2. 455 V. HAFEEDA, S. BINUMOL, A.V HEGDE AND SUBBA RAO
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 07, No. 02, April, 2014, pp. 454-460
water circulation and clearance creating a clean
environment, by providing passage for fishes and
microorganisms. Due to its high effectiveness in energy
dissipation, it became very popular. The main
advantages are improved hydraulic performance,
decrease in total cost, quality control, environmental
aspects, construction time and maintenance. Later many
research works are conducted on semicircular
breakwater and quarter- circle breakwater under
submerged conditions; only a few on emerged quarter-
circle breakwaters.
(Jiang et al., 2008) have conducted a 2-D (vertical)
wave numerical model and physical model studies to
research the performances of QBW by comparing the
hydraulic behaviour of SBW and QBW under same
hydraulic conditions. As far as reflection is concerned,
they found that the reflection coefficients of QBW and
SBW are close with values less than 1.0 under same
conditions, even if hc reaches 2 to 3 times of incident
wave height. The reflection coefficient Kr increases with
hc/Hi increasing. They also stated that wave reflection
for SBW and QBW should concern closely and also the
behaviour of flow field around breakwater. They found
that, high flow velocity and vortexes occur near the rear
wall of QBW during wave overtopping in case of
submerged condition, which was caused by the top
sharp corner of and sudden expansion of flow field
around QBW. They concluded, the flow fields in front
of breakwater in both cases of submerged and emerged
are similar, which imply the resemblance of reflection
coefficients for both breakwaters.
SHI Yan-Jiao et al. (2011) conducted a series of regular
and irregular wave experiments to study the reflective
and transmitting performances of quarter circular
breakwater in comparison with those of semi-circular
breakwater. Two kinds of reflection coefficients are
discussed: 1. “Resolution reflection coefficient” based
on the standard concept of reflection coefficient with the
expression of Kr = Hr/ Hi which represents the whole
effect of wave reflection by breakwater. 2. “Circular-
surface reflection coefficient” which was denoted as Krc,
which is used to describe the reflective effect by circular
surface on the adjacent flow, field in front of the
breakwater. They found that the fact of Krc< Kr at the
same relative freeboard height (hc/Hi) indicates that the
entire reflective effect of QBW is stronger than that by
circular surface on the adjacent flow field. They also
stated that the reflection and transmission performances
of QBW are more sensitive to the relative freeboard
height (hc/Hi) than to the wave steepness (Hi /L). Both
kinds of reflection coefficients are reduced as hc/Hi
increases for submerged breakwater (hc/Hi <0) and
conversely show a noticeable increase as hc /Hi
increases under the emerged cases (hc/Hi >0). The
experimental and numerical results of the resolution
reflection coefficients for QBW under regular waves are
compared with the consequent experimental results of
the synthesis. Reflection coefficients under irregular
waves, overall, they concluded that the reflective effects
for irregular waves are stronger than those for regular
waves.
(Sundar and Subbarao, 2003) have done experimental
work on hydrodynamic pressures and forces on
quadrant front face pile supported breakwater. Quadrant
front face pile supported breakwater is a combination of
semicircular and closely spaced pile breakwaters, which
couples the advantages of these two types. This type of
structure consists of two parts. The bottom portion
consists of closely spaced piles and the top portion
consists of a quadrant solid front face on the seaside.
The leeward side of the top portion with a vertical face
would facilitate the berthing of vessels. An experimental
investigation on this breakwater model in a wave flume
is carried out for three water depths. For each water
depth, three different spacing’s between the piles were
adopted for the investigation. The dynamic pressures
exerted along the quadrant front face due to regular
waves were measured. The variation of dimensionless
pressures with respect to scattering parameter for
different gap ratio (spacing between the piles/diameter
of pile) and for relative pile depth (water depth/pile
height) are presented and discussed. In addition, the
dimensionless total forces exerted on the breakwater
model as well as its reflection characteristics as a
function of scattering parameter is reported. Kr increases
with increase in ka, from about 0.25 to 0.50, 0.25 to 0.70
and 0.20 to 0.85 for d/h=1.45, 1.63 and 1.81,
respectively. Further, the rate of increase is found to be
higher for higher d/h. A superposition of the lines of
best fit reveals that Kr is lesser for lesser water depth
(d/h=1.45) and Kt decreases with increase in ka. The loss
coefficient Kl from the evaluated Kr and Kt was
obtained as Kl = √1− (Kr
2
+ Kt
2
). For lesser water depth,
Kl increases with increase in ka, whereas for higher
water depths, Kl decreases with increase in ka.
2. Test Model:
The breakwater model consists of two parts, top quarter
circular shaped caisson and a base. The fabrication of
the model is done in two steps, one the casting of base
slab and the fabrication of the quarter circular caisson.
