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The necessity to implement solutions that guarantee the protection and recovery of the coastal area makes that the submerged breakwater employment is evaluated as a viable variant of application because these works contribute to the conservation of the nat ural and aesthetic conditions of the beaches, which is part of the tourist product that is marketed. However, the parameters that intervene in their functional design are not very well established, propitiating in many cases circulation patterns in the cur rents that contribute to the erosion and the degradation of the coast. The present work is part of the development of the Coastal and Marine Engineering System (SICOM) that carries out the Hydraulic Investigations Center of the Technological University of Havana, centered in to simulate so much the hydrodynamic changes as morphological that happen in the Cuban beaches before the presence of submerged breakwater, and in obtaining the design parameters for the employment of these works in the mitigation of th e erosion of the beaches, using numeric models as predictive tools.
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2022, Instituto Mexicano de Tecnología del Agua
Open Access bajo la licencia CC BY-NC-SA 4.0
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Tecnología y ciencias del agua, ISSN 2007-2422, 13(1), 377-426. DOI: 10.24850/j-tyca-2022-01-09
DOI: 10.24850/j-tyca-2022-01-09
Articles
Determination of design parameters of submerged
breakwater by means of numeric simulation for their
employment in beaches
Determinación de parámetros de diseño de rompeolas
sumergidos mediante simulación numérica para su
empleo en playas
Kenia Hernández-Valdés1, ORCID: https://orcid.org/0000-0003-0373-
2592
Luis Fermín Córdova-López2, ORCID: https://orcid.org/ 0000-0001-
8175-6819
1Inversiones Gamma S.A, La Habana, Cuba, kenia@gamma.com.cu
2Universidad Tecnológica de La Habana, Cuba,
cordova@tesla.cujae.edu.cu
Corresponding author: Kenia Hernández-Valdés, kenia@gamma.com.cu
Abstract
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Tecnología y ciencias del agua, ISSN 2007-2422, 13(1), 377-426. DOI: 10.24850/j-tyca-2022-01-09
The necessity to implement solutions that guarantee the protection and
recovery of the coastal area makes that the submerged breakwater
employment is evaluated as a viable variant of application because these
works contribute to the conservation of the natural and aesthetic
conditions of the beaches, which is part of the tourist product that is
marketed. However, the parameters that intervene in their functional
design are not very well established, propitiating in many cases circulation
patterns in the currents that contribute to the erosion and the degradation
of the coast. The present work is part of the development of the Coastal
and Marine Engineering System (SICOM) that carries out the Hydraulic
Investigations Center of the Technological University of Havana, centered
in to simulate so much the hydrodynamic changes as morphological that
happen in the Cuban beaches before the presence of submerged
breakwater, and in obtaining the design parameters for the employment
of these works in the mitigation of the erosion of the beaches, using
numeric models as predictive tools.
Keywords: Submerged breakwater, morphological changes, numeric
models.
Resumen
La necesidad de implementar soluciones que garanticen la protección y
recuperación de la zona costera hace que se evalúe el empleo de
rompeolas sumergidos como una variante viable de aplicación, pues estas
obras contribuyen a la conservación de las condiciones naturales,
estéticas y paisajísticas de las playas, lo que forma parte del producto
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Tecnología y ciencias del agua, ISSN 2007-2422, 13(1), 377-426. DOI: 10.24850/j-tyca-2022-01-09
turístico que se comercializa. Sin embargo, los parámetros que
intervienen en su diseño funcional no están muy bien establecidos y llegan
a propiciar en muchos casos patrones de circulación en las corrientes que
contribuyen a la erosión y la degradación de la costa. El presente trabajo
forma parte del desarrollo del Sistema de Ingeniería Costera y Marítima
(SICOM), que lleva a cabo el Centro de Investigaciones Hidráulicas de la
Universidad Tecnológica de La Habana, centrado en simular tanto los
cambios hidrodinámicos como morfológicos que ocurren en las playas
cubanas ante la presencia de rompeolas sumergidos, y en obtener los
parámetros de diseño para el empleo de estas obras en la mitigación de
la erosión de las playas, utilizando modelos numéricos como herramientas
predictivas.
Palabras clave: rompeolas sumergidos, cambios morfológicos, modelos
numéricos.
Received: 05/22/2018
Accepted: 17/01/2021
Introduction
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The coastal zone constitutes a resource of incalculable economic and
social value that man has been using since ancient times and that has
suffered in recent years a process of significant and generalized erosion,
largely as a consequence of anthropic actions that interrupt the coastal
transport of sediments and massive urbanism, among others. This
problem is further accentuated in the context of Global Climate Change,
in which numerous factors associated with atmospheric warming and
rising mean sea levels have led to an increase in the incidence and
intensity of storms that affect the geographical area, as well as the
generalization of erosive problems, which entails great economic damage,
the significant loss of spaces and extreme risks due to coastal flooding.
The need to implement solutions that guarantee the protection of
the coastal zone, makes the use of submerged breakwaters be considered
as a viable variant of application, since these works contribute to the
conservation of the natural, aesthetic, and landscape conditions of the
beaches, together at a lower economic cost by requiring less volume of
materials. However, the parameters that intervene in its functional design
are not very well established, so, if they are not correctly modeled and
designed, they can promote circulation patterns in the currents that
contribute to erosion and degradation of the coast (Ranasinghe, Larson,
& Savioli, 2010).
