Verification of BREAKWAT for berm breakwaters and low-crested structures

F '

Prepared for: C U R C 6 7

Verification of BREAKWAT for berm

breakwaters and low-crested structures

June 1990

breakwaters and low-crested structures

J.W. van der Meer

CONTENTS

LIST OF FIGURES

1. I n t r o d u c t i o n

2. The model BREAKWAT

3. Data s o u r c e s

3.1 Ahrens and Heimbaugh 3.2 H y d r a u l i c s Research 3.3 B u r c h a r t h and F r i g a a r d 3.4 D a n i s h H y d r a u l i c I n s t i t u t e 3.5 Tarura e t a l

4. V e r i f i c a t i o n

4.1 Ahrens and Heimbaugh 4.2 H y d r a u l i c s Research 4.3 B u r c h a r t h and F r i g a a r d 4.4 D a n i s h H y d r a u l i c I n s t i t u t e 4.5 T0rum e t a l 5. C o n c l u s i o n s REFERENCES FIGURES

1 . Schematised p r o f i l e f o r BREAKWAT; P r o f i l e s on v a r i o u s i n i t i a l s l o p e s 2 . V e r i f i c a t i o n w i t h Ahrens - t e s t 7 3 . V e r i f i c a t i o n w i t h Ahrens - t e s t 1 5 4 . V e r i f i c a t i o n w i t h Ahrens - t e s t 22 5. V e r i f i c a t i o n w i t h H y d r a u l i c s Research 6 . V e r i f i c a t i o n w i t h B u r c h a r t h ; I n f l u e n c e o f wave h e i g h t 7. V e r i f i c a t i o n w i t h B u r c h a r t h ; I n f l u e n c e o f wave p e r i o d 8 . V e r i f i c a t i o n w i t h B u r c h a r t h ; I n f l u e n c e o f nxomber o f waves 9. Data o f DHI, case SKP

1 0 . V e r i f i c a t i o n w i t h DHI, case SKP t e s t 1 8 1 1 . V e r i f i c a t i o n w i t h DHI, case SKP t e s t 1 9 1 2 . Data o f DHI, case GLR

1 3 . V e r i f i c a t i o n w i t h DHI, case GLR 1 4 . Data o f DHI, case EID

1 5 . V e r i f i c a t i o n w i t h DHI, case EID

1 6 . V e r i f i c a t i o n w i t h DHI, case EID; I n f l u e n c e o f D ^ ^ Q and 1 7 . V e r i f i c a t i o n w i t h DHI, case SLV 1 8 . V e r i f i c a t i o n w i t h DHI, case SLV 1 9 . Data o f Tarum 2 0 . V e r i f i c a t i o n w i t h Tarum. Damage c u r v e f o r s t a t i c s t a b i l i t y 2 1 . V e r i f i c a t i o n w i t h Tarum. Damage p r o f i l e s f o r s t a t i c s t a b i l i t y ( p r o f i l e s 1 - 4 ) 2 2 . V e r i f i c a t i o n w i t h Tarum. P r o f i l e s 4 - 7 2 3 . V e r i f i c a t i o n w i t h Tarum. P r o f i l e s 7 - 1 1

1

-VERIFICATION OF BREAKWAT FOR BERM BREAKWATERS AND LOW-CRESTED STRUCTURES

1. I n t r o d u c t i o n

CUR i n t h e N e t h e r l a n d s and CIRIA i n t h e U n i t e d Kingdom a r e w o r k i n g t o g e t h e r on t h e "Manual on t h e use o f r o c k i n c o a s t a l and s h o r e l i n e e n g i n e e r i n g " . V a r i o u s c o n t r a c t o r s , e n g i n e e r i n g f i r m s and r e s e a r c h i n s t i t u t e s c o n t r i b u t e t o t h i s manual. B e s i d e s w r i t i n g p a r t s o f t h e manual D e l f t H y d r a u l i c s had t h e o p p o r t u n i t y t o d e f i n e r e s e a r c h p r o j e c t s w i t h t h e aim o f i m p r o v i n g t h e manual on s p e c i f i c i t e m s . Four o f these r e s e a r c h p r o j e c t s were s e l e c t e d by t h e CUR c o m m i t t e e . These were:

Desk s t u d y on s t a b i l i t y o f l o w - c r e s t e d and r e e f b r e a k w a t e r s . Desk s t u d y on wave t r a n s m i s s i o n due t o o v e r t o p p i n g .

- V e r i f i c a t i o n o f t h e model on dynamic s t a b i l i t y f o r berm b r e a k w a t e r s . - C o o p e r a t i o n between D e l f t H y d r a u l i c s and H y d r a u l i c s Research L i m i t e d on

model t e s t s on wide g r a d i n g s and v e r i f i c a t i o n o f t h e wave model ENDEC.

T h i s r e p o r t d e s c r i b e s t h e v e r i f i c a t i o n o f t h e model on dynamic s t a b i l i t y f o r berm b r e a k w a t e r s . The model runs on a pc and i s c a l l e d BREAKWAT. The d a t a r e c e i v e d f r o m v a r i o u s p e o p l e a l l o v e r t h e w o r l d c o n t a i n e d n o t o n l y berra b r e a k w a t e r s , b u t a l s o d y n a m i c a l l y s t a b l e l o w - c r e s t e d s t r u c t u r e s . The t i t l e of t h e r e p o r t was t h e r e f o r e changed t o " V e r i f i c a t i o n o f BREAKWAT f o r berm b r e a k w a t e r s and l o w - c r e s t e d s t r u c t u r e s " . The c a l c u l a t i o n s were p e r f o r m e d and the r e p o r t was w r i t t e n by Dr. J.W. van d e r Meer o f D e l f t H y d r a u l i c s .

Thanks a r e due t o Mr. J.P. Ahrens f r o m t h e U.S. Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , C o a s t a l E n g i n e e r i n g Research C e n t e r , USA; P r o f . H.F. B u r c h a r t h f r o m A a l b o r g U n i v e r s i t y , Denmark; Mr. O.J. Jensen f r o m t h e D a n i s h H y d r a u l i c I n s t i t u t e , Denmark and P r o f . A. T^rum f r o m t h e Norwegian I n s t i t u t e of T e c h n o l o g y , Norwegian H y d r o t e c h n i c a l L a b o r a t o r y , Norway f o r s u b m i t t i n g a l l t h e d a t a r e q u i r e d t o p e r f o r m t h i s s t u d y .

2. The model BREAKWAT

I n Van d e r Meer (1988) s t a t i c a l l y s t a b l e and d y n a m i c a l l y s t a b l e r o c k s t r u c -t u r e s were -t r e a -t e d . S -t a -t i c a l l y s -t a b l e means no o r o n l y m i n o r d i s p l a c e m e n -t o f m a t e r i a l under severe wave a t t a c k and t h e b e h a v i o u r o f t h e s t r u c t u r e i s d e s c r i b e d by "damage" d e s c r i p t i o n s . D y n a m i c a l l y s t a b l e means t h a t t h e waves w i l l f o r m a more o r l e s s s t a b l e p r o f i l e f o r t h a t wave c o n d i t i o n . The beha-v i o u r i s d e s c r i b e d by t h e " p r o f i l e " - f o r m a t i o n under wabeha-ve a t t a c k .

