functional and environmental design of detached, low crest level breakwaters

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Functional and Environmental Design of Detached, Low Crest Level BreakwatersAuthor(s): Laura Bricio, Vicente Negro, J. Javier Diez, and José S. LópezSource: Journal of Coastal Research, 28(1A):131-142. 2012.Published By: Coastal Education and Research FoundationDOI: http://dx.doi.org/10.2112/JCOASTRES-D-10-00083.1URL: http://www.bioone.org/doi/full/10.2112/JCOASTRES-D-10-00083.1

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Functional and Environmental Design of Detached, LowCrest Level Breakwaters

Laura Bricio, Vicente Negro, J. Javier Diez, and Jose S. Lopez

Escuela de Ingenieros de CaminosCanales y PuertosUniversidad Politecnica de Madridc/ Profesor Arangurens/n. 28040 Madrid, [email protected]

ABSTRACT

BRICIO, L.; NEGRO, V.; DIEZ, J.J., and LOPEZ, J.S., 2012. Functional and environmental design of detached, low crestlevel breakwaters. Journal of Coastal Research, 28(1A), 131–142. West Palm Beach (Florida), ISSN 0749-0208.

In this article we research the design of detached breakwaters, a type of coastal defence work designed to combat erosionon beaches in a stable, sustainable fashion. Our aim is to formulate a functional and environmental (nonstructural)method of design that defines the fundamental characteristics of a detached breakwater as a function of the desired effecton the coast whilst meeting social demands and preserving or improving the quality of the littoral environment. We aimto make this method generally applicable by considering relations between variables of different natures (climatic,geomorphologic, and geometric) influencing the changes experienced on the coast after the detached breakwater hasbeen built. We carried out the study of the relations between the different variables on the data from 19 actual, existingdetached breakwaters on the Spanish Mediterranean coastline, and we followed a methodology based on theimplementation of nondimensional monomials and on a search for relations of dependency between them. Finally, wediscussed the results obtained and came up with a proposal for a design method that uses some of the graphic relationsfound between the variables studied and that achieves the main objective. For example, a case of a detached breakwater’sgeometric presizing is solved as a practical demonstration of how the method is applied.

www.JCRonline.org

ADDITIONAL INDEX WORDS: Detached breakwater, functional design, tombolo, salient.

INTRODUCTION

The coast forms a narrow strip under heavy pressure

subjected to large imbalances as a consequence of multiple,

varying causes, both natural (wave action, tides, increase in

average sea level, etc.) and man-made (construction of marine

works interrupting the transport of sediments, mass urban

development in coastal areas, etc.). This is why a large number

of beaches are today suffering erosion problems, and the search

for solutions to protect them and guarantee their stability is a

prime requirement from both the social and the environmental

points of view. Building detached breakwaters able to achieve

such a purpose is amongst possible actions that can be taken on

a coast.

Detached breakwaters are outer marine works, isolated

and noticeably parallel to the coastline, and are built a

certain distance from the shore. They protect a stretch of

coastline from wave action, creating an area of shelter and

reducing the amount of energy penetrating therein whilst

potentially creating accretion areas on the stretch of coast

they protect. They are artificial structures, inspired by

natural formations such as coral reefs, bars, or islets close

to the shore (Figure 1).

These constructions have been used to protect beaches since

the middle of the 20th century, and the results obtained with

them since then have varied in nature, from notable successes

to acknowledged failures. They have been studied on multiple

occasions, and many researchers are investigating design

methods for this type of construction.

In fact, in 2008, the Journal of Coastal Research published

an article presenting an overview of the state of the art of

detached breakwaters (Bricio, Negro, and Diez, 2008). This

article investigated a set of cases on the Spanish Mediterra-

nean shoreline and concluded that the effect of a detached

breakwater on the coast is notably sensitive to the value of the

B/X ratio describing the relation between the structure’s length

(B) and its distance to the initial shoreline (X).

However, despite advances in this field, there is still a

notable dispersion of analytical sizing schemes, which demon-

strates the actual difficulty existing when tackling the design of

a detached breakwater due to the lack of clear, reliable, and

simple guidelines. Consequently, adopting this type of con-

struction as a solution for protecting or stabilizing a beach

usually proves less attractive than other possible actions.

This contrasts with the theoretical convenience of using

detached breakwaters, since the latter provide the advantage

of a smaller impact on littoral dynamics because, initially, they

do not interrupt longitudinal sediment transport. This is why

systematic research has been undertaken at the Ports

Laboratory of the Madrid Civil Engineers’ University School

DOI: 10.2112/JCOASTRES-D-10-00083.1 received 2 June 2010;accepted in revision 26 September 2010.’ Coastal Education & Research Foundation 2012

Journal of Coastal Research 28 1A 131–142 West Palm Beach, Florida January 2012

to develop a method for the functional and environmental

design of detached breakwaters defining their fundamental

characteristics as a function of the desired effect on the coast

whilst meeting social demands and preserving or improving

the quality of the littoral environment.

