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Ocean Engineering 29 (2002) 151175

Wave interaction with T-type breakwaters

S. Neelamania,*, R. Rajendranb

a Ocean Engineering Centre, Indian Institute of Technology Madras, Chennai 600 036, Indiab Assistant Executive Engineer, Chennai Port Trust, Chennai 600 001, India

Received 15 March 2000; accepted 28 June 2000

Abstract

The wave transmission, reflection and energy dissipation characteristics of partially sub-merged T-type breakwaters (Fig. 1) were studied using physical models. Regular and randomwaves, with wide ranges of wave heights and periods and a constant water depth were used.Five different depths of immersions of the T-type breakwater were selected. The coefficientof transmission,Kt, coefficient reflection,Kr, were obtained from the measurements and thecoefficient of energy loss,Kl is calculated using the law of conservation of energy. It is foundthat the coefficient of transmission generally reduces with increased wave steepness andincreased relative water depth,d/L. This breakwater is found to be effective closer to deep-water conditions.Kt values less than 0.35 is obtained for both normal and high input waveenergy levels, when the horizontal barrier of the T type breakwater is immersed to about 7%of the water depth. This breakwater is also found to be very efficient in dissipating the incidentwave energy to an extent of about 65% (i.e.Kl0.8), especially for high input wave energylevels. The wave climate in front of the breakwater is also measured and studied. 2001Elsevier Science Ltd. All rights reserved.

Keywords: T type breakwater; Wave transmission; Reflection; Energy dissipation; Special breakwater;Wave climate

1. Introduction

Rubble mound structures are widely used around the world for the constructionof breakwaters. Concrete caissons are adopted, when sufficient quantity and goodquality rubbles are not available in the vicinity of the proposed port construction

* Corresponding author. Tel.:+91-44-445-8639; fax:+91-44-235-0509.E-mail address: [email protected] (S. Neelamani).

0029-8018/02/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.PII: S0029 -8018(00 )00060-3

152 S. Neelamani, R. Rajendran / Ocean Engineering 29 (2002) 151175

Fig. 1. Schematic view of the T-type breakwater.

site. Both these types are becoming expensive in increased water depths. In deeperwaters special type of breakwaters, which require less concrete per unit run, but atthe same time are capable of transmitting less wave energy are to be invented. Sincein deeper waters, most of the wave energy is concentrated near the water surface, astructure which can effectively destroy this energy or reflect it is required. Partiallyimmersed horizontal plates were found to be good energy dissipaters due to artificialsimulation of wave breaking on the top of the plates (Patarapanich (1984)). Partiallyimmersed vertical barriers are capable of reflecting the incident wave energy effec-tively in deeper waters (Ursell (1947), Wiegel (1960) and Reddy and Neelamani(1992)). Combining these characteristics of a horizontal and a vertical barrier intoa T -type breakwater is expected to improve the performance as a breakwater dueto the additive properties of wave breaking and reflection. Hence this type of break-water is expected to reduce the energy transmission towards the lee side of the struc-ture. This has motivated the authors to investigate the wave transmission, reflectionand energy dissipation characteristics of the T -type breakwaters. A good breakwatershould transmit the incident wave energy as low as possible and dissipate the energyas high as possible. In the present study, the depth of submergence of the breakwateris varied in order to find out the depth of immersion, at which the wave transmissionis minimum.

T-type breakwaters can be supported on piles and the load from waves can betransferred to the seabed through these piles (Fig. 1). This type of breakwater can

153S. Neelamani, R. Rajendran / Ocean Engineering 29 (2002) 151175

be mass fabricated and assembled on the land, and quickly installed using floatingbarges. This breakwater can be installed as a permanent structure at any desireddepth of submergence of the horizontal part of the barrier, depending upon the hydro-dynamic performance and the aesthetic aspects.

Fig. 2 shows the definition sketch of T-type breakwater. The following processcan dissipate a part of the wave energy available with the incident waves:

1. Vortex shedding at the bottom tip of the vertical barrier of the breakwater dur-ing transmission.

2. Wave breaking over the horizontal barrier of the breakwater, due to sudden changein the depth of wave propagation.

3. Boundary shear friction on the surface of the structure.

The present investigation with a partially submerged T-type breakwater has beencarried out with the following objectives in mind:

1. To investigate experimentally the wave transmission, reflection and energy dissi-pation characteristics of this breakwater for different incident wave characteristicsand for different depth of submergence of these breakwaters due to regular andrandom waves.

2. To investigate the water surface fluctuations in front of these breakwaters fordifferent incident wave characteristics and for different depth of submergence.

3. To compare the hydrodynamic performances due to regular and random waves.

The investigations on the characteristics of wave transmission for a wide rangeof wave conditions and different depth of submergence of the structure is essentialfor design, once the permissible wave transmission for a particular activity at thelee side of the structure is decided. For example, for a given wave condition (saypeak period and significant wave height), if the permissible transmission is 0.5 m,

Fig. 2. Definition sketch.


then it is possible to select the depth of immersion and size of this breakwater toachieve this requirement (see Appendix A, for a worked out example). The studyof energy dissipation character is important to understand the efficiency of the struc-ture as a breakwater. A breakwater can be considered better if the energy dissipationcapability is high. The wave reflection character is necessary to understand the waveclimate at the seaside of the structure, which is essential for the safe navigation ofapproaching vessels.