In this sense, the work shows the application of the Coastal and
Maritime Engineering System (SICOM), developed by the Hydraulic
Research Center ( Hernández & Córdova, 2015; Hernández & Córdova,
2016; Córdova, Hernández, & Benítez, 2017), focused on simulating both
the hydrodynamic and morphological changes that occur on Cuban
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beaches in the presence of submerged breakwaters, and on obtaining for
the first time in the country, the design parameters for the use of these
works in the mitigation of beach erosion, using the XBeach model
(Roelvink et al., 2009), as it is capable of simulating both hydrodynamic
and morphological processes in beaches, dune beaches and barrier
beaches under high energy conditions. This model has been extended,
applied, and validated by its authors with a series of analytical and
laboratory cases and with field measurements in a large number of
beaches bordering the regional seas of the European Union. As part of the
work, the hydrodynamics of the model is previously calibrated and
validated, using the results obtained from the physical modeling carried
out in the laboratory of the University of Naples, Italy, for the case of the
breakwater design in the traditional Havana seawall.
Materials and methods
The research design was carried out in two stages:
1. Calibration and validation of the XBeach model. The calibration
and validation of the morphology of the model are reflected in Hernández
and Córdova (2016), where the options break 1 is established as an
energy dissipation model; as a gamma break index the value of 0.4; the
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value of gammax 2 as the model limiter, and as the critical submerged
slope wetslp the value of 0.3.
The hydrodynamics validation was carried out by reproducing with
the XBeach the modeling carried out in the laboratory of the University of
Naples as part of the campaign in physical models aimed at the design of
breakwaters on the traditional Havana seawall. For this, the results
obtained from the numerical modeling were compared with the values
measured by the sensors in the wave tank of the physical model, where
the characteristic profile of the traditional seawall was reproduced at 1:30
scale in a 1.56 m wide and 18.37 m long channel built inside the Random
wave Tank (RATA). The experiments were carried out with two
breakwaters, one with a wide crest with its freeboard at medium water
level and the other with a narrow crest that emerges at 0.80 m. The
coefficients of determination obtained were 0.86 for the significant wave
heights and 0.97 for the wave setup, showing that the XBeach model is
capable of correctly simulating the hydrodynamics that is generated in
the presence of submerged breakwaters.
2. Establishment of the model and simulation of the hydrodynamic
and morphological variables. A non-equidistant working mesh was
established using profiles measured on the Varadero beach to which the
equilibrium profile was determined using the expression given by García
(2005) for the sediment scale parameter, which presents a better fit for
characterizing the conditions of Cuban biogenic beaches (Figure 1). The
mesh covers an area of 492 000 m2 comprised by 615 m in a
perpendicular direction to the coast with a resolution of 5 m (123 nodes)
and 800 m along the coast with a resolution of 10 m (80 nodes), with
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depths starting from the 8m isobath to reaching heights of 3 m above
mean sea level in the dune area, which allowed us to visualize the
processes that occurred in each simulation.
Figure 1. Working mesh. Source: Author's own.
Breakwaters were modeled both inside and outside the surge
breaking zone. For the analysis, the values of 0.5 m, 1.5 m, and 2.5 m as
significant wave heights with periods of 5.5 s and 6.5 s were selected,
according to the data presented in the Global Wave Statistics for the
geographic area that covers Cuba, Area 33, as observed in Table 1. Both
the normal and oblique incidence of the waves is considered.
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Table 1. Wave height and studied periods. Source: Global Wave
Statistic, Area 33.
Hs
(m)
8,5
1
7,5
1
1
1
1
6,5
1
2
3
2
1
5,5
1
5
6
5
2
1
4,5
4
12
15
10
4
2
3,5
2
13
31
32
49
7
2
1
2,5
6
37
70
59
29
10
3
1
1,5
22
90
49
74
28
7
2
0
0,5
56
96
66
25
6
1
0
0
Tm(s)
4,5
5,5
6,5
7,5
8,5
9,5
10,5
11,5
The hydrodynamic and morphological variables studied are reflected
in Table 2. The simulations were carried out by varying the variables to
know the changes that are generated on the beach, for a total of 440
variants analyzed.
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Table 2. Hydrodynamic and morphological variables to study. Source:
Author's own.
Variables
Description
Units
Hydrodynamics
Hs
Significant wave height (0.5, 1.5, 2.5)
m
Tm
Mean wave period (5.5, 6.5)
s
Ɵ
Wave incidence angle (90, 315)
°
Breakwater geometry
Lb
Length (100, 200, 300)
m
Wb
Crest wight (10, 20)
m
Sb
Submergence (-0.00, -0.50, -1.00)
m
Xb
Distance to the coast (30, 60, 90, 120,
150, 180, 210, 240, 270, 300)
m
Physical
m
Submerged beach slope (0.025)
-
D50
Mean sediment diameter (0.26)
mm
Fall velocity (4.49)
cm/s
s
Specific weight of sediment (2.716)
kg/cm3
Results
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Effect of the length of the submerged breakwater (Lb)
The most relevant results obtained from the modeling of the
hydrodynamic, breakwater geometric, and physical variables are
presented.
