Applied Ocean Research 30 (2008) 92–99

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Applied Ocean Research

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Experimental study on scour occurring at a vertical impermeablesubmerged breakwaterKwang-Ho Lee ∗, Norimi MizutaniDepartment of Civil Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan

a r t i c l e i n f o

Article history:Received 12 April 2007Received in revised form25 January 2008Accepted 26 June 2008Available online 5 August 2008

Keywords:Local scourImpermeable submerged breakwaterMaximum scour depthReflection coefficient

a b s t r a c t

In recent years, local scour has been brought to attention because it may have a negative effect on coastalstructures. This paper describes an experimental investigation of local scour in front of an impermeablesubmerged breakwater with a vertical offshore face. Experimental results show that the scour patternin front of the submerged breakwater is similar to that in front of a vertical-wall breakwater, althoughthere is a slight difference in the locations of the scour and the deposition. The maximum scour depthnormalized by the incidentwave height is found to decrease exponentially with relativewater depth (theratio of the water depth to wavelength of the incident wave height). Also, the scour depth is dependenton the reflection coefficient of the submerged breakwater. A new estimation method for evaluatingscour depth is developed and provides excellent correlation with all experimental data available in theliterature.

© 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Coastal areas serve many purposes, and various coastalstructures have been constructed to meet the increases in coastaluse demands. Most of these structures are designed to dissipatewave energy, and the fluid fields around coastal structures arerelatively complicated. These fluid motions produce the localscour by interacting with the seabed resulting in local scournear coastal structures, i.e. the local scour on these coastalstructures is one of the representative phenomena resulting fromthe interactions between fluid motions, structures and sediments.Scour occurring around coastal structures can threaten structuralstability; undesired deposition caused by scour can also lessenthe intended performance of coastal structures. Over the lastthree decades, numerous researchers have assessed scour deptharound coastal structures, including piles [10–12], rubble moundbreakwaters [14,15], and composite breakwaters (or seawalls) [19,20,3,6,13]. Irie and Nadaoka [3] reported that nearly 6 m of realscour had occurred over an approximately 100 m long breakwaterin Japan. Nine research institutions from six European countrieshave also collaborated on the Scour Around Coastal Structures(SCARCOS) project under the Marine Science and Technology(MAST) program of the European Union (EU), and a summary ofthese efforts has been provided by Sumer et al. [18]. SCARCOSresearchers have conducted experiments for various types of

∗ Corresponding author. Tel.: +81 52 789 3731; fax: +81 52 789 1665.E-mail address: leekh@civil.nagoya-u.ac.jp (K.-H. Lee).

0141-1187/$ – see front matter© 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.apor.2008.06.003

coastal structures to elucidate the scour mechanisms and haveproduced practical guidelines for different structural types. Anempirical expression that can evaluate the maximum scour depthmay become useful during a structural design phase because thepotential risks can then be predicted in advance.Although scour has been assessed for various coastal struc-

tures, few studies have examined the effect of scour on a sub-merged breakwater [17,7]. Recently, submerged breakwaters havebeen constructed as an alternative to emerged structures becausesubmerged breakwater has fewer impacts on the coastal environ-ments. Also, the crown of submerged breakwater allows the ex-change of seawater between lee and seaward sides. Furthermore,submerged breakwaters can serve not only as breakwaters butalso coastal protection structures. Sumer et al. [17] experimen-tally studied trunk scour (2-D scour) and roundhead scour (3-Dscour) around impermeable and permeable inclined submergedbreakwaters. They found that the trunk scour depth was of thesame order of magnitude as that for inclined emerged rubble-mound breakwaters. Their research for 2-D scour, however, didnot consider wave breaking on the crown of the submerged break-waters, which is the principal wave dissipation mechanism forsubmerged breakwater. Sánchez-Arcilla [7] also examined scourmechanisms for inclined permeable submerged breakwaters, buttheir hydraulic model experiments had a limited range. Further-more, no studies have focused on vertical submerged breakwaters,which can prevent severe sand washout at artificial beaches. In re-cent years, advances in computer capabilities have allowed for nu-merical calculations and simulations of seabed deformation causedby interaction betweenwaves and sediments. However, due to the