AIMS

Our aim is to approach the problem from the scientific,

technical, and design point of view, assuming we already know

the climate, geomorphologic, and geometrical characteristics

and the littoral dynamics of the location where the detached

breakwater is being studied. Likewise, the desired result on the

coast after it has been built is also known, and, therefore, it

must be possible a priori to set the final balance status.

Our aim is, therefore, to propose a generally applicable,

predictive analytical model for the functional design of

detached breakwaters that takes into account

(1) The climate and geomorphologic characteristics of the

place of construction

(2) The best breakwater location on the coastal strip

considering the interaction between the construction

and longitudinal sediment transport and the concepts of

littoral and closure depth

(3) The geometric and structural characteristics of the

breakwater in relation to the effects produced on the

coast (the potential possibility of generating submerged

tongues of sand or giving rise to tombolo or salient type

formations)

(4) Social demands and preservation or improvement of the

littoral environment’s quality, favouring with its effects

the use and enjoyment of beaches and allowing typical

biocenosis of coral reef systems to be developed, thus

strengthening the environment’s biodiversity.

METHODOLOGY

We reviewed the state of the art of detached breakwaters,

and we found many design models that relate the type of

response induced on the coast with the two basic geometric

parameters of this type of construction, which are the length of

the detached breakwater and its distance to the initial

shoreline. The models we found were proposed by Dally and

Pope (1986), Suh and Dalrymple (1987), Herbich (1989), Hsu

and Silvester (1990), and Ahrens and Cox (1990) (Bricio, Negro,

and Diez, 2008).

However, practically none of them relates the coast’s

response after the breakwater was constructed with variables

of another nature, such as those characterising the local

marine climate or the site’s geomorphology. Since the effects

produced on the coast by a detached breakwater are notably

sensitive to incident wave action and, therefore, to the states of

the sea and local bathymetry, design methods that do not

consider surrounding conditions as variables of the problem

can only be applied in those cases where these surrounding

climate and geomorphologic conditions are similar to those of

the original cases that were considered for drawing up the

model. This implies that these models cannot be applied in a

generalized fashion.

After this analysis, we concluded that in order to make the

design method general, the possible relations between vari-

ables of a different nature influencing hydrodynamic and

morphological changes in the coast after a detached breakwa-

ter was built should be studied. To do so, a working

methodology was established, based on three key issues:

(1) First, we selected detached breakwaters to be consid-

ered as original sources of the study’s data.

We considered all the breakwaters on the Spanish coastline,

and selection criteria were laid down allowing the sample to be

limited. So, we considered only those breakwaters that were

Figure 1. Blanes Beach (Municipal District of Blanes, Gerona) [left] and Posiguet Beach (Municipal District of Alicante, Alicante) [right].

132 Bricio et al.

Journal of Coastal Research, Vol. 28, No. 1A (Supplement), 2012

homogeneous in terms of the parameters influencing the

coast’s response but that were not going to be considered as

variables of the problem in the research were practically the

same (later, the hypotheses adopted as selection criteria would

have to be understood as limitations to be taken into account

when applying the design method obtained as a result).

The selection criteria were as follows: breakwaters had to be

detached and isolated on open sandy beaches, with a low crest

level (freeboard between 20.50 and 2 m) and permeable

structure with a homogeneous, granular cross section, located

in areas where the tidal range was less than or equal to 1 m.

On applying these filters, we found 19 detached breakwaters

to use as data sources (Figure 2 and Table 1).

(2) Second, we chose variables to be studied (bearing in

mind only determining ones, with the purpose of simplifying

the problem) and the definition of nondimensional monomials

amongst which to search for relations of dependency.

The variables considered in the research that needed to be

measured or calculated for each of the 19 detached breakwaters

are those shown in Table 2, and their values are in Table 3.

It should be pointed out that the following criteria were used

for defining the type of response produced on the coast by each

detached breakwater:

N Tombolo: If the size of the salient emerging as formed

is greater or equal to 90% of the detached breakwater’s distance

from the initial shoreline (Y $ 0.9X), the detached breakwater

is deemed to be effective (Figure 3).

N Salient: If the size of the salient emerging as formed is

between 10% and 90% of the detached breakwater’s distance

from the initial shoreline (0.9X . Y . 0.1X), the detached

breakwater is deemed to be partially effective (Figure 4).

N Limited/nil response: If the size of the salient emerg-

ing as formed is less than or equal to 10% of the detached

breakwater’s distance from the initial shoreline (Y # 0.1X), the

detached breakwater is deemed to be noneffective (Figure 5).

Likewise, the overall nondimensional monomials used for

studying the relations between the different variables are as

defined in Table 4.

(3) The third and last step in the working methodology

consisted of searching for relations between the breakwater’s

geometric factor (B/X) and the rest of the nondimensional

monomials and of adjusting functions between the monomials

for which some type of relation was found using the least-

squares method.

Figure 2. Location map of the detached breakwaters considered in

the research.

Table 1. Overall detached breakwaters on the Mediterranean coastline used in the research.

