Design of Breakwaters

Rubble Mound Breakwater

BY

Dr. Nagi M. Abdelhamid

Department of Irrigation and Hydraulics

Faculty of Engineering

Cairo University

2013

Rubble mound breakwater

Dr. Nagi Abdelhamid

Breakwater design

2

Advantages of Rubble mound breakwater:

Failure of the armour layer is not sudden

but gradually;

It allows high energy dissipation due to its

slope and transmission through porous of

mound;

It can be used for weak soil;

Easy maintenance and construction;

Small wave reflection;

Minimum overtopping less than Vertical

Breakwater.

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Breakwater design

Design Criteria For Breakwaters

ECONOMIC LIFE

• Very Important Marine Structures 100 years

• Important Marine Structures 50 years

• Normal Marine Structures 25 years

• Temporary Marine Structure 1-2 years

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Breakwater design

Design Wave Height

Non-Breaking Wave Condition, Hd

• Normal Marine Structures H1/3

• Temporary Marine Structures Hm

Breaking Wave Condition, Hb

• All Marine Structures Hb = 0.78 d

Note : d is the available water depth .

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Breakwater design

Design Rubble-Mound Breakwater

Structure Response

The design of the rubble mound cross section includes

the following:

1. design Armour (primary cover layer) of breakwater

a) weight of armour (primary cover layer) Wa

b) Thickness of armour layer(ta)

c) Placement density ( number of units/m2)Nr

2. design Secondary ( under Layer) of breakwater

a) weight of under layer Ws

b) Thickness of under layer(ts)

3. design Core

4. design of Crest level and width

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Breakwater design

Mound Breakwaters-Design of Rubble

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Breakwater design

Design Of Rubble Mound Armour (primary layer) of breakwater esignD -1

The armour layer is probably the most important feature of a

rubble mound breakwater since damage or failure can

lead to failure of other parts

a)weight of individual armor : “Hudson Formula”

W50 = γa H3/{KD (Sa-1)3 Cot θ}

Where: W50 weight of individual armor unit, natural rocks or

artificial concrete unit H design wave height γa unit weight of armor unit material = 2.65 t/m3 for rocks and 2.40 t/m3 for concrete

γw = 1.025 t/m3

Sa specific gravity of armor material, γa/ γw

θ angle between seaward structure slope and horizontal, cot θ = t KD armor unit stability coefficient

Where:

D is the nominal size(equivalent cube); the suffix ’50’ refers to the

percentage of stone passing that size

D50 = {W50/ γrock}1/3

ta = 2K0 D50

Dmax 4.000 D50

D85 1.960 D50

D15 0.400 D50 Dmin 0.125 D50

b) Thickness of armour layer

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Dr. Nagi Abdelhamid

Breakwater design

Massive Bulky Slender

Cube Accropode 1980 Tetrapods 1950

Dolos 1963

Depend the stability on

own weight

Depend the stability on

own weight and

interlocking

Depend the stability on

interlocking

Concrete Armour Units

Dolos

Tetrapod

Cube

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Breakwater design

Concrete Armour Units

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Breakwater design

armour unit Concrete (Tetrapods )

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Breakwater design

Suggested KD No-Damage Criteria and Minor Overtopping

Structure Head Structure Trunk

Placement n Armor Units Slope KD KD

Cot Non Br.

wave

Break

wave

Non Br.

wave

Break

Wave

1.5 3.2 2.9

4.0 3.5 random 2 Quarry Stone

Rough

angular 2.0 2.8 2.5

30 2.3 2.0

1.5 6.5 5.9 8.3 7.2 random 2

Tetrapod &

Quadrapod

2.0 5.1 5.5

2 to 3 16.5 15.0 25.0 22.0 random 2 Dolos

3 16.0 13.5

5.0 - 7.3 6.8 random 2 Modified

Cube 13 Dr. Nagi Abdelhamid

Breakwater design

Layer Coefficient and Porosity

Porosity (p)

%

Layer Coeff.,

ko Placement n Armour Unit

31 1.15 random 2 Quarrystone (rough)

47 1.10 2 Cube (modified)

50 1.04 2 Tetrapod

49 0.95 2 Quadripod

63 1.00 2 Dolos

37 - random graded Quarrystone

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Breakwater design

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Breakwater design

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Breakwater design

NT DENSITYPLACEME C.

where:

Nr = number of units for a given surface area

A = Surface area

P% = Percentage of average porosity of layer

Nr = A.n.K∆ [1- P%/100].[γu/W]2/3

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Breakwater design

2. Design Secondary ( under Layer) of

breakwater

a) weight of under layer Ws

W50 =W armour /10 - W armour /15

D50 = {W50/ γrock}1/3

Dmax = 4.000 D50

D85 = 1.960 D50

D15 = 0.400 D50

Dmin =0.125 D50

Filter Criteria

(D15)armor/(D85)secondary ≤ 5

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Breakwater design

)sThickness of under layer(t b.

where:

t s = total thickness of layer

n = number of layers of protection units

K∆ = layer coefficient

γrock = unit weight of material

Wrock = weight of individual protection

unit in layer

ts = n K∆[Wrock/γrock]⅓

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Breakwater design

3. Core Design W50 =Warmour /200 - Warmour /6000

D50 = {W50/ γrock}1/3

Dmax = 4.000 D50

D85 = 1.960 D50

D15 = 0.400 D50

Dmin = 0.125 D50

Filter Criteria

(D15) secondary/(D85)core ≤ 5

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Breakwater design

4. DESIGN OF CREST LEVEL AND WIDTH

Crest width1 .4

Where:

B = crest width

Note:

Controlled by construction method and

maintenance equipment.

