1/3seaward from breakwater

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uplift pressure

1 3 0 max0.5(1 cos )up w Hβ α α= +

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safety factors

against sliding μ(W-U)/P >1.2against overturning (Wt-MU)/MP >1.2

MP moment of total wave pressure around the heel

MU moment of total uplift pressure around the heelP total thrust of wave pressuret horizontal distance between centre of gravity

and the heelU total uplift pressureW weight of the unitμ coefficient of friction (order of 0.6)

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Example• “runup” η = 17.2 m• safety factors “just sufficient”

H0 = 7 mT1/3= 11 sβ = 10 º

h = 18 m hcc=11.5 m

hc = 4.5 m

seabed slope 1:50

Wc=

FH

examples: H 7-15; Fslide; T(6) 10-15H 7-15; Fslide; hcc(6) 10-15H 7-15; Fslide; h(6) 15-20H 7-15; Fslide; wc(6) 15-25H 7-15; Foverturn; wc(6) 15-25

d=10 m

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Damage due to typhoon Togage (Oct 2004)

Susami Wakayama

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Overflow over a caisson (1)

3 4.30.2 exp b

ss

Fq gH

Hγ⎛ ⎞−

= ⎜ ⎟⎝ ⎠

formula of Van der Meer and FrancoFb freeboardγ parapet shape factor

0.7 normal parapet1.0 perforated caisson1.15 is maximum value

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Overflow over a caisson (2)TAW-report “waterkerende kunstwerken”based on research at HR Wallingford

qgem = 5.013 10-3 kwkagHsTzexp(-20.12 kb Fb/(Tz√(gHs))kw wind effect surcharge ka,kb correction for oblique wavesFb freeboard

example:Hs = 1.8 m; Tz = 3 s; Vwind = 15 m/sFb 0.25 - 2; q; Ftype(3)1-3

1= Van der Meer & Franco2= Wallingford/TAW3= Van der Waal, Delft Hydraulics

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Overflow over a vertical wall

North Wirral Coast, near Liverpool

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Hanstholm caisson

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JarlanCaisson

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Cylindrical breakwater, Nagashima

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breakwater with wave power generating system

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semi-circular caisson(for extremely high breakers)

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The Miyazaki breakwater

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Curved slit breakwaterFunakawa Port

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Composite, curved breakwater

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Honey comb wall breakwater

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erosion pattern depending on the grain size

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Vermelding onderdeel organisatie

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Do not forget the filter layersct4310