Beach Erosion Control
Beach erosion is an important problem in many
countries all over the world. The European countries
on the North Sea-Denmark, England, Germany and
Holland-have suffered many times from floods. On
January 31st, 1953, the southwest section of The
Netherlands was struck by a disaster the like of which
had scarcely been considered possible. Villages and
towns were completely or partially devastated and
1,795 people lost their lives. In the United States
many problems of beach control exist, and some of the
most important ones are located in Florida.
Florida has a long shore line. In round figures
there are over 778 miles of sandy beach included in
1277 miles of general coastline. Florida has extensive
beach problems, both in magnitude and variety. But
there is a big difference between the problems in
Florida and those around the North Sea. While the
European countries rimming the North Sea turn their
backs to their big enemy-the sea-Florida faces its
waters; its beaches are tourist beaches; they constitute
Florida's "face." The property behind many of these
beaches has been developed, resulting in prosperous
communities. Additional development of beaches is
under way at an increasing rate, but many beaches
erode and the buildings fronting these beaches are
liable to damage. Moreover as pointed out by Colonel
Matthews23 "too many of the things men do to
improve beach-front property merely increase these
rates of erosion". and "there is probably no field
of human endeavor where more money has been spent
more uselessly and even harmfully than in so-called
The European countries on the North Sea have, in
only a few cases, developed their beaches. They have
their problems only from one side-the sea. Florida
has two problems: the sea and the owners of property
at the seashore who very often build their homes too
close to the shore line or even try to steal property
from the sea; but it is very risky to steal from the sea
which is an unmerciful adversary.
This paper deals only with the engineering prob-
lems of beach erosion control, but it should be men-
tioned that there is another important aspect of
the Florida problem-the lack of beach laws to govern
*Associate Research Professor of Engineering Mechanics, Uni-
versity of Florida.
construction of coastal protection and development
of sea-front areas.
All coastal protection problems are closely con-
nected with littoral drift problems because protection
of a coast is only necessary when the erosion exceeds
the supply of material. As an introduction this paper
therefore gives a short summary of littoral drift.
The Littoral Drift
Littoral drift problems require careful considera-
tion in the control of floods, reclamation, construc-
tion of harbors and coastal protection works. Today
it is not possible to deal rationally with the littoral
drift problem on seashores. Until now the practice
has been adopted of splitting up the complex prob-
lem into single problems, and investigating them
separately. This work has heretofore given several
practical results for littoral drift and coastal protec-
Material drifts in two ways, partly as bed-load
transportation and partly as suspended-load transpor-
tation. Bed-load transportation starts because the move-
ment of water over the bed of the river or the sea exerts
a sheer stress upon surface particles of the bottom.
When the force exceeds the resistance of the particle to
movement, transport will begin. Coarser material
always moves along the bottom, usually in such a
way that the individual grains are continuously re-
placed by particles of the same size in the bottom layer.
Finer material moves in suspension because the tur-
bulence prevents particles from settling.27
In order to understand the problems involved in
beach erosion control it will be of interest to con-
sider two very important factors in the coastal pro-
tection technology: the source and drain of beach
material, and the beach profile.
Sources and Drains of Materials
A source of materials is a coastal area which de-
livers materials to other beaches. A source might be an
area where erosion takes place, a shoal in the sea, for
instance; the shallow area in front of an inlet which
has been closed; a river which transports sand ma-
terial, sand drift from one beach to another or to the
sea, etc. Artificial nourishment of beaches of any kind
is an artificial source.
A drain of materials is a coastal area where ma-
terials are deposited. A drain might be a marine fore-
land of any kind, a spit, a tombolo, angular foreland,
etc. It might also be a bay, an inlet, or a shallow area.
Manmade constructions as harbors, jetties or groins
as well as dredged sand traps are also drains.
These terminologies are very important for an
understanding of problems in the practical coastal en-
gineering field (see Table 1).
The following general rules are valid:
1) A coastal protection should be built in such a
way that it functions as a drain. It should therefore
have a source but not a drain on the updrift side.
2) A harbor or an improved inlet on a littoral drift
coast should not act as a drain. It should therefore
have no source, but if possible a drain on the updrift
It will be seen that coastal protection problems are
the reverse of harbor problems.
A beach profile is a cross section in the beach and
offshore area perpendicular to the shore line on some
established base line. A beach profile indicates what
water depth exists at the different distances from the
An equilibrium beach profile is defined as a beach
profile which maintains its form regardless of the num-
ber of waves which attack the profile.
Beach Profiles in the Laboratory
(a) Reference is made to Fig. 1. Ho equals the deep
water wave height, Lo equals the water depth. In-
vestigations with equilibrium beach profiles carried
out in a wave tank have shown that waves with a high
(A) 6.r profile
srtorm-18 9 ; aa
0.04. e3: L0 SO W0k 2.,5m
smtwi st*4A = 0.028
e9: IY 50m 1.L t.4m
WL. Q+ Cz
steepness ratio, e.g., o equals 0.043, will produce a bar
profile as shown in Fig. 1 (A). Waves with a low
steepness ratio, e.g., o equals 0.018, will make a beach
ridge profile (see Fig. 1 (C).
(b) Waves with a high steepness ratio (i.e., storm
waves) will erode the beach; waves with a low steepness
ratio (i.e., swells) will build up the beach.
(c) There are two types of littoral drift, bed-load trans-
portation on the beach itself (beach drift) due to up-
rush and backrush; and suspended-load transportation
in the breaker zone due to the breaking waves and the
generated longshore currents.
(d) In storm profiles, the transportation is produced
mainly as material in suspension by longshore cur-
rents. In swell profiles, transport is mainly beach drift.
(e) The transport along summer profiles is much
greater than that along winter profiles for waves with
the same energy content.
Several other results of more or less academic in-
terest have been obtained.2' 8, 0, 18, 29
Actual Beach Profiles
The form of the actual beach profile depends on
such factors as wave characteristics and their mutual
ratios, direction of wave propagation, and change in
wave action. Different waves, for instance, try to
destroy the system of bars not belonging to their pe-
culiar profile and build up a new system of bars. It
must also be assumed that the profile is a function of
grain-size, grain-size distribution, and specific gravity.
Where bed rock exists, bars cannot be formed. In ad-
dition, the coastal currents, especially the longshore
current due to wave-breaking, may play a role.8, c
(C) bech ikld3e pooffe
wege L* I O. I, O0-0
egg Lx Soon KM C69M
t One- 46Cc
f5~ Beoch PihAc 'prf
Figure -Equilibrium beach profiles, laboratory experiments.
