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D E S I G N C A I S S O N B R E A K W A T E R
A n
evaluation of the formula of
G o d a
C a r l i t a L. Vis
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D E S I G N
C A I S S O N
B R E A K W A T E R
A n e v a l u a t i o n o f t h e f o r m u l a o f G o d a
C L .
V i s
D e l f t , A u g u s t 1 9 9 5
D e l f t U n i v e r s i t y o f
T e c h n o l o g y
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page ii
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summary
S U M M A R Y
The g row ing need fo r b reakwate rs in deep wa te r due to the inc reas ing d raugh t
o f l a rge vesse ls d raws the a t ten t ion to ca isson b reakwate rs . These mono l i th i c
s t ruc tu res a re more economica l compared to rubb le mound b reakwate rs .
Espec ia l l y i n deep wa te r l ower cons t ruc t ion and ma in tenance cos ts and
considerab le savings in construct ion t ime can be rea l ised. A ca isson is bu i l t on
shore and towed ou t to the ac tua l o f fshore s i te . Un fo r tuna te ly , damage a t a
ca isson i s o f ten p rogress ive . Th is causes an abrup t co l l apse o f the s t ruc tu re . By
unders tan d ing the dynam ic p rocesses invo lve d , the des ign o f the s t ruc tu re can
be sound ly based .
The fo rmu la o f Goda (19 85 ) is a wo r ldw ide used des ign meth od fo r ve r t i ca l
b reakwate rs based on the quas i -s ta t i c approach . H is des ign method i s ve ry
usefu l as a f i rs t ind icat ion for the d imensions of the ca isson. In order to be ab le
to ana lyse Goda 's method , the des ign o f a ca isson b reakwate r i s rough ly
d iv ided in three phases. Fi rs t the crest e levat ion of the ca isson, the design
wave and the des ign wa te r dep th , a re de te rmined w i th p robab i l i s t i c
cons ide ra t ions abou t the economy o f the ha rbour . Subsequen t l y the wave load
fo l l ows f rom the wave p ressure fo rmu lae . Th i rd l y , the w id th o f the s t ruc tu re
se ts the we igh t o f the s t ruc tu re wh ich de f ines the sa fe ty aga ins t fa i l u re .
Goda se ts the des ign pa ramete rs on de f in i te va lues regard less the cos t -bene f i t
ana lys is o f the harbour . H is design wave is the h ighest wave in the design sea
s t a t e ,
which is based on the pr inc ip le that a breakwater should be designed to
be sa fe aga ins t the s ing le wave w i th the la rges t p ressure among s to rm waves .
From the compar i son o f the measured wave fo rces o f the hydrau l i c mode l
s tudy and the va lues ca lcu la ted w i th the wave p ressure fo rmu lae o f Goda and
o f the l i near wave theory no conc lus ions can be d rawn. Th is i s pa r t l y due to the
c lose resemb lance o f the resu l ts o f the l i near wave theory and Goda 's fo rmu la
fo r the cond i t i ons a t Europoor t Ro t te rdam and par t l y caused by the sca t te r i n
th e m e a su re m e n ts .
An exper imen t abou t the fa i l u re mechan isms o f the ca isson con f i rms the
in t roduc ing o f uncer ta in t i es concern ing the p lac ing o f the ca isson on the rubb le
m o u n d fo u n d a t i o n .
Goda 's wave p ressure fo rmu lae tu rned ou t to be in fac t des ign fo rmu lae . No t
on ly h i s des ign pa ramete rs bu t the fo rmu lae themse lves inc lude sa fe ty
cons ide ra t ions . Eva lua t ion o f God a 's fo rmu la i s the re fo re on ly va l i d w he n the
who le des ign p rocess i s taken in to accoun t .
I t i s no ted tha t the accuracy o f the ca lcu la ted wave p ressure on the wa l l i s ve ry
good w i th respe c t to the uncer ta in t i es in t roduce d in the found a t ion fo rces and
the de te rmina t ion o f the des ign pa ramete rs .
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page iv
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table of contents
T A B L E O F
C O N T E N T S
S U M M A R Y P
a
g
e
'»
P R E F A C E page vi i
1 I N T R O D U C T I O N
Page 1
1.1 W hy bu i ld ing a ca isso n bre akw ater ? page 1
1.2 Design process page 2
1.3 A im s of th is s tu dy page
4
1.4 Out l ine o f co nte nts page 5
2 D E S I G N P R I N C I P L E S
Page 7
2.1 Fa i lure me cha nism s page 7
2 .1 . 1 Break wate r s l i d ing page 9
2 .1 .2 Break wate r ove r tu rn ing page 11
2.2 Probab i l is t ic design process page 12
2 .2 . 1 The des ign pa ram ete rs resu l t f rom an econom ic
decis ion prob lem page 12
2 .2 .2 D imens ions o f ca isson page 14
2.3 Design acc ord in g to Goda page 16
2 .3 .1 Des ign pa ram ete rs page 16
2. 3. 2 Resis tan ce again st fa i lure page 17
2 .3 .3 D imens ions o f ca isson page 8
2 .3 .4 Rubb le mo und foun da t io n page 20
3 H Y D R A U L I C D E S I G N C O N D I T I O N S page 23
3.1 W av e sta t is t ic s in open sea page 23
3 .1 .1 D is t r i bu t ion o f wa ve he igh ts page 25
3 .1 .2 D is t r i bu t ion o f wa ve per iods page 26
3 .2 Tra ns fo rma t ion o f deep wa te r da ta to da ta a t the s i te . page 29
3 .3 Chance tha t des ign wa ve he igh t
H
d
is excee ded page 32
4 L I N E A R W A V E T H E O R Y
Page 35
4.1 Formu lae of wa ve pressure page 35
4 .1 .1 The re f lec t ion o f i ncom ing wa ve s page 36
4 . 1 . 2 W ave p ressure on the f ron t o f the ve r t i ca l wa l l . page 37
4. 1. 3 Wav e pressure on the base of the ca iss on page 41
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table of contents
4 . 2 Spec t ra l ana lys i s page 42
4 .3 Ca lcu la t ion fo r Europoor t Ro t te rd am page 45
F O R M U L A O F G O D A page 49
5.1 Formulae of w av e pressure page 49
5.1 .1 W av e pressure on the f ront o f a ver t ica l wal l . . . page 49
5 .1 .2 W ave p ressure under a wa ve t roug h page 53
5 .2 Ca lcu la t ion fo r Europoor t Ro t te rd am page 53
E X P E R I M E N T S I N W A V E C H A N N E L page 57
6 .1 A im s o f exper im en ta l s tud y page 58
6 .2 Sca l ing cons ide ra t ions page 59
6.3 Exp er ime nta l set up page 61
6 .3 .1 Co ns t ruc t ion o f the ca isson mode l page 61
6 .3 .2 Meas ur ing sys tem page 62
6 .4 Exper imen t 1 : De te rm ine hor i zon ta l dynam ic wa ve fo rce page 64
6 .5 Exper imen t 2 : De te rm ine the ho r i zon ta l dynam ic wa ve fo rce a t
m om en t o f fa i lure o f the ca isso n page 66
R E S U L T S A N D D I S C U S S I O N page 69
7.1 An alys is o f Go da 's design pr inc ip les page 69
7 .2 L inear wa ve theo ry com pared w i th God a 's fo rm u la . . . page 70
7 .2 .1 W ave p ressure fo r wa ve c res t page 70
7 .2 .2 W ave p ressure fo r wa ve t roug h page 72
7 .3 The exper im en ta l da ta com pared w i t h the theo ry page 72
7.3 .1 Exp er ime nt 1 page 76
7 .3 .2 Exper imen t 2 page 77
7 .4 R e co m m e n d a t i o n s p a ge 7 7
C O N C L U S I O N S Page 79
L I S T O F
S Y M B O L S
page 81
R E F E R E N C E S page 87
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preface
P R E F A C E
This repor t is wr i t ten as a par t o f my study for the MSc. degree at the Facul ty
of Civ i l Engineer ing at the Del f t Univers i ty o f Technology, Hydraul ic engineer ing
group .
Part o f th is s tudy about the design of a breakwater is per formed at the Imper ia l
Co l lege fo r Sc ienc e , Tec hno logy and Med ic ine in London . In the hydrau l i cs
labora to r ies o f the de par tm en t o f C ivi l Eng ineer ing , a hydrau l i c m ode l s tud y has
been carr ied out in order to compare exper imenta l resu l ts w i th the resu l ts o f
the ore t ica l ca lc u la t ions . I rea l ise tha t learn ing about the Engl ish w a y of
hydrau l i c eng ineer ing a t Imper ia l Co llege was a g rea t opp or tu n i ty , fo r wh ich I
am very g ra te fu l .
The advice and pract ica l ass is tance of Professor P. Holmes and Dr. D. Hardwick
o f Imper ia l Co llege o f Sc ien ce , Tec hno logy and Med ic ine a re g ra te fu l l y
a c k n o w l e d g e d .
Fina l ly , I w ou ld l ike to expre ss my gra t i tude to Professo r J .K. Vr i j l ing and Mr.
K .G. Bezuyen o f the De l f t Un ive rs i ty o f Techno logy fo r the i r superv i s ion .
D e l f t , Au g u s t 1 9 9 5
Carl i ta L. Vis
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page vi i i
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I N T R O D U C T I O N
A b re akw ate r ca n be des igned fo r severa l d i f fe re n t pu rpose s . In the f i r s t sec t ion
o f th i s chap te r backgrou nd in fo rma t ion i s g i ven abou t ca isson b reakw ate r s in
gene r a l . The des ign p rocess o f a ca isson b reakwate r i s d i scussed in the second
s e c t i o n .
Subsequen t l y , the ob jec t i ve o f th i s s tudy i s de f ined in the th i rd sec t ion
fo l l owed by the exp lana t ion o f the ou t l i ne o f th i s repor t i n the las t sec t ion .