K.-H. Lee, N. Mizutani / Applied Ocean Research 30 (2008) 92–99 93

Fig. 1. Schematic diagram of the experimental arrangement.

complexity of the underlying mechanisms involved in sedimenttransport, this problem still requires further analysis.The purpose of this study is to investigate seabed deformation

caused by local scouring which occur in front of an impermeablesubmerged breakwater with a vertical front face, using 2-Dhydraulic model experiments. The measured seabed deformationpatterns are compared to those of an emerged breakwater and themaximum scour depth is investigated under different widths andsubmersion depths.

2. Experimental setup and measurements

2.1. Dimensional analysis

The steady streaming pattern caused by standing wave isthe most important mechanism of scour occurring in front ofthe structures [1,19,20,3,16,17]. Therefore, considering the steadystreaming, scour processing in front of a vertical-type submergedbreakwater is governed by dimensional parameters such as theincident wave height Hi, the wave period T , the still waterdepth h, the gravitational acceleration g , the water density ρ,the median diameter of the bed material (sand particles) D50, thedensity of the bed material ρs, the molecular viscosity of waterµ, the width of the submerged breakwater B and the submergeddepth of the submerged breakwater q̂h. Applying the Buckinghamπ theorem to these dimensional parameters, the scour occurringfor the submerged breakwater is dependent on the following non-dimensional parameters:

f(hL,HiL,LD50

, q̂,Bh, ϕc, Re

)= 0 (1)

where h/L is the ratio of thewater depth to thewave length,Hi/L isthewave steepness, L/D50 is the ratio of wave length to themediandiameter of the bed material, q̂ and B/h is the parameters relatedto the geometry of the submerged breakwater, ϕc is the Shieldsparameter and Re is the Reynolds number. In the above equation,the Reynolds number can be ignored because the seabed acts asa rough wall with scour occurring. Also, the Shields parameter

and L/D50 can be omitted because one kind of sand was usedand only movable bed conditions, always larger than the criticalShields parameter, were employed in this experiment. Accordingto the previous study by Xie [19], L/D50 only slightly affects theend results of scour processing. These parameters are discussed inSection 3.2.

2.2. Experimental setup

The laboratory experiments were conducted at Nagoya Univer-sity in a wave flume. The wave flume was 0.7 m in width, 0.9 m indepth, and 30 m in length. A flap-type wave generator producedwaves at one end of the wave flume; at the other end of the waveflume, waves passing a submerged breakwater were absorbed bya wave absorption layer composed of cobbles and tetrapod mod-els. The flap-type wave paddle can be controlled by a regular sig-nal generator as required. Moreover, the capacitance-type wavegauge is attached in thewave paddle for controlling themovementof paddle to minimize the effect of the reflected waves from thestructure installed in the wave flume, so the desired incident wavegeneration in the wave flume is possible. The model of an imper-meable, vertical submerged breakwater was placed 16.5 m fromthe wave generator and seated on the bottom of the wave flume,not the movable sand bottom, to minimize wave–structure inter-actions during scouring, because this study focused on the scour;only in front of the submerged breakwater. It dos not consider thedisplacement of structures due to sliding, overturning, and slip-ping. Sumer and Fredsøe [15], however, it have been indicated fora rubble-mound breakwater, the scour depth for a wave-flume-seated model was slightly smaller than that for a sand-bottom-seated model. A movable sand bed, with a median sand diameterof D50 = 0.2 mm and specific gravity s = 2.65, was placed in frontof the submerged breakwater. The sand bed was 2 m long, 0.2 mthick, and has the same width as the wave flume. A wooden platestep, which has the same height as the movable sand bed, was alsoplaced inside the wave flume apart from themovable sand bottomand model structure. A schematic diagram and photograph of theexperimental arrangement are shown in Figs. 1 and 2, respectively.