In Figure 2 you can see from left to right, the representation of the
simulations referring to breakwaters of lengths of 100 m, 200 m, and 300
m respectively, with a crest width of 10 m and submergence -0.5 m,
located 60 m from the coastline. The profiles where there is greater
interest for analysis were defined, which are:
Profile 41: Profile that passes through the center of the breakwater
in all variants, being called a profile with the presence of
breakwaters.
Profile 16: Profile that passes through an area far from the
breakwater and the border of the working mesh, called profile
without the presence of breakwater.
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Figure 2. Representation of the working mesh with the breakwaters
located at 60 m and waves incident perpendicular to the coast. Source:
Author's own.
The influence exerted by the breakwater on the mean square height
of the gravity waves can be assessed qualitatively and quantitatively in
Figure 3 and Table 3, observing how after interacting with the breakwater
its values decrease in all variants. It is also seen that the transmission
coefficient, which relates the transmitted and incident wave heights,
presents very similar values in the three variants, although the length of
the breakwater varies.
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Figure 3. Representation of the mean square height of gravity waves
for breakwaters of 100 m, 200 m, and 300 m in length located 60 m
from the coast. Source: Author's own.
Table 3. Transmission analysis as a function of breakwater length.
Source: Author's own.
Variants
Length
(m)
HrmsG (m)
Kt
Point 1
Point 2
2
100
0,7826
0,2466
0,32
122
200
0,7140
0,2288
0,32
212
300
0,7801
0,2397
0,31
Notice: Points 1 and 2 are located to 5 m towards the sea and toward
the coast of the crest of the breakwater respectively.
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Table 4 shows the mean square height of the gravity waves in Profile
16, without the presence of breakwaters, and in Profile 41 with the
presence of breakwaters, where the effectiveness of the breakwater can
be verified by attenuating the energy of the incident wave and the
percentage of dissipation that it guarantees.
Table 4. Mean square wave height of gravity waves in profile 16 and
profile 41. Source: Author's own.
Variants
Length
(m)
HrmsG (m)
Dissipation
(%)
Point 2
Profile 16
Point 2
Profile 41
2
100
0,6428
0,2466
61,63
122
200
0,5437
0,2288
57,91
212
300
0,5168
0,2397
53,61
When interacting with the breakwater, the speed reached by the flow
increases as a result of the strong turbulence that is generated, being
greater for the breakwater that is 100 m long (Figure 4).
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Figure 4. Flow velocities for the breakwater are located 60 m from the
coastline with lengths of 100 m, 200 m, and 300 m. Source: Author's
own.
The flow patterns are shown in Figure 5, which resemble the two-
cell erosive pattern described by Ranasinghe et al. (2010), where the red
line indicates the initial position of the coast. Although the behavior of
currents and, therefore, how the bottom changes are similar in all three
variants, the zone of influence increases the longer the breakwater length.
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Figure 5. Representation of flow patterns and bottom variation for
breakwaters located 60 m from the coast. Source: Author's own.
Figure 6 reveals how the value of the wave setup increases after
the interaction with the breakwater. Comparing the setup around the
coastline, it is noted how this variable decreases in the three variants
analyzed just in the center of the sheltered zone, where Profile 41 transits.
Table 5 shows the setup in Profile 16 without the presence of breakwaters
and in Profile 41 with the presence of breakwaters, both for point 1 located
5 m after the breakwater crest has been surpassed, and for point 2 located
on the coastline. In it, it can be seen how in Profile 16 the values of the
setup at point 2 when reaching the coast are higher than for the variant
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with breakwaters, which can be seen in Figure 6, where the red line
represents the initial position of the coast.
Figure 6. Representation of the setup Zs for the breakwaters located 60
m from the coast with lengths of 100 m, 200 m, and 300 m. Source:
Author's own.
Table 5. Wave setup in Profile 16 and Profile 41. Source: Author's own.
Variants
Length
(m)
Profile 16
Profile 41
Point 1
Point 2
Point 1
Point 2
2
100
0,1133
0,2283
0,1101
0,1709
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122
200
0,1447
0,1899
0,1271
0,1803
212
300
0,0413
0,2430
0,1049
0,1484
The red line in Figure 7 shows the position of the coast before the
location of the breakwater, attesting to the morphological changes
suffered by the bottom and the erosive process that occurred. The
currents generated by the presence of the breakwater, transport the
sediments found in the sheltered area out to sea, creating at its end’s
areas of greater depth and the erosion of the coastline throughout the
beachfront. The formation of scour at the ends of the breakwater shelter
area can affect their stability causing abrupt failure and coincides with the
research developed in physical models by (Papadopoulos, 2012).
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Figure 7. Representation of sediment transport and bottom variation.
Source: Author's own.
The resulting profile that passes through the center of the
breakwater for the analyzed variants, shows the morphological evolution
of the seabed, where the coastline presents sediment loss and retreat, as
seen in Figure 8. For the 100 m long breakwater, the profile undergoes a
greater erosive process, which is associated with the speeds reached by
the currents.
