CETA 81-1 u ...... - \

Wave Loading on Vertical Sheet-Pile Groins and Jetties

by

J. Richard Weggel

COASTAL ENGINEERING TECHNICAL AID NO. 81 -1

JANUARY 1981

Approved for pu bl ic re lease;

distribution unlimited.

U.S. ARMY, CORPS OF ENGINEERS

COASTAL ENGINEERING RESEARCH CENTER

Kingman Building

Fort Belvoir, Va. 22060

Repr in t or r e publ ' c a tion of shall g i ve a ppro p r iate credit to Engineeri ng Re s a r ch Ce nt r.

any of th : s materi a l the U.S. Army Coastal

Li mit d free dis t r ibu t i o n within the United States of s ing l e copies of thi pu blication has be n made by this Ce nt e r . Add itiona l c.opies a r e ava i lable from:

N t i ona "l Tee YI.1:caZ Tnf oY'l1la ion Se r>vice AJ""N: Or>erut -i onB !h: v isi on S28 Pon RO./fal. Roa SVY'inqfie lrf, Vi r>ginia .? Z 61

The fin d ings i n this r ep or t a r c not to be cons true d as an o f f i cial Depar tmen t of t he Ar my position unle ss so desig nated by o t her a u t ho r ized do c ument s .

UNCLASS IflED

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REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM

1. REPORT NUMBER 12. GOVT ACCESSION NO. 3 . RECIPIENT'S CATALOG NUMBER

Cc:TA 81-1

4. TITLE (8T1d Sub,trl.) 5 . TYPE OF REPORT II PERIOD COVERED

Coastal Engineering \~AVE LOADING ON VERTICAL SHEET-PILE Technical Aid GROINS AND JETTIES 6 . PERFORMING ORG. REPORT NUMBER

7. AUTHOR(.) B. CONTRACT OR GRANT NUMBER(o)

J. Richard \~eggel

9. PERFORMING ORGANI ZATION NAME AND ADDRESS 10 . PROGRAM ELEMENT. PROJECT, TASK

Department of the Arony AREA II WORK UNIT NUMBERS

Coastal Engineering Resea rch Center (CEREN-EV) F31 232 Kingman Build ing , Fort Belvoir,. Virginia 22 060

II. CONTROLLING OFFICE NAME AND ADDRESS 12 . REPORT DATE Department of the Army January 1981 Coastal Engineering Research Center 13. NUMBER OF PAGES Kingman Build ing, Fort Belvoir, Virginia 22060 17

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Approved for public release; distribution unlimi ted.

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lB. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on rev6r 36 3ido if ne cessary llI1d Identify by block number)

Groins Jetties t-tach-s tem reflection Wave loading Waves

20 . ABSTRACT (ContInue On rever~(J :fide tl nccc" •• ry 8:r1d Identlfy by block number)

A method is presented for calculating the distribution of force and over-turning moment resulting from incident wa ter waves moving along the axis of a groin or jetty with vertical sides. Wave height at the st ructure is determined from experimental data on l1ach-stem re f lec t ion. The distribution of force is assumed to be in proportion to the nonlinear shallow-water wave profile given by eit he r the cnoidal or strear.l-function wave theory. An example problem demonstrates how the cnoidal theory may be used to estimate the wave force and overturning moment distribution along a structure.

DO FOR .. I JAH 7) 1473 EDITION OF I NOV 6~ IS OBSOLETE UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (,",.n D",,, en'.,ed)

PREFACE

This report is an outgrowth of consultations with personnel from the U.S. Army Engineer District, Savannah, concerning wave loading on a concrete sheet­pile groin proposed for Tybee Island, Georgia. The Shore Protection Manual (SPM) provides methods for calculating wave forces due to waves acting normal to vertical-sided structures. The SPM also gives a method for reducing the dynamic component of force when waves approach at an angle to the structure; however, no methodology is presented for estimating the distribution of force and overturning moment along a structure's axis, particularly for waves propa­gating with crests nearly perpendicular to the structure. This report provides such a methodology. For sheet-pile groins and sheet-pile jetty sections, cost savings can sometimes be realized if wales are assumed to longitudinally distribute some of the wave force. The wave loading methodol­ogy presented will provide the information needed to calculate the forces transmitted by the wales. The work was carried out under the coastal structures research and development program of the U.S. Arr.lY Coastal Engineering Research Center (CERC).

