Defense of Shorelines by Structural Approaches

285

DEFENSE OF SHORELINES

BY

STRUCTURAL APPROACHES

by R. G. Dean 1. INTRODUCTION

Structural approaches can be employed to stabilize shorelines against erosion, to provide sheltered areas for swimming or for a myriad of other benefits. In this section, the emphasis will be on shoreline stabilization although much of the information and discussions presented would be equally applicable to accomplish other objectives. Three general types of structures are discussed in this treatment of defense of shorelines: (1) detached breakwaters, (2) groins, and (3) armoring. Artificial headlands and perched beaches will be considered here in as a subclass of detached breakwaters. It should be noted that each of these structure types can be employed for stabilization purposes in conjunction with beach nourishment. The sections below discuss each of the types.

2. DETACHED BREAKWATERS

Although not completely descriptive, detached breakwaters as discussed here will include those which due to their length and proximity to the shoreline become attached to the shoreline, thereby forming a "tombolo". This type of structure has been of substantial interest to many investigators due in part to their wide usage and the opportunities provided to "architect" the shoreline and to retain sand placed in conjunction with beach nourishment. There are reportedly some 2500 detached breakwaters in Japan.

Figure 1 illustrates a detached breakwater. These structures can be emergent or submerged. Their primary purpose is to provide wave sheltering of the beach, thereby reducing the sand transporting capacity of the waves and causing a wider beach than would otherwise be present. Several aspects of detached breakwaters are discussed in the following sections.

2.1 critical Conditions for Attachment

The critical conditions governing attachment of a breakwater to a shoreline have not been established definitively. Certainly the closer the breakwater to the shoreline relative to its length, t, the more likely the occurrence of attachment. Considering the diffracted wave fronts to be represented by quarter, circle

286 R.G.DEAN

I

~I

Figure 1. Schematic of a Single Detached Breakwater

~I-6

~ _{EI Dally & Pope}

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Figure 2. Non-Dimensional sa~ient Value versus Non-Dimensional Breakwater Length. From Hsu and Silvester (1990).

DEFENSE OF SHORELINES BY STRUCTURAL APPROACHES ₂₈₇

segments, one can easily develop the following simple criterion for attachment

s

"1

so .5 (1)

This relationship may be considered as a first approximation; however, the actual conditions also depend on beach profile and wave height and direction characteristics and several other

factors.

Hansen and Kraus (1990) employed a numerical model (GENESIS) to evaluate conditions which would result in various depositional types in the lee of a single detached breakwater. The results were found to compare favorably with field data. It is stated that there are at least 14 parameters controlling the depositional form. Of particular interest is the inclusion of wave transmission as could occur over a submerged breakwater or wave penetration through a permeable breakwater. The conditions for a tombolo to form were determined to be

(2)

in which L is the "local" wave length presumably evaluated at the breakwater, Ho is the de ep water wave height, hs is the water depth at the breakwater, and

Kr

is the transmission coefficient past the breakwater. It is surprising that this result is independent of the breakwater separation distance, s, from the shoreline.

2.2 Single Detached Breakwaters

Hsu and silvester (1990) have analyzed laboratory and field data representing a single detached breakwater and have developed empirical relationships between the non-dimensional separation distance, (S-X)j!, and the non-dimensional breakwater length,!js, as shown in Figure 2. Although the fit between these variables appears good, it is not clear that the prediction of tombolo attachment is an improvement over other approaches. Two empirical fits were made to the data in Figure 2. One of these fits resulted in no tombolo formation and the other predicted tombolo format ion when sj!

=

0.2, much smaller than normally considered.

288 R.G.DEAN

2.3 Multiple Detached Breakwaters

Pope and Dean (1986) assembied data from ten segmented

breakwater projects in the united States and proposed a

classification scheme which ranged from tombolos to salients to no sinuosity as shown in Figure 3. The dominant controlling parameters were found to be the ratio of effective distance offshore to water depth at the breakwater, s/h~, and the ratio of segment length to

gap length, tt/tg. Although ~here is some uncertainty as to the

boundaries of tne three regions, the general effects of the

identified parameters are evident in Figure 3.

70 00 (AST ...

.