94 K.-H. Lee, N. Mizutani / Applied Ocean Research 30 (2008) 92–99

Table 1Experimental conditions

Test Water depth h(cm) Submerged breakwater Wave height Hi (cm) Wave period T (s) h/Li Hi/Li CrWidtha B (cm) Submerged depth qh (cm)

Run 1 30 20 4 9.34 1.20 0.1681 0.052 0.63Run 2 30 20 4 7.12 1.30 0.1514 0.036 0.68Run 3 30 20 4 7.92 1.35 0.1440 0.038 0.68Run 4 30 20 4 7.07 1.35 0.1444 0.034 0.68Run 5 30 20 4 6.81 1.45 0.1322 0.030 0.65Run 6 30 20 4 5.42 1.50 0.1273 0.023 0.64Run 7 30 20 4 5.61 1.60 0.1177 0.022 0.66Run 8 30 20 4 6.46 1.80 0.1022 0.022 0.62Run 9 30 20 4 7.35 1.80 0.1020 0.025 0.65Run 10 30 20 4 6.88 1.90 0.0961 0.022 0.62Run 11 30 20 4 7.20 1.90 0.0959 0.023 0.62Run 12 30 20 4 7.35 2.05 0.0878 0.022 0.65Run 13 30 20 14 7.94 1.30 0.1511 0.034 0.38Run 14 30 20 14 7.40 1.40 0.1378 0.034 0.30Run 15 30 20 14 9.07 1.50 0.1257 0.038 0.31Run 16 30 20 14 8.77 1.60 0.1163 0.034 0.34Run 17 30 20 14 8.28 1.70 0.1087 0.030 0.28Run 18 30 20 14 9.83 1.80 0.1019 0.033 0.34Run 19 20 20 4 5.02 1.10 0.1446 0.036 0.46Run 20 20 20 4 3.41 1.10 0.1455 0.025 0.39Run 21 20 20 4 5.70 1.20 0.1292 0.037 0.51Run 22 20 20 4 3.75 1.20 0.1304 0.024 0.42Run 23 20 20 4 5.87 1.30 0.1170 0.034 0.59Run 24 20 20 4 5.35 1.35 0.1122 0.030 0.60Run 25 20 20 4 4.40 1.40 0.1081 0.024 0.56Run 26 20 20 4 4.12 1.50 0.0999 0.021 0.56Run 27 20 20 4 5.58 1.50 0.0992 0.028 0.62Run 28 20 20 4 4.98 1.60 0.0924 0.023 0.63Run 29 20 20 4 5.37 1.70 0.0859 0.022 0.62Run 30 20 20 4 5.50 1.80 0.0804 0.022 0.57Run 31 20 20 4 5.02 1.90 0.0760 0.020 0.52Run 32 20 50 4 5.70 1.20 0.1292 0.037 0.53Run 33 20 50 4 5.87 1.30 0.1170 0.034 0.59Run 34 20 50 4 4.40 1.40 0.1081 0.024 0.53Run 35 20 50 4 5.58 1.50 0.0992 0.028 0.64Run 36 20 50 4 4.98 1.60 0.0924 0.023 0.56Run 37 20 50 4 5.50 1.80 0.0804 0.022 0.50Run 38 20 50 4 5.02 1.90 0.0760 0.019 0.47a The length in the direction of wave propagation.

Fig. 2. Photograph of the experimental arrangement.

2.3. Experimental conditions and measurements

The experiment was conducted for regular waves, rangingfrom 0.019 to 0.052 in wave steepness and from 1.10 s to1.9 s in wave period. A partial standing wave was formed bythe incident and reflected waves from the submerged breakwateron the offshore side. The incident waves were chosen withinthe range in which the standing wave on the offshore side of asubmerged breakwater would not dissipate. This partial standingwave could undesirably dissipate if its surface profile reached a

certain limit, which was undesirable in this experimental study.Furthermore, this phenomenon can occur before the incidentwave arrives at the submerged breakwater model, thus impedingthe propagation of the following incident wave in the onshoredirection. The still water depth above the movable sand bottomwas kept constant (20 cm or 30 cm). Table 1 provides a summaryof all the experimental conditions.Capacitance-type wave gauges (KENEK CHT 6-30, Tokyo, Japan)

were used at five locations; three on the offshore side and two onthe onshore side to record the wave deformations caused by the