The report was Branch, under the Development Division.

prepared by Dr. J. general supervision

Richard of N.

Co~ments on this publication are invited.

Weggel, Parker,

Chief, Chief,

Evaluation Engineering

Approved for publication approved 31 July 1945, as approved 7 November 1964.

in accordance with Public Law 166, 79 th Congress, supplemented by Public Law 172, 88 th Congress,

Colonel, Corps f Engineers Co~mander and Director

3

CONTENTS Page

CONVERSION FACTORS, U.S. CUSTOMARY TO t1ETRIC (S1)..... ... ... ... ...... 5

I INTRODUCTION......................................................... 7

II SPH METHODOLOGY FOR COMPUTI NG FORCES AND HOMENTS..................... 7

III MACH-STE~1 REFLECTION................................................. 8

IV CALCULATION OF WAVE FORCE AND OVERTURNING MOMENT ....•.....•.....••.•• 10

V EXA.fv1PLE PROBLEM...................................................... 10

VI SUm1ARY. • • • • • • • • • • • • • • • • • • • • • • • . • • • . • • • • • • • • • . • • • • • • • • • • . • • . • • • • • . • . • 16

LITERATURE CITED...................................................... 17

TABLE Variation of force along structure ..•.....•.•...•.•...•.....•.......... 14

FIGURES Reflection patterns of a solitary wave................................. 8

2 Oblique reflection of a solitary wave, experimental results; water depth, d = 0.132 foot.......................................... 9

3 Oblique reflection of a solitary wave, experiQental results............ 9

4 Beac11 and groin profile ........................•.........•.....•.....•. 10

5 Dimensionless cnoidal wave profile, 2 _ -4.5 k - 1 - 10 .•.•.•.•••••..••.•.• 13

6 Variation of force and moment along groin ............................. . 14

7 Loading on windward side of groin ...................................... 15

4

CONVERSION fACTORS, U.S. CUSTOflARY TO tlETR1C (S1) UNITS 01:' t·1I::ASURErtEiH

U.s. customary units of measurement used in this report can be converted to metric (SI) units as follows:

Hultiply

inches

square inches cubic inches

feet

square feet cubic feet

yards square yards cubic yards

miles square miles

knots

acres

foot-pounds

mUll ba rs

ounces

pounds

ton, long

ton, short

degrees (angel)

fahrenheit degrees

by

25.4 2.54 6.452

16.]9

]0.48 0.]048 0.0929 0.028]

0.9144 0.836 0.7646

1. 6093 259.0

1.852

0.4047

1.]558

1.U197

28.]5

45'3.6 O.453b

1.U160

0.9072

0.U1745

5/9

x 1U- j

millimeters centimeters

To obtain

square centimeters cubic centimeters

centimeters meters

square meters cubic meter::;

meters square meters cubic meters

kilometers hectares

kilometers per hour

hectares

newton meter::;

kilograms per square centimeter

grams

grams kilograms

Gle t ric t Otl~,

Jletric ton::;

radians

Celsius degrees or Kelvins l

lTo obtain Celsius (C) temperature readings from Fahrenheit (F) rcadings, use formula: C = (5/9) (1:' -32).

To obtain Kclvin (K) readings, use formula: K (5/':) (F -]2) + 273.l5.

5

\-JAVE LOADING ON VERTICAL SHEET-PILE GROINS AND JETTIES

by ,1. Richar>d Weggel

I. INTRODUCTION

The Shore Protection Manual (SPt<I) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977) provides guidance for the design of verti­cal wall structures subjected to either breaking, nonbreaking, or broken waves; however, the design methods [.lresented are for waves approaching perpen­dicular to a structure. The SPM also presents a rational, though untested, procedure for reducing forces when waves approach a structure at an angle. The SPM force reduction appears to be valid if the direction of wave approach is not too different from a perpendicular, i.e, ex > 70°, where ex is the angle between a wave crest and a perpendicular to the structure. For structures essentially normal to shore such as groins and jetties, waves usually prop­agate along the axis of the structure rather than normal to it. For this sit­uation, the SPi"l force reduction factor, which varies as sin 2 ex, underpredicts the maximum wave force since ex + 0° and sin 2 ex + O. Furthermore, the instan­taneous distribution of force along the structure is not uniform when ex is small since wave crests act along some parts of the groin or jetty while wave troughs act along other pA.rts. Consequently, the maximlun wave force acts over only a small part of the structure at anyone tiLle <lnd the point on the struc­ture where the maximum furce acts moves landward along the structure as the wave propagates to shore. This report outlines a Jesicir1 prucedure for esti­mating the force acting on a ;sroin or jetty when waves [Jropagate along the axis of the structure, Le., when ex, the angle between the incoming wave crests and a perpendicular to the structure, is less than about 45°.

