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Formulas for the Calculation of Breakwaters

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 Formulas for the Calculation of Breakwaters
Miguel A. Losada
Grupo de Puertos y Costas. Universidad de Granada.
C/. Ramón y Cajal, 4, Granada 18071, mlosada@platon.ugr.es

Introduction
This article analyzes the research done by Iribarren and his colleagues on
rubble mound breakwaters. The first part is a description of the impact that his initial
1938 formula had on the calculation of these structures, and the following sections
examine the experiments that he carried out in the 50’s and 60’s, which were based
on this formula. Apart from his important contribution to our knowledge about the
calculation of rubble mound breakwaters, Iribarren, whose work was afterwards
continued by Suarez Bores, also laid the scientific and technical foundations for
maritime engineering in Spain. This article studies the validity of Iribarren’s
proposals, and evaluates his technical and scientific legacy .
Throughout history, maritime structures, such as harbors and ports, have
played a vital role in transportation and communication systems. In ancient times,
harbors were built in places that were naturally protected from the sea, such as bays,
coves, inlets, estuaries, etc. From the end of the 19th century on into the 20th, the
progressive increase in maritime traffic, as well as ship size meant that breakwaters
had to be built in deeper waters. This was an even greater necessity on the Iberian
Peninsula because of its orography, and the scarcity of rivers and navigable estuaries.
Initially, such maritime structures were always built in protected areas, and
their shape depended on the configuration of embayments and existing rocky areas.
In the majority of cases, the typology of the breakwater section was that of a vertical
wall constructed by means of masonry. With the passage of time, new construction
materials, such as concrete, permitted the construction of artificial ashlars, e. g. the
floating caisson. The calculation methods of this section were very rudimentary with
little or no theoretical basis. In the first half of the 20th Century several failures
occurred in vertical structures, which brought to light the need for an immediate
solution, one that would be both technically viable and economically feasible.

1
Iribarren’s first period as a maritime engineer
In 1929 Iribarren was appointed Director of the recently created Grupo de
Puertos de Guipúzcoa, (Marín Balda 1999). From the very beginning, there were three
elements that would have a profound influence on his professional life: (1) his
responsibility for the protection of human life, property, ships, and maritime
structures; (2) the vulnerability of vertical breakwaters against the action of the
waves; (3) the lack of available methods and technical devices with which to evaluate
the effect of the action of the sea on breakwaters.
Iribarren thus embarked upon his professional activity as a maritime engineer
with dedication, enthusiasm, intelligence, and realism. He made full use of his talent
for observation, as well as his knowledge of the principles of rational mechanics
(among other things). After studying structures designed by other engineers and
observing the devastating effect of the action of the sea on the harbors of Guipúzcoa,
the region of his birth, he realized that vertical breakwaters were not capable of
withstanding the action of the waves breaking against their walls. He thus conceived
the idea of constructing sloping breakwaters with granular elements, which would
force the waves to break. This was the premise upon which he based all of his work.
Initially, Iribarren protected the vertical breakwaters with a layer of natural
elements, such as quarry stones, or artificial ones such as parallelpipedical concrete
blocks. When he saw that this solution worked, he decided to focus his activity on
the design of rubble mound breakwaters, which when built with successive layers of
granular material, caused the waves to break, thus gradually dissipating the energy
of the waves. He devoted almost thirty years of his life to this activity. The resulting
procedure for the design and calculation of such breakwaters was used very
successfully in the construction of more than 10 kms of breakwaters in Spain as well
as many other countries.
However, Iribarren’s path was fraught with obstacles. The sea, of course, was
the principal obstacle involved, but there were others, such as the lack of
comprehension of certain colleagues, which did not facilitate his work. Nonetheless,
his publications and the structures that he designed are testimony to his success in
overcoming all of these difficulties.

