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Recent updates on parts of Conceptual design of Rubble Mound

Breakwaters

The papers can be downloaded from internet:

www.infram.nl under products&services and then publications.

Publication 1.A code for dike height design and examination based on wave run-up and waveovertopping.Update of sections 3.1 and 3.2

Publication 21.Effectiveness of recurve walls in reducing wave overtopping on seawalls andbreakwatersUpdate of section 3.2 pages 28-30.

Publication 22.Applications of a neural network to predict wave overtopping at coastalstructuresNew information on section 3.2.

Publication 20.Wave transmission at low-crested structures, including oblique wave attackUpdate of section 3.3.

Publication 2.Geometrical design of coastal structures

Additional information to section 3.3 on percentage of overtopping waves.

Publication 3.Application and stability criteria for rock and artificial unitsAdditional information to section 4.2 on probabilistic approach.Additional information to section 4.2.4 on effect of armour shape and grading.

Publication 5.Design of concrete armour layersUpdate of section 4.3.
http://www.infram.nl/http://www.infram.nl/

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1

BREAKWATERS I

UNESCO-IHE

Dr J.W. van der Meer

INFRAM BV

Contents of lectures

First day, 4 periods

Introduction

Functions, requirements,types

Cross-section Sheet show

Boundary conditions waves

Second day, 4 periods

Governing parameters

Hydraulic response

Stability formulae

Rock armour stability

Video

Third day, 4 periods

Concrete armour

Low-crested structures

Berm breakwaters

Toe and head

Video

Functions

House Breakwater

Shelter (rain, Protection against waves

cold, wind, heat Protection agains currents

Privacy Provision dock/quay

Comfort (sleep, Prevent channel siltation

rest)

Requirements

House

good location,position

roof, walls,windows

heating, airco

rooms

durable

costs

Breakwater

lay-out

permeability

crest level

access

lee side

reflection

Types

House

apartment

double house

single house

farm

factory

Breakwater

rubble mound

berm breakwater

monolithic vertical

vertically composite

horizontally composite

dams, low-crested

seawalls

(rubble) revetments

Boundary conditions

Soil bearing capacity; tests

Hydrographic data bathymetry

Water levels

tides astronomical tidespring tide

storm surge depression rise due toatmospheric pressure

wind set-up stress by wind shear

wave set-up by wave groups

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2

Boundary conditions: waves

Wave seconds

Sea state hours

Daily wave climate year

Extreme wave climate many years

Part of wave record

H

T

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.1 0.2 0.3 0.4 0.5

frequency (Hz)

Energydensity(m2/Hz)

P011

P013

P015

Examples of spectra

Wave heightsH1/3 = 1.43 m

H1/10 = 1.82 m

H2% = 2.00 m

H1% = 2.17 m

H0.1% = 2.65 m

H2%/H1/3 = 1.40

0

0.5

1

1.5

2

2.5

3

3.5

probability of exceedance (%)

waveheight(m)

100 90 70 50 30 20 10 5 2 1 0.5 0.1

Rayleigh distribution on deep water

Wave heights

H1/3 = 1.53 m

H1/10 = 1.75 m

H2% = 1.85 m

H1% = 1.94 m

H0.1% = 2.17 m

H2%/H1/3 = 1.21

0

0.5

1

1.5

2

2.5

3


waveheight(m)

100 90 70 50 30 20 10 5 2 1 0.5 0.1

Double Weibull distribution on shallow water

One wave versus sea state

H H1/3; Hm0 = 4 m00.5

surplus: H2%; H1/10; Hmax

T Tm; Tp

surplus: Tm-1,0 = m-1/m0

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3

0

5

10

15

20

25

1 10 100 1000

Return period (years)

Hs

Bilbao

Sines

TripoliNorth Sea

Follonica

Pozallo

Examples of extreme wave climates (deep water)

From deep water to the coast

Refraction

Shoaling

Breaking

rule of thumb for gentle foreshore >1:50

Hs/h = 0.5 0.6

for breaker index: CIRIA/CUR p 211

Breaker index Hs/h (CUR/CIRIA)

sop=Hs/Lop=2Hs/(gTp2)

h=local water depth

Governing parametersbreakwater design

Waves

Hydraulic response parameters

Cross-section

Response of the structure

Waves

H1/3; Hm0; H2%; Tp; Tm; Tm-1,0

wave steepness: s = H/L = 2H/(gT2)

sop with Tp

and som with Tm

maxima: sop = 0.05; som = 0.07

breaker parameter = tan/s0.5

Hydraulic response parameters

Run-up: RuRu2%/Hs

Run-down: RdRd2%/Hs

Overtopping: q q/(gHs3)0.5

Transmission: Ct Ht/Hi

Reflection: Cr Hr/Hi

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4

Parameters rock

Nominal diameter Dn50

Dn50 = V1/3 = (M50/r)1/3 = cubic size

r= 2600 2700 kg/m3 (rock)r= 2400 kg/m3 (normal concrete

Concrete units: Dn

Relative buoyant density:

= (r w)/ w = 1.4 1.6 in most situations

Stability number

Hs/Dn50

Relation between wave

attack (Hs) and size of

unit (Dn50)

Rock shape Rounding of rocks

Examples of rock types Example of grading curve

0

10

20

30

4050

60

70

80

90

100

100 1000

Weight (g)

Percentage

exceeding

grading box 2

W15 (%) 234

W85 (%) 390

W85/W15 1.67

Dn85/Dn15 1.19W50 (g) 302

W50 cu rve (g) 30 3

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Example of shape curve

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4

largest/minimum dimension L/H

Percentagelarger shape box 2

> 2 L/H (%) 81

> 3 L/H (%) 4

Blockiness 0.41

Response of the structure

Damage level S

S = Ae/Dn502

number of squares that fit in erosion area

Damage level Nodnumber ofdisplacedunits in

a strip Dn wide

slope initial

damage

intermediate

damage

failure (under

layer visible)

1:1.5 2 3-5 8

1:2 2 4-6 8

1:3 2 6-9 12

1:4 3 8-12 17

1:6 3 8-12 17

Applicable damage levels S Damage level Nod

Damage parameter Nod: the actual number of

displaced units related to a width along the

longitudinal axis of the breakwater of one

nominal diameter Dn

Example: cubes 15 ton; Dn = 1.84 m; stretch 100 m long

Nod = 0.2 11 units In cross-section:

Nod = 0.5 27 units 20 units: 0.5/20*100%=2.5%

Nod = 1.0 54 units 40 units: 0.5/40*100%=1.25%

Nod = 2.0 109 units

Hydraulic response: run-up

Ru2%/Hs breaker parameteropRecent developments: o with Tm-1,0

Smooth slope: upper boundary

Reductions by:

roughness (rock!)

berm

angle of wave attack

Run-up rock slope compared to smooth slope

P>0.4

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6

Run-up rock slope: Weibull distributions

Hs = 2 m

Tm = 6 s

P = 0.4

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5 6 7 8 9 10

breakerparameter o

waverun-upRu2%/Hm

0

Run-up smooth slope, very shallow water; Tm-1,0

Hydraulic response: wave run-down on rock slopes Hydraulic response: wave overtopping run-up

Wave overtopping: basic formula

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

dimensionless crest height Rc/Hm0

dimensionlessovertoppingq/(gH

m0

3)0.5

Q=a exp(bR)

b

a

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

dimensionless crest height

dimensionlesswaveovertopping

Wave overtopping: breaking waves, all tests

0.1 l/s/m

1 l/s/m

10 l/s/m

100 l/s/m

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7

)1

H

R(-4.7

0.06=

gH

q

vfbops

c

opb3s

exp

tan

)1

H

R(-2.30.=

gH

q

fs

c

3

s

exp2

with as maximum:

breaking waves

non-breaking waves

Wave overtopping: general formulae Percentage of overtopping waves

Hydraulic response: transmission

Ct = Ht/Hi

Ct Rc/Hm0

and B, sop, Dn50

Change of spectral shape

Parameters wave transmission

General trend wave transmission; large scatter

for -2 < Rc/Hi < -1.13 Ct = 0.8

for -1.13 < Rc/Hi < 1.2 Ct = 0.46 0.3 Rc/Hi

for 1.2 < Rc/Hi < 2 Ct = 0.1

de Jong (1996) and dAngremond et al. (1996):

Ct = a 0.4 Rc/Hi

with a maximum of Ct = 0.8

and a minimum of Ct = 0.075

The parameter a describes all the other relevant influences:

a = (B/Hi)-0.31

* (1 e-0.5) * Astr

with: B = crest width

= breaker parameterAstr = a coefficient depending on the type of

structure:

rock slopes and concrete units: Astr= 0.64

smooth impermeable dam (asphalt) Astr= 0.80

impermeable smooth block revetment Astr= 0.80

block mattresses Astr= 0.75

gabion matresses Astr= 0.70

More accurate transmission formula

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8

Transmission, recent information

Large influence ofberm width is only

relevant forrubble mound structures

Smooth structures: no influence

New tests in EU-programme DELOS

confirm the formula

Spectral shape changes0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Relative crest height Rc/Hm0,i

transmissioncoefficientKt

B = 2 m

B = 4.5 m

B = 15 m

Influence crest width; smooth structures 1:4 slope

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.1 0.2 0.3 0.4 0.5

frequency (Hz)