II. SPt-l :--lETHODOLOCY FOR COMPUTING FORCt.S Aim HOMEtHS

The SPM presents three procedures for calculating wave forces on vertica L or near-verticA.l walls. For nonbreaking waves, the :'liche-Rundgren r.tethod is given. ,The SPt'l design curves for this r.Jethod were developed from [{undgren's (l958) equations and, for small values of the incident wave steepness Hi/gT2, from Sainflou's (l928) equations where Iii is the incident wave height, g the acceleration of gravity, and T the incident wave period. For breaking waves, the i"!inikin (l963) method is given in the SPH. When waves break against a structure ::hey exert extremely high impact pressures of very short duration. The impA.ct with the structure of the translatory water mass associ­ated with the moving wave crest causes the hi~h pressures. The Minikin method attempts to describe these pressures but in applying the method the force is assumed to act statically against the structure. The problelll is in reality a dynamic one. Wave pressures exceeding those predicted by the ;'--linikin method have been r.teA.sureJ; however, their duration is so short that the assumption that the force is a static one makes the method extrer.Jely conservative even though the force itself r':\i1y be underpredicted. Since it is the impact of a translatury mass of water that results in the high pressure, it seems doubtful that waves approaching a vertical wall at an angle could cause them. The Minikin method is thus inappropriate for calculating forces by waves approach­ing a structure at an angle. For broken waves, the SPM presents a rational method for calculating forces based on computing the stagnation pressure. Again, this method is for normal wave approach.

7

A modification of the Miche-Rundgren method as presented in the SPM appears to be applicable to breaking, nonbreaking, and broken waves for situa­tions when waves approach at an oblique angle.

II 1. MACH-STEH REFLECTION

Waves in the vicinity of a vertical wall are comprised of incident waves and superimposed reflected waves. For a perfectly reflecting vertical wall with waves of normal incidence, the reflected wave height equals the incident wave height resulting in wave heights in front of the wall equal to twice the incident height. When waves approach a structure at an angle, reflection is not complete resulting in a wave height less than the sura of the incident and reflected waves. For angles of incidence, a > 45°, a phenomenon termed Mach­stem reflection may occur. Instead of reflecting at the angle of incidence, near the structure the incident wave crest turns so that it intersects the structure at a right angle. This gives rise to three separate parts of the wave--an incident wave, a reflected wave, and a Mach--stem wave propagating along the axis of the structure with its crest perpendicular to the structure face (see Fig. 1). The amplitude of the Mach-stem wave, which is the wave causing the force on the wall, was investigated by Perroud (1957) and Chen (1961). The relative amplitude of tile 1'Jdch-stem wave as a function of angle of incidence and Hi/2d is given in Figure 2 (Hi is the incident wave height and d the water depth). A more general relationship tor average reflection data, independent of Hi /2d, is given in Figure 3. For 0. > 45° the relative amplitude of the wave is about 2.0, Le., the wave height along the wall is the sum of an incident and reflected wave which has a height equal to twice the incident wave height; for a < 45°, the relative amplitude of the tuch-stem wave is less than 2.0.

H i = Height of Incident Wave

H r - Height of Reflected Wave

Hm - Height of Mach -Stem Wave

a - Angle of Incidence (angle between wave crest and perpendicular to structure)

r = Angle of Reflection

wave/

a Hi

Vertical Structure

a < 20°

Wave Crests

Vertical Structure

20°< a<45°

Wave Crest --...--

Vertical Structure

a >45 0

Figure 1. Reflection patterns ot a solitary wave.