B ≥ 3 K∆ [W/γu]1/3

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Breakwater design

4.2 CREST LEVEL

Where:

CL = Crest Level of Breakwater

DWL = Design Water Level

R = Wave Run-Up

CL = DWL + R

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Breakwater design

Wave Run-Up R

b

aHR d

1Where:

a = 0.775 b = 0.361 for Quarry Stones

= 1.010 = 0.910 for Tetrapods

= 0.590 = 0.350 for Quadripods

= 1.810 = 1.570 for Tribars

similaritySurf

Tg

Hd

2

2

tan

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Breakwater design

Overtopping Discharge:

R

dh

do eHQgQ

1tanh217.0

2

13*

Where:

= 0.06 - 0.0143 ln (sin )

h = structure height

d = water depth

R = wave run-up

spedestrianFor L/s/m 0.1 discharge, govertoppinQ

0.02tcoefficiengovertoppin*

oQ

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Breakwater design

Typical crest structures for rubble mound

breakwaters

Dr. Nagi Abdelhamid

Breakwater design

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Typical crest structures for rubble mound

breakwaters

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Breakwater design

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Toe details for rubble mound breakwaters

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Breakwater design

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Example

Given:

A rubble mound breakwater with two-diameter of rock armour layer:

Crest level = +4.5 m (LCD)

Side slope of sea-side = 1:2

Design water level = +3.2 m (LCD)

Significant wave height at sea-side = 2.0 m

Mean wave period = 4.4 s

Overtopping Coefficient = 0.02

Find:

Mean overtopping rate of the rubble mound.

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Breakwater design

Solution:

1.94

(4.4)*9.81

2*π*2

0.5

Tg

Hπ2

tanθζ

2:1slopesidefor0.5tanθ

stonesQuarryfor0.361b0.775a

s4.4T

m2.0H

22

d

d

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Breakwater design

0.072

)26.57sin (ln 0.0143-0.06

) θsin (ln 0.0143-0.06α

govertoppin of Case

m) 4.5(CL

m 4.971.773.20

RDWLCL

m 1.771.94*0.3611

1.94*0.7752.0

bζ1

aζH R d

30 Dr. Nagi Abdelhamid

Breakwater design

)

)l/s/m 29.2/s/mm 0.0292

e2.0*0.02*9.81

eH Q g Q

0.02Q

m 1.77 R

m 3.2 d

m 4.50h

3

1.77

3.24.5 tanh

0.072

0.217

2

13

R

dh tanh

α

0.217

2

13

d

*

o

*

o

1

1

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Breakwater design

Design of Ruble Mound Breakwaters

Mid Term – May 2011

A trunk cross-section with side-slope 2:1 has to be designed

based on breaking wave condition, where

the wave period is 8s. The cross-section is located at 9m water

depth where the crest level is 5m above water level.

(a) Design the sea-side rock armor and secondary layers, and

estimate wave run-up.

(b) Re-estimate wave run-up if Tetrapods armor-units are used.

Data

Trunk – Breaking Condition

t = 2

T = 8s

d = 9.0m

h-d = 5.0m 32 Dr. Nagi Abdelhamid

Breakwater design

Rock-Armor Layer

H = 0.78 d = 0.78 * 9.0 = 7.0m

W50 = γrH3/[Kd(γr/γw-1)3cot θ]

= 2.65(7)3/[3.5(2.65/1.025–1)32.0] 33t

t = n K (W/γr)1/3

= 21.15(33/2.65)1/3 = 5.3m

D50= (W/γr)1/3 = (33/2.65)

1/3 = 2.3m

D15 = 0.400 D50 = 0.40 2.3 = 0.9m

Secondary Layer

W50 = Warmor/10 Warmor/15 = 33/10 = 3.3t

t = = 21.15(3.3/2.65)1/3 = 2.47m

D50= (W / γ r)1/3 = (3.3/2.65)

1/3 = 1.1m

D85 = 1.960 D50 = 1.96 1.1 = 2.2m

Check: (D15) armor / (D85)secondary = 0.9/2.2 = 0.4 ≤ 5 OK 33

Dr. Nagi Abdelhamid

Breakwater design

Wave Run-up for Rock-Armor Layer

Wave Run-up for Tetrapod-Armor Layer

1.9

(8)*9.81

7*π*2

0.5

Tg

Hπ2

tanθζ

22

d

bζ1

aζH R d

1.6

1.9*361.01

1.9*0.7757

bζ1

aζH R d

9.4

1.9*91.01

1.9*1.017

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Breakwater design