Based on a v e r y e x t e n s i v e s e t o f t e s t s Van d e r Meer (1988) d e r i v e d f u n c t i o n a l r e l a t i o n s h i p s t h a t d e s c r i b e d t h e p r o f i l e as a f u n c t i o n o f wave c o n d i -t i o n s and s -t r u c -t u r a l p a r a m e -t e r s . The s c h e m a -t i s e d p r o f i l e ( o n a 1:5 i n i -t i a l s l o p e ) i s shown i n F i g . 1. The p r o f i l e i s g i v e n by a number o f h e i g h t and l e n g t h p a r a m e t e r s , two power c u r v e s around t h e s t i l l w a t e r l e v e l and t w o a n g l e s . The l o w e r g r a p h i n F i g . 1 g i v e s t h e p r o f i l e s f o r v a r i o u s i n i t i a l s l o p e s . The main p a r t , f r o m beach c r e s t t o t h e t r a n s i t i o n f r o m t h e g e n t l e p a r t below s w l t o a s t e e p e r p a r t , i s t h e same f o r a l l t h r e e p r o f i l e s . The f o r m a t i o n o f a beach c r e s t and t h e d i r e c t i o n o f m a t e r i a l t r a n s p o r t depends on t h e i n i t i a l s l o p e . A beach c r e s t i s formed f o r g e n t l e i n i t i a l s l o p e s , t o g e t h e r w i t h a " s t e p " ( a b r e a k e r h o l e ) below s w l . F o r a s t e e p i n i t i a l s l o p e o n l y e r o s i o n w i l l t a k e p l a c e around s w l and w i l l g i v e a c c r e -t i o n below s w l .

The f u n c t i o n a l r e l a t i o n s h i p s were used i n a computer model on a p e r s o n a l computer i n o r d e r t o c a l c u l a t e t h e p r o f i l e . T h i s model i s a p a r t o f t h e computer package BREAKWAT. The f u n c t i o n a l r e l a t i o n s h i p s were m a i n l y based on 1:3 and 1:5 s t r a i g h t i n i t i a l s l o p e s and berm b r e a k w a t e r s on deep w a t e r w i t h a seaward s l o p e o f 1:1.5. I n a l l cases H /AD > 3, where H » t h e s i g n i f i

-s no u -s c a n t wave h e i g h t , A = t h e r e l a t i v e buoyant d e n s i t y and D ^ ^ Q = t h e n o m i n a l d i a m e t e r . The i n f l u e n c e o f t h e w a t e r d e p t h ( b r e a k i n g waves, n o n - R a y l e i g h d i s t r i b u t i o n ) was i n v e s t i g a t e d f o r a s l o p e o f 1:3 on a 1:30 s l o p i n g f o r e -s h o r e . The i n f l u e n c e o f a low c r e -s t wa-s i n v e -s t i g a t e d ( o n deep w a t e r ) f o r a s t r u c t u r e w i t h a s l o p e o f 1:1.5.

I n o r d e r t o be a b l e t o a p p l y t h e program a l i t t l e beyond t h e t e s t e d range (H /AD c _ - v a l u e s below 3 ) t h e f u n c t i o n a l r e l a t i o n s h i p s were m o d i f i e d f o r

s u

t h i s range. The m o d i f i c a t i o n s were based on sound e n g i n e e r i n g j u d g e m e n t and n o t on a c t u a l t e s t r e s u l t s .

_3-Berm b r e a k w a t e r s have r e l a t i v e l y low H / A D „„-values, o f t e n l o w e r t h a n 3. ' s' n50

These s t r u c t u r e s w i l l be reshaped d u r i n g s e v e r e wave a t t a c k and a r e more o r l e s s s t a t i c a l l y s t a b l e a f t e r t h i s r e s h a p i n g . T h i s means t h a t w i t h H ^ / A D ^ ^ Q -v a l u e s o f 3 and l o w e r , t h i s t y p e o f s t r u c t u r e s i s s i t u a t e d a t t h e l o w e r boundary f o r a p p l i c a t i o n o f t h e computer program.

As berm b r e a k w a t e r s g a i n more and more a t t e n t i o n and a r e s i t u a t e d i n s h a l l o w w a t e r and t h e model was o n l y v e r i f i e d f o r H ^ / A D ^ ^ Q- v a l u e s h i g h e r t h a n 3, t h e CUR/CIRIA committee d e c i d e d t o v e r i f y t h e model f o r berm b r e a k w a t e r s .

The model B R E A K W A T needs as i n p u t t h e n o m i n a l d i a m e t e r D ^ ^ Q, t h e g r a d i n g o f

t h e s t o n e c l a s s D„c/Dir» t h e r e l a t i v e buoyant d e n s i t y A , t h e s i g n i f i c a n t

oo Id

wave h e i g h t H , t h e mean wave p e r i o d T , t h e number o f waves ( s t o r m d u r a -s m

t i o n ) N and t h e w a t e r d e p t h . F u r t h e r m o r e , i t needs t h e i n i t i a l s l o p e g i v e n by a number o f ( x , y ) c o o r d i n a t e s .

3. Data s o u r c e s

Data on berm b r e a k w a t e r s and d y n a m i c a l l y s t a b l e s t r u c t u r e s i n g e n e r a l was asked f r o m v a r i o u s people and i n s t i t u t e s . The d a t a s e t s r e c e i v e d and used i n t h i s s t u d y w i l l be d e s c r i b e d i n t h i s Chapter.

3 .1 Ahrens and Heimbaugh

Ahrens and Heimbaugh (1989) d e s c r i b e d t e s t s on dvimped r i p r a p . I n t o t a l 22 t e s t s were p e r f o r m e d ( o n l y 13 a r e g i v e n i n t h e r e f e r e n c e ) . The boundary con-d i t i o n s ancon-d p r o f i l e s of a l l t e s t s were s u b m i t t e con-d by Ahrens on f l o p p y con-d i s k and were used f o r v e r i f i c a t i o n .

The s t r u c t u r e was c o n s t r u c t e d on a 1:30 s t r a i g h t f o r e s h o r e and t h e s t r u c t u r e was s i t u a t e d i n s h a l l o w w a t e r . The s t r u c t u r e c o n s i s t e d o f a c r e s t a t a

c e r t a i n h e i g h t and w i t h a c e r t a i n l e n g t h and a seaward s l o p e o f 1:1. The seaward s l o p e i s v e r y s t e e p ( n o t t e s t e d f o r BREAKWAT). F u r t h e r m o r e , t h e c r e s t h e i g h t i s r a t h e r low and waves o v e r t o p t h e f r o n t s i d e o f t h e c r e s t . The n o m i n a l d i a m e t e r was 0.007 m and t h e g r a d i n g D.^/D,^ = 2 , 0 . Three t e s t s were s e l e c t e d f o r v e r i f i c a t i o n . A l l ' o f them had t h e l o w e s t H /AD ^- v a l u e s

s u of t h e t e s t s . These v a l u e s were 4.4, 7.0 and 3.6 f o r r e s p e c t i v e l y t e s t s 7, 15 and 22. The i n i t i a l p r o f i l e s , t h e p r o f i l e s a f t e r wave a t t a c k and t h e boundary c o n d i t i o n s f o r each t e s t a r e shown i n F i g s . 2 - 4 .

