This paper presents results obtained from a series of experiments conducted in wave flume to assess the influence of the offshore lowcrested breakwater as a defence structure in reducing the wave forces on vertical seawall. The main aim of the tests was to know the effect of crest elevation of the offshore lowcrested breakwater as a rehabilitation structure for the existing damaged shore protection structures. In this study five relative breakwater heights are used and associated flow evolution was analyzed. With the sections proposed in this study, it is possible to achieve considerable reduction of wave force on the seawall. Modification factor is proposed to estimate the shoreward force on the seawall defenced by lowcrested breakwater.
Trang 1vertical seawalls / caissons due to
an offshore breakwater
Article in Indian Journal of Geo-Marine Sciences · December 2004
DOI: 10.1115/OMAE2003-37074
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Subramaniam Neelamani
Kuwait Institute for Scientific Research
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Note Hydrodynamic studies on vertical seawall
defenced by low-crested breakwater M.G Muni Reddya, S Neelamanib,*
a
Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai-600 036, India
b
Coastal Engineering and Air Pollution Department, Environmental and Urban Development Division,
Kuwait Institute for Scientific Research, P.O Box 24885, 13109 Safat, Kuwait
Received 21 January 2004; accepted 9 July 2004
Abstract
This paper presents results obtained from a series of experiments conducted in wave flume to
assess the influence of the offshore low-crested breakwater as a defence structure in reducing the
wave forces on vertical seawall The main aim of the tests was to know the effect of crest elevation of
the offshore low-crested breakwater as a rehabilitation structure for the existing damaged shore
protection structures In this study five relative breakwater heights are used and associated flow
evolution was analyzed With the sections proposed in this study, it is possible to achieve
considerable reduction of wave force on the seawall Modification factor is proposed to estimate the
shoreward force on the seawall defenced by low-crested breakwater
q2005 Published by Elsevier Ltd
Keywords: Low-crested breakwater; Shoreward force; Overtopping; Submerged breakwaters; Seawall;
Modification factor
1 Introduction
Coastal erosion is one of the challenging coastal engineering problems faced by human
being around the world This calls for the proper remedial measures to protect valuable
properties situated along the coast Many seawalls and vertical caisson breakwaters
(CIRIA, 1986b; Oumeraci, 1994) around the world are being damaged Such failures are
0029-8018/$ - see front matter q 2005 Published by Elsevier Ltd.
doi:10.1016/j.oceaneng.2004.07.008
Ocean Engineering xx (xxxx) 1–18
www.elsevier.com/locate/oceaneng
* Corresponding author Tel.: C965 483 6100x5351; fax: C965 481 5192.
E-mail addresses: reddy_muni@hotmail.com (M.G Muni Reddy), nsubram@kisr.edu.kw (S Neelamani).
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mainly caused by extreme wave actions, through displacement of the entire structure, or
progressive failure starting from locally weak point, or through overall foundation failures,
or through overtopping and toe erosion It may be economical to allow the less frequent
storm wave to spill over the crest of the seawall rather than to its full height to reflect fully
all the waves The disadvantage, however, is that overtopping waves plunge over the crest
and inundates lee side leading to high economical loss
The need for force reduction on these structures to increase the life span has resulted in
different force reduction techniques like, introduction of porosity at the front face of the
caisson, slotted seawalls, construction of horizontally composite caissons and construction
of low-crested caissons etc Introduction of porosity into the structure leads to reduction of
the strength of the structure Construction of horizontally composite structure in dynamic
environment is risky Low-crested breakwater attracts lesser forces but the overtopping of
waves create significant disturbance on the lee side These drawbacks can be overcome by
constructing a low-crested breakwater in front of these structures to reduce the incident
wave energy levels The offshore breakwater can be constructed after installation of
caisson without much risk for floating vessels and caisson For existing weak or damaged
structures construction of a protection structure such as submerged offshore breakwater is
relatively an easy task
Submerged breakwaters with deeper submergence would give larger wave energy
transmission, which might eventually lead to failure in sheltering function of the
breakwaters Therefore how to reduce the incident wave energy levels becomes a great
challenge for coastal engineers In the present study an offshore low-crested rubble mound
breakwater is considered as a defence structure to reduce the incident wave energy levels
that reach the vertical impervious structure viz., seawall/caisson This type of protection
can also be used in situations wherein it is required to reduce the wave forces to enhance
the functional life of protection structures that are damaged by extreme wave forces, as a