8

1.0r---------------------------------------------------~ f-oII(------ Machi Reflection ------Jl.~II ........ f_- Regular Reflection ~

C1' no reflected wave: reflected wave (no Mach -stem wave) g appears I appears ~ 0.8~--r---,_-~I_.--_,---r_--,_-----_r------i

~ 1 __ IH I /2d=0.38

~ /~'-. -+~f ~l 034 =i jrS

Vi/J'''-f--/{/' ~L 028 1 ~£ .,/'.,/'v ~x---:=x/ _________ 023 x -g, -0.4+:-- x'./ ,/" ~ 1.---/ j / ___ - __ ______ -

---r.---' -- --

,~ ---­, __ e--0.16

<J)

'" OJ

c 0.2 0

'" c a, E a

oo~

O~~------~--~~--~------~----~I o 15 30 45 60 "15

Angle of Incidence (a)

Figure 2. Oblique reflection of a solitary wave, experiwental results; water depth, d = 0.132 foot (from Perroud, 1957).

2.5

- Mach Reflection Reguiar Reflection--. I

no reflected wave I ref lected wave appears I appears I

I -Average curvJ

/'''1 -- "1--,- ...... // Re:ative Height of Mach-Stem

'-.s-- / " 17 '-, ...... 4....r-- Wave Running Along Wall, - Hms/Hi I

I 2.0 ...... L..

I

"0 C 0

.-I ...... 1.5

/ /

/

'" E .:c

/ ~ / _c /

.,./ 0>

Ql 1.0 I

Q.> :> 0

3: OJ :>-

~ 0.5 <l.> 0::

o o

A>~

// ~ Relative Height of Reflected

! WOV8, Hr I Hi

I I

30° 45° Angle of [ncidence (a)

Figure 3. Oblique reflection of a solitary wave, experimental results (frol\\ Perroud, 1957).

9

-

!

IV. CALCULATION OF \~AVE FORCE AND OVERTURNIL'lG MOHENT

The Miche-Rundgren Dethod in SPM Section 7.32 provides a method for deter­mining wave force and overturning moment when either a wave crest or trough acts against a wall. For oblique incidence some parts of the wall are acted on by wave crests while others are acted on by wave troughs. Thus, there is a variation in force along the wall that can be assumed in proportion to the wave profile along the wall; Le., the maximum wave force corresponds to the wave crest, the minimum wave force corresponds with the wave trough, and the variation in force between is assur:led proportional to the oruinate of the wave profile.

It rel~ains to select an appropriate description of the wave profile. For waves in shallow water the cnoidal theory outlined in Section 2.26 of the SPM provides a satisfactory description. Stream-function wave theory (Dean, 1974) will also provide a satisfactory description of the profile; however, for pur­poses of illustration and convenience the cnoidal theory will be used here.

V. EXAMPLE PROBLEM

The computation of forces and mor;1ents is best illustrated by an example problem.

GIVEN: A concrete sheet-pile groin perpendicular to shore is subjected to waves 6 feet (1.83 meters) high with a period of 8.0 seconds. \~aves

approach the groin so that the angle between the wave crest and a perpen­dicular to the groin is 30°. The water depth at the end of the groin is 10 feet (3.05 meters). The beach profile along the wind\vard side of the groin is given in Figure 4.

15

I I I I Concrele Sheel-Plle Groin

ElevG:,OIl + 70 fl ') 10

5 '" \W~ ~ ~ \ \ SWL

"\\

~ --- --- --~- f----- --

I'. 'I

", 'I,

II , Beach Pr of lie

~ -, "\\\\\\\\\ "\\,\\,,\\

.\\\\\\\\\\\ , \11,',\'i

c o 0 o ,. '" w _ 5

-10

-15 - 300 - 200 - I 00 o 100 200 3JO 400 500 600 700

D,slance from Shoreline (ft)

Figure 4. Bea~h dnd groin profile.

FIND: Ignorin3 chan3es in wave direction as the wave propagates to\.;ard shore ~efraction) and changes in depth near shore (shoaling), determine the I;)axi­

mum wave force and overturning moment acting on the groin when the wave crest passes a point 400 feet (121.9 meters) from shore (100 feet or 30.5 meters from the seaward end of the 6roin) and estir:late the distribution of force and Moment ;-dong the groin at that instant.