Figure 1.--Equilibrium beach profiles, laboratory experiments.
--- ---- r~ru
---- T JR ....
Ultimately the form depends on the initial con-
ditions. On very steep coasts a single bar may appear,
or perhaps none at all. It appears that the number of
bars depends on the magnitude of littoral drift. When
the drift increases, the possibility of formation of bars
will also increase, but it cannot be maintained that a
profile with three bars carries more material than a
profile with only one bar because many other factors
may influence the magnitude of littoral drift.8,
Field experiments mentioned in 3 and s, c have
shown that actual beach profiles fluctuate in just the
same way as beach profiles in the laboratory. The
difference between the summer profile and the winter
profile is that the summer profile has a "beach ridge"
(often built up in sand) and at the same time is steeper
than the winter profile. The fact confirms the value of
laboratory experiments even if only a qualitative com-
parison can be made.
Beach Profiles Classified in Accordance with Nourish-
ment. Results of research on the development of
beach profiles built up of sand with grain size 0.2 to
0.3 mm seem to show that we can distinguish between
profiles in another way; that is, between the over-
nourished, the sufficiently nourished, and the under-
nourished profiles.8, c These terminologies are
especially valuable for an understanding of the prob-
lem of what kind of coastal protection should be
preferred and how satisfactory such construction will
The overnourished beach profiles are fed with
more material than the waves can shape into real beach
profiles. These, therefore, are irregular and often
perform as irregular shoals. On the Florida shore
lines we have examples of such profiles along the
Florida Keys where part of the material eroded on the
east coast of Florida accumulates.
There are two different types of sufficiently-nour-
ished profiles. At one of them the profiles are not fed
with more material than the waves can shape into a
profile having the same "equilibrium form." At the
other, the loss of material equals the supply of material
and the profile has still the same form. The beach pro-
files for some length north of Cape Canaveral might
be of the first-mentioned kind while the beach profiles
at Daytona Beach and several other beaches in the
northern part of Florida, might approximate the last-
The undernourished beach profiles are eroded,
which means that the coastline retrogrades. Profiles of
that kind are found at several spots along the southern
part of the east coast of Florida from Jupiter to Miami.
From this, it seems that progradation of a coast
may take place with or without equilibrium profiles,
while retrogradation of a shore line can only take place
with equilibrium profiles having a maximum steepness
corresponding to quantities of littoral drift. An actual
equilibrium profile, therefore, should be defined as
a stable profile with maximum steepness (including
seasonal fluctuation of the beach profile).
The discussion above might seem to be slightly aca-
demic, but as will be pointed out later it is very im-
portant to know what kind of beach profiles we act-
ually have before we start construction of any kind of
Before we can start construction of a coastal pro-
tection work we first must make a decision as to what
kind of coastal protection we should prefer. The right
answer depends very much on what we expect from
our coastal protection.
If we want to build up a beach we should have a
source on the updrift side. If we actually have a
drain we should try to render it harmless in some
way or other. If we have to construct our coastal pro-
tection in a source area, before starting construction
we should know the water depth up to which erosion
takes place. If erosion takes place to only a limited
depth there should be a good chance of building up
and maintaining a beach. If erosion takes place up to
deep water we will have to move back our coastal
protection after a time interval, the length of which
depends on the rate of erosion and the rate of a pos-
sible artificial nourishment to the beach (see Table 1).
If we do not necessarily want a beach, a source on
the updrift side is not so important, but if there is
no source we must expect that erosion will continue.
In this case it is absolutely necessary that we know the
depth up to which erosion takes place. If erosion
takes place to only a limited depth we should be able
to stop the erosion at that depth, but if erosion takes
place up to deep water it will be impossible to main-
tain the beach by groins, sea walls or breakwaters (see
Table 1). After some time we will have to withdraw
our constructions and give up a certain land area if
we do not replace all the material eroded artificially.
In most cases this will be impossible because of eco-
nomic reasons. Unless these important facts are taken
into consideration it will be very risky to build any
Table 1 gives a general outline of what type of
coastal protection is best in relation to the type of
beach profiles and source of materials. When we have
these facts in hand we can estimate from the table what
can be expected from the different kinds of coastal
protection and in that way determine what kind of
protection is preferable.
Four different measures against erosion are men-
Coastal Protection in Relation to Source of Materials and Condition of Beach Profiles.
1 2 3 4 5
Coastal Protection Groins or Jetties Sea Walls Breakwaters Artificial Nourishment
Source of Materials and Beach Profiles
A. Plenty of source-material
Over-nourished profiles Not necessary Can never build up beach. Not necessary Not necessary
Might be necessary to avoid un-
der extreme high-water attack
and storm conditions.2
B. Source material available If a beach is wanted in a par-Can never build up beach. If a beach is wanted in a par- If a beach is wanted in a par-
Sufficiently nourished ticular location Might be necessary to avoid un- ticular location. Breakwaters will ticular location in short time.
profiles der extreme high-water attack almost always cause erosion of Groins might be necessary to
Balance between material and storm conditions.2 the beaches on the leeside. Al- maintain the beach especially if
eroded and deposited ways danger of flanking. the beach protrudes in propor-
tion to the adjacent shorelines.s
C.a C.a.l If groins or jetties are extended Can never build up beach. If a beach is wanted in a par-If a beach is wanted in a par-
Erosion only Source of beyond the depth up to which They can stop erosion provided ticular location. Must be built ticular location in a short time.
up to limited material erosion takes place they should they are stable at the depth at outside the depth up to which Groins together with periodic
depth in the be able to maintain the beach which erosion takes place. Even erosion takes place. Will almost nourishment will in most cases
C. Only limited sea in a future not too limited.1 if groins are built a sea wallalways cause erosion of beachesbe necessary for maintenance of
source of might also be necessary to avoid on the leeside. Always danger beach. (See columns 2 and 3).
materials or attack at the foot of dune or cliff of flanking.
none at all. under extreme high-water and
Under-nour- storm conditions. It is very im-
ished beach portant that condition2 is ful-
C.a.2 Will not work well even if they Can never build up beach. They Will not work. If material is If a beach is wanted in a partic-
No source are extended beyond the depth can stop erosion if they are stable supplied artificially they will ular location in a short time.
C of material up to which erosion takes place at the depth up to which erosion work for a limited time. Should Only continued supply to bal-
unless material is supplied arti-takes place. Even if groins are be built outside the depth up ance erosion totally can main-
ficially to balance erosion to- built and material is supplied to which erosion takes place. Al- tain the beach. Groins will help
tally. Footnote 1 is not im- artificially a sea wall might also ways danger of flanking. to maintain the beach. (See col-
portant. be necessary to avoid attack at umns 2 and 3)
the foot of dune or cliff under
extreme high-water and storm
conditions. It is very important
that condition2 is fulfilled.
