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Experimental study on scour occurring at a vertical impermeable submerged breakwater
Applied Ocean Research 30 (2008) 92–99
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Applied Ocean Research journal homepage: www.elsevier.com/locate/apor
Experimental study on scour occurring at a vertical impermeable submerged breakwater Kwang-Ho Lee ∗ , Norimi Mizutani Department of Civil Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
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Article history: Received 12 April 2007 Received in revised form 25 January 2008 Accepted 26 June 2008 Available online 5 August 2008 Keywords: Local scour Impermeable submerged breakwater Maximum scour depth Reflection 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 coastal structures. This paper describes an experimental investigation of local scour in front of an impermeable submerged breakwater with a vertical offshore face. Experimental results show that the scour pattern in front of the submerged breakwater is similar to that in front of a vertical-wall breakwater, although there is a slight difference in the locations of the scour and the deposition. The maximum scour depth normalized by the incident wave height is found to decrease exponentially with relative water depth (the ratio of the water depth to wavelength of the incident wave height). Also, the scour depth is dependent on the reflection coefficient of the submerged breakwater. A new estimation method for evaluating scour depth is developed and provides excellent correlation with all experimental data available in the literature. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Coastal areas serve many purposes, and various coastal structures have been constructed to meet the increases in coastal use demands. Most of these structures are designed to dissipate wave energy, and the fluid fields around coastal structures are relatively complicated. These fluid motions produce the local scour by interacting with the seabed resulting in local scour near coastal structures, i.e. the local scour on these coastal structures is one of the representative phenomena resulting from the interactions between fluid motions, structures and sediments. Scour occurring around coastal structures can threaten structural stability; undesired deposition caused by scour can also lessen the intended performance of coastal structures. Over the last three decades, numerous researchers have assessed scour depth around coastal structures, including piles [10–12], rubble mound breakwaters [14,15], and composite breakwaters (or seawalls) [19, 20,3,6,13]. Irie and Nadaoka [3] reported that nearly 6 m of real scour had occurred over an approximately 100 m long breakwater in Japan. Nine research institutions from six European countries have 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 of these efforts has been provided by Sumer et al. [18]. SCARCOS researchers have conducted experiments for various types of
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coastal structures to elucidate the scour mechanisms and have produced practical guidelines for different structural types. An empirical expression that can evaluate the maximum scour depth may become useful during a structural design phase because the potential risks can then be predicted in advance. Although scour has been assessed for various coastal structures, few studies have examined the effect of scour on a submerged breakwater [17,7]. Recently, submerged breakwaters have been constructed as an alternative to emerged structures because submerged breakwater has fewer impacts on the coastal environments. Also, the crown of submerged breakwater allows the exchange of seawater between lee and seaward sides. Furthermore, submerged breakwaters can serve not only as breakwaters but also coastal protection structures. Sumer et al. [17] experimentally studied trunk scour (2-D scour) and roundhead scour (3-D scour) around impermeable and permeable inclined submerged breakwaters. They found that the trunk scour depth was of the same order of magnitude as that for inclined emerged rubblemound breakwaters. Their research for 2-D scour, however, did not consider wave breaking on the crown of the submerged breakwaters, which is the principal wave dissipation mechanism for submerged breakwater. Sánchez-Arcilla [7] also examined scour mechanisms for inclined permeable submerged breakwaters, but their hydraulic model experiments had a limited range. Furthermore, no studies have focused on vertical submerged breakwaters, which can prevent severe sand washout at artificial beaches. In recent years, advances in computer capabilities have allowed for numerical calculations and simulations of seabed deformation caused by interaction between waves and sediments. However, due to the
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Fig. 1. Schematic diagram of the experimental arrangement.
complexity of the underlying mechanisms involved in sediment transport, 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 impermeable submerged breakwater with a vertical front face, using 2-D hydraulic model experiments. The measured seabed deformation patterns are compared to those of an emerged breakwater and the maximum scour depth is investigated under different widths and submersion depths. 2. Experimental setup and measurements 2.1. Dimensional analysis The steady streaming pattern caused by standing wave is the most important mechanism of scour occurring in front of the structures [1,19,20,3,16,17]. Therefore, considering the steady streaming, scour processing in front of a vertical-type submerged breakwater is governed by dimensional parameters such as the incident wave height Hi , the wave period T , the still water depth h, the gravitational acceleration g, the water density ρ , the median diameter of the bed material (sand particles) D50 , the density of the bed material ρs , the molecular viscosity of water µ, the width of the submerged breakwater B and the submerged depth of the submerged breakwater qˆ h. Applying the Buckingham π theorem to these dimensional parameters, the scour occurring for the submerged breakwater is dependent on the following nondimensional parameters:
f
h Hi L
,
L
,
L D50
B
, qˆ , , ϕc , Re = 0 h
(1)
where h/L is the ratio of the water depth to the wave length, Hi /L is the wave steepness, L/D50 is the ratio of wave length to the median diameter of the bed material, qˆ and B/h is the parameters related to the geometry of the submerged breakwater, ϕc is the Shields parameter and Re is the Reynolds number. In the above equation, the Reynolds number can be ignored because the seabed acts as a rough wall with scour occurring. Also, the Shields parameter
and L/D50 can be omitted because one kind of sand was used and only movable bed conditions, always larger than the critical Shields parameter, were employed in this experiment. According to the previous study by Xie [19], L/D50 only slightly affects the end results of scour processing. These parameters are discussed in Section 3.2. 2.2. Experimental setup The laboratory experiments were conducted at Nagoya University in a wave flume. The wave flume was 0.7 m in width, 0.9 m in depth, and 30 m in length. A flap-type wave generator produced waves at one end of the wave flume; at the other end of the wave flume, waves passing a submerged breakwater were absorbed by a wave absorption layer composed of cobbles and tetrapod models. The flap-type wave paddle can be controlled by a regular signal generator as required. Moreover, the capacitance-type wave gauge is attached in the wave paddle for controlling the movement of paddle to minimize the effect of the reflected waves from the structure installed in the wave flume, so the desired incident wave generation in the wave flume is possible. The model of an impermeable, vertical submerged breakwater was placed 16.5 m from the wave generator and seated on the bottom of the wave flume, not the movable sand bottom, to minimize wave–structure interactions during scouring, because this study focused on the scour; only in front of the submerged breakwater. It dos not consider the displacement of structures due to sliding, overturning, and slipping. Sumer and Fredsøe [15], however, it have been indicated for a rubble-mound breakwater, the scour depth for a wave-flumeseated model was slightly smaller than that for a sand-bottomseated model. A movable sand bed, with a median sand diameter of D50 = 0.2 mm and specific gravity s = 2.65, was placed in front of the submerged breakwater. The sand bed was 2 m long, 0.2 m thick, and has the same width as the wave flume. A wooden plate step, which has the same height as the movable sand bed, was also placed inside the wave flume apart from the movable sand bottom and model structure. A schematic diagram and photograph of the experimental arrangement are shown in Figs. 1 and 2, respectively.
