1.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
7
PERFORMANCE OF WAVE ABSORPTION BY USING PERMEABLE
SUBMERGED RECTANGULAR STEPPED BREAKWATER FOR THE
DEFENCE OF THE SHORE LINE
El Saie Yasser Mohamed
Teacher of Coastal Engineering,
AinShams University
ABSTRACT
Rectangular submerged vertical breakwater (RSVB) is a barrier with its crest below the still
water level. For economical solution of submerged rectangular vertical breakwater, I have to make
some holes in it to be permeable with different permeability ratios (p) to use as wave energy
absorption for the defence of the shore line. So in this paper experiments were done in the wave
flume in the laboratory of Hydraulics, Civil Engineering Department, Shorouk Academy, Higher
Institute of Engineering. This is under normal and regular waves with different ranges of wave
heights and periods under different water depths. The efficiency of the break water is presented as a
function of the transmission, the reflection and the wave energy loss coefficients. A permeable
(RSVB) with constant width (W) = 50 cm as the total width of the experimental flume and different
heights (Y) worked one by one or with each other’s (stepped) with different water depths (dw),
different wave heights (Hi) and some holes with diameter φ = 4.0 and 2.0 cm acting from one to
fourth rows, with different heights (S) from base. Comparing the percentage of energy reduction
calculated between this type and impermeable (RSVB), working as single or as a group (stepped) as
shown in figure (1).
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING
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ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 5, May (2014), pp. 07-26
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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
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Elevation Side View
Figure (1): Definition sketch of the permeable (RSVB) with different heights and porosities
1- INTRODUCTION
Submerged vertical porous breakwaters are becoming economic structures, to protect
harbours, marinas, fishing harbours and beaches from wave and current action and to control
shoreline erosion. Submerged or low-crested breakwaters function by provoking wave breaking and
by allowing some wave transmission so that a milder wave climate is obtained in lee of the
submerged structure.
Vertical rectangular porous structures offer an alternative to conventional fixed breakwaters,
such as rubble mound breakwaters. This type of breakwaters is considered as a good and cost-
effective substitute for the conventional type of breakwaters, especially for coastal works where the
tranquillity requirements are low.
In addition, the land side of the emerged types of this breakwater kind can be used for
berthing purposes more popular as a potential alternative to coastal protection measures where a
moderate degree of energy transmission is acceptable.
Such situations include areas where vegetative shore protection is existing or proposed or in
the event that an existing shore protection structure has become damaged or under designed and a
method is needed to reduce the incident wave energy.
Physical model studies were performed at the wave flume in the laboratory of Hydraulics,
Shorouk Academy, Civil Engineering Department, Higher Institute of Engineering as shown in
figure (2), to assess the performance of rectangular submerged vertical permeable breakwater
(RSVPB).
Many parameters affect the design; several researches studied the wave reflection and
transmission from similar perforated breakwaters.
However, there are benefits associated with the potentially smaller material requirements for
stable submerged structures and the ability to rehabilitate existing structures by simply reducing the
incident wave conditions with a submerged rectangular permeable breakwater.

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
9
Figure (2): Modelling Wave Flume
2. LITERATURE REVIEW
Seeling[9](1980), obtained the most information about wave transmission, reflection, and
energy dissipation from hydraulic model tests. The measurements in the model tests were generally
limited to the free surface oscillations on the landward and seaward sides of submerged breakwater.
Dalrymple et al. [3](1991), examined the reflection and transmission coefficient from porous
structures under oblique wave attack. Losada et al.[5](1996), investigated non-breaking regular
waves and non-breaking directional random waves interacting with permeable submerged
breakwaters.Méndez, F., Losada, I., and Losada, M.[7](2001), studied the influence of wave
reflection and energy dissipation by breaking and by porous flow induced by a permeable submerged
structure on second-order mean quantities such as mass flux, energy flux, radiation stress, and mean
water level is analyzed.
Twu et al. [12] (2001), studied theoretically, using the Eigen Function Expansion method, the
problem of wave transmission over a rectangular and vertically stratified with multi-slice porous
material. Chao, L., Ming, C.,Chih, Y. [1] (2004), investigated how the porosity of submerged
breakwaters affects non-breaking wave transformations. Eight model geometries each with six
different porosities, from 0.421 to 0.912, were also considered. Experimental results reveal that the
model width has little effect on wave reflection and transmission when the model heights are fixed.
Ching, P., Hong, B., and Juinn, R.[11](2004), presented numerical solutions to investigate the wave
reflection from a vertical breakwater with front submerged permeable structures. Homogeneous and
isotropic porous medium at the front of the impermeable vertical wall. Ting et al. [11] (2004),
investigated how the porosity of submerged breakwaters affects non-breaking wave transformations.
Eight model geometries each with six different porosities, from 0.421 to 0.912, were also considered.
Shirlal et al.[10](2007), experimentally investigated the armor stone stability of the submerged reef
and the influence of its varying distances from shore and crest width on ocean wave transmission. O.
S. Rageh[8](2009), studied the efficiency of the vertical thick submerged or emerged porous
breakwaters under normal and regular waves with wide ranges of wave heights and periods under
constant water depth. The efficiency of the breakwater is presented as a function of the transmission,
the reflection and the wave energy loss coefficients in experimental study. It is clearly seen from this
experiment that a submerged breakwater is very effective in reducing the transmitted waves. Yi-
Chun Liao [13] (2013), he made an experimental study of wave breaking criteria and energy loss