2. Literature review

Even though no previous study is carried out on T type breakwaters, literatureon some of the special breakwaters more related to the present investigations arereviewed and discussed here. Ursell (1947) has developed a theory for the trans-mission and reflection of gravity water waves in deep water for fixed vertical infi-nitely thin barrier extending from the water surface to some depth below the surface.He has proposed an equation for the coefficient of transmission as a function ofmodified Bessel function. Wiegel (1960) has developed a theory based on the wavepower transmission past a rigid vertical thin barrier, which extends from above thewater surface to some distance below the surface. A satisfactory comparison of thetheory with laboratory measurements were noticed for a limited set of data. A consist-ent trend of decreasing transmission coefficient with increasing wave steepness wasnoticed from the experimental studies, which was attributed due to the excess lossin energy during transmission by separation at the bottom of the barrier.

The model tests of Hattori (1975) comprising a horizontal plate, fixed at the stillwater level (surface plate) and submerged plate fixed at a quarter and at half of thewater depths, exhibited a trend of lower transmission and higher reflection at smallsubmergence depth ratio. These rather limited results led to the conclusion that thesurface plate is more effective than the submerged plate in reducing the wave trans-mission.

Experimental results subsequently by Dattatri et al. (1977) also showed that thewave transmission decreased with decreasing submergence, but reflection wasmaximum at /d=0.07 (where is the depth of submergence of the plate and d isthe water depth) and not when the plate was at the surface. The optimum plate widthfor minimum transmission was found to be 0.30.4 times the incident wave length.

Patarapanich (1984) has analytically studied the wave reflection characteristics ofa submerged horizontal plate. The conditions for maximum and zero reflection wereanalyzed. In the theoretical model, zero energy loss is assumed. It was concludedthat the wave reflection from a submerged horizontal plate depends on the platewidth to wave length ratio, relative depth of immersion and relative water depth. Itwas found that the reflection coefficient generally increases with decreasing relativedepth of immersion and relative water depth. Wave transmission to the lee side wasfound to be the minimum when the plate width is about 0.7 times the wave length.

Patarapanich and Cheong (1989) have investigated experimentally the reflectionand transmission characteristics of a submerged horizontal plate due to regular and


random waves. It was found that the maximum reflection and minimum transmissionof regular waves are achieved, if the plate width to wave length ratio is 0.50.71,when the relative depth of immersion is in the range of 0.05 to 0.15.

Neelamani and Reddy (1992) have experimentally investigated the wave trans-mission and reflection characteristics of rigid surface fixed and submerged horizontalplate. It was found that for a rigid plate, the coefficient of transmission is minimumand coefficient of reflection is maximum, but the maximum value of energy dissi-pation occurs for plates submerged closer to SWL. Reddy and Neelamani (1992)have also experimentally investigated the wave transmission and reflection character-istics of a partially immersed rigid vertical barrier. The results of power transmissiontheory proposed by Wiegel (1960) were compared with the measurements. Thistheory is found to predict satisfactorily the wave transmission for wave steepnessup to 0.05, especially when the depth of immersion of the plate is more than about20% of the water depth.

Abul-Azm (1993) has used the Eigen function expansion method to find the velo-city potential around partially immersed horizontal barriers and other configurations.The reflection and transmission coefficients were obtained from the velocity poten-tial.

A detailed survey of existing literature shows that the experimental and theoreticalstudies pertaining to the performance characteristics of either partially immersedhorizontal plate (or) partially immersed vertical barrier is available. The performanceof a breakwater combining the advantage of horizontal plate and vertical barrier hasnot yet been investigated. Hence combination of these two barriers in the form ofT type barrier is selected for the present investigations.

3. Experimental investigations

The wave transmission, reflection and dissipation characteristics of T type break-water are investigated by using physical models. Different hydrodynamic conditionsand five different depths of submergence of these breakwaters were used. Both reg-ular and random waves are used for the present investigation.

3.1. Model scale

Froude scaling is adopted for physical modelling, which allows for the correctreproduction of gravitational and fluid inertial forces. A scale of 1:25 is chosen forthe selection of model dimension and wave properties in the present study.

Table 1 gives the details of prototype conditions considered and the correspondingmodel dimensions obtained.

The T-type breakwater supported on piles can be used for water depths rangingfrom 10 m to 25 m. However, studies are carried out in the laboratory for a constantwater depth of 0.70 m, which corresponds to 17.5 m water depth in the prototypefor 1:25 scale. Since the results are presented in normalized forms, design curves


Table 1Prototype and model details

Description Unit Prototype Model (1:25)

Water depth (d) m 17.5 0.70Wave period (T) Sec. 5 to 15 1 to 3Wave height (H) m 1.25 to 7.5 0.05 to 0.3Width of breakwater m 25 1.0

can be used for other water depths also. A worked out example provided at the endof this paper gives further informations.