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Table 1 Experimental conditions Test
Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Run 11 Run 12 Run 13 Run 14 Run 15 Run 16 Run 17 Run 18 Run 19 Run 20 Run 21 Run 22 Run 23 Run 24 Run 25 Run 26 Run 27 Run 28 Run 29 Run 30 Run 31 Run 32 Run 33 Run 34 Run 35 Run 36 Run 37 Run 38 a
Water depth h(cm)
30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
Submerged breakwater Widtha B (cm)
Submerged depth qh (cm)
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 50 50 50 50 50 50 50
4 4 4 4 4 4 4 4 4 4 4 4 14 14 14 14 14 14 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Wave height Hi (cm)
Wave period T (s)
h/Li
Hi /Li
Cr
9.34 7.12 7.92 7.07 6.81 5.42 5.61 6.46 7.35 6.88 7.20 7.35 7.94 7.40 9.07 8.77 8.28 9.83 5.02 3.41 5.70 3.75 5.87 5.35 4.40 4.12 5.58 4.98 5.37 5.50 5.02 5.70 5.87 4.40 5.58 4.98 5.50 5.02
1.20 1.30 1.35 1.35 1.45 1.50 1.60 1.80 1.80 1.90 1.90 2.05 1.30 1.40 1.50 1.60 1.70 1.80 1.10 1.10 1.20 1.20 1.30 1.35 1.40 1.50 1.50 1.60 1.70 1.80 1.90 1.20 1.30 1.40 1.50 1.60 1.80 1.90
0.1681 0.1514 0.1440 0.1444 0.1322 0.1273 0.1177 0.1022 0.1020 0.0961 0.0959 0.0878 0.1511 0.1378 0.1257 0.1163 0.1087 0.1019 0.1446 0.1455 0.1292 0.1304 0.1170 0.1122 0.1081 0.0999 0.0992 0.0924 0.0859 0.0804 0.0760 0.1292 0.1170 0.1081 0.0992 0.0924 0.0804 0.0760
0.052 0.036 0.038 0.034 0.030 0.023 0.022 0.022 0.025 0.022 0.023 0.022 0.034 0.034 0.038 0.034 0.030 0.033 0.036 0.025 0.037 0.024 0.034 0.030 0.024 0.021 0.028 0.023 0.022 0.022 0.020 0.037 0.034 0.024 0.028 0.023 0.022 0.019
0.63 0.68 0.68 0.68 0.65 0.64 0.66 0.62 0.65 0.62 0.62 0.65 0.38 0.30 0.31 0.34 0.28 0.34 0.46 0.39 0.51 0.42 0.59 0.60 0.56 0.56 0.62 0.63 0.62 0.57 0.52 0.53 0.59 0.53 0.64 0.56 0.50 0.47
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, ranging from 0.019 to 0.052 in wave steepness and from 1.10 s to 1.9 s in wave period. A partial standing wave was formed by the incident and reflected waves from the submerged breakwater on the offshore side. The incident waves were chosen within the range in which the standing wave on the offshore side of a submerged breakwater would not dissipate. This partial standing wave 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 incident wave arrives at the submerged breakwater model, thus impeding the propagation of the following incident wave in the onshore direction. The still water depth above the movable sand bottom was kept constant (20 cm or 30 cm). Table 1 provides a summary of 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 on the onshore side to record the wave deformations caused by the
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submerged breakwater. The recorded water wave profiles were used to estimate the reflection coefficients for the submerged breakwater, using the three-point methods proposed by Iwata and Kiyono [4]. The bottom profile was also measured using the ultrasonic 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 checked before the experiment was performed and the sand bed was leveled 2 mm below water. Given that the scour depth around the structure did not generally exceed 10 cm for this small-scale laboratory, test, it was determined that the initial bed conditions might affect the final results. Therefore, to minimize the error caused by the initial bed profile, the sand bed was repeatedly leveled until the measured bed profile was within a tolerance range of 2 mm based on the ideal conditions. After setting the initial sand bed, water was allowed to rise along the wave flume until the required the still water level was reached; water was added at a sufficiently slowly so as to reduce air entrainment inside the seabed and prevent disturbances of the initial bed conditions. Wave action was conducted for 5000 cycles of incident wave periods, and the bottom topography was measured by the ultrasonic 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 nodes and deposited near anti-nodal points mainly by the suspended transport mode; coarse material was scoured halfway between the nodal and anti–nodal points by the bed-load transport mode. Sumer and Fredsøe [15] reported the same pattern of bed material scouring. In general, coarse sand has a ratio of maximum wave orbital velocity Ub max to settling velocity ws ratio smaller than 10; for fine sand, this ratio is greater than 10 [7,6]. The settling velocity of the sand size in the present study was estimated as 2.61 cm/s based on Soulsby’s [9] research, and therefore, the ratio of the settling velocity to the water particle velocity near the bottom, based on the small amplitude theory, was smaller than 10, indicating that the sand used in this hydraulic model experiments was coarse and mainly transported by the bed-load transport mode. Fig. 3 shows the measured bed profiles in front of the submerged breakwater after applying 5000 cycles of incident wave periods, which is sufficient time to reach the equilibrium states [19,20,15]. Sumer et al. [17] showed that there was no clear scour or deposition pattern for a slopped submerged breakwater. In this study, on the other hand, there was a little phase difference between the scour and deposition points. For coarse sand, the scour pattern of the submerged breakwater was similar to that shown with the vertical-wall breakwaters tested by Xie [19,20] and Sumer and Fredsøe [15]. That is, the scour closest to the structure occurred midway between the anti-nodal and nodal points, and deposition developed near the nodal point. The steady streaming structure formed in front of the vertical submerged breakwater resembled that found in other studies of vertical-wall breakwaters, but was different for the submerged crowns of the vertical and inclined submerged breakwaters. Furthermore, scour occurred when the still water depth was 20 cm at the interface of the sand bed and the structure, as shown in Fig. 3(c); however, scour was not observed when the still water depth was 30 cm, as shown in Fig. 3(a) and (b). This scouring behavior at the interface of the sand
