Coastal Engineering 56 (2009) 868–875
Contents lists available at ScienceDirect
Coastal Engineering
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o a s t a l e n g
Onshore scour characteristics around submerged vertical and
semicircular breakwaters
D. Morgan Young, Firat Y. Testik ⁎
Civil Engineering Department, Clemson University, Clemson, SC 29634-0911, USA
a r t i c l e
i n f o
Article history:
Received 19 April 2008
Received in revised form 13 March 2009
Accepted 6 April 2009
Available online 8 May 2009
Keywords:
Submerged breakwaters
Vertical breakwater
Semicircular breakwater
Scour
Sediment transport
a b s t r a c t
A laboratory study is presented herein investigating the two-dimensional onshore scour along the base of
submerged vertical and semicircular breakwaters. Experiments were conducted with normally incident
monochromatic waves breaking at the breakwater on both sloping and horizontal sandy bottoms. A principle
conclusion of this investigation is that the characteristics of onshore breakwater scour are independent of
submerged breakwater shape/type. It is also concluded that the onshore scour patterns can be divided into
Hi π
; Wbw — breakwater crest
two distinct regimes that solely rely on the Keulegan–Carpenter number (KC = W
bw
width, Hi — incident wave height). For KC values larger than π, the scour forms “detached” from the
breakwater while for KC values smaller than or equal to π, the scour occurs “attached” to the onshore
breakwater face. Three important scour characteristics are investigated: maximum scour depth (Smax), scour
). Smax value
length (Ls), and the distance of Smax location from the onshore breakwater face (Ds
is observed to
be regime independent and rely on both KC and the mobility number (ψ
=
Hi π
T sinhðkhÞ
g⁎ d
2
; g⁎ — reduced
gravitational acceleration, d — median diameter of the sediment, k — wave number, h — still water depth, T — wave
period) while Ls and Ds are observed to be regime dependent and rely only on KC. Semi-empirical
parameterizations to predict Smax, Ls, and Ds values for onshore breakwater scour are proposed.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
Offshore breakwaters are coastal structures that are commonly
employed to provide protection to valuable coastal areas such as
marinas, ports, and beaches from energetic ocean waves. The principle
function of breakwaters is to cause waves to prematurely break,
thereby reducing destructive wave forces often imparted on vulnerable shorelines. Traditionally, emerged breakwaters, or breakwaters
whose crest pierces the mean water level, have been used to
accomplish this task. Recently, submerged breakwaters, or breakwaters that lie entirely beneath the mean water level, have become
more common (see Lamberti et al., 2005 which documents several
low-crested coastal structures in Europe). Hence, there has been an
increased amount of research conducted on submerged breakwaters
[e.g., see special issue (Vol. 52, 2005) of Coastal Engineering dedicated
to low crested structures].
Submerged breakwaters are designed to offer protection by
inducing partial reflection–transmission and/or breaking of large
waves (Grilli et al., 1994). According to Hur and Mizutani (2003),
⁎ Corresponding author. Civil Engineering Department, 110 Lowry Hall, Clemson
University, Clemson, SC 29634-0911, USA. Tel.: +1 864 656 0484; fax: +1 864 656 2670.
E-mail address: [email protected] (F.Y. Testik).
0378-3839/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.coastaleng.2009.04.003
submerged breakwaters have become increasingly popular due to
their many advantages. One advantage of submerged breakwaters is
that they are often more aesthetically pleasing than emerged breakwaters, which is critical to the tourism industry in most coastal areas
(Johnson, 2006). Another advantage of submerged breakwaters is
their ability to maintain the landward flow of water, which may be
important for water quality considerations (Kobayashi et al., 2007).
On the other hand, submerged breakwaters allow more wave
overtopping and usually dissipate less wave energy than emerged
breakwaters; hence, they allow higher sediment transport rates
(Lamberti et al., 2005).
Various types of submerged breakwaters exist; examples include
vertical breakwaters, semicircular breakwaters, rubble mound breakwaters, and geosynthetic breakwaters. This study centers on the
analysis and comparison of submerged vertical and semicircular
breakwaters. Submerged vertical breakwaters typically exist as a
sturdy vertical wall while submerged semicircular breakwaters are
composed of a precast reinforced concrete structure built with a
semicircular vault and bottom slab (Yuan and Tao, 2003). The concrete
structure is placed over a formed rubble mound foundation (see
Fig. 1). While submerged vertical breakwaters usually reflect more
incident wave energy than submerged semicircular breakwaters,
submerged semicircular breakwaters are oftentimes more stable
under wave forcing.
D.M. Young, F.Y. Testik / Coastal Engineering 56 (2009) 868–875
869
Fig. 1. Illustrative sketch of a typical submerged semicircular breakwater.
