Experimental study on the performance characteristics of porous perpendicular pipe breakwaters

Ocean Engineering 50 (2012) 53–62

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Ocean Engineering

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Experimental study on the performance characteristics of porousperpendicular pipe breakwaters

Ruey-Syan Shih

Department of Construction Technology, Tungnan University, New Taipei City, Taiwan

a r t i c l e i n f o

Article history:

Received 13 August 2011

Accepted 12 May 2012

Editor-in-Chief: A.I. IncecikThis article addresses highly-pervious dense pipe with small apertures, which can be beneficial for

convection and interchange of sea water within the harbor district, and furthermore, perform
Available online 4 June 2012
Keywords:

Porous

Pipe breakwater

Wave transmission

Energy dissipation

18/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.oceaneng.2012.05.010

ail address: [email protected]

a b s t r a c t

Several investigations of the physical properties of wave–structure interactions and absorption of

structures in coastal areas discussed the development of several permeable and porous breakwaters.

effectively in wave absorption. This study investigates the dissipation of porous perpendicular pipe

breakwaters, and presents laboratory investigations of wave transmission from permeable pipe

breakwaters with different wave conditions and various combinations of diameter and tube length.

Since wave energy is mainly dissipated due to drag and interception of the resultant motion by the pipe

breakwaters, the reflectivity of such effects is discussed by the evaluation of partly reflected and

transmitted ratio. Consequently, the performance of the pipe breakwater for predicting the wave

transmission coefficient is investigated. Experimental results reveal that dissipation and/or reflection is

more effective when decreasing pipe diameter than increasing pipe length, specifically when

dimensionless frequency s2h/g41.5. Nevertheless, the effect is relatively inconspicuous when s2h/

go0.75. A partial outcome demonstrates the influence of pipe diameter and variations of reflection

coefficients corresponding with dimensionless frequencies for incident waves with various wave

heights.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Investigations of the physical properties of wave–structureinteractions and the absorption of structures in the vicinity ofcoastal area have been a topic of great interest for shore protec-tion in coastal engineering practice over the past few decades. Theobjective may be attained by either reflecting or dissipatingapproaching wave energy by induced turbulent motions.

In nearshore regions, the sea wall, jetty and detached breakwatersare traditionally adopted as absorbing facilities to eliminate waveenergies. Coastal jetty and detached breakwaters were progressivelyconstructed for coastal protection. Formerly, armor units were piledoutside the protecting embankment for efficient absorptions. Yetthey destroyed the landscape and ecological environment. Ecologicalengineering methods attempt many substitutes to preserve thenatural landscape and enforce so-called ‘‘amenity-oriented policy,’’modifications such as submerged breakwaters, artificial submergedreefs, artificial beaches, amenity oriented sea dike, etc., can now befound by the seashore. Submerged breakers may not only decreasedamage to the landscape, but also force waves to break either aboveor behind the obstacles. In some cases, permeable timber-plank

ll rights reserved.

barriers are preferred; predictions of wave interactions with perme-able barriers are of interest.

Issacon et al. (1998) discussed the effects of porosity, relativewave length, wave steepness and irregular waves at length, basedon an eigenfunction expansion method, to adequately account forthe energy dissipation of a vertical slotted barrier. Further, theypredict energy dissipation and wave interactions within a pair ofthin slotted vertical barriers (Issacon et al., 1999), showing thatboth the transmission coefficient and the maximum horizontalforce on the upwave barrier are much lower for a double barrier.The numerical model was verified by laboratory tests.

Investigating and designing floating breakwaters were also of greatinterest, because of the advantages of construction time, environ-mental friendliness, freedom from silting and scouring, economy inregions with comparatively lower capital expenditure, and applicabil-ity in temporary protection for deeper offshore areas.

Homma et al. (1964) and Yamamoto (1981) showed that theresponse of elastically-moored floating breakwaters and floating-pipe breakwaters from random wave test was essentially thesame as from periodical wave tests. In contrast, Ouellet and Morin(1975) reported that the response was completely different.