W h y b u i l d i n g a
c a i s s o n
b r e a k w a t e r ?
T h e
m a i n f u n c t i o n s o f a b r e a k w a t e r
The bas ic fun c t ion o f a b rea kwa te r i s to p rov ide p ro te c t ion aga ins t w av es . Th is
protect ion may be necessary for an approach channel or for a harbour i tse l f , in
order to prov ide a suf f ic ient t ranqui l harbour basin for sh ips to navigate and
moor . Other pu rposes o f a b reakwate r can be :
• Reduce the am ou nt o f dredg ing requi red in a harbour entra nce by cu t t in g
o f f the l i t to ra l t ranspor t supp ly .
• Guide the cur ren t in the app roac h chan nel or a long the co as t .
Reduce the grad ient o f the cross current in an approach channel in order
to make the sh ips enter ing the harbour bet ter s teerab le .
In th i s s tudy the p ro te c t ion aga ins t wa ve s i s cons ide red to be the on ly fun c t io n
o f a b reakwate r .
A c a i s s o n
b r e a k w a t e r
The cho ice o f a b reakwate r type
for a g iven s i tuat ion depends on
m a n y fa c to r s . Tw o t yp e s o f
b reakwate rs can be
d is t i ngu ished :
• Ca isson b reak wate r
• Rubb le mo und b rea kwa te r
iiirfflTin
1
i h
iiirfflTin
a . JBfflmm
mÊMËsêmm^
caisson
rubble mound
Figure 1.1
Caisson breakwater and rubble mound
breakwater
Mono l i th i c s t ruc tu res , the so
ca l led ca isson b reakwate rs , have
ma jo r advan tages compared to
rubb le mound b reakwate rs in
deep wa te r . Fo r i ns tance the
volume of a ca isson in deep water is less than that needed for a rubble mound
breakwate r because the la t te r i nc reases w i th the square o f the wa te r dep th
see f i gu re 1 1 Mono l i th i c b reakwate rs a re a l so more economica l because o f
the i r l ower cons t ruc t ion and ma in tenance cos ts and the i r cons ide rab le sav ings
in cons t ruc t ion t ime , fo r a ca isson i s bu i l t onshore and towed ou t to the ac tua l
o f fshore s i te . A rubb le mound b reakwate r can on ly be bu i l t o f fshore wh ich i s
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introduction
cons ide rab ly more expens ive . Rubb le mound b reakwate rs are never th e less more
popular in w e s te rn co u n t r i e s b e ca u se th e y can fu l f i l the i r func t ion e ven w he n
t h e y
are
se ve re ly d a m a g e d . D a m a g e
at a
ca i sso n b re a kw a te r
is on the
o ther
h a n d m o s t
of the
t ime s p rogress ive , wh ich resu l ts
in an
ab rup t co l l apse
of the
m o n o l i t h .
1 . 2 D e s i g n p r o c e s s
The des ign of a ca isso n b re a kw a te r is an i te ra t ive
p ro ce ss .
It can be
d iv ided rough ly in to thre e
p h a se s ,
see
f i gu re
1.2.
F i rs t ly
the
des ign
paramete rs have to be d e te rm i n e d in a cco rd a n ce
w i t h the des ign p r inc ip les . The des ign pr inc ip les
co n s i s t of econ om ica l cons ide ra t ions because an
very h igh
and
h e a vy s t r u c tu re
is not
favourab le .
S e c o n d l y ,
the
des ign pa ramete rs
are
used
as
i npu t for the w a ve p ressu re fo rm u l a e , w h i c h
resu l ts in a d e s i g n w a v e l oad . Su b se q u e n t l y the
d i m e n s i o n s of the ca i sson can be c a l cu l a te d .
These d imens ions have
to be
c h e c k e d w i t h
the
design pr inc ip les again because
the
o p t i m u m
s t re n g th of the s t r u c tu re is re la ted to the s tab i l i t y
of the s t ru c t u r e , w h i c h is prov ided on ly by the
w e i g h t of the s t r u c tu re . In o th e r w o rd s , the
o p t i m u m ra t i o b e tw e e n
the
w i d t h
and the
he ight
of
the
s t r u c tu re
has to be
d e te rm i n e d .
design principles:
design parameters
dimensions :
width
height
Figure
1.2
General design
process
A s tandard des ign method for ve r t i ca l wa l l
b r e a k w a t e r s
wa s
deve loped
by the
Japanese Goda
[ref 4] and is
used
w o r l d w i d e .
He
m a d e
his
fo rm u la a f te r numerous hy drau l i c mode l s tud ies .
The
wave p ressure fo rmu lae
of
Goda were emp i r i ca l l y de r i ved
and
va l i d a te d
by the
p e r fo rm a n ce of p ro to t yp e b re a kw a te r s .
D e s i g n
p r i n c i p l es
A b re a kw a te r is a ssu m e d to have fa i l ed when the m a i n fu n c t i o n is no longer
f u l f i l l ed .
T h a t
is, the
p ro te c t i o n a g a i n s t w a ve s
is
less than requi red.
Ove r to p p i n g of w a v e s is the re fo re con s ide red as fa i l u re . A d i s t i n c t i o n has to be
made be tween fa i l u re in the sense of to ta l co l l apse of the s t r u c tu re and
m a l f u n c t i o n of the b r e a k w a t e r .
The s t reng th aaa ins t co l l apse of a s t ruc tu re
shou ld be des igned in su ch a way t h a t the
s t r u c tu re can res is t the ex t re me hydrau l i c des ign
load on the s t ru c tu re , o the rw ise u l t ima te fa i lu re
occurs . These chosen ex t reme des ign cond i t i ons
d e te rm i n e th e re fo re the needed s t reng th or
s tab i l i t y of the ca i sson .
h a r b o u r
Figure 1.3
Sliding
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introduction
The fu l f i lmen t o f func t ion ing o f the s t ruc tu re under no rma l l oad ing cond i t i ons i s
depend ing on the c res t e leva t ion o f the b reakwate r . The amoun t o f a l l owed
over top p ing shou ld resu l t f rom a cos t -b ene f i t ana lys i s in re la t i on w i th ' the
economy ' o f the ha rbour and the hydrau l i c des ign cond i t i ons . In o the r words ,
the ques t ion needs to be answered i s : 'Wha t i s the accep ted downt ime o f the
harbour resu l t i ng f rom over topp ing o f waves fo r the l i fe t ime o f the ca isson ' .
Th is des ign cond i t i on se ts the min imum cres t e leva t ion o f the b reakwate r .
The s t reng th aga ins t ex t reme load ing resu l ts f rom
the u l t ima te fa i l u re mechan isms w i th i nc lud ing
sa fe ty measures aga ins t fa i l u re . The judg ing o f
the accep ted chance o f u l t ima te fa i l u re o f the
caisson dur ing i ts l i fe t ime is a lso an economic
dec is ion p rob lem, because the p robab i l i t y o f
exceedance o f the des ign pa ramete rs se ts the
probabi l i ty o f u l t imate fa i lure o f the ca isson.
The most impor tan t u l t ima te fa i l u re mechan isms
fo r a ca isson b reakwate r a re :
• Sl id ing (see f igu re 1.3)
• Ov er tur n ing (see f igure 1 .4)
• Fa i lure o f the fou nd at io n ( f igure 1 .5 g ives
two fa i lure possib i l i t ies)
h a r b o u r
Figure 1.4
Overturning
h a r b o u r
Figure 1.5
Failure of the
foundation
D e s i g n
p a r a m e t e r s
Once the amoun t o f a l l owed over topp ing i s de te rmined , the c res t e leva t ion o f
the ca isson i s es tab l i shed w i th tak ing in to accoun t the requ i rements f rom
mar ine rs . Accord ing ly the des ign wa te r dep th and the des ign wave w i th an
accep ted p robab i l i t y shou ld be chosen .
W a v e l o a d i n g
The wave load on the s t ruc tu re can be ca lcu la ted w i th the wave p ressure
fo rmu lae i f the fo l l ow ing paramete rs a re known:
• cres t he igh t
• chara c te r i s t i cs o f the rubb le mou nd foun da t io n
• wa te r dep th
• wa ve he igh t and wa ve per iod
D i m e n s i o n s
c a i s s o n
The proba bi l is t ic load ing on the ca isson dete rmin es the prob abi l i ty o f u l t im ate
fa i l u re th rough the fa i l u re mechan isms. S l id ing and over tu rn ing a re caused by a
hor i zon ta l wa ve fo rce ac t ing on the exposed f ro n t and by a ve r t i ca l up l i f t fo rce
ac t ing on the base o f the ca isson . Bo th fo rces a re resu l t i ng f rom the dynamic
wa ve p ressure . Immed ia te to ta l fa i lu re of a ca isson b rea kwa te r occ urs by
de f in i t i on when the des ign cond i t i ons a re exceeded . The w id th o f the ca isson
se ts the to ta l we igh t o f the s t ruc tu re wh ich p rov ides the des igned s tab i l i t y fo r a
cons tan t he igh t o f the ca isson .
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introduction
1.3 A i m s of t h i s s t u d y
In th i s s tudy
the
des ign p rocess
of a
ca i sson b reak wate r w i l l
be
ana lysed .
Goda 's des ign method w i l l the re fo re be co m p a r e d w i t h a d e s i gn m e th o d th a t
m a k e s use of the l i near wave theory for the co n d i t i o n s of a b r e a k w a t e r at
Europoor t Ro t te rdam.
An i m p o r ta n t a sp e c t of the eva lua t ion of the des ign p rocess is the co m p a r i so n
o f Goda 's wave p ressure fo rmu lae w i th the l i near wave theory and w i t h the
resu l ts of a hyd rau l i c mode l s tu dy .
The l i near wave theory is based upon the c o n c e p t t h a t w a v e s can be
ch a ra c te r i se d as l inear , s inusoida l waves [ref 1], The resu l t ing s imple
m a th e m a t i ca l r e p re se n ta t i o n is easy to app ly and g i ves a g o o d a p p ro x i m a t i o n of
wave behav iou r .