2
The first formulas
In 1938 Iribarren wrote the article (or paper, according to the author), titled
“A formula for the calculation of rubble mound breakwaters”. In it he proposes a
procedure for the deduction of a formula that combines the resistance characteristics
of the breakwater, weight [P], and density of the pieces [ γ s , ] and angle of the

protective level [ α , ] with the characteristics and height of the largest possible wave

that can break against the dike [H] ...”,

N ∗H 3 ∗d
P= (1)
(cosα − senα ) 3 ∗ (d − 1) 3
In this formula, d = γ s / γ w , y, γ w is the specific weight of the water, and the practical

dimensional coefficient is N = N a ∗ γ w , where N a is adimensional.

Five years earlier in 1933, Eduardo de Castro, another well-known engineer,

had published an article, co-authored by Briones, in the Revista de Obras Públicas, in
which for the first time a formula was proposed for the calculation of breakwaters.
The author’s assertions are modest and almost poetic “far be it for me to try to solve
what others of greater renown and daring have been unable to...”. Iribarren, who
was a student of Castro’s, read the article before graduating in 1927. He was
impressed by Castro’s ideas, and Castro encouraged him to continue along the same
lines.
However, the fact that Iribarren used Castro’s ideas as a starting point does
not make his research any less impressive. In all likelihood, in the past, formulas
with the structure of admimensional monomials, such as those proposed by Castro,
were not uncommon since they could be obtained by the simple application of
dimensional analysis. In our opinion, the importance of Iribarren’s work does not lie
so much in the formula that he proposed, but rather in all that his formula entails.
Anyone with a knowledge of fluid mechanics can propose a well-structured formula
to evaluate the actions of a fluid in movement around a rigid solid. However, the
validation of this formula, the adjustment of its coefficients, the delimitation of its
range of application, the quantification of the reliability of its results, and the logical,
coherent explanation of its validity are aspects that only lie within the reach of a
privileged few. I am referring to those who possess the necessary education and
training, willingness to work, as well as the strength and intellectual integrity not to

3
become discouraged by the many failed attempts and errors, which are an inherent
part of any research.
It is evident that Iribarren possessed all of these qualities in abundance since
he was obliged to endure the harsh and even hostile context prevalent in post-Civil
War Spain for those who wished to engage in research.

Impact of Iribarren’s article (1938)

In 1948 Iribarren’s 1938 article was translated and published by Heinrich of

the University of California, and in 1949 it appeared in the Bulletin of the Beach Erosion
Board Office of the Department of the Army (USA). From 1942-1950 Hudson directed
a series of experiments at the Waterways Experiment Station of Vicksburg (USA) in
order to obtain the values of the coefficients of a formula for the calculation of rubble
mound breakwaters, analogous to Iribarren’s 1938 formula. The results were
published in Technical Memorandum, No. 2-365, and presented at the XVII
International Navigation Conference. The conference paper proposed an “American”
formula, which ultimately became known as Hudson’s formula. This formula was
very similar to the one Iribarren had proposed in 1938, and only modified the term
designating the angle of the slope, as shall be seen in the following section.
In 1952 in France, Larras published a formula to study the equilibrium of a
quarry stone breakwater subject to wave action. Iribarren and Nogales (1954) prove
that Larras’ formula is basically the same as the 1938 formula, even showing identical
values for the coefficients. In 1953 Hedar (see Hedar, 1960) published the results of a
series of experiments carried out at the University of Chalmers (Sweden) to verify
Iribarren’s 1938 formula, and obtain the values of the coefficients.
Iribarren and Nogales (1950) and Iribarren and Nogales (1954) published the
articles "Generalización de la fórmula para el cálculo de los diques de escollera y
comprobación de sus coeficientes" [Generalization of the formula for the calculation
of rubble mound breakwaters and the verification of its coefficients] and "Otras
comprobaciones de la fórmula para el cálculo de los diques de escollera" [Other
verifications of the formula for the calculation of rubble mound breakwaters]. Both
articles discuss and analyze the work previously mentioned, and on the basis of the
results obtained, confirm the values proposed for the coefficients in the 1938 formula.
Iribarren’s obsession with verifying all aspects of the formula is the defining feature
of his research from 1954-1964.