10 s h. 40 0.' 1.0 I.' Z.O t.s s.o l.S

Figure 3. Classification For Various Shoreline Forms Behind a Detached Breakwater. From Pope and Dean (1986) Suh and Dalrymple (1987) carried out model tests in a spiral

wave basin to investigate shoreline response to multiple

breakwaters. The resulting data were co~ined with other lab and field data to predict the salient projection, X, and the volume deposited, Vdf as a result of the breakwater. The following results were developed results were

DEFENSE OF SHORELINES BY STRUCI1JRAL APPROACHES 289 , ••. > f s -2.8J(..:c) X

=

14_8 s ( ~) e ( ~~ and

in which a is a factor found to be approximately 2.0 and m is a

representative beach slope.

2.4 Effect on Longshore Sediment Transport

The question of the effect of detached breakwaters on the

longshore sediment transport system is relevant to the stability of

the adjacent beaches. Considering the idealized case of waves

approaching at a constant oblique direction and the formation of a

protuberance or "bulge" in the shoreline, leads to the following

conclusion. The breakwater will cause the updrift shoreline to

continue to accrete and the downdrift shoreline wil I continue to

erode at the same volumetric rate as the updrift accretion. This is

based on the Pelnard Considere (1956) solution for the case of a

single shore perpendicular structure for constant wave direction in

which regardless of the structure length, the updrift and downdrift

shorelines continue indefinitely to accumulate and lose sand

respectively, albeit at a decreasing rate as time progresses. In

fact it is surprising that according to the Pelnard Considere

theory, the amount of sand stored on the updrift shoreline

approaches infinity as time approaches infinity! Counter arguments

have been advanced that a detached breakwater will cause a

longshore current ·which will result in the updrift volume

impoundment reaching an equilibrium: however, this result does not

appear to be documented.

Considering the more realistic case of variable wave

direction, the net effect on longshore sediment transport is not so

evident. Two subcases could be considered, one in which the waves

arrive from a range of directions which all contribute to the same

transport direction and the second in which the wave directions

produce varying transport directions, but with a finite net

transport. In the first case the transfer around the breakwater

would occur in a more variabie fashion than without a changing wave

direction. Perhaps this problem could be addressed through a

careful application of numerical modelling. Although this question

must still be regarded open, this author believes that the correct

answer for each subcase is a variation of that obtained by Pelnard

Considere for constant wave direction: that is, the updrift volume

deposited would approach infinity with time.

290 R.G.DEAN

2.5 Artificial Headlands

Artificial headlands are structures which anchor the shoreline usually in a sediment deficient area and, through interaction of the incoming wave field, can result in a variety of planforms. The planforms have been given several names including: crenulate bays, spiral bays, half-heart bays and others. As is the case with other types of coastal structures, this type has natural analogues which probably have contributed to their interest. An idealization of an artificial headland with a predominant oblique wave direction is presented in Figure 4.

~ =sinl3

b (4)

Artificial headlands have been studied by 'lasso (1965), silvester (1970), silvester and Ho (1972), and Rea and Komar (1975), among others. To the first approximation, the associated beach planforms may be considered as parallel to the wave fronts as affected by diffraction and refraction. segmented breakwaters, 'each with a tombolo connection to shore are artificial headlands. Depending on the wave direction, magnitude of sediment transport and the headland geometry, a range of planforms can ensue as can be imagined by considering the shapes of the modified wave fronts.

Silvester and Ho (1972) have combined data from the laboratory and field for the ratio of indentation to gap between headlands as shown in Figure 4. Considering the ambient longshore sediment transport to be zero, and a simple wave pattern in which the diffracted crests in the "shadow zone" are circular arcs and are unaffected in the "illuminated zone", the ratio a/b is given by

which has been added to Figure 4 and is seen to yield a/b va lues larger than measured. One partial explanation is that, as seen in Figure 5, that qualitatively, the indentation ratio is a function of the ratio of actual to poten·tial sediment transport, Q./Qo. The potential sediment transport Qo is the amount of transport that would occur if an ample amount we re available to be transported.

Artificial headlands and their associated beaches may be considered (in a similar manner as will be discussed for groins) as compartmenting and reorienting the shoreline such that the waves approach dominantly directly shore-normal. Thus a shoreline can be maintained, perhaps in a more advanced position, than would otherwise be the case. silvester and Ho (1972) have reported on a land reclamation project in singapore where artificial headlands were used to stabilize the placed material. It is clear that the viability of such a project is absolutely dependent on the maintenance of the connection between the headland and the shore.