R e s t r i c t i o n s of t h i s s t u d y
The fo l l ow ing l im i t i ng cond i t i ons are
app l ied :
• A quas i -s ta t i c approach is used to
ana lyse the w a ve fo r ce s on the
m o n o l i t h i c b re a kw a te r .
• The w a v e s are cons ide red not to
break as breaking is not taken in to
a c c o u n t
in the
ca l cu la t ion
of the
w a ve p re ssu re s w i th the l inear
w a ve th e o ry .
• The ve ry com p lex p rob lems of the
founda t ion fa l l ou ts ide the scope
o f th i s s tudy .
•
The
hydrau l ic design data
of a
Europoort
Rotterdam
Figure 1.6
The Netherlands
b r e a k w a t e r at Eu ropoor t Ro t te rdam w i l l be used for the ca l cu l a t i o n s , see
f i gu re 1.6 and f igure 1.7.
The d i rec t ion of
t h e w a ve c re s ts is
a s s u m e d
to be
c o n s t a n t and
n o rm a l to the
breakwate r ax i s .
Th e b re a kw a te r is
co n s i d e re d to
have a ce r ta in
l e n g t h , see f igure
1.8.
The
i n te ra c t i o n w i th
th e S id e s ( O th e r
Figure 1.7
ca issons) is
n e g l e c te d .
Situation approach channel Europoort Rotterdam
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O u t l i n e o f c o n t e n t s
Figure 1.8
Length of caisson
In order to analyse the design process of a
ca isson b reakwate r the des ign ph i losophy i s f i r s t d i scussed in chap te r 2 . Th is
inc ludes the fa i l u re mechan isms, the de te rmina t ion o f the des ign pa ramete rs by
means o f an economic dec is ion p rob lem and Goda 's des ign p r inc ip les .
Pr ior to the actua l descr ip t ion of the design wave pressure formulae in chapter
4 ( l inear wave theory) and 5 (Goda), chapter 3 summar ises the hydrau l ic design
cond i t i ons fo r Europoor t Ro t te rdam. The hydrau l i c cond i t i ons a t deep wa te r a re
t rans fo rmed dur ing the p ropaga t ion in to sha l lower wa te r wh ich in f l uences the
probab i l i t y dens i ty func t ion o f the wave he igh t .
In chap te r 6 the exper imen ta l s tudy i s descr ibed . Hydrau l i c mode l tes ts were
car r ied ou t to compare the theore t i ca l resu l ts w i th exper imen ta l da ta . A mode l
ca isson was p laced in a wave channe l and a t tacked w i th regu la r waves . The
hor i zon ta l dynamic wave fo rce has been measured and the u l t ima te fa i l u re
mechan ism have been cons ide red .
The resu l ts o f the p robab i l i s t i c des ign method w i th the l i near wave theory , the
formula o f Goda and the exper imenta l data are d iscussed in chapter 7 .
Recommenda t ions fo r fu r the r research a re g i ven a lso .
The f ina l conclus ions are g iven in chapter 8 .
I t i s no ted tha t de ta i l ed background in fo rmat ion abou t the exper imen ts a re
g iven in the append ices .
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design principles
D E S I G N P R I N C I P L E S
Goda developed an easy to apply pract ica l design method [ re f 4 ] . In order to be
ab le to ana lyse h i s des ign ph i losophy , th i s chap te r dea ls w i th the ques t ion :
W he n is a b reakw ate r d es ign a t an op t imu m fo r a pa r t i cu la r s i te ? The answ er
is:
The best design is defined as the structure that fulfils the requirements
at minimum total costs.
An inves tmen t i n a b reakwate r s t ruc tu re i s an economic dec is ion p rob lem and
depends on a l l harbour re la ted act iv i t ies. For a breakwater protects the harbour
aga ins t waves in such a way tha t the ha rbour bas in i s su f f i c ien t t ranqu i l fo r the
sh ips to nav iga te and moor . Wi thou t the b reakwate r the sh ips wou ld on ly be
ab le to use the ha rbour w i th reasonab le good wea ther cond i t i ons . Whether the
breakwate r can improve the ea rn ing capac i ty o f the ha rbour depends fo r
instance on the type and number o f sh ips us ing the harbour , the needed quay
fac i l i t i es , the meteoro log ica l da ta , the hydrograph ica l da ta , the ha rbour re la ted
economic sys tems, the fu tu re deve lopment o f the ha rbour , e tc . Th is imp l ies
tha t the func t iona l requ i rements o f a b reakwate r a re re la ted to the economy o f
the harbour .
The to ta l cos ts o f the des ign depend on the inves tmen t and ma in tenance o f the
s t ru c tu re . The inves tm en t w i l l be h igh fo r a s t ruc tu re w i th a h igh s t re ng th . The
strength o f the structure wi l l be designed so as to res is t the extreme design
cond i t i ons . These ex t reme des ign cond i t i ons resu l t f rom the accep ted
probab i l i t y o f u l t ima te fa i l u re fo r the l i fe t ime o f the s t ruc tu re , wh i le the
probabi l i ty o f fa i lure due to the amount o f over topping is dependent on the
cres t e leva t ion o f the s t ruc tu re .
In order to determine the probabi l i ty o f fa i lure , i t is f i rs t necessary to def ine
when fa i l u re o f a ca isson b reakwate r occurs . Th is i s descr ibed in sec t ion 1 . The
second sec t io n p resen ts subseq uen t l y a theo ry o f ho w to f ind the o p t im um
design load in re la t ion to the costs. Goda 's design pr inc ip les concern ing the
design parameters and accord ing ly fa i lure o f the structure are g iven in the th i rd
s ec t i on .
2 .1
Fa i lu re me chan isms
A b reakwate r fa i l s when i t does no t fu l f i l i t s ma in func t ion : p ro tec t the ha rbour
aga ins t waves . Fo r examp le , when a c r i t i ca l va lue o f wave d is tu rbance in the
harbour bas in i s exceeded , the sh ip hand l ing has to s top , wh ich reduces the
earn ing capac i ty o f the ha rbour . The des ign o f a b reakwate r depends the re fo re
on the requi red degree of protect ion of the harbour against the waves. Th is
degree o f p ro tec t ion i s de f ined by the layou t o f the s t ruc tu re , the pe rmeab i l i t y ,
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design principles
the c res t l eve l (amoun t o f ove r topp ing ) and the energy absorp t ion (pe rcen tage
o f re f l ec t ion o f the incoming waves) . The de f in i t i on o f fa i l u re o f a b reakwate r
is:
The b reakwate r fa i l s when the waves in the ha rbour a re h igher than a l l owed
accord ing to the des ign c r i te r ia .
A l though fa i l u re can occur du r ing bo th cons t ruc t ion and opera t ion , i n th i s s tudy
only fa i lure dur ing operat ion of the breakwater has been considered because the
cons t ruc t ion can be ca r r ied ou t du r ing good wea ther cond i t i ons . The p robab i l i t y
of fa i lure represents the probabi l i t ies o f exceeding a g iven l imi t s ta te . The two
d i f fe ren t s ta tes a re the se rv i ceab i l i t y l im i t s ta te and the u l t ima te l im i t s ta te
T h e S e r v i c e a b i l i t y L i m i t S t a t e ( S L S )
The serv ic eab i l i ty l imi t s ta te is the sta te o f the bre ak wa ter dur ing norm al
load ing cond i t i ons . Fo r th i s s ta te the pe r fo rmance o f the b reakwate r i s
eva lua ted under the ' no rma l ' o r da i l y cond i t i ons to wh ich the s t ruc tu re w i l l be
exposed dur ing most o f i t s l i fe t ime .
Fai lure is def ined in th is s ta te as: the breakwater does not fu l f i l i ts funct ion
because the am oun t o f ove r topp ing i s too h igh , wh ich d i s tu rbs the ha rbour
ac t i v i t i es . The harbour has to be c losed down. Th is can happen regu la r l y and
there fo re the cos ts , whereas the losses due to the c los ing o f the ha rbour fo r a
ce r ta in pe r iod can be subs tan t ia l , shou ld be taken in to accoun t . The h igher the
cres t he igh t o f the b reakwate r the less over topp ing w i l l occur .
An o the r s ta te o f fa i lu re i s , tha t the b re akw ate r does no t fu l f i l i ts requ i rem ents
any more a f te r a few years , wh ich i s de te r io ra t ion o f s t ruc tu ra l res i s tance over
t i m e .
Th is means fo r i ns tance tha t the s t ruc tu re has moved th rough the years
o r tha t the scour p ro tec t ion i s d i smant led . Th is type o f fa i l u re can be p reven ted
by:
• Inc reas ing the des ign res is tance in o rder to guaran tee su f f i c ien t s t reng th
dur ing the serv ice l i fe .
• Con t ro l l i ng the de te r io ra t ion th rou gh inspec t ion and ma in tenan ce
procedures .
Bo th me thod s o f imp rove me nt shou ld be take n in to acco un t a t the des ign s tage
and w i l l a f fec t the cos ts o f the des ign .
T h e Ultimate
L i m i t S t a t e ( U L S )
The u l t ima te l im i t s ta te occurs du r ing ex t rem e cond i t i ons and has a ve ry sma l l
p robab i l i t y o f occur rence . The b reakwate r fa i l s when the ex t reme hydrau l i c
load ing is h igher than the res is tance of the structure. By eva luat ing a l l the
fa i l u re mechan isms tha t a re l i ke l y to occur under spec i f i ed ex t reme cond i t i ons ,
the ab i l i t y o f the s t ruc tu re to su rv i ve ex t reme cond i t i ons i s checked .
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design principles
The th ree most impor tan t fa i l u re mechan isms of the u l t ima te l im i t s ta te are
s l i d ing , o ve r tu rn i n g and fa i lu re of the f o u n d a t i o n , see f ig u r e 2 . 1 , 2.2 and 2.3.