When a structure is placed in a marine environment, the presence
of the structure changes the flow field in its immediate environment,
resulting in the formation of vortices around the structure which may
induce scour (Sumer et al., 2001). Due to the substantial improvement
on the measurement techniques and computational resources, the
vortex generation in the vicinity of submerged obstacles under water
waves has become an active research area (Chang et al., 2005). Tang
and Chang (1998) and Chang et al. (2001) investigated flow
separation and vortex generation of a solitary wave passing over a
submerged obstacle. Both the experimental and numerical results
illustrated that as the wave passed over the structure a large vortex
was first formed onshore of the structure accompanied by a secondary
vortex below it (ideal conditions for potential onshore scour). With
regards to oscillatory flows, Testik et al. (2005) observed that periodic
horseshoe vortices form on both sides of a submerged finite length
horizontal bottom-mounted cylinder that can be considered to
resemble a submerged breakwater. As the flow changes direction,
these vortices flip from one side of the submerged cylinder to the
other. Chang et al. (2005) studied the periodic wave conditions,
namely cnoidal waves, over a submerged rectangular obstacle, and
elucidated the obstacle-generated vortex strength and turbulence
intensities. On the other hand, presence of a submerged breakwater
may cause the waves break prematurely. Breaking waves generate
large coherent vortices, which can reach the bottom and stir up
considerable amounts of sediment (Fredsøe and Deigaard, 1992).
When the vortices and the altered bed shear stress are sufficiently
strong enough to induce initiation of sediment motion, sediment
adjacent the coastal structure is transported away from the structure,
and the process known as scouring occurs (see Sumer and Fredsøe,
2002). If a structure experiences significant scour, the foundation
integrity may be compromised and the structure could fail. Structural
failure due to overturning/settling and structural failure due to sliding
are common failure modes for submerged breakwaters (Hughes, 2002).
The depth at which a breakwater is installed into the seabed, reinforcing
depth and size, and foundation size are breakwater design parameters
whose efficiency relies heavily on the awareness of scour characteristics. Scour can occur along the trunk of breakwaters (two-dimensional) or at the head, or end, of a breakwater (three-dimensional).
Since the majority of breakwater research has historically focused on
emerged breakwaters, the majority of breakwater-induced scour studies focus on the evolution of scour offshore of the breakwater (e.g., Xie,
1981; Hughes and Fowler, 1991). Sumer et al. (2001), reviewing results
from submerged breakwater studies, concluded that offshore scour at
the trunk of submerged breakwaters experiences deposition and
sometimes small scour due to significantly reduced wave reflection; a
result mirrored by the current study. Therefore, this study centers on
the analysis of two-dimensional scour that forms onshore of the
breakwater.
This manuscript is organized as follows. A scaling analysis is given in
Section 2. Experimental setup, methodology, and data processing are
described in Section 3. Results for breakwater-induced onshore scour are
presented in Section 4. Conclusions and discussions are given in Section 5.
2. Preliminary analysis
Consider a submerged breakwater of crest width Wbw and
submergence depth of a under linear waves. This breakwater is
located at a water depth of h in a coastal region with median sand
grain diameter d and sand density ρs. The incident wave height at the
location where the breakwater would be located is Hi and the wave
period is T. The water density is ρ and kinematic viscosity is ν. Taking
into account that the gravitational acceleration g plays an important
role in the sediment transport, g should also be included in the set of
external parameters. The full set of the primary external parameters
determining the scour characteristic, say A, of the breakwater is then
given by:
A = ΦðWbw ; a; h; d; ρs ; Hi ; T; ρ; v; g Þ;
ð1Þ
where Φ is a function. Here, it is assumed that the breakwater has an
infinite length and is parallel to the wave front direction and Hi takes into
account the slope effects (horizontal and sloping beach profiles
considered in our experiments). Therefore, wave incidence angle, slope
angle, and breakwater length do not appear in the set of external
parameters. Note that the selected flow parameters (i.e., Hi and T, instead
of for example the magnitude of the horizontal water velocity) are surface
observables that have been monitored and recorded for a long time for
various coastlines worldwide and, if needed, can be measured relatively
easily through various means including remote sensing methods.
Three of these eleven parameters, including A, in Eq. (1) have
independent dimensions, leading to eight dimensionless governing
parameters. It is clear that the parameters ρs, ρ and g are important
only in a combination g⁎ = g(s − 1) = g(ρs / ρ − 1), which is the
reduced gravitational acceleration. This gives:
A = ΦðWbw ; a; h; d; Hi ; T; m; g Þ
ð2Þ
Using some additional physical arguments relevant to the problem
considered and linear wave theory parameterizations, governing dimensionless parameters can be chosen as breakwater Reynolds number,
Re =
ðHi π = T ÞWbw
, Keulegan–Carpenter
KC =
0 number,
m
2 1
B
lity parameter at the seafloor, ψ = @
Hi π
T sinhðkhÞ
g⁎ d
Hi π
Wbw , mobi-
C
A, dimensionless submer-
gence depth, a/Hi, dimensionless grain diameter, d/Hi, dimensionless
wave height, Hi/Wbw, dimensionless water depth, h/Hi, and lastly nondimensionalized form of parameter of interest A as the dimensionless
dependent parameter. Here, k is the wave number which is a function of
Hi and T.