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
10
caused by a submerged porous breakwater on horizontal bottom in a 2-D wave tank. Wave
conditions as well as the freeboard of the submerged breakwater, with the front slope of 1/2 and 1/5,
are varying in the experiments.
El Saie Yasser Moh. [4] (2014), studied the effect of using submerged rectangular stepped
breakwater for the defense of the shore line, under variable water depth and different wave heights
and studying the energy reduction by using different heights of the submerged rectangular vertical
breakwater. Md. Ataur Ra., AyshaAk. [6](2014), studied the effect of porosity of submerged and
emerged breakwater on wave transmission, at 50 cm still water depth, interactions between regular
waves (wave period, T= 1.5 sec, 1.6 sec, 1.8 sec and 2.0 sec) and the fixed vertical porous
breakwater of three different porosity (n= 0.45, 0.51 and 0.7) having three different structure heights
(hb= 40 cm, 50 cm and 60 cm) have been studied experimentally.
3. EXPERIMENTAL STUDY
Physical modeling is performed in the wave flume in Shorouk Academy laboratory of
Hydraulics, Civil Engineering Department, Higher Institute of Engineering.
The layout of the experimental wave flume and the measurement sections (elevation and
plan) as shown in figure (3).The flume which is 12 m long, 0.5 m wide and 0.6 m deep. It is
equipped with a wave generator at one end. Two wave absorbers in the two ends to prevent reflected
waves and wave gauges for measuring wave height before and after the physical model. The water
depth in the flume (dw) ranged as (25, 27.5, 30, 32.5 and 35 cm), the wave generator makes five
eccentricities by the flying wheel (leads to five wave period) to produce minimum and maximum
wave heights as shown in figure (4).
Breakwater heights = (Y1= 15 cm, Y2= 20 cm and Y3= 25 cm), holes with diameter 4.0 cm is
fixed for the two rows in the three breakwaters, and the third and fourth rows with diameter 2.0 cm,
location of holes from base equal (S1 =3.5cm, S2 = 11.5 cm, S3 = 17.5 cm and S4= 22.5 cm) thickness
of any single submerged breakwater (X) = 5.0 cm.
Figure (3): experimental Wave Flume

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
11
Undistorted models are usually not used for wave studying, for instance there is no theory
which satisfactorily describes the wave breaking. Also wave effects from generator as shown in
figure (4) are reproduced by means of mechanical devices and this prevents the distortion of modeled
waves. The holes in the flying wheel leading to five eccentricities to produce minimum and
maximum wave heights acting on the physical model.
Figure (4): Photo of the wave generator
The main forces affecting waves are gravity forces and all other forces such as fluid friction
and surface tension can be neglected. Therefore in this study Froude Number Fn are considered in
modeling and similarity.
Fn for model = Fn for prototype
Where:
Fn = Froude's Number
V = velocity
g = acceleration due to gravity
L = characteristic length of flow
p
m
v
v
v
n = ….(1)
mP
gL
v
gL
v