Ul t ima te fa i l u re w i l l be cons ide red to h a ve o ccu r re d w h e n :
•
A
d i sp l a ce m e n t
is
caused
by the
ho r i zon ta l wave fo rce exceed ing
the
hor i zon ta l f r i c t i on fo rce ,
see
se c t i o n
2 . 1 . 1 .
• An ove r tu rn ing is caused by the ho r i zon ta l and u p l i f t w a ve fo r c e s , see
se c t i o n 2 .1 .2 .
harbour
harbour
harbour
Figure 2.1
Sliding
Figure 2.2
Overturning
Figure 2.3
Failure of the
foundation
Fai lure of the f o u n d a t i o n can be ca u se d by se ve ra l p h e n o m e n a . Wa ve i m p a c t
fo r ce s
for
i ns tance
are
re la t i ve l y h igh because the y resu l t f ro m w av e b reak ing .
These fo rces can cause the f o r m a t i o n of q u i cksa n d due to r o ck i n g m o t i o n s of
the ca isson . These p rob lems fa l l ou ts ide the s co p e of t h i s s tu d y but in order to
avo id tha t p rob lems w i th the f o u n d a t i o n w i l l o ccu r , a reasonab ly th i ck po rous
fi l ter layer has to be p laced on the sa n d b o t to m to prevent h igh pore pressures.
2.1.1 B r e a k w a t e r s l i d i n g
Breakwate r s l i d ing
is the
ho r i zon ta l t rans la t ion
of the
ca i sso n , w h i ch o ccu rs
w h e n the ho r i zon ta l wave load is h igher than the ho r i zon ta l f r i c t i on f o rc e .
s e a
harbour
X
' v hydrostatic
/
_X
s
pressure
W
s e a
Fw
c
Figure 2.5 Wave pressure on caisson for <
wave crest
h a r b o u r
flu
Ff
N
N
Figure 2.4
Th e w a te r l e ve l at the harbour s ide is
a s s u m e d to be the sa m e as the
w a t e r l e v e l at the seas ide . So the same
hydros ta t i c p ressure ac ts on bo th
s ides
of the
ca i sso n ,
see
f igure
2.5.
The resu l t i ng fo rce is co n se q u e n t l y the ho r i zon ta l dynamic w av e fo rce
F
w
.
Disp lacement w i l l occur when th i s fo rce
F
w
e xce e d s
the
ho r i zon ta l fou nda t ion
Schematization of forces under a
wave crest
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design principles
f r i c t i on fo rce F
f
, see f i gu re 2 .4 . As an approx imat ion i t i s assumed tha t the
ca isson fa i l s when the f r i c t i on fo rce i s exceeded and any d i sp lacement occurs .
The hor i zon ta l dynamic wave fo rce
F
w
is:
F
w
=F
w
smut
[ 2 1 ]
i n w h i ch cu is the angular f req uen cy =2n/T
T is the w av e per iod
r is the t im e
The load f requency w is far less than the natura l f requency of the structure
the re fo re the fo rces can be cons ide red as s ta t i c .
When the re i s no ve r t i ca l mo t ion , the re i s ve r t i ca l equ i l i b r ium:
N - W - U - N '
[ 2 2
is the resu l t i ng upw ard no rma l fo rce
is the weight o f the ca isson
is the bu oya nt forc e of the ca iss on
is the ins tan taneo us resu l tan t ve r t i ca l dynam ic fo rce
caused by propagat ion of wave pressures under the
s t ruc tu re
The ins tan taneous resu l tan t ve r t i ca l dynamic fo rce N' can be expressed in
te rms o f the ho r i zon ta l wave fo rce
F
w
:
N'
= e
F
w
= e F
w
sinca
t
[ 2
-
c
i n w h i ch e i s a co e f f i c ien t , wh ich can be foun d f rom a foun da t io n
mode l
in w hi ch A/
W
U
AT
The hor i zon ta l f r i c t i on fo rce
F
f
\s
depend ing on the no rma l fo rce
N
and on the
f r i c t i on be tween concre te and rubb le mound . The fo rmu la i s :
F
f
)
l
2
-
5 ]
3
i n w h i ch 6 is the angle o f f r ic t ion be tw ee n so i l and co ncr ete
0 is th e angle of intern al fr i ct ion of the soi l
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design principles
For 0 = 4 5 ° : fJ = t a n ( 2 /3 -4 5 ° ) = t a n 3 0 ° = 0 .5 8
This is actua l ly an in terna l fa i lure mechanism and is considered as ' fa i lu re o f the
f o u n d a t i o n ' .
The ac tua l f r i c t i on be tween the top laye r o f the founda t ion and the base o f the
caisson has to be empi r ica l ly der ived. For a r ibbed ca isson base the design
va lue fo r th i s f r i c t i on fac to r i s approx imate ly 0 .5 . Th is decreases to
f j =
0 .4 for
a f la t base [ re f 11] .
I f the re i s ho r i zon ta l mo t ion , i t fo l l ows tha t :
1 2 6 1
i n w h i ch
m
b
is the v i r tua l ma ss of the ca isso n
dv/dt
is the acc e lera t ion of the ca isson
The water and so i l mass surrounding the ca isson wi l l in f luence the iner t ia
charac te r i s t i cs o f the ca isson by tak ing pa r t i n the movement as w e l l . Th e re fo re
the v i r tua l mass i s de f ined as an equ iva len t mass wh ich wou ld beg in to move
wh en a d i sp lacem ent o f the ca isson occu rs . Mo t ion s ta r ts wh en the s ta t i c
f r i c t i on fo rce i s f i r s t exceeded . The ex t ra v i r tua l mass wh ich has to s ta r t
acce le ra t ing i s cons ide red to con t r ibu te ex t ra res is tance aga ins t any m ov em ent
o f the s t ruc tu re .
2 . 1 . 2 B re a kw a te r o ve r tu rn i n g
The hor i zon ta l dynamic wave fo rce F
v
and the ve r t i ca l dynamic wave fo rce
AT ten d to ro ta te the ca is son to the
harbour s ide, see f igure 2 .6 . The
coun te r moment i s p rov ided by the
tu rn ing moment o r ig ina t ing f rom the
we igh t o f the s t ruc tu re .
width o f c a i s s o n
ru b b le mou nd
s e a
w-u
h a r b o u r
F w
1
N'
Figure 2.6
Turning moments
Figure 2.7
Dynamic wave pressure
Th e ve r t i ca l d yn a m i c w a ve fo r ce
N'
is assu me d to have a t r iangu lar d is tr ibut ion
over the base, see f igure 2 .7 . However, the pressure at the heel o f the ca isson
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design principles
does not have to be zero. I t depends on the character is t ics o f the rubble mound
founda t ion because the dynamic up l i f t p ressure depends on the ve loc i ty
d is tr ibut ion of the water par t ic les underneath the ca isson. The la t ter is in i ts
tu rn dependen t on the pe rmeab i l i t y o f the rubb le mound founda t ion . The
ve loc i ty w i l l decrease due to f r i c t i on and tu rbu lence . The ve loc i ty d i s t r i bu t ion i s
assumed to be l inear but the curve in the pressure d is tr ibut ion wi l l p robably be
mu ch m ore gen t le . So a t r i angu la r p ressure d i s t r i bu t ion fo r the ve r t i ca l d ynam ic
fo rce AT seem s a conse rva t i ve assu mp t ion .
Equ i l i b r ium o f moments a round the hee l , see f igure 2 .6 , y ie lds:
(F
w
• arm,) • (N
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design principles
fa i l u re o f the s t ruc tu re t imes the p robab i l i t y o f fa i l u re . The income f rom the
harbour ac t i v i t i es and the to the ha rbour re la ted economic sys tems on accoun t
o f the b reakwate r shou ld compensa te the to ta l cos ts .
Every design wave or design load has a
p robab i l i t y o f exceedance . I f the des ign wave i s
s m a l l , the cos ts o f cons t ruc t ion w i l l be re la t i ve l y
low but the r isk wi l l be re la t ive ly great . As the
magni tude of the design load increases, the r isk
w i l l decrease , due to the decreas ing p robab i l i t y
tha t the des ign cond i t i ons w i l l be exceeded . Th is
imp l ies tha t the des ign load must be such tha t the
to ta l cos ts a re min im ized , see f i gu re 2 .8 .
C o s t
l-AV+B
Fo
D e s ig n w ave o r l oad
Figure 2.8 Determine
optimum design
wave
I f design load F
0
i s exceeded then d isp lacement x
wi l l occur (s l id ing is considered as the f i rs t
occurr ing fa i lure mechanism). Fa i lure wi l l be
de f ined as d i sp lacem ent x = x
0
, the load is then
F..
Thus the probabi l i ty o f co l lapse is the
probabi l i ty o f force F
1
be ing exceeded (P(F
7
) ) . The d imensions of the ca isson
are known i f the design load F
0
i s chosen . Hence the cos t o f cons t ruc t ion ,
inves tmen t / , i s a func t ion o f F
0
:
i - m [ 2 . 8 ]
Dam age i s de f ined as a ce r ta in change in the s ta te o f the s t ruc tu re , wh ich does
no t i n f l uence the func t ion ing o f the b reakwate r . Damage to a mono l i th i c
b reakwate r i s o f ten p rogress ive . However , i t i s assumed tha t a second s to rm o f
a g i ven in tens i ty causes jus t as much d isp lacement as the f i r s t one . Repa i r
work wi l l on ly be carr ied out in the ca lm season once per year . The annual
chanc e o f damage repa ir cos ts is the n independen t o f the numbe r o f d ama ge
occur rences in tha t year . Because i f a b reakwate r moves tw ice as much as a
resu l t o f a second storm, i t w i l l cost as much to jack i t in to p lace again .