K.-H. Lee, N. Mizutani / Applied Ocean Research 30 (2008) 92–99 95

submerged breakwater. The recorded water wave profiles wereused to estimate the reflection coefficients for the submergedbreakwater, using the three-point methods proposed by Iwataand Kiyono [4]. The bottom profile was also measured using theultrasonic bottom profiler (MASATOYO, MM-EPI-2, Tokyo, Japan)mounted on the wave flume cart.

2.4. Experimental procedure

For each test run, the bed conditions were thoroughly checkedbefore the experiment was performed and the sand bed wasleveled 2 mm below water. Given that the scour depth aroundthe structure did not generally exceed 10 cm for this small-scalelaboratory, test, it was determined that the initial bed conditionsmight affect the final results. Therefore, to minimize the errorcaused by the initial bed profile, the sand bed was repeatedlyleveled until the measured bed profile was within a tolerancerange of 2 mm based on the ideal conditions. After setting theinitial sand bed, water was allowed to rise along the wave flumeuntil the required the still water level was reached; water wasadded at a sufficiently slowly so as to reduce air entrainmentinside the seabed and prevent disturbances of the initial bedconditions. Wave action was conducted for 5000 cycles of incidentwave periods, and the bottom topography was measured by theultrasonic bottom profiler.

3. Results and discussion

3.1. Bed profile by local scour

In hydraulic experimental studies of vertical-wall breakwaters,[19,20] showed that fine material was scoured at the nodesand deposited near anti-nodal points mainly by the suspendedtransport mode; coarse material was scoured halfway betweenthe nodal and anti–nodal points by the bed-load transport mode.Sumer and Fredsøe [15] reported the same pattern of bed materialscouring. In general, coarse sand has a ratio of maximum waveorbital velocity Ubmax to settling velocity ws ratio smaller than10; for fine sand, this ratio is greater than 10 [7,6]. The settlingvelocity of the sand size in the present study was estimated as2.61 cm/s based on Soulsby’s [9] research, and therefore, the ratioof the settling velocity to the water particle velocity near thebottom, based on the small amplitude theory, was smaller than 10,indicating that the sand used in this hydraulic model experimentswas coarse and mainly transported by the bed-load transportmode.Fig. 3 shows the measured bed profiles in front of the

submerged breakwater after applying 5000 cycles of incidentwaveperiods, which is sufficient time to reach the equilibrium states[19,20,15]. Sumer et al. [17] showed that there was no clear scouror deposition pattern for a slopped submerged breakwater. Inthis study, on the other hand, there was a little phase differencebetween the scour anddeposition points. For coarse sand, the scourpattern of the submerged breakwater was similar to that shownwith the vertical-wall breakwaters tested by Xie [19,20] and Sumerand Fredsøe [15]. That is, the scour closest to the structure occurredmidway between the anti-nodal and nodal points, and depositiondeveloped near the nodal point. The steady streaming structureformed in front of the vertical submerged breakwater resembledthat found in other studies of vertical-wall breakwaters, but wasdifferent for the submerged crowns of the vertical and inclinedsubmerged breakwaters. Furthermore, scour occurred when thestill water depth was 20 cm at the interface of the sand bedand the structure, as shown in Fig. 3(c); however, scour was notobserved when the still water depth was 30 cm, as shown inFig. 3(a) and (b). This scouring behavior at the interface of the sand