=








….(2)
gL
v
Fn =

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
12
….(3)
p
m
T
T
T
n = ….(4)
….(5)
LT nn = ….(6)
….(7)
p
m
c
C
C
n = ….(8)
….(9)
( )2
Tnn =λ ….(10)
Where:
n = scale (ratio), C = celerity, λ = wave length, T = wave period
The efficiency of the system is evaluated through the transmission coefficient Ct where it is
equal to (Ht/Hi), additional information of the system response under the wave action is obtained
through the evaluation of the reflection and dissipation coefficient, Cr = (Hr/Hi) and finally
(Cd) 2
= (1 – Ct
2
– Cr
2
), evaluated indirectly through energy conservation concept, where:
Hi = incident wave height, Hr = reflected wave height and Ht= transmitted wave height, Also,
Hi = (Hmax+Hmin) /2 and Hr= (Hmax- Hmin) /2
From the previous analysis, the best linear scale was found to be 1:25 and for the study of
wave transmission, reflected and dissipation the wave period of 2.0 seconds as maximum is more
sufficient.
Therefore, four parameters are to be modeled; these are fluid properties, generated waves,
breakwater geometry and depth of water.
p
m
L
L
L
n =
p
m
v
L
L
n =
T
C
λ
=
p
m
n
λ
λ
λ =

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
13
The experimental program is as follows:
Where:
W = crest width = 50 cm, constant.
Y = height of Breakwater (step by step, their heights will be 15, 20, 25 cm)
dw = water depth (25, 27.5, 30, 32.5 and 35 cm)
N = number of breakwaters as single, double or triple (back to back).
X = width of breakwater (5, 10 and 15 cm).
S = location of different holes from base.
G.W. = generated wave heights (5 eccentricities from wave generator, leads to 5 wave period, To = 1,
1.25, 1.5, 1.75 and 2 seconds).
Run the experiments for all parameters, so wave generator produces different waves in such a
way that they covered the possible range found in nature. The wave then traveled pass the vertical
rectangular breakwater and was absorbed almost entirely at the other end of the wave flume. Wave
heights were measured in front of and behind the system of breakwaters.
Starting with single rectangular vertical breakwater with height(Y = 15 cm), with different
porosities (p = 0.1 and 0.185)and width X = 5.0 cm as shown in figure (4).
Single Y = 15 cm, p = 0.1 Single Y = 15 cm, p = 0.185
Figure (4): photos of different porosities by using single rectangular vertical breakwater with height
= 15 cm, X = 5 cm and S = 3.5cm and 11.5 cm
Repeating these experiments by using single vertical rectangular breakwater with height
(Y = 20 cm), with different porosities (p = 0.08, 0.13.8 and 0.185) as shown in figure (5).
Y dw N X S G.W

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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Single Y = 20 cm, p = 0.075 Single Y = 20 cm, p = 0.138 Single Y = 20 cm, p = 0.185
Figure (5): Photos of different porosities by using single rectangular vertical breakwater with
height = 20 cm, X = 5 cm and S = (3.5, 11.5 and 17.5 cm)
Ending these experiments by using the last single type with height(Y = 25 cm), with different
porosities (p = 0.06, 0.11, 0.148 and 0.185) as shown in figure (6).
Y = 25 cm, p = 0.06 Y = 25 cm, p = 0.11 Y = 25 cm, p = 0.148 Y = 25 cm, p= 0.185
Figure (6): photos of different porosities by using single rectangular vertical breakwater with height
= 25 cm, X = 5 cm and S = (3.5, 11.5, 17.5 and 22.5 cm)
Repeating the same experiments with double rectangular vertical breakwater with different
heights (Y = 15, 20 cm) and different porosities and total width x = 10 cm as shown in the following
figures.

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
15
Y = 15, 20 cm, p = 0.075 Y = 15, 20 cm, p = 0.138 Y = 15, 20 cm, p = 0.185
Figure (7): Photos of different porosities by using double rectangular vertical breakwater with
height = 15, 20 cm, X = 10 cm and S = (3.5, 11.5 and 17.5 cm)
By changing the height of the double breakwater to be (Y = 15, 25 cm), with different
porosities, X = 10 cm and variable (S) as shown in the following figures.
Y = 15, 25 cm, p = 0.06 Y = 15, 25 cm, p = 0.11 Y =15, 25 cm, p = 0.148 Y =15, 25 cm, p= 0.185
Figure (8): photos of different porosities by using double rectangular vertical breakwater with height
= 15, 25 cm, X = 10 cm and S = (3.5, 11.5, 17.5 and 22.5 cm)
By making another changing for height of the double breakwater to be (Y = 20, 25 cm), with
different porosities, (S) and X = 10 cm as shown in the following figures.