To de te rmine the amoun t o f r i sk , o r the so ca l l ed an t i c ipa ted damage, i t i s
assumed tha t an insu rance company i s w i l l i ng to i nsu re a ca isson aga ins t
damage . I f the theore t i ca l annua l p remium i s s :
s = (proba bi l i ty o f dam age) • ( the cos t of repai r ing dam age)
The ant ic ipated damage per year is :
s = P ( F
1
) W
[ 2 . 9 ]
in w h ic h P(F
?
) is the prob abi l i ty tha t forc e F
1
i s exceeded , wh ich i s the
probabi l i ty o f u l t imate fa i lure
W is the cos t o f repai r ing w he n a fa i lure o f the struc tur e
occurs
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design principles
The capi ta l ized va lue of the sum of the 'premiums' s depends on the l i fe o f the
s t ruc tu re . I f i t s l i fe i s 100 years , the cap i ta l i zed an t i c ipa ted damage D is [ref
16 ] :
D = M
( 1
1 ) . s [2.10]
i n w h i ch 6 is the rate of inte res t in % per year
The to ta l cos ts C are de f ined as the cos ts o f cons t ruc t ion / and the cap i ta l i zed
a n t i c i p a te d d a m a g e D. Hence C = l + D. I t is assumed that the cost o f
construct ion / is a l inear funct ion of the requi red vo lume of the ca isson per
met re o f exposed f ron t V, so
l - A V + B
[ 2
'
1 1 ]
i n w h i ch A is the pr ice per cub ic me tre vo lum e of the ca iss on
B is the addi t iona l pr ice per cub ic me tre leng th o f the
caisson (cost o f toe protect ion etc . )
The re la t ion between the requi red vo lume of the ca isson per metre o f exposed
f ron t Vand the des ign load F
0
resu l ts f rom the fa i l u re mechan isms.
2 . 2 . 2 D i m e n s i o n s o f c a i s s o n
Fai lure wi l l be considered to have occurred when the ca isson is t ransla ted
(s l id ing) or ro ta ted (over turn ing) . Both fa i lure mechanism are re la ted to the
we igh t and the geometry o f the s t ruc tu re . Fo r a p r i smat i c ca isson the he igh t
and the w id th have to be op t im ized .
Th e m i n i m u m re q u i r e d w i d th b is re la ted to the s l id ing mechanism because for a
ce r ta in c res t he igh t ( resu l t i ng f rom the over topp ing c r i te r ion ) the w id th
de te rmines the we igh t o f the ca isson wh ich p rov ides the s tab i l i t y . A Sa fe ty
Factor i l lustra tes the stab i l i ty through a ra t io o f the force of res is tance and the
dr iv ing force. The Safety Factor o f s l id ing is expressed as:
S-F;
Mng
- 5-
*
constant,
> 1
[ 2 . 1 2 ]
The va lue o f constant
1
depends on the uncer ta in t i es in the assu mp t ions and
fo rm u lae bu t shou ld be a t l eas t more than 1 to assure s tab i l i t y . W he n the inpu t
data are not very re l iab le , the va lue of the safety factor should be made h igher
than 1 .
Ano ther impor tan t sa fe ty requ i rement fo r the s tab i l i t y i s tha t the en t i re base
shou ld con t r ibu te to the upward no rma l p ressure . The moment a rm o f
N
is in
that case equal to 1 /3 o f the width . A t r iangular pressure d is tr ibut ion for N is
a s s u m e d ,
see f i gu re 2 .9 . The max imum bear ing p ressure p
max
ac ts a t the heel
o f the s t ruc tu re fo r a wa ve c res t . Th is max imu m bear ing p ressure depend s on
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design principles
Th is p rocedure has to be execu ted fo r severa l he igh ts i f the min imum cres t
he igh t can be taken h igher as the op t imum he igh t . Accord ing to the theory
op t imum des ign fo l l ows f rom an economic ana lys i s .
2 . 3 D e s i g n a c c o r d i n g t o G o d a
The fo rm u la o f Goda [ re f 4 ] i s a wo r ldw ide used des ign metho d fo r ve r t i ca l
b reakwate rs based on the quas i -s ta t i c approach . See chap te r 5 fo r the wave
pressure form ula e. Goda made h is form ula a f te r a lo t o f hydra u l ic sca le m ode l
stud ies He judg ed the re l iab i l ity o f h is form ula by pred ic t in g the acc ura cy of
b reakwate r s tab i l i t y w i th the a id o f the pe r fo rmance o f p ro to type b reakwate rs .
His formula is va l id for breaking and nonbreaking waves. The basic source of
th i s sec t ion is God a 's 'Random seas and des ign o f ma r i t ime s t ruc tu re s (19 85 ) .
2 . 3 . 1 D e s i g n p a r a m e t e r s
The des ign pa ramete rs a re the des ign wave , charac te r i zed by i ts wave he igh t
and wave per iod and the des ign wa te r dep th .
D e s i g n
w a v e h e i g h t
Goda s ta tes tha t the h ighes t wave in the des ign sea s ta te mus t be emp loyed .
This is based on the pr inc ip le that a breakwater should be designed in order to
be safe against the s ing le wave that has the largest pressure among storm
w a ve s . Acco rd i n g to Go d a th e d e s i g n w a ve
H
d
is the h ighes t wav e ou t of 25 0
wa ve s Th is wa ve has a p robab i l i t y of exceed ance o f 0 .4 % se awa rd o f the
sur fzone wh erea s w i th in the su r fzone the he igh t i s take n as the h ighes t o f
random break ing waves a t a d i s tance 5 - /V
s
(H
s
is the mean of one- th i rd o f the
h ighes t waves , see chap te r 3 ) seaward o f the b reakwate r . Goda de f ines the
sur fzone or breaking zone as: 'A re la t ive ly wide zone of var iab le water depth in
wh ich wave b reak ing takes p lace . Concern ing the b reak ing o f random sea
w av es , the b reak ing po in t as we l l as the b reak ing wa ve h e igh t cann o t be
de f ined c lea r l y , i n con t ras t to the case o f regu la r waves ' . So H
d
- H
max
-H
0A
%-
Goda s ta tes tha t the ra t io H
m
JH
s
i s a f fe c te d by the numb er o f wa ve s in a
r ec o r d . The va lue of H
max
shou ld the re fo re be es t im a te d , based upon the
dura t ion o f the s to rm and the number o f waves . He wr i tes tha t the p red ic t i on
genera l ly fa l ls in the range:
H
d
= (1.6 ... 2.0) H
s
I
2
14 1
To avoid possib le confus ion in the design, a def in i te va lue of H
d
= 1.8 H
s
is
recommended in cons ide ra t ion o f the pe r fo rmance o f many p ro to type
breakwate rs as we l l as w i th regard to the accuracy o f the wave p ressure
es t ima t ion . Cer ta in l y the re rema ins the poss ib i l i t y tha t some waves exceed ing
1 8 H w i l l h i t the s i te of the b reak wate r w he n s to rm w av es equ iva len t to the
design condi t ion a t tack. But the d is tance of s l id ing of an upr ight sect ion, i f i t
were to s l i de , wou ld be ve ry sma l l . I t shou ld be remarked , however , tha t the
prescr ip t i on
H
d
= 1.8-H
S
is a reco mm end a t ion and no t a ru le .
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design principles
D e s i g n w a ve h e i g h t H
d
is the sm al ler one of 1.8-H
s
or H
b
. H
b
is the l im i t ing
wave he igh t o f a b roken wave a t 5-H
s
d i s ta n ce o f f sh o re .
D e s i g n w a v e p e r io d
The per iod o f the h ighes t wa ve i s take n as tha t o f the s ign i f i can t w av e ,
T
d
= T
s
. The wave per iod does no t exh ib i t a un ive rsa l d i s t r i bu t ion law such as
the Ray le igh d i s t r i bu t ion fo r wave he igh ts accord ing to Goda . Never the less
found emp i r i ca l l y tha t the rep resen ta t i ve pe r iod pa ramete rs a re in te r re la ted .
Go d a fo u n d th a t T
d
l i es i n the range (0 .6 . . .1 .3 )7 ; and takes T
d
in the midd le o f
tha t range .
D e s i g n
w a t e r d e p t h
The recommended des ign wa te r dep th i s based on the fac t tha t the g rea tes t
wave p ressure i s exe r ted no t by waves jus t b reak ing a t the s i te , bu t by waves
wh ich have a l ready begun to b reak a t a d i s tance . Fo r the sake o f conven ience ,
the d i s tance 5-H
s
f rom the b reakwate r w i l l be used fo r the des ign wa te r dep th .
Goda der i ved th i s f rom labora to ry da ta on b reak ing wave p ressures .
2 . 3 . 2 R e s i s t a n c e a ga i n s t f a i l u re
The ca isson must be sa fe aga ins t s l i d ing and over tu rn ing . The sa fe ty fac to r
against s l id ing of Goda is def ined as:
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design principles
M
i
s
t h e tu rn i n g m o m e n t d u e to t h e d yn a m i ca l w a ve
'Fw_goda .
fo rce accord ing to Goda
The sa fe ty fac to rs shou ld no t be less than 1 .2 accord ing to Goda . He takes the
coe f f i c ien t o f f r i c t i on
f j
as 0 .6 ( f r i c t i on coe f f i c ien t be tween concre te and rubb le
s tones ) .