The wave h e i g h t s were measured 6.1 m i n f r o n t o f t h e s t r u c t u r e a t a l a r g e r w a t e r d e p t h t h a n a t t h e t o e o f t h e s t r u c t u r e ( d i f f e r e n c e o f 0.20 m). The wave h e i g h t a t t h e s t r u c t u r e t o e was n o t measured, b u t c a l c u l a t e d .

3.2 H y d r a u l i c s Research

H y d r a u l i c s Research L t d , W a l l i n g f o r d , UK, t e s t e d a berm b r e a k w a t e r d u r i n g the d e s i g n s t a g e o f a b r e a k w a t e r . D e l f t H y d r a u l i c s was i n v o l v e d i n p r e d i c t i o n o f t h e b e h a v i o u r o f t h e s t r u c t u r e i n o r d e r t o d e s i g n t h e f i r s t c r o s s -s e c t i o n f o r t e -s t i n g . The r e p o r t i -s c o n f i d e n t i a l .

The f o r e s h o r e was 1:100 and t h e s t r u c t u r e was s i t u a t e d a t s h a l l o w w a t e r . The wave h e i g h t was ( d e p t h ) - l i m l t e d t o about 5 m. The b r e a k w a t e r had an u p p e r

5s l o p e o f 1:1.5, a berm a t 5s w l and a l o w e r 5s l o p e o f 1:1.5. The n o m i n a l d i a -meter was 0.88 ra and t h e maximum H^/AD^^Q-value was 3.5. F i g . 5 g i v e s t h e c r o s s - s e c t i o n o f t h e s t r u c t u r e and t h e measured p r o f i l e a f t e r a c e r t a i n t e s t p e r i o d .

3.3 B u r c h a r t h and F r i g a a r d

B u r c h a r t h and F r i g a a r d ( 1 9 8 8 ) d e s c r i b e d f u n d a m e n t a l t e s t s on a berm b r e a k -w a t e r p r o f i l e i n a -wave b a s i n . B o t h p e r p e n d i c u l a r -wave a t t a c k and o b l i q u e wave a t t a c k was used. The s t r u c t u r e was c o n s t r u c t e d on a h o r i z o n t a l b o t t o m w i t h o u t a f o r e s h o r e . The w a t e r d e p t h was 0.5 m. The s t r u c t u r e c o n s i s t e d o f a h o r i z o n t a l c r e s t w i t h a l e n g t h o f 0.5 m and sea- and l a n d w a r d s l o p e s o f 1:1.5. The n o m i n a l d i a m e t e r was 0.0169 m and t h e H /AD ,,„values were 3.5

-s nSO 7.1.

F i g s . 6 8 show t h e c r o s s s e c t i o n and t h e p r o f i l e s f o r v a r i o u s wave c o n d i -t i o n s . F i g . 6 g i v e s -t h e i n f l u e n c e o f -t h e wave h e i g h -t . F i g . 7 -t h e i n f l u e n c e o f t h e wave p e r i o d and F i g . 8 t h e i n f l u e n c e o f t h e s t o r m d u r a t i o n .

3.4 Danish H y d r a u l i c I n s t i t u t e

Mr. O.J. Jensen o f DHI was asked t o s u b m i t d a t a on berm b r e a k w a t e r t e s t s . As a l l r e p o r t s were c o n f i d e n t i a l t h e d a t a was s u b m i t t e d as cases, c a l l e d SKP, GLR, EID and SLV.

Case SKP c o n s i s t e d o f a b r e a k w a t e r a t a d e p t h o f 20 ra. Only t h e berm c o n s i s -t e d o f l a r g e s -t o n e s and had a seaward s l o p e o f 1:1. The s -t o n e s above and below t h e berm were s m a l l e r . The c r o s s - s e c t i o n i s shown i n F i g . 9, t o g e t h e r w i t h t h e p r o f i l e s a f t e r two t e s t s e r i e s .

The n o m i n a l d i a m e t e r o f t h e s t o n e s was 1.65 ra and t h e maximum H /AD ,.„-value s n50 amounted t o 2.5 w h i c h i s l o w e r t h a n t e s t e d f o r t h e model BREAKWAT.

Case GLR c o n s i s t e d o f t h e c o r e o f a b r e a k w a t e r w i t h q u a r r y r u n under r e l a t i -v e l y m i l d wa-ve a t t a c k ( w i t h r e g a r d t o t h e b r e a k w a t e r i t s e l f ) . The s t r u c t u r e was l o c a t e d a t 24 m deep w a t e r and c o n s i s t e d o f a c r e s t w i t h a w i d t h o f 15 m j u s t above s w l and sea- and landward s l o p e s o f 1:0.9. The s t r u c t u r e i s v e r y low and has v e r y s t e e p s l o p e s . The n o m i n a l d i a m e t e r amounted t o 0.3 ra and

t h e g r a d i n g t o Dg^/D^^ - 1.95. The wave h e i g h t s ranged f r o m 1 t o 3 m. The c r o s s - s e c t i o n w i t h t h e p r o f i l e s a r e shown i n F i g . 12.

Case EID i s more o r l e s s comparable w i t h case GLR. A q u a r r y r u n core w i t h a low b u t wide c r e s t and s l o p e s o f 1:1.2 was c o n s t r u c t e d on a d e p t h o f 10.4 m. The n o m i n a l d i a m e t e r amounted t o 0.15 m and t h e g r a d i n g t o D^^/D^^ = 3 . 0 w h i c h i s v e r y w i d e and o u t s i d e t h e range t e s t e d f o r t h e model BREAKWAT. The wave h e i g h t ranged f r o m 0.7 t o 3.1 m. F i g . 14 g i v e s t h e c r o s s - s e c t i o n and t h e p r o f i l e s .

Case SLV i s a g a i n a berm b r e a k w a t e r . The t e s t s were r u n i n a wave b a s i n w i t h a more o r l e s s i r r e g u l a r f o r e s h o r e . The c r o s s - s e c t i o n t a k e n f o r v e r i f i c a t i o n

i s c l o s e t o t h e head o f t h e s t r u c t u r e and i s s i t u a t e d i n about 15 m deep w a t e r . The c r o s s - s e c t i o n and t h e f i n a l p r o f i l e s o f some t e s t s e r i e s a r e shown i n F i g . 17. The seaward s l o p e o f t h e berm i s s t e e p , 1:1. The n o m i n a l d i a m e t e r o f t h e s t o n e s amounted t o 1.45 m (5-15 t r o c k ) . The s l o p e above t h e berra c o n s i s t e d o f 2-5 t r o c k . The s t r u c t u r e has a l a r g e t o e berm.