Code Province Municipal District Beach Coast Response

T1 Tarragona Tarragona (Altafulla) Tamarit Salient

T2 Tarragona Cambrils Cap de Sant Pere Salient

C1 Castellon Benicasim Terrers Salient

C2 Castellon Burriana El Serradal Tombolo

C3 Castellon Chilches Chilches Tombolo

C4 Castellon Chilches Chilches Tombolo

A1 Alicante Denia Les Basetes Limited/Nil

A2 Alicante Altea La Roda Salient

A3 Alicante Alicante Postiguet Tombolo

MU1 Murcia Aguilas Poniente Salient

AL1 Almerıa Almerıa Las Conchas Salient

AL2 Almerıa Roquetas de Mar Aguadulce Salient

AL3 Almerıa Adra San Nicolas Tombolo

G1 Granada Almunecar Puerta del Mar Salient

MA1 Malaga Rincon de la Victoria Cala del Moral Salient

MA2 Malaga Malaga Malagueta Salient

MA3 Malaga Estepona La Rada Limited/Nil

CA1 Cadiz La Lınea Levante Salient

ME1 Melilla Melilla Carabos Limited/Nil

Most of these breakwaters were built in the 1980–90s, except for that of Cap de Sant Pere beach (2004) and that of Carabos (2005). Except for these two cases,

all the beaches and stretches of coast adjacent to the breakwaters may be considered stable. Also, no negative effect at all on the nearby stretches of coast is

known, but it may be assumed that should any have occurred, the impact was minimal, because it is normal practice on Spanish beaches to accompany the

construction of detached breakwaters with artificial supplies of sand. These supplies prevent sedimentary material from the littoral flow from being caught,

minimise the negative impact on adjacent beaches, and accelerate equilibrium on the beach along the detached breakwater.

Design of Detached Breakwaters 133


RESULTS

The search for ratios between the pairs of nondimensional

monomials studied led to a series of graphic results.

Different shapes were assigned to the detached breakwaters

depending on the type of response they induced on the coast:

breakwaters that caused a tombolo formation were represented

with a circle; cases where a salient was formed were represented

with a cross; cases of limited or nil response were represented

with a triangle. Thus, interpreting the graphic results takes the

effect of the detached breakwaters on the coast into account and

links the latter with the ratio between the variables studied.

The results obtained were as follows:

N B/X and H12/L0: We studied the relationship between

these two monomials in order to find a relation between wave

characteristics and the detached breakwater’s geometric factor

(Figure 6).

From analysing this relationship, we inferred that there is no

clear relation between the breakwater’s geometric factor and

the wave steepness in deep water, meaning that in 95% of the

breakwaters used in the study, the wave steepness figure in

deep water is less than 0.034. (The different performance of

point MU1 is due to the particular maritime climate conditions

occurring where that detached breakwater is located. The

correlation there between the wave height and the period at the

reference buoy used for data taking [Cabo de Palos buoy]

provides very high wave height figures for smaller periods than

in other areas.)

N B/X and NI (both NI0 and NId): This result allows the

detached breakwater’s basic geometric characteristics and the

climate and morphological characteristics of the site to be

linked (Figures 7 and 10).

The cluster of dots shows a growing trend and was

concentrated inside a strip limited by two limit bands in

exponential fashion. The latter were adjusted by means of the

minimum squares method, using the sample points T1, T2,

AL3, and C2 for adjusting the upper limit band and points C4,

C3, C1, and MU1 for the lower limit band. The regression

coefficient obtained was higher than 0.99 in both cases. (In all

likelihood, point G1 performs differently through representing

the only breakwater in the sample located outside the surf

zone.)

N B/X and Y/X: The relation between these monomials

establishes the desired response on the coast in the shelter of

the detached breakwater and relates it to the construction’s

fundamental characteristics (Figure 8).

In this case, the least-squares method did not reveal an

adjustment function, but we saw well-differentiated graphic

areas according to the values adopted by the geometric

factor B/X for the cases of a limited or nil response

formation, undeveloped salient, and well-developed salient

cases.

The figures of the breakwater’s geometric factor and of the

salient shape’s factor for the case of a salient forming (i.e., when

the maximum dimension thereof is higher than 10% of the

breakwater’s distance from the initial shoreline but less than

90%) are related as follows:

N For values of B/X , 1.14, an undeveloped salient forms

with a position factor Y/X , 0.5.

Table 2. Variables influencing the coast’s response to a detached breakwater.

Variable Explanation

Parameters related to the local marine climate

H12 Significant wave height in deep waters exceeded 12 h a year in average regime

Ts Significant wave period correlated with the wave height H12, according to Waves Recommendation Annex I:

‘‘Climate on the Spanish Coastlines’’ (pp.43–45) (State Ports, 1994)

L0 Deep water wavelength associated with the significant period

Ld Wavelength at the foot of the breakwater associated with the significant wave period

Parameters related to the detached breakwater

X Distance of the detached breakwater to the initial shoreline

B Length of detached breakwater

A Crest width

CC Crest elevation

d Depth of detached breakwater

Parameters related to the beach and sedimentary material

mt Average theoretical slope of the submerged beach. (mt 5 d/X)

S Ratio between specific weight of the sediment and of the fluid.