When comparing the dimensionless parameters given in the
preceding paragraph with those introduced by Sumer et al. (2005),
the two sets of parameters are mostly harmonious; however, several
differences exist. The present study uses surface observables wave
height (Hi) and wave period (T) instead of water velocity (U) and
870
D.M. Young, F.Y. Testik / Coastal Engineering 56 (2009) 868–875
Fig. 2. Wave tank schematic: (1) linear actuator and motor; (2) breakwater; (3) wave paddle; (4) sloping beach; (5) wave absorber; (6) moveable cart assembly with wave gauges
and acoustic Doppler velocimeter (ADV). Symbols: a — depth of submergence, Wbw — breakwater crest width, Hbw — breakwater height, Hi — incident wave height just offshore of
breakwater, ε — amplitude of wave paddle excursion, T — wave period, h —water depth offshore of breakwater. Notes: d1 = 50 cm, d2 = 100 cm.
wavelength (Li) as independent parameters due to practical purposes
and ease of use. The angle of breakwater face (α) is not considered as
an independent parameter since the breakwaters' faces were either
vertical or circular in this present study. Moreover, breakwater crest
width, Wbw, is also considered as an important geometric parameter
in this study, which is not considered by Sumer et al. (2005).
3. Experimental setup and methodology
The experiments are carried out in a wave tank (12 m ×
0.6 m × 0.6 m) that mimics the oceanic coastal zone (see Fig. 2 for a
sketch of the wave tank). The tank consists of a beach with adjustable
sandy slope (0–1:20), a wave generator assembly, and walls
composed of 1 cm thick Plexiglas for visualization.
The offshore face of the breakwater is set as the x-axis origin with
the positive x-direction being offshore. The bottom of the wave tank is
set as the z-axis origin with the positive z-direction set towards the
water surface. Six spatial locations onshore and offshore of the
breakwater (see Fig. 2) are used in measuring wave elevations and
water particle velocities. Velocities are measured at each location
0.1 m above the initial sand–water interface while the wave heights
are measured at locations offshore of the breakwater.
The sediment used in the experiments is quartz sand with a
median diameter (d) of 0.67 mm, a mean diameter of 0.58 mm, and a
density of 2650 kg m− 3. The standard deviation of the size of the sand
sample is 0.465 and indicates that the sand is well sorted (Dean and
Dalrymple, 2004). According to Dean and Dalrymple (2004), typical
sand sizes of U.S. beaches are between 0.15 mm and 2 mm (mean
diameter); a range which includes the mean sediment diameter of the
current study (0.58 mm). The mobility parameter is the governing
dimensionless parameter that relates the sediment and flow characteristics to sediment transport characteristics. Therefore, particular
attention is given to match our laboratory experimental mobility
parameter values with the typical values for oceanic coastal regions in
order to reproduce the oceanic coastal sediment transport characteristics in the laboratory environment as close as possible. Note that for
typical oceanic conditions of d = 1 mm, Hi = 1 m, and T = 7.5 s,
mobility parameter value can be estimated to be around 16. In our
experiments, the value of the mobility parameter is varied from 6.3 (a
value that is slightly larger than the critical mobility parameter value
of 4–5 for the initiation of sediment motion) to 58.5 (a value that
corresponds to storm conditions); hence, covering a broad range of
oceanic mobility parameter values.
The wave generator consists of a computer-controlled linear
actuator coupled with a wave paddle. The wave generator can achieve
accelerations up to 6 m s− 2 and velocities up to 1.5 m s− 1. The
precision of the wave paddle motion is 2 µm. A computer code in
LabView is written to control the wave generator. Two submerged
semicircular breakwaters and four submerged vertical breakwaters
are used in this study. The vertical breakwaters are constructed of
oriented strand board and the semicircular breakwaters of PVC pipe
(see Table 1 for breakwater dimensions). The length of each breakwater is set equal to the width of the tank due to the two-dimensional
nature of the study. The breakwaters are also built to allow for a height
adjustment in order to provide a larger range of experimental
parameters.
In order to collect information regarding flow field characteristics
and sediment transport, several experimental apparatuses are used.