DEFENSE OFSHORELINES BYSTRUCTURAL APPROACHES 291 o/b O. 0.6 O.S

\.~b--i

LEGEND

•

VlchctpQII exp. ~

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Hoexp. JI prototype boy.

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typlcol boy

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kdoclr S'"90pore 7

V

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_aIIG~

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V

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•

/ ~

...

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.

/ _~/~

I,,""

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o o 10 .20 )0 ₄₀

l

_{50 60 70 10 90} ;..

Figure 4. A Crenulate Bay Formed by Oblique Waves Approaching Headlands at an Angle,

p.

Indentation Ratio, a/b

versus

p.

From silvester and Ho (1972l!

Rock or Other Type Structure ~ves /waves -_.:_.'_... ... al 0.100 = 0 hl 0.100 0.5 cl 0.100 1.0

Figure 5. Qualitative Variation of Indentation Ratio, a/b with Ratio of Actual to Potential Sediment Transport,

Q·/Qo·

292 R.G. DEAN

One approach is to construct a rubble mound or sheet pile stem from the headland to shore, thereby contributing to the integrity of this connection.

2.6 Perched Beaches

The concept of a perched beach in its most simple form is two-dimensional in which an underwater structure, hereafter termed a sil1 is placed offshore to "perch" sand placed to widen the beach,

see Figure 6. The primary advantage of this type structure is the

potential substantial reduc't.Lonin required sand volumes to achieve

a desired additional beach width, especially if the sand is fine

and therefore of a naturally mild slope. In application, there is

need to consider sand losses at the ends of the installation and

therefore it may be desirabie to connect the ends of the sill to

the shoreline with "return" structures.

Apart from concerns of the effects of this type project on

adjacent beaches which could be greater if the returns we re

constructed, model tests by Chatham (1972) and Sorensen and Beil

(1988) have shown that, especially if wave breaking occurs on the

sill, the equilibrium depth on the landward side of the sill can be

substantially deeper than the sill crest. This depth forms a

boundary condition for the landward profile and the addi tional

beach width associated with the equilibrium profile will be

considerably less than expected if this scour landward of the sill

is not taken into consideration. If the area landward of the sill

is initially filled to the top of the si11, there can be a

substantial amount of sand transported seaward over the sill from

which it is unlikely to return landward of the sill as shown in

Figure 6. 0.9 0.8 !0.7 ,: Z _0.6 0 ;:: ~

_'0

w o.s

_0'

...J W :z: 0.4 u

..

W 111 _0.3 O.Z 0 Z 3 4 , •

DlSTANCE FROII IULKHEAD. X.(11)

7

Figure 6. Laboratory Test Results of a Perched BeaCh.

From Sorensen and Beil (1988)

2.7 Summary

DEFENSE OF SHORELINES BY STRUCTURAL APPROACHES 293

Detached breakwaters can be effective in impounding sand from the longshore sediment transport system or in stabilizing sand placed to widen the beach. Applications mayalso include reduction of wave energy to improve recreational beach usage. It appears that detached breakwaters placed on a long beach characterized by a net longshore transport will exert a long-term effect by impounding sediment on the updrift side and causing an equivalent amount of volumetrie eros ion on the downdrift side. If the breakwaters are submerged or substantially overtopped, the mass transport of water to the lee side may cause undesirable longshore and/or rip currents.

3. GROINS

Groins are structures oriented normal or nearly normal to the shoreline. The purpose of groins is to interact with the longshore sediment transport to advance the shoreline seaward or to stabilize sand placed for the same purpose. The method by which groins function may be regarded as providing lateral support which resists the longshore stresses exerted by waves arriving at an angle. Through this process, the beach planform is locally reoriented into the incoming waves, thereby resulting in alocal reduction of sediment transport. Figure 7 presents an example. Instead of transporting sand along the shoreline, the longshore force is resisted by the groins. A different way of viewing the interaction is that the groins cause the shoreline inside the groin compartment to reorient itself into the incoming waves such that locally there is no longshore shear stress.

Waves

,/

... Waves G1mIii:4>.. / .... .-:: b) Q./Qo = 0.5

Figure 7. Shoreline Planforms For Various Values of the Ratio

of Ambient to Potential Longshore Sediment

Transport, Q./Qo'

294 R,G,DEAN

The amount of additional shoreline resulting from a field of groins of a particular length and spacing is of design interest. The additional beach width, w, can be expressed as

in which hs is the water depth at the end of the groin, s is the spacing between groins, p is the incident wave direction, m is the average slope of the beach profile over the groin length, Q.is the ambient longshare sediment transport, and Hb is the breaking wave height. The qualitative manner in which same of these variables contribute to beach width wil! be discussed in the following paragraph.