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bed and the structure is similar to the behavior that Sumer and Fredsøe [15] observed with rubble-mound breakwater, but does not agree with that of at a vertical-wall breakwater. They described two differences in the bed profiles of vertical and rubble-mound breakwaters. First, scour at the junction point between the sand bed and structure occurred with the rubble-mound breakwater but not with the vertical-wall breakwater. Second, scour was observed below the anti-nodal point for the rubble-mound breakwater, but was not observed for the vertical-wall breakwater. Although Sumer and Fredsøe [15] did not clearly explain the reason for the latter for the rubble-mound breakwater, they concluded that steady streaming at the rubble-mound breakwater must have had a significant effect at the junction point between the seabed and the structure. That is, the slope of the structures and the flow from inside the breakwater towards the sand layer triggered scour at those points. However, the present laboratory experimental study considered a vertical-type impermeable submerged breakwater; thus, the slopes of the structures and the flow that originated from inside the breakwater would have had no influence on scour at the junction points between the seabed and the structure. Therefore, in Fig. 3(c) the scour at the toe of the submerged breakwater was caused by a different mechanism from that observed for the rubble-mound breakwater. The observed scour in the experimental program may be explained by the vortex near the toe, which was generated by the interaction between the return flows formed on the crown after wave breaking and the incident waves. Sediment transport at the toe of the submerged breakwater may be particularly sensitive to this vortex when the water depth is shallow. For 2-D experiments, the mean water level behind the submerged breakwater was increased and then the increased water level intensified 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 water level behind the submerged breakwater magnified the vortex. This feature was clearly observed in the experiments performed with 20 cm water depth. Unfortunately, the equipments for flow visualization such as particle image velocimetry (PIV) were not installed, and the occurrence of vortex generation at the toe of the submerged breakwater was only observed through the analysis of the images recorded by video camera. As shown in Fig. 4, however, vortex formation was clearly observed in front of the submerged breakwater. This vortex generation was also confirmed by Chang et al. [2]. 3.2. Maximum scour depth Sumer and Fredsøe [15,16] and Sumer et al. [17] showed that the scour depth is a function of the following parameters from dimensional analysis. The scour depth for a rubble-mound breakwater and a permeable submerged breakwater with inclined offshore face is expressed as follows:
(ZS )max Hi
h L aUm , α, ϕ , , f c D50 ν L for a rubble mound breakwater = L aUm h ˆ , α, ϕc , , ,q f D50 ν L
(2)
for a submerged breakwater
where (Zs )max is the maximum scour depth, α is the breakwater slope, a is the orbital excursion of the water particles, ν is the kinematic viscosity, Um is the maximum orbital velocity near the bottom, and qˆ is the submerged depth normalized by the still water depth. They also indicated that maximum scour depth can be estimated with the parameter h/L and α for a
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(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 qˆ for a permeable submerged breakwater with a inclined offshore face from the first approximation. This dimensional analysis for a sloped permeable submerged breakwater is similar to Eq. (1) for the vertical-type submerged breakwater except α . The effects of α were dropped because the present experimental study was confined to only a vertical-type submerged breakwater. Instead of the breakwater slope, the effect of the width of the submerged breakwater was considered as the parameters of the maximum scour depth. Furthermore, in the case of the scour occurring in front of the submerged breakwater, the effects of the structural configurations, including the width and submerged depth, can be effectively expressed by considering the reflection coefficients of breakwater, Cr because the reflection coefficient is capable of reflecting features of submerged breakwaters. Submerged breakwaters have a wide range of reflection coefficients according to the submerged depth, and width shape, and the reflection coefficient can also explain the effects of standing waves generated in front of these structures, which are the key mechanism, as previously mentioned. Consequently, we investigated the maximum scour depth 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 the wave length, submerged depth, structure width and reflection coefficient.
K.-H. Lee, N. Mizutani / Applied Ocean Research 30 (2008) 92–99
(a) In case of qˆ = 0.13.
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(b) In case of qˆ = 0.47. Fig. 5. Effect of submerged depth on the maximum scour depth.
The reflection coefficients, defined as the ratio of reflected waves to incident waves, were estimated from Eq. (3) based on the three-gauge method, using the fast Fourier transform technique [4]. Cr =
p
ER /EI .