C.b C.b.l Will retard retrogradation of the Can never build up beach or stop Will only work for a limited If a beach is wanted in a par-
Erosion up Source of shoreline especially immediately erosion. Unless material is sup- time. After this they might do ticular location in a short time.
to deep material after the construction. But ero- plied artificially to balance ero- more harm than good if material Periodic nourishment in quan-
water sion will continue and continu-sion and groins might be built, is not supplied for balance of cities which balance the erosion
in the ous prolongation of land-ends they will in any case only work erosion. Will almost always cause can maintain the beach. Groins
sea will soon be necessary if materials for a limited time before col- erosion of beaches on the leeside. will help to maintain the beach.
are not supplied artificially to lapsing. It is very important that Always danger of flanking. (See columns 2 and 3)
balance erosion.1 condition2 is fulfilled.
C.b.2 Will not work unless material Can never build up beach or stop Will not work. If material is If a beach is wanted in a par-
No source is supplied artificially and con- erosion. Unless material is sup- supplied artificially they will ticular location in a short time.
of material tinuously to balance erosion to- plied artificially for total balance work for a limited time. After Only continued supply in the
tally. Footnote 1 is not im- lf erosion and groins might be this they might do more harm same quantity as total erosion
portant. built, they will in any case only than good if material is not sup- can maintain the beach. Groins
work for a limited time before plied for total balance of erosion, will help to maintain the beach.
collapsing. It is very important Always danger of flanking. (See columns 2 and 3)
that condition2 is fulfilled.
1. Should be constructed in such way as to let the material pass from the updrift side to the
downdrift side as soon as they are filled with material.
2. Should be constructed in such a way that they contribute to erosion of the beach as little
3. Sand selected for artificial nourishment should contain the same gradation of materials as
those found on the beach to be nourished, if the original beach slope is to be maintained.
tioned but any of these measures can be carried out
in different ways fitting each special case. For example,
at Palm Beach the situation is as follows: source to
the north; improved Lake Worth Inlet acts as drain;
beach profiles are undernourished, but the 12- and
18-ft. off-shore depths show relatively little change
(based on investigations in 1883 and 1927, see House
Document No. 772, 80th Congress, 2nd Session).
Table 1, column 2 case C, a, 2 indicates that "groins
will not work well unless material is supplied arti-
ficially to balance erosion." These groins "should be
constructed in such a way as to let the material pass
from the updrift side to the downdrift side as soon as
they are filled with material."
Review of Methods for Defense
There are four types of coastal protection: groins,
sea walls, breakwaters, and artificial nourishment. A
few general rules are given here in regard to protection
by each of these. Technical details are not included
in this paper. A few constructions are shown (Figs.
2-11). For further information the author recommends
the publications indicated by (5), (6), (7), (8, d, e),
(9), (24) and (32) in the references.
Groins are built perpendicular to, or at an incli-
nation with the shore line and interpose a total or
partial barrier to the littoral drift. The ability of a
groin to accumulate material depends on such natural
factors as grain size of the beach material, the shape
of the beach profile, the types of waves, and the in-
tensity of the littoral drift. As a general rule, groins
should never be constructed where there is no littoral
As described above, the fine material (grain size less
than 0.15 mm.) mainly migrates in suspension and
settles only when motion of the water is very slow or
has stopped. This means that there is not much chance
of accumulation of very fine material along a groin,
whereas coarser material, such as shingle, moves over
the bed, for which reason it is of great value as beach
protecting material. If the migrating material con-
sists of sand the groins will produce a selection of
material, the coarse grains being accumulated on the
updrift side of the groin .14, 22
The shape of the beach profile is also very im-
portant for the ability of a groin to accumulate ma-
terial. If there are no bars a very essential part of
the littoral drift will take place on the beach, which
means that in most cases groins will work well if a
sufficient amount of rather coarse material is available.
On the other hand, the beach will often not be very
stable, and considerable seasonal fluctuations may take
If there are one or more bars, much littoral drift
will take place on and between the bars. It appears
that the number of bars increases with the intensity
of the littoral drift, but this is no indication of the
quantity of littoral drift. This means that a group
of groins may work well even if there are several bars.
Still, what is said above regarding the influence of
the different types of waves on the beach profile and
on the littoral drift will have to be considered. When
groins accumulate material in summer it must be due
to the influence of swells which produce a pronounced
Finally, the intensity of littoral drift must play
a role because the stronger the littoral drift, the faster
a groin or a group of groins will accumulate material.
Groins may be classified as permeable or imperme-
able, fixed or adjustable. When wave action is the
principal cause of transportation, permeable groins
are unlikely to prove fully satisfactory as a shore pro-
tection measure. As a general rule impermeable
groins are preferred.
It is always good when the height of a groin can
be adjusted because it is difficult to fix the most favor-
able height of the groin at any time. A group of ad-
justable groins will always permit adjustment so that
we can raise and lower the beach as we like and pass
material to the leeside of the groin if necessary. More-
over, adjustable groins are practicable in cases where
we wish to interfere with beach traffic as little as pos-
sible. In seasons where the height of the groin is not
essential, such groins can be lowered. Adjustable
groins have been used with success in England and
Denmark (see Fig. 3), but most groins all over the
world are still fixed.
A general rule for spacing of groins cannot be
given because, as already mentioned, this depends
on many different factors including the length of the
groin. The ratio between the space and the length
of the groin between the extreme end and the mean
sea level (when tide or high water is not essential)
varies in practice between 1 to 1.5 and 1 to 4. As a
general rule it can be said that the ratio increases with
increasing size of material and increasing quantity of
littoral drift and decreases with increasing steepness
of the beach profile and increasing steepness ratio of
the waves. If the ratio is less than 1 to 1.5, groins in
most cases will not work well. In such cases the length
of the groins should vary in such way that every second
or third groin is longer, a practice which is used on
"shingle beaches" in England. Groups of groins exist
where the ratio is 1 to 5, but these groins are located
on beaches with an extremely strong littoral drift.
The length of a groin is determined by the depth
in the offshore area and the extent to which it is
ND PLE-S ,l /-f* j ILE
E T PILTS L T
e exiO LOCK .- TSd WASHERS
deire to ine t t... l dt. T
S6... d OLT 4a LONG.