3.2. Model details

The breakwater model was fabricated by using Hylam sheet of thickness 3 mm.The model consists of two portions: (1) horizontal plate; and (2) vertical plate. Thesize of the horizontal plate is 1.95 m1 m and the vertical plate is 1.95 m0.25 m.Slotted angles of size 50 mm50 mm6 mm were braced widthwise and lengthwiseto ensure strength and rigidity. 8 mm G.I. bolts with washers were used to fix theslotted angles and sheets. The model was fixed rigidly in between the side walls bymeans of teak wooden planks/wedges. The flume width is 2.0 m, whereas this modelwidth is 1.95 m. The 5 cm clearance is filled with wooden planks and wedges.

3.3. Hydrodynamic testing facility

3.3.1. Wave flumeThe present experimental investigations were carried out in the 2.0 m wide, 72.5

m long and 2.7 m deep wave flume at Ocean Engineering Centre, IIT Madras, Chen-nai, India. A wave maker is installed at one end of the flume and the other end ofthe flume is provided with an absorber which is a combination of a parabolic perfor-ated sheet and a rubble mound below it to effectively absorb the deep water wavesas well as shallow water waves respectively. In this flume, water depth can be variedfrom 0.50 m to 2.0 m. The details of the flume, position of the model and the wavegauges used to measure the wave elevation in front of the model are shown in Fig.3. The breakwater model was fixed at a distance of 40.5 m from the mean positionof the wave maker.

3.3.2. Flume wave maker and wave generating systemWithin the mechanical, geometric and hydrodynamic limitations, the wave gener-

ating system is capable of generating any kind of two-dimensional regular or randomwaves. The wave maker can operate in two different modes: (a) in piston modemainly for the generation of shallow water waves, and (b) in hinged mode for gener-ating primarily deep water waves. The maximum water depth in the flume mustnever be more than 1.0 m and 2.0 m for the piston mode and hinged mode operations


Fig. 3. Details of flume, position of the model and wave gauges.

respectively. The 2D wave generating system comprises of Wave synthesizer andHost Personal Computer, Wave Controller and Hydraulic Servo Actuator.

3.4. Instrumentation

3.4.1. Wave probesThe wave probe comprises of two thin parallel stainless steel electrodes. When

immersed in water, the electrodes measure the conductivity of the instantaneouswater volume between them. The conductivity changes proportionately to the vari-ation in water surface elevation. A set of compensation electrodes mounted at thebottom end of the wave gauge balance the influence of temperature or salinitychanges of the water.

3.4.2. Calibration of wave probesStatic calibration of the wave probes was carried out every day and at the begin-

ning and at the end of each set of experiments. The calibration constants were foundto repeat with a standard deviation of less than 1%.

3.4.3. Positioning of wave probes for measuring the incident and reflected wavesTo measure the incident and reflected wave heights from the structure, three wave

probes were positioned in front of the structure at 10 m away from the breakwatermodel (Fig. 3). The distance between the wave probes were selected as follows:

The distance between wave probe No.1 and 3 (i.e. l13), according to DHI Manual


(1994) should satisfy the criteria, l13Lmax/20, where Lmax is the maximum wavelength to be generated. For the present work though, the maximum length of wavegenerated is 7.45 m, a wave length of 10.0 m is considered for this calculation togive a leverage for any possible long waves generated in the random waves. Hencel13 is selected as 0.5 m. According to the DHI manual, the distance between waveprobe 2 and 3, l23 is given as 0.1 l13 (or) 0.3 l13. Hence l23=0.15 m is selected.These guidelines are followed in order to avoid singularity in the estimation of inci-dent and reflected wave heights as described by Goda and Suzuki (1976). Fig. 3shows the positions of the three wave probes WP1, WP2, WP3 used to measure thepartial standing waves in front of the structure, from which the incident wave height(Hi) and reflected wave height (Hr) are estimated.

3.4.4. Transmitted wave heightTo measure the transmitted wave height, a wave probe (WP5) was fixed 7 m away

from the breakwater model at its lee side, which is approximately one wave lengthof the longest wave studied.

3.4.5. Water surface fluctuations at the leading edge of the modelTo measure the water surface fluctuation at the leading edge of the model, a wave

probe WP4 is fixed just in front of the structure (Fig. 3).

3.4.6. Data acquisitionTotally, 5 channels were employed for data collection. A 12 bit A/D converter

has been used for converting analogue signals to digital data. The data of the wavetime series were collected by the same computer, which was used for generatingwaves.

3.4.7. Regular wavesData for each run was acquired for a total duration of 30 s at a sampling frequency

of 20 Hz. Waves were generated for a total duration of 60 s. Depending upon theperiod of wave generated, data collection was commenced 3065 s after starting thewave generation. This is to make sure that the data collection was started only afterrepeatability of the same wave heights at the model location has established. Thestarting time for data collection was set based on trial runs with different periodsof waves.