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Figure 8. Evolution of the seabed for breakwaters of 100 m (left), 200
m (center), and 300 m long (right). Source: Author's own.
Effect of the crest width (Wb)
Figure 9 shows the simulations of breakwaters of 100 m, 200 m, and 300
m in length, with a crest width of 20 m and submergence -0.5 m, located
at 60 m with waves incident perpendicular to the coast. Table 6 shows
the mean square wave height of the gravity waves obtained. Its values
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prove that the transmission coefficient is lower compared to the 10 m
wide variants, being the breakwater more effective in dissipating the wave
height, which coincides with the study of Makris and Memos (2007).
Figure 9. Working mesh with breakwaters of 20 m crest width and
lengths of 100 m, 200 m, and 300 m located 60 m from the coast.
Source: Author's own.
Table 6. Analysis of the transmission as a function of the crest width of
the breakwater. Source: Author's own.
Variants
Hrms (m)
Kt
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Length
(m)
Width of
breakwaters
(m)
Punto 1
Punto 2
2
100
10
0,7826
0,2466
0,32
92
20
0,8183
0,2197
0,27
122
200
10
0,7140
0,2288
0,32
392
20
0,7867
0,2172
0,28
212
300
10
0,7801
0,2397
0,31
402
20
0,8055
0,2177
0,27
Note: Points 1 and 2 are located 5 m towards the sea and the coast of the breakwater
crest respectively.
Figure 10 reflects the relationship of the dimensionless parameter
Wb / Hi and the transmission coefficient Kt, for the breakwaters of 100
m, 200 m, and 300 m in length located in the different positions studied.
As can be seen, the highest transmission coefficient values correspond to
breakwaters with a crest width of 10 m, while they decrease significantly
for breakwaters that are 20 m wide.
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Figure 10. Relationship between the dimensionless parameter (Wb / Hi)
and the transmission coefficient Kt, for breakwaters of 10 m and 20 m
wide. Source: Author's own.
Table 7 can observe the speed of the flow reached by the waves in
their interaction with the breakwater. When comparing the variants with
widths of 10 m and 20 m, it is appreciated how it is greater for the latter,
due to the turbulence that is generated by the increase in wave breakage.
Table 7. Flow velocities when interacting (Point 1) and after interacting
with the breakwater (Point 2). Source: Author's own.
Variants
Length (m)
Speed (m/s)
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Width of
breakwaters
(m)
Punto 1
Punto 2
2
100
10
1,2546
0,4467
92
20
1,6576
0,5511
122
200
10
0,5803
0,3137
392
20
0,6180
0,4264
212
300
10
0,2050
0,1299
402
20
0,4631
0,1204
Regarding the flow and circulation patterns of the currents, the
analyzed variants are erosive in nature. In Figure 11 these patterns are
observed, with the retreat of the coastline for both the 10 m wide crest
breakwater and the 20 m wide breakwater, with the latter being more
pronounced, where the red line represents the initial position of the coast.
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Figure 11. Current circulation patterns for the 100 m long breakwater
located 60 m from the coast. Left: variant 10 m wide. Right: variant 20
m wide. Source: Author's own.
Table 8 shows the surge elevation in Profile 16 without the presence
of breakwaters and in Profile 41 with the presence of breakwaters, both
for point 1 located 5 m from the crest of the breakwater and at point 2
located on the coastline, corresponding to breakwaters 20 m wide. When
comparing the values with those given in Table 5 for the 10 m wide
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breakwaters, it is observed how the sea-level rise on the coastline
increases, which can be seen in Figure 12.
Table 8. Sea level rise in Profile 16 and Profile 41 for breakwaters of 20
m wide crest. Source: Author's own.
Variants
Length
(m)
Profile 16
Profile 41
Punto 1
Punto 2
Punto 1
Punto 2
92
100
0,0857
0,1899
0,1756
0,2129
392
200
0,1628
0,2066
0,1429
0,1951
402
300
0,1244
0,2052
0,2409
0,1676
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Figure 12. Wave setup for 20 m wide breakwaters located 60 m from
the coast with lengths of 100 m, 200 m, and 300 m. Source: Author's
own.
When observing the behavior of Profile 41, which passes through
the center of the 100 m long breakwater, the morphological evolution of
the seabed is noted, where the coastline presents loss of sediment and
retreat, as seen in Figure 13. For the 20 m wide breakwater, there is
marked erosion throughout the profile, which intensifies at its base due
to increased flow velocities, which could cause the failure of the structure.
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Figure 13. The behavior of the bottom. Right: Breakwater 10 m wide.
Left: Breakwater 20 m wide. Source: Author's own.
Effect of submergence (Sb)
The effect of submergence is observed through the transmission
coefficient in Figure 14, where for 0.00 m submergence breakwaters the
values decrease until very close to zero while they increase with the
increase in submergence until reaching values of 0.54 for breakwaters
with the submergence of -1.00 m.
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Figure 14. Effects of submergence on the transmission coefficient.
Source: Author's own.
Figure 15 reflects the sediment transport generated by the
presence of the breakwater located 120 m from the coast with the
submergence of 0.00 m, -0.50 m, and -1.00 m, where its effect on the
beach decreases as submergence increases, which was pointed out by
(Calabrese, Vicinanza, & Buccino, 2008) and verified by Ranasinghe et al.