The farther the groins extend offshore relative to the active zone of sediment transport, the greater the added beach width. Thus for a particular wave height and groin length, a mildly sloping beach will have a narrower beach than will a steeper beach. Obviously, waves arriving at a more oblique wave angle will result in a narrower ave rage beach width than will waves with less obliquity. Considering the detailed transport fields within the groin compartments, it is seen that if the longshore sediment transport potential is large but the availabili ty of sediment to be transported is significantly smaller, the width will be less as the forces which tend to remove sand from the compartment are related to the potential transport whereas addition of sand depends on the actual transport.

The effectiveness of groins can be influenced greatly by the tendency for large seasonal or storm related cross-shore sediment transport. Sand transported seaward from the groin compartment to form a bar will be available for longshore sediment transport and thus can move downdrift. If the volume of longshore transport on the bar is large relative to that available during the time that the bar is not present and thus the conditions are conducive for

filling the compartment, then groins may be less effective.

Groins interact with the longshore sediment transport system in much the same manner as discussed previously for a detached breakwater. A single groin or a groin field extending beyond the shoreline will impound sand bath updrift and in the case of multiple groins, within the compartments, first at a'rapid rate, then at a decreasing rate as bypassing occurs. However, as noted previously, the theory of Pelnard Considere predicts that the groin will continue to trap sediment and that the total volume impounded will approach infinity as time approaches infinity.

A groin can fail functionally if it is flanked, that is if the shoreline recedes on one or both sides to the degree that water and sand flow landward of the groin. This constricted flow'can cut a

DEFENSE OF SHORELINES BY STRUCTIJRAL APPROACHES 295

fairly deep channel and render the groin ineffective. This will usually occur during a major storm or as a result of an erosional trend.

An additional effect of groins is for the sand which bypasses a single or multiple groin installation to form a bar with an alignment trending shoreward and eventually attaching to the shore. The tendency for this attachment to occur at a greater distance downdrift is enhanced during conditions under which a bar would tend to form naturally. The effects of groin fields on adjacent shorelines will be reduced if the groin compartments are pre-filled and if the groin field is tapered. High groins can cause rip currents which carry both sand and water seaward. If the groin" profile is configured as a slightly higher vers ion of the desired beach profile, water can flow over the groins and rip currents will be less likely to form.

With the above mentioned effects on adjacent shorelines, the most appropriate locations for groin usage appear to be at the ends of littoral systems, such as immediately updrift of inlets, where,

if the groins were not installed, the sand would be effectively

lost to the nearshore system. Groins placed on a continuous beach should definitely be tape red in planform and pre-filled to minimize impact on adjacent beaches.

4. ARMORING

Coastal armoring as used here can encompass any type of shore parallel structure which, upon construction, has dry land behind

it. Thus, such structures can include stone or other type

revetments and seawalls. The purpose of armoring is to protect the

land from the sea, either against a chronic erosional trend, an

episodic event, or a combination of the two. there has been much

discussion regarding the adverse effects of coastal armoring,

however unless the structure projects into the active surf zone, the adverse effects are relatively limited. Two types of adverse

effects of seawalls that are manifested during storms will be

discussed below. The reader is referred to the series of eight

articles on the interaction of seawalls and beaches in the volume edited by Kraus and Pilkey (1988).

During storms, on an unseawalled profile, sand is transported seaward from the beach and shallow water to form an offshore bar. If a seawall limits the supply of sand from the upper beach from

which it would normally be taken, experience has shown that the

waves will remove the sand from a region as close to that from

which it would have otherwise originated, i.e. at the toe of the seawall. The amount of sand eroded from near the seawall toe has been determined through laboratory studies to be somewhat less than

would have been removed from landward of the seawall location,

Darnett and Wang, 1988. This effect is two-dimensional as would

296 RG.DEAN

occur in a wave tank, see Figure 8a. There is also a three-dimensional effect wherein during storms, there is an increased erosional pressure on the shorelines adjacent to an armored shoreline segment. The armored segment limits the seaward transfer of sediment during the storm and thUs the supply of sediment available for construction of the offshore bar is diminished. Considering the offshore bar to have a certain level of "demand" for sand, a portion of this demand wi11 be satisfied by sand flowing from the adjacent regions as shown in Figure 8b. Walton and Sensabaugh (1975) have documented this effect through field surveys after Hurricane Eloise in 1975 and have deveLoped the results presented in Figure 9. The amount of additional shoreline recession at the ends of the armoring increases with seawall length.