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
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Y = 20, 25 cm, p = 0.06 Y = 20, 25 cm, p = 0.11 Y =20, 25 cm, p = 0.148 Y =20, 25 cm, p= 0.185
Figure (9): photos of different porosities by using double rectangular vertical breakwater with
height = 20, 25 cm, X = 10 cm and S = (3.5, 11.5, 17.5 and 22.5 cm)
Finally by using three heights together back to back (Y = 15, 20 and 25 cm) as vertical
breakwater with different porosities, X = 15 cm and S = (3.5, 11.5, 17.5 and 22.5 cm) as shown in
the following figures.
Y = 15, 20, 25 cm, p = 0.06 Y = 15, 20, 25 cm, p = 0.11 Y =15, 20, 25 cm, p = 0.148 Y =15, 20, 25 cm, p= 0.185
Figure (10): photos of different porosities by using three heights of rectangular vertical breakwater
with X = 15 cm and S = (3.5, 11.5, 17.5 and 22.5 cm)
4. EXPERIMENTAL RESULTS
Some of these experiments results were plotted in group of curves figures (11, 12, and 13)
with different depths of water (25, 30 and 35 cm) indication for minimum, average and maximum
water depth and with different porosities with different location of these holes from base (S = 3.5,
11.5, 17.5, and 22.5 cm) and X= 5 cm to give relations between wave steepness Hi/L and coefficient
of transmission Ct to realize the effect of using single submerged, permeable, vertical, rectangular
breakwater with different heights as wave energy dissipation.

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Figure (11): Hi/L versus Ct, for Y = 15 cm, with different (p), constant width X = 5 cm and different
water depth, (S) and ds/dw
The difference between using different porosities at minimum depth 25 cm is more effective
than maximum depth 35 cm as shown in figure (11).
Figure (12): Hi/L versus Ct, for Y = 20 cm, with different (p), constant width X = 5 cm and different
water depth, (S) and ds/dw
0.8
0.85
0.9
0.95
1
0 0.05 0.1 0.15 0.2
Ct
Hi/L
p=0.1, d=25cm
p=0.185, d=25cm
p=0.1, d=30cm
p=0.185, d=30cm
p=0.1, d=35cm
p=0.185, d=35cm
0.7
0.75
0.8
0.85
0.9
0.95
1
0 0.05 0.1 0.15
Ct
Hi/L
p=0.075, d=25cm
p=0.138, d=25cm
p=0.185, d=25cm
p=0.075, d=30cm
p=0.138, d=30cm
p=0.185, d=30cm
p=0.075, d=35cm
p=0.138, d=35cm
p=0.185, d=35cm

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Therefore for depth 35 cm with different porosities there was nearly no effect for chosen
different porosities because almost the total energy will pass through this breakwater, and for depth
25 cm maximum Ct for short wave nearly (0.788) and for depth 30 cm Ct also = (0.924) for minimum
porosities as shown in figure (12).
Finally for using single breakwater with height Y3 = 25 cm, for studying its effect as wave
energy dissipater by changing its porosities with different wave steepness, (X = 5cm) and different
(S)and (ds/dw)as shown in figure (13).
Figure (13): Hi/L versus Ct, for Y = 25 cm, with different (p), constant X = 5 cm and different water
depth, S and ds/dw
From data of experiments for depth of water = 35 cm most of the incident energy passes
through this single breakwater, and for depth 25 cm maximum Ct for short wave nearly (0.765) for
(p = 6 %) and for depth 30 cm Ct also = (0.875) for (p = 6 %) as shown in figure (13).
So the coefficient of dissipation and energy reduction varied as shown in table (1) for
minimum depth = 25 cm, Computing the total wave energy in front of and behind the single,
submerged breakwater with different heights using the equation:
E = 0.125 (ρ.g.h2
),
where:
E is the total average wave energy per unit surface area.
ρ is the water density, g is the gravity acceleration and h is the wave height.
Table (1) discus the effect of using these different breakwaters with different heights as
(Y = 15, 20 and 25 cm) with all variables as wave energy dissipater.
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0 0.05 0.1 0.15
Ct
Hi/L
p=0.06, d=25cm
p=0.11, d=25cm
p=0.148, d=25cm
p=0.185, d=25cm
p=0.06, d=30cm
p=0.11, d=30cm
p=0.148, d=30cm
p=0.185, d=30cm