Figure 2.-American steel sheet pile groin.
desired to intercept the littoral drift. The length
should be such as to interrupt such part of the littor
drift as will supply enough materials to create the
desired stabilization of the shore line or the desired
accretion of new beach areas. On the seashores of the
United States groins very often are extended up to
about a 6-ft. depth below mean water level. On the
North Sea coast the extreme end of a groin is very
often situated at about a 12-ft. depth below mean
water level. If there is a bar rather close to the shore
line the groins will accumulate more material if they
are extended across the bar. In any case the groins
should not stop just inside the bar. It is difficult to
give complete general rules. Some are given in (6)
With regard to the height, most groins built in
the U. S. have a horizontal shore section and inter-
mediate sloped section, and a horizontal outer section
(see Fig. 2). The intermediate section of the groin
should approximately parallel the slope of the fore-
shore which the groin is expected to maintain. The
elevation at the lower end of the slope will usually
be determined by the construction methods used and
the degree to which it is desirable to obstruct the
littoral drift. The horizontal shore section extends
from the desired location of the crest of berm as far
landward as is required to anchor the groin to prevent
flanking which is very dangerous for the beach. The
height of the shore section depends on the degree to
which it is desirable for sand to overtop the groin
and replenish the downdrift beach. Minimum height
should be the height of maximum high water plus
height of normal wave uprush. The outer section in-
cludes all of the groin extending seaward of the sloped
section. The height of the outer section usually de-
pends on constructional practice.
In Europe the groins are often constructed with a
slight slope all the way through because it fits better
to the cross sections of many eroding beaches.
Figure 2 shows a typical American steel sheet pile
groin designed by the Beach Erosion Board. The groin
is a fixed groin. It works well on many shore lines
in the United States.5'6,16 Figure 3 shows a
Danish "headland-groin" as designed by the author
for use at Saeby Seaside resort in Denmark. The outer
end of the groin (the headland) is built of granite.
The adjustable land end is constructed of timber.
The height of the groin varies from one season to
another. In the summer season traffic can pass freely
on the beach because the land end is lowered and
the upper end of a couple of piles are removed. Be-
cause of these arrangements the construction might
by more expensive than the American designs.
Meanwhile the serious drawback of any group of
groins or any jetty is that they act as a littoral barrier,
which means that they push the migrating material
from the updrift side out into deeper water, where
it is possibly lost for the coast or, in any circumstances,
is only carried ashore again at a greater distance from
Measures Against Leeside Erosion
In many cases it would probably have been better
if groins had never been constructed, because they
have done more harm than good. Measures against
lee-side erosion can be divided into two groups: (a)
those with short-range influence; and (b) those with
(a) Short-Range Influence
The measures are:7
(1) A Sea Wall on the Leeside (see Fig. 4a). This
measure is the most primitive one, but is often used,
and it is effective when the coast recession is not so
strong that the shore line becomes eroded rapidly
at the end of the sea wall.
ADJUSTABLE HEADLAND GROIN
REVETMENT (SEE FIG. II)
SECTION A-A SECTION B-B
1:100 GRANITE STONES 1:50
M.S.L. I ON 2 SLOPAEE I ON 2 SLOPE-
MATTRESS IF NECESSARY FOR
PROTECTION OF BOTTOM
1:00 10 ,15 2 25S 3'0 FT.
10 15 FT.
Figure 3.-Danish Headland groin
(2) Corner Groins (see Fig. 4b). The corner groins
prevent the erosion from running in directly along
the main groin. It is an expensive method, however,
and the effect is limited to a very small area.
(3) Inclined Groins (see Figs. 4c and 5, which show
a groin-group in Denmark). The groins are con-
structed with slanting land ends, particularly ad-
vantageous at the last groin in the group,
because when it is so built, the erosion on the lee
side does not run close to the stem of the land end.
(4) T-Groins (see Fig. 4d). In his report to the
XVIIth International Navigation Congress in 1949,
Col. Frech writes about the T-groin, built at As-
bury Park, New Jersey, as follows: "Several of these
groins have been experimentally supplemented by
breakwater members, extending 100 to 150 ft. at
right angles, at their outer ends forming a T. It is
too early to judge the results produced by these
structures, but the following observation may be
made: certainly, further erosion of the bluff has
been stopped, the groins not having the break-
water feature at their outer end have not accumu-
lated much sand, if any, but those with the break-
water addition (known now as T-groins) have had
a paradoxical effect, sand having accumulated along
both sides of the stem of the T, but with deposits
PILING ONLY IF NECESSARY
with adjustable land-end.
on the downdrift side exceeding considerably the
accumulations in the updrift side."15
T-groins have been used in Great Britain be-
The successful effect of the T-groin is explained
by the theory of the angular groin.
(5) Angular Groins (see Fig. 4e). The angular
groin also accumulates materials on the lee side
which fact can be explained theoretically from
light diffraction theories8, d and has been veri-
1:80 1-- I i----
0 1 2 3 4 5
r 1 .
The Skager Rack
Figure 5.-Groins with slanting land-ends, Denmark. A,
fled by laboratory experiments. Angular groins
are more costly to build and maintain than the
straight groins normal to the shore line, but the
space between the groins can be enlarged. Prac-
tice seems to favor a modification of the angular
groin to the Z-groin.
(6) Z-Groins (see Figs. 4f and 6) have all the prop-
erties of angular groins and accumulate material
on the lee side. A Z-groin is cheaper than the
angular groin because the breakwater addition is
closer to the shore line than for the angular groin.
In laboratory experiments the Z-groin was made
uneven by the use of piles. Part of the wave energy
running along the groin was destroyed, which
tends to the possibility of deposits along the stem
of the groin. It appears to the author that an ideal
group of groins is obtained when Z-groins are used
on the principle of shortening.7 8, d Fig. 6
shows an old groin under reconstruction on the
Z-principle on the Danish west coast (1953). Four-
ton contrete blocks are used for the construction.
(b) Long-Range Influence
The principle of shortening by Kressner20 is
illustrated in Fig. 7. Kressner's laboratory experiments
and some practical experience in Holland31 and
Denmark8, d are in favor of the use of groups of
groins, the groins on the lee side being shortened at a
very small angle, 4 to 6 degrees. Fig. 8 shows the
principle of shortening with Z-groins which should
ire 6.-Z-groin under construction in Denmark.
have adjustable land ends. The coast is in this way
divided into small headlands which look better than
the zig-zag shore lines which often result with normal
groins. Z-groins are in this way a modification of the
Dutch headland groins which are mentioned by
Thierry and Van der Burgt.31 A group of groins
built on the "headland" or the Z-principle, on the
principle of shortening and with adjustable groins
is the most flexible and streamlined groin-construc-
tion which exists in coastal protection technology
which especially is important on beaches which are
composed of fine material like the Florida beaches.