The data collection duration is set at 30 s, based on the following criteria:

1. The regular wave time series should have at least 10 wave cycles.2. The data collection must be completed before any reflected waves, either from the

wave maker or from the beach affects the measurements around the test section.

3.4.8. Random wavesRandom waves were generated for a total period of 120 s. Theoretical Pierson

Moskowitz spectra of different peak periods and significant wave heights were selec-


ted for random wave generation. The details of starting time for data acquisition,duration of data collection and running time of wave maker are given in Table 2.A total of 2100 data points for each channel is collected and the first 2048 datapoints are used for the FFT analysis. As soon as the run was completed, real timeseries (which is the time series in volts multiplied by the appropriate calibrationconstants) were viewed on the monitor as a preliminary check on the quality of thedata collected. The data was stored for further analysis.

3.5. Experimental procedure

3.5.1. GeneralThe investigations were carried out for 5 different depths of immersion, : =0.0

m, 0.05 m, 0.10 m, 0.15 m and 0.20 m. =0.0 corresponds to the case whenthe horizontal barrier of the breakwater is kept at SWL. For all the other cases, thehorizontal barrier of the T type breakwater is submerged. The breakwater modelwas subjected to the action of regular waves of heights ranging from 0.05 m to 0.30m with intervals of 0.05 m. Wave periods ranging from 1.0 s to 3.0 s with intervalsof 0.5 s is used. For 1.0 s wave period, wave heights up to 0.15 m only was generated.Wave heights more than this was found breaking at the generation point itself. Forwave period of 3.0 s, it was difficult to generate higher heights, due to large displace-ment of the paddle. The selected wave height and period combinations were repeatedfor different depth of immersion of the breakwater, for a constant water depth of0.7 m. For random waves, significant wave height (Hs) from 0.05 m to 0.15 m andpeak period (Tp) of 1.0, 2.0 and 3.0 s were selected.

3.5.2. Non-dimensional parametersThe details of the various non-dimensional parameters obtained in the present

study are:

Regular waves

1. Range of incident wave steepness, Hi/L = 0.004 to 0.1332. Range of relative water depth, d/L = 0.094 to 0.4523. Range of relative depth of Immersion, /d = 0 to 0.2864. Range of relative wave height, Hi/d = 0.037 to 0.527

Table 2Data acquisition details for random waves

Peak period Tp (s) Starting time for data Duration of data Runtime of the waveacquisition (s) acquisition (s) maker (s)

1.0 50 105 1202.0 40 105 1203.0 30 105 120


For the calculation of Hi/L and Hi/d, the actually measured Hi was used.

Random waves

1. Range of incident wave steepness, (Hi)s/L = 0.006 to 0.048.2. Range of relative water depth, d/Lp = 0.094 to 0.4523. Range of relative depth of immersion, /d =0 to 0.2864. Range of relative wave Height, (Hi)s/d =0.054 to 0.206.

For the calculation of (Hi)s/L and (Hi)s/d, the actually measured (Hi)s, valueswere used.

3.6. Data analysis

3.6.1. Analysis of time series of WP1, WP2 and WP3 for incident and reflectedwaves

Frequency domain analysis using the DHI software package was used to carryoutthe reflection analysis. The response of the three wave probes installed in front ofthe model and the distance between the probes were the input for this package. TheDHI software separates the incident and reflected wave components from therecorded response of these three wave probes. The reflection analysis gives incidentsignificant wave height (Hi) and average reflection coefficient (Kr) based on the spec-tral analysis. The average reflection coefficient is the ratio of reflected and incidentwave height, (i.e.) Kr=Hr/Hi. Hence the significant reflected wave height is computedusing the relationship Hr=Kr*Hi.

3.6.2. Analysis of time series of WP4 and WP5Frequency domain analysis is carried out on the transmitted wave history. The

significant transmitted wave height is obtained from the zeroth moment of the trans-mission spectrum, m0t by using the equation Ht=4.0(m0t)0.5. A similar procedure isadopted for the analysis of the water surface fluctuations in front of the structure.

Zero down crossing analysis of the time series WP4 (Water surface fluctuationsin front of the breakwater) is also carried out and Hmin, H, and Hmax is obtained,where Hmin is the minimum, Hmax is the maximum and Hmean is the average waveheights respectively of the wave probe 4. Similar analysis is also carried out on thetransmitted waves.

3.7. Estimation of coefficient of energy loss, Kl

Law of conservation of energy is used for the estimation of coefficient of energyloss, Kl, since it is not possible to measure it. A breakwater is said to be better ifit dissipates most of the incident wave energy. From Law of conservation of energy

K 2t K 2r K 211 (1)


K11K 2tK 2r (2)

This formula is used to estimate Kl values where Kt is the coefficient of trans-mission; Kr is the coefficient of reflection and Kl is the coefficient of dissipation.

3.8. Uncertainity analysis

12 bit A/D conversion card is used in the present measurement. The voltage rangeis 10 V. Calibration was carried out with an increment of 5 cm. An analysis onthe measurements shows that the uncertainty in the measurement of wave heightis 2%.