bed and the structure is similar to the behavior that Sumer andFredsøe [15] observed with rubble-mound breakwater, but doesnot agreewith that of at a vertical-wall breakwater. They describedtwo differences in the bed profiles of vertical and rubble-moundbreakwaters. First, scour at the junction point between the sandbed and structure occurredwith the rubble-moundbreakwater butnot with the vertical-wall breakwater. Second, scour was observedbelow the anti-nodal point for the rubble-mound breakwater,but was not observed for the vertical-wall breakwater. AlthoughSumer and Fredsøe [15] did not clearly explain the reason forthe latter for the rubble-mound breakwater, they concluded thatsteady streaming at the rubble-mound breakwater must have hada significant effect at the junction point between the seabed andthe structure. That is, the slope of the structures and the flow frominside the breakwater towards the sand layer triggered scour atthose points. However, the present laboratory experimental studyconsidered a vertical-type impermeable submerged breakwater;thus, the slopes of the structures and the flow that originated frominside the breakwater would have had no influence on scour at thejunction points between the seabed and the structure. Therefore,in Fig. 3(c) the scour at the toe of the submerged breakwaterwas caused by a different mechanism from that observed for therubble-mound breakwater.The observed scour in the experimental program may be

explained by the vortex near the toe, which was generated bythe interaction between the return flows formed on the crownafter wave breaking and the incident waves. Sediment transportat the toe of the submerged breakwater may be particularlysensitive to this vortex when the water depth is shallow. For2-D experiments, the mean water level behind the submergedbreakwater was increased and then the increased water levelintensified the offshore return flow on the crown of the structure,which was closely related to the vortex formed at the toe.Therefore, it was conclude that the ascent of the mean waterlevel behind the submerged breakwater magnified the vortex.This feature was clearly observed in the experiments performedwith 20 cm water depth. Unfortunately, the equipments for flowvisualization such as particle image velocimetry (PIV) were notinstalled, and the occurrence of vortex generation at the toe of thesubmerged breakwater was only observed through the analysis ofthe images recorded by video camera. As shown in Fig. 4, however,vortex formation was clearly observed in front of the submergedbreakwater. This vortex generation was also confirmed byChang et al. [2].

3.2. Maximum scour depth

Sumer and Fredsøe [15,16] and Sumer et al. [17] showedthat the scour depth is a function of the following parametersfrom dimensional analysis. The scour depth for a rubble-moundbreakwater and a permeable submerged breakwater with inclinedoffshore face is expressed as follows:

(ZS)maxHi

=

f(hL, α, ϕc,

LD50

,aUmν

)for a rubble mound breakwater

f(hL, α, ϕc,

LD50

,aUmν, q̂)

for a submerged breakwater

(2)

where (Zs)max is the maximum scour depth, α is the breakwaterslope, a is the orbital excursion of the water particles, ν isthe kinematic viscosity, Um is the maximum orbital velocitynear the bottom, and q̂ is the submerged depth normalized bythe still water depth. They also indicated that maximum scourdepth can be estimated with the parameter h/L and α for a

96 K.-H. Lee, N. Mizutani / Applied Ocean Research 30 (2008) 92–99

(a) Run 4.

(b) Run 14.

(c) Run 24.

Fig. 3. Scour patterns in front of an impermeable submerged breakwater

rubble-mound breakwater and h/L, α, and q̂ for a permeablesubmerged breakwater with a inclined offshore face from the firstapproximation. This dimensional analysis for a sloped permeablesubmerged breakwater is similar to Eq. (1) for the vertical-typesubmerged breakwater except α. The effects of α were droppedbecause the present experimental study was confined to only avertical-type submerged breakwater. Instead of the breakwaterslope, the effect of the width of the submerged breakwater wasconsidered as the parameters of the maximum scour depth.Furthermore, in the case of the scour occurring in front of thesubmerged breakwater, the effects of the structural configurations,including the width and submerged depth, can be effectivelyexpressed by considering the reflection coefficients of breakwater,Cr because the reflection coefficient is capable of reflectingfeatures of submerged breakwaters. Submerged breakwaters havea wide range of reflection coefficients according to the submergeddepth, and width shape, and the reflection coefficient can alsoexplain the effects of standing waves generated in front ofthese structures, which are the key mechanism, as previouslymentioned. Consequently, we investigated the maximum scourdepth in front of submerged breakwaters subject to the ratio of the

Fig. 4. Snapshot of the vortex generation in front of the submerged breakwater.

water depth to thewave length, submerged depth, structurewidthand reflection coefficient.