Meanwhile, general rules cannot be given for the con-
struction. Each case will have to be investigated
Other measures against erosion on the leeside are
in progress. The most direct and practical seems to
be artificial nourishment of the beaches on the lee side,
which is used in a number of places in the United
Order of Construction of Groins
Construction should be started from the lee side
and progress towards the updrift side. Thus, the groins
are successively filled from the most lee side groin to
the one on the updrift side as construction pro-
ceeds. In case of artificial nourishment there is no
general rule. The construction should be finished as
a whole under favorable weather conditions.
Figure 8.-Z-groins arranged on the principle of shortening.
Sea walls are used alone or in connection with
groins. As the function of a sea wall is exclusively
of a defensive nature, the pure sea-wall construction
is mainly used where there is no littoral drift and,
consequently, no possibility of building and main-
taining a beach by means of groins. Sea walls in
connection with groins are used for protection of
valuable areas and buildings, chiefly at places where
either the littoral drift is small or where the beach
is maintained by artificial replenishment of sand (see
Table 1). Sea walls with or without groins are con-
structed on the same principles, but as a rule the
strongest types are used in the latter case.
The following deals with a problem of great im-
portance to the construction of a good sea wall, namely,
the energy-absorbing ability.
Different Types of Sea Walls
The following four main types are in common use:
(1) Vertical Walls. These are built only where
valuable areas must be protected. Some of the biggest
and most well-constructed walls are found in Eng-
land.24 In the United States the Galveston Sea Wall in
Texas is well known.10
Most sea walls are impermeable, but permeable
types are also found in the so-called "stone cribs,"
i. e. wooden boxes filled with stones. However, stone
cribs have not been very successful, as they are not
(2) Sheet pilings. Sheet pilings serve the same
purpose as sea walls. They are generally used where
the wave attack is not very strong and often with a
rubble mound in front.
(3) Sloping walls or revetments. Sloping walls may
be impermeable or permeable. They must solve the
same problem as sea walls and sheet pilings; but in
most cases they do so in a more rational way.
Impermeable sloping walls are generally used in
Holland, and probably were developed to protect the
feet of dykes in an economical and effective way.
Stepped walls are of Dutch origin. The technique is
highly developed (for instance the walls in North
Holland, the Zuidersea-dam, etc.) and it is still being
developed, cf. (21) and (32). Also in England re-
markable new constructions have been built, cf. (13).
The sloping wall at Pett Level west of Dungeness,
England (cf. (13) and Fig. 9), consists of two slopes
of concrete blocks, enclosing an inclined berm, 25
ft. wide covered with sheet asphalt. The joints be-
tween the blocks are filled with bitumen. The berm
increases the loss of energy in the uprush and down-
rush of the waves. The wall is segregated by cross
walks to prevent any damage to the facing extending
into adjacent sections of the wall.
Permeable sloping walls (revetments) appear in
rubble mounds and in rough stone revetments. Figure
10 shows a typical American construction designed
by the Beach Erosion Board. It works well when the
Figure 9.-The Pett Level Sea Wall, England.
Figure 10.-American Revetment.
foundation conditions are good and when it is con-
structed with care. Figure 11 shows a Danish con-
struction designed by the author. The rugged revet-
ment is supported by a "half on half" wooden sheet
piling and provided with a rubble mound. A hydraulic
stilling basin is formed behind the rubble mound. The
wave energy is almost completely dissipated. The con-
struction might be more expensive than the corre-
sponding American. It should be constructed with
Comparison Between the Different Types of Sea Walls
As will appear from the discussion in the previous
pages, breakwaters can be classed as: vertical walls or
sloping walls, and impermeable or permeable construc-
tions. There is a disagreement as to which type of
structure is better, the vertical or sloping wall. Gen-
erally, vertical walls should be used only where the
subsoil is non-erodible or where the possibility of ero-
sion is small, which is generally the case with inward-
bent coasts and bays.
Sloping walls can be used where the subsoil is
erodible. They should be constructed so that they are
conducive as little as possible to erosion. The differ-
ence between the impermeable and the permeable con-
struction is that of the percolation and the loss of
energy involved. In consequence of percolation the
energy loss at the permeable construction will be
greater than that at the corresponding impermeable
construction, unless the latter is supplied with a special
roughened surface (see below). This advantage is,
however, nullified when the water volume of the waves
is large in proportion to the volume of voids. The
advantage of using permeable structures is especially
great for slopes steeper than 1 on 1.5 which are subject
to storm waves, i.e. waves with Ho > about 0.04.
With slopes >1 on 1.5 the waves will break, and the
advantage of using a permeable structure is decreased.
The permeable structure has, however, one advantage
over the impermeable-viz. the structure, when sub-
jected to severe wave action, is not prone to complete
failure as it will follow a process of disintegration
stone by stone rather than total collapse, and the
damaged structure will be far easier to repair than
the impermeable one, as it is necessary only to sup-
plement the material.
Demands on a Sea Wall
As a breakwater must provide permanent protec-
tion against erosion, it must fulfill the following de-
(1) The placement in the beach profile must be
If a sea wall collapses, because it has been built so
high that a cliff is formed in front of the structure, a
serious mistake has been made. Before constructing
a sea wall, an exact investigation of the seasonal fluc-
tuations of the beach must be carried out; the winter
profile should govern the base depth.
(2) The sea wall should not be built where the
Figure 11.-Danish Revetment.
Waves, striking a jetty or a sea wall may oe oscil-
lating waves, waves that are breaking or broken waves.
A jetty or a sea wall must be built so that breaking
waves do not attack the structure. Exceptions to the
rule are certain types of sloping walls which are de-
signed to produce wave-breaking in order to cause
as much loss of energy as possible.
(3) The configuration must not increase the erosion
in front of the wall.
The problem is the ordinary lee side problem at
groins and jetties. It is evident that any erosion on
the lee side of some projecting part of a sea wall is
detrimental to the wall on the lee side of "the bas-
tion".8, As a general rule, a breakwater must
never follow the shore line exactly in a small-tongued
coast, as the bases of the small tongues may become
exposed to particularly heavy wave attack. It is sug-
S gested that a better solution would be to construct
walls across the tongues.
(4) The sea wall must fulfill the following main
a) It must be stable. The problem is especially in-
teresting, if the cliff consists of low shear strength clay.
