design of breakwaters - unimasr · design of breakwaters rubble mound breakwater by dr. nagi m....
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Design of Breakwaters
Rubble Mound Breakwater
BY
Dr. Nagi M. Abdelhamid
Department of Irrigation and Hydraulics
Faculty of Engineering
Cairo University
2013
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Rubble mound breakwater
Dr. Nagi Abdelhamid
Breakwater design
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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
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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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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
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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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Mound Breakwaters-Design of Rubble
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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
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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
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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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Concrete Armour Units
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armour unit Concrete (Tetrapods )
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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
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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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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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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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)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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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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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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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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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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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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Typical crest structures for rubble mound
breakwaters
Dr. Nagi Abdelhamid
Breakwater design
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Typical crest structures for rubble mound
breakwaters
Dr. Nagi Abdelhamid
Breakwater design
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Toe details for rubble mound breakwaters
Dr. Nagi Abdelhamid
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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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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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
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)
)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
31 Dr. Nagi Abdelhamid
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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
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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
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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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