4
Research: 1954-1964
The positive response of the breakwaters in Orio and San Juan de Luz, the
accurate evaluation of the damage to the Mustafá Breakwater in Algeria, as well as
the enthusiastic reception of the formula in Navigation Conferences, not to mention
his evident vocation for research, encouraged Iribarren to continue with his work.
However, he perceived that only by carrying out experiments based on his own
criteria would he be able to arrive at a definitive formula and truly evaluate its
coefficients. Finally, Iribarren with the help of Nogales, undertook the construction
of the Laboratorio de Puertos of the Centro de Estudios y Experimentación de Obras
Públicas. He built a wave tank and a wave basin near the Retiro1, in a building
contiguous to the former Civil Engineering School in Madrid. This became his
headquarters, so to speak, or the place where he carried out his research with the
help of Suárez Bores, Tejedor and Sánchez-Naverac, all of whom are cited in
Iribarren’s 1965 article.

Justification and specification of the problem

After 15 years of experiments and theoretical design, constructing

breakwaters, and observing their behavior, Iribarren had accumulated sufficient
knowledge and experience to tackle the problem of mound breakwater stability with
accuracy and precision on the basis of his 1938 formula. However, before beginning
the actual experiments, Iribarren summarizes the different factors that affect the
stability of a breakwater:
1. Environmental parameters:
• depth at the toe of the slope, h

• slope at the bottom, tan β

• specific weight of the water, γ w

• kinematic viscosity of the water, υ

• acceleration of gravity, g
2. Wave parameters
• wave height, H
• wave period, T

1 Translator’s note: the Retiro is a large park located in downtown Madrid.

5
 • direction of approach, θ
3. Parameters of the dike
• angle of the slope, α
• weight of the pieces of the main layer, P
• specific weight of the pieces of the main layer, γ s

• thickness of the main layer, e 1

• friction and interlocking of the pieces of the main layer, f

• characteristics of the secondary layers, P s ,e s

• permeability and width of the core, b, n

The formula that evaluates the stability of the pieces of the main layer in an
undefined slope under the action of a wave train can be written in the following way:
φ ( α , H , T , θ , γ s , γ w , P , e1 , Ps , e s , n , b , type of piece, failure criterion) = 0 (2)
The equality of the equation indicates the limit of stability. P is thus the
minimum weight that one of the pieces must have in order to be stable. In other
words, the formula and value of its coefficients can entail either a stability criterion,
or negatively, a failure criterion. With a view to limiting the number of experiments
and simplifying the analysis of the results, Iribarren first specified certain parameters
and criteria for the construction of the breakwater, examples of which are thickness
of the main layer, sequence, size and thickness of the secondary layers, permeability
and width of the core, placement method of the pieces, and the normal incidence of
wave trains.

Iribarren number, I r

Most of the experiments were carried out with waves breaking on the slope.
In order to know beforehand the wave height and period, Iribarren adopted a
“threshold value” for the quotient of the slope of the breakwater and the wave

H
steepness, ( tan α / ). This criterion was presented in a research paper given at
L0

the Navigation Conference held in Lisbon in 1949. The quotient is known today as
the Iribarren number (often termed the “surf similarity parameter”), and is generally

represented by the abbreviation, I r .

6
 The research carried out in recent years had shown that the distribution of the
energy flow of a wave train reaching a slope in The research carried out in recent
years had shown that the distribution of the incoming energy flux reaching a slope
into (1) dissipated energy (2) transmitted energy flux, and (3) reflected energy flux

depends on the value of I r . Iribarren affirmed that for a certain “threshold value” of

the parameter, the wave does not break on the rubble mound. Years later, the type of
breaker associated with the “threshold value” became known as collapsing type of
wave breaking. The stability of the pieces of the slope is critical for this type of
breaker, and under these conditions, the reflection coefficient as defined by the
reflection quotient of the wave heights of the reflected and incident trains is superior
to 0.40.
Given that the flow regime is turbulent and according to dimensional
analysis, the weight of the pieces of the main layer can be expressed by the formula:
H d
P = φ (α , , failure criterion, type of piece) ∗ ( )∗ H3 (3)
L0 (d − 1)3