The principle measurements of interest are flow velocities, water
surface profiles, and sand surface profiles. Flow velocity measurements are taken using a 10 MHz acoustic Doppler velocimeter (ADV)
from Sontek/YSI. The ADV provides three-dimensional velocity
components at the sampling volume 0.05 m below the probe tip by
using a physical principle called the Doppler Effect. The ADV is capable
of a sampling rate of 25 Hz with an accuracy of 1%. Water surface
elevation data are collected by three capacitance-type wave gauges
that are capable of sampling data at a rate of 50 Hz with an accuracy of
0.001 m and a measurement range of 0.005–1 m. Each wave gauge is
located at a different along slope location and voltage readings from
each gauge are acquired simultaneously. Incident wave heights used
in the scour parameterizations are measured at a location 0.5 m
offshore of where the breakwater face would be located. It should be
noted that incident wave characteristics are measured in the absence
of the breakwater in order to simulate field construction (i.e., prebreakwater) conditions. Following a standard procedure, these readings are then converted to water surface elevations by using a
calibration curve. A Laser Displacement Sensor (LDS) is used to collect
sand surface elevation data. The LDS measures distance by emitting a
laser beam that reflects off any solid surface within its measurement
range. The LDS is coupled with a linear actuator that moves it
horizontally along the length of the tank above the water surface (see
Table 1
Breakwater dimensions.
Breakwater Name
Type
Wbw (cm)(a)
Hbw (cm)(b)
Radius (cm)
SC-1
SC-2
V-1
V-2
V-3
V-4
NB
Semicircular
Semicircular
Vertical
Vertical
Vertical
Vertical
No breakwater
28
50
15
8
17
30
–
23
30
23
30
30
30
–
15
30
–
–
–
–
–
(a)
(b)
Wbw — breakwater crest width.
Hbw — breakwater height.
D.M. Young, F.Y. Testik / Coastal Engineering 56 (2009) 868–875
Fig. 2). The actuator is 0.75 m in length and is able to move in
increments of 0.025 mm, resulting in 30,000 available positions to
collect sand surface elevation data along the length of the actuator.
The sampling rate of the LDS is set constant at 1000 samples/s and the
actuator velocity is varied to alter the number of samples per inch. A
LabView code was written to acquire data and control the velocity,
position, and acceleration/deceleration of the actuator and LDS
system simultaneously.
Before each experiment, several preparatory tasks are completed
to ensure consistency and accuracy. First, the appropriate breakwater
is installed at a specific distance from the wave paddle and the beach is
formed as either a 1:20 sloping beach or a flat beach. Then, an LDS scan
of the beach is conducted over a length of 4 m (from x = −2 m to
x = 2 m) to obtain the initial sand elevation profile. Finally, the tank is
filled with water to a depth of 0.3 m to 0.40 m in front of the wavepaddle and the wave gauges' initial voltages are recorded from the
computer to be used as the reference to the still water level in the
tank.
Because preliminary experiments revealed negligible changes in
velocity and wave elevations due to changing bottom morphology,
velocities and wave elevations were measured after approximately
3000 waves. Wave elevation measurements are collected at x = 0.5 m,
1 m, 1.5 m, 2 m from the breakwater face (measurement locations can
be seen in Fig. 2) for 40 wave periods at each location in order to
spatially profile wave development and to calculate wave reflection.
The ADV is then used to collect 40 wave periods of velocity data 0.1 cm
above the sandy bed at the same locations. Once the raw velocity and
wave elevation data are collected, a MATLAB code is used to periodaverage the data for 40 wave periods. Once the experiments are
completed, the tank is drained slowly so as not to disturb the bedform
morphology. A final LDS profile scan over the same distance as the
initial scan (from x = − 2 m to x = 2 m) is completed in order to
gather data on bottom morphology around the breakwater, in
particular data on breakwater-induced scour formation.
The number of dimensionless parameters relevant to the problem
discussed in Section 2 is too large for a systematic experimental study.
Therefore, preliminary experiments were conducted to identify the
primary governing dimensionless parameters. These preliminary
experiments indicated the importance of only two of the dimensionless parameters: the Keulegan–Carpenter number (KC) and the
mobility number (ψ). Consequently, experiments were conducted
for a wide range of these dimensionless parameters to elucidate the
functional dependences of equilibrium scour characteristics on the
relevant dimensionless parameters. Experimental conditions are
summarized in Table 2 (see also Fig. 8, later). Note that in the
calculation of these dimensionless parameters, experimental incident
wave height measurements are employed.
4. Breakwater-induced onshore scour
This section describes the two-dimensional scour formations
onshore of the submerged breakwaters. Scour formations offshore of
submerged breakwaters are studied in detail by Sumer et al. (2005).
Therefore, this study and the study by Sumer et al. (2005) form a
complimentary set of two studies that is expected to be useful for
practical submerged breakwater applications.