10

SOLUTION: An estimate of the reflection coefficient can be obtained frow Figure 2 or 3. Calculate

[-1. ~

2d 0.30

From Figure 2, with Hi/ 2d 0.3 and Ct = 30°, read f\~sl 2d 0.47. Ther e fore,

II ;us 0.47 ( 2d)

IUternatively, frolll Figure 3 for a

H ms 1.61(6)

9.4 feet (2.87 meters)

3UO, Ii sl tIl· \.l

L.61 or

9.7 feet (2.96 meters)

This estimated ~L3.ch-steTOl wave hei g ht is subject to limitations imposed by the maximLun breaker height that can exist in the given water depth. This breaking wave height is given 3[lproximately by Hb/d = 0.78 or, for the example

0.78d O. 78( LO) 7.8 feet (2.38 meters)

The wave at the structure is thus limited to a height of 7.8 feet. The re(~ainder of tile calculations ilre based on tilis maximul<! wave height.

The figu re of an high.

and

(~aXimW;l wave force (crest at the wall) can 7-7U by assuming that incident wave Ca lcula t i ng

and

ll. 1

d

a the TOlaximum wave heLgh t reflected

3.9 1.0

3.9

u.39

'J

(32.2)(3)-

wave, each

0.00189

be estimated using SPt1 of 7.8 feet is the sum

3.9 feet ( 1. L9 meters)

from SPM Figure 7-70, read from the top part of the figure,

L. 1. 4

and from the bottom [lart of the figure,

0.38

L 1.

where F c structure (64 pounds Therefore,

and Ft are the wave force when the crest and trough respectively, and w is the specific weight of per cubic foot (10,000 newtons per cubic meter) for

Fc 1.14(wd 2) = 1.14(64)(10)2

7,300 pounds per foot (106,500 newtons per meter)

and

Ft 0.38(wd 2) = 0.38(64)(10)2

2,400 pounds per foot (35,000 newtons per meter)

are at the the water seawater).

Similarly, from SPM Figure 7-71, the maximum and minimum overturning moments are

Mc 0.64(wd 3) = 0.64(64)(10)3

41,000 foot-pounds per foot (182,400 newton meters per meter)

Mt O. 1 1 ( wd 3) = O. 11 ( 64 ) ( 10) 3

7,000 foot-pounds per foot (31,100 newton meters per meter)

where Mc and 1'\ are the overturning mOlaents caused by the waves when the crest and trough are at the structure.

To determine the distribution of force along the groin, the appropriate cnoidal wave profile must be found. Calculate

and

T ffi= 8 /32.2 = 1436 \jd \J 10 •

H d

0.78

which is the limiting value of Hid. From SPf"1 Figure 2.11 for the calcu­lated values of T Ig/d and Hid, find the value of k 2 = 1 - 10-4 • 5• From SPM Figure 2-12 with k 2 = 1 - 10- 4. 5 , find

The wavelength, T '-', is the refore

3 240 ~

H

240

3 240(10) = 30 770

7.8 '

L 175 feet (53.3 meters)

12

This wavelength is rr.easured perpendicular to the wave crests. To obtain the wavelength along the structure, this value must be divided by cos a. Thus,

where L' prof ile is files for Figure 5 in

1.2

L L' - --­

cos a 175

is the wavelength along obtained from SPM Figure

k2 = 1 - 10-4 and k2 = 1 dililensio:11ess form.

203 feet (61.9 meters)

the structure. The appropriate wave 2.9 by in te r po la t ing between the pro-- 10-5• This prof ile is plot ted in

1.0

\ 0.8

Tj 0 .6

0.4

0.2

o o

\

-

1\

\ \

"\. --- -"

~

0.1

Figure 5.

~-SWL

_L----~ ............

0.2 0.3 0.4 0 .5 x/L

Dimensionless cnoidal wave profile, k2 = 1 - 10-4 • 5 •

The distribution of force along the structure is then obtained by letting the maximum correspond to 7,300 pounds per foot and the minimum to 2,400 pounds per foot. Then Fc - Ft = 7,300 - 2,400 = 4,900 pounds per foot or 71,500 newtons per meter and

F(x) 2,400 + 4,900 ~(x)

where F(x) is the variation of force with distance along the structure, and ~(x) is the variation of the dimensionless surface profile with x. Similarly, the distribution of the overturning mument along the structure can be determined. Mc - ~\ = 41,000 - 7,000 = 34,000 foot-pounds per foot or 151,200 newton meters per meter and therefore,

M(x) 7,000 + 34,000 ~(x)

13

Values of f(x) M(x) dre tabulat ed for the example in the Table and plotted in Figu re 6. The force distribution along the groin is shown in Figure 7.