In that case, unless measures are not taken against
possible slides, e.g. by establishing effective drainage,
a sea wall might some day slide. It is therefore of
great importance that the sea wall is drained in an
effective manner. In general, drainage should be pro-
vided even under the monolithic type of concrete
The sea wall must be able to resist the wave attack
and other forces.
When a sea wall is overturned this may be caused
by hydrostatic pressure, wave force or attack from
foreign bodies, especially when rubbish has been
washed away .from behind the structure. This applies
especially to dykes and dams. The sea wall should be
S constructed so that it withstands hydrostatic force and
wave force. Concerning wave force, and dimensioning
for wave attack, the reader is referred to (9), Iribar-
ren's dimensioning of rubble mounds (17), Minikin's
diagram for breaking waves (25), and Sainflou's dia-
gram for unbroken waves (30). At the moment it is
not possible to calculate exactly the wave force on
sloping walls, even if by means of the characteristic
theory, progress is made in the calculation of the up-
rush on a smooth slope. Therefore, the dimensioning
of sloping walls, impermeable as well as permeable,
depends on practical experience.
S b) Wash-outs of the backfill caused by back-rush or
overflowing water must be avoided. It often
happens that a sea wall is damaged because the water
striking the structure falls down behind it, washing
away the back fill or damaging roads, etc. One mea-
sure against this consists of building the sea wall to
such height that no water can overtop the wall re-
gardless of wave attack. However, it is not ordinarily
economically feasible to do this, and certain lesser
criteria must be adopted. For example, if it is desired
to prevent overtopping water which has damaging
horizontal momentum, the wall crest height of vertical,
concave curved, or re-entrant face walls above the low
water datum according to (5) may be set at h =- h +
0.7Hb, if the wall is located in or landward of the
breaker zone; at he = ht + 0.6 H, if the wall is lo-
cated seaward of the breaker zone, where h, is the wall
crest elevation above mean low water, h, is the highest
still water level above mean low water, H is the wave
height before breaking, Hb is the wave height at
breaking. Stepped or sloping faced sea walls should
be higher; in Reference (5), he = h, + 1.3 Hb is recom-
mended, but this height can be lowered by special
arrangements as shown below.
Measures against oversplash are use of a tight
pavement behind the sea wall,28 or reduction of
the uprush by wave screens, steps, or other ruggedness
arrangements-a common practice in Holland.
A berm is sometimes used in order to absorb the
force of the falling water.24 A cornice or a small
vertical wall at the upper end of the slope is often
satisfactory.24, 28, The uprush is reduced by ar-
rangements of steps, sleepers, wave screens or prisms
of concrete put down in the slope.
c) The sea wall must not contribute to the erosion
in front of the structure.
Sea walls should never be constructed on coasts
subjected to continuous erosion in deep water; if so,
they will soon be destroyed. Yet, a sea wall has often
collapsed or been damaged as a consequence of erosion
in front of the structure. Any impermeable wall put
in a beach may have a destructive effect on the beach.
Three different effects are possible.
(1) The effect of the clapotis, or reflected wave, in
front of a vertical or a steep sloping wall, possibly re-
Figure 12.-Effect of reflected wave.
Figure 13.-Effect of backrush.
inforced by pressure of the water falling from the wave
rise after impact (Fig. 12).
(2) The effect of the collision of the back-rush
with the beach (Figs. 13 and 14).
(3) The effect of reflection (Figs. 13 and 15).
The effects (1), (2) and (3) appear together or in
pairs. With vertical walls (1) and (3) appear; with
vertical walls provided with a protective apron, a berm,
or a slope, a combination of (1), (2) and (3) may
occur, whereas with sloping walls only (2) and (3)
appear, since (3) is usually due to (2).
Many experiments have been made with sea walls
built in a beach. In the following outline, Reynolds'
investigations,26 Bagnold's investigations,' and some
investigations made in Copenhagen in 1949 are men-
Reynolds noticed that there is a certain critical
height for a beach in front of a vertical wall. When a
beach is higher than a certain level it builds up. Con-
versely, if it is below this level it will be eroded.
:.. :;, : .
... ."..'... .. .-i' ':. '
Figure 14.--Backrush, English Channel Coast.
Bagnold's corresponding investigations of beach
profiles, with special reference to shingle beaches,
proved that the erosion of the beach started as soon
as the uprush reached the impermeable vertical or
sloping wall, so that part of the backrush thereafter
took place above the surface of the stones.
Experiments with beach profiles carried out in
1949 in the Hydraulic Laboratories in Copenhagen
showed that some wave energy is reflected from the
beach. The reflection appeared by a formation of low
waves in the sand bottom, where the wave length was
-, and L = the water-wave length. The author shall
not here try to explain the reason why those waves
arise, but the influence of the reflection on the littoral
drift will be mentioned. As to backrush, this repre-
sents reflected energy, and the less energy in the back-
rush, the less will the backrush contribute to the re-
flection. In special cases the backrush might cause
a wave-break, which otherwise would not have taken
place. In general, however, it can undoubtedly be
taken for granted that the suitability of a sea wall can
be measured by its energy-absorbing ability, i.e. the
best sea wall is the one that gives the least reflection.
The Influence of Sea Walls on the Littoral Drift
As mentioned earlier a systematic discussion- of
littoral drift problems as a whole is not possible, be-
cause the knowledge of the primary causes is insuf-
Some investigations made by Shields, Kalinske and
Einstein give some reason to believe that the bed-load
transportation-within a limited range-depends on
the average water velocity raised to the 5th or 6th
power, i.e. the shear stress to the 2.5th or 3rd power
(8, e) and (27). Because of this, a small increase in
the velocity caused by reflection of waves will cause
a considerable increase in the littoral drift. With 30
per cent reflection of wave height, the maximum velo-
city at the bottom will be increased by 30 per cent.
If there is no reflection, the littoral drift is 1. With
30 per cent reflection the littoral drift is increased by
about 60 per cent. With 60 per cent reflection the in-
crease is 300 per cent. As a consequence of this, the
bottom will be eroded. The level of the bottom, how-
ever, is not only determined by the shear stresses due
to the oscillating wave action, but by a combination of
wave action and currents, in connection with the pos-
sible addition of materials from the sides. As to the
longshore current, this is weakened by a lowering of
the bottom, but its effect upon the detachment of the
sand particles will usually be small compared with
that of the oscillating wave action. It is of great im-
Figure 15.-Reflection, Bridlington, South Yorks, England.
portance that the reflection is less than about 20 per
Investigations Made in the Hydraulic Laboratory
A brief mention of investigations made in Copen-
hagen, 1949-1952, is instructive. The object of the in-
vestigations was to find the best principle for the con-
struction of an economical sea wall which reflects as
little wave energy as possible.