rehabilitation structure A theoretical analysis of the present problem is cumbersome Due
to the complexity of the physical processes at the submerged breakwaters, physical
modeling is necessary to define the site-specific interactions between the structure and the
local wave climate The defence structure may become submerged or emerged during the
tidal variation
dynamically stable reef breakwaters, statically stable low-crested breakwaters and
statically stable submerged breakwaters A reef breakwater is low-crested homogenous
pile of stones without a filter layer or core and is allowed to be reshaped by wave attack
(Ahrens, 1987)
Statically stable low-crested breakwaters are close to non-overtopping structures, but
are more stable due to the fact that large part of the wave energy can pass over the
breakwaters and the stability increases remarkably if the crest height decreases
Submerged breakwaters have been widely used as wave energy dissipaters Efficiency
of the submerged breakwaters depends on the crest free board, crest width and permeable
(1968); Dattatri et al (1978); Losada et al (1997), have studied the wave transmission
and reflection characteristics The stability and wave transmission characteristics of
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(1989); van der Meer and Pilarczyk (1990); van der Meer and d’Angremond (1991);
Seabrook and Hall (1998), and Yamashiro et al (2000) and, the design formulae were
investigations Behavior of the deeply submerged breakwaters with multi vertical sliced
Based on the monitoring results of a submerged breakwater and resulted model
wave and current fields depending substantially on the crest elevation relative to the
still water level However, not much study on the present topic except the work by
Gonzleg Madrigal and Olivares Prud’homme (1990) on the reduction of forces on
vertical breakwater defenced by seaward submerged breakwater For partial barrier of
any configuration, irrespective of the porosity and flexibility, full reflection always
occurs when the distance between the end-wall and the barrier is an integer multiple of
Many investigators have studied analytically and numerically the wave transmission
and reflection characteristics of the submerged breakwaters Yet these mathematical
models cannot reproduce some of the features observed such as strong mean water
level gradients on the submerged breakwater, pumping effect of the submerged
breakwater and vertical circulation induced by breaking waves on the submerged
breakwater
2 Experimental procedure and investigation
Experiments have been carried out in a 30 m length 2 m wide and 1.7 m deep
wave flume at Indian Institute of Technology Madras, Chennai, India Seawall was
force balance is flushed with the flume bed The sensitivity of the transducers (strain
gauge type) of six-component force balance at rated loading is about G2 mV/V
Force balance consists of a stainless steel platform 850!850 mm size, below which
Fig 1 Experimental set-up for the present study.
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tightly fixed to the flume sidewalls to arrest the movement of force balance Seawall
model was mounted on top of the steel platform so that the force on the seawall will
be transferred to the transducers The height of the seawall model was fixed based on
the theoretically estimated maximum run-up over the seawall, to ensure no
overtopping of waves Crest width of the offshore low-crested breakwater was chosen
as 0.40 m The stable weight of the armour unit of the breakwater was estimated by
submerged breakwater Here our aim was not the damage of the low-crested
breakwater, so a stable armour weight was used Breakwater was constructed with two
layers, an armour layer and core Weight of the armour stone was 14.70–19.62 kN
one at still water level) were used in this study A stable slope of 2H:1V was adopted
as the effects of breakwater slope on the wave transformation were found to be
water depth h/d is varied from 0.66 to 1.33, keeping the water depth ‘d’ constant at
0.30 m and varying the height of the breakwater, ‘h’ from 0.20 to 0.40 m with 0.05 m
increment This simulates the investigation on site where the tidal fluctuations are
2.1 Data collection and analysis procedure
The wave synthesizer (WS4) involving an application software package, along with
analogue-digital and I/O modules installed in personal computer was employed in the
measurement and analysis The software is capable of controlling the wave paddle and at
the same time acquires data from sensors used in the tests The force balance transducers
are connected to the data acquisition system through carrier frequency amplifiers Each set
of data for regular wave was sampled at frequency of 40 Hz The filtered signals are
analyzed using the wave synthesizer It contains the options for synthesis of regular and
random 2D waves Regular waves of different predetermined wave period and wave
amplitude combinations are generated for the testes The horizontal force (force in the
direction of wave propagation), vertical force on the seawall, run-up on the wall and wave
elevations in front of the model were acquired
2.1.1 Range of inputs
Relative breakwater height, h/d 0.66–1.33
Non-dimensional pool length, L p /L 0.035–0.641
Here L is the deep-water wavelength and H i is the incident wave height.