According to the investigation of Koftis and Prinos (2005) onthe hydrodynamic efficiency of three types of floating break-waters (a box type, a catamaran and a trapezoid type), theperformance of the breakwaters correlates with wave-structure

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Nomenclature

ai Incident amplitudear Reflected amplitudeD Diameter of pipesD/h Relative pipe diameterEi Energy of incident wavesEr Energy of reflected wavesf Wave frequencyg Gravitational accelerationh Water depthHi Incident wave heightHr Reflected wave heightHt Transmitted wave heightHi/h Relative wave height

k Wave numberKr Coefficient of reflectionKt Coefficient of transmissionKL Coefficient of dissipationL Wave lengthSi(f) Frequency spectrum of incident wavesSr(f) Frequency spectrum of reflected wavesT Wave periodw Length of pipe (Breakwater’s width)w/h Relative pipe lengthw/L Relative ratio of breakwater width to wave lengths2h/g Dimensionless frequencys Angular frequencyy Phase angleDl Spacing between two probes

R.-S. Shih / Ocean Engineering 50 (2012) 53–6254

hydrodynamics. Particularly important is velocity at the edges ofthe structure, associated turbulence and the wave run-up andrun-down on seaward inclined face.

Laju et al. (2005) investigated the transmission and reflectionof pile-supported skirt breakwaters both numerically and experi-mentally, proposing that the transmission of waves may dependon maximum submergence of both the front and rear skirt.Reflection depends on the front skirt.

However, instead of considering geometrical configuration ofwave attenuation, force in floating moorings is also observed.A great variety of floating breakwaters, such as anchored porousbreakwaters, have been devised to achieve optimum design toattenuate wave energy and lessen force in the moorings. Diffrac-tion of waves by porous breakwaters has been studied numeri-cally by Yu (1995). This research was based on linear potentialwave theory and derived the porous boundary condition to solvea vertically two-dimensional problem. It tried to solve wavediffraction by a semi-infinite porous wall using the boundary-layer theory.

Hegde et al. (2008) studied forces in the moorings of horizon-tally interlaced, multilayered, moored floating pipe breakwaters,using breakwater models with three layers subjected to variedwave steepness, relative width and relative spacing. Their researchreveals that force increases in the seaward side mooring as wavesteepness increases and relative width w/L41.3. Force decreasesas relative width increases when w/Lo1.3 (where w represents thewidth of the breakwaters and L, the wave length, respectively).Study of wave attenuation of such breakwaters (Hegde et al., 2011)showed that performance is better for a breakwater configurationof w/Lo0.7. Based on wave attenuation and mooring forcedebasement, Wang and Sun (2010a,b) studied experimentally theinfluence of an innovative floating breakwater using a largenumber of diamond-shaped blocks to find out the favorablecharacteristics of geometrical configurations. The results revealfavorable performance.

Mandal et al. (2009) examined a support-vector regressionmodel in estimating transmitted waves of floating breakwaters.They point out that wave steepness and wave length are influen-tial variables for correlation results. As none of the presentmethods can easily predict wave transmission through floatingbreakwaters, Patil et al. (2011) used an ‘‘Adaptive Neuro-FuzzyInference System’’ (ANFIS) to determine wave transmission ofhorizontally interlaced multilayer moored floating pipe break-water (HIMMFPB). This system provides a fast and reliableprediction of the wave transmission, and the ANFIS is trainedbased on data obtained from experimental tests in a physicalwave flume. Many other experimental and theoretical studies

were carried out determining the characteristics and efficiency ofexperiment facilities and theoretical models (reviewed by Ragehand Koraim, 2010).

As mentioned earlier, the large oscillatory force in the mooringsystems is one of the main problems with floating breakwaters.It is practical to consider freely floating and/or porous structureswith very soft moorings to overcome these difficulties. Stiassnieand Drimer (2003) derived a solution of the flow field obtained bythe interaction of a linear shallow water wave with a freelyfloating porous box, a relatively small drift forces was obtainedwhich indicates the advantages in future-use of porous structures,and the suitability of freely floating porous structures whichabsorb part of the wave energy was examined. Ren and Wang(1994) investigated the behavior of a flexible, porous, floatingbreakwater anchored to the sea bed, and indicated that thetransmission coefficient increases as porous effect increaseswhereas the reflection coefficient decreases for any finite rigiditybreakwaters, and the hydrodynamic force on the breakwaterincreases as structural rigidity increases, but decreases as porosityincreases. Liu et al. (2007) discussed over the wave interaction ofa perforated wall breakwater consists a solid back wall andsubmerged horizontal porous plate, their results showed thatthe reflection coefficient is rather small if the relative waveabsorbing chamber width exceeds a certain small value, and theforce on the horizontal plate decrease significantly with theincreasing of the plate porosity. Wang and Sun (2010a,b) presentsa porous floating breakwater with large numbers of diamond-shaped blocks to reduce transmitted wave height and the moor-ing force. The experimental results show that the proposedfloating breakwater is capable in reducing incident wave heightby dissipating wave energy more than reflecting it.