Tahle. Variation of force along structure.

x/L' 1 ll(x) rex) 2 M(x) '3 x (ft) (lh/ft) (ft-lh/ft)

0 . 0 o.n 1.0 7,'300 41 ,000 ().O2 4.06 0.9] 6,%0 3fl,620 0.04 iL 12 0.76 6, 120 3Z,B40 0.00 12.1P. 0.57 ') , 190 26,3P.O O.OR 111.24 0.40 4,lAO 20,AOO O. In 20.30 0.2') 3,620 1'),500 O. 1 2 24.30 0.10 3 , 1 P.O 12,440 O. t 4 28.42 O. 1() 2,R90 1(),400 O. 111 32.4R 0.00 2,1190 9,040 o. 1 R 3h.s4 0.04 2,596 R,3hO 0.20 40.00 o. (12 2 , ')00 . 7,oRO 0.2') 50.75 0 .005 2,42 0 "} , l70 0.10 00.90 0.0 2 ,400 7,000 iI.40 P.t.20 0.0 2,400 1,000 0.')0 ten • ')0 0.0 2,400 7,000

, COT'lpllterl frOM x = 201 x/L'

2 (OT'lputed frOM rex) 2,400 + 4,900 ll(x) 1 (omputerl from M(x ) = 7,000 + ]4,000 ll(x)

8,000

7,000 k t-)\

6,000 \

5,000 .:: ...... VI

\ ~

/' Force

'\ .n = 4,000 \

\ \ '" u ~

0 LL 3,000

2,000

I,O CO

o o

\. 'x

1\ "x

~x-x_ x x-

'\ Moment

~ ------

10 20 30 40 50 60 70 80 90 Distance Along Groin (ft)

Figure 6 . Va riation ot f o rce d nd moment along grOin .

14

8 o

7 o

6

c:: Q)

x E o

20 ~

10

o 100

= 10,000 L I. ~ s I I c:; . oodlnQ on nl Ide 0 rOln

...... /' ' :e

5,000 ,

- I ~~-- I ,

'" , v - ----' ----' ~--

0 0 u..

10 -

Concrete Sheet-Pile Groin-~

5 """ 1\\\' """ -.....

0 c 0 -0 > -5 Q)

w

-10

'\\\\\\\~~~

~ , r---- - c---- --- -- SWb·_

~

Beach prd~ ~ \\\~

-15 -300 -200 -100 o 100 200 300 400 500 600 700

Distance from Shoreline ( ft )

Figure 7. Loading on windward side of groin.

As a check on the wave force when the trough is ':It the structure, the hydrostatic force can be cOfi1puted using the minimufi1 water surface eleva-tion. From SPH Figure 2-13, the value of (Y t - d)/H + 1 is found to be 0.850 where Yt is the height of the wave trough above the bottom. Therefore,

0.850

rearranging and solving for Yt'

Yt (0.850 - 1.0) Ii + d

or

-0.150 (7.~) + 10 3.83 feet (2.69 meters)

COfi1puting the hydrostatic pressure

F t

2,495 puunds per foot or

36,400 newtons per ~eter

compared with Ft "" 2,400 pounds per foot for the value computed from the Miche-Rundgren figures in the SPM.

1 ')

When actually computing forces on sheet-pile groins and jetties, the re­storing force caused by water and wave action in the structure's leeward side must also be considered. The critical design situation occurs when the water surface on the leeward side is a minimum; i.e., when a wave trough acts there. For the example, the worst case for overturning moment exists when the water level on the leeward side is equal to y t = 8.83 feet. This corresponds to a minimum restoring force of 2,400 pounds per foot.

A critical factor not included in the example that must be considered in any real design problem is the force arising because of the differential sand elevation on each side of the structure. These forces must be based on estimates of the maximum deposition and scour that will be experienced dur­ing the lifetime of the structure. It is also possible that this critical condition will occur during construction unless a scour blanket is placed adjacent to the structure.