(2010).
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Figure 15. Sediment transport. Left: Submergence 0.00 m. Center:
Submergence -0.50 m. Right: Submergence -1.00 m. Source: Author's
own.
Effect of wave obliquity (Ɵ)
The modeling carried out under the oblique influence of the waves,
experience a behavior similar to that obtained under the waves acting
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perpendicular to the coast, which coincides with the investigations carried
out by Vanlishout (2008) and with the proposals of Ranasinghe et al.
(2010). Table 9 and Table 10 show the transmission coefficients and wave
setup for breakwaters located 60 m from the coast with 100 m, 200 m,
and 300 m in length under the oblique action of the waves, which can be
compared with Tables 3 and 6 where the waves act perpendicular to the
coast.
Table 9. Analysis of the transmission according to the incidence of the
waves. Breakwaters with a crown width of 10 m and submergence of -
0.50 m. Source: Author's own.
Variants
Length (m)
HrmsG (m)
Kt
Punto 1
Punto 2
302
100
0.7864
0.2399
0.31
332
200
0.5452
0.1680
0.31
362
300
0.7879
0.2466
0.31
Table 10. Wave setup values. 10 m crown width breakwaters and -0.50
m submergence. Source: Author's own.
Variants
Length
(m)
Profile 16
Profile 41
Punto 1
Punto 2
Punto 1
Punto 2
302
100
0.1241
0.2329
0.1038
0.1899
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332
200
0.1130
0.1923
0.1219
0.1733
362
300
0.0532
0.2312
0.1148
0.1609
The patterns of flow and circulation of the currents present a
behavior similar to that observed for the waves acting normal to the coast,
with the retreat of the coastline for the nearby locations, as shown in
Figure 16. The morphological evolution of the seabed under the oblique
incidence of the waves can be observed in Figure 17, where the coastline
presents a behavior very similar to that obtained under the waves acting
perpendicular to the coast, with loss of sediment and retreat, which shows
that the obliquity of the waves does not exert significant influence in
coastal response mode.
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Figure 16. Current patterns for breakwaters 100 m long and 10 m wide
are located 60 m from the coast with a -0.5 m submergence. Left:
Perpendicular swell. Right: Oblique swell. Source: Author's own.
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Figure 17. Evolution of the seabed for breakwaters 100 m long and 10
m wide located 60 m from the coast with the submergence of -0.5 m.
Left: Perpendicular swell. Right: Oblique swell. Source: Author's own.
Effect of the distance to the coast of the submerged
breakwater (Xb)
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The analysis was carried out by varying the distances to the coastline,
locating the breakwaters at 30, 60, 90, 120, 150, 180, 210, 240, 270,
and 300 m apart. The effect of the breakwater placement distance on the
mean square height of gravity waves and on the transmission, coefficient
is shown in Figure 18, which decreases as the breakwater moves away
from the coast, corresponding to the lowest values in all the cases to the
20 m wide breakwaters.
Figure 18. Transmission coefficient as a function of the breakwater
placement distance from the coast for breakwaters of 100 m, 200 m,
and 300 m in length and a crest width of 10 m and 20 m.
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Figure 19 reflects the speed and circulation patterns of the currents
for the nearshore locations, where erosive two-cell patterns occur. As the
breakwater moves away from the coast, cumulative patterns of four cells
begin to appear and an advance of the coastline concerning its initial
position, highlighted by the red line, behaviors described by (Ranasinghe,
Larson, & Savioli, 2010).
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Figure 19. Circulation of currents. Left: Breakwater 90 m away and
erosive two-cell patterns. Right: Breakwater 300 m away and
cumulative four-cell patterns. Source: Author's own.
The behavior of the flow velocity patterns is confirmed in the
representation of the sediment transport given in Figure 20, which agrees
with the morphological changes suffered by the bottom and with the
position adopted by the coastline. The evolution of the seabed o ver time
is reflected in Figure 21, where the left image, corresponding to the
breakwater located 90 m from the coast, shows the erosion suffered by
the beach while the right image, for the breakwater, is located 300 m
away from the coast, it shows the accumulation of sediments and the
progress achieved.
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Figure 20. Sediment transport for breakwaters 10 m wide. Left
breakwater 90 m away from the coast and right 300 m. Source:
Author's own.
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Figure 21. The behavior of the bottom for breakwaters of 10 m wide
crest located 90 m from the coast (left) and 300 m (right). Source:
Author's own.
Figure 22 indicates the results of the movement of the coastline
(erosion/accretion) obtained depending on the location of the breakwater,
both for waves with incidence perpendicular to the coast and for waves
with oblique incidence.
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Figure 22. Response of the shoreline (erosion/accretion) as a function
of the breakwater placement distance. Source: Author's own.
Figure 23 shows how for near positions up to 100 m away, the
coastline recedes in all the studied breakwater lengths, which is
highlighted with a red box. From the 120 m separation of the breakwater
from the coast, advances in the coastline begin to be observed, although
erosive processes are also manifested, behaving as a transition zone
(green box). For positions greater than 150 m there is always an
accumulation of sediments on the beach, which can reach up to 18 m in
width and are delimited in yellow.