Two different onshore scour patterns/regimes with different
characteristics are identified in the experiments: attached scour and
detached scour. Definition sketches and typical scour profiles obtained
by LDS scans for these two scour regimes are given in Figs. 3 and 4,
respectively. Onshore scour is classified as attached scour when the
scour hole is connected to the onshore face of the breakwater while
detached scour occurs when the scour hole is not connected to the
breakwater (see Figs. 3 and 4). For both scour regimes, the important
scour characteristics of engineering importance are scour length (Ls),
maximum scour depth (Smax), and the distance of Smax location from
871
Table 2
Experimental conditions.
Exp#(a)
BW
h
T
name(b) (cm) (s)
Hi
KC Ψ
(cm)(c)
Ds
Smax m(d)
Ls
(cm) (cm) (cm)
Scour
type
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
SC-1
SC-2
V-1
V-3
V-4
NB(e)
SC-1
SC-2(f)
V-1
V-3
V-4
NB(e)
SC-1
SC-2
V-1
V-3
V-4
NB(e)
SC-1
SC-2
V-1
V-3
V-4
NB(e)
SC-2
V-3
V-4
NB(e)
V-3
V-3
V-3
V-3
V-3
V-3
V-3
V-3
V-2
V-2
V-2
13.9
13.9
13.9
13.9
13.9
13.9
9.9
9.9
9.9
9.9
9.9
9.9
13.0
13.0
13.0
13.0
13.0
13.0
13.9
13.9
13.9
13.9
13.9
13.9
8.0
8.0
8.0
8.0
17.3
18.9
16.3
18.1
19.8
20.4
20.0
22.1
16.3
20.4
22.1
45.1
48.8
48.5
39.5
51.4
12.9
18.2
14.3
13.2
18.4
3.4
4
2.5
1.7
2.2
a
a
a
a
a
40.5
14.6
1.8
34.7
29
33.6
10.8
11.2
10.8
1.8
1.4
1.8
32.4
45.1
39
37.8
37.7
8.2
20.1
15
12.8
20.2
1.8
2.7
1.7
1.4
1.1
48.8
56.7
39.4
46.6
38.9
10.1
15.0
11.2
14.0
14.2
3.0
2.2
2.1
1.9
2.5
25.3
30.2
34.1
1.7
11.5
11.5
1.6
1
1.6
24.0
26.2
32.1
32.0
32.3
30.1
41.0
36.0
26.0
32.2
33.1
40.1
48.0
52.0
62.1
63.0
55.1
64.0
67.2
52.1
59.1
67.0
4
3.8
3.8
4
5.5
4.5
5.5
5.4
3
5
6.4
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
1.33
1.33
1.33
1.33
1.33
1.33
2.00
2.00
2.00
2.00
2.00
2.00
1.33
1.33
1.33
1.33
1.33
1.33
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
1.45
1.50
1.80
1.90
1.90
1.70
1.95
1.98
1.80
1.70
1.98
1.6
0.9
2.9
2.6
1.5
1.1
0.6
2.1
1.8
1.0
1.5
0.8
2.7
2.4
1.4
1.6
0.9
2.9
2.6
1.5
0.5
1.5
0.8
3.2
3.5
3.0
3.3
3.7
3.8
3.7
4.1
6.4
8.0
8.7
13.0
13.0
13.0
13.0
13.0
13.0
12.4
12.4
12.4
12.4
12.4
12.4
6.7
6.7
6.7
6.7
6.7
6.7
19.2
19.2
19.2
19.2
19.2
19.2
6.3
6.3
6.3
6.3
26.2
33.6
26.7
33.8
54.2
42.0
50.7
54.7
26.7
42.0
58.5
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
0
0
0
0
0
0
0
0
0
0
0
0
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
1:20
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
d
d
d
d
d
d
d
d
d
d
d
Notes: For scour type column: a — attached scour; d — detached scour.
(a)
Exp. # — experiment number.
(b)
BW name — breakwater name.
(c)
Hi — incident wave height 50 cm offshore of breakwater's face.
(d)
m — beach slope.
(e)
NB — no breakwater installed.
(f)
— scour measurement error; therefore, not included.
the onshore breakwater face (Ds). Hence, in this study quantitative
scour modeling efforts are focused on identifying the conditions for
the occurrence of each scour regime and estimation of the values of
the aforementioned scour characteristics.
The principal factor in the selection of the scour regime is
concluded to be the Keulegan–Carpenter number (KC), and the
following conditions determine the scour type:
attached scour : KC =
Hi π
Vπ
Wbw
detached scour : KC =
Hi π
Nπ
Wbw
ð3Þ
ð4Þ
Two-dimensional scour formation onshore of a submerged breakwater is driven by the turbulent jet formed by the breaking wave.