The bear ing capac i ty o f the founda t ion shou ld be ana lysed . Goda assumes tha t
a t rapez oida l d is tr ibut ion of bear ing pressure ex is ts bene ath the bas e. The
largest bear ing pressure at the heel p
m a x g o d a
is ca lc u la te d as:
2 W 1 u
/ W * -
T i ^
1
^
3
'
[ 2 1 7 ]
i n w h i ch N
o d a
is the upw ard no rma l fo rce accord ing to Goda
a
3
°f is the lever arm of the up wa rd norm al forc e
M
goda
accord ing to Goda :
_ _
M
N
g o d
. [ 2 . 1 8 ]
goda f j
' goda
i n w h i ch M
N o d a
is the tu rn ing m om ent o f the upw ard no rma l fo rce
~
9
°
3
acc ord in g to Goda around the heel o f the str uct ure
P r e c a u t i o n s a g a i n s t I m p u l s i v e B r e a k i n g W a v e p r e s s u r e
The p ressure due to b reak ing waves may r i se to more than ten t imes the
hydros ta t i c p ressure co r respond ing to the wave he igh t , though i ts du ra t ion w i l l
be very shor t . Goda exp la ins that i t would be ra ther foo l ish to design a ver t ica l
b reakwate r tha t i s d i rec t l y exposed to impu ls i ve b reak ing wave p ressures . A
rubb le moun d b rea kwa te r w ou ld be the na tu ra l cho ice in such a s i tua t ion . I t i s
no t the magn i tude o f the g rea tes t p ressure bu t , ra the r , the occur rence o f the
impu ls i ve b reak ing wave p ressure tha t i s mos t impor tan t . Tab le 2 .1 i s a gu ide
for judg ing the possib le danger o f impuls ive breaking wave pressure.
2 . 3 . 3 D i m e n s i o n s o f
c a i s s o n
The w id th sa t i s fy ing the cond i t i ons o f the sa fe ty fac to rs and the max imum
bear ing pressure is the m in im um requi red wi d th in re la t ion to a cer ta in c res t
e l e v a t i o n . The cr i ter ion of the crest e levat ion in Japan is a t a he ight o f 0 .6
t ime s the s ign i f i can t w av e he igh t above des ign wa te r l eve l . Th is c r i te r ion is
used in s i tua t ions w her e a sma l l amoun t o f wa ve o ver topp ing and res u l tan t
w a ve t r a n sm i ss i o n i s t o l e ra te d .
Goda 's exper imen ts showed tha t the requ i red ca isson w id th depends on the
wave per iod . The w id th has to i nc rease w i th an inc reas ing wave per iod (see
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design principles
Table 2.1
Questionnaire for judging the danger of impulsive breaking wave pressure
A - l Is the angle between the wave direction
and the line normal to the breakwater
less than
20°
?
1
Y e s
A-2
Is the rubble mound sufficiently small
to be considered negligible?
1
Y e s
A-3 Is the sea bottom slope steeper than 1/50?
I Yes
A - 4 Is the
steepness
of the equivalent
deep water wave less than about
0.03?
1
Y e s
A-5
Is the breaking point of a progressive
wave (in the absence of a structure)
located only
slightly
in front of the
breakwater?
1
Y e s
A-6
Is the
crest
elevation so high as
not to allow much overtopping?
I Yes
No
L i t t l e
Danger
No
Go to B-l
No
Li t t l e Danger
No
• L i t t l e Danger
No
- > L i t t l e Danger
No
— L i t t l e
Danger
Danger of Impulsive Pressure Exists
B - l
Is the combined sloping section and
top berm of the rubble mound broad
enough (refer to Fig. 4.20)?
1
Y e s
B-2 Is the mound so high that the wave
height
becomes
nearly equal to or
greater than the water depth above
the mound (refer to Fig. 4.21)?
1
Y e s
B-3 Is the
crest
elevation so high as not to
cause
much overtopping?
I Yes
No
— > - L i t t l e Danger
No
• Li t t l e Danger
No
— •
L i t t l e
Danger
Danger of Impulsive Pressure Exists
ch a p te r 5 for explanation and appendix F for the
ca l cu la t ions) .
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design principles
2 . 3 . 4 R u b b l e m o u n d fo u n d a t io n
Berm he i gh t
" It is best to set the he ight o f the rubble mound foundat ion as low as possib le
to p reven t the genera t ion o f l a rge wave p ressure . Bu t the func t ion o f a rubb le
mo und - to sp read the ve r t i ca l load due to the we ig h t o f the up r igh t se c t ion
a n d
the wave fo rce over a w ide a rea o f the seabed- necess i ta tes a m in imum he igh t ,
which is requi red not to be less than 1.5 m in Japan. Fur ther more the t o p
should not be too deep, in order to fac i l i ta te underwater operat ions of d ivers in
leve l l i ng the su r face o f the rubb le mound fo r even se t t i ng o f the up r igh t sec t ion .
A cos t ana lys i s w i l l y ie ld the op t imum he igh t . "
1
Berm width
" I f the seabed is sof t , the d imensions of the rubble mound should be
de te rmined by sa fe ty cons ide ra t ions aga ins t c i rcu la r s l i p o f the g round . The
berm in f ron t o f an up r igh t sec t ion func t ions to p rov ide p ro tec t ion aga ins t
possib le scour ing of the seabed. A wide berm is desi rab le in th is respect , but
the cost and the danger o f inducing impuls ive breaking wave pressure prec ludes
the des ign o f too g rea t a be rm w id th . The p rac t i ce in Japan i s fo r a m in imum o f
5 m under no rma l cond i t i ons and abou t 10 m in a reas a t tacked by la rge s to rm
waves . The berm to the rea r o f an up r igh t sec t ion has the func t ion o f sa fe l y
t ransmi t t i ng the ve r t i ca l l oad to the seabed . I t a l so p rov ides an a l l owance o f
some d is tance i f s l id ing should occur .The grad ient o f the s lope of the rub le
mound is usual ly set a t 1 :2 or 1 :3 for the seaward s ide and 1:1 .5 to 1 :2 for the
h a r b o u r "
2
F o o t - p r o t e c t i o n b l o c k s
" In b reakw ate r con s t ruc t ion in Jap an , i t is cus tom ary to p rov ide a fe w r ow s o f
foo t -p r o te c t io n conc re te b locks a t the f ron t and rea r o f the up r igh t sec t ion see
f i g u re 2 .1 2 .
Cres t E leva t ion
v iO.O
C o n c r e t e C r o w n
v iO.O
Upr igh t Sec t ion
oot - P ro tec t i on
Concre te B locks
A r m o r S t o n e s ( B l o c k s )
N X
\
X
Upr igh t Sec t ion
Foot P ro tec t i on
Concre te B locks
Upr igh t Sec t ion
3 Rubble Mnund Foun dat ion
Figure 2.12 Idealized typical section [ref 4]
The foo t p ro tec t ion usua l l y cons is ts o f rec tangu la r b locks we igh ing f rom 10 to
40 tons , depend ing on the des ign wave he igh t . Foo t -p ro tec t ion b locks a re
Goda, V., Random seas and design of maritime structures. University of Tokyo Press, 1985. page 139
Goda, Y., Random seas and design of maritime structures. University of Tokyo Press, 1985. page 139
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design principles
p a g e 2 2
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hydraulic design conditions
H Y D R A U L I C D E S I G N
C O N D I T I O N S
To be ab le to say someth ing about the probabi l i ty o f fa i lure o f the breakwater ,
the p robab i l i t y o f the wave load shou ld be de te rmined wh i le the s t reng th o f the
s t ruc tu re i s cons ide red to be cons tan t . A b reakwate r fa i l s i n the u l t ima te l im i t
s ta te (ULS) when the ex t reme wave load i s h igher than the res is tance o f the
s t ruc tu re . The p robab i l i t y o f exceedance o f th i s ex t reme wave load de te rmines
the re fo re the res is tance and the d imens ions o f the s t ruc tu re (chap te r 2 ) .
The wave load i s a func t ion o f the wa te r dep th h, t h e w a ve h e i g h t H and the
wave per iod T. The re fo re the jo in t p robab i l i t y dens i ty func t ion o f the h igh w a te r
leve l ( i nc lud ing t i des and meteo ro log ie e f f ec ts ) , the wa ve h e igh t and the wa ve
per iod is needed.
The ex t reme wave load resu l ts f rom a s ing le wave in a s to rm. The p robab i l i t y o f
exceedance of th is s ing le wave cannot be re la ted to the probabi l i ty o f
exceedance o f a charac te r i s t i c wave he igh t . There fo re the f requency o f
exceedance o f i nd iv idua l des ign wave he igh ts i s needed . The chance tha t a
ce r ta in des ign wave he igh t H
d
is exceeded dur ing the l i fe t ime / o f the structure
needs to be found . When the jo in t p robab i l i t y dens i ty func t ion o f
H
and
T
is
g i ven fo r a con s tan t wa te r de p th , the p robab i l i ty o f exceedan ce o f H and 7 can
be de te rmined .
The var ia t ion in the seabed leve l has a s ign i f icant in f luence on the hydrau l ic
load ings because a change in the wa te r dep th w i l l a f fec t the charac te r i s t i cs o f
the waves . Th is imp l ies tha t fo r a cons tan t des ign wa te r dep th , shoa l ing and
break ing o f waves in f l uence the jo in t p robab i l i t y dens i ty func t ion o f the wave
he igh t and the wave per iod . The p robab i l i t y o f the wave loads changes
accord ing ly .
In the f i r s t sec t ion the p robab i l i ty dens i ty func t ion s o f the wa te r d ep th , the
wave he igh t and the wave per iod a re g i ven fo r the Nor th Sea (deep wa te r ) . In
the second sec t ion the t rans fo rmat ion o f waves en te r ing f rom deep wa te r i n to
sha l lowe r w a te r i s descr ibed . The chance tha t a ce r ta in des ign wa ve he igh t i s
exceeded i s de te rmined in the th i rd sec t ion .
W a v e
s t a t i s t i c s
i n o p e n s e a
A wave can be charac te r i zed by i ts wave he igh t and wave per iod . There fo re the
dis tr ibut ion of wave he ights and wave per iods g ive the probabi l i ty o f
occur re nce o f a s ing le wa ve fo r a con s tan t wa te r d ep th .
In deep wa te r a s to rm can be charac te r i zed by the s ign i f i can t wave he igh t H
s
and the peak per iod
T ,
assuming a s ta t i s t i ca l l y s ta t iona ry sea s ta te du r ing the
s t o r m .
Fo r sha l low wa te r cond i t i ons th i s assumpt ion can be unrea l i s t i c due to
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hydraulic design conditions
var ia t i ons
in
wa te r l eve l caused
by
t ida l and/or
set up
e f f e c t s .