Energydensity(m

2/Hz)

P014-Jonswap

P014a-PM

Incident spectra

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

frequency (Hz)

Energydensity(m

2/Hz)

P004

P005

Transmitted spectra

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

frequency (Hz)

energydensity(m2/Hz)

reduced incident spectrum

proposed transmitted spectrum

0,6m0,it

0,4m0,it

Transmitted spectrum; rough estimation Oblique wave transmission

Does Ct change with direction?

Yes!

Does direction change?

Yes!

Difference between rubble mound and smooth

structure?

For sure, treat them differently

Spectral change dependent on direction?

No.

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9

Hydraulic response: wave reflection

Hs/Dn50 = (KD cot)1/3

Limitations Hudson formula (1958)

the use of regular waves only,

no account taken in the formula of wave period or storm duration, no description of the damage level, the use of non-overtopped and permeable core structures only.

Hudson formula

for plunging waves:

and for surging waves:

0.5-

m

0.2

0.18

50n

s N

SP6.2=

D

H

P

m

0.2

0.13-

50n

s cotN

SP1.0=

D

H

Van der Meer formulae

0.5-

m

0.2

0.18

50n

s N

SP6.2=

D

H

0.5-

m

0.2

0.18

50n

s N

SP6.2=

D

H

Van der Meer formulae; influences

Van der Meer formulae; S N

N8000 maximum

Van der Meer formulae: Hs S

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10

Reliability

6.2 and 1.0 are stochastic variables

normal distribution

= 6.2 and 1.0 = 0.4 and 0.08 (V=6.5 and 8%) confidance intervals:

90%: +/- 1.6495%: +/- 1.96

Wave heightsH1/3 = 1.53 m

H1/10 = 1.75 mH2% = 1.85 m

H1% = 1.94 m

H0.1% = 2.17 m

H2%/H1/3 = 1.21

0

0.5

1

1.5

2

2.5

3


waveheight(m)

100 90 70 50 30 20 10 5 2 1 0.5 0.1

Double Weibull distribution on shallow water

Shallow water: H2% or H1/10 better?

0.5-

m

0.2

0.18

50n

%2 N

SP7.8=

D

H

P

m

0.2

0.13-

50n

%2cot

N

SP41.=

D

H

plunging waves:

surging waves:

Shallow water equations

Minimum crest width Bmin:

Bmin = (3 to 4) Dn50

The thickness of layers:

ta = tu = tf= n kt Dn50

The number of units per m2:

Na = n kt (1 nv)/Dn502

where:ta, tu, tf = thickness of armour, under layer or filtern = number of layerskt = layer thickness coefficientn

v= volumetric porosity

=packing density

Crest width and thickness of layers

= /Dn2

Values of kt and nv (SPM, 1984)

kt nv

smooth rock, n = 2 1.02 0.38

rough rock, n = 2 1.00 0.37rough rock, n > 3 1.00 0.40

graded rock - 0.37

cubes 1.10 0.47

tetrapods 1.04 0.50

dolosse 0.94 0.56

Values of kt and nv

Under layers and filters

Geotechnical filterrules:

roughly: D15A/D85f< 4 5

SPM under layer:1/10 1/15 of W50A D15A/D85u = 2.2 2.3

Large under layer gives large P and

higher stability

Smaller under layer can be cheaper

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11

Design of concrete armour layersIntroduction

Hudson/Van der Meer (rock)

Two-layer systems

cubes

tetrapods

crest height

packing density

One-layer systems

accropode

core-loc

cubes

Overall view

3/1)cot( Dn

s KD

H =

Stability FormulaeHudson

Van der Meer - rock: plunging and surging waves

),,,( PNSfD

Hm

n

s =

Hs/Dn = stability numberm = breaker parameterS = damage level

N = number of waves

P = notional permeability factor

Concrete armour layers

cot =1.5 sm remains; m disappears

P = 0.4 (breakwater with under layer)

Damage level Nod

),,( modn

s sNNf

D

H=

Two-layer systems

Research 85 - 87

Cubes

1.0

3.0

4.0

0.17.6

+=

mod

n

s sN

N

D

H

Tetrapods

2.0

25.0

5.0

85.075.3

+=

mod

n

s sN

N

D

H

Cubes 15 ton; = 1.35; sm = 0.04; N = 3000

0

0.5

1

1.5

2

2.5

4 5 6 7 8 9

Wave height Hs

(m)