3.5 T^rum e t a l .

T?5rum e t a l . ( 1 9 8 8 ) d e s c r i b e t e s t s on a berm b r e a k w a t e r f o r t h e f i s h i n g p o r t o f A r v i k s a n d , Norway. D e t a i l e d d a t a o f t h e t e s t s was s u b m i t t e d by P r o f . T/rura. The s t r u c t u r e was c o n s t r u c t e d a t 0.5 m deep w a t e r on a 1:30 s l o p i n g f o r e s h o r e . The berra was j u s t above s w l , t h e upper s l o p e was 1:3 and t h e s l o p e below t h e berra was 1:1.5. The c r o s s - s e c t i o n o f t h e b r e a k w a t e r i s shown i n F i g . 19.

The n o m i n a l d i a m e t e r amounted t o 1.19 m ( o n a l i n e a r s c a l e o f 1:40) and t h e g r a d i n g was Dg^/D^^ = 1.48. The wave h e i g h t ranged f r o m 2 m up t o 8.6 m. F o r t h e l o w e s t wave h e i g h t s t h e s t r u c t u r e i s s t a t i c a l l y s t a b l e and t h e d i s p l a c e -ment o f m a t e r i a l i s v e r y l i m i t e d i n t h a t case. F o r t h e h i g h e r wave h e i g h t s t h e s t r u c t u r e becomes d y n a m i c a l l y s t a b l e .

The p r o f i l e s f o r t e s t s e r i e s B l , 2 a r e g i v e n i n F i g . 19. A l s o t h e sequence o f wave h e i g h t s w i t h a c e r t a i n d u r a t i o n a r e g i v e n i n F i g . 19. S h o r t t e s t r u n s were p e r f o r m e d ( c u r v e B l - 4 ) up t o 8.6 m, t h e n t h i s wave h e i g h t was r u n f o r a

l o n g e r t i m e . The l o w e r g r a p h i n F i g . 19 g i v e s a l s o t h e "damage" S, d e f i n e d as S = A/D , where A i s t h e e r o s i o n a r e a . S = 2-3 means s t a r t o f damage

-7-( o n l y some s e t t l e m e n t ) , S = 4-7 means moderate damage t o a t w o - d i a m e t e r t h i c k armour l a y e r and S > 8-12 means one l a y e r o f s t o n e s removed. F o r S > 20 t h e s t r u c t u r e becomes d y n a m i c a l l y s t a b l e .

^- V e r i f i c a t i o n

The d a t a d e s c r i b e d i n C h a p t e r 3 were used t o make c a l c u l a t i o n s w i t h t h e model BREAKWAT and t h e r e s u l t s were compared w i t h t h e d a t a o f t h e t e s t s . T h i s C h a p t e r d e s c r i b e s t h i s v e r i f i c a t i o n .

J- Ahrens and Heimbaup;h

F i g s . 2-4 g i v e t h e r e s u l t s f o r t h r e e t e s t s o f Ahrens and Heimbaugh ( 1 9 8 9 ) . The s o l i d l i n e s g i v e t h e i n i t i a l s l o p e and o b t a i n e d p r o f i l e and t h e o t h e r l i n e s g i v e t h e computed p r o f i l e s .

The wave h e i g h t was measured 6.1 m i n f r o n t o f t h e s t r u c t u r e . The w a t e r d e p t h a t t h e s t r u c t u r e t o e was about 0.15 m, a t t h e wave gauge about 0.35 m. The wave h e i g h t s a t t h e gauge f o r t e s t s 7 and 22 were 0.070 and 0.056 ra. T e s t 15 had a h i g h e r wave h e i g h t o f 0.114 m. The t e s t s w i t h t h e two l o w e s t wave h e i g h t s g i v e no b r e a k i n g on t h e f o r e s h o r e . T e s t 15 g i v e s b r e a k i n g waves and a r e d u c t i o n i n wave h e i g h t a t t h e t o e . Ahrens g i v e s a l s o f o r t e s t s 7 and 22 a r e d u c t i o n i n wave h e i g h t s o f about 25 % ( c a l c u l a t e d ) . T h i s seems a r a t h e r h i g h r e d u c t i o n .

As t h e wave h e i g h t a t t h e s t r u c t u r e i s n o t e x a c t l y known, c a l c u l a t i o n s were done f o r b o t h t h e measured one a t t h e gauge 6.1 m i n f r o n t o f t h e s t r u c t u r e and f o r t h e c a l c u l a t e d one a t t h e t o e o f t h e s t r u c t u r e . F i g s . 2-4 g i v e t h e r e s u l t s . The i n p u t f o r t h e c a l c u l a t i o n s ( b o u n d a r y c o n d i t i o n s and i n i t i a l s l o p e ) t o g e t h e r w i t h some r e s u l t s ( d i m e n s i o n l e s s wave c h a r a c t e r i s t i c s and t h e p r o f i l e p a r a m e t e r s ) a r e g i v e n i n t h e F i g s . t o o .

T e s t 7 ( F i g . 2) has a low wave h e i g h t and a l o n g wave p e r i o d w h i c h r e s u l t s i n a r a t h e r l o w wave s t e e p n e s s o f 0.010. T e s t 22 ( F i g . 4 ) has a b o u t t h e same wave h e i g h t and a s h o r t e r wave p e r i o d w h i c h r e s u l t s i n a wave s t e e p n e s s o f 0.017. The c a l c u l a t e d p r o f i l e s f o r t e s t 7 g i v e t h e same o r d e r o f m a g n i t u d e f o r t h e c r e s t h e i g h t and t h e same s l o p e above s w l , b u t a t o o l o n g s l o p e below s w l . T h i s r e s u l t s i n more e r o s i o n t h a n o b s e r v e d i n t h e t e s t . The c a l c u l a t e d p r o f i l e s f o r t e s t 22 ( F i g . 4 ) a r e v e r y c l o s e t o t h e o b s e r v e d one. The c r e s t h e i g h t i s a l i t t l e u n d e r p r e d i c t e d , b u t d i f f e r e n c e s a r e s m a l l .