Of course, if seawalls are constructed on an eroding shoreline, they will eventually protrude into the active surf zone and will cause the usual updrift accretion and downdrift eros ion if a net longshore sediment transport is present.

In the United States, seawalls have been judged to have a wide range of adverse effects on beaches. Most of these claims do not have any basis in measurement or field data, and some of the more unrealistic suggest a net sand loss to the system or sand being carried out to deep water. An assessment by Dean (1986) on the effects of seawalls on the adjacent shorelines is presented in Table 1.

5. REFERENCES

Ahrens,J. P. (1987) "Characteristics of Reef Breakwaters", U. S. Army Corps of Engineers, Coastal Engineering Research Center, Tech. Rept. CERC-87-17.

Barnett, M. and H. Wang (1988) "Effects of a vertical Seawall on Profile Response," Proceedings, Twenty-First International Conference on Coastal Engineering, Chapter 111, pp 1493-1507. Chatham, C. E. (1972) "Movable-Bed Model Studies of Perched Beach Concept, "Proceedings, Thirteenth International Conference on Coastal Engineering, Chapter 64, pp. 1197-1216.

Dally, W. R. and J. Pope (1986) "Detached Breakwaters for Shore Protection," Technical Report CERC-86-1, U. S. Army Engineer Waterway Experiment Station. Vicksburg, MS, 62 pages.

Dean, R. G. (1980) "Coastal Structures and Their Interaction with the Shoreline" Chapter 18 in "Application of Stochastic Processes in Sediment Transport" edited by H. C. Shen and H. Kikkawa. Water Resources Publications, Littleton, Colorado.

DEFENSE OF SHORELINES BY STRUCTURAL APPROACHES 297 Shore ContiruaJsSeowall -:::.:... --- :::}"-Nonnol BeochProfile :.'-_ without Seowall ,~~~;:%; S~rm Beoch Profile '~- :--- wIthout Seowoll

..;... '- Storm Profile with Seowall

NormolBeoch Profile with or without Seowoll ELEVATION VIEW

a) Qualitative Effects of Continuouo Seawall on Storm Beach Profile •

Waves

...I~:__; Initial Shorefine Rlsition Under Normol WoveConditions

Length

b) Effect of Seawall of Limlted Length on Storm or Long-Ter. Be.eb Planform.

PLAN VIEW

Figure 8: Two- and Three Dimensional Effects of a Seawall on a Beach System durinq Storms. From Dean (1986).

298 R.G.DEAN

Reen.'on ., Be.eh Durin; Slorm " s. ••• U I. "Ol P,. ....ts x Po.,ulaIH Upper Limitlor

Aankln; ol Relurn W.U (Irom "EIol••·•Dal.)

;J--·E

__

:

-,.

--J----~'-I'js

a

a•

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,k

r

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r-

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~

Cap Hal;hl. ~ --I----++----lf.---.-.- ~Conlour Prol. 10 Slorm

--- '1Conlour Aftar Slorm ,.Conlour Racession Dlllinca

dua 10 Enael. ol s.a.aU

200 400 1000 1&00

lENGTH OF SEAWALL (OR STRUCTURE)

Figure 9. Additional Bluff Recession During storms Due to Proximity to Seawalls. Based on Post-Hurricane Eloise Observations by Walton and Sensabaugh (1976)

Table 1

Assessment of Some Commonly Expressed Concerns Related to Coastal Armoring. From Dean (1988)

Concern Assessllent

Coa.tal .r-orl"g placed in en area _{Bypreventing the uplond froID erodlng.} the beachea

of "I!Jtlstlng eroaional stress C8USI!a _{TRUt adjacent to the anaarlng share. greater portion of the}

lnere.eed eroslongt stress on the _{aame total eros ion.! stress.} beaches adlaeent to the armorinll.

eoaatal anltoring ia designed to proteet the upland, but Coaotal ItrlDOrlng plaeed In an doe. not prevent erosion of. the beach profile w.ter".rd

of the armoe!ng. Thus an erodlng beaeh viII continue to area of eJtlltlng eroalonal stresa

TRU! erode. lf the armorlng had not been plaeed. the width of

viII cause ehe be.~hea fronting

the beach vould have remained approximately the SRllle, but

the or.oring to dlminhh.