DamageNod

Formula

Hudson, KD=7

Stability formulae give damage curve

Recent research Research 85 - 87:

steep slope 1:1.5: no transitionplunging-surging waves

De Jong (1996):

MSc-student TUDelft

research WL|Delft Hydraulics

flume tests tetrapods

also steeper waves

influence crest height

influence packing density

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12

De Jong: formula for plunging waves

tetrapods

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.01 0.02 0.03 0.04 0.05 0.06wave steepness sm

stabilitynumberHs/Dn

Van der Meer (1987)

De Jong (1996)

plungingsurging

surging:

plunging:

f(Rc/Dn) = influence of crest height

Rc = crest freeboard

f() = influence of packing density

Na/A = n k (1 - nv)/Dn2 = /Dn2

Total formula for tetrapods

)/(s)(94.3+N

N.68=D

H 20.om

5.0

od

n

snc DRff

)/(s)(0.85+3.75=D

H 0.2-om

5.0

n

s

ncod DRff

N

N

Influence of crest height

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-2 -1 0 1 2 3 4 5 6 7

Relative freeboard Rc/Dn

Influenceofcrestheightf(Rc

/Dn

)

f(Rc/Dn) = 1.0 + exp(-0.61 Rc/Dn )

Influence of packing density

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.5 2 2.5 3 3.5

Stability number Hs/Dn

DamagelevelNod

= 1.02

= 0.95

= 0.88

= 0.48

Influence of packing density

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2

Packing de nsity / SPM

Reductioncoefficientf(

)

f() = 0.40 + 0.61/SPM

one layer: Bhageloe, 1998

One-layer systems

Advantages (accropode, core-loc)

strong units, no breaking; if breaking: 10% loss

no rocking: packed

under design: no damage! (safety factor)

accropode: experience of 100 constructed breakwaters

large saving in concrete

CHEAP AND RELIABLE STRUCTURE

Disadvantages

strict placing pattern (not always possible)

not yet much experience with core-loc

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13

One-layer systemsAccropode, core-loc, ..cubes

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5

stability number Hs/ Dn

damageNod

accropode

start damage

failure

tetrapods

One-layer systemsAccropode

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5


damageNod

accropode

start damage

failure

design KD=12

tetrapods

One-layer systemsAccropode and core-loc

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5


damageNod

accropode

start damage

failure

design KD=12

core-loc KD=16

tetrapods

Overall view concrete units

Accropode Core-Loc Tetrapod Cube Cube

number of layers 1 1 2 2 1

slope 1:4/3 1:4/3 1:1,5 1:1,5 1:1,5

KD (breaking waves) 12 16 7 7 7

Hs/Dn = Ns 2,5 2,8 2,2 2,2 2,2damage Nod 0 0 0,5 0,5 0

damage % 0 0 5 5 0

packing density 0,61 0,56 1,04 1,17 0,70concrete per m2 on slope 0,182Hs 0,148Hs 0,350Hs 0,370Hs 0,236Hs

relative volume of concrete 100% 81% 208% 220% 140%

Reef type (Ahrens): reduction in crest height Conventional structure: emerged, small damage

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Reef type: crest at still water level Reef type: crest below still water level

Reef type: smaller material Reef type: wide crest

Conventional low-crested structure Reef type: lowering of the crest

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Conventional low-crested structure; various crest heights Reef type (Ahrens): reduction in crest height

Division of low-crested structure in three parts (Vidal) Low-crested structure: design of front, crest, rear

Conventional breakwater

Stable structure (damage S)

Reliable design formulae

Well-known structure

Various/many gradings (armour, underlayer(s), toe, bedding layer, etc.)

Heavy equipment (concrete units)

Limited size of rock concrete(expensive)

Berm breakwater,original concept

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Berm breakwater

Use ofrock up to Hs = 6 m cheap (?)

Two classes of rock: large and small

Easy construction

Not many in the world: around 30 (25 on Iceland)

Initially unstable: profile reshaping. After

reshaping statically stable.