Practical experience has proved that damage to
sea walls will appear during storms and high water,
and, consequently, under these conditions a sea wall
must prove its efficiency; therefore, the experiments
were carried out under storm conditions.
Concerning the placing of the structure in the
beach profile, the general rule is that the sea wall
should be constructed where it can be built best and
cheapest with the desired effect. Sea walls with a verti-
cal or slightly sloping front should, as mentioned be-
fore, never be constructed on erodible coasts; they will
at any time have to be placed so far away from the
shore line that they will never be subjected to un-
broken, or, especially breaking waves. A sloping wall
must cause a loss of energy as large as possible, by
causing the waves to break. The waves break at a
depth of about 1.3 Hb, H, being the wave height at
the breaking. If a sloping wall is to be built on a
coast consisting of erodible material, it is necessary to
construct the wall so that the maximum effect of the
waves bears upon the slope itself and under no cir-
cumstances on the bottom just in front of the struc-
ture, as in that case the structure might collapse
through underscour. The revetment, therefore, must
be made in such a way that it is able to stand such
action, and it should be as flexible as possible.
On a coast consisting of less erodible material it
is easier to select a construction. A berm, built in a
sea wall should be placed where it causes the greatest
loss of energy. The height of the berm must be such
as to effect the greatest possible energy loss, whether
it is smooth or roughened. Its width will have to be
reasonable and economical. If the sea wall is rough-
ened corresponding to storm conditions, this roughness
must be arranged so that it does no harm under more
normal water and wave conditions. There may be
two degrees of roughness, a big and a small one, with
open spaces between the big roughness (e.g. sleepers)
and the slope, so that the uprush during more normal
wave conditions may partly pass under the big rough-
ness. Finally, the uprush will have to be as small as
possible. The measures against the reflection may
under no circumstances increase the turbulence in
the backrush at the intersection of the slope and the
Below is given only one example of the experiments
carried out. The test refers to the actual water level
and wave conditions. The results have a fundamental
character. The tests were carried out in a 50 ft. long,
2 ft. wide wave tank with a water depth of about 2 ft.
and with storm waves. For further information the
reader should consult (8, e).
The reflection is defined as
height of the 2 to 3 highest waves
height of the incoming wave
The height of the uprush is defined as the height
of the 2 to 3 highest uprushes.
Figure 16 shows results of an experiment with a
sea wall. The experiment was carried out with 12-
centimer (5 in.) high oscilating waves and with a 12-
centimeter (5 in.) high solitary wave (results indicated
by an S). The reflection coefficient in per cent and
the uprush (or rather upsplash) in centimeter over
a fixed level are the ordinates. Reflection and uprushes
are separated by a heavy line. The water level was 69
centimeters over a fixed level. The experiments were
made with base levels of the wall 60 centimeters and
66 centimeters over the fixed level (see abscisses of
Defects, especially common in sea walls are:
(a) Tendency to erosion behind the structure due
to falling water and uprush.
(b) Tendency to erosion in front of the struc-
ture due to falling water, backwash and re-
Measures against (a) are: a high wall, use of a
wave nose, introduction of a berm in the wall or
protection of the area behind the wall by a tight cover.
Measures against (b) are: a protective apron in
front of the wall-often to a considerable extent-con-
structions of groins and/or artificial replacement of
In Figure 16 the sea wall has been provided with
a stilling basin at the foot, and with a roughness con-
sisting of 2 x 2-centimeter (about 1 x 1-inch) steps.
From the figure it can be seen that:
(a) The reflection has been considerably reduced
by the building of a stilling basin at the foot of the
wall. The reflection is least with a berm height of 66
(b) Tests with a solitary wave with the water level
at 60 centimeters gave the same results concerning the
effect of the stilling basin.
(c) The uprush is reduced considerably.
(d) Tests at berm level 66 with 2 x 2-centimeter
(about 1 x I-inch) steps gave the same reflection as
without steps, but less uprush.
(e) From the above discussion it appears that the
protective apron in front of the wall should be made
.sea wall only
ru. .. ____ _
Zf ---- ~ ^ : y ------
Figure 16.-Experiment with a Sea Wall.
as a stilling basin, whereas the pavement of the wall
should be laid in steps, and the wall should be sup-
plied with a wave nose. The final cross section must
naturally depend on special investigations in each in-
The above example demonstrates the value of
hydraulic experiments in coastal engineering. No sea
wall should be constructed before such very simple
and rather inexpensive experiments have been carried
In coastal engineering isolated breakwaters have
been used especially in Italy, Spain and the United
States. They are expensive but effective. Breakwaters
in connection with groins, according to the above, are
used to form T-groins, angular groins and Z-groins.
ARTIFICIAL NOURISHMENT OF BEACHES
Artificial nourishment of beaches is an American
idea, and there is some reason to believe that much
coastal protection in future will be carried out in this
way due to a growing recognition of the fact that pre-
vention of erosion by means of protective structures
might be a dangerous practice; because in many cases
such protection is obtained by the production of an
ever expanding problem area because of the lee-side
erosion. Artificial nourishment, on the other hand, is
of benefit not only to the shore upon which it is placed
but to adjoining shores as well.
As pointed out by Eaton and Hall,4, 14 the
method, even if it has been employed without a
complete understanding of all factors controlling an
ideal installation, has given good results.
When the quantitative deficiency in the material
supply in the area considered and the predominant
direction of the littoral drift are determined, the
problem one is faced with is that of selecting a suitable
beach material. The selection of a material of the
proper gradation to produce the required slope of
---------- ---------- -.-
I r-l 1 I
i'- '-'--t--- -
with sil .g h asi
wi/h steps 2 2 cm ..-.sb ,-4 .
- . ....... .. ;- i .
-, ~ ~ ~ ~ ~ 4 a.! !! !.!:6 .0r;.11w. -M ,
the beach at the present time can only be determined
by analysing the sand taken from a beach in the sur-
rounding area, which has a similar orientation and is
acted upon by the same wave forces. Sand selected for
artificial nourishment should ideally contain the same
gradation of materials as those found on the beach to
be nourished, if the original beach slope is to be
maintained. Material of coarser characteristics may be
expected to produce a steeper beach than normal.
Material finer than that occupying the natural beach,
when exposed on the surface, will move seaward to a
depth compatible with its size.4
There are four types of artificial nourishment:
(a) the offshort dumping method, the stockpiling
method, the continuous-supply method, and the direct
The offshore dumping method was tried at Long
Branch, New Jersey, and at Santa Barbara, California.