See
f i gu re
3.1 for
the or ig in
of the
p robab i l i t y dens i ty func t io ns (p .d . f . ) .
In f igure
3.1 the
fo l l ow ing express ions
are
used :
• m e a n
sea
l eve l (MSL) , w h ic h
is the
re fe rence wa t e r l eve l . A rise
o f
the MSL due to
l ong te rm c l ima t i c va r ia t i ons (usua l l y taken
as
0 .1
- 0 . 1 5 m) is not
t a ke n i n to a cco u n t ;
• ve r t i ca l t i de , wh ich
is
because
of the
as t ron om ica l d r i ven fo rc e
en t i re l y de te rmin is t i c ;
astronomic forces
T I D E
Mean sea level
Tide
(vertical)
Wind set up
' J
I p.d.f.. storm surge level h
X
global climatic conditions
meteorological conditions
W I N D
Waves
Wind
waves
I
p.d.f. wave steepnes s j p.d.f. wave height H
1 L
J
JOINT P R O B A B I L I T Y
D E N S I T Y
F U N C T I O N
H,TJ
A )
Figure
3.1
Hydraulic design conditions
for
deep water
• w i n d
set up,
w h i c h
is
ca u se d
by
shear s t ress , exe r ted
by
w i n d ,
on
the
wa te r su r fac e causes
a
s lope
in the
w a te r su r fa ce
as a
resu l t
of
w h i c h w i n d
set up and set
d o w n o c c ur
at
d o w n
and up
wind shore l i nes ;
• s to rm su rge leve l , wh ich
is the
h ighe st s t i l l wa te r leve l dur ing
a
s t o r m ;
I n d i v i d u a l s e a s t a t e s
A n ac tua l wave record f rom
a
w a ve g a u g e
in the sea
g i ves
an
i r regular w av e
pro f i l e .
For an
e xa m p l e
see
f igure
3.2. On the
hor izonta l ax is
the
t i m e
is
g i ven
page
24
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hydraulic design conditions
>-
Figure 3.2
Typical wave record Iref 5]
and the wa te r su r face e leva t ion
n
is g iven on the ver t ica l ax is . To be ab le to
ana lyse the waves , the mean wa te r su r face leve l i s de f ined as the ze ro l i ne .
A wa ve i s de f ined as a wa te r m ove me nt b e tw een a po in t where the s u r face
prof i le crosses the zero l ine upward and the next zero-up-cross ing po in t . So the
hor i zon ta l d i s tance be tween two ad jacen t ze ro -up-c ross ing po in ts de f ines the
wave per iod T. The ve r t i ca l d i s tance b e tw een the h ighes t and low es t po in ts i n
a wave i s de f ined as the wave he igh t
H.
When the waves a re l i s ted in
inc reas ing o rder o f the wave he igh t , a rep resen ta t i ve wave he igh t can be
d e f i n e d .
Of ten the s ign i f i can t wave he igh t H
s
i s used , wh ich i s the mean o f
one- th i rd o f the h ighes t waves .
The s tandard record ing pe r iod o f a wa ve record i s 20 m inu tes and rep resen ts
wave cond i t i ons over a 3 hour pe r iod , du r ing wh ich the cond i t i ons a re assumed
to be ' s ta t i on ary ' . Dur ing each s ta t iona ry sea s ta te a sho r t - te rm w av e he igh t
d i s t r i bu t ion app l ies .
3 .1 .1 D is t r i bu t ion o f w a ve h e i g h ts
When the charac te r i s t i c va lues , the s ign i f i can t wave he igh ts H
s
o f e a ch s to rm ,
a re p lo t ted , a s ign i f i can t re la t i on i s found : the long te rm d is t r i bu t ion .
Frequen t i e
X
Figure 3.3 Histogram of wave heights /ref 15]
A smooth d i s t r i bu t ion o f wave he igh ts i s ob ta ined by us ing many wave records ,
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hydraulic design conditions
in which the ord inate is then the re la t ive f requency so that the area under the
h is tog ra m is equa l to 1 , see f i gu re 3 .3 . No rma l l y the wa ve he igh ts a re
norma l i sed by the s ign i f i can t wave he igh t wh ich can be the Ray le igh
d is t r i bu t ion fo r the d i s t r i bu t ion o f i nd iv idua l wave he igh ts (see f i gu re 3 .4 ) :
[ 3 . 1 ]
H In m
Figure 3.4 Rayleigh distribution for H
so
= 9 m (R=100 years)
Tab le 3 .1 g i ves the long te rm d is t r i bu t ion o f s ign i f i can t wave he igh ts fo r deep
wate r (Nor th Sea) .
. 2 D i s t r i b u t io n o f w a v e p e r i o d s
The wave per iod does no t exh ib i t an un ive rsa l d i s t r i bu t ion law . The range o f the
per iods depends on the or ig in o f the waves. In some cases, the per iod
d is t r i bu t ion i s even b i -moda l , w i th 2 peaks co r respond ing to the mean per iods
o f the w ind waves and swe l l (waves genera ted in ano ther w ind f i e ld a rea ) .
The wave per iods can be ana lysed by assuming tha t sea waves cons is t o f an
in f in i te number o f waves w i th d i f fe ren t f requenc ies , see chap te r 4 .
To de te rmine the p robab i l i t y dens i ty func t ion o f the wave per iod , the p robab i l i t y
dens i ty func t ion o f the wave s teepness s i s used . The re la t i on be tween the
wave per iod and the wave s teepness i s :
[ 3 . 2 ]
2n
i n w h i ch s
p
i s the wa ve s teepness w i th pe r iod T
p
H
s
i s the s ign i f i can t wa ve he igh t
L
p
i s the wa ve leng th o f the wa ve w i th pe r iod T
p
T
p
is the peak per iod (around w hi ch the w av e ene rgy is
co n ce n t ra te d )
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' hydraulic design conditions
H and s a re assum ed to be independen t s toc has ts . Th is ass um pt ion i s fa i r l y
0 . 1 2 i " 1
0.1¬
0.08¬
0.06¬
0.04¬
0.02-
O-l r
«(%)
Figure 3.5 Probability dens ity function of the wave steepness in the North Sea [ref 15]
conserva t i ve because the re i s a re la t i on be tween H
s
and s
p
: h i g h s te e p w a ve s
are more l ike ly to occur than smal l s teep waves. Figure 3 .5 g ives the probabi l i ty
dens i ty func t ion o f the wave s teepness o f the Nor th Sea .
Table 3.1 Hydraulic design conditions [ref 13]
Hydrau l i c des ign cond i t i ons
At deep water
At the site
R (years)
Hso (m)
T (s)
h (m)
0.1
4 .5
7 .4
1 2 .8
0 .5
5.5
9 .0
1 3 .0
1
6.0
1 0 .0
1 3 . 2
5
7.0
1 1 .0
1 3 .7
10 7.5 1 1 .5 1 3 .9
2 0
8.0
1 2 .0
1 4 .2
5 0
8.5
1 2 .5
1 4 .4
1 0 0
9.0
1 3 .0
1 4 .6
5 0 0
1 0 .0
1 4 .0
15 .1
1 0 0 0
10 .5
1 5 .0
1 5 .3
5 0 0 0
1 1 .5
1 6 .0
1 5 .8
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hydraulic design conditions
I t is a normal d is tr ibut ion g iven by:
1 1 _
( s - O
2
,
/2rc
°
ex p [ -
[ 3 . 3 ]
2 o
s
i n w h i ch s i s the wa ve s teepne ss
f i s the mea n = 3 . 7 %
a i s the s tandard dev ia t ion = 0 .5 %
When the two p robab i l i t y dens i ty func t ions a re comb ined the boundar ies o f the
jo in t p robab i l i t y dens i ty func t ion o f the wave he igh t and the wave per iod i s
c
Figure 3.6 Boundaries of the joint probability density function of H
s
and T
p
and the given values from
Table 3.1 Iref 13)
f o u n d , see f igure 3 .6 and appendix A for the der ivat ion.
As t ronomic t i des and meteoro log ie e f fec ts g i ve the s ta t i s t i cs o f h igh wa te r
leve ls .
I t i s assumed tha t bo th the wa te r l eve ls and the s to rm waves occur
s imu l taneous ly and tha t one s to rm las ts 6 hours . Wave cond i t i ons measured
and extrapola ted at deep water near the design locat ion are g iven in Table 3 .1
i n w h i ch
R
H
s
T
h
i s the re turn per iod •
i s the s ign i f i can t wave he igh t a t deep wa te r
is the wave per iod
is the water depth a t the s i te
The chance o f occur rence in te rms o f the re tu rn pe r iod can be t rans fo rmed by
assuming that a year can be d iv ided in a number o f s torm in terva ls . Th is is a
con serva t i ve as sum pt ion because a s to rm does no t occur i n every in te rva l i n
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hydraulic design conditions
rea l i ty . Th is t rans fo rmat ion i s on ly va l i d when the p robab i l i t y o f exceedance i s
expressed in years , wh ich i s ca l l ed the long te rm d is t r i bu t ion . Fo r such a
d is t r i bu t ion ma ny wa ve records over a ce r ta in pe r iod o f t ime a re needed .
Th e f r e q u e n cy f= 1/R is the num ber o f s torm in terv a ls in a year m ul t ip l ied by
the chance tha t the wave he igh t H i s exceeded dur ing a s to rm. A s to rm
durat ion is taken as 6 hours. So
f
_ 3 65 d a y s * 2 4 h o u r s
# m
_ 365 * 24
p (
^
= 1 4 6 Q p ( f y ) [ 3 4 ]
s t o rm d u ra t i o n
h o u r s
6
Which imp l ies tha t 1460 s to rms per year occur . Fo r examp le :
R = 1 year f=\ -» ?(H) = 1/1460 = 6 . 8 5 * 1 0 "
4
R=
10 years -*
f=0A
-»
?{H) =
0 . 1 / 1 4 6 0 = 6 . 8 5 * 1 0 ~
5
T r a n s f o r m a t i o n o f d e e p w a t e r d a t a t o d a t a a t t h e s i t e
The t rans fo rmat ion o f waves p ropaga t ing f rom deep wa te r i n to sha l lower wa te r
can be schemat i sed as i l l us t ra ted in f i gu re 3 .7 . Waves can be t rans fo rmed due
to shoa l ing , b reak ing , d i f f rac t ion and re f rac t ion .