V I. SUMHARY

The proposed method for computing the distribution of wave force and overturning moment along a vertical sheet-pile groin or jetty is approxi­mate. It assumes that the force and moment are in proportion to the nonlinear wave profile as given by the cnoidal wave theory. Alternatively, any other appropriate wave theory to describe the profile could be used. D1e assllli1ption that a wave crest or trough acts uniformly along structures oriented nearly perpendicular to shore grossly overpredicts the total force since only a small part of the structure is acted on by a wave crest at any instant. The use of wales on sheet-pile groins and jetties can distribute these forces longi­tudinally, allowing the safe use of smaller structural sections.

16

LITERATURE CITED

CHEN, T.C., "Experimental Study on the Solitary Wave Reflection Along a Straight Sloped Wall at Oblique Angle of Incidence," TM-124, Beach Erosion Board, Washington, D.C., Mar. 1961.

DEAN, R.G., "Evaluation and Development of Water Wave Theories for Engineering Application," SR-1, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Nov. 1974.

MINIKIN, R. R., Winds, Waves and 11aY'itime StY'uctuY'es: Studies in HaY'boY' Making and in the PY'otection of coasts, 2d ed., Griffin, London, 1963,

PERROUD, P.H., "The Solitary Wave Reflection Along a Vertical at Oblique Incidence," Ph.D. Thesis, University of California, Berkeley, Cali". (also Institute of Engineering Research, Report No. 99-3, unpublished, Sept. 1957).

RUNDGREN, L., "Water Wave Forces," Bulletin r~o. 54, Royal Institute of Tech­nology, Division of Hydraulics, Stockholm, Sweden, 1958.

SANIFLOU, M., "Treatise on Vertical Breakwaters," Annals des Ponts et Chaus.sees, Pa ris, France, 1928.

U. S. ARHY, CORPS OF ENGINEERS, COASTAL ENGINEERING IlliSEARCH CENTER, ShoY'e PY'otection Manual, 3d ed" Vols. I, II, and III, Stock No. 008-022-00113-1, U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp.

17

-----------------------------------------------------------~--------------------------------------------------------------,

loIegge L, lUe 11:.1 rd J. Ws '"., loading on

J. Rl ... h"rd \,/" ~d

uVI:'rLur l.lL

th «;,:15 "f 'J

5 r.ru-.; l U j '

re!'l"l .011. t u tho nonlln,,:H sh, I , U",- 'oJ [{H

Lnulo1.a1 ul ~Lre ,l l11-i"nction ""Vb. theoq'.

croina and j etties by J . 5 . Coastal Engineer i ,'!;

JiV Lt.ibl~ Irolll "altonal

1 Ai i.. U. S. Coss l

disl lbutlvn ~l lor~e ~nd

"v,, _ ;)i) jill; :llunb Wav~ h ,aghe at the

, n Mac 11-5 telll

11 prope.rt lorr by "ith",r t he

1. Cr ... Lns , 2. J " tlle'> . J . 101 \", Lo rce,;. ~ . Io.all" 1. 1itle. t " ,- irni.;..1i 101 [1. ::,~rldS: .S, ('od" t~l £n~ln""r III,; R..2 e. rell \.., nr" r.

n • ill - I. TC~O)

Weggel, Rllhc1,d J .

.U:>61 ta

WdV'- 10,.LlJllg IJIl v«rt to:al ~ \".!..,t-pllL

J . Ricl"'d I;"SS'l F(,rL klvatr, \". Res._Ol't",h C' nt~r - l-rl nglltld, Va. Technical lntormlltlun Se1'l.'1"". 19,~J,

b27

grulnb ~nd j e lte~ by U.S . Co:\s t oll r.nl.in""rJnlS

.lY'1l1abLu H O NaUo nal

1l7 ] p. 111. 27 LUi. il hn ... ,,1 Aid c. Coastal Engine ' rlng R",.ellrch Ce nter ; no. dl-1 ,'

lnc lu~ea Plbllog,sphlca re(er~oc

A me thod i ii prc~en (ed [or <:al.:. ... 1arlnl,; lht! d slrlbuLl f force a nd ave £turning IlomCIIC result1nb rom InL lde"t "ter '.lVe" movl ns l ong thl:< ilxis of a gr io wr jeet" with yerrlcll "ldbs . Wa ve height dC t he structure is dec rmined from eltp"riAlenc 1 data (JI' Ma h - stem reflec t io . The dl. s tr butlon 0f fill''''' is 3>1bumed co b" prop" t n t o t he l)o(l1 i n(,8 aha1 -ow- water Ye profile give n by eithe r the c no ld,ll o r s t r ealll - f ui1 c l on \oIa ll e t he o r y .