Y Length of the salient formed in the shelter of the detached breakwater

Beach response Type of response induced on the coast (tombolo, salient, limited/nil response)

Parameters related to the littoral dynamics

dsaLittoral depth calculated from the formula of Hallermeier (1983) dsa ~

2:9:H12ffiffiffiffiffiffiffiffiffiffiffiffiffiffi(S{1)p {

110:H212

(S{1):g:T2s

Xsa Width of the littoral strip or surf area. (Xsa 5 dsa/mt)

NI0 Iribarren number in deep water, which relates the average slope of the beach to the wave steepness in

indefinite depths NI0 ~mtffiffiffiffiffiffi

H12

L0

qNId Iribarren number at foot of breakwater relating the average beach slope to the wave steepness at the depth

where the detached breakwater is located NId ~mtffiffiffiffiffiffi

H12

Ld

q

134 Bricio et al.


N For values of B/X . 1.14, a well-developed salient forms

with a position factor Y/X . 0.5.

N The breakwater’s geometric factor for a tombolo to form is

in any event higher than 0.85.

N B/X and X/Xsa: This result relates the detached break-

water’s geometric characteristics to littoral dynamics and

enables the relative position of the construction inside the surf

zone to be determined (Figure 9).

The function graphically adjusted to the cluster of dots

representing detached breakwaters located inside the surf zone

(all except G1) is a fourth degree polynomial function. It shows

a high adjustment factor (regression coefficient of 0.9), and it is

worth noting that its shape is similar to the longitudinal

sediment transport distribution’s shape, which reaches a

maximum at a distance of two-thirds of the distance between

the shore line and the wave front breaking line. This similarity

is obvious as a result of the monomial B/X’s graphic

representation on the horizontal axis and the X/Xsa’s on the

vertical axis. (Point A3 is probably outside the polynomial

adjustment because it represents a breakwater regularly

experiencing artificial deliveries of sand on its beach. This is

why the link between its geometry, its response at the coast,

and littoral transport is not representative of the normal

performance of detached breakwaters in the surf zone.)

DISCUSSION: DESIGN METHOD OFDETACHED BREAKWATERS

General

We analyzed these results and proposed a design method

that achieves the goal of the research and that makes use of the

relations found between the monomials.

This predictive methodology for design makes it possible to

locate a detached breakwater at a certain place on the coast

Table 3. Values of the variables considered in the research for each of the 19 detached breakwaters.

Code

Parameters Related to the

Detached Breakwater

Parameters Related

to the Beach

Parameters Related to the Local

Marine Climate

Parameters Related to the Littoral

Dynamics

X (m) B (m) CC (m) A (m) d (m) mt Y (m) H12 (m) Ts (s) L0 (m) Ld (m) dsa (m) Xsa (m) NI0 NId

T1 180 100 0.50 5 4.0 0.022 82 2.30 7.31 83.43 43.13 4.66 210 0.134 0.096

T2 195 120 2.00 12 4.5 0.023 34 2.30 7.31 83.43 47.34 4.66 202 0.139 0.105

C1 149 205 0.70 10 3.0 0.020 132 2.83 7.41 85.65 34.66 5.55 276 0.111 0.070

C2 50 82 0.50 9 3.0 0.060 50 2.83 7.41 85.65 34.66 5.55 93 0.330 0.210

C3 138 138 0.50 8 2.0 0.014 138 2.83 7.41 85.65 23.86 5.55 389 0.079 0.041

C4 177 150 0.50 7 2.0 0.011 177 2.83 7.41 85.65 23.86 5.55 492 0.062 0.033

A1 290 183 20.50 12 2.5 0.009 24 3.07 7.68 92.05 31.59 6.01 697 0.047 0.028

A2 180 190 0.20 12 5.0 0.028 59 3.07 7.68 92.05 56.52 6.01 216 0.152 0.119

A3 78 155 1.00 7 3.0 0.038 78 3.07 7.68 92.05 37.25 6.01 156 0.211 0.134

MU1 120 200 1.00 12 4.0 0.033 105 3.86 7.24 81.75 42.27 6.95 209 0.153 0.110

AL1 120 190 0.50 8 4.5 0.038 92 3.14 7.80 94.91 53.86 6.16 164 0.206 0.155

AL2 88 100 0.50 6 3.0 0.033 63 3.14 7.80 94.91 38.41 6.16 185 0.183 0.117

AL3 72 102 0.50 6 3.5 0.049 72 3.14 7.80 94.91 43.92 6.16 127 0.267 0.182

G1 130 150 0.00 8 6.5 0.050 108 2.85 8.23 105.65 77.19 5.79 116 0.304 0.260

MA1 200 175 0.50 10 5.0 0.025 80 2.85 8.23 105.65 64.87 5.79 232 0.152 0.119

MA2 180 205 0.25 6 5.0 0.028 30 2.85 8.23 105.65 64.87 5.79 209 0.169 0.133

MA3 170 160 0.00 12 3.5 0.021 14 3.85 9.38 137.48 63.61 7.78 378 0.123 0.084

CA1 145 165 1.80 15 3.7 0.024 30 3.85 9.38 137.48 66.66 7.78 322 0.144 0.100

ME1 186 200 20.50 10 3.5 0.019 13 3.14 7.80 94.91 43.92 6.16 327 0.103 0.070

Figure 3. Example of a detached breakwater with a tombolo formation.