Design parameter: mound of berm

Erosion gives gentle and stable slope

Dynamic stability: S-shaped profile independent of

ininital profile

Schematised profile: BREAKWAT

Three curves with BREAKWAT

Basic design parameters

Hs/Dn50 = 3.0

Determine berm level

Draw slope 1:4

Redesign to berm profile

Use BREAKWAT to determine berm

length

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Crest height: rear side stability

Rear side stability is very important for berm

breakwaters: unstable rear side may cause

failure of the breakwater

Consider developed profile

Rc/Hs * sop1/3 = 0.25: start of damage

0.21: moderate damage

0.17: severe damage

A lower value gives more overtopping

Erosion of berm breakwater head

Head, St. George, Alaska. 3D tests

Longshore transport

Longshore transport during reshaping

S(x) = number of rocks displaced per wave

Maximum between 15-40 degrees attack

Ho = Hs/Dn50

Top = Tp/(gDn50)0.5 dimensionless period

S(x) = 0 for HoTop < 105

S(x) = 0.00005 (HoTop- 105)2

Longshore transport: rock/gravel beach; Hs/Dn50 < 8 Longshore transport: onset

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Stable Berm Breakwaters,Sigurdur SigurdarsonIcelandic Maritime Administration

Stability test of the Icelandic type,Juhl and Sloth (EU-programme)

Some of the profiles tested

Conventional

Stability test of the Icelandic type,

Juhl and Sloth

conventional

Husavik berm breakwater, 2001-2002

Stone Classes and Quarry Yield Prediction.

Stone wmin-wmax wmean wmax/ dmax/ Expected For Hs=6.8 m

class (tonnes) (tonnes) wmin dmin quarry yield Ho HoTo

I 16.030.0 20,7 1.9 1.23 5% 1.9 46II 10.016.0 12.0 1.6 1.17 5% 2.3 62

III 4.0 10.0 6.0 2.5 1.36 9% 2.9 87

IV 1.0 4.0 2.0 4.0 1.59 14% 4.2 151

V 0.3 1.0 0.5 3.3 1.49 12% 6.5 291

Grindavik berm breakwaters, 2001-2002

Stone Classes and Quarry Yield Prediction.

Stone wmin-wmax wmean wmax/ dmax/ Expected For Hs=4.4 m

class (tonnes) (tonnes) wmin dmin quarry yield Ho HoTo

I 15.030.0 20,0 2.0 1.26 5%

II 6.015.0 9.0 2.5 1.36 9% 1.7 47III 1.5 6.0 6.0 4.0 1.59 17% 2.4 80

IV 0.3 1.5 2.0 5.0 1.71 20% 3.9 166

Sirevg berm breakwater, NorwayDesign by Icelandic Maritime Administration

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Sirevg berm breakwater, Norway

Design wave height and worst casescenario

Station number

along thebreakwater (m)

Design wave

height 100 yearreturn period

Worst case

scenario 1000year return period

Hs (m) Hs (m)

0 to 70 4.8 5.3

75 to 125 3.5 3.9

145 to 210 6.2 6.8

215 to 240 6.4 7.3

245 to 275 6.2 6.8

280 to 400 6.7 7.4

Breakwater head 7.0 7.7


Quarry Yield PredictionSIREVG - QUARRY YIELD PRE DICTION

0

10

20

30

40

50

60

70

80

90

100

0,10 1,00 10,00 100,00

Weightof s tones (tonnes)

Quarry A: Yieldprediction

Quarry B: Yieldprediction

Quarries A, B, andC -weighed averages: Yieldprediction

DesignCurve


Stability number, Ho, for various design

wave heights, Hs

Stone wmin - wmean dmax/ Ho for various Hs

class wmax dmin 3.5 m 4.8 m 6.2 m 6.7 m 7.0 m

I 20 - 30 23.3 1.14 1.05 1.45 1.87 2.02 2.11II 10 - 20 13.3 1.26 1.27 1.74 2.25 2.43 2.54

III 4 - 10 6.0 1.36 1.66 2.27 2.94 3.17 3.31

IV 1 - 4 2.0 1.59 2.39 3.28 4.23 4.57 4.78

Stable berm breakwaters,concluding remarks (Sigurdarson)

18 year experience

27 structures have been built

Design wave 2.5 to 7.0 m

Constructed on 25 m water depth

Breaking waves / non breaking

On weak soil with large settlements

More economical and more stable than the

homogeneous berm breakwater

Toe stability Different toe heights

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Different toe widths Damage definition Nod

Toe stability: old results Toe stability: new results

Hs/Dn50 * Nod-0.15 = 2 + 6.2 (h t/h)

2.7

Application area;

0.4 < ht/h < 0.9

3 < ht/Dn50 < 25

Toe stability: final results (Infram publication nr 2) Damage location head (Jensen, 1984)

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Head stability

No good formulae, too many parameters

Rules of thumb:

increase weight by 50% to 100%

decrease slope angle

increase radius of head

or a combination

3D-tests for important breakwaters

Videos

Scheveningen: land based construction

Maasvlakte: construction from water

Reina Sofia: caisson

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