The dependence of the weight, P, of the pieces of the main layer on its relative
density appears with the original mathematical structure of the 1938 formula. Years
later, Losada and Giménez Curto (1982) showed that with that structure it is possible
to obtain an accurate adjustment of the experimental data for pieces with a relative
density in the range, d>2.00, which is normal in practical engineering. Furthermore,
the formula establishes the dependence of P on the cube of the wave height. This
dependence is derived from the dimensional analysis, and Iribarren very wisely did
not try to modify it.
The main objective of the research carried out by Iribarren and his colleagues
in 1954-1964 was the study of the influence of the four factors included in the
functional, φ , on the stability of the pieces of the main layer. For this reason, he

finally set his formula down in the following way:

N ∗H 3 ∗d
P= (4)
( f ∗ cosα − senα ) 3 ∗ (d − 1) 3
In his work during that period the following elements were studied:
• the type of wave breaking and the ascending and descending equilibrium
• the friction and the interlocking between pieces
• the evolution of the failure and the temporal sequence of wave heights

7
• the type of failure and its dependence on the connection between pieces
This research was so complicated because all four factors intervened in each
of the four elements. The solution to the problem, expressed as a formula with
known coefficients, necessarily required data that would permit the effects to be
separated from the causes. Iribarren knew that the only way that he could do this
was to carry out experiments with a very specific type of design. The desire to obtain
a wave flume became almost an obsession for him, a need which he fortunately was
able to satisfy.

The friction and interlocking coefficient

In the 1938 formula, the difference between the sine and cosine of the angle of
the slope was used to evaluate the dependence of the weight of the piece of the angle
of the slope, supposing that the friction coefficient and the interlocking between the
pieces is approximately equal to the unit. In posterior derivations, Iribarren and
Nogales (1965) kept a friction coefficient, f, between the pieces which affected the
cosine function in the following way: f ∗ cosα − senα .

In the American formula, published in 1953, 1959 and 1961, along with the
experimental results, this dependence was expressed by means of the function cotan
α , without the friction coefficient and interlocking between the pieces. The
variability of the experimental results was expressed by a sole coefficient that

Hudson called K D . Iribarren, who was convinced that the totally theoretical

deduction of his formula was correct, tried to discover which of the two formulas
was the most accurate. In order to do this, he first proceeded to determine the friction
coefficients, f, corresponding to different forms of elements, quarry stones, artificial
blocks, and tetrapods. The formula used by Iribarren is both intelligent and precise
since it reflects the mentality of an engineer who asks himself which formula leads to
fewer errors and provides more information about the task to be carried out.
To evaluate the friction coefficient, Iribarren devised the slopemeter with
which he could measure the angle at which a slope breaks in function with the
number and shape of the pieces. Thanks to a series of carefully planned experiments,
Iribarren discovered that the friction coefficient increases as the number of pieces of
the slope decreases, and that only when the slope consists of an important number of
edges, does the friction coefficient approach the unit. Moreover, his experiments
confirmed that the pieces with a tendency to rub against and interlock with each

8
other (i.e. tetrapods), have a larger coefficient than the pieces that only rub against
each other (i.e. quarry blocks).
The experimental results obtained with the slopemeter explained and
quantified why tetrapods are more resistant to waves than quarry blocks of the same
weight. However, with these results there arose the question of the number of pieces
that made up the “unit of response” of the slope in the face of the action of the waves
(in the words of Iribarren, the active or resistant slope). As will be discussed in one of
the following sections, Iribarren considered that this active slope was made up of six
equal sides of a cube, independently of the type of piece involved.
Some years after Iribarren first proposed this basic aspect of the stability of
the pieces, very slender pieces began being used, such as the dolo, whose hydraulic

stability was analyzed in the laboratory by applying the coefficient K D and ignoring

the mechanism by which the piece resisted the action of the waves.