Generated turbulence and complex fluid motion exert shear stress on
the sea bottom, which causes sediment suspension and transport at
the breaking zone and within the swash zone (Suzuki et al., 2007) (see
also Fredsøe and Sumer, 1997 for the analogy between the breaker
induced scour and submerged vertical jet induced scour). Attached
872
D.M. Young, F.Y. Testik / Coastal Engineering 56 (2009) 868–875
Fig. 3. Definition sketch for scour patterns and parameters: (a) attached scour, (b) detached scour.
scour occurs when the incident wave height at the breakwater is less
than or equal to the crest width of the breakwater. In this case, the
turbulent jet formed by the breaking wave impacts on the crest of the
breakwater, thereby scouring sediment starting from the immediate
vicinity of the onshore face of the breakwater. The scoured sediment is
transported onshore of the scour gap and may be deposited along an
extended stretch of the sandy slope until the shoreline rather than a
localized accumulation in the form of a hump. In Fig. 4a, a typical sand
surface elevation profile of an attached scour gap is presented.
However, the accumulation of scoured sediment cannot be seen in this
figure as the scoured sediment is deposited beyond the extents of the
viewing frame. On the other hand, for detached scour, the large
coherent vortex formed by a breaking wave whose height is larger
than the crest width of the breakwater will scour sediment that lies
farther away from the onshore face of the breakwater, forming the
primary scour area. Scoured sediment from this area is mainly pushed
offshore towards the breakwater by this vortex, causing sediment
accumulation at the onshore face of the breakwater, forming the
primary deposition area. A relatively small amount of this scoured
sediment is transported to the onshore vicinity of the primary scour
area by the vortex, forming a small secondary deposition area. As the
vortex moves onshore, it continues to scour sediment and pushes it
offshore, forming a secondary scour area just onshore of the secondary
deposition area. The secondary scour area, which lies beyond the
extents of the viewing frame of Fig. 4b, is characterized by a large
length and shallow depth, and partially supplies the sediment
deposited in both deposition areas. The primary scour area and the
primary and secondary deposition areas can be clearly seen for the
detached scour regime in Fig. 4b.
While the maximum scour depth (Smax) does not depend on the
scour regime, scour length (Ls) and the distance of Smax location from
the onshore breakwater face (Ds) do depend on the scour regime.
Semi-empirical parameterizations for Smax, Ls, and Ds are elucidated
below.
Analysis of the experimental
data showed that the dimensionless
maximum scour depth
Smax
Wbw
is a function primarily of the Keulegan–
Carpenter number and the mobility number only. The dimensionless
maximum scour depth is observed to vary linearly with the KC and to
the one half power with ψ, indicating that maximum scour depth is a
4.1. Maximum scour depth, Smax
The maximum scour depth is defined as the maximum vertical
difference between the initial sand level (t = 0 min) and the final sand
level (after ~ 3000 waves) in the scour hole onshore of the breakwater.
Fig. 4. Initial (dashed line) and final (solid line) beach profiles: (a) attached scour
(Exp #4, KC = 2.6, Hi = 13.9 cm, T = 1.33 s, 1:20 slope); (b) detached scour (Exp #35,
KC = 3.7, Hi = 20.0 cm, T = 1.95 s, 1:20 slope).
D.M. Young, F.Y. Testik / Coastal Engineering 56 (2009) 868–875
S
Fig. 5. Relationship between Wmax and ψ0.5KC. Solid line — estimate by Eq. (5); symbols —
bw
measured values.
quadratic function of incident wave height. Since wave height and
maximum flow velocity are related linearly from linear wave theory, it
can be concluded that maximum scour depth is a quadratic function of
maximum flow velocity; hence, a linear function of drag force.
Therefore, as the incident wave height increases, the breaking waves
impart a larger force on the localized onshore sediment, causing deeper
scour. The proposed semi-empirical parameterization for the dimensionless maximum scour depth is given by Eq. (5).
Smax
0:5
= 0:0125W KC
Wbw
ð5Þ
The dimensionless maximum scour depth data from all of the
experiments are presented in Fig. 5. Since the scour regime does not
factor into the maximum scour
depth value, the estimate by Eq. (5)
(solid line) fits well to the
Smax
Wbw
4.2. Scour length, Ls
L
Fig. 6. Comparison of W s measurements (symbols) and estimates (solid lines). Solid
bw
line where KC ≤ π is estimated by Eq. (6) and solid line where KC N π — is estimated by
Eq. (7). Solid squares — attached scour measurements; open squares — detached scour
measurements. Dashed line at KC = π indicates the separation between attached and
detached scour regimes.
4.3. The distance of Smax location to the onshore breakwater face, Ds
Even though the maximum scour depth is observed to be
independent of the scour regime, the distance of Smax location from the
onshore breakwater face (Ds) is observed to depend on the scour regime.