4. Results and discussions

4.1. General

The interaction of regular and random waves on T type breakwaters are discussedby using the Kt, Kr, and Kl values. Under regular wave interaction, the effect of wavesteepness, Hi/L, relative water depth, d/L and relative depth of immersion /d onKt, Kr and Kl are discussed. The importance of Hi/L, d/L and /d for the design ofT type breakwater is as follows:

1. Investigating the effect of wave steepness, Hi/L on Kt, Kr and Kl is necessary tounderstand the performance of the breakwater for normal and extreme waveactions.

2. The effect of relative water depth, d/L on Kt, Kr and Kl is essential to understandthe hydrodynamic characteristics of the present breakwater for coastal and deepwater regions.

3. Investigation on the effect of relative depth of immersion, /d on Kt, Kr and Klis required to select the appropriate structure configuration (depth of immersion)as required from the hydrodynamic performance and aesthetic point of view.

For random waves, the effect of /d is investigated. Then, the wave climate infront of the T -type breakwater is discussed. Here again for the case of regularwaves, the effect of Hi/L, d/L and /d on the wave climate at the leading edge ofthe breakwater is discussed. For the case of random waves, the influence of /d onHmean/(Hi)s and Hmax/(Hi)s is investigated.

4.2. Transmission, reflection and dissipation due to regular waves

The experimental investigation with regular waves is essential for basic under-standing of the wave-structure interaction problem.


4.2.1. Effect of wave steepness, Hi/L on Kt, Kr and KlThe effect of wave steepness on Kt, Kr and Kl for three different d/L values

(d/L=0.115, 0.152 and 0.224) for the case of zero immersion of the horizontal barrierof the T type breakwater is provided in Fig. 4. In general, the increase in wavesteepness does not change the Kt values for this case, whereas the reflection coef-ficient reduces significantly and the energy loss coefficient increases considerably.Prominent wave breaking on the horizontal barrier was observed during the experi-mental investigation, when the wave steepness was increased from 0.015 to 0.12.This is the reason for increased energy dissipation when Hi/L is increased. Increasedenergy dissipation has resulted in less reflection of energy as depicted in this plot.The average Kt value of 0.3 and 0.46 is achieved for d/L=0.224 and 0.152 respect-ively. For example, if the incident wave height is 1.0 m, then the transmitted waveheight is 0.3 m and 0.46 m respectively for these d/L values. In terms of energy,the transmitted wave energy is only (0.3)2 and (0.46)2 times the incident wave energy.

The effect of wave steepness, for similar d/L values (including d/L=0.452), forthe case of /d=0.286 is provided in Fig. 5. In general, the Kt value reduces withincreased Hi/L for d/L=0.452, 0.224 and 0.152. For these relative water depths, theKl value is also found to increase with increased wave steepness. The wave steepnessseems to have insignificant influence on wave reflection. For a low wave steepness

Fig. 4. Effect of wave steepness on Kt, Kr and Kl.


Fig. 5. Effect of wave steepness on Kt, Kr and Kl (regular waves).

of 0.02 and for d/L=0.224, the average measured Kt value is about 0.57. For thesame d/L value, for wave steepness of 0.117 (waves closer to breaking) the Kt valueis only 0.34. This is considered as a beneficial character of this breakwater. This isdue to significant energy dissipation by wave breaking on the horizontal barrier ofthe breakwater for higher wave steepness.

4.2.2. Effect of relative water depth, d/L on Kt, Kr and KlThe effect of relative water depth on Kt, Kr and Kl for normal wave climate

(Hi/d=0.087 to 0.089) and a hostile wave climate (Hi/d=0.467 to 0.523), when thehorizontal barrier of the T type breakwater kept at SWL is provided in Fig. 6. Ingeneral, increase of d/L has resulted in the reduction of Kt values. This is due to thefact that when d/L is smaller (approaching to shallow water conditions), the waveenergy distribution from SWL to seabed level is almost of the same order. Hencethe total energy available below the bottom of the vertical barrier is significant. Thisenergy is used for transmission below the barrier. Whereas, for higher d/L values(closer to deeper water condition), the wave energy is maximum closer to SWLand reduces significantly towards the seabed. Hence the total energy available fortransmission is less compared to the case for lower d/L values. It is also noticedfrom this plot that the Kt value at any d/L is higher for higher input energy level.


Fig. 6. Effect of relative water depth on Kt, Kr and Kl (regular waves).

This confirms that the T type breakwater dissipates more energy, when the incidentwave energy is increased.

Similar plot for /d=0.071 is given in Fig. 7. For higher energy level (Hi/d=0.467to 0.526), the Kt value is found to be reduced with increase in d/L, whereas for thelower energy level (Hi/d=0.087 to 0.099), there is no reduction in the Kt value withincreasing d/L value. Energy dissipation coefficient increases with increased d/L,which is due to the fact that near to deep waters, most of the wave energy availablecloser to SWL interacts with the breakwater. Especially, steep waves were observedbreaking on the horizontal barrier of the T -type breakwater better than the mildwaves. Overall, when relative water depth is increased, both Kt and Kr values reduce,whereas, Kl value increases predominantly. That shows that T type breakwater ismore effective for regions closer to deep water conditions.