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 07-26 © IAEME
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Table (1): % of energy reduction for Y = 15 cm, with different porosities and water depths
Y = 15 cm, dw= 25 cm
Hi/L
P
(%)
S
(cm) ds/dw Cd
% Energy
reduction
P
(%)
S
(cm) Cd
% Energy
reduction
0.0414
10 3.5 0.4
0.4939 34.47
18.5
3.5,
11.5
0.4511 28.94
0.0560 0.5392 33.65 0.4964 28.49
0.0774 0.5710 32.67 0.5282 27.95
0.1105 0.5796 29.16 0.5334 24.7
0.1718 0.5867 24.51 0.5376 20.44
Y = 15 cm, dw = 30 cm
Hi/L
P
(%)
S
(cm) ds/dw Cd
% Energy
reduction P (%)
S
(cm) Cd
% Energy
reduction
0.0472
10 3.5 0.5
0.3094 22.86
18.5
3.5,
11.5
0.234 13.65
0.0491 0.3298 16.76 0.248 8.43
0.0738 0.3542 12.57 0.265 6.76
0.0925 0.4089 10.95 0.2748 5.87
0.1138 0.4776 9.32 0.369 5.31
Y = 15 cm, dw = 35 cm
Hi/L
P
(%)
S
(cm) ds/dw Cd
% Energy
reduction P (%)
S
(cm) Cd
% Energy
reduction
0.0541
10 3.5 0.57
0.1619 5.18
18.5
3.5,
11.5
0.1202 3.45
0.0577 0.1754 4.66 0.1429 3.06
0.0624 0.1896 4.02 0.161 2.63
0.0887 0.2012 3.39 0.1853 2.06
0.0921 0.227 2.75 0.1987 1.47

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From table (1) the difference in energy reduction is very clear with increasing in water depth
by using different porosities, for minimum porosities (p = 10 %, more effective) ranged between
(34.47 and 5.18).
The same experiments for single submerged breakwater Y2 = 20 cm with different water
depths and different variables as below in table (2).
Table (2): % of energy reduction for Y = 20 cm, with different porosities and water depths
From table (2) the difference in energy reduction is very small when exposed to maximum
water depth by using different porosities, but for short wave for minimum porosities (p = 7.5 %,
more effective) ranged between (42.85 and 5.43).
Finally for the last single submerged breakwater Y = 25 cm, with different water depths and
different variables the results of experiments were tabulated as below in tables (3).
Hi/L
P(%)
S(cm)
ds/dw
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
0.0381 0.6208 0.5482 0.4810
0.0504 0.6367 0.5522 0.5059
0.0683 0.6443 0.5568 0.5114
0.0952 0.6497 0.5596 0.5178
0.1448 0.6540 0.5613 0.5252
40.63 27.88 25.66
38.65 26.89 23.20
31.89
18.5
3.5,11.5,17.5
27.65
42.27 30.18 26.88
41.56 28.91 26.22
Y = 20 cm
% Energy reduction % Energy reduction % Energy reduction
7.5
3.5
0.2
42.85
13.8
3.5,11.5
Hi/L
P(%)
S(cm)
ds/dw
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
0.0436 0.3882 0.2498 0.2016
0.0491 0.3924 0.2865 0.2132
0.0738 0.4456 0.3283 0.2215
0.0925 0.4756 0.3805 0.2939
0.1138 0.4868 0.4042 0.2997
Y = 20 cm
16.41
14.49
10.81
% Energy reduction
18.5
3.5,11.5,17.5
15.11 2.89
8.26
3.5,11.5
22.67 6.56
19.88 4.93
15.58 3.65
6.27
% Energy reduction % Energy reduction
7.5
3.5
0.333
23.72
13.8
8.99
Hi/L
P(%)
S(cm)
ds/dw
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
0.0561 0.2700 0.1985 0.1514
0.0617 0.2715 0.2093 0.1598
0.0691 0.2726 0.2186 0.1666
0.0887 0.2729 0.2259 0.1711
0.0921 0.2731 0.2328 0.1754
4.40 2.57
6.95 3.96 2.31
18.5
3.5,11.5,17.5
3.08
7.34 5.11 2.93
7.24 4.79 2.79
7.11
Y = 20 cm
% Energy reduction % Energy reduction % Energy reduction
5.43
7.5
3.5
0.428
7.47
13.8
3.5,11.5