The N coefficient

Once the value of the friction coefficient was resolved, the results of the
experiments in the wave flume were used to evaluate the N coefficient, which in
Iribarren’s proposal should only depend on the type of piece, and whether the
dominant water flow over the slope is ascending or descending.
Firstly, he observed that after various series of waves of increasing height
during which the structure remained intact when a certain wave height was reached
(which Iribarren called the breaking point), the accumulated curve of the number of
edges separated from the layer tended to increase with the wave height. The slope
thus would become stabilized after a certain number of series of waves of the height
that had been tested.
When the wave would reach a certain height, known as total breakage, the
damage would extend with increased velocity, finally affecting the layer at the depth
of an edge, or more specifically, of the equivalent side of the cube. In this way the
first layer became totally damaged, and the stability of the breakwater, seriously
affected. According to Iribarren, the average accumulated curve of loosened pieces
under conditions of partial stability was practically identical for quarry blocks,
artificial blocks, and tetrapods.
The relocation in the slope of the pieces detached from the damaged area
depended on the characteristics of the water flow over the slope. Accordingly, the

9
deposit for steeper slopes forms a berm underneath the damaged area. Just the
opposite occurs in the case of mild slopes, in which the berm builds upwards the
failure area. By analyzing the profiles of mild slopes under total damage, it was
possible to obtain the approximate location of the transition point between both
types of behavior. As it turned out, this depended on the type of piece involved. The
behavior associated with the formation of the berm below the damaged zone was
called descending equilibrium, since the pieces became detached when the water
mass was descending the slope. Iribarren was able to define with great precision the
worst conditions of descending equilibrium. According to him, such conditions occur
when the water flow falls freely, and is not slowed by the lowering of the contact
level with the slope, originated by the oscillatory movement.
Iribarren and Nogales (1964) considered that the dikes should be designed so
that for the calculation height, no damage would be produced. Taking into account
that the relation of the wave heights of total damage (100%) and the initiation of
damage (0%) is around 1.6, the relation between the weights of the elements or the
coefficients N 100% and N 0% of the formula should be 4.1. Therefore, these values of N

presuppose a safety coefficient of only 1 at the initiation of damage, and of 1.6

represented in the wave height, or of 4.1 in the weight of the pieces for the total
damage.
Finally, in a preliminary study, Iribarren warned us that the breakwater head
is a very vulnerable zone, and suggested that the weight of the pieces be increased by
more than 50% over the weight given by the formula to guarantee stability.

Pressures and subpressures on the crown

In order to reduce the volume of the quarry block, Iribarren proposed the
construction of a leveled parapet “...at low tide or a little above in order to be able to
work above the water (in dry conditions)...” and crowned “...at the height of 1.5*H
over the highest level of the sea at rest, which is that reached by the pressure
diagram of the breaker, although the almost vertical foam, which scarcely pushes,
can reach greater heights.” Furthermore, Iribarren recommended that the quarry
layer, “...ought to reach a height of 0.75*H, the same as the crest of the breaker...”.
To calculate the crown, Iribarren and Nogales (1964) proposed, “..to only use
the pressure diagram of the breaker very approximately and conveniently
modified…. and admit that the presence of the rubble mound reduces this pressure

10
by half”. They add, “It should be pointed out that the pressure diagram of the
breaker is only provisional and must be made more precise in the future..”.
Unfortunately, Iribarren died before he could finish the huge task that he had set
himself. He would have liked to have carried out new experiments to quantify the
behavior of the head, the effects of oblique wave incidence, the laws of pressure on
the crown, the influence of the randomness of the wave heights and periods, etc.

Iribarren’s research (1954-1964)

More than 40 years have gone by since 1954-64 when Iribarren carried out
this research. The results were presented in a paper given at the Navigation Congress
held in Stockholm in 1965, and published in the Revista de Obras Públicas (September
1965). In this section, we discuss the results of Iribarren’s work, and analyze its
influence on the development of maritime engineering and research.

The importance of the friction coefficient, f

Independently of the validity of the friction coefficient obtained by

experiments carried out with a slopemeter, perhaps the principal virtue of keeping a
friction coefficient in the formula is that it is a warning that the pieces of the slope
withstand the wave action because of their weight and also because of the
contribution either by the friction or interlocking of the surrounding pieces. This
contribution triggers the structural solicitation of the piece, which increases as its
capacity to interlock increases. Probably, the breakage and the total destruction of
various breakwaters would never have occurred if Iribarren’s formula and
calculation criteria had been applied.
Forty years of scientific discussion as well as ensuing events have shown that
Iribarren’s formula calculates breakwaters more accurately than the American
formula since it contains more and better information regarding the breakwater’s
response to wave action. Consequently, it is all the more surprising that in Spain one
frequently finds breakwaters, whose design has been calculated on the basis of the
American formula.