The present study carries out an experimental test of aparticular type of pipe breakwater in the irregular wave flume,intended for higher wave attenuation and less force persecutionfrom the waves. The surface of the protecting embankments isstuffed with PVC (Polyvinyl Chloride) pipes for high porosity andpermeability by decreasing the reflecting area, whereas waveenergy is dissipated by destroying customary particle trajectoryand the flow of water through the hole. Pipe breakwaters mainlydissipate wave energy, and partly reflect and transmit.

2. Experimental setup

Physical experimental testing was conducted in a 16 m waveflume at the Fluid Mechanics Lab of Tungnan University (Fig. 1).The flume had tempered glass on one side to facilitate observation.

Fig. 1. Physical experimental setup.

R.-S. Shih / Ocean Engineering 50 (2012) 53–62 55

The channel was 0.8 m wide and 0.6 m high and constant waterdepth h was 25 cm. A piston type wave generator was located atone end of the flume; the other end had an absorbing 1:2.5 slopewith four pieces of porous thin steel plates. The Wave GeneratorFilter Unit, produced by the Canadian Hydraulics Center, con-trolled the wave generator system.

The porous breakwater was tested using regular waves toassess the efficiency and prove the design concept. In this study,the constant water depth h is adopted for fundamental research,because variations of incident waves and dispersion effects mayoccur in arbitrary water depth or varying water depth, and arehowever more complicated with different configurations. Waveswere measured using five capacitance wave gauges with anadapter linked to the PC (Personal Computer). Incident waveheights were measured with the first gage, the second and thirdgauges calculated reflection coefficient, and the fourth and fifthgauges estimated transmission. The breakwater was installed inthe middle of the tank, 10 m from the generator.

The pipe breakwaters were modeled with 12 mm-thick plywoodand fixed as an 80 cm�60 cm rigid frame in the flume. The frameswere stuffed with PVC pipes of various diameters ranging fromD¼6 mm to 16 mm (D/h¼0.024�0.064), while the length of thelongitudinal pipes defined the width of the breakwaters, i.e.w¼5 cm, 10 cm, 15 cm and 20 cm (w/h¼0.2�0.8) (Fig. 2). Thepipes were placed parallel to each other without spacing. Pipes werelongitudinally parallel to the direction of incoming waves, and thebreakwater was perpendicular. In practical engineering application,the pipe breakwater can be conveniently cast as a module in acommercial foundry, whereas the outer frame may be constructedby traditional cement with concrete in substitution for the plywood,or by reformed materials such as GFRC (Glass Fiber ReinforcedConcrete) which can be widely used as construction materials due toits high flexural strength and toughness and low drying shrinkage.

In this study, the performance characteristics of the perpendi-cular stationary pipe breakwaters are conducted with an incidentwave height of Hi¼1 cm, 2 cm, 3 cm and 4 cm for the periodranging from T¼0.5 s to 1.5 s. Wave elevations were measuredwith five capacitance wave probes.