-9-T e s t 15 has a h i g h e r wave h e i g h t t h a n t h e o t h e r two t e s t s and has a wave s t e e p n e s s o f 0.031. The c a l c u l a t e d p r o f i l e f o r = 0.0812 ra i s c l o s e t o t h e o b s e r v e d p r o f i l e . The s i z e o f t h e beach c r e s t i s a l i t t l e u n d e r p r e d i c t e d and the p r o f i l e below s w l i s a l i t t l e t o o l o n g . The c r e s t h e i g h t and t h e shape of t h e p r o f i l e around s w l i s c o r r e c t . The wave h e i g h t o f 0.1141 ra can n o t e x i s t a t t h e d e p t h a t t h e t o e o f 0.157 ra. T h e r e f o r e t h e c a l c u l a t e d p r o f i l e i s n o t r e a l i s t i c . I t shows, however, t h e i n f l u e n c e o f t h e w a t e r depth/wave h e i g h t r a t i o on t h e p r o f i l e : t h e p r o f i l e below s w l becomes s h o r t e r . A wave h e i g h t w h i c h i s a l i t t l e h i g h e r t h a n 0.0812 m, b u t s m a l l e r t h a n 0.1141 ra w i l l g i v e a p r o f i l e v e r y c l o s e t o t h e o b s e r v e d one. The g e n e r a l c o n c l u s i o n i s t h a t t h e c a l c u l a t e d p r o f i l e s a r e c l o s e t o t h e o b s e r v e d p r o f i l e . The s i z e o f t h e c r e s t h e i g h t i s a l i t t l e u n d e r p r e d i c t e d and t h e l e n g t h o f t h e p r o f i l e below s w l a l i t t l e o v e r p r e d i c t e d . The r e l a t i o n s h i p s f o r t h e s i z e o f t h e c r e s t ( p a r a m e t e r 1^) a r e based on o n l y a few t e s t s . I n most t e s t s o f Ahrens and Heimbaugh a c r e s t was formed above t h e o r i g i n a l c r e s t l e v e l . E l a b o r a t i o n o f t h e p r o f i l e s w o u l d g i v e a b e t t e r r e l a t i o n s h i p f o r t h e s i z e o f t h e c r e s t .

4.2 H y d r a u l i c s Research

F i g . 5 g i v e s t h e c r o s s - s e c t i o n and t h e measured and c a l c u l a t e d p r o f i l e s o f t h e berra b r e a k w a t e r t e s t e d by H y d r a u l i c s Research. The p r o f i l e was c a l c u l a -t e d d u r i n g -t h e r e s e a r c h by D e l f -t H y d r a u l i c s and was s e n -t -t o H y d r a u l i c s Research f o r c o m p a r i s o n w i t h t h e t e s t r e s u l t s . The p r o f i l e was c a l c u l a t e d f o r Hg = 4.66 m and a wave p e r i o d o f 9.9 s w h i c h g i v e s a wave s t e e p n e s s o f 0.030. The Hg/AD^5Q-value was 3.5.

The l o w e r g r a p h i n F i g . 5 g i v e s t h e c o m p a r i s o n o f p r o f i l e s and was p l o t t e d by H y d r a u l i c s Research. Note t h a t t h e s e a s i d e i n t h e b o t h g r a p h s o f F i g . 5 i s n o t on t h e same s i d e o f t h e g r a p h s .

The c o n c l u s i o n i s t h a t t h e c a l c u l a t e d p r o f i l e i s v e r y c l o s e t o t h e o b s e r v e d one.

4. 3 B u r c h a r t h and F r i p a a r H

F i g s . 6-8 g i v e t h e r e s u l t s o f 8 t e s t s and c a l c u l a t i o n s . F i g . 6 g i v e s t h e i n f l u e n c e o f t h e wave h e i g h t on t h e p r o f i l e . The wave h e i g h t o f 0.13 m g i v e s no beach c r e s t , t h e wave h e i g h t o f 0.15 m a v e r y s m a l l one and t h e h i g h e s t wave h e i g h t o f 0.20 m g i v e s a beach c r e s t . E x a c t l y t h e same was f o u n d f o r t h e c a l c u l a t i o n s .

The measured p r o f i l e s show a l a r g e r e r o s i o n t h a n a c c r e t i o n . B u r c h a r t h and F r i g a a r d s t a t e t h a t : "The m a t e r i a l d e f i c i t i s due t o s e t t l e m e n t s caused by wave c o m p a c t i o n and m a t e r i a l t r a n s p o r t a c r o s s t h e c r e s t " . The e f f e c t o f p o s s i b l e s e t t l e m e n t s and m a t e r i a l d e f i c i t i s n o t t a k e n i n t o a c c o u n t i n t h e r e l a t i o n s h i p s f o r t h e c a l c u l a t i o n o f t h e p r o f i l e . There t h e mass b a l a n c e has t o be f u l f i l l e d w h i c h g i v e s t h e r i g h t l o c a t i o n o f t h e p r o f i l e . T h i s i s t h e r e a s o n why t h e a c c r e t i o n f o r t h e c a l c u l a t e d p r o f i l e s i s l a r g e r t h a n f o r t h e measured ones. I f s e t t l e m e n t i s t a k e n i n t o a c c o u n t i n t h e c a l c u l a t i o n s , t h e p r o f i l e w o u l d have been s h i f t e d t o t h e r i g h t i n t h e g r a p h s . I n t h a t case t h e c a l c u l a t e d and measured p r o f i l e s would become even c l o s e r .

F i g . 7 g i v e s t h e i n f l u e n c e o f t h e wave p e r i o d on t h e p r o f i l e . A l o n g e r wave p e r i o d g i v e s a l i t t l e l o n g e r p r o f i l e . E x a c t l y t h e same was found f o r t h e c a l c u l a t i o n s .

F i g . 8 g i v e s t h e i n f l u e n c e o f t h e s t o r m d u r a t i o n (number o f waves) on t h e p r o f i l e . A l o n g e r d u r a t i o n w i l l g i v e a l i t t l e l o n g e r p r o f i l e . T h i s i s a l s o f o u n d f o r t h e c a l c u l a t i o n s .

The c a l c u l a t e d p r o f i l e s f o r t h e t e s t s o f B u r c h a r t h and F r i g a a r d a r e v e r y c l o s e t o t h e measured ones. S e t t l e m e n t caused by wave c o m p a c t i o n i s n o t s i m u l a t e d by t h e model.

^-^ D a n i s h H y d r a u l i c I n s t i t u t e

F i g . 9 g i v e s t h e c r o s s - s e c t i o n and measured p r o f i l e s f o r two t e s t s o f t h e case SKP. F i g s . 10 and 11 g i v e t h e c a l c u l a t e d p r o f i l e s f o r t h e two t e s t s . T e s t 18 has a w a t e r d e p t h o f 21 m and a wave h e i g h t o f 6.5 m and t e s t 19 has a w a t e r d e p t h o f 19 m and a wave h e i g h t o f 6 m. F o r t h e c a l c u l a t i o n s i t has t o be assumed t h a t t h e whole s t r u c t u r e c o n s i s t s o f t h e same m a t e r i a l ( w i t h

•

11-°n50 ^-^^ T h i s i s n o t t h e case f o r t h e upper s l o p e and t h e p a r t below t h e berm.