(3)
In the above equation, ER and EI are the reflected and incident wave energy, respectively, and can be calculated as follows:
Z EI = SI (f )df Z 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 depth The effect of the submerged depth of an impermeable submerged breakwater on the maximum scour depth was investigated. Fig. 5(a) and (b) show the maximum scour depths as functions of the relative water depth (the ratio of the water depth to wavelength) for non-dimensional submerged depths qˆ equaling 0.13 and 0.47, respectively. The reflection coefficients computed by Eq. (3), based on the water surface profile measured from the three wave gauges installed in front of the structure, are also depicted in the figures. During the experiments, spilling–plunging-type wave breaking [5] was observed on the crown of the submerged breakwater for the relatively shallow submerged depth of qˆ = 0.13, and spilling-type wave breaking occurred for a relatively deep submerged depth of qˆ = 0.47. As indicated in Fig. 5, the maximum scour depth increased with the wavelength (or wave period). This scour-depth tendency along the wavelength is similar to that shown for vertical and rubble-mound breakwaters by Xie [19,20] and Sumer and Fredsøe [15]. The maximum scour depth for the relatively shallow submerged depth was larger than that for the relatively deep submerged depth. This result may be caused by the difference in the reflection coefficients for the permeable submerged breakwater: the reflection coefficient was Cr ≈ 0.65 in Fig. 5(a) and Cr ≈ 0.3 in Fig. 5(b).
3.2.2. Effect of the width Next, 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 of the submerged breakwater. The scour depth increased as the ratio of water depth to wavelength decreased, similar to that in Fig. 5. There was, however, a slight difference in the variation of the maximum scour depth with the width, compared to the submerged depth of the submerged breakwater. This can also be explained by the reflection coefficient. In general, the reflection coefficient is more sensitive to the submerged depth than to width of impermeable submerged breakwaters, as shown in Figs. 5 and 6. For this reason, a clear difference in the maximum scour depth between the two cases was not observed in Fig. 6. This result suggests that the reflection coefficient of the submerged breakwater might be useful for estimating the maximum scour depth because of the reflection coefficients can reflect the wave fields in front of the structure. 3.2.3. Comparison with other structures As mentioned above, numerous studies have assessed the maximum scour depth for various coastal structures, providing empirical expressions for several types of structures; these expressions allow estimations of the maximum scour depth. Among these studies, [19,20] proposed an empirical formula for a vertical-wall breakwater based on the experimental data:
(ZS )max Hi
−1.35 h = A sinh 2π Li
(5)
where A is the non-dimensional constant, which is 0.4 for fine sand and 0.3 for coarse sand. For a rubble-mound breakwater, Sumer and Fredsøe [15] provided the following empirical formula including the breakwater slope:
−1.35 h = f (α) sinh 2π Hi L iα . (α) = 0.3 − 1.77 exp −
(ZS )max f
(6)
15
In the above equation, the applicable range of the rubblemound breakwater slope is 30◦ ≤ α < 90◦ .
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(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 present experimental results were compared with Eqs. (5) and (6) and experimental results for a vertical-wall breakwater reported by Xie [19,20] to investigate the magnitude of maximum scour depth as shown in Fig. 7. The scour depth of the submerged breakwater was clearly less than that of the vertical-wall breakwater. This is natural result because the incident wave is reflected completely in the case of a vertical-wall breakwater but transmitted over the crown of the structure in the case of a submerged breakwater. The experimental results for the submerged breakwater correspond to the computed results obtained with the empirical formula proposed by Sumer and Fredsøe [15] for a rubble-mound breakwater within the range of 32◦ ≤ α < 55◦ . This could have been caused by the similarity of the reflection coefficients reflecting the wave motion in front of the structures. The reflection coefficient of the submerged breakwater obtained in the present experiments ranged from 0.3 to 0.7. For rubble-mound breakwater, the reflection coefficient generally ranged from 0.3 to 0.6, but could differ depending on the inclination of the breakwater [8]. Therefore, from Figs. 5–7 the reflection coefficient containing standing wave information is useful as initial guidance for estimating the maximum scour depth. 3.3. Estimation of maximum scour depth
Fig. 7. Comparison of scour depth with other structures.
In the design stage, a simple empirical formula for maximum scour depth may be useful for predicting potential risk of coastal structures. For this reason, many empirical expressions for the scour depth have been proposed. For submerged breakwaters, however, the maximum scour depth is not uniform but is scattered according to features of the structure such as the submerged depth and width, as shown in Fig. 7. Therefore, the experimental data were re-sorted by considering the reflection coefficients; the results are shown in Fig. 8. The results indicate that the scour depth in front of an impermeable submerged breakwater can be expressed as follows:
(ZS )max Hi
=
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
scour depth goes infinite for Cr = 1. From Fig. 8, the proposed estimation method of the scour depth including the effects of wave reflection gives good estimations of the maximum scour depth for various reflection coefficients. The findings of this study are limited to configurations of tested breakwaters. 4. Conclusions The scour in front of a vertical-type impermeable submerged breakwater resulting from interactions between waves and the seabed was examined based on the hydraulic model experiments. Special attention was given to the initial bottom condition for accurate measurement of the seabed deformations including the maximum local depth. Wave action was conducted for 5000 cycles of incident wave periods, and the bottom topography was measured by the laser bottom profiler. Based on the experimental
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depth can be expressed as an empirical equation including the reflection coefficients (5) The estimation method for the scour depth proposed in this study gives good estimations of the maximum scour depth for the vertical-type impermeable submerged breakwater. References
Fig. 8. Scour depth considering the reflection coefficients. For the comparison with empirical formula of other structures for scour depth, Cr = 0 is applied in vertical wall and rubble-mound breakwaters because the reflection coefficients are not included 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 breakwater, the local scour occurs midway between the anti-nodal point and the nodal point, and the deposition generates near the nodal point, similar to the case of the vertical-wall breakwater. (2) The maximum scour depth at the vertical-type impermeable submerged breakwater increases exponentially as the wave length increase. (3) The maximum scour depth at the vertical-type impermeable submerged breakwater corresponds to the range of that at the rubble-mound breakwater with similar reflection coefficients to those of the vertical-type impermeable submerged breakwater. (4) The maximum scour depth at the vertical-type impermeable submerged breakwater mainly depends on the reflection coefficients of the submerged breakwater. Therefore, the scour
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Experimental study on scour occurring at a vertical impermeable submerged breakwater Kwang-Ho Lee ∗ , Norimi Mizutani Department of Civil Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