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Figure 23. Response of the coast (erosion/accretion) as a function of
the breakwater placement distance and its delimitation. Source:
Author's own.
The simulations varying the distance from the breakwater to the
coast, show the presence of erosive two-cell circulation patterns or
cumulative four-cell patterns, this being one of the dominant parameters
that determine the coastal response mode.
Figure 24, Figure 25, and Figure 26 show the morphological
response of the beach through the length of the shaped spit (Xs), which
varies depending on the length of the breakwater (Lb) and the distance
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concerning the original coast (Xb), through the dimensionless parameter
Lb/Xb, which constitute the main design parameters that govern the
functional behavior of these works.
Figure 24. Relationship Length of breakwater/initial distance to shore
vs. distance to resulting shoreline (Xs). Hs = 0.5 m, Tm = 5.5 s.
Source: Author's own.
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Figure 25. Relationship Length of breakwater / Initial distance to shore
vs. distance to resulting shoreline (Xs). Hs = 1.5 m, Tm = 5.5 s.
Source: Author's own.
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Figure 26. Relationship Length of breakwater / Initial distance to shore
vs. distance to resulting shoreline (Xs). Hs = 2.5 m, Tm = 6.5 s.
Source: Author's own.
The results obtained in the research allowed to establish predictive
relationships on the behavior of the coastline (erosion/accretion) based
on the dimensionless parameter (Lb/Xb), proposing a parametric model
of a potential type that responds to the general formulation:
Xs= a(LbXb
)−b
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The parameter a and the exponent b are listed in Table 11, Table 12, and
Table 13.
Table 11. Parameter a and exponent b of the potential function for
breakwaters of length Lb = 100 m. Source: Author's own.
Hydrodynamics
Submergence
(m)
a
b
Hs = 0.5 m
Tm = 5.5 s
0.00
100
-1
-0.50
99.50
-0.924
-1.00
98.91
-0.978
Hs = 1.5 m
Tm = 5.5 s
0.00
98.98
-0.970
-0.50
103.05
-0.867
-1.00
97.75
-0.956
Hs = 2.5 m
Tm = 6.5 s
0.00
100.87
-0.888
-0.50
99.88
-0.897
-1.00
102.11
-0.893
Table 12. Parameter a and exponent b of the potential function for
breakwaters of length Lb = 200 m. Source: Author's own.
Hydrodynamics
Submergence
(m)
a
b
Hs = 0.5 m
0.00
200
-1
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Tm = 5.5 s
-0.50
194.95
-0.938
-1.00
196.51
-0.978
Hs = 1.5 m
Tm = 5.5 s
0.00
189.68
-0.928
-0.50
192.97
-0.893
-1.00
196.40
-0.939
Hs = 2.5 m
Tm = 6.5 s
0.00
184.26
-0.902
-0.50
196.29
-0.973
-1.00
189.60
-0.865
Table 13. Parameter a and exponent b of the potential function for
breakwaters of length Lb = 300 m. Source: Author's own.
Hydrodynamics
Submergence
(m)
a
b
Hs = 0.5 m
Tm = 5.5 s
0.00
300
-1,00
-0.50
290.95
-0.946
-1.00
291.63
-0.965
Hs = 1.5 m
Tm = 5.5 s
0.00
285.06
-0.971
-0.50
283.60
-0.893
-1.00
290.52
-0.945
Hs = 2.5 m
Tm = 6.5 s
0.00
290.18
-0.948
-0.50
290.95
-0.986
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-1.00
289.76
-0.932
As a practical result for the use of predictive relationships, a
methodology consisting of four steps was developed, using the graphs in
Figures 24, Figure 25, or Figure 26.
1. Calculate the Lb/Xb ratio
2. Plot the relationship Lb/Xb (abscissa axis) in the graph of Figure 24,
Figure 25, or Figure 26 as appropriate with the swell and submergence
defined as starting data.
3. Obtain, by the intercept of the abscissa axis with the curve
corresponding to the breakwater length, the value Xs (distance between
the formed coastline and the breakwater) on the ordinate axis.
4. Determine the expected response of the coast by subtracting from the
initial distance to the coast Xb established in the design, the value Xs
obtained from the graph. Answer (erosion or accretion) = Xb Xs.
The application of the methodology is presented in the case study
of the Meliá Varadero hotel. This hotel is located on a rocky massif, on
both sides of which there are low terrace areas with lengths of 200 m and
altitudes between 1.6 m and 2.5 m that make access to the beach difficult
and limit its use as a bathing area (Figure 27).
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Figure 27. Location of the Meliá Varadero hotel. Source: Author's own.
The location of 100 m long submerged breakwaters is a viable
solution to stabilize the beach. It is proposed to place it separated from
the coast at a distance of 150 m with submergence of -0.50 m and a crest
width of 10 m. The values of significant wave height Hs = 1.5 m and mean
wave period Tm = 5.5 s are established.
1. Calculate the relationship Lb/Xb = 100 m / 150 m = 0.666.
2. The relation Lb/Xb = 0,666 is plotted in the graph of Figure 25, and
the intercept with the 100 m length curve is obtained.