3. Estimation of wave attenuation

The reflection and transmission of wave energy are estimatedby using the method of Goda and Suzuki (1976) for separation ofincident and reflected wave. Based on the time histories of waterelevations measured with two wave gages on the free watersurface, i.e. second and third probe, the amplitude are analyzed bythe FFT (Fast Fourier Transform) technique, thus, the reflectioncoefficients Kr were estimated as follows:

The composite wave profiles of incident and reflected waves atlocation x¼x1 and x¼x1þDl can be expressed as:

Z1 ¼ ðZiþZrÞx ¼ x1 ¼ A1 cos stþB1 sin st

A1 ¼ ai cos yiþar cos yr

B1 ¼ ai sin yiþar sin yr

(ð1Þ

Z2 ¼ ðZiþZrÞx ¼ x1þDl ¼ A2 cos stþB2 sin st ð2Þ

A2 ¼ ai cosðyiþkDlÞþar cosðyrþkDlÞ

B2 ¼ ai sinðyiþkDlÞþar sinðyrþkDlÞ

(ð3Þ

where yi¼kx1þei, yr¼kx1þer, k is the wave number, s is theangular frequency and e is the phase angle, the subscript ‘‘i’’ and‘‘r’’ denotes incident and reflected waves, respectively. Dl is thespacing between two measuring stations.

The amplitudes ai and ar can thus be calculated by

ai ¼1

29sin kDl9½ðA2�A1 cos kDl�B1 sin kDlÞ2

þðB2þA1 sin kDl�B1 cos kDlÞ2�1=2 ð4Þ

ar ¼1

29sin kDl9½ðA2�A1 cos kDlþB1 sin kDlÞ2

þðB2�A1 sin kDl�B1 cos kDlÞ2�1=2 ð5Þ

The energies of the incident and reflected waves, Ei and Er

could be obtained by

Ei ¼

Z f max

f min

Siðf Þdf ð6Þ

Er ¼

Z f max

f min

Srðf Þdf ð7Þ

Si(f) and Sr(f) denotes the frequency spectrum of incident andreflective waves, and f is the frequency. Consequently, the reflec-tion coefficient, Kr, can be determined:

Kr ¼ffiffiffiffiffiffiffiffiffiffiffiEr=Ei

pð8Þ

The wave transmission coefficients Kt were estimated by

Kt ¼Ht=Hi ð9Þ

where Hi and Ht is the incident wave height and transmitted waveheight, respectively.

Consequently, estimation of wave attenuation (loss coefficient, KL)can be determined from:

KL ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�K2

r�K2t

qð10Þ

4. Results and discussion

This study investigates interactions and influences betweenwaves and the porous pipe breakwater with different diametersand pipe lengths (breakwater widths). Reflection coefficients,transmission coefficients and attenuation demonstrate the resultsof these investigations. The efficiency of the pipe breakwaters aredetailed as the following section.

Fig. 2. Portrait and diagram sketch of pipe breakwaters.

Fig. 3. Variation of reflection coefficient Kr versus dimensional frequency s2h/g for

D/h¼0.024 and w/h¼0.2.


4.1. Attenuation relative to pipe length, w/h

The variation of reflection coefficient Kr of pipe diameterD¼6 mm (D/h¼0.024) and length, w, varied from 5–20 cm (w/h¼0.2�0.8) comprises four curves which denote the variation ofKr for different incident wave heights (Figs. 3–6). A wide range ofreflection coefficients Kr are observed as the dimensionlessfrequency s2h/g increases from 1.5–5 (Fig. 3). s2h/g is a simplifiedform of the dispersion relations s2

¼gktanhkh which representsthe interrelations of wave properties like wavelength, frequency,wavenumber for surface gravity wave on water of arbitrary, butconstant depth. The tendency of reflecting performance becomeslarger when s2h/g increases, variations of Kr showed a vibratingbut intensive range when s2h/go1.5. The values of Kr areapproximately equal, which indicated that the increase of Hi/hseems to have less influence on reflection coefficients for com-paratively long waves, where Hi/h is a dimensionless parametercomparing the relative height of the wave to water depth. Incontrast with the Kr values for w/h¼0.4�0.8 (Figs. 4–6), theresults reveal a similar tendency to that of w/h¼0.2. The valuesof Kr increased progressively from 0.2�0.5 to 0.25�0.65 whens2h/go1.5, and exhibited an even wider range of Kr valuesbetween s2h/g¼1.5 and 3.

In the variation of reflection coefficients Kr with Hi/gT2 and w/hfor D/h¼0.024, the power fit curve was adopted for regressions(Fig. 7). For a given w/h, the reflection coefficient increases for anincrease in Hi/gT2, which also demonstrates that Kr values forw/h¼0.8 are comparatively greater than w/h¼0.2�0.6. Theresults indicate that a longer pipe is more efficient in reflecting


D/h¼0.024 and w/h¼0.4.