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Article history: Received 12 April 2007 Received in revised form 25 January 2008 Accepted 26 June 2008 Available online 5 August 2008 Keywords: Local scour Impermeable submerged breakwater Maximum scour depth Reflection 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 coastal structures. This paper describes an experimental investigation of local scour in front of an impermeable submerged breakwater with a vertical offshore face. Experimental results show that the scour pattern in front of the submerged breakwater is similar to that in front of a vertical-wall breakwater, although there is a slight difference in the locations of the scour and the deposition. The maximum scour depth normalized by the incident wave height is found to decrease exponentially with relative water depth (the ratio of the water depth to wavelength of the incident wave height). Also, the scour depth is dependent on the reflection coefficient of the submerged breakwater. A new estimation method for evaluating scour depth is developed and provides excellent correlation with all experimental data available in the literature. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Coastal areas serve many purposes, and various coastal structures have been constructed to meet the increases in coastal use demands. Most of these structures are designed to dissipate wave energy, and the fluid fields around coastal structures are relatively complicated. These fluid motions produce the local scour by interacting with the seabed resulting in local scour near coastal structures, i.e. the local scour on these coastal structures is one of the representative phenomena resulting from the interactions between fluid motions, structures and sediments. Scour occurring around coastal structures can threaten structural stability; undesired deposition caused by scour can also lessen the intended performance of coastal structures. Over the last three decades, numerous researchers have assessed scour depth around coastal structures, including piles [10–12], rubble mound breakwaters [14,15], and composite breakwaters (or seawalls) [19, 20,3,6,13]. Irie and Nadaoka [3] reported that nearly 6 m of real scour had occurred over an approximately 100 m long breakwater in Japan. Nine research institutions from six European countries have 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 of these efforts has been provided by Sumer et al. [18]. SCARCOS researchers have conducted experiments for various types of
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coastal structures to elucidate the scour mechanisms and have produced practical guidelines for different structural types. An empirical expression that can evaluate the maximum scour depth may become useful during a structural design phase because the potential risks can then be predicted in advance. Although scour has been assessed for various coastal structures, few studies have examined the effect of scour on a submerged breakwater [17,7]. Recently, submerged breakwaters have been constructed as an alternative to emerged structures because submerged breakwater has fewer impacts on the coastal environments. Also, the crown of submerged breakwater allows the exchange of seawater between lee and seaward sides. Furthermore, submerged breakwaters can serve not only as breakwaters but also coastal protection structures. Sumer et al. [17] experimentally studied trunk scour (2-D scour) and roundhead scour (3-D scour) around impermeable and permeable inclined submerged breakwaters. They found that the trunk scour depth was of the same order of magnitude as that for inclined emerged rubblemound breakwaters. Their research for 2-D scour, however, did not consider wave breaking on the crown of the submerged breakwaters, which is the principal wave dissipation mechanism for submerged breakwater. Sánchez-Arcilla [7] also examined scour mechanisms for inclined permeable submerged breakwaters, but their hydraulic model experiments had a limited range. Furthermore, no studies have focused on vertical submerged breakwaters, which can prevent severe sand washout at artificial beaches. In recent years, advances in computer capabilities have allowed for numerical calculations and simulations of seabed deformation caused by interaction between waves and sediments. However, due to the
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Fig. 1. Schematic diagram of the experimental arrangement.
complexity of the underlying mechanisms involved in sediment transport, 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 impermeable submerged breakwater with a vertical front face, using 2-D hydraulic model experiments. The measured seabed deformation patterns are compared to those of an emerged breakwater and the maximum scour depth is investigated under different widths and submersion depths. 2. Experimental setup and measurements 2.1. Dimensional analysis The steady streaming pattern caused by standing wave is the most important mechanism of scour occurring in front of the structures [1,19,20,3,16,17]. Therefore, considering the steady streaming, scour processing in front of a vertical-type submerged breakwater is governed by dimensional parameters such as the incident wave height Hi , the wave period T , the still water depth h, the gravitational acceleration g, the water density ρ , the median diameter of the bed material (sand particles) D50 , the density of the bed material ρs , the molecular viscosity of water µ, the width of the submerged breakwater B and the submerged depth of the submerged breakwater qˆ h. Applying the Buckingham π theorem to these dimensional parameters, the scour occurring for the submerged breakwater is dependent on the following nondimensional parameters:
f
h Hi L
,
L
,
L D50
B
, qˆ , , ϕc , Re = 0 h
(1)
where h/L is the ratio of the water depth to the wave length, Hi /L is the wave steepness, L/D50 is the ratio of wave length to the median diameter of the bed material, qˆ and B/h is the parameters related to the geometry of the submerged breakwater, ϕc is the Shields parameter and Re is the Reynolds number. In the above equation, the Reynolds number can be ignored because the seabed acts as a rough wall with scour occurring. Also, the Shields parameter
and L/D50 can be omitted because one kind of sand was used and only movable bed conditions, always larger than the critical Shields parameter, were employed in this experiment. According to the previous study by Xie [19], L/D50 only slightly affects the end results of scour processing. These parameters are discussed in Section 3.2. 2.2. Experimental setup The laboratory experiments were conducted at Nagoya University in a wave flume. The wave flume was 0.7 m in width, 0.9 m in depth, and 30 m in length. A flap-type wave generator produced waves at one end of the wave flume; at the other end of the wave flume, waves passing a submerged breakwater were absorbed by a wave absorption layer composed of cobbles and tetrapod models. The flap-type wave paddle can be controlled by a regular signal generator as required. Moreover, the capacitance-type wave gauge is attached in the wave paddle for controlling the movement of paddle to minimize the effect of the reflected waves from the structure installed in the wave flume, so the desired incident wave generation in the wave flume is possible. The model of an impermeable, vertical submerged breakwater was placed 16.5 m from the wave generator and seated on the bottom of the wave flume, not the movable sand bottom, to minimize wave–structure interactions during scouring, because this study focused on the scour; only in front of the submerged breakwater. It dos not consider the displacement of structures due to sliding, overturning, and slipping. Sumer and Fredsøe [15], however, it have been indicated for a rubble-mound breakwater, the scour depth for a wave-flumeseated model was slightly smaller than that for a sand-bottomseated model. A movable sand bed, with a median sand diameter of D50 = 0.2 mm and specific gravity s = 2.65, was placed in front of the submerged breakwater. The sand bed was 2 m long, 0.2 m thick, and has the same width as the wave flume. A wooden plate step, which has the same height as the movable sand bed, was also placed inside the wave flume apart from the movable sand bottom and model structure. A schematic diagram and photograph of the experimental arrangement are shown in Figs. 1 and 2, respectively.