3. Value of the intercept on the ordinate axis Xs = 138 m.
4. Since the initial distance to the coast Xb is proposed to be 150 m, with
this location the expected response of the shoreline is determined:
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Answer = 150 m -138 m = 12 m.
The coastline will undergo a cumulative process with the formation
of a 12 m wide overhang, as seen in Figure 28.
Figure 28. Formation on the beach of a 12 m wide spit due to the
location of a 100 m long submerged breakwater. Source: Author's own.
Conclusions
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The behavior of the currents and, therefore, the way the bottom changes
is similar for breakwaters with different lengths. The zone of influence
increases with the increasing length of the breakwater.
As the crest width increases, the transmission coefficient decreases,
and the water levels in the sheltered area of the breakwater decrease,
being more effective in dissipating the wave height.
The location of the breakwaters for the coast has a strong relationship
with the morphological response of the beach, highlighting erosive or
cumulative patterns.
Submergence is a parameter closely related to the transmission
coefficient and the morphology of the beach. By increasing the
submergence to levels of -1.00 m, the dissipative effect of the breakwater
decreases, so the use of submersions with values greater than -1.00 m is
not recommended.
Wave obliquity does not have a significant influence on the mode of
the response of the coast or wave transmission, obtaining results that are
very similar to those achieved with waves perpendicular to the coast.
It is determined that the functional design parameters of the submerged
breakwaters that most influence the response of the beach are the
distance to the coast, the length of the breakwater, and the submergence.
Predictive relationships are presented in the form of graphs, which
respond to a parametric model of a potential type, where the evolution
that the coastline will have according to dimensionless parameters can be
known, a methodology being developed as a practical result for the
functional design of the submerged breakwaters.
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Acknowledgments
The authors wish to thank all those people who have allowed, helped, and
collaborated with the obtaining of the results referred to in this work.
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The increment and development of investments associated with sun and beach tourism, together with population increase in coastal areas at world level, make that every day bigger importance is given to know the behavior of the interaction between the surf and the structures of coastal defense, together with the need of predicting in a quick and correct way the morphodinamics processes happening under extreme situations. The present work evaluates the capacity of the mathematical model XBeach for simulating the interaction wave - submerged breakwater by simulating the behavior of a group of hydrodynamic as well as morphological variables, which tests the capacity of the model to reproduce phenomena happening on the beaches under the presence of submerged breakwaters.
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RESUMEN El aumento creciente de la población en la zona costera unido al incremento y desarrollo de las inversiones asociadas al turismo de sol y playa, hacen que cada día cobre mayor importancia conocer el comportamiento de la interacción entre el oleaje y las estructuras de defensa costera, junto con la necesidad de pronosticar de forma rápida y correcta los procesos morfodinámicos que ocurren en las playas de arena ante situaciones extremas. El presente trabajo evalúa la capacidad del modelo matemático XBeach para simular de forma correcta la interacción oleaje – estructuras de protección costera, fundamentalmente la capacidad del modelo para reproducir los fenómenos asociados con la hidrodinámica y los cambios morfológicos en presencia de obras como espigones y rompeolas. Palabras clave: espigones, estructuras de protección costera, modelación matemática, rompeolas. Mathematical simulation of the interaction wave-coastal protection structures ABSTRACT The significant increase of the population in coastal areas together with the increment and development of the investments associated to sun and beach tourism, make that every day becomes more important to recognize the behavior of the interaction between wave and coastal defense structures, together with the necessity to predict in a quick and correct way the morphodynamic processes ocurring in sand beaches under extreme situations. The present work evaluates the capacity of the mathematical model Xbeach to correctly simulate the wave-coastal protection structures interaction, mainly its capacity to reproduce the phenomena associated with the hydrodynamic and morphology changes in the presence of groin sand breakwaters.
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The wave transmission over submerged breakwaters is investigated using existing formulae and wave models. The objective is to assess their performance and pinpoint research paths for their improvement. Application was made on a case study with two submerged detached breakwaters. It was found that some of the recent relations give satisfactory results of the transmission coefficient, while the predictability of the models tested depends on the wave breaking formulation assumed. In general, wave breaking and porosity of the structure are the most crucial factors that need further study for the improvement of the prediction of wave transmission over submerged breakwaters.
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Recently the numerical model Xbeach has been developed, able to simulate the morphological changes and the nearshore processes such as wave breaking, including dune erosion, overwashing and breaching, developed for open beaches, beaches with dunes and beaches barrier under conditions of high energy. The model solves coupled 2DH equations for wave propagation, flow, sediment transport and bottom changes, for varying (spectral) wave and flow boundary conditions. In this work it is presented the calibration and validation of Xbeach model for the case of the Varadero beach, Cuba, simulating the morphological changes happened during the hurricane Michelle in October - November of the 2001.