,,{th incree!!ng time, vould have been located

progree-aively landword.

eoastal .reorin! cause s an _PROBABLY No knovn date or phyaical argUftlents.upport thll

acceleration of beach era. ion _{FALSE concern.}

leoward of the 8<lDOrinll.

lf an illolsted s erue eure 11 ar",of~d on nn erodinR be.ch,

the "trH~turewlll eventunl1y rrotrude tnto the ftctlve

An t,,()lntedc,uu,tnl nfmnrtnR

TRUI! beoeh zone nnd wlll aet to eome degree ••• groln,

inter-can accelerate downdrift erosion.

ruptlng long.hore .edlment transport end thereb,. eaulins downdrift erosion.

eo_et_l _r.orlns results In a _{PROBABLY No known data or phy.leal} argnents lupport thh IreoH,. delayed post-etorll _{FALSE concern.}

recovery.

Coeetal erllOr!n! eaus es the PROBABLY No known data or physical argument! support thlo beach profile to steepen FALSE concern.

dra •• tleallT.

In order to have 8n1 substantiel effect!! to the beachea,

Contil arllOrlng plaeod

well-the ar.oring mu.t be .cted upon by the wave. and

s=

back fro •• st.bie beach Ie

FALS! Horeover, armoring set veIl-back fro. the nor •• ll, act!.e detri.ent.l to the.beach end

eC~1ve .hoee Eone can provide "lneue.nee" for uptand serve. na ueeful purpoae.

.t.ruct.urea •• alnat aevere ItOr.I.

DEFENSE OF SHORELINES BY STRUCTIJRAL APPROACHES ₂₉₉

Dean, R. G. (1986) "Coastal Armoring: Effects, Principles and Mitigation", Proceedings, Twentieth International Conference on Coastal Engineering, pp. 1843-1857.

Hansen, H. and N. C. Kraus (1990) nShoreline Response to a Single Transmissive Detached Breakwater", Proceedings, Twenty-Second International Conference on Coastal Engineering, Chapter 154, pp. 2034-2046.

Hsu,J. R. C. and R. Silvester (1990) "Accretion Behind Single Offshore Breakwater," J. Waterway, Port Coasta1 and Ocean Division, ASCE, Vol. 116, No. 3 pp. 362-380.

Kraus, N.C. and O. H. Pilkey (Editors) (1988) "The Effects of Seawalls on Beaches", A Series of Eight Individua1ly Authored Papers, Journalof Coasta1 Research, Special Issue No. 4, Autumn. Pelnard-Considere, R. (1956). "Essai de Theorie de l'Evo1ution des Formes de Rivate en Plages de Sable et de Galets." 4th Journees de I'Hydraulique, Les Energies de la Mar, Question III, Rapport No. 1

(in French).

Pope, J. and J. L. Dean (1986) "Development of Design Criteria for Segmented Breakwaters," proceedings of the Twentieth International Conference on Coastal Engineering,Volume 3, Chapter 158, pp.2144-2158.

Rea, C. C. and P. D. Komar (1975) "Computer Simulation Models of a Hooked Beach Shoreline Configuration," J. Sedimentary Petrology, v.

45, no. 4, pp. 276-287.

Silvester, R. (1970) "Growth of Crenu1ate Shaped Bays to Equilibrium", J. Waterways and Harbors Division, American Society of civil Engineers, WW2, pp. 276-287.

Silvester, R. and S. Ho (1972) "Use of Crenulate Bays to Stabilize Coasts", Proceedings, Thirteenth International Conference on Coasta1 Engineering, Chapter 74, pp. 1345-1965.

Sorensen,R. M. and N. J. Reil (1988) "Perched Beach Profile Response to Wave Action," Proceedings, Twenty-First International Conference on Coastal Engineering, Chapter 110, pp. 1482-1492. suh, K. and R. A. Dalrymple (1987) "Offshore Breakwaters in Laboratory and Field", J. Waterways, Port, Coastal and Ocean Engineering, ASCE, Vol. 113, No. 2, pp.105-121.

Walton, T. L. and W. M. Sensabaugh (1979) "Seawall Design on the Open Coast" Florida Sea Grant, Report No. 29.