Chilches Beach (Municipal District of Chilches, Castellon).Figure 4. Example of a detached breakwater with a salient formation.

Aguadulce Beach (Municipal District of Roquetas de Mar, Almerıa).



(with specific climate and geomorphologic characteristics and

with certain littoral dynamics), first setting the final state of

desired equilibrium on the coast after it has been built.

This method is developed in five steps and can be applied

once the problem’s starting data are known and the coast’s

desired response has been set. Specifically, it requires

(1) Assuming that it is applicable to the design of a detached,

rectilinear breakwater noticeably parallel to the coast-

line, with a low crest level (freeboard between 20.50 and

2 m) and a permeable structure and homogeneous

granular cross section

(2) Choosing an open stretch of coast not affected by the

presence of any other construction or element that will

alter the characteristics of the incident waves for locating

the detached breakwater

(3) Knowing those data related to the local marine climate,

the beach, the sediment material, and the littoral

dynamics, defined in Table 2, as previously studied and

calculated starting data relating to the construction’s

location

(4) Setting the coast’s desired response (tombolo, salient, or

limited response)

(5) Considering an artificial provision of sediments that is

stable according to the local littoral dynamics’ character-

istics, for guaranteeing and accelerating the desired final

status of balance on the coast, as well as minimizing the

possible negative effects of erosion in the bordering

beaches.

Design Steps

Once all the premises and conditions have been verified, the

design steps are as follows:

Step 1

Check whether the case involves the wave steepness at

indefinite depths not exceeding 0.034. Should this figure be

exceeded, the use of the proposed graphs is not recommended

because we would be outside the range of values obtained with

the original data for which the method’s applicability is

guaranteed (Figure 6).

Step 2

Obtain a first range of possible values of the geometric

factor (B/X) of the desired detached breakwater, from the

graph in Figure 7 and from the detail of the Iribarren

Figure 5. Example of a detached breakwater with a limited or nil

response from the coast. Les Basetes Beach (Municipal District of

Denia, Alicante).

Table 4. Nondimensional monomials considered in the research.

Monomial Explanation

Related to the breakwater’s characteristics

B/X Geometrical factor of the breakwater or ratio between the length of the detached breakwater (B) and its initial distance to the

shoreline (X)

Related to the characteristics of the surroundings

H12/L0 Deep water wave steepness, where H12 is the significant wave’s height exceeded 12 h a year in average regime and L0 is the

deep water wavelength associated with the significant wave period (Ts)

H12/Ld Wave steepness at the depth at which the breakwater is located, where H12 is the significant wave height exceeded 12 h a year

in average regime and Ld is the wavelength of the wave at the foot of the breakwater associated to the significant wave

period (Ts)

NI0 Iribarren number in deep waters relating the average theoretical slope of the beach (mt) to the square root of the wave

steepness in deep water (H12/L0)

NId Iribarren number at the foot of the breakwater relating the average theoretical slope of the beach (mt) to the square root of the

wave steepness at the depth where the detached breakwater is located (H12/Ld).

X/Xsa Breakwater position factor or ratio between the initial distance of the detached breakwater to the shoreline (X) and the width

of the surf area (Xsa), where most of the longitudinal sediment transport takes place

d/dsa Breakwater depth factor or ratio between the depth at which the detached breakwater is located (d) and the littoral limit

depth (dsa)

Y/B Geometric factor of the salient or ratio between the length of the salient formed in the shelter of the detached breakwater (Y)

and the length of the structure (B)

Y/X Salient’s position factor or ratio between the length of the salient formed in the shelter of the detached breakwater (Y) and the

initial distance of the breakwater to the shoreline (X)

136 Bricio et al.


Number in deep water, that may cause a significant response

on the coast.

Step 3

Depending on the magnitude of the desired response on the

coast, fine tune the range of possible values for the geometric

factor from the results obtained in the Figure 8 graph, which

relates the detached breakwater’s geometric factor (B/X) to the

position factor of the salient generated (Y/X), where Y is the

size of the emerged salient formed in the shelter of the

detached breakwater and measured from the initial shoreline.

That is to say:

Tombolo: B/X . 1.67 (in any event B/X . 0.85).

Salient (well-developed salient Y/X . 0.5): B/X M [1.14, 1.67].

Salient (undeveloped salient Y/X , 0.5): B/X M [0.56, 1.14].