D/h¼0.024 and w/h¼0.6.


D/h¼0.024 and w/h¼0.8.

Fig. 7. Variation of reflection coefficient Kr versus Hi/gT2 for D/h¼0.024.

Fig. 8. Variation of transmission coefficient Kt versus Hi/gT2 for D/h¼0.024.

Fig. 9. Variation of loss coefficient KL versus Hi/gT2 for D/h¼0.024.


incident waves. Similar tendencies are also found in the case ofD/h¼0.032 to 0.064. However, in terms of Kt, the transmissioncoefficient decreases in conjunction with the increasing of Hi/gT2

(Fig. 8). Since Kt is determined by Kt¼Ht/Hi, Kt decrease indicatesreduction of incident wave height. Comparing present results,pipe breakwater competence is slightly affected by pipe lengthand breakwater width (configuration) when Hi/gT240.004, andthe divergence is larger for Hi/gT2o0.004, e.g. when Hi/gT2

¼0.004,the transmission coefficient Kt is equal to 0.375 and 0.298 for w/h¼0.2 and w/h¼0.8, respectively. When Hi/gT2

¼0.016, Kt is thusequal to 0.733 and 0.475, accordingly (Fig. 8). However, wavetransmission is minor through longer pipes, which demonstratesthat the transmission coefficient Kt for w/h¼0.8 is comparativelylower than w/h¼0.2�0.6.

The influence of pipe length on breakwater performance of thebreakwaters is evaluated here using the loss coefficient (Fig. 9).

The loss coefficient changes seriously when w/h¼0.2 and 0.4.When w/h¼0.2, the increase of Hi/gT2 yields a higher KL, varyingapproximately from 0.2–0.9. When w/h¼0.4, the KL valuesincrease from 0.4–0.9. These results reveal that pipe breakwaterswith shorter lengths have better wave attenuation with shorterincident waves, but perform poorly for longer waves. However, asw increases toward 15 cm, i.e. w/h¼0.6, a peculiar tendencyof loss coefficient KL appears: the parameter Hi/gT2 weaklyinfluences attenuation of the configuration, in which the values


of KL are closely assembled between 0.6 and 0.7 according to theregressions curve. Similarly, when w/h¼0.8, the loss coefficient isdistributed symmetrically. Hence, the attenuation efficiency ofthe pipe breakwaters for w/h40.6 is approximately equivalent.This remarkable outcome will be corroborated by irregularwave tests.

Fig. 12. Variation of reflection coefficient Kr versus dimensional frequency s2h/g

for Hi/h¼0.12 and w/h¼0.4.


4.2. Attenuation relative to pipe diameter, D/h

The variation of reflection coefficient Kr of pipe lengthw¼10 cm (w/h¼0.4) and pipe diameter varied from 6 mm to16 mm (D/h¼0.024�0.064) are shown in Figs. 10–13, respec-tively. Despite different aperture diameters, the pipes have highperviousness, and PVC pipe thicknesses are equivalent in sub-stance. Therefore, the porosity and permeability should be veryclose. As predicted, the tendency did agree with the generalwave–structure interaction characteristics: attenuation forshort-period waves and/or small waves is better, while attenua-tion efficacy for long waves can be less effective.

The variations of reflection coefficients with s2h/g and D/h forw/h¼0.4 and Hi/h¼0.2�0.8 are examined and discussed in threeranges: s2h/go1.0, s2h/g43.0 and the outcome between(Figs. 10–13). The values of reflection coefficient Kr within s2h/g43.0; where Kr is between 0.6�0.9, reveal that the breakwaterefficiently reflects incident waves. Through the ranges betweens2h/g¼1.0 and 3.0, it is obviously found that the reflectancechanges evidently with enlargement of wave height. The reflec-tion coefficient decreases as s2h/g increases; particularly in thevicinity of s2h/g¼2.0, the highest value diminished from approxi-mately 0.8 to 0.4. Furthermore, varying Kr values are approxi-mated when s2h/go1.0, which indicate that pipe diameters






Fig. 14. Variation of reflection coefficients Kr versus Hi/gT2 for w/h¼0.4.

variation w/h also appears to have less influence on reflectioncoefficients for comparatively long waves.