The variability of the N coefficient

Years later after the 1965 publication, Bruun and Johannesson (1978) Bruun
and Gunbak (1978) for crowns, and Losada and Giménez Curto (1979) based on data

11
from Iribarren y Nogales (1965) for rip-rap, rubble mounds, blocks, and tetrapods,
confirmed that the worst stability conditions of a slope of these pieces is produced
when the wave breaks in collapsing. In this type of wave breaking, the time that
elapses between the two waves that consecutively arrive at the slope is practically
equal to the time taken by the water flow to ascend and descend the slope, there
being no interference between the two movements. This situation corresponds to the
worst case of free fall. When the wave breaks in plunging, the variation of the
average sea level affects the descent of the water down the slope, whereas when the
wave breaks in surging, the movement on the slope is basically governed by the
partially stationary oscillation that is produced on it.
The experiments always used the same core material, shape of the section
type and position in the canal, by which the reflected energy flow only depended on
the type of damage in the slope, which in turn depends on I r . Under those

conditions, Iribarren obtained N coefficients with constant values, except in a few

experiments where N had very different values. Reanalyzing those experiments

López and Losada (1998) showed that for breakers with I r > 2.5 full plunging,

collapsing and surging and taking into account the reflection produced in the slope
to define the calculated wave height, the N coefficient of Iribarren’s formula is
h
constant for total damage and weakly depends on the relative depth , , at the foot
L
of the breakwater for the initiation of damage.

Ascending and descending equilibriums

In 1953 and afterwards in 1960, Hedar, in the light of the 1938 formula,
deduced expressions to analyze ascending and descending equilibriums. On the
basis of this research, Iribarren established the worst conditions of descending
equilibrium of the pieces when the slope is rigid and the ebb of the water is free. He
also defined the conditions for which the worst change of equilibrium, whether
ascending or descending, is produced for each type of piece.
In recent years in certain countries where there are a lot of available quarry
stones close to the structure, deep water, and very high waves, breakwaters called
berms have been designed in which the stones can move with the action of the waves,
and the behavior of the section is similar to that of a beach with coarse-grained sand.
These breakwaters are built with gently inclined slopes in the section where the wave

12
breaks. In Spain such structures can be found in Tarragon and Alicante, among other
places. Iribarren was critical of the construction of breakwaters under conditions of
ascending equilibrium since the coefficient of the formula is greater than that of
descending equilibrium. In other words, all other parameters being equal, the piece
needs more weight.

The evolution and the shape of the failure

Iribarren and Nogales (1965) proposed a safety coefficient in the application

of the formula that was based on the evolution curve of the failures and the relation
between wave heights as they begin to break and the total damage. To this end, they
proposed that the structures should be calculated with the N coefficient
corresponding to the initiation of damage, in other words, with a safety coefficient of
1 in regards to that initiation, and with no visible damage. This criterion represents a
safety coefficient of 1.6 in wave height and of 4.1 in the weight for the total damage.
Iribarren and Nogales (1965) were aware of the many uncertainties in the
calculation of breakwaters, such as the following: variations and impossible increase
in wave height, dispersion of the experiments, the inevitable defects in the
construction of breakwaters whose slopes, level thickness, and general shape could
not be adapted to the project design (especially in the difficult conditions under
which maritime structures must be built), not to mention other deficiencies,
impossible to predict.
Using Iribarren’s experimental data, Losada and Giménez Curto (1979)
proposed confidence bands to evaluate the uncertainty originating from experiments
for the calculation of the initiation of damage. Their research showed that the
approximation of one evolution curve of the failure for the three types of pieces that
were studied, was perhaps not entirely correct since in the case of tetrapods (and also
dolos), because of the interlocking, the danger zone was smaller than what had been
supposed in relation to wave heights 1.6. In other words, the pieces that interlock,
make the section more fragile.
Moreover, Iribarren was aware of the uncertainty associated with the
representation of the calculation waves for a wave train, though the lengthy
discussions that he had with his colleague, Suárez Bores. In their 1965 publication,
Iribarren and Nogales mention this uncertainty, and state that its study was one of