4.2.3. Effect of relative depth of immersion, /d on Kt, Kr and KlFig. 8 is provided to show the effect of /d on Kt, Kr and Kl for two different

relative water depths (d/L=0.115 and 0.452). This plot is for normal wave conditions(Hi/d=0.084 to 0.099). It is found that the transmission is minimum, when the hori-zontal barrier of the T type breakwater is closer to the SWL, especially ford/L=0.452. Increase of immersion of the barrier generally has resulted in the increase


Fig. 7. Effect of relative water depth on Kt, Kr and Kl (regular waves).

of Kt values. For d/L=0.452, transmission coefficient has increased from 0.15 to 0.55,when the barrier submergence is increased from 0.0% to about 28% of the waterdepth. Whereas the Kr value is found to be high, when the horizontal barrier ofthe T type breakwater is at SWL. Patarapanich and Cheong (1989) found similarobservations by conducting the experimental study on submerged horizontal platealone due to regular and random waves. This trend is due to the fact that the T -type breakwater reflects much of the wave energy concentrated near SWL and allowsvery little energy to transmit, when /d=0.0. It can be seen that transmission of theorder of 0.15 to 0.2 can be obtained by keeping the horizontal barrier of the break-water closer to SWL. It is also found that the Kl value does not show any significantvariation, when the /d is changed from 0.0 to 0.28. On an average, the Kl valueis about 0.55 for d/L of 0.115 and is about 0.70 for d/L=0.452. It means that Ttype breakwater dissipates about 50% of the incident wave energy during normalwave action near deep water conditions.

Similar plot for higher energy level (Hi/d=0.210 to 0.526) for different d/L valuesare provided in Fig. 9. In this figure, the Kt, Kr and Kl values vary significantly withincreased /d for d/L=0.452. For other d/L values (d/L=0.115, 0.152 and 0.224), thevariation of Kt, Kr and Kl values with increased /d is insignificant. On an average,the Kt value is 0.35, 0.45 and 0.60 for d/L of 0.224, 0.152 and 0.115 respectively.It can be imagined that when the T -type breakwater is closer to SWL, it is expectedto attract significant wave forces compared to the one which is more submerged.From this point of view and from the character of Kt for different /d, it is rec-


Fig. 8. Effect of relative depth of immersion on Kt, Kr and Kl (regular waves).


Fig. 9. Effect of relative depth of immersion on Kt, Kr and Kl (regular waves).

ommended to select /d of about 0.20 to 0.30, if the wave climate in the siteis more energetic, like a cyclone prone area. If the wave climate is normal (sayHi/d=0.1), then T -type breakwater with /d=0.0 to 0.10 can be recommended.

In conclusion, the performance of the T -type breakwater is better, when thehorizontal plate is kept closer to SWL for normal wave activities. The transmissioncoefficient is almost independent of /d (except closer to deep water conditions),for higher incident wave energy levels. Hence it is recommended to select the con-figuration of T -type breakwater, such that the horizontal plate is closer to SWL,for sites which are free from cyclone activities. This will facilitate lesser force onthe breakwater. For sites where cyclone waves are significant the T -type breakwaterwith /d of about 0.20 to 0.30 is recommended. This will facilitate less waveloads on the structures compared to the one which is placed closer to SWL, and henceless bending moment at the mud level of the pile. It is recommended to investigateon wave forces and moments on the T-type breakwater in order to complimentthese conclusions.


4.3. Transmission, reflection and dissipation due to random waves

4.3.1. Effect of relative depth of immersion, /d on Kt, Kr and KlFig. 10 describes the effect of /d on Kt, Kr and Kl for three different d/Lp

(d/Lp=0.094, 0.152 and 0.452) and for lower incident energy level ((Hi)s/d=0.054 to0.074). It is seen that for higher d/Lp (i.e. d/Lp=0.452), the Kt value increases andKr value reduces with increased immersion of the structure. Hence for this d/Lp value,T type breakwater with /d=0 is found to be more efficient, when the mild waveclimate predominates the field. For other d/Lp values, minimum Kt value is about0.35, which occurs when /d=0.071. The Kl values range from 0.65 to 0.85. Thisindicates that the T -type breakwater is more efficient in dissipating random waveenergy. Overall for the lower energy level, it is recommended to place the T -typebreakwater with /d=0.071 in order to obtain Kt less than 0.35, for d/Lp from 0.094to 0.452.

Similar plot for higher energy level ((Hi)s/d of 0.100 to 0.206) for d/Lp of 0.094,0.152 and 0.452 is provided in Fig. 11. It is observed that the maximum value ofKt is only 0.55 and minimum is about 0.30. Similarly the maximum value of Kr is0.60 and the minimum is only 0.30. It is interesting to see that the Kl value ranges

Fig. 10. Effect of relative depth of immersion on Kt, Kr and Kl (random waves).