Fig. 14 shows the variation of reflection coefficients Kr withHi/gT2 and D/h for w/h¼0.4. Comparing the reflection coefficientbetween variant D/h, as illustrated previously, the porosity andpermeability are very close since the pipes with different dia-meters are highly pervious, The tendency of wave reflections overthe breakwaters are almost identical in each case, implying thatreflection of the pipe breakwater is slightly affected by pipediameter. However, Kr values increased along with Hi/gT2, com-pare with that in Fig. 7, pipe length is more crucial in reflectingincident waves than pipe diameter.


Breakwater performance can be expressed by comparingtransmission coefficient Kt with Hi/gT2 and D/h for w/h¼0.4(Fig. 15). Incident wave height can be reduced by over 85% forHi/gT240.004 when D/h¼0.24, and even the largest diameterD/h¼0.064 is capable of attenuating incident wave height by over75%. However, a minor diameter causes higher substantiveattenuation. Pipe efficiency on wave energy loss is in clear contrastto the loss coefficient KL (Fig. 16). Consequently, the breakwaterwith D/h¼0.024 demonstrated comparatively higher competencein energy loss. However, energy attenuation efficacy with relativelylong waves resembles that of conventional breakwaters, yieldinglow performance for Hi/gT2o0.002. In summary, though modifica-tions of pipe diameter cause very little variation in reflectioncoefficient, Kr, decreasing pipe diameter will bring lower transmis-sion waves, Kt, and greater loss coefficient, KL.

4.3. Attenuation related to breakwater width relative to wave

length, w/L

Several previous investigations have demonstrated that ratioof width to wave length is an important governing factors. Mostenergy is transmitted because breakwater width is too smallcompared to the width of the wavelength. Therefore, the variationof Kr, Kt and KL are discussed according to the relative ratio ofbreakwater width to wave length (w/L) to compare the effects ofdifferent diameters and/or wave heights after energy dissipationof the breakwater, and is discussed as follows:

Fig. 15. Variation of transmission coefficients Kt versus Hi/gT2 for w/h¼0.4.

Fig. 16. Variation of loss coefficients KL versus Hi/gT2 for w/h¼0.4.

4.3.1. Variation of Kr, Kt and KL related to different pipe diameters,

D/h

As shown in Fig. 17, when the incident wave height is underthe same conditions, the impact on the variation of the reflectioncoefficient Kr is not obvious under varying pipe diameters, butgradually increases in conjunction with the w/L ratio. Thisphenomenon indicates that the impact of the pipe length (break-water thickness) is greater than that of the pipe diameter, whichalso reveals that the pipe length is more efficiently in thecompetence of reflecting incident waves.

Fig. 18 shows a result of the variation of the transmissioncoefficient related to the pipe diameter D/h and w/L. The figureshows that D/h had a poor impact as w/Lo0.065, but the effect isrelatively obvious when w/L40.065. The figure also shows thatwhen w/L40.1, the transmission coefficient Kt is less than 0.418(with the condition that the incident wave height Hi/h is 0.16, andthe minimum diameter D/h is 0.024).

The variation of loss coefficients (energy dissipation) shown inFig. 19 can be obtained from the results displayed in Figs. 17 and18, which show that w/L increased the effect of energy dissipationsignificantly (e.g., the efficiency of the energy dissipation coeffi-cient KL can reach more than 0.6 when w/L40.1).

4.3.2. Variation of Kr, Kt and KL related to different wave heights,

Hi/h

Figs. 20–22 show the variations of Kr, Kt and KL with the relativew/L ratio under varying incident wave heights. Although Fig. 20

Fig. 17. Variation of reflection coefficients Kr versus w/L ratio for Hi/h¼0.16.

Fig. 18. Variation of transmission coefficients Kt versus w/L ratio for Hi/h¼0.16.

Fig. 19. Variation of loss coefficients KL versus w/L ratio for Hi/h¼0.16.

Fig. 20. Variation of reflection coefficient Kr versus w/L ratio for D/h¼0.024

between various incident wave heights, Hi/h.