13
their immediate objectives. It has often been discussed whether or not the calculation
wave proposed is adequate, in the light of what we now know about waves.
Iribarren determined the coefficient of the formula for the calculation of
wave height at undefined depths in function with the fetch, after collecting data
pertaining to the Cantabrian Sea. After all of these years and considering the fact that
Iribarren was a person accustomed to observing the sea, it can be assumed that the
calculation wave determined by the fetch formula, is an approximation of the
significant wave height, H s of a sea state in zones of depth limited wave heights. It is

thus possible to calculate breakwaters by applying the formula, as long as they are
found in depth limited wave heights, and the expected damage will be equal to or
less than the so -called total damage.
However, in areas without limitation of wave height by the depth or by the
generation process, the application of Iribarren’s formula gives optimistic results
since the arrival of larger waves is possible, whose relation with the significant wave
height is substantially greater than 1.8. With such waves arriving at the breakwater,
damage can occur that is greater than the so-called total damage. This important
topic was the object of a series of experimental and theoretical studies by Vidal,
Losada and Mansard (1995), who proposed as the calculation wave height a statistics
of order of the sea state.
Iribarren was aware of the occurrence of groups of waves, but to our
knowledge, never analyzed their influence on the stability of the pieces of the main
layer. Medina, Fassardi and Hudspeth (1990) and Medina, Hudspeth and Fassardi
(1994) focus on this problem. Their work has opened a line of research that would
surely have been of great interest to Iribarren.
A global analysis of all of three factors that affect breakwater stability was
proposed in the 1980’s by Suárez Bores, who like Iribarren, showed himself to be
ahead of his time by elaborating a multivariate method for the calculation of
maritime structures. Suárez Bores continues to work in this line of research to this
day. The results of his work can be found in the publication, Recommendations for
Maritime Structures, R.O.M. 0.0 (Losada 2001), as well as in research on the
application of neural networks on the calculation of maritime structures (Medina,
1999).

14
Oblique incidence and head stability

Following in Iribarren’s wake, Losada and Giménez Curto (1982) quantified

the influence of oblique wave incidence on the stability of the pieces of the slope.
Vidal, Losada and Medina (1991) verified the fact that generally Iribarren’s
recommendation to increase the weight of the pieces of the head by 50% is correct.
New experimental and numerical techniques have permitted a more detailed
analysis of the flow generated by the waves in the head, and therefore, an evaluation
of its effect on the pieces. Iribarren would have taken great pleasure today in being
able to use these new techniques to carry out new experiments.

The calculation of the crown

Laboratory experiments (Martín, Losada and Medina, 1999) as well as the

campaign of pressure measurements on the crown of the dike Príncipe de Asturias del
Puerto de Gijón (Díaz Rato, Negro, and Losada 1994) have led to the elaboration of a
calculation method for these structures when the worst waves break in collapsing on
the slope and reach the broken crown (i.e. under the same conditions in which
Iribarren’s formula is applied). This research has shown that the proposed method
for the calculation of the laws of pressures and subpressures on the breakwater
crown is pessimistic, and produces overestimated structures. Nevertheless,
experiments have confirmed that a 50% reduction of the pressure on the crown
protected by the main layer is correct.
It has taken three decades as well as the most modern techniques of
measurement and analysis to improve Iribarren’s calculation method, which had
only erred on the side of safety.