T e s t 18 ( m i d d l e g r a p h o f F i g . 9) shows t h e f o r m a t i o n o f a beach c r e s t above t h e berm, e r o s i o n o f t h e berm t o a d e p t h about 2/3 o f i t s h e i g h t and a c c r e -t i o n below -t h i s p o i n -t . There i s a -t e n d e n c y a l s o h e r e -t h a -t -t h e e r o s i o n p a r -t i s l a r g e r t h a n t h e a c c r e t i o n p a r t w h i c h may l e a d t o t h e c o n c l u s i o n t h a t t h e r e was some s e t t l e m e n t i n t h e t e s t . F i g . 10 g i v e s t h e c a l c u l a t e d p r o f i l e . The g e n e r a l t r e n d i s t h e same as f o r t h e measurements. The beach c r e s t and a l s o t h e a c c r e t i o n p a r t a r e more pronounced f o r t h e c a l c u l a t e d p r o f i l e , p r o -b a -b l y caused -by n o t t a k i n g i n t o a c c o u n t t h e s e t t l e m e n t .

T e s t 19 ( l o w e r g r a p h o f F i g . 9 ) shows no f o r m a t i o n o f a beach c r e s t ( n o t e t h a t m a t e r i a l I V i s s m a l l e r t h a n t h e m a t e r i a l i n t h e berm) and shows a l s o e r o s i o n o f t h e p a r t o f t h e s t r u c t u r e below t h e berm. The c a l c u l a t e d p r o f i l e i n F i g . 11 g i v e s t h e same t e n d e n c y .

The c o n c l u s i o n f o r case SKP i s t h a t t h e c a l c u l a t i o n s a r e c l o s e t o t h e t e s t r e s u l t s .

The c r o s s - s e c t i o n and p r o f i l e s o f case GLR a r e g i v e n i n F i g . 12. The s l o p e o f t h e s t r u c t u r e i s v e r y s t e e p and t h e c r e s t v e r y low. F o r H = 1 m t h e s t r u c t u r e i s c l o s e t o s t a t i c s t a b i l i t y w i t h H ^ / A D ^ ^ Q » 2.0. J i t h t h i s s t e e p s l o p e and l o w c r e s t t h e s t r u c t u r e f a l l s o u t o f t h e range o f c o n d i t i o n s on w h i c h t h e p r o f i l e r e l a t i o n s h i p s were based. F u r t h e r m o r e , damage t o t h e r e a r s l o p e i s n o t t a k e n i n t o a c c o u n t . T h i s means t h a t as soon as m a t e r i a l i s t r a n s p o r t e d t o t h e r e a r o f t h e s t r u c t u r e , t h a t c o n d i t i o n i s beyond t h e range f o r a p p l i c a t i o n .

F i g . 13 g i v e s t h e c a l c u l a t e d p r o f i l e s . For t h e c a l c u l a t i o n t h e c r e s t w i d t h was i n c r e a s e d t o 30 i n s t e a d o f 15. The amount o f e r o s i o n f o r t h e wave h e i g h t o f 1 m i s t o o l a r g e f o r t h e c a l c u l a t i o n . T h i s c o n d i t i o n i s n o t a d y n a m i c a l l y s t a b l e c o n d i t i o n . The second c o n d i t i o n w i t h H = 1.5 m g i v e s p r o f i l e s i n c a l c u l a t i o n and t e s t w h i c h a r e r a t h e r c l o s e . The l o c a t i o n o f t h e c r e s t i n t h e c a l c u l a t e d p r o f i l e s u g g e s t s a l r e a d y t h a t o v e r t o p p i n g o f t h e c r e s t can cause damage t o r e a r o f t h e s t r u c t u r e . The t h i r d c o n d i t i o n w i t h

i n i t i a l c r e s t and r e a r . T h i s means t h a t t h e s t r u c t u r e i n r e a l i t y w i l l hea-v i l y be o hea-v e r t o p p e d and t h a t t h e c r e s t h e i g h t w i l l be reduced t o below s w l . T h i s i s a l s o what happened i n t h e t e s t .

I t can be c o n c l u d e d f o r t h i s case GLR t h a t t h e c a l c u l a t i o n s a r e a c c o r d i n g t o t h e t e s t r e s u l t s as l o n g as t h e c o n d i t i o n i s d y n a m i c a l l y s t a b l e and t h e

c r e s t remains above s w l (no severe o v e r t o p p i n g ) .

Case EID i s more o r l e s s s i m i l a r w i t h case GLR. The c r e s t i s w i d e r , t h e n o m i n a l d i a m e t e r i s two t i m e s s m a l l e r and t h e g r a d i n g i s v e r y w i d e . F o r s e v e r a l a s p e c t s t h i s s t r u c t u r e f a l l s o u t s i d e t h e range where t h e p r o f i l e r e l a t i o n s h i p s were based upon. The s l o p e i s v e r y s t e e p , t h e c r e s t i s v e r y low and t h e g r a d i n g i s v e r y w i d e . F u r t h e r m o r e , t h e wave p e r i o d i s v e r y l o n g f o r t h e r e l a t i v e l y l o w wave h e i g h t s (peak p e r i o d o f 13 s f o r wave h e i g h t s f r o m 0.7-3.1 m). T h i s g i v e s f o r t h e l o w e s t wave h e i g h t a wave s t e e p n e s s o f 0.005 w h i c h i s v e r y low. The c r o s s - s e c t i o n and p r o f i l e s a r e shown i n F i g 14.

F i g . 15 g i v e s f o u r p r o f i l e s f o r a n o m i n a l d i a m e t e r o f 0.15 m. T h i s d i a m e t e r was e s t a b l i s h e d f r o m t h e g r a d i n g c u r v e . I t i s n o t c e r t a i n , however, t h a t w i t h t h i s wide g r a d i n g t h e D^^^ i s t h e c o r r e c t v a l u e f o r use as i n p u t . Maybe t h e p r o f i l e i s more d e t e r m i n e d by a s m a l l e r o r l a r g e r s i z e i n t h e g r a d i n g c u r v e . The b u i l d up o f a beach c r e s t f o r - 1.6 m and c e r t a i n l y f o r H = 2.3 m i n d i c a t e s t h a t t h e s t r u c t u r e i s a l r e a d y h e a v i l y o v e r t o p p e d f o r t h e s e c o n d i t i o n s . T h e r e f o r e , t h e p r o f i l e f o r a wave h e i g h t o f 3.1 m was n o t c a l c u -l a t e d . I t i s c e r t a i n t h a t t h a t wave c o n d i t i o n w o u -l d -l e a d t o e r o s i o n o f t h e r e a r o f t h e c r e s t . The w a t e r t h a t o v e r t o p s t h e c r e s t and erodes t h e c r e s t a t t h e r e a r can n o t be m o d e l l e d . F i g . 15 i n d i c a t e s t h a t wave h e i g h t s h i g h e r t h a n say 1.6-2 m may g i v e e r o s i o n a t t h e r e a r . F i g . 16 g i v e s t h e i n f l u e n c e o f t h e n o m i n a l d i a m e t e r and o f t h e wave p e r i o d on t h e p r o f i l e f o r a c o n s t a n t wave h e i g h t o f 1.6m. When t h e n o m i n a l d i a -m e t e r t o be used f o r t h e c a l c u l a t i o n , i n o r d e r t o a c c o u n t f o r t h e e f f e c t o f t h e v e r y wide g r a d i n g , i s 0.12 m i n s t e a d o f 0.15 m, t h e beach c r e s t w i l l s h i f t t o t h e l e f t (upper g r a p h ) . T h i s i n d i c a t e s more e r o s i o n a t t h e r e a r .