Base plate dimensions are
55 cm QBW 0.6 m × 0.73m × 0.05m
57.5 cm QBW 0.675 m × 0.73m × 0.05m
60 cm QBW 0.7 m × 0.73m × 0.05m
These dimensions were chosen in order to increase the
weight of the QBW to make them stable during wave
attack. Galvanized iron (GI) sheet of 0.002 m thickness
was used to fabricate the quarter circular shaped caisson
and the sheet was coated with cement slurry to simulate
3. 456
Wave Reflection by Emerged Seaside Perforated Quarter-Circle Breakwater
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 07, No. 02, April, 2014, pp. 454-460
concrete surface. The sheet was fixed to the base slab
with the help of stiffeners. The perforations are
provided in the quarter circular front portion of the
breakwater model, by drilling the holes. Diameter of the
perforations (D) are equal to 16 mm, and spacing
between perforations are kept constant, that is 80 mm
(i.e. centre to centre spacing between perforations;
S/D=5).Models are then placed over the rubble mound
foundation of thickness 0.05 m on the scale of 1:30
[equal to the prototype minimum thickness of 50 cm
prescribed by CEM, (2001)] and stones weighing from
50 g to 100 g were used to form the foundation.
Figure1: Quarter circular-breakwater model setup (not
to scale, all dimensions are in m)
3. Experimental Details:
The experiment is conducted in a two dimensional
monochromatic wave flume available in the marine
structural laboratory of department of applied
mechanics and hydraulics, national institute of
technology Karnataka, Surathkal, Mangalore, India. The
model is placed on a rubble mount foundation having
the slope 1:2 as shown in Figure 1, and 28 m away from
the wave flap. Three probe method proposed by
(Isaacson, 1991) is used for measuring the incident and
reflected wave height. The first probe is placed L
distance from the centre of the probe, and the distance
between the probes is equal to L/3, where L is the wave
length. A burst of five waves is generated to avoid the
successive reflection. The surface elevation measured
by the probes are recorded by the wave recorder and the
voltage signals are converted into wave heights and
wave period by using the lab wave recorder software
provided by EMCON (Environmental Measurements
and Controls), Kochi, India. The Figure 2 shows the
diagrammatic representation of the wave flume used for
this study.
Figure2: Diagrammatic representation of the wave
flume
3.1. Range of Experimental Variables:
Table1: Range of experimental variables
Parameters
Experimental
Range
Wave Specific Parameters
Incident wave height, Hi
(m)
0.03, 0.06, 0.09,
0.12, 0.15, 0.18
Water depth, d (m) 0.35, 0.40. 0.45
Time period, T (S)
1.2, 1.4, 1.6, 1.8,
2.0, 2.2
Structure specific parameter
Radius of the structure, R
(m)
0.55, 0.575, 0.6
S/D ratio 5
Diameter of perforation, D
(m)
0.16
3.2. Test Conditions:
The test conditions used in the experiments conducted
on quarter circle breakwater are as follows:
x Flume bed is horizontal and rigid.
x Secondary waves during wave generation are not
considered.
x Wave reflection from the structure does not
interfere with freshly generated incident waves,
since the waves are generated in bursts.
x The density difference between fresh water and
seawater is not considered.
x Generated waves are of simple regular type.
x Bottom frictional effects have not been accounted.
4. Analysis of Results and Discussion:
Some of the energy of the incident waves is reflected by
the structure. The reflection of the waves depends on the
relative free board (hc/R), emergence ratio (d/hs) and the
wave parameters. The graphs are plotted for the
variation of Kr with incident wave steepness, Hi/gT2
and
R/Hi (ratio of radius to incident wave height) values for
for different non-dimensional size parameter (R/gT2
)
4. 457 V. HAFEEDA, S. BINUMOL, A.V HEGDE AND SUBBA RAO
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 07, No. 02, April, 2014, pp. 454-460
and non-dimensional depth parameter (d/gT2
). The
results of these graphs are discussed below.
Figures 3 to 5 show the variation of reflection
Coefficient with respect to incident wave steepness,
Hi/gT2
for a different size parameter range; R/gT2
by
keeping radius of the structure (R) as constant and
different water depth. In all the cases it has been
observed that Kr is increases with increase in wave
steepness. Because for smaller wave heights with large
wave periods, the reflection coefficient is found to be
low and it is also found that if the free board (hc) is
increasing then the reflection coefficient is also
increasing. That is if water depth is increasing then the
Kr value is decreasing, because for smaller water depths,
waves encounter more planar (relatively vertical)
surface and hence less perforations are encountered and
more reflection, whereas for larger water depths, waves
encounter more perforated surface due to curvature
effect and less Kr value.
Figures 6 to 8 show the variation of reflection
coefficient with respect to incident wave steepness
Hi/gT2
for a different depth parameter range; d/gT2
by
keeping the depth of the water (d) as constant and
different height of the structure. It is found that Kr is
decreases with increase in d/hs. When height of the
structure (hs) increases, smaller height of the QBW
portion of the caisson is exposed to waves that is effect
of the curvature is less pronounced, thus, resulting,
lesser dissipation more reflection. Further, as d/hs
increases, there will be a reduction in reflection
coefficient.