Fig. 11. Effect of relative depth of immersion on Kt, Kr and Kl (random waves).

from 0.78 to 0.83. It means that T -type breakwater dissipates about 65% of theenergy in random waves. Here again for /d=0.071 to 0.142, the Kt value isonly about 0.35.

4.4. Comparison of Kt, Kr and Kl due to regular and random waves

The comparison of regular and random wave interaction on T -type breakwatercan be carried out by using Figs. 8 and 9 which pertains to regular waves and Figs.10 and 11, which is for random waves. The following are the important points:

1. The trend of Kt, Kr and Kl with increased /d is similar for both regular andrandom wave interaction.

2. For the case of regular waves, the maximum Kt is about 0.65, whereas, for thecase of random waves, it is only 0.52.

3. The range of Kr value for the case of regular wave is from 0.65 to 0.95, whereas,it is from 0.28 to 0.58 only for the case of random waves.

4. The Kl value for the case of regular waves ranges from 0.30 to 0.85, whereas forthe random waves the range is very narrow (0.70 to 0.85).

5. Overall, the T -type breakwater performs better (by reducing the wave trans-


mission and reflection and increasing the dissipation) when it is interacted withrandom waves, than with regular waves.

4.5. Wave climate in front of the T-type breakwater due to regular waves

The effect of /d on Hmean/Hi for two different d/L values (d/L=0.452 and 0.094)and for two different Hi/d values (Hi/d=0.037 to 0.091 and 0.146 to 0.276) is givenin Fig. 12. It is seen that increase in /d reduces the Hmean/Hi value significantly forboth the energy levels, when d/L=0.452. The maximum value of Hmean/Hi is about1.06 for this d/L value, which occurs for /d=0.0. For the case of d/L=0.094, themaximum value of Hmean/Hi is about 2.18 and it occurs when /d=0. However, withthe increased /d, Hmean/Hi reduces up to /d=0.142 and increases thereafter.

4.6. Wave climate in front of the T-type breakwater due to random waves

Here the effect of /d on Hmax/(Hi)s and Hmean/(Hi)s are discussed. Hmax and Hmeanare the maximum and mean wave height of the random wave time series measuredat the leading edge of the T -type breakwater. Fig. 13 provides the effect of /don Hmax/(Hi)s and Hmean/(Hi)s for two different d/Lp (d/Lp=0.094 and 0.452) and fortwo different input energy levels ((Hi)s/d=0.054 to 0.069 and 0.100 to 0.206). Forlower input energy level, the maximum value of Hmax/(Hi)s is 2.36, which occursfor d/Lp of 0.452, when /d=0. The corresponding Hmean/(Hi)s is only 0.93. A closeobservation of this plot shows that Hmean/(Hi)s appears independent of d/Lp, whereasd/Lp has significant influence on Hmax/(Hi)s. The range of Hmax/(Hi)s is 1.14 to 2.35.But the range of Hmean/(Hi)s is only 0.56 to 0.93. In general, increase in the /dvalue results in the reduction of Hmax/(Hi)s and Hmean/(Hi)s.

4.7. The wave climate in front of the structure comparison of regular andrandom wave results

A critical comparison of Figs. 12 and 13 provides the following information:

1. In regular waves, Hmean/Hi value is higher for the case of smaller d/L of 0.094,whereas in the case of random waves Hmax/Hi is higher for higher d/Lp of 0.452.

2. For both regular and random waves, maximum value of Hmean/Hi and Hmax/(Hi)soccurs when /d=0. With the increased /d, the wave height ratio reduces signifi-cantly.

5. Conclusions

The hydrodynamic characteristics, such as the wave transmission, reflection,energy dissipation and water surface fluctuations at the leading edge of T -type


Fig. 12. Effect of relative depth of immersion on Hmean/Hi (regular waves).


Fig. 13. Effect of relative depth of immersion on Hmax/(Hi)s and Hmean/(Hi)s (random waves).


breakwaters are assessed based on physical model studies. Regular and randomwaves of different combinations of wave heights and periods are used. A constantwater depth of 0.7 m is selected. Five different depths of immersions of the break-waters were selected. The effects of incident wave steepness, relative water depthand relative depth of immersion on the hydrodynamic parameters were investigated.The salient conclusions of this study are as follows:

5.1. Transmission, reflection and energy dissipation characteristics

5.1.1. Regular waves1. The coefficient of transmission generally reduces and coefficient of energy dissi-

pation generally increases with increased wave steepness.2. The coefficient of transmission reduces with increased d/L values and confirms

that the T -type breakwater is effective closer to deep water conditions.3. For higher input energy level, the Kr value reduces and Kl value increases with

increase in d/L, values. For normal input energy level, T -type breakwater isefficient in reducing the wave transmission when /d=0, especially closer to deepwater conditions. The breakwaters efficiency in reducing the Kt value does notchange much for different /d values, when the incident wave climate is hostile.Hence T -type barrier with /d=0.20 to 0.30 is recommended, if the proposedsite is hostile.