Project design criteria and standards of good practice

The book, Obras Marítimas: Oleaje y Diques [Maritime Structures: Waves and
Breakwaters] (Iribarren and Nogales, 1964) and their 1965 publication are full of
project design criteria and standards of good practice, which have been widely
taught all over Spain, and which are a part of our cultural and engineering heritage.
Such norms guarantee the durability of the structure during its useful life, as well as
the correct behavior of all of its elements that do not have a calculation or verification
formula. Such elements include layer sequence or thickness, weights of secondary
layer, geometry of the section, and the maximum depth of the extension of the main

15
layer, which has a surprising level of accuracy. Losada and Giménez Curto (1981)
studied the run-down of the water flow of the slope, R d for different types of

Rd
damage and pieces. For collapsing breakers, the quotient < 1 , this limit
H
depending on the type of piece. Evidently, the maximum flow occurs slightly above
the point of maximum run-down. For this reason, when the result is lower than this
figure, it is not necessary to continue with the main layer.
Most of these criteria and standards are generally included in the technical
prescriptions for maritime structures built in Spain. However, certain engineers,
dazzled by the light coming from foreign shores, have occasionally built maritime
structures without following Iribarren’s criteria and standards. The result has been at
the very least, a loss of durability, and at the most, important failures in the structure.
Following Iribarren and Nogales’ book, it is possible to design a breakwater,
based on a geometry that previously defines its principal components, such as the
crown (ibid, p. 275). Paraphrasing the authors, this book is “... an important source
regarding such an important question as the design of breakwaters with a certain
technical basis, and without recurring to a deceptive comparison with already
existing structures...”. Although this contribution is mentioned somewhat less often,
it is doubtlessly one of the most important legacies that Iribarren left to maritime
engineering.

The Iribarren School of breakwaters

In Spain Iribarren’s school of thought was followed by Suárez Bores, with
whom Iribarren shared his ideas. They had lengthy and intense discussions on the
subject, and Suárez Bores also became an advocate of many of the new proposals
regarding the description of waves. In fact, in Spain he was a veritable pioneer in this
area, as well as the creator of a network for the observation of atmospheric and
maritime parameters. Iribarren implemented and developed laboratory
experimentation; Suárez Bores conceived and fostered the systematic measurement
of oceanographic parameters. Suárez Bores received from Iribarren a passion for
research and knowledge, and like Iribarren, his ideas are in the process of providing
Spanish maritime engineering with a strong scientific and technical foundation. Not
surprisingly, on many occasions he has also suffered from the incomprehension of

16
certain colleagues, who from their administrative ivory towers could not or would
not lend their support and assistance to the research efforts of two brilliant and
irreplaceable engineers.
Suárez Bores, recently retired from the Escuela de Ingenieros de Caminos,
Canales y Puertos in Madrid, has left an important group of followers, who now are
professors in Civil Engineering Schools and Faculties of Oceanography all over
Spain. In many of these academic institutions research has been and is presently
being carried out on the behavior of breakwaters (e.g. references in text).

Conclusion: Iribarren, the man

Iribarren had a strong, multi-faceted personality, which allowed him to lead a
rich and varied life, committed to the pursuit of knowledge. He was a certainly a
man of his time. In all of his many facets, he is an example for all generations to
follow, as a researcher, an engineer, and a man. In each of his multiple dimensions,
Iribarren left an important legacy.
As a researcher, he based his activity on the scientific method: observation,
inference, the establishment of laws, followed by deduction. In other words, what he
did was to apply knowledge, and then observe if his experiments produced the
desired effects, after which he would begin a new induction process. As a thinker, he
fervently believed in Leonardo da Vinci’s words: "In Nature there is no effect
without a cause. Once you understand the cause, you do not need to experiment any
more.” As an engineer, his constructions were invariably more than structures. He
transformed them into scientific events from which he could extract conclusions.
However, Iribarren was also the professor who built an experimental
laboratory and taught in the Escuela Técnica Superior de Ingenieros de Caminos, Canales
y Puertos, where he managed to implant his technical style and scientific habits in
engineers who, perhaps as a consequence of the historical context of the country,
had initially been taught to profess such deplorable ideas as: "the sea and its contents
are in the hands of God".….”research is for others, but not for us”.
Iribarren, the man, rebelled against such dogmatic assertions, and in the
process laid the scientific and technical foundations for Spanish maritime
engineering. However, its future now lies in our hands, and it is for us to preserve
and enhance his valuable legacy. This was Professor Iribarren’s most valuable gift to

17
us all, and with respect and admiration for the teacher as well as the man, we give
him our most heartfelt thanks.

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Castro, E. 1933. “Diques de Escollera. Revista de Obras Públicas”. Madrid: 183-185.
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