K.-H. Lee, N. Mizutani / Applied Ocean Research 30 (2008) 92–99 97

(a) In case of q̂ = 0.13. (b) In case of q̂ = 0.47.

Fig. 5. Effect of submerged depth on the maximum scour depth.

The reflection coefficients, defined as the ratio of reflectedwaves to incident waves, were estimated from Eq. (3) basedon the three-gauge method, using the fast Fourier transformtechnique [4].

Cr =√ER/EI . (3)

In the above equation, ER and EI are the reflected and incidentwave energy, respectively, and can be calculated as follows:EI =

∫SI(f )df

ER =∫SR(f )df

(4)

where, SI and SR are incident and reflected wave spectrum,respectively, and f is frequency.

3.2.1. Effect of the submerged depthThe effect of the submerged depth of an impermeable

submerged breakwater on the maximum scour depth wasinvestigated. Fig. 5(a) and (b) show the maximum scour depths asfunctions of the relative water depth (the ratio of the water depthto wavelength) for non-dimensional submerged depths q̂ equaling0.13 and 0.47, respectively. The reflection coefficients computed byEq. (3), based on thewater surface profile measured from the threewave gauges installed in front of the structure, are also depictedin the figures. During the experiments, spilling–plunging-typewave breaking [5] was observed on the crown of the submergedbreakwater for the relatively shallow submerged depth of q̂ =0.13, and spilling-type wave breaking occurred for a relativelydeep submerged depth of q̂ = 0.47. As indicated in Fig. 5, themaximum scour depth increased with the wavelength (or waveperiod). This scour-depth tendency along thewavelength is similarto that shown for vertical and rubble-mound breakwaters byXie [19,20] and Sumer and Fredsøe [15]. Themaximumscour depthfor the relatively shallow submerged depthwas larger than that forthe relatively deep submerged depth. This result may be causedby the difference in the reflection coefficients for the permeablesubmerged breakwater: the reflection coefficient was Cr ≈ 0.65 inFig. 5(a) and Cr ≈ 0.3 in Fig. 5(b).

3.2.2. Effect of the widthNext, the effect of the width of submerged breakwater on

the maximum scour depth is presented in Fig. 6. In both cases,spilling–plunging-type wave breaking occurred on the crown ofthe submerged breakwater. The scour depth increased as theratio of water depth to wavelength decreased, similar to that inFig. 5. There was, however, a slight difference in the variationof the maximum scour depth with the width, compared to thesubmerged depth of the submerged breakwater. This can also beexplained by the reflection coefficient. In general, the reflectioncoefficient is more sensitive to the submerged depth than towidth of impermeable submerged breakwaters, as shown in Figs. 5and 6. For this reason, a clear difference in the maximum scourdepth between the two cases was not observed in Fig. 6. Thisresult suggests that the reflection coefficient of the submergedbreakwater might be useful for estimating the maximum scourdepth because of the reflection coefficients can reflect the wavefields in front of the structure.

3.2.3. Comparison with other structuresAs mentioned above, numerous studies have assessed the

maximum scour depth for various coastal structures, providingempirical expressions for several types of structures; theseexpressions allow estimations of the maximum scour depth.Among these studies, [19,20] proposed an empirical formula fora vertical-wall breakwater based on the experimental data:

(ZS)maxHi

= A sinh(2πhLi

)−1.35(5)

where A is the non-dimensional constant, which is 0.4 for finesand and 0.3 for coarse sand. For a rubble-mound breakwater,Sumer and Fredsøe [15] provided the following empirical formulaincluding the breakwater slope:(ZS)maxHi

= f (α) sinh(2πhLi

)−1.35f (α) = 0.3− 1.77 exp

(−α

15

).

(6)

In the above equation, the applicable range of the rubble-mound breakwater slope is 30◦ ≤ α < 90◦.

98 K.-H. Lee, N. Mizutani / Applied Ocean Research 30 (2008) 92–99

(a) In case of B = 20 cm. (b) In case of B = 50 cm.

Fig. 6. Effect of the submerged breakwater width on the maximum scour depth.