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Table 1 Experimental conditions Test
Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Run 11 Run 12 Run 13 Run 14 Run 15 Run 16 Run 17 Run 18 Run 19 Run 20 Run 21 Run 22 Run 23 Run 24 Run 25 Run 26 Run 27 Run 28 Run 29 Run 30 Run 31 Run 32 Run 33 Run 34 Run 35 Run 36 Run 37 Run 38 a
Water depth h(cm)
30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
Submerged breakwater Widtha B (cm)
Submerged depth qh (cm)
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 50 50 50 50 50 50 50
4 4 4 4 4 4 4 4 4 4 4 4 14 14 14 14 14 14 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Wave height Hi (cm)
Wave period T (s)
h/Li
Hi /Li
Cr
9.34 7.12 7.92 7.07 6.81 5.42 5.61 6.46 7.35 6.88 7.20 7.35 7.94 7.40 9.07 8.77 8.28 9.83 5.02 3.41 5.70 3.75 5.87 5.35 4.40 4.12 5.58 4.98 5.37 5.50 5.02 5.70 5.87 4.40 5.58 4.98 5.50 5.02
1.20 1.30 1.35 1.35 1.45 1.50 1.60 1.80 1.80 1.90 1.90 2.05 1.30 1.40 1.50 1.60 1.70 1.80 1.10 1.10 1.20 1.20 1.30 1.35 1.40 1.50 1.50 1.60 1.70 1.80 1.90 1.20 1.30 1.40 1.50 1.60 1.80 1.90
0.1681 0.1514 0.1440 0.1444 0.1322 0.1273 0.1177 0.1022 0.1020 0.0961 0.0959 0.0878 0.1511 0.1378 0.1257 0.1163 0.1087 0.1019 0.1446 0.1455 0.1292 0.1304 0.1170 0.1122 0.1081 0.0999 0.0992 0.0924 0.0859 0.0804 0.0760 0.1292 0.1170 0.1081 0.0992 0.0924 0.0804 0.0760
0.052 0.036 0.038 0.034 0.030 0.023 0.022 0.022 0.025 0.022 0.023 0.022 0.034 0.034 0.038 0.034 0.030 0.033 0.036 0.025 0.037 0.024 0.034 0.030 0.024 0.021 0.028 0.023 0.022 0.022 0.020 0.037 0.034 0.024 0.028 0.023 0.022 0.019
0.63 0.68 0.68 0.68 0.65 0.64 0.66 0.62 0.65 0.62 0.62 0.65 0.38 0.30 0.31 0.34 0.28 0.34 0.46 0.39 0.51 0.42 0.59 0.60 0.56 0.56 0.62 0.63 0.62 0.57 0.52 0.53 0.59 0.53 0.64 0.56 0.50 0.47
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, ranging from 0.019 to 0.052 in wave steepness and from 1.10 s to 1.9 s in wave period. A partial standing wave was formed by the incident and reflected waves from the submerged breakwater on the offshore side. The incident waves were chosen within the range in which the standing wave on the offshore side of a submerged breakwater would not dissipate. This partial standing wave 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 incident wave arrives at the submerged breakwater model, thus impeding the propagation of the following incident wave in the onshore direction. The still water depth above the movable sand bottom was kept constant (20 cm or 30 cm). Table 1 provides a summary of 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 on the onshore side to record the wave deformations caused by the
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submerged breakwater. The recorded water wave profiles were used to estimate the reflection coefficients for the submerged breakwater, using the three-point methods proposed by Iwata and Kiyono [4]. The bottom profile was also measured using the ultrasonic 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 checked before the experiment was performed and the sand bed was leveled 2 mm below water. Given that the scour depth around the structure did not generally exceed 10 cm for this small-scale laboratory, test, it was determined that the initial bed conditions might affect the final results. Therefore, to minimize the error caused by the initial bed profile, the sand bed was repeatedly leveled until the measured bed profile was within a tolerance range of 2 mm based on the ideal conditions. After setting the initial sand bed, water was allowed to rise along the wave flume until the required the still water level was reached; water was added at a sufficiently slowly so as to reduce air entrainment inside the seabed and prevent disturbances of the initial bed conditions. Wave action was conducted for 5000 cycles of incident wave periods, and the bottom topography was measured by the ultrasonic 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 nodes and deposited near anti-nodal points mainly by the suspended transport mode; coarse material was scoured halfway between the nodal and anti–nodal points by the bed-load transport mode. Sumer and Fredsøe [15] reported the same pattern of bed material scouring. In general, coarse sand has a ratio of maximum wave orbital velocity Ub max to settling velocity ws ratio smaller than 10; for fine sand, this ratio is greater than 10 [7,6]. The settling velocity of the sand size in the present study was estimated as 2.61 cm/s based on Soulsby’s [9] research, and therefore, the ratio of the settling velocity to the water particle velocity near the bottom, based on the small amplitude theory, was smaller than 10, indicating that the sand used in this hydraulic model experiments was coarse and mainly transported by the bed-load transport mode. Fig. 3 shows the measured bed profiles in front of the submerged breakwater after applying 5000 cycles of incident wave periods, which is sufficient time to reach the equilibrium states [19,20,15]. Sumer et al. [17] showed that there was no clear scour or deposition pattern for a slopped submerged breakwater. In this study, on the other hand, there was a little phase difference between the scour and deposition points. For coarse sand, the scour pattern of the submerged breakwater was similar to that shown with the vertical-wall breakwaters tested by Xie [19,20] and Sumer and Fredsøe [15]. That is, the scour closest to the structure occurred midway between the anti-nodal and nodal points, and deposition developed near the nodal point. The steady streaming structure formed in front of the vertical submerged breakwater resembled that found in other studies of vertical-wall breakwaters, but was different for the submerged crowns of the vertical and inclined submerged breakwaters. Furthermore, scour occurred when the still water depth was 20 cm at the interface of the sand bed and the structure, as shown in Fig. 3(c); however, scour was not observed when the still water depth was 30 cm, as shown in Fig. 3(a) and (b). This scouring behavior at the interface of the sand