Step 4

Set the relative position of the detached breakwater with

respect to the breaker line (X/Xsa) from the graph in Figure 9,

bearing in mind the estimated range of possible values for the

geometric factor B/X obtained in the above steps. In this way,

make the decision to locate the breakwater in the littoral or

active area of the beach profile (if the depth at the foot of the

Figure 6. Relation between wave steepness in deep water and the

breakwater’s geometric factor.

Figure 7. Relation between the Iribarren Number in deep water and the

detached breakwater’s geometric factor.

Figure 8. Relation between the position factor of the salient formed on the

coast and the detached breakwater’s geometric factor.

Figure 9. Relation between the position factor and the geometric factor of

the detached breakwater.



breakwater is less than the littoral depth: X , X/Xsa and

d , dsa), in the transition or shoaling area (if the detached

construction is between the active depth and the closure depth:

dsa , d ,dc), or at greater depths (offshore depths if the neutral

point or closure depth is exceeded: d . dc).

Likewise, with the X/Xsa value set, we would be in a position

to determine the value of the detached breakwater’s geometric

factor (B/X) and that of the structure’s distance to the initial

shoreline (X). The detached breakwater’s length (B) would be

calculated with the latter.

Step 5

With the graph of Figure 10 and the Iribarren Number detail

at the breakwater’s foot (NId), check to see whether the

detached breakwater’s geometric factor value is within the

range of values obtained with the original data.

PRACTICAL APPLICATION OF THEDESIGN METHOD

The design of a detached breakwater, located at a beach SE of

the Spanish Mediterranean shoreline, specifically ‘‘El Toyo’’

beach (Almerıa, Spain), is discussed in this section (Figure 11).

Starting Specifications

The following starting specifications must first be taken into

account for the practical application of the design method

(these specifications derive from the starting hypotheses

assumed during the first phase of the investigation):

(1) Assume that the method is applicable to the design of a

single, detached, straight line breakwater noticeably

parallel to the coast with a low crest level (freeboard

between 20.5 and 2 m) and a permeable structure with a

homogeneous, granular cross section.

(2) Select a stretch of open coast for the detached breakwa-

ter’s location, not too affected by tidal effects or the

influence of any construction or natural element that

might distort the characteristics of the incident waves.

Once the starting specifications have been considered, the

values of all starting data needed to complete the table of

characteristics of the construction’s location must be studied

and calculated. These parameters refer to the characteristics of

the local marine climate (wave height, tide period, and range),

of the beach (average slope, size and nature of the sediment),

and of the littoral dynamics (littoral depth, width of surf zone,

and Iribarren Number) (Table 5).

Finally, the desired response on the coast after building the

detached breakwater has to be set (in this case: well-developed

salient).

Once the characteristics of the site are known, once the

method’s conditioning factors referring to the type of structure

that will be geometrically designed are assumed, and once the

response required of the coast has been preset, the following

five steps of the design method necessary to determine the

unknown parameters of the problem (B, X, Y, and d

[Figure 12]) can be applied.

B 5 length of the detached breakwater

X 5 distance of the detached breakwater to the initial

shoreline

Y 5 size of the desired salient on the coast, measured from

the initial shoreline

d 5 depth to which the detached breakwater is set

Design Steps Applied to the Practical Case

Step 1

Check that the value of the wave steepness in deep water

(Hs12/L0) is within the range of values obtained with the

original data used for formulating the method (,0.034).

Hs12

L0~ 0:033v0:034

Step 2

Obtain a first range of possible values of the geometric factor

(B/X) of the desired detached breakwater for which a

significant response may be expected from the coast, using

the Iribarren Number in deep water (Figure 13).

For NI0 ~ 0:2199?B

X[ 1:1637, 2:0194½ �

Step 3

Depending on the size of the desired response on the coast,

make more precise the range of values possible for the

geometric factor from the results obtained in the graph relating

the said geometric factor (B/X) to the position factor of the

salient generated (Y/X) (Figure 14).

Since the desired effect on the coast is the formation of a

well-developed salient (i.e., the position factor of the salient

generated should be greater than 0.5 (Y/X . 0.5) with the latter

Figure 10. Relation between the Iribarren Number at the foot of the

breakwater and the detached breakwater’s geometric factor.

138 Bricio et al.


exceeding at least 50% of the distance between the shore and

the detached breakwater), then the range of figures possible

for the geometric factor has to lie between 1.14 and 1.67.

Taking the interval as imposed by the climate and morpho-

logical characteristics of the site into account in the above step,

the range of figures possible for B/X is as follows:

1:1637 , 2:0194½ �\ 1:14 , 1:67½ �? B

X[ 1:1637, 1:67½ �

Step 4

Bearing in mind the estimated range of possible factors for

the geometric factor (B/X) obtained in the above steps, the

detached breakwater’s relative position with respect to the

breaker line (X/Xsa) can be set from the graph relating the

above variables (Figure 15).

The decision made in the example being solved is to locate the

breakwater inside the beach profile’s active zone at a distance

from the shore such that the strip between the latter and the

construction is approximately equal to 70% of the width of the

surf zone, since we hope to obtain a well-developed salient and

to avoid a tombolo formation.