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Table (3): % of energy reduction for Y = 25 cm, with different porosities and water depths
Table (3) expressed the reduction of energy by using different single permeable submerged
breakwater with different porosities, for minimum porosities (p = 6 %, more effective) ranged
between (48.80 and 18.50), and increasing of (ds/dw) leads to minimum energy reduction as shown in
tables (1, 2 and 3).
But by using double permeable breakwater back to back in the previous photos figures (7,8
and 9) and from the experiments results, graphs shown in figures ( 14, 15 and 16) express the
different between them at average water depth = 30 cm.
Figure (14): the relation between Hi/L and % of energy reduction for Y1, Y2 with different porosities
Hi/L
P(%)
S(cm)
ds/dw
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
0.0314 0.6354 0.5713 0.5291 0.4825
0.0427 0.6519 0.5760 0.5454 0.4989
0.0591 0.6709 0.5817 0.5597 0.5179
0.0848 0.6830 0.5898 0.5624 0.5236
0.1324 0.6979 0.5999 0.5643 0.5309
Hi/L
P(%)
S(cm)
ds/dw
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
0.0485 0.4947 0.4135 0.3387 0.2389
0.0491 0.4963 0.4169 0.3465 0.2402
0.0772 0.4999 0.4180 0.3466 0.2604
0.0925 0.5030 0.4207 0.3510 0.2740
0.1138 0.6282 0.5874 0.5501 0.5006
Hi/L
P(%)
S(cm)
ds/dw
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
P(%)
S(cm)
Cd
0.0486 0.3444 0.2873 0.2579 0.2143
0.0544 0.3669 0.3162 0.2885 0.2519
0.0620 0.3886 0.3432 0.3170 0.2856
0.0887 0.4092 0.3681 0.3432 0.3156
0.0921 0.4295 0.3920 0.3682 0.3437
6.37
11.92 8.29 6.68 4.62
11.85
16.80 13.59 11.81 9.99
15.15 11.81 10.08 8.18
15.41
14.8
3.5,11.5,17.5
13.60
18.5
3.5,11.5,17.5,22.5
10.03 8.35
6
3.5
0.285
18.50
11
3.5,11.5
13.50
22.65
18.5
3.5,11.5,17.5,22.5
17.59
Y = 25cm, dw = 35 cm
% Energy reduction % Energy reduction % Energy reduction % Energy reduction
29.45
11
3.5,11.5
24.89
14.8
3.5,11.5,17.5
Y = 25cm, dw = 25 cm
26.89
24.96
23.35
42.64 33.28 29.83
Y = 25cm, dw = 30 cm
% Energy reduction
18.5
3.5,11.5,17.5,22.5
28.26
27.49
3.5,11.5,17.5
31.93
46.76 34.92 31.71
% Energy reduction % Energy reduction % Energy reduction % Energy reduction
33.95 31.41
% Energy reduction % Energy reduction % Energy reduction
40.53 32.73 28.08
36.14
14.8
6
3.5
0
48.80
11
3.5,11.5
45.14
25.35 20.44 17.88 14.87
6
3.5
25.04
24.54
0.1667
16.32 9.45 8.45
18.78 13.43 12.68
24.73 17.79 11.51 10.56
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
0.0436 0.0491 0.0738 0.0925 0.1138
%OFENERGYDERUCTION
Hi/L
Y1,Y2, P=7.5%
Y1,Y2, P=13.8%
Y1,Y2, P=18.5%

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Figure (15): the relation between Hi/L and % of energy reduction for Y1, Y3 with different porosities
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
0.0436 0.0491 0.0738 0.0925 0.1138
%OFENERGYREDUCTION
Hi/L
Y2,Y3, P=6%
Y2,Y3, P=11%
Y2,Y3, P=14.8%
Y2,Y3, P=18.5%
Figure (16): the relation between Hi/L and % of energy reduction for Y2, Y3 with different porosities
The relation between the different double breakwater heights for different wave steepness,
the more effective for Y2, Y3 than Y1, Y3 than Y1, Y2 as wave energy reduction with minimum
porosities (41.85, 38.92 and 28.95 respectively).
Finally by using triple permeable breakwater back to back in the previous photos figure (10)
and from the experiments results, figure (17) shows the effect of different porosities between them
and the percentage of energy reduction.
Figure (17): The relation between Hi/L and % of energy reduction for Y1, Y2 and Y3 with different
porosities
0.00
10.00
20.00
30.00
40.00
50.00
0.0436 0.0491 0.0738 0.0925 0.1138
%OFENERGYREDUCTION
Hi/L
Y1,Y3, P=6%
Y1,Y3, P=11%
Y1,Y3, P=14.8%
Y1,Y3, P=18.5%
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
0.0436 0.0491 0.0738 0.0925 0.1138
%OFENERGYREDUCTION
Hi/L
Y1,Y2,Y3, P=6%
Y1,Y2,Y3, P=11%
Y1,Y2,Y3, P=14.8%
Y1,Y2,Y3, P=18.5%