• Shoa l ing is a change in wa ve he igh t wh en wa ve s p ropaga te in
vary ing water depths as a resu l t o f the change in the ra te o f
energy f l ux .
• W ave b reak ing occurs because o f the l im i ta t i on o f the wa ve
he igh t i n re la t i on to the wa te r dep th and the wave s teepness .
• D i f f ra c t ion is the t ran s fo rm at ion of the wa ve s due to the
in te r fe rence o f the waves w i th the s t ruc tu res they mee t . The
resu l t i ng wave f i e ld a round a b reakwate r i s d i f fe ren t f rom the
u n d i s tu rb e d w a ve f ie ld . The wave d i rec t ion i s neg lec ted in th i s
s tudy the re fo re on ly the in f l uence o f waves re f lec ted by the
s t ruc tu re w i l l be take n in to acco un t (see chap te r 4 fo r the t heo ry
o n s ta n d i n g w a ve s ) .
• Re f rac t ion is the change in the wa ve p ropaga t ion ve lo c i ty and in
the d i rec t ion o f wave p ropaga t ion when waves p ropaga te in
va ry i n g w a te r d e p th .
When waves approach sha l lower wa te r w i th the i r c res ts a t an ang le to the
dep th con tours , the wave c res ts appear to cu rve in a way tha t the ang le w i th
the dep th con tours decreases . The wave ce le r i ty decreases as the wa te r dep th
decreases . Fo r s imp l i c i ty , re f rac t ion in f l uences w i l l be neg lec ted .
W a v e s h o a l i n g
The var ia t ion in wave he ight due to var ia t ion in the speed of energy
propagat ion, i .e . the group ve loc i ty is g iven by [ re f 1 ] :
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hydraulic design conditions
joint probability
density
function H.TJi)
shoaling
breaking
limit f h) limit f L )
censored probability density function
H,T)
P(failure)
Figure 3.7 Transformation deep water data
i n w h i ch
H
Ho
Cg
( C J
k
h
g'o
H
Ho
N °
0
2kh
[ 3 . 5 ]
„ [ 1 +
N s i n h ( 2 / c / j )
] tanh/V/j
i s the shoa l ing coe f f i c ien t
is the wave he ight a t the s i te
i s the wave he igh t a t deep wa te r
i s the g roup ve loc i ty o f the waves
is the g roup ve loc i ty o f the waves in deep wa te r
i s the wave number
(2nlL)
i s the water depth a t the s i te
The phenomenon o f shoa l ing can no t be neg lec ted because K
s h
is purely a
fu n c t i o n o f h/L. The shoa l ing coe f f i c ien t fo r Europoort R o t te rda m i s i nd ica ted in
Tab le 3 .2 .
Table 3.2
Transformed hydraulic design conditions
R
( y r s ) H s o (m) h ( m ) H m a x l
=0.5h
L ( m ) K s h = H / H o H m a x 2 = H s o * K s h
H s
(m)
H x P(H a)
N
0.1
4.5
12.8
6.4
70
0.9133
4.1
4.1
6.2
0.00685
3000
0.5 5.5
13
6.5
91 0.9308
5.1
5.1
7
0.00137
2500
1 6
13.2
6.6
104
0.9487
5.7
5.7
7.5
0.000685
2000
5
7
13.7
6.9
118
0.9667
6.8
6.8
8
0.000137
1000
10
7.5
13.9
7
125
0.9766
7.3
7
8.2
6 .85E-05
1000
20 8
14.2
7.1
132
0.9858
7.9
7.1
8.5
3 . 4 2 E - 0 5
1000
50 8.5
14.4
7.2
139
0.9958
8.5
7.2
8.7
1 .37E-05
900
100
9
14.6
7.3
147
1.006
9.1
7.3
8.9
6 .85E-06
800
500 10
15.1
7.6
162
1.025
10.3
7.6
9.3
1.37E-06
600
1000
10.5
15.3
7.7
175
1.048
11 7.7
9.5
6 .85E-07
500
5000
11.5
15.8
7.9
191
1.066
12.3
7.9
9.9
1 .37E-07
500
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hydraulic design conditions
The ra t io
H/H
0
is obta ined f rom the va lue of
h/L
0
us ing appen d ix C f ro m the
Shore Protection Manu al [ ref 14 ] . The deep wa te r wa ve leng th is L
0
=gT
2
/2n.
W av e break in g . .. . . .
Break ing o f waves can occur fo r two reasons . The f i r s t reason i s the l im i ta t i on
o f wave he igh t due to the wa te r dep th . Second ly , the wave s teepness i s
l im i t ed .
The breaking cr i ter ion due to the water depth is normal ly g iven by the breaker
index
(y
br
)
de f ined as the ra t io o f the max imu m wa ve he igh t to wa te r de p th
rat io (H/h):
2
* r - i - y „
[ 3
-
6 1
.
s
l . J max •
b r
h h
For regular waves
y
br
has a theore t i ca l va lue o f 0 . 78 . W h i le fo r ir regu la r wa ve s
( rep resen ted by H
s
) va l u e s a re fo u n d fo r ^ = 0 . 5 - 0 . 6 [ re f 5 ] . Th e a c tu a l li m i t in g
w a ve h e i g h t r a t io ^ d e p e n d s m a i n l y o n th e be d s lo p e m and the wave
s teepness s . In th i s s tudy y
br
=0.b is tak en for i r regular w av es .
Waves in deep wa te r b reak when a ce r ta in l im i t i ng wave s teepness s i s
exceeded . M iche [ re f 5 ] s ta tes tha t the max imum s teepness o f a nonbreak ing
wave i s 0 .142 = 1 /7 . The wave s teepness i s de f ined as the ra t io o f wave he igh t
to w a ve l e n g th H/L.
However the b reak ing c r i te r ium fo r s tand ing waves d i f fe rs f rom those fo r
t rave l l i ng waves accord ing to Wiege l [ re f 13 ] :
H
x
= 0.109
L
tanh
kh
[ 3
-
7 1
i n w h i ch H
x
is the ma x im um progress ive wa ve he igh t
k is the wa ve number (2nlL)
h i s the wa te r dep th
L i s the wa ve leng th
As ind ica ted in Tab le 3 .2 , the s tand ing wave b reak ing c r i te r ium i s never a
govern ing fac to r fo r the s ign i f i can t wave , s ince the h igher o f these b reak long
be fo re reach ing the b reakwate r .
The numer ica l model ENDEC [re f 5 ] g ives design graphs in which the in f luence
of both shoal ing and wave breaking is inc luded. See f igure 3 .8 .
The inpu t pa ramete rs fo r Europoor t a re :
1 .
Loca l re la t ive wa te r dep th
i n w h i c h L
op
h
i s the deep wa te r w av e leng th (w i th
peak per iod 7^ = 1 0 s ) = qT
p
2
l2n =
( 9 .8 1 * 1 0
2
) / 2 r r = 56 m
is the de sign w at er de pth (R = 50
years has been taken) = 14 .4 m
= 1 4 . 4 / 1 5 6 = 0 . 0 9
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hydraulic design conditions
3 . Deep wa te r wa ve s teepness s
op
= H
so
IL
op
i n w h i ch H
so
= 9 m (R = 10 0 years has been tak en)
s
op
= 9 / 1 5 6 = 0 . 0 6
The max imum s teepness ava i lab le in the des ign g raphs i s 0 .05 . Fo r 0 .05 the
ou tpu t i s :
HJh =
0 . 4 5 :
H
s
= 0.
45-14.4 = 6. 5 m
So H
s
= 0.5-h seem s to be a good ap prox ima t ion .
W h e n h = 14 .4 m the des ign s ign i f i can t wave he igh t H
s
is:
/V - = 0 . 5 - 14 .4 = 7 .2 m
C h a n c e
that
d e s i g n w a v e h e i g ht
H
d
i s e x c e e d e d
Each storm can be character ized by a g iven va lue of
H
s
,
t h e s i g n i f ica n t w a v e
he igh t . Assume th i s s to rm cons is ts o f n w a ve s , w h i ch a re d i s t r i b u te d a cco rd i n g
to a Ray le igh d i s t r i bu t ion .
The chance tha t an a rb i t ra ry chosen des ign wave he igh t H
d
is exc eed ed by any
g iven wave i s :
- z &
2
[ 3 . 8 ]
f \ H = e
The chance that th is wave is not exceeded in a ser ies o f
n
w a ve s i s :
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hydraulic design conditions
[ - F X H ^ Y
1
I
3
-
9
So the chance tha t
H
d
is exceeded at least once in a s ing le s torm conta in ing
n
w a ve s i s :
E j -
1 - [1 - F \ H } \
n
[ 3 -
1
° ]
Th is chance has to be comb ined w i th the chance tha t H
s
o cc u rs , w h i ch m u s t
com e f rom a long te rm d is t r i bu t ion o f s ign i f i can t wav e he igh ts , p ^ ) can be
de te rmined as the chance tha t some wave he igh t H
S
-A H
S
i s excee ded minus the
chance tha t the he igh t H
S
+ AH
S
i s exce eded . p(H
s
) i s the chance tha t H
s
fa l ls in
the in te rva l hav ing a w id t h o f 2AA/
S
. Take as an approx imat ion
AH
S
is 0 .5 m
t h e n E
1
i s no t changed s ign i f i can t l y . So the chance tha t H
d
occurs du r ing any
sing le s torm per iod is :
E
Z
=
P H J E , [ 3 . 1 1 ]
I t is s t i l l possib le that the chosen