Fig. 21. Variation of transmission coefficient Kt versus w/L ratio for D/h¼0.024

between various incident wave heights, Hi/h.

Fig. 22. Variation of loss coefficients KL versus w/L ratio for D/h¼0.024 between

various incident wave heights, Hi/h.


shows that the variation of the pipe diameter affects the reflectioncoefficient Kr slightly, for an identical pipe diameter D/h, arelatively large reflection can be obtained when the incident waveheight Hi is comparatively small, and the reflectivity increases inconjunction with w/L.

Perceiving the contrast between Kt and Kr is easy. For trans-mission, in contrast with the trend of reflectivity, transmissiondecreased rapidly with an increase in w/L. When w/L40.08,Kt values can be less than 0.54, and decrease together as thew/L ratio increases. However, Fig. 21 shows that the overall trendtends to be an approximation (constant or specific values) whenw/L40.8.

Finally, the difference in attenuation of varying incident wavesrelative to the w/L ratio (as shown in Fig. 22) reveals that thedistinction between each Hi/h is relatively noticeable, and theimpact of energy dissipation is generally higher for relativelygreater waves in a substance (e.g., the loss coefficient KL reached0.9 for Hi/h¼0.16, and the KL value exists over 0.5 mostly asw/L40.5).

4.4. Wave height distributions

These positive results can be confirmed by viewing the timehistory of wave-height distributions of incident and transmissionwaves. The case of T¼0.4 s and T¼1.5 s when Hi/h¼0.04 andw/h¼0.4, attenuation of wave heights is obviously found in shortwaves, but not conspicuous in longer waves (Fig. 23). When

Hi/h¼0.16 and w/h¼0.8 (better results are obtained for T¼0.5 s),the effectiveness is still inconspicuous when T¼1.5 s (Fig. 24).Comparing Fig. 24 with Fig. 23, the effect of reflective waves whenT¼0.5 s correlates with water elevation seemed to be unevenalong the time series after t¼25 s. Transmitted wave heights arecomparatively lower as well.

5. Conclusion

Numerous facilities have been constructed along the coast tocontrol wave disturbances. This has led to extensive study ofbreakwaters with comparatively lower capital expenditure, con-venient construction, unsophisticated configuration, environmen-tal-friendliness and applicability of temporary protection. Thisarticle presents a distinct porous pipe breakwater constructed ofvarious PVC pipes; the pipes are highly pervious, and the porosityand permeability of the pipe breakwaters are nearly approximate.The effect of the pipe breakwater on the reflection coefficient (Kr),transmission coefficient (Kt) and loss coefficient (KL) are thereforeinvestigated experimentally, obtaining favorable. Salient conclu-sions are drawn below.

Under identical pipe diameter, performance is greatly influ-enced by increased incident wave heights for shorter waves whens2h/g41.5, but comparatively long waves seem to have lessinfluence when s2h/go1.5.

Fig. 23. Time history of water elevation of incident waves and transmission for (a) T¼0.4 s and (b) T¼1.5 s (Hi/h¼0.04, D/h¼0.024, w/h¼0.4).

Fig. 24. Time history of water elevation of incident waves and transmission for (a) T¼0.5 s and (b) T¼1.5 s (Hi/h¼0.16, D/h¼0.024, w/h¼0.8).



The reflection coefficient increases with Hi/gT2, and thereforelonger pipe is more efficient in reducing the reflection coefficient.Shorter pipe lengths attenuated shorter waves well, but wereunsatisfactory for longer waves. This results also imply that thetransmission coefficient is slightly affected by the length of thepipes when Hi/gT240.004 while the divergence is larger when Hi/gT2o0.004.

Pipe breakwater reflection is slightly affected by the diameters,but due to the similarity of the porosity and permeability, it isalmost the same for all cases. Comparisons of transmissioncoefficients and loss coefficients, however, imply that minordiameters create higher substantive attenuation.

Since the structure is fixed in this study, the hydrodynamicwave force on the structure was not estimated presently, thedynamic response of the breakwater will be discuss in our furtherstudy by considering the breakwater as a ‘freely floating struc-ture’ with very soft moorings.

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Documents

Experimental study on the performance characteristics of porous perpendicular pipe breakwaters