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The rates of energy reduction for critical wave steepness with different porosities (6, 11, 14.8
and 18.5 %) are about (39.78, 33.82, 27.56 and 24.12 respectively) and the effect of (X) and the
reduction of energy were directly proportional in this case.
5. COMPARISON WITH (El-Saie Yasser)
Comparing the results by (El-Saie), effect of using submerged rectangular stepped breakwater
for the defense of the shore line, at the same wave flume, in the laboratory of Hydraulics, Civil
Engineering Department, Shorouk Academy, Higher Institute of Engineering.
The water depth in the flume (dw) ranged as (25, 27.5, 30, 32.5 and 35 cm), the wave
generator makes five eccentricities (leads to five wave period) to produce minimum and maximum
wave heights, breakwater height = (Y1= 15 cm, Y2= 20 cm and Y3= 25 cm), different height of water
above crest level (ds) ranged between (10, 12.5, 15, 17.5 and 20cm), this was a solid breakwater
(impermeable).
So to show how the permeable submerged breakwater is economic or no, by comparing the
percentage of energy reduction between them at different porosities at the average depth 30 cm,
thickness of any single submerged breakwater (X) = 5.0 cm, as shown in table (4).
Table (4): % of energy reduction between different heights and porosities at average water
depth = 30 cm
Hi/L ds/dw
0.0472
0.0491
0.0738
0.0925
0.1138
30.56
25.64
23.03
21.35
19.79
% Energy reduction (P= 0%)
Y = 15 cm
5.31
% Energy reduction (P = 10%)
0.4
22.86 13.65
16.76 8.43
12.57 6.76
10.95 5.87
9.32
% Energy reduction (P = 18.5%)
Hi/L ds/dw
0.0472
0.0491
0.0738
0.0925
0.1138
26.76
23.93
Y = 20 cm
8.99
6.56
4.93
3.65
2.89
% Energy reduction (P= 18.5%) % Energy reduction (P= 0%)
32.05
29.79
26.90
6.27
% Energy reduction (P = 7.5%)
0.333
23.72 16.41
22.67 14.49
19.88 10.81
15.58 8.26
15.11
% Energy reduction (P = 13.8%)
Hi/L ds/dw
0.0472
0.0491
0.0738
0.0925
0.1138
25.04
24.89
20.44
18.78
17.79
% Energy reduction (P = 6%)
0.1667
29.45
24.54
% Energy reduction (P = 11%)
25.35
16.32
% Energy reduction (P= 14.8%) % Energy reduction (P= 18.5%)
17.59
14.87
12.68
10.56
22.65
17.88
13.43
11.51
9.45 8.45
Y = 25 cm
24.73
% Energy reduction (P= 0%)
37.45
32.66
30.08
29.68
28.55

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The difference between percentages of energy reduction by using permeable or impermeable
single submerged vertical breakwater for high conditions and minimum porosities for (Y = 15, 20
and 25 cm) nearly 25 %as shown in table (4).
Table (5): % of energy reduction between Y = 15, 20 cm with different porosities at average water
depth = 30 cm
But the difference between percentages of energy reduction by using permeable or
impermeable double submerged vertical breakwater for high conditions and minimum porosities for
(Y = 15 and 20 cm) nearly 17.2 % as shown in table (5).
Table (6): % of energy reduction between different heights and porosities at average water
depth = 30 cm
But the difference between percentages of energy reduction by using permeable or
impermeable double submerged vertical breakwater for high conditions and minimum porosities for
(Y = 15 and 25 cm) nearly 16.3 %, and also for (Y = 20 and 25 cm) nearly 13.72 % and finally for
(Y = 15, 20 and 25 cm) about 9.78 % as shown in table (6).
Hi/L ds/dw
0.0472
0.0491
0.0738
0.0925
0.1138 21.45 13.34 8.82 49.75
24.17 18.78 10.74 34.92
23.32 15.11 9.26 41.88
34.97
26.05 20.06 11.80 38.97
%Energy reduction(P= 0%)
0.333
28.94 22.45 16.83
Y = 15,20 cm
%Energy reduction(P=7.5%) % Energy reduction (P =13.8%) % Energy reduction (P=18.5%)
Hi/L ds/dw
0.0472
0.0491
0.0738
0.0925
0.1138
Hi/L ds/dw
0.0472
0.0491
0.0738
0.0925
0.1138
Hi/L ds/dw
0.0472
0.0491
0.0738
0.0925
0.1138
Y = 15,25 cm
%Energy reduction (P =6%) %Energy reduction(P= 11%) % Energy reduction (P=14.8%) % Energy reduction (P= 18.5%) %Energy reduction (P= 0%)
0.1667
39.34 27.32
34.88 23.77
30.31 20.37
23.08 19.43 46.88
36.72 25.08 20.47 17.90 43.88
%Energy reduction (P= 0%)
18.21 15.46 41.09
32.41 22.47 16.96 12.19 37.75
37.80
32.55
13.71 9.36 36.88
Y = 20,25 cm
%Energy reduction (P =6%) %Energy reduction(P= 11%) % Energy reduction (P=14.8%) % Energy reduction (P= 18.5%)
29.81 25.45 19.14 45.21
0.1667
41.32
35.54 24.58 20.86 16.17 41.56
33.56 28.87 21.35 47.89
38.72
% Energy reduction (P= 18.5%) %Energy reduction (P= 0%)
27.32 23.50 17.32 43.45
38.44
33.77
22.78 18.75 13.68 38.87
Y = 15,20,25 cm
%Energy reduction (P =6%) %Energy reduction(P= 11%) % Energy reduction (P=14.8%)
32.21 27.87 22.34 46.65
0.1667
43.79
36.55 26.45 21.25 18.12 41.98
36.56 31.54 23.34 48.54
40.32
24.32 20.23 17.42 39.11
29.12 24.56 21.20 43.66