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bed and the structure is similar to the behavior that Sumer and Fredsøe [15] observed with rubble-mound breakwater, but does not agree with that of at a vertical-wall breakwater. They described two differences in the bed profiles of vertical and rubble-mound breakwaters. First, scour at the junction point between the sand bed and structure occurred with the rubble-mound breakwater but not with the vertical-wall breakwater. Second, scour was observed below the anti-nodal point for the rubble-mound breakwater, but was not observed for the vertical-wall breakwater. Although Sumer and Fredsøe [15] did not clearly explain the reason for the latter for the rubble-mound breakwater, they concluded that steady streaming at the rubble-mound breakwater must have had a significant effect at the junction point between the seabed and the structure. That is, the slope of the structures and the flow from inside the breakwater towards the sand layer triggered scour at those points. However, the present laboratory experimental study considered a vertical-type impermeable submerged breakwater; thus, the slopes of the structures and the flow that originated from inside the breakwater would have had no influence on scour at the junction points between the seabed and the structure. Therefore, in Fig. 3(c) the scour at the toe of the submerged breakwater was caused by a different mechanism from that observed for the rubble-mound breakwater. The observed scour in the experimental program may be explained by the vortex near the toe, which was generated by the interaction between the return flows formed on the crown after wave breaking and the incident waves. Sediment transport at the toe of the submerged breakwater may be particularly sensitive to this vortex when the water depth is shallow. For 2-D experiments, the mean water level behind the submerged breakwater was increased and then the increased water level intensified 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 water level behind the submerged breakwater magnified the vortex. This feature was clearly observed in the experiments performed with 20 cm water depth. Unfortunately, the equipments for flow visualization such as particle image velocimetry (PIV) were not installed, and the occurrence of vortex generation at the toe of the submerged breakwater was only observed through the analysis of the images recorded by video camera. As shown in Fig. 4, however, vortex formation was clearly observed in front of the submerged breakwater. This vortex generation was also confirmed by Chang et al. [2]. 3.2. Maximum scour depth Sumer and Fredsøe [15,16] and Sumer et al. [17] showed that the scour depth is a function of the following parameters from dimensional analysis. The scour depth for a rubble-mound breakwater and a permeable submerged breakwater with inclined offshore face is expressed as follows:
(ZS )max Hi
h L aUm , α, ϕ , , f c D50 ν L for a rubble mound breakwater = L aUm h ˆ , α, ϕc , , ,q f D50 ν L
(2)
for a submerged breakwater
where (Zs )max is the maximum scour depth, α is the breakwater slope, a is the orbital excursion of the water particles, ν is the kinematic viscosity, Um is the maximum orbital velocity near the bottom, and qˆ is the submerged depth normalized by the still water depth. They also indicated that maximum scour depth can be estimated with the parameter h/L and α for a
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(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 qˆ for a permeable submerged breakwater with a inclined offshore face from the first approximation. This dimensional analysis for a sloped permeable submerged breakwater is similar to Eq. (1) for the vertical-type submerged breakwater except α . The effects of α were dropped because the present experimental study was confined to only a vertical-type submerged breakwater. Instead of the breakwater slope, the effect of the width of the submerged breakwater was considered as the parameters of the maximum scour depth. Furthermore, in the case of the scour occurring in front of the submerged breakwater, the effects of the structural configurations, including the width and submerged depth, can be effectively expressed by considering the reflection coefficients of breakwater, Cr because the reflection coefficient is capable of reflecting features of submerged breakwaters. Submerged breakwaters have a wide range of reflection coefficients according to the submerged depth, and width shape, and the reflection coefficient can also explain the effects of standing waves generated in front of these structures, which are the key mechanism, as previously mentioned. Consequently, we investigated the maximum scour depth 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 the wave length, submerged depth, structure width and reflection coefficient.
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(a) In case of qˆ = 0.13.
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(b) In case of qˆ = 0.47. Fig. 5. Effect of submerged depth on the maximum scour depth.
The reflection coefficients, defined as the ratio of reflected waves to incident waves, were estimated from Eq. (3) based on the three-gauge method, using the fast Fourier transform technique [4]. Cr =
p
ER /EI .