Similar to the dimensionless scour length, Ds scaled by the breakwater
crest width is found to be linearly proportional to KC with different
proportionality constants for each scour regime [see Eqs. (8) and (9)].
attached scour :
Ds
1
= KC
Wbw
π
ð8Þ
detached scour :
Ds
= KC
Wbw
ð9Þ
observations for both attached and
detached scour regimes (symbols).
Dimensionless scour length
Ls
Wbw
Comparison
of the measured (symbols) and estimated (solid lines)
Ds
Wbw
is observed to be a linear
function of the Keulegan–Carpenter number with different proportionality constants for the attached and detached scour regimes [see
Eqs. (6) and (7)]. Note that dependency of scour length on KC has been
documented previously for piles (Carreiras et al., 2000; Mory et al.,
2000) and cylinders (Voropayev et al., 2003; Testik et. al., 2007) with
different functional forms.
attached scour :
Ls
= KC
Wbw
ð6Þ
detached scour :
Ls
KC
=
Wbw
2
ð7Þ
873
values from experimental runs with both attached and
detached scour regime occurrences
are presented in Fig. 7. Since the
scour
regime factors into the
Ds
Wbw
Ds
Wbw
value, Eq. (8) is used to estimate
when
KC ≤π (i.e., attached scour regime) while Eq. (9) is used
to estimate
Ds
Wbw
when KC N π (i.e., detached scour regime). As can
be seen in the
figure,
the transition zone is associated with a sudden
D
values from one regime to the other similar to the
jump in the W s
bw
dimensionless scour length observations presented in Fig. 6.
Fig. 6 shows a comparison of the measured (symbols) and estimated
(solid lines) dimensionless scour length data from experimental runs
with both attached and detached scour regime occurrences. Since the
scour regime factorsinto the
dimensionless scour length value, Eq. (6)
is used to estimate
Ls
Wbw
when KC ≤π(i.e., attached scour regime)
while Eq. (7) is used to estimate
Ls
Wbw
when KC N π (i.e., detached
scour regime). In Fig. 6, it can be seen that the transition zone between
attached and detached scour regimes (i.e. vicinity of the regime
separation point, KC =π or Hi =Wbw) is characterized by a sudden
change in the dimensionless scour length value from one regime to the
other. Collected data points close to the regime separation point
indicate that accuracy of the proposed dimensionless scour length
parameterizations decrease around this discontinuity.
D
Fig. 7. Comparison of W s measurements (symbols) and estimates (solid lines). Solid
bw
line where KC ≤ π is estimated by Eq. (8) and solid line where KC N π — is estimated by
Eq. (9). Solid squares — attached scour measurements; open squares — detached scour
measurements. Dashed line at KC = π indicates the separation between attached and
detached scour regimes.
874
D.M. Young, F.Y. Testik / Coastal Engineering 56 (2009) 868–875
5. Discussions and conclusions
This study provides a fundamental analysis of the effects of
submerged vertical and semicircular breakwaters on the scour development. The primary goal of the conducted research is to provide accurate
parameterizations for estimating the geometrical characteristics of the
two-dimensional onshore scour induced by the breakwater. Results of
this study are expected to be useful in the conceptual design of
submerged semicircular and vertical breakwaters.
When introducing a structure to a coastal environment, it is
important to consider the alterations in the local sediment transport.
A common cause for breakwater failure is scour, or the removal of
sediment by altered hydrodynamic forces. Breakwater-induced
onshore scour by bed-load sediment transport mode is studied and
two different scour regimes, attached and detached scour regimes, are
identified. Scour is classified as attached scour when the scour hole is
connected to the onshore breakwater face and as detached scour
when the scour hole is not connected to the onshore face of the
breakwater. Selection of the scour regime is governed by the KC
Hi π
) value of the flow. Attached scour occurs when KC value is
(= W
bw
less than or equal to π while detached scour occurs when KC value is
greater than π [see Eqs. (3) and (4)]. Therefore, detached (attached)
scour occurs when the height of the incident wave is larger than (less
than or equal to) the crest width of the breakwater. Given the
relatively small KC values in the field, attached scour is much more
likely on a daily basis. However, the occurrence of detached scour is
still possible for submerged breakwaters with small crest widths
under large amplitude waves. Examples of submerged breakwaters
with small crest widths (from 2 m to 4.6 m) can be found in
Ranasinghe and Turner (2006) and Dean et al. (1997). Moreover,
Lamberti et al. (2005) document emerged breakwaters with crest
widths from 2 m to 5 m. These breakwaters have an emergence height
of about 1 m, and considering tidal variations in the field a comparison
to the current study is possible. In many cases, storm-type wave
heights can surpass three meters in height, which would make
detached scour regime possible. Moreover, from the evolution of
breakwater design and construction point of view, a breakwater with a
smaller crest width may be more desirable for some cases as it would
allow for less construction cost while producing similar wave
reflection results. Therefore, detached scour results of this study
may serve as a preliminary resource for new breakwater concepts
with narrower crests. The finding on the field conditions necessary for
the occurrence of each regime is expected to be useful to coastal
engineers designing a breakwater that induces either of these
reported scour regimes under design wave conditions. For example,
attached scour may be preferable to reduce the length of the armoring
layer from the breakwater face while detached scour may be
preferable for a reduced sliding failure threat.