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But also the overall percentage of excess energy passes than impermeable submerged vertical
breakwater with different kinds (single, double or (stepped) triple) with different porosities as shown
in table (7).
Table (7): % of excess energy passes through permeable submerged vertical breakwater with
different kinds and porosities than impermeable submerged vertical breakwater
Kind Height (cm) S(cm) ds/dw
X
(cm)
P (%)
% Of excess energy
passes than
impermeable
Single
15
3.5
0.5 5 10 10
20 0.333 5 7.5 8.25
25 0.167 5 6 7.42
Double
15, 20 0.333 10 7.5 6.15
15, 25 0.167 10 6 5.87
20, 25 0.167 10 6 5.21
Triple 15, 20, 25 0.167 15 6 4.89
6. CONCLUSION
From the physical model results, the performance of using rectangular submerged vertical
permeable breakwater (RSVPB) as a single or double or (stepped) triple with different heights and
porosities to reduce energy we can found that:
1- The difference in energy reduction for height of single breakwater (Y1= 15 cm) when using
minimum (p = 10 %) is more effective in low depth of water (dw= 25cm) than high depth of
water (dw= 35cm), so energy reduction is ranged between (34.47 and 5.18) respectively.
2- The difference in energy reduction for height of single breakwater (Y2= 20cm) when using
minimum (p= 7.5%) is more effective in low depth of water (dw= 25cm) than high depth of water
(dw= 35cm),so energy reduction is ranged between (42.85 and 5.43) respectively.
3- The difference in energy reduction for height of single breakwater (Y3= 25cm) when using
minimum (p= 6%) is more effective in low depth of water (dw= 25cm) than high depth of water
(dw= 35cm), so energy reduction is ranged between (48.80 and 18.50), and increasing of (ds/dw)
leads also to minimum energy reduction.
4- The relation between the different double breakwater heights for different wave steepness, the
more effective for Y2, Y3 than Y1, Y3 than Y1, Y2 with minimum porosities as wave energy
reduction were (41.85, 38.92 and 28.95 respectively).
5- The rates of energy reduction for critical wave steepness with different stepped breakwater Y1,
Y2 and Y3 with different porosities (6, 11, 14.8 and 18.5 %) are about (39.78, 33.82, 27.56 and
24.12 respectively) and the effect of (X) and the reduction of energy were directly proportional in
this case.

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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6- For comparison between the difference in percentages of energy reduction by using permeable or
impermeable single submerged vertical breakwater for high conditions and minimum porosities
for (Y1 or Y2 or Y3) nearly 25%, but for double breakwater (Y1 and Y2) nearly 17.2 %, or using
(Y1 and Y3) nearly 16.3 %, and also for (Y2 and Y3) nearly 13.72 % and finally for stepped
breakwater (Y1, Y2 and Y3) about 9.78 %.
7- The overall percentage of excess energy passes for (RSVPB) than (RSVB) with different kinds
(single, double or triple) with different heights and minimum porosities (10, 8.25, 7.42, 6.15,
5.87, 5.21 and 4.89).
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