X

Xsa~ 0:7

Likewise, with the X/Xsa value set, the value of the detached

breakwater’s geometric factor (B/X) and that of the structure’s

distance to the initial shoreline (X) can be determined.

B

X~ 111:67|

X

Xsa

� �4

{297:22|X

Xsa

� �3

z276:38|X

Xsa

� �2

{105:11|X

Xsa

� �z14:937

Table 5. Starting data for applying the design method in the case of ‘‘El Toyo’’ beach.

Variable Explanation Value

Parameters related to the local marine climate

H12 Significant wave height in deep waters exceeded 12 h a year in an average regime 3.14 m

Ts Significant wave period correlated with the wave height H12, according to Waves Recommendation

Annex I: ‘‘Climate on the Spanish Coastlines’’ (pp. 43–45) (State Ports, 1994)

8 s

L0 Deep water wavelength associated with the significant period 94.91 m

Ld Wavelength at the foot of the breakwater associated to the significant wave period (Ld 5 H12 / L0) 0.033

S.L. Sea level 0.6 m (,1 m)

Parameters related to the beach and sedimentary material

mt Average theoretical slope of the submerged beach (mt 5 d/X) 0.04

S Ratio between specific weight of the sediment and of the fluid 2.6/1.025 5 2.537

Parameters related to the littoral dynamics

dsaLittoral depth calculated from the formula of Hallermeier (1983) dsa ~

2:9:H12ffiffiffiffiffiffiffiffiffiffiffiffiffiffi(S{1)p {

110:H212

(S{1):g:T2s

6.16 m

Xsa Width of the littoral strip or surf area (Xsa5 dsa/mt) 154 m

NI0 Iribarren number in deep water, which relates the average slope of the beach to the wave steepness

in indefinite depths NI0 ~mtffiffiffiffiffiffi

H12

L0

q0.2199

Figure 11. Location of ‘‘El Toyo’’ beach in the Gulf of Almerıa (Spain).



ForX

Xsa~ 0:7 ?

B

X~ 1:65

As Xsa ~ 154 m ? X ~ 0:7 | 154 ~ 107:8 m

Finally, the value of the detached breakwater’s length (B) could

be calculated:

B ~ 1:65|107:8 ~ 178 m

The order of magnitude of the salient that would be formed in

the shelter of the detached breakwater would therefore be at

least 54 m (Y 5 0.5 ? X 5 0.5 3 107.8 5 53.9 m).

Step 5

The Iribarren Number at the foot of the breakwater can be

calculated. Using this number, we can check the value of the

detached breakwater’s geometric factor (B/X) to see if it is

within the range of values obtained with the original data

(Figure 16).

The figure for the depth at which the detached breakwater is

located can be calculated from the submerged beach’s theoret-

ical slope and from the construction’s distance to the initial

shoreline:

d ~ mt X ~ 0:04|107:8 ~ 4:3 m

Figure 14. Relation between the position factor of the salient formed on

the coast and the detached breakwater’s geometric factor, applied to the

practical case.

Figure 15. Relation between the position factor and the geometric factor

of the detached breakwater, applied to the practical case.

Figure 13. Relation between the Iribarren Number at indefinite depths

and the detached breakwater’s geometric factor, applied to the

practical case.

Figure 12. Unknown parameters relating to the detached breakwater to

be designed on ‘‘El Toyo’’ beach and the expected response on the coast

after its construction.

140 Bricio et al.


The wavelength at the breakwater’s depth equals

Ld ~gT2

s

2ptanh

2pd

Ld

� �~ 94:91 tanh

2p4:3

Ld

� �

Ld ~ 48:23 m

The Iribarren Number at the foot of the breakwater is

NId ~mtffiffiffiffiffiffiffiffiH12

Ld

s ~0:04ffiffiffiffiffiffiffiffiffiffiffiffi3:14

48:23

r ~ 0:157

Results of the Practical Case

Table 6 and Figure 17 show the results of the design drawn

up and the response expected from the beach after building the

detached breakwater.

CONCLUSIONS

We conclude by proposing a method for designing detached

breakwaters that responds to the aims initially proposed: to

approach the design problem from the point of view of the

engineer who has a series of data as a starting point and is

seeking a final result. The design method is innovative in that

it considers variables of a different nature, enabling the typical

characteristics (climatological, geomorphological, and littoral

dynamics) of the construction site to be taken into account for

its geometrical sizing, which broadens its sphere of application

compared with those that do not consider them.

However, it is fundamental to draw attention to this

proposal’s limited applicability, at least temporarily, for the

case of isolated detached breakwaters that fulfil the hypotheses

initially raised in the research, which constitute the limitations

of the design method proposed. Since the method is based on

design graphs adjusted to real data from existing breakwaters

in a certain place (the Spanish Mediterranean coastline), it will

only be valid from a quantitative standpoint for cases where the

surrounding conditions are similar.