Figures 9 to 14 shows the variation of reflection
coefficient; Kr with R/Hi (ratio of model radius to
incident wave height) for different Hi/gT2
and d/gT2
ranges. As R/Hi increases Kr is found to decrease.
Considering all the above cases the reflection
coefficient is found to vary from 0.23 to 0.69 for
perforated emerged QBW. A logarithmic curve is found
to be the best fit showing the variation of reflection with
incident wave steepness and R/Hi.
Table 2 shows the percentage reduction of reflection
coefficient for a particular range of size parameter;
R/gT2
and different water depths by taking the depth of
the water d = 35 cm as a base. And Table 3 shows the
percentage increase of reflection coefficient for a
particular range of depth parameter d/gT2
and different
heights of the structure by taking hs= 60 cm (radius of
the structure equal to 55 cm) as the base.
Table 2: Percentage reduction of reflection coefficient
with Water depth
Water
depth
(cm)
Percentage reduction of reflection
coefficient, Kr (%)
Size parameter, R/gT2
0.0105 to
0.0463
0.0116 to
0.0484
0.0126 to
0.0505
40 3.8 – 8 7.9 – 15.15 8.3 – 8.7
45 11.5 - 30
33.33 –
34.92
18.8 –
22.22
Table 3: Percentage increase of reflection coefficient
with height of the structure
Height
of the
structure,
hs (cm)
Percentage increase of reflection
coefficient, Kr (%)
Depth parameter, d/gT2
0.007 to
0.027
0.008 to
0.031
0.009 to
0.035
67.5 26 – 26.9
12 –
26.08
4.3 –
17.17
70 38 – 38.78
32 –
36.95
21.7 - 60
Figure3: Variation of Kr with Hi/gT2
for R/gT2
=0.0105 -
0.0463
Figure4: Variation of Kr with Hi/gT2
for R/gT2
=0.0116-
0.0484
5. 458
Wave Reflection by Emerged Seaside Perforated Quarter-Circle Breakwater
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 07, No. 02, April, 2014, pp. 454-460
Figure5: Variation of Kr with Hi/gT2
for R/gT2
=0.0126
-0.0505
Figure6: Variation of Kr with Hi/gT2
for d/gT2
= 0.007 -
0.027
Figure7: Variation of Kr with Hi/gT2
for d/gT2
= 0.008-
0.031
Figure8: Variation of Kr with Hi/gT2
for d/gT2
= 0.009 -
0.035
Figure9: Variation of Kr with R/Hi for R/gT2
=0.0105 -
0.0463
Figure10: Variation of Kr with Hi/gT2
for
R/gT2
=0.0116-0.0484
6. 459 V. HAFEEDA, S. BINUMOL, A.V HEGDE AND SUBBA RAO
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 07, No. 02, April, 2014, pp. 454-460
Figure11: Variation of Kr with Hi/gT2
for R/gT2
=0.0126-0.0505
Figure12: Variation of Kr with Hi/gT2
for d/gT2
= 0.009
-0.035
Figure13: Variation of Kr with Hi/gT2
for d/gT2
= 0.008
-0.031
Figure14: Variation of Kr with Hi/gT2
for d/gT2
= 0.007
-0.027
5. Conclusions:
Based on the results obtained and discussions carried
out, following conclusions have been drawn,
x Kr increases as incident wave steepness increases
for all the models tested and water depths. Kr
ranges from 0.23 to 0.69 for perforated emerged
QBW used in the experiments.
x As relative depth d/hs increases, Kr value decreases,
but Kr increases with increase in relative freeboard,
hc/R.
x Kr value decreases as R/Hi (ratio of quarter circular
model radius to incident wave height) increases for
d/gT2
ranges of 0.007 – 0.027, 0.008 – 0.031 and
0.009 – 0.035.
6. Acknowledgements:
The authors are thankful to the Director, National
Institute of Technology Karnataka, Surathkal, and also
to the Head, Department of Applied Mechanics and
Hydraulics, National Institute of Technology Karnataka,
Surathkal, Mangalore for their constant support and
encouragement in the preparation of this paper.
7. Notations:
D = water depth
D =diameter of the perforations
G = Acceleration due to gravity
Hi = Incident wave height
Hr = Reflected wave height
hc = Vertical distance from water level to the top of
the structure.
hs =Height of the structure
Kr = Reflection coefficient
L = Wavelength
R =Radius of the QBW
T = Wave period
8. Reference:
[1] Isaacson, M., 1991. Measurement of regular wave
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[3] Jiang, X.L., Gu, H.B. and Li, Y.B., 2008.
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7. 460
Wave Reflection by Emerged Seaside Perforated Quarter-Circle Breakwater
International Journal of Earth Sciences and Engineering
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