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In addition to reducing the incoming wave energy, submerged breakwaters also cause a setup of the sea level in the protected area, which is relevant to the whole shadow zone circulation, including alongshore currents and seaward flows through the gaps. This study examines such a leading hydraulic parameter under the simplified hypothesis of 2D motion and presents a prediction model that has been validated by a wide ensemble of experimental data. Starting from an approach originally proposed by Dalrymple and Dean [(1971). Piling-up behind low and submerged permeable breakwaters. Discussion note on Diskin et al. (1970). Journal of Waterways and Harbors Division WW2, 423–427], the model splits the rise of the mean water level into two contributions: one is due to the momentum flux release forced by wave breaking on the structure, and the other is associated with the mass transport process. For the first time, the case of random wave trains has been explicitly considered.
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Submerged breakwaters (SBWs) are becoming a popular option for coastal protection, mainly due to their low aesthetic impact on the natural environment. However, SBWs have rarely been employed for coastal protection in the past and therefore, their efficacy remains largely unknown. The main objective of the present study was to investigate the structural and environmental conditions that govern the mode of shoreline response (i.e shoreline erosion vs shoreline accretion) to SBWs. The relative importance of the key structural and environmental parameters governing the response mode to a single shore parallel SBW is investigated through a combination of theoretical analysis and numerical modelling. Using physical considerations, a theoretical response-function model is derived under several simplifying assumptions including parallel depth contours, linear wave theory, shore normal waves, and no wave–current interaction. Numerical modelling is undertaken with the Mike21 model suite to simulate the depth averaged velocity fields (without morphological updating) due to waves acting on a single shore-parallel SBW located on a schematised beach with parallel depth contours. In total 92 coupled wave–current simulations were undertaken. The results indicate that the mode of shoreline response to the SBW can be expressed in terms of the two non-dimensional parameters hB/H0 and (sB/hB)3/2(LB/hB)2(A3/hB)1/2 (variables defined in the text).
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Low crested structures are primarily designed as a coastal defence mechanism, making the prediction of the energy in the lee of the structure of utmost importance. As wave transmission is a measure for the energy that passes the breakwater, experiments on oblique wave transmission have previously been performed by the European project DELOS (Environmental Design of Low Crested Coastal Defence Structures) and analysed further by Van der Meer et al. From these experiments, it is unclear whether it is the roughness or the permeability of the core that determines the behaviour of the structure. Therefore, the objective of this study is to improve the understanding of oblique wave transmission through rough impermeable rubble mound submerged breakwaters by means of a 3D physical model. An experimental study is conducted based on the same set-up of DELOS but the permeability of the core of the rough structure will be varied. Finally, by comparing the data of this study with the data of DELOS and the formulations of Van der Meer et al., insight should be gained on the matter. In total, four structures are tested using irregular long crested waves; ranging from a fully permeable to a fully impermeable rough rubble mound breakwater. In order to test for oblique waves, the model is rotated progressively by 15°, ranging from 0° to 60°. Secondary effects due to the physical constraints of the wave basin are minimised by placing an additional mound of rubble between the model and the edge of the basin. This prevents a large scale circulation pattern from occurring and reduces wave diffraction effects. The directional spectral analysis software DIWASP is used to calculate the variance density spectra of the data. The wave climate is estimated with the IMLM method (Iterated Maximum Likelihood Method) because it is the most suited to portray the narrow directional spread. The aim of this study is to analyse the influence of the incident wave direction βi on the transmitted wave direction βt, the transmission coefficient Kt and the spectral changes of the transmitted spectrum. An analysis of the data shows that for rough structures there is no significant change in wave direction. The incident wave direction is approximately equal to the transmitted wave direction (βt=0.94βi for 0° ≤ βi ≤ 60°). The data of this study also show a slight increase in the transmission coefficient with increasing incident wave angle. However, when considering a combined data set, which includes the data of this study and the rough permeable data of DELOS, the data show that oblique wave attack has a negligible influence on the transmission coefficient for rough structures. The spectral changes of this study support the model proposed by Van der Meer et al. Finally, it is concluded that it is the roughness of the structure rather than the permeability of the core that determines the behaviour of the breakwater with respect to the incident wave direction.
Actuaciones para el control de la erosión en playas biogénicas. El caso de la playa de Varadero (tesis presentada en opción al grado científico de Doctor en Ciencias Geográficas), Instituto de Geografía Tropical
  • C García
García, C. (2005). Actuaciones para el control de la erosión en playas biogénicas. El caso de la playa de Varadero (tesis presentada en opción al grado científico de Doctor en Ciencias Geográficas), Instituto de Geografía Tropical, La Habana, Cuba.
Scour below the toe of breakwaters (thesis submitted for the degree of Master of Science in Hydraulic Engineering
  • D Papadopoulos
Papadopoulos, D. (2012). Scour below the toe of breakwaters (thesis submitted for the degree of Master of Science in Hydraulic Engineering), Delf University of Technology, The Netherlands.
Modelling storm impacts on beaches, dunes and barrier islands
  • D Roelvink
  • A Reniers
  • A Van Dongeren
  • J Van Thiel -De-Vries
  • R Mccall
  • J Lescinski
Roelvink, D., Reniers, A., van Dongeren, A., van Thiel -de-Vries, J., McCall, R., & Lescinski, J. (2009). Modelling storm impacts on beaches, dunes and barrier islands. Coastal Engineering, 56, 1133-1152. DOI: 10.1016/j.costaleng.2009.08.006