Although the type of structure is different, the presentexperimental results were compared with Eqs. (5) and (6) andexperimental results for a vertical-wall breakwater reported byXie [19,20] to investigate the magnitude of maximum scour depthas shown in Fig. 7. The scour depth of the submerged breakwaterwas clearly less than that of the vertical-wall breakwater. This isnatural result because the incident wave is reflected completelyin the case of a vertical-wall breakwater but transmitted over thecrown of the structure in the case of a submerged breakwater. Theexperimental results for the submerged breakwater correspondto the computed results obtained with the empirical formulaproposed by Sumer and Fredsøe [15] for a rubble-moundbreakwater within the range of 32◦ ≤ α < 55◦. This couldhave been caused by the similarity of the reflection coefficientsreflecting thewavemotion in front of the structures. The reflectioncoefficient of the submerged breakwater obtained in the presentexperiments ranged from0.3 to 0.7. For rubble-moundbreakwater,the reflection coefficient generally ranged from 0.3 to 0.6, butcould differ depending on the inclination of the breakwater [8].Therefore, from Figs. 5–7 the reflection coefficient containingstanding wave information is useful as initial guidance forestimating the maximum scour depth.

3.3. Estimation of maximum scour depth

In the design stage, a simple empirical formula for maximumscour depth may be useful for predicting potential risk of coastalstructures. For this reason, many empirical expressions for thescour depth have been proposed. For submerged breakwaters,however, themaximum scour depth is not uniform but is scatteredaccording to features of the structure such as the submergeddepth and width, as shown in Fig. 7. Therefore, the experimentaldata were re-sorted by considering the reflection coefficients; theresults are shown in Fig. 8. The results indicate that the scourdepth in front of an impermeable submerged breakwater can beexpressed as follows:

(ZS)maxHi

=0.06

(1− Cr)[sinh(kh)]2.04(7)

which is illustrated by the solid line in Fig. 8. In the above equation,the refection coefficient value should be less than 1 because the

Fig. 7. Comparison of scour depth with other structures.

scour depth goes infinite for Cr = 1. From Fig. 8, the proposedestimationmethod of the scour depth including the effects of wavereflection gives good estimations of the maximum scour depth forvarious reflection coefficients. The findings of this study are limitedto configurations of tested breakwaters.

4. Conclusions

The scour in front of a vertical-type impermeable submergedbreakwater resulting from interactions between waves and theseabed was examined based on the hydraulic model experiments.Special attention was given to the initial bottom condition foraccurate measurement of the seabed deformations including themaximum local depth. Wave action was conducted for 5000cycles of incident wave periods, and the bottom topography wasmeasured by the laser bottom profiler. Based on the experimental

K.-H. Lee, N. Mizutani / Applied Ocean Research 30 (2008) 92–99 99

Fig. 8. Scour depth considering the reflection coefficients. For the comparisonwithempirical formula of other structures for scour depth, Cr = 0 is applied in verticalwall and rubble-mound breakwaters because the reflection coefficients are notincluded in the empirical formula proposed by Xie [19] and Sumer and Fredsøe [15].

results obtained, the following conclusions are made:

(1) In case of the vertical-type impermeable submerged break-water, the local scour occurs midway between the anti-nodalpoint and the nodal point, and the deposition generates nearthe nodal point, similar to the case of the vertical-wall break-water.

(2) The maximum scour depth at the vertical-type impermeablesubmerged breakwater increases exponentially as the wavelength increase.

(3) The maximum scour depth at the vertical-type impermeablesubmerged breakwater corresponds to the range of that at therubble-mound breakwater with similar reflection coefficientsto those of the vertical-type impermeable submerged break-water.

(4) The maximum scour depth at the vertical-type impermeablesubmerged breakwater mainly depends on the reflectioncoefficients of the submerged breakwater. Therefore, the scour

depth can be expressed as an empirical equation including thereflection coefficients

(5) The estimation method for the scour depth proposed in thisstudy gives good estimations of the maximum scour depth forthe vertical-type impermeable submerged breakwater.

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