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2.1.2 Data analysis
The data collected were converted to physical variables by using the corresponding
calibration constants/coefficients The raw data (in the form of time series) were analyzed
in time domain to get the clear understanding of the phenomenon under investigation The
measured wave height, wave periods and forces were obtained by analyzing the measured
time histories of wave surface elevations and force amplitudes using the
threshold-crossing analysis The threshold-threshold-crossing option is a generalization of classical
zero-crossing analysis For a pre-defined reference level, the input time series is divided into
events For each event, the peak–peak value, the minimum and maximum values, and the
duration are determined
The time series of the different parameters stated earlier were viewed to pickup the part
of time series with regular trend by omitting the transient part This also ensures that no
re-reflected waves were present in the selected window of the time series The regular time
series of force was then subjected to threshold-crossing analysis to get the mean amplitude
of the time history The mean of the all amplitudes above the reference level in a time
series is taken as a positive or shoreward force Similarly mean of all the amplitudes below
the reference level on a time series is taken as negative or seaward force The mean
amplitudes of measured hydrodynamic force were obtained using the above procedure for
each test run
absence of the low-crested breakwater to shoreward force in the direction of wave
propagation in the presence of low-crested breakwater ½ Fxseais the ratio of seaward force
in the direction opposite to wave propagation in the absence of the breakwater to the
seaward force in the direction opposite to wave propagation in the presence of the
breakwater These forces are obtained using procedure for the respective case of with and
without low-crested breakwater
Incident wave elevations are measured using DHI capacitance wave gauges in the
absence of model in the flume, for pre-determined sets of different wave period and wave
height combinations This procedure is repeated thrice and the average value is taken for
the wave height for that particular combination It is done with a view to check the
repeatability of wave heights at the same point later when tests are conducted with the
model in position
3 Results and discussion
3.1 General
The non-breaking wave forces on seawalls are pulsating A substantial portion of the
horizontal momentum of the wave is imparted to the wall Methods to calculate the wave
forces for simple vertical structures and pulsating wave conditions are relatively well
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p4Z p1ð1 K hc=hÞ : hOhc
(
(5)
a2Z min ½ðhbKdÞ=3hbðHmax=dÞ2; 2d=Hmax
(6) where Fh, total horizontal force per meter length of the wall/caisson; hb, water depth at a
from 0 to 1.0); b, angle between the direction of wave approach and a line normal to the
pressure exerted; hc, min{h*, hc}; Hmax, maximum or design wave height
p1, p2, p3and p4are the representative wave pressure intensities Pressure coefficient a2
represents the tendency of the pressure to increase with the height of the rubble mound
in the present study Hence the Eqs (1) and (2) can be written as
p1modis less than p1in Eq (2) because of additive term a2cos2b vanishes From Eqs (3)
Fhin Eq (8)
Eq (8) for validation of the present shoreward force measurements The measured
forces are more than the estimated forces Increase of wave pressure/force due to the
presence of a rubble foundation may regarded as the result of the change in the
behavior of wave from non-breaking to breaking although actual waves never exhibit
such marked changes
Most design methods for caisson and the other vertical wall concentrate on forces that
act landward, usually termed as positive forces It has however, been shown that some
breakwaters/walls failed by sliding or rotation seaward indicating that net seaward forces
may indeed be greater than positive forces
The time series of incident wave height and wave force on the wall for different
force on the seawall with increased h/d is very clear The time series of wave forces on
the seawall defenced by an low-crested breakwater show that the wave breaking on the
breakwater generates high frequency waves on the lee side of breakwater, which results
in irregular force time series consisting of superposition of fundamental wave