Three principle onshore scour characteristics that were studied are
maximum depth of scour (Smax), length of scour (Ls), and distance of
Smax location from the onshore breakwater face (Ds). These three
scour geometrical characteristics are important in analyzing a breakwater project for potential failure. An important conclusion of the
study is that the breakwater shape plays no role in determining the
scour characteristics. It is also concluded that the beach slope does not
have a noticeable effect on the scour characteristics. However, it
should be noted that developed scour parameterizations involve
incident wave characteristics in the vicinity of the breakwater location
along the slope; hence, effects of wave transformations (e.g., shoaling)
associated with the sloping beach are already included in these
parameterizations. It is observed that Smax value does not depend on
scour regime and is determined by KC and ψ [Eq. (5)]. On the other
hand, Ls and Ds values are observed to depend on the scour regime
and are determined by KC solely [Eqs. (6)–(9)]. From physics point of
view, one would expect to observe smaller scour characteristics,
especially scour depth, as the value of a/Hi increases and vice-versa.
Fig. 8. Hai and KC values for all experimental runs. The number next to each data point is
the mobility number for the associated experimental conditions.
However, Eqs. (5)–(9) do not include this expected dependency
explicitly, yet provide accurate predictions for scour characteristics.
Working out from Fig. 8, it can be shown that the dimensionless
parameters a/Hi and W0:5 KC are correlated for the range of experimental parameters studied (see Table 2 and Fig. 8). Therefore it is
possible that Fig. 5, in fact Eq. (5), is picking up the dependence of Smax
on a/Hi for this range. This statement may be extended to Ds and Ls. In
Fig. 8, values of dimensionless submergence depth, Keulegan–
Carpenter and mobility parameters for each of our experimental
runs are presented. One might consider the experimental range of KC
to be limited; considering that there are only four experimental runs
with KC values larger than 4. However, it was the authors' purpose to
focus on this KC parameter range as KC values larger than 4 are less
likely to occur in the field.
The proposed dimensionless scour length parameterization for the
attached scour [Eq. (6)] is π times larger than the dimensionless scour
length parameterization proposed by Voropayev et al. (2003) for the
scour onshore of a horizontal cylinder. The basis of this difference is
that the study by Voropayev et al. (2003) focused on scour in the
shoaling zone, where oscillatory motion is well defined, thereby
limiting the scour length. In contrast, our present study focused on
scour in the surf zone where oscillatory motion is weaker and breakerinduced vortices propagate further onshore.
Maximum scour depth alone is not enough to predict breakwater
failure due to overturning or sliding. The distance of the maximum
scour depth from the breakwater face allows engineers to determine
the amount of supporting sand that might remain at the breakwater
after dynamic equilibrium is reached on the seafloor. The closer the
maximum scour depth is to the breakwater, the more likely the
breakwater will be unable to resist the tilting and sliding forces
D
imparted on it by the waves. The L s ratio for attached scour is
s
calculated to be equal to π1 indicating that the location of the maximum
scour depth will occur at a distance approximately equal to one-third
of the length of scour. For the detached scour regime, it is possible for
D
Ds to be larger than Ls. and the L s ratio is calculated to be a constant
s
value of 2.
The importance of breakwaters cannot be overstated. The financial
advantages of establishing these breakwaters as part of a comprehensive beach nourishment plan, together with their obvious use as
environmental support systems, can positively impact vulnerable
coastlines in times of need. In fact, surveys of Italian beachgoers
indicate “that coastal visitors are sensitive to the protection of coastal
sites from erosion and flooding and that they are generally in favor of
defense projects” (Polome et al., 2005). The authors expect this
sentiment to be echoed across many coastal areas. Submerged
breakwaters serve both these purposes while remaining hidden
D.M. Young, F.Y. Testik / Coastal Engineering 56 (2009) 868–875
beneath the water surface and maintaining attractive aesthetics. This
study, investigating the principal factors of breakwater-induced scour,
presents solutions for the onshore scour characteristics. It is expected
that these innovative concepts will be used by civil engineers in their
continuously difficult and admirable endeavor of protecting
coastlines.
Acknowledgments
This research was supported by the funds provided by College of
Engineering and Science at Clemson University to the second author.
This work is part of the M.Sc. thesis of the first author conducted under
the guidance of the second author. The authors are grateful to the
anonymous referees for their valuable comments.
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