In both cases dredged sand was deposited in about
20 ft. of water (MLLW). The results, however, were
not good, but this may be due to unfavorable con-
The stockpile method was first tried at Santa Bar-
bara, California, and has been in successful operation
since 1938. The problem at Santa Barbara was created
by the construction of a breakwater in 1929 which
blocked the littoral drift. In 1938 a co-operative pro-
ject was developed at the recommendation of the
Beach Erosion Board, providing for establishment of
a stockpile beach fill along 4,000-ft. of shore down-
drift from the harbor to be initially filled and period-
ically maintained with material dredged from the
harbor. Since 1938, replenishment has been accom-
plished at two- or three-year intervals. The average
rate of artificial nourishment has been 300,000 cu.yds.
a year and is accomplished with pipeline dredging
The continuous-nourishment method is used at
Salina Cruz, Mexico, a harbor on a littoral drift
coast.'0 Six suction pipes run by special derricks were
arranged on the updrift side of the harbor, and sand
was pumped to the lee side.
One of the best examples of continuous nourish-
ment to a beach downdrift from an inlet is the sand
by-passing plant at South Lake Worth Inlet, Florida.
South Lake Worth Inlet is located on the east coast
of Florida near the southern limit of Lake Worth,
which separates the mainland from the sand barrier
on which the town of Palm Beach is located. The
inlet is protected by two jetties about 250 ft. long.
Due to abundant littoral drift from north to south in
this area, the littoral reservoir formed by the northern
jetty was quickly filled, and sand was carried around
the jetty and into the inlet.
A pumping plant was installed in 1937 on the
northern jetty.9 The plant consisted in the main
of an 8-in. suction line and a 6-in. centrifugal pump.
During the four years between 1938 and 1941 beach
material was pumped past the inlet at the rate of about
48,000 cu. yd. per year. The result was that the beach
on the lee side was restored.
The direct placement method differs from the
stockpile method in that the fill is completed at one
time over the entire shore to be protected. This type
of beach rehabilitation was used at Atlantic City, New
Jersey, in 1948, to quickly restore the ocean beach.
The beaches were replenished with sand moved across
Absecon Inlet. In the summer of 1948, 700,000 cu. yds.
were placed on the beach off Atlantic City over a 6,000-
It appears that beach erosion control in the future
(1) Structures consisting of specially designed
groups of groins or sea walls and/or artificial nourish-
(2) Investigations in the field made to find out the
kind of coastal protection which should be preferred
in relation to the actual situation of source of materials
and development of beach profiles.
(3) Investigations in a hydraulic coastal engineering
laboratory to determine the details of the construction.
(4) Concerning the conditions in Florida the order
of development of the best coastal protection appears
(a) At all beaches where beach erosion, however
slight, takes place, depth soundings should be car-
ried out regularly to determine the actual situation.
(b) The coastal protection experience already
gained in the United States and in Europe should
be used in relation hereto.
(c) The development of the coastal protection
technology should be carried out in coastal engi-
neering laboratories. In Florida, the special Florida
conditions should be taken into account. Much
money could have been-but still can be-saved in
1. Bagnold, R. A. (1940), "Beach Formation by Waves, Some
Model Experiments in a Wave Tank," Journal Inst. Civil Eng.
1940-1941, pp. 27-52.
2. Beach Erosion Board (1952), Bulletin No. 1, pp. 1-17, Corps
of Engineers, Washington, D. C.
3. Beach Erosion Board (1951), Technical Memorandum No. 26.
4. Beach Erosion Board (1952), Technical Memorandum No. 29.
5. Beach Erosion Board (1953), Bulletin, Special Issue No. 2,
"Shore Protection Planning and Design."
6. Beach Erosion Board (1954), Technical Report No. 4, "Shore
Protection Planning and Design."
7. Bruun Per (1953), Coastal Protection, Review of Methods for
Defence, 10 pp.
8. Bruun, Per (1954), Coast Stability, 380 pp.
a. The Erosion of the Lime Inlet Barriers, Denmark-255 pp.
b. Forms of Equilibrium of Coasts with a Littoral Drift-
c. Small Scale Experiments in Plans for Coastal Protection-
d. Measures Against Erosion at Groins and Jetties-30 pp.
e. Breakwaters for Coastal Protection, Hydraulic Principles
in Design-40 pp. Danish Technical Press, Copenhagen.
9. Council on Wave Research, (1951), Coastal Engineering, No.
1, 334 pp.
10. Council on Wave Research, (1952), Coastal Engineering, No.
2, 393 pp.
11. Council on Wave Research, (1953), Coastal Engineering, No.
3, 343 pp.
12. Council on Wave Research, (1954), Coastal Engineering, No.
4, 398 pp.
13. Dobbie, C. H. (1949), Report to the XVIIth International
Navigation Congress, S II, C I, pp. 75-84.
14. Eaton, R. 0. (1951), "Littoral Processes on Sandy Coasts,"
Coastal Engineering, No. 1, pp. 140-154.
15. Frech, F. F. (1949), Report to the XVIIth International
16. Hansen, Howard (1947), "Beach Erosion Studies in Florida,"
Engineering and Industrial Experiment Station, Bulletin No.
17. Iribarren Cavavilles (1950), "Generalization of the Formula
for Calculation of Rock Fill Dikes and Verification of its
Coefficients;" Revista de Obras Publicas Mayo de 1950; see
also Coastal Engineering No. 1 pp. 217-219 and 237-241.
18. Johnson, J. W. (1949), "Scale Effects in Hydraulic Models In-
volving Wave Motion," Transactions American Geophysical
Union, Vol. 30, pp. 517-525.
19. Johnson, J. W. (1953), "Sand Transport by Littoral Currents,"
Proceedings of the Fifth Hydraulic Conference, Bulletin 34,
State University of Iowa, Studies in Engineering.
20. Kressner, B. (1928), "Modellversuche Uber die Wirkungen
der Brandungswellen und des Kustenstromes auf einem
Sandigen Meeresstrand und die Zweckmassige Anlage von
Strandbuhnen," Die Technische Hochshule der Freien Stadt
21. Kuiper, E. (1951), "The Construction of the Harlingen Break-
water," Bulletin No. 34 of the International Navigation Con-
gress, pp. 123-135.
22. Iee, Charles E. (1954), Filling Patterns of the Fort Sheridan
Groin System," Coastal Engineering No. 4, pp. 227-248.
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