Coastal protectionRubble mound breakwaters

Physical modelling

Dominique Mouazédominique.mouaze@unicaen.frM2C, Caen

Design flow diagram

Identify need

Existing coastal information

Problem definition Environmentalconsiderations

DesignRequirementsOptions

DataCollection

Sources of materials

Soils, geologymorphology

Wind, waves,Tide, currents

DESIGN

Rear armortoe

UnderlayerCore

Core below water

Main armor

antiscour

Rear armortoe

UnderlayerCore

Core below water

Main armor

antiscour

enroc hements

Port Talbot, GB

Tetrapodes

Cresc ent c ity, USA

Sines, Portugalfiltre

c ouronnement enbéton

blocs d ’Antifer

Wave deformations

-Shoaling-Refraction-Diffraction-Reflection-Breaking-Transmission

cap baie

Ombre de la jetée

Ligne d ’ombre

vagues diffractéeshoule inc identehoule r fl chieé é

Deep water (H, T, L, c, d)

Shallow water

( )kdkgc tanh2 =

⎟⎠⎞

⎜⎝⎛=

LdgTL π

π2tanh

2

2

d < L/20

d < L/2

Significant wave height from ‘Fetch’

0 1 2 3 4 5 6 70

5

10

15

20

25

Nom

bre

de v

ague

s, n

Hauteur de houle, H(m)

0 1 2 3 40

2

4

6

8

Fréquencen/N

H (m)

Statistics of waves

Fréquence de houle (Hz)

dens

ité s

pect

rale

S(f)

en

ms

2.

JONSWAP

-Probability distribution P(x) :P(x) = Prob [ x(t) ≤ x ]P(x=-∞) = 0 et P(x=∞) = 1

- Q = 1 - P

Hs = 4 x (under curve area)^(1/2)

Design wave = Hs = H1/3

Hmax (m) N P Q 1.75 1019 0.37217 0.62783 2 549 0.57268 0.42732 2.25 382 0.7122 0.2878 2.5 254 0.805 0.195 2.75 174 0.86852 0.13148 3 113 0.90979 0.09021 3.25 81 0.93937 0.06063 3.5 60 0.96129 0.03871 3.75 40 0.97589 0.02411 4 27 0.98576 0.01424 4.25 19 0.9927 0.0073 4.5 10 0.99635 0.00365 4.75 4 0.99781 0.00219 5 2 0.99854 0.00146 5.25 1 0.9989 0.0011 5.5 2 0.99963 3.65E-04 5.75 0 0.99963 3.65E-04 6 1 1 0 total 2738

‘Long term’ design

probability distribution

P(H<1.75)=1019/2738=0.37217

P(H<2)=(1019+549)/2738=0.57268

probability of a wave greater than 2m

Q(H>2)=1-P(H<2)=1-0.57268 =0.42732

1 0.1 0.01 1E-3 1E-4 1E-51

2

3

4

5

6

7

8

houl

e ce

nten

aire

houl

e an

nuel

le

houl

e dé

cenn

ale

Probabilité cumulée d'occurrence

Hmax(m)

365.n1Q =

Cumulative occurrence probability

For ten years Q=1/(365x10)=2.7.10-4

Hs = -α log(Q)

-Significant wave heightHs

-Extreme wavesHmax

-Run-up / Run-downOvertopping

Construction

From the ‘earth’

From a ‘pier’ / from the ‘sea’

Placement (Armour layer)

Placement (Armour layer)

HgDF nwhoule2ρ= 3)( nwr gDBW ρρ −=− 3

nr gDW ρ=

33

3

)sincos( ααμρ

+Δ≥

gHNW r Irribaren

αρ

cot3

3

D

r

KHgW

Δ≥ Hudson

Kd Stability coefficientΔ=(ρb – ρw)/ ρw

Design formula

Interlude

SPM 1984

SPM 1977

Stability coefficient KD

Natural rocks

Filter rules

Artificial blocks (Armour layer)

Concrete breakwater armour unit classification (1/2)

Concrete breakwater armour unit classification (2/2)

TETRAPODE

Artificial blocks (Armour layer)

C.

Artificial blocks (Armour layer)

CUBE ANTIFERArtificial blocks (Armour layer)

DOLOS

Artificial blocks (Armour layer)

ACCROPODE

Artificial blocks (Armour layer)

ACCROPODE II

Artificial blocks (Armour layer)

CORELOCX-BLOC

Artificial blocks (Armour layer)

Stability performance

Musoir

Overtoppingwww.overtopping-manual.com HR Wallingford

Physical modelling

Physical modelling

“When dealing with water, first experiment then use judgment”Leonardo da Vinci

Physical modelling / numerical modelling

Advantages1. cost effective2. physical processes without simplification3. large number of tests with controlled parameters4. turbulence 5. advanced experimental techniques

Disadvantages1. scale effects2. laboratory effects3. missing conditions4. more expensive than numerical models

“A physical model is a physical system reproduced (reduced size) so that the major dominant forces are represented in the correct proportion”

(Hughes, 1993)

Wave bassin (3D)

Wave bassin (3D)

Modèles numériquesModèle physique

4,75 m4,75 m1,9 m1,9 mDistance Distance MontMont--barragebarrage

256 m256 m22 mm41 km41 km22Surface zone Surface zone

12,5 12,5 àà 37 cm/s37 cm/s1 1 àà 3 m/s3 m/sVitesse Vitesse courantscourants

20,7 cm20,7 cm13,5 m13,5 mAmplitude Amplitude marmarééee

15 15 mnmn12h25 12h25 mnmnDurDuréée mare marééee

modmodèèlelenaturenature

Wave bassin (3D)Mobile bed

Wave Flume (2D)

Length L = 22mWater depth d = 0.3m to 0.7mMaximum significant wave height Hs ~ 0.25m

Regular and Irregular wave generationFocused wave generationPiston type wavemaker ( Edinburgh Designs) ‏

Dynamical wave absorptionPVC and glass flume bottomGlass walls

Wave generation area Wave field Reflection areaAbsorption area

020

40

60

80

100

120

140

160180

200

220

240

260

280

300

320

340

V

U

r

(en degrés)θ

D

e

0,000

0,002

0,004

0,006

0,008

-0,15 -0,10 -0,05 0,00 0,05 0,10 0,15 0,20

phasesπ 3π/4 5π/8 π/2 3π/8 π/4 0

U (m/s)

z (m)

Applications (1/4)

Fluid Mechanics

Applications (2/4)

Sediment transport / Scour

Applications (3/4)

Fluid-Structure Interaction

Applications (4/4)

Coastal Engineering

Physical modelling

“Theorem 1”

If there is a discrepancy between a theory and the experiment carriedout to verify it, it is likely to be due to inaccuracies in the experiment

“Theorem 2”

It is so far difficult to make good experiments than it is to make good theorie

Similitude / Similarity

Dimensional analysisL LengthT TimeM Mass

physical process = f( L

geometric α ≠ 0 β = 0 γ = 0kinematic α ≠ 0 β ≠ 0 γ = 0dynamic α ≠ 0 β ≠ 0 γ ≠ 0

Criteria of similitude“scale laws”

Dimensional analysis

Scale ratio NX = Xp / Xm = X in prototype / X

NL = Lp / Lm = 25m/1m =

Hydraulic similitude

Froude criterion Fr = inertial force / gravity force = U / (gL)1

Reynolds criterionRe = inertial force / visc

Shields criterion

Froude time scale

Nt = NL1/2

Real wave of 12.3s peri

Tmodel = 12.3 / (100)1/2 =

Thank you for attention!