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frequencies and the higher wave frequencies It would be worth mentioning at this
water level inside the protected area and that of open sea This component is inherent
force measurement, because the force balance measures total effect For laboratory
measurements this effect is unavoidable due to the fact that the water will confine
between the sidewalls of the flume and between two structures and there will be very
little scope for water to escape In the field situations, in open sea this effect will not be
of much significant as there will be sufficient space for water to escape laterally
between the two structures It should be noted that experiments were conducted in the
two-dimensional flume, and thus the values of mean water levels may be overestimated
in comparison with the values of mean water levels in three-dimensional wave field
About 14% deviation observed from the forces estimated by Eq (8) and the forces
measured from the experiments
3.2 Effect of relative height of the breakwater, h/d on the normalized wave
forces on the seawall
Fig 4 provides the effect of h/d on fore ratio ½ Fxshore for different incident wave
steepness Force ratio 1.0 means that the breakwater has no effect on the reduction of
forces on the caisson and zero means 100% protection of the caisson by low-crested
breakwater The value of force ratio lies in-between zero and 1.0 Oscillatory nature of
force ratio ½ Fxshoreis observed when the h/d is varied from 0.66 to 1.33 The amplitude
of the oscillation decreases with increase of h/d The high value of force ratio for
h/dZ0.83 is due to wave jetting on the seawall after overtopping over the low-crested
breakwater This increased force is unwarranted for the general presumption that as the
barrier height increases force will have to decrease correspondingly Designers and
Fig 2 Comparison of non-dimensional shoreward force on vertical seawall with Goda’s (1974) formulae [dZ
0.30 m, H i /dZ0.29K0.48].
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coastal engineers should take care of this while decision making in choosing the range
h/d values For h/dO1.0, the wave energy is effectively dissipated which result in
significant wave force reduction on the seawall When h/dZ1.0, the reduction in
following wave-structure interaction processes were identified during the experimental
Fig 3 Typical force time series for different relative breakwater height h/d [H i Z0.152 m, dZ0.3, d/LZ0.059,
B/dZ1.33, L p /LZ0.071–0.64].
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investigations, which are explained below for the type of normalized wave force trend
observed:
(a) For offshore breakwater with more submergence (say h/dZ0.66), the wave transmit
freely, reflects from the seawall These reflected waves contribute significantly for
the amplification of waves and the corresponding wave forces on the seawall/
caisson
(b) For offshore breakwater with smaller submergence (say h/dZ0.83), the propagating
wave on the breakwater attains the characteristics of wave breaking and the
overtopping jet of mass acts on the seawall/caisson resting behind the breakwater
and imparts higher order of forces
(c) For the case of offshore breakwater with crest level flushing with still water level
(h/dZ1.0), most of the interacting energy is expected to be dissipated on the crest
of the breakwater and hence the wave force reduction is significant
(d) For the offshore breakwater with less emergence i.e crest located just above the
still water level (here h/dZ1.16), the dominant mode of wave transmission is by
run-up and overtopping and the efficiency of transmission process increase as wave
height increases The energy available with this overtopping water mass imparts
forces on the seawall The wave energy dissipation due to the interaction with the
breakwater reduces to the significant overtopping processes
(e) For the offshore breakwater with significant emergence of the crest (h/dZ1.33),
overtopping will be prevented for most of the waves and the waves may be allowed
to transmit through the pores of the breakwater The energy available with this
transmitted wave imparts forces on the rear side structures
ratio variation is oscillatory with increased h/d It was observed that the force ratio at any
Fig 4 Variation of shoreward force ratio with relative reakwater height h/d for three different wave steepness
[L p /LZ0.198, B/dZ1.33, d/LZ0.059].
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