This is why we hope the research work will continue: the

sample will be extended with data from physical model and

numerical model tests, as well as with data on actual detached

breakwaters located elsewhere and with other surrounding

conditions, with the purpose of improving the adjustment of the

functions obtained.

It would also prove interesting to continue searching for

relations with other important parameters that also influence

the coast after building a detached breakwater, apart from

those taken into consideration in this study, for example: the

tide, the obliqueness of the waves, the breakwater’s transmis-

sion coefficient (which takes into account the structure’s

permeability), the average nominal diameter of the sediment

present in the stretch of coast in question, or the gap opening

between the heads of a series of detached breakwaters. An

analysis of the influence of these factors on the design of the

detached breakwater’s geometrical characteristics and on the

size of the response induced on the coast would contribute

toward generalising the applicability of the detached break-

water design method.

ACKNOWLEDGMENTS

This work has been undertaken within the Madrid

Polytechnical University researchers’ training programme.

The authors wish to acknowledge the contribution made

and support provided by the Directorate General for the

Sustainability of the Coast and Sea belonging to the Ministry

for the Environment and Rural and Marine Environment and

Figure 16. Relation between the Iribarren Number at the foot of the

breakwater and the detached breakwater’s geometric factor, applied to the

practical case.

Figure 17. Sketch of the detached breakwater as designed at ‘‘El Toyo’’

beach and the expected response on the coast after its construction.

Table 6. Results obtained for the design of ‘‘El Toyo’’ beach detached

breakwater.

B X B/X d Y

178 m 108 m 1.65 4.4 m .54 m



by the Ports and Coasts Studies Centre (CEPYC), which

allowed us to access their files, to consult their documenta-

tion, and to read their research work in matters of detached

breakwaters, which were all fundamental for undertaking

this research.

LITERATURE CITED

Ahrens, J.P. and Cox, J., 1990. Design and performance of reefbreakwaters. In: Kobayashi, N. and Losada. M. (eds.), RationalDesign of Mound Structures. Journal of Coastal Research, SpecialIssue No. 7, pp. 61–75.

Dally, W.R. and Pope, J., 1986. Detached breakwaters for shoreprotection. Technical Report CERC-86-1. Vicksburg (Mississippi):U.S. Army Corps of Engineers; Waterways Experiment Station.

Hallermeier, R.J., 1983. Sand transport limits in coastal structuredesign. In: Proceedings of the 2nd Coastal Structures Conference

(Arlington, Virginia, American Society of Civil Engineers [ASCE]),pp. 703–716.

Herbich, J.B., 1989. Shoreline changes due to offshore breakwaters.In: Proceedings of the 23rd International Association for HydraulicResearch Congress, August 1989, Ottawa (Canada).

Hsu, J.R.C. and Silvester, R., 1990. Accretion behind single offshorebreakwater. Journal of Waterway, Port, Coastal and OceanEngineering, 116(3), 362–380.

Suh, K.D. and Dalrymple, R.A., 1987. Offshore breakwaters inlaboratory and field. Journal of Waterway, Port, Coastal and OceanEngineering, 113(2), 105–121.

Bricio, L.; Negro, V., and Diez, J.J., 2008. Geometric detachedbreakwater indicators on the Spanish Northeast Coastline. Journalof Coastal Research, 24(5), 1289–1303.

State Ports (Ministry of Public Works), 1994. Wave recommendations,Appendix I: Climate of the Spanish Coastlines. Madrid, Spain:Centro de Publicaciones, Secretarıa General Tecnica, Ministerio deFomento.

% RESUMEN %

La investigacion que se presenta en este artıculo aborda el diseno de los diques exentos, por constituir estos un tipo de obras de defensa costera con el que poder luchar

de una forma estable y sostenible contra muchos de los problemas de erosion que existen en las playas. El objetivo principal de este trabajo es la formulacion de un

metodo de diseno funcional y ambiental (no estructural) que permita definir las caracterısticas fundamentales de un dique exento en funcion del efecto que se quiera

inducir en la costa, satisfaciendo las demandas sociales y preservando o mejorando la calidad del medio ambiente litoral. Ademas, se busca la aplicabilidad general del

metodo mediante la consideracion de relaciones entre variables de distinta naturaleza (climaticas, geomorfologicas y geometricas) que tienen influencia en los cambios

que se experimentan en la costa tras la construccion del dique exento. El estudio de las relaciones entre las distintas variables se realiza sobre los datos de una base de

diecinueve diques exentos reales, existentes en el litoral mediterraneo espanol, y sigue una metodologıa basada en el planteamiento de monomios adimensionales y en

la busqueda de relaciones de dependencia entre ellos. Finalmente, la discusion de los resultados obtenidos conduce a la propuesta de un metodo de diseno que utiliza

algunas de las relaciones graficas encontradas entre las variables estudiadas y con el que se consigue el objetivo principal anteriormente expuesto. Para demostrar la

aplicacion practica del metodo se resuelve un caso de predimensionamiento geometrico de un dique exento a modo de ejemplo.

142 Bricio et al.


functional and environmental design of detached, low crest level breakwaters

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