(3)
In the above equation, ER and EI are the reflected and incident wave energy, respectively, and can be calculated as follows:
Z EI = SI (f )df Z 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 depth The effect of the submerged depth of an impermeable submerged breakwater on the maximum scour depth was investigated. Fig. 5(a) and (b) show the maximum scour depths as functions of the relative water depth (the ratio of the water depth to wavelength) for non-dimensional submerged depths qˆ equaling 0.13 and 0.47, respectively. The reflection coefficients computed by Eq. (3), based on the water surface profile measured from the three wave gauges installed in front of the structure, are also depicted in the figures. During the experiments, spilling–plunging-type wave breaking [5] was observed on the crown of the submerged breakwater for the relatively shallow submerged depth of qˆ = 0.13, and spilling-type wave breaking occurred for a relatively deep submerged depth of qˆ = 0.47. As indicated in Fig. 5, the maximum scour depth increased with the wavelength (or wave period). This scour-depth tendency along the wavelength is similar to that shown for vertical and rubble-mound breakwaters by Xie [19,20] and Sumer and Fredsøe [15]. The maximum scour depth for the relatively shallow submerged depth was larger than that for the relatively deep submerged depth. This result may be caused by the difference in the reflection coefficients for the permeable submerged breakwater: the reflection coefficient was Cr ≈ 0.65 in Fig. 5(a) and Cr ≈ 0.3 in Fig. 5(b).
3.2.2. Effect of the width Next, 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 of the submerged breakwater. The scour depth increased as the ratio of water depth to wavelength decreased, similar to that in Fig. 5. There was, however, a slight difference in the variation of the maximum scour depth with the width, compared to the submerged depth of the submerged breakwater. This can also be explained by the reflection coefficient. In general, the reflection coefficient is more sensitive to the submerged depth than to width of impermeable submerged breakwaters, as shown in Figs. 5 and 6. For this reason, a clear difference in the maximum scour depth between the two cases was not observed in Fig. 6. This result suggests that the reflection coefficient of the submerged breakwater might be useful for estimating the maximum scour depth because of the reflection coefficients can reflect the wave fields in front of the structure. 3.2.3. Comparison with other structures As mentioned above, numerous studies have assessed the maximum scour depth for various coastal structures, providing empirical expressions for several types of structures; these expressions allow estimations of the maximum scour depth. Among these studies, [19,20] proposed an empirical formula for a vertical-wall breakwater based on the experimental data:
(ZS )max Hi
−1.35 h = A sinh 2π Li
(5)
where A is the non-dimensional constant, which is 0.4 for fine sand and 0.3 for coarse sand. For a rubble-mound breakwater, Sumer and Fredsøe [15] provided the following empirical formula including the breakwater slope:
−1.35 h = f (α) sinh 2π Hi L iα . (α) = 0.3 − 1.77 exp −
(ZS )max f
(6)
15
In the above equation, the applicable range of the rubblemound breakwater slope is 30◦ ≤ α < 90◦ .
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(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 present experimental results were compared with Eqs. (5) and (6) and experimental results for a vertical-wall breakwater reported by Xie [19,20] to investigate the magnitude of maximum scour depth as shown in Fig. 7. The scour depth of the submerged breakwater was clearly less than that of the vertical-wall breakwater. This is natural result because the incident wave is reflected completely in the case of a vertical-wall breakwater but transmitted over the crown of the structure in the case of a submerged breakwater. The experimental results for the submerged breakwater correspond to the computed results obtained with the empirical formula proposed by Sumer and Fredsøe [15] for a rubble-mound breakwater within the range of 32◦ ≤ α < 55◦ . This could have been caused by the similarity of the reflection coefficients reflecting the wave motion in front of the structures. The reflection coefficient of the submerged breakwater obtained in the present experiments ranged from 0.3 to 0.7. For rubble-mound breakwater, the reflection coefficient generally ranged from 0.3 to 0.6, but could differ depending on the inclination of the breakwater [8]. Therefore, from Figs. 5–7 the reflection coefficient containing standing wave information is useful as initial guidance for estimating the maximum scour depth. 3.3. Estimation of maximum scour depth
Fig. 7. Comparison of scour depth with other structures.
In the design stage, a simple empirical formula for maximum scour depth may be useful for predicting potential risk of coastal structures. For this reason, many empirical expressions for the scour depth have been proposed. For submerged breakwaters, however, the maximum scour depth is not uniform but is scattered according to features of the structure such as the submerged depth and width, as shown in Fig. 7. Therefore, the experimental data were re-sorted by considering the reflection coefficients; the results are shown in Fig. 8. The results indicate that the scour depth in front of an impermeable submerged breakwater can be expressed as follows:
(ZS )max Hi
=
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
scour depth goes infinite for Cr = 1. From Fig. 8, the proposed estimation method of the scour depth including the effects of wave reflection gives good estimations of the maximum scour depth for various reflection coefficients. The findings of this study are limited to configurations of tested breakwaters. 4. Conclusions The scour in front of a vertical-type impermeable submerged breakwater resulting from interactions between waves and the seabed was examined based on the hydraulic model experiments. Special attention was given to the initial bottom condition for accurate measurement of the seabed deformations including the maximum local depth. Wave action was conducted for 5000 cycles of incident wave periods, and the bottom topography was measured by the laser bottom profiler. Based on the experimental
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depth can be expressed as an empirical equation including the reflection coefficients (5) The estimation method for the scour depth proposed in this study gives good estimations of the maximum scour depth for the vertical-type impermeable submerged breakwater. References
Fig. 8. Scour depth considering the reflection coefficients. For the comparison with empirical formula of other structures for scour depth, Cr = 0 is applied in vertical wall and rubble-mound breakwaters because the reflection coefficients are not included 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 breakwater, the local scour occurs midway between the anti-nodal point and the nodal point, and the deposition generates near the nodal point, similar to the case of the vertical-wall breakwater. (2) The maximum scour depth at the vertical-type impermeable submerged breakwater increases exponentially as the wave length increase. (3) The maximum scour depth at the vertical-type impermeable submerged breakwater corresponds to the range of that at the rubble-mound breakwater with similar reflection coefficients to those of the vertical-type impermeable submerged breakwater. (4) The maximum scour depth at the vertical-type impermeable submerged breakwater mainly depends on the reflection coefficients of the submerged breakwater. Therefore, the scour
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