The r a t i o between t h e peak p e r i o d and t h e mean p e r i o d was g i v e n by Mr. Jensen and amounted t o 1.42. T h i s i s a r a t h e r l a r g e r a t i o and was used f o r

-13-h , p r o f U e s 1„ F i g . J5. T-13-he l o „ „ , „ p -13-h o f F l , . 16 s-13-hows t -13-h e l„,l„,„c, o£ the „eve p e r i o d , , s s ™ i „ g t h . t t h e p e , . p e r i o d l s s t i l l 13 s, h u t t h a t t h e

p e r . o d have been lo„,er t h a n , . 1 s. I t l s c l e a r £ro„ t h e g r a p h t h a t l o n g e r p e r i o d (a s m a l l e r peak period/„ean p e r i o d r a t i o ) has l a r g e i n f l u ¬

ence on t h e p r o f i l e . ^nzxu

The measured p r o f i l e s a r e g i v e n i n t h e l o w e r g r a p h o f F i g . 14. The two l o w e s t wave h e i g h t s gave o n l y s m a l l e r o s i o n . F o r a wave h e i g h t o f 2 3 m about h a l f o f t h e c r e s t was eroded and a beach c r e s t was f o r m e d t o g e t h e : w i t h some e r o s i o n o f t h e r e a r . The h i g h e s t wave h e i g h t gave a l o t o f o v e r ¬ t o p p i n g m a t e r i a l .

c o m p a r i s o n o f t h e measured and c a l c u l a t e d p r o f i l e s shows t h a t t h e e r o s i o n area f o r t h . t h r e e l o w e s t wav. h e i g h t s i s o v e r p r e d i c t e d by t h e „„del. A l s o t h e b u n t up Of a beach c r e s t f o r t h e s , wave h e i g h t s d i d n o t happen I n t h e t e s t s . The p r o f i i . s f o r 2.3 . a r e s i m i l a r , a l t h o u g h t t h e beach c r e s t i s t o o h i g h m t h e c a l c u l a t i o n s .

The o v e r a l l c o n c l u s i o n f o r case EID i s t h a t t h e model was a p p l i e d f o r a v e r y wide g r a d i n g and a v e r y s t e e p s l o p e and t h a t t h e model o v e r p r e d i c t e d t h e e r o s i o n f o r t h e l o w e s t wave h e i g h t s v e r y much. The f i n a l s i t u a t i o n was p r e -d i e t e -d r a t h e r c l o s e .

The c r o s s - s e c t i o n and t h . p r o f i l e s o f case SLV a r e shown 1„ F i g . u. F r o . , t e r r e s , two s e r i e s were chosen f o r v e r i f i c a t i o n . I n b o t h cases t h . wave ^ i r . c t r o n was mK w h i c h i s a b o u t p e r p e n d i c u l a r t o t h e a l i g n m e n t o f t h e

b r e a k w a t e r , l e s t s e r i e s 6 had a „ a x l „ s i g n i f i c a n t wave h e i g h t ( a t deep

l e t i T I 7 ' °' ' •"™"') •

l e v e l o f *0,7 m. T e s t s e r i e s 7 had a „a.l„u„, s i g n i f i c a n t wave h e i g h t o f 8 „ a peak p e r i o d o f u s ( T ^ . 12,3 s was assu„ed) and a w a t e r l e v. 1 o f -0.7

6 ( a f t e r 242) r s v a r y c l o s e t o t h e measured one. A l s o t h e shape and volume o f t h , beach c r e s t a r . ,l„ost . x a c t l y t h . sa„e, I h , f i n a l p r o f i l e a f t e r t e s t

3, r . e s 7 ( a f t e r 24,) g i v e s „ore e r o s i o n i n t h e t e s t . I t shows „ 0 beach

c r e s t . The p r e d i c t e d p r o f i l e shows a l s o no c r e s t , b u t g i v e s t h . sa.e e r o s i o n .n t . s t s e r r e s 6. T h . p r o f i l e i s lo„g,r, however. The u p p e r s l o p e was a r c ed a l i t t l e i n t h e t e s t s . T h , m a t e r i a l t h e r , was s m a l l e r , however, t h a n i n t h e berm ( 2 - 5 t i n s t e a d o f 5-15 t ) .

The o v e r a l l c o n c l u s i o n f o r case «ït v • .

p r o f i l e s a r e c l o s e . c a l c u l a t e d and measured

4- 5 Tj^rum e t a i

F i g . 19 g i v e s t h e c r o s s - s e c t i o n o f f h o k

, . p . . _

r,::.:::;"--"

The wave h e i g h t s ranged f r o m 2- 8 . 6 m. I t i s c l e a r that- f

2 m and a n o m i n a l d i a m e t e r o f 1 19 m (mea ^ "'^^ ^^^^^^

i s s t a t i c a l l y s t a b l e A l s o .1 \ ' ^^-'^^-^

d i s p l a c e m e n t o s t es

Hi I 'T '""^"^ ^^^^ ^

Should f i r s t be t r e a t d ^ ^ ^ ^ ^ ^ ^ _{a r i r s t be t r e a t e d as s t a t i c a l l y s t a b l e .}

used. ^ l o n g e r wave p e r i o d was

' '"'-^ ~

• " " - - ^ - - - - ¬

4. F i g „ e 21 Shows t h . t r e . 1 p r o f i l e d e f o r m a t i o n s t a r t s f o r t h e l a , t

wave c o n d i t i o n , h u t I s o n l y l i m i t e d t o a s m a l l p a r t o f t h . b Z

a c c o r d i n g t o t h e t e s t r e s u l t s , see F i g . 1 , . "

•JU/. r i g . g i v e s t h e r e s u l t s . The wavp h^^^u*. •

•15-f o r P 4 .s l a r g e r t h a n c a l c u l a t e d w i t h t h e s t a t i c a l l y s t a b l e „odel I n F i g and .s a l s o l a r g e r t h a n t h e o b s e r v e d e r o s i o n . The o b s e r v e d p r o f i l e P 4 i s l u s t r n between t h e c a l c u l a t e d ones w i t h t h e s t a t i c a l l y s t a b l e and t h e

dyna-f t t 7 ? " " " " " ' ' - •

c t . " °' " c a l -c u l a t e d p r o f r l e r n F i g . 22. a l t h o u g h t h e r e m a i n i n g p a r t I s a l i t t l e s m a l l e r .

F i n a l l y p r o f i l e s F 7 - P „ w „ a c a l c u l a t e d , a l l w i t h a wave h e i g h t o f 8.6 «, u f o r onger d u r a t i o n s . The r e s u l t s a r e g i v e n i n F i g . 23. The f i n a l p r o f u e P U shows a s m a l l beach c r e s t above t h e b e r . and a l m o s t no r e m a i n i n g h o r r z o n t a l p a r t o f t h e berm. T h i s I s shown b o t h f o r t h e measured p r o -t l i e ( F i g . 19) and -t h e c a l c u l a -t e d p r o f i l e ( F i g . 2 3 ) .