1. Gro i ns . 2 . J e tt i e s . 3 . Wave forces . I •• 1.'<lYt's. I. T t h:. II. S rie' : U. S. Coa s t a l Engi n<': e r ing Research Clen t<-r . j c~,n ~ ca L aid no . 8 1-1. TC203 . U5 8 lt a no. 8J. -l 6 2 7

• egge l, R.1,cI a J . Wave loading ~n vertical 8heet - pi l e

J. Ri ch ~d \oI",,~t l -- rt Belvoir, 8 .

~ ~ an:h Cen_L'r j Sprl.ngflt·l.d Va. technical Informacion Service, 1981 .

g roins and j e t 1es ! by U. S. CO.lst 1 En);lnce['Lns 8v81lilbl~ f rom t tlomn

117l p. ill. n ClIJ. (fe Lhnl cal.Aid . s. At ta l En~in~erl~~ Ke~ear~h C~ot~r i n u •• 8 1- 1 1

Incl ude. blb~lYA aphlc 1 r~iere n ~es .

A method i s pre,s"nLt!d l or laL(' u l,.tinl , the distrlb"lton u \' , cl ur1l1n~ rtlyme!lL rc ulr ln~ froll. :.m:ld lit Io:ater "'"v

0 1 £OrL.:L a nd III _ f ng 11",,1:.

tho.: l:t~.J a ~r"1n " r jetty .. llr. vertle J ;l.d'·:1 I. v .. IPJ!;hl t th .. .. 71 K<.Cll-1i tem 1" prop" r Lion

b y t:lther lil"

stluccur 1. et~nolned frut<l cxp [lw n~ .. l d"L r"fld~Llon. 111. Gl~trlbut.i.or. 01 h rL ' ~j H._<I Cu b­[0 th~ n 01. ",,:t[' " t.alloIJ-" .. ter lJa"~ profll" gIVen

nelidal or 6t reac:-runcr hlfl \o'~t\'e theory. 1, Croinl;. Je t ties . 3. Wave forc>!,;. 4 . \1;1""

11. 5 r1 " II : l. S. !last,'! Eng ne .. rin' Re edrch Center . no. BI-L . T(20)

l.'e&&"J, Rt,lta:rd J.

. US!!l ca no . bj - l

1. THit! . TedlOi~"J aid

W!ve l~dlng un ver t i cftl heeL- ile J. kJ~tl rd \/egge1 - - Fort l>elvolr, .. "., .

gr Dins .nci J ' llles by

Resoac~h l.t! ntc r ; Springtleld, VII. T chni cal niurmBtlon S rvlce . 198L.

U •• C"obtJi Engln"'''ril'lg available trOIll Sartc"l;.l

( 17] p. ill. ~7 o:m . (Tedtnl .... l 1\1\1 u.s. C"i1"" t al Englna~rl n~ R"St!dCC~ Center , no. bl-l)

Includeb blbl l ogrdpit l al references. A melho Is pr~sen[t!d for c alculB(tn~ ' h~ 15t r lbutluo ['or~e , od

oYerturn!n!!. ruOQlcnr resulting trolll inc1dent "'iller waves moviog ala n' the a':ls ot a sroin o r jetty wi th vertical 61.1 .. 5 . I~ave height a t the t['uc tur i s de terAlined f" xp r1au:nta l data on Mao: - e r em

re leet 00 . Th~ ctlbc r ibu r ion t fo r ce 1 as'uwed [ v ~ i pr op r 10 to t he n0I1 11near sha l l ow- wate r wave pro tile g i ven by ei t he r t he cnol .11 or slre m- f unc:tlon wa " " L: ,eo r y .

J . C ui.ns . 2. Jett i s , Wa ve for ,e s . 4 . \oJ ve s . 1. Tt t l • II. Sta tl!>;: U • • CDas t a l t.ng 1oeerin, Re s .. r c:.h C" ote r . Tec hn i cal a i d no. 81 - 1 . Te' 03 . US81ta no . 8J - 1 6 27