5.1.2. Random waves1. Kt less than 0.35 can be achieved for both normal or higher wave energy level

if /d=0.071.2. T -type breakwater with /d=0.0 is very effective (Kt0.2) for conditions closer

to deep water (d/Lp=0.452).3. T -type breakwater is efficient to dissipate the random wave energy to the order

of 65% (i.e. Kl0.8), especially when the input wave energy is high.

5.1.3. Comparison of regular and random wavesA comparison of the ranges of Kt, Kr and Kl values (for the range of wave steep-

ness, relative water depth and relative depth of immersion as studied in the presentcase) for regular and random waves are as shown in Table 3.

Table 3

Coefficient Regular waves Random waves

Kt 0.15 to 0.67 0.15 to 0.55Kr 0.65 to 0.95 0.28 to 0.58Kl 0.30 to 0.85 0.75 to 0.85


Overall the performance of T type breakwater is better due to random waveinteraction, compared to regular wave interaction with the breakwater.

5.2. Wave climate in front of the breakwater

For regular waves the maximum wave height in front of the structure can go upto 2.2 times that of incident wave height. For random waves, the maximum waveheight can be as high as 2.4 times the significant input wave height. These maximumwave heights are at the leading and occur when the horizontal barrier of the Tbreakwater is at SWL.

Appendix A. Sample design calculation to illustrate the use of the presentstudy

A.1. Given

Design water depth, d =9.0 mDesign peak wave period, Tp =8.0 sSignificant incident wave height, (Hi)s =1.0 m

A.2. Find

The immersion depth of T type breakwaters, if Kt0.40.

A.3. Solution

Lo = 1.56Tp2 = 1.5682 = 99.84 md/Lo = 9.0/99.84 = 0.09014d/Lp = 0.1323(Hi)s/d = 1/9 = 0.111

For this d/Lp, and (Hi)s/d, use the design curve Fig. 11. This curve is for(Hi)s/d=0.1000.206. Since d/Lp available only for three different d/Lp values(d/Lp=0.452, 0.152 and 0.094) proper interpolation is needed. Interpolations of Ktvalue between d/Lp of 0.094 and 0.152 shows that /d of 0.0, 0.071, 0.142 and0.214 values for the breakwater, if adopted will provide Kt0.40.

The corresponding values are 0.0, 0.64, 1.28 and 1.93 m. Out of thesefour immersion values, it is sufficient to select =1.93 m to obtain the transmittedwave height of 0.40 m or less. The width of the horizontal barrier will be 13.0 m(since the model scale is about 1:13) and depth of the horizontal barrier is 3.25 m.

For the same peak period of 8.0 s and significant wave height of 1.0 m, if thewater depth is 18.0 m, then to obtain wave transmission of 0.4 or less, the designshows that the depth of submergence can be anywhere from 0.0 to 2.56 m. The


width of the horizontal barrier is worked out as 26 m (since the model scale is 1:26)and the vertical barrier height is 6.5 m. Depth of submergence of 2.56 m will bebetter due to the reduction of supporting pile height.

References

Abul-Azm, A.G., 1993. Wave diffraction through submerged breakwaters. Journal of Waterway, Port,Coastal and Ocean Engineering 119 (Part 6), 587605.

Dattatri, J., Shankar, N.J., Raman, H., 1977. Laboratory investigations of submerged platform breakwaters.In: Proceedings of the 17th Congress of the IAHR, Baden Baden, Germany 4, 8996.

DHI Manual, 1994. Flume Wavemaker User manual, vol. I to IV, Ocean Engineering Centre, IIT, Madras.Goda, Y., Suzuki, Y., 1976, Estimation of incident and reflected waves in random wave experiments, In:

Proceedings of the 15th Coastal Engineering Conference, Hawaii, 828-845.Hattori, M., 1975. Wave transmission from horizontal perforated plates. In: Proceedings of the 22nd

conference on Coastal Engineering, Japan, pp. 513-517.Patarapanich, M., 1984. Maximum and zero reflection from submerged plate journal of the waterways.

Harbors and Coastal Engineering Division 110 (2), 175181.Patarapanich, M., Cheong, H.F., 1989. Reflection and transmission characteristics of regular and random

waves from a submerged horizontal plate. Journal of Coastal Engineering XIII, 161182.Reddy, M.S., Neelamani, S., 1992. Wave transmission and reflection characteristics of partially immersed

rigid vertical barrier. Ocean Engineering 19 (3), 313325.Neelamani, S., Reddy, M.S., 1992. Wave transmission and reflection characteristics of a Rigid surface

and submerged Horizontal plate. Ocean Engineering 19 (4), 327341.Ursell, F., 1947. The effect of a fixed barrier on surface waves in deep water. Proceedings of Cambridge

phi. society 41 (part 3), 231236.Wiegel, R.L., 1960. Transmission of waves past a rigid vertical thin barrier. Journal of Waterways and

Harbors Division, ASCE 86, 112.

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