Th. o v e r a l l c o n c l u s i o n I s t h a t t h e b e h a v i o u r o f t h e berm b r e a k w a t e r w i t h wave h e r g h t s r a n g i n g f r o m 2-8.6 m I s v a r y w e l l p r e d i c t e d by a combined u s . o f t h e s t a t r c a l l y s t a b l e f o r m u l a e ( o r model) and t h e d y n a m i c a l l y s t a b l e

5. C o n c l u s i o n a

The d y n a m i c a l l y s t a b l e model, p a r t o f t h e computer program BREAKWAT, was v e r i f i e d f o r berm b r e a k w a t e r s and l o w - c r e s t e d s t r u c t u r e s . V a r i o u s d a t a s e t s f r o m a l l o v e r t h e w o r l d were used f o r t h i s v e r i f i c a t i o n . The g e n e r a l c o n c l u -s i o n -s f o r each o f t h e -s e d a t a -s e t -s a r e :

^l}£5S5_52Ë_52i5ba'^ih (1989)

The c a l c u l a t e d p r o f i l e s a r e c l o s e t o t h e observed p r o f i l e s . The s i z e o f t h e c r e s t h e i g h t i s a l i t t l e u n d e r p r e d i c t e d and t h e l e n g t h o f t h e p r o f i l e below swl a l i t t l e o v e r p r e d i c t e d .

The r e l a t i o n s h i p s f o r t h e s i z e o f t h e c r e s t ( p a r a m e t e r 1^) a r e based on o n l y a few t e s t s . I n most t e s t s o f Ahrens and Heimbaugh a c r e s t was formed above t h e o r i g i n a l c r e s t l e v e l . E l a b o r a t i o n o f t h e p r o f i l e s would g i v e a b e t t e r r e l a t i o n s h i p f o r t h e s i z e o f t h e c r e s t .

H y d r a u l i c s _ R e s e a r c h

The c a l c u l a t e d p r o f i l e i s v e r y c l o s e t o t h e observed one.

ly££!}f£t!}_52d_Frigaard (1988)

The c a l c u l a t e d p r o f i l e s f o r t h e t e s t s o f B u r c h a r t h and F r i g a a r d a r e v e r y c l o s e t o t h e measured ones. S e t t l e m e n t caused by wave c o m p a c t i o n i s n o t s i m u l a t e d by t h e model.

2 5 D i 5 h _ H ^ d r a u l i c _ I n s t i t u t e

The c o n c l u s i o n f o r case SKP i s t h a t t h e c a l c u l a t i o n s a r e c l o s e t o t h e t e s t r e s u l t s . F o r case GLR t h e c a l c u l a t i o n s a r e a c c o r d i n g t o t h e t e s t r e s u l t s as l o n g as t h e c o n d i t i o n i s d y n a m i c a l l y s t a b l e and t h e c r e s t r e m a i n s above s w l (no s e v e r e o v e r t o p p i n g ) . The o v e r a l l c o n c l u s i o n f o r case EID i s t h a t t h e model was a p p l i e d f o r a v e r y wide g r a d i n g and a v e r y s t e e p s l o p e and t h a t t h e model o v e r p r e d i c t e d t h e e r o s i o n f o r t h e l o w e s t wave h e i g h t s v e r y much. The f i n a l s i t u a t i o n was p r e d i c t e d r a t h e r c l o s e . The o v e r a l l c o n c l u s i o n f o r case SLV i s t h a t t h e c a l c u l a t e d and measured p r o f i l e s a r e c l o s e .

? ^ E y 5 _ 2 t _ a l i ( 1 9 8 8 )

The b e h a v i o u r o f t h e berm b r e a k w a t e r w i t h wave h e i g h t s r a n g i n g f r o m 2-8.6 m i s v e r y w e l l p r e d i c t e d by a combined use o f t h e s t a t i c a l l y s t a b l e f o r m u l a e ( o r m o d e l ) and t h e d y n a m i c a l l y s t a b l e model.

I I •17-?ï2rfll_£onclusion The o v e r a l l c o n c l u s i o n i s t h a t •->, . , d i f f e r e n c e s w i t h "'^"^ ^^^^^ u n e x p e c t e d

:^ :~i:ri:,?::::

-Proo. C o a s t a l Zona 89, C h a r l e s t o n , ASCE.

B u r c h a r t h , H.F. and F r i g a a r d , P., 1,88. On 3-dl„ansio„.l s t a h U i t y o , r e s h a p i n g b r e a k w a t e r s . ASCE, Proc. 2 U h ICCE, Malaga, S p a i n .

* u „ . A., Haess, S. , i n s t a n e s , A. and V o i d , S. , 1,88. On ber„ b r e a k w a t e r s . ASCE, Proc. 2 1 t h ICCE, Malaga, Spain.

P r o f i l e s on 1:2, 1:3 and 1:5 I n i t i a l s l o p e s S C H E M A T I S E D P R O F I L E F O R B R E A K W A T P R O F I L E S O N V A R I O U S I N I T I A L S L O P E S D E L F T H Y D R A U L I C S

1

—

H 9 8 6 _{\f\g. 1}

Grading R e l . l a s s d e n s i t y Have height Wave period S t o r i d u r a t i o n Hater depth ftngle ( n o r s a m » <l) _{DnSO = .007} (-) D85/D15 = 2 (-) d e l t a = 1.65 (•) Hs = .0512 (s) TB = 2.12 (-) N = 5000 (•) d = .159 (degr) 0 = 0 INITIAL SLOPE x l = 0 x2 = .666 x3 = .7081 x4 = .951 x5 = 0 x6 = 0 x7 = 0 y l = . 2 7 U y2 = .2714 y3 = .2454 y4 = 0 y5 = 0 y6 = 0 y7 = 0 RESILTS Hs/dDnSO = 4.4 HoTo = 352 Hs/Li = .007 I r = .227 he = .155 I c = .204 hs = .089 I s = .642 tanB = 1.123 ht = .089 tanY = .518 Dn50 = .007 D85/D15 = 2 d e l t a = 1.65 Hs = .0701 T l N d = 2.12 = 5000 = .159 = 0 RESULTS Hs/dDn50 = 6.1 HoTo = 482 Hs/Li = .010 I r = .303 he = .197 l e = .265 hs = .110 I s = .780 tanB = 1.118 ht = . 1 1 0 tanV = .514 H 9 8 6

BOUNDARY CONDITIONS N o i i n a l d i a i e t e r Grading Rel. l a s s d e n s i t y Wave height Wave period St o n duration Hater depth ftngle (norial=0) ( l ) _{Dn50 = .007} (-) D85/D15 = 2 (-) _{d e l t a = 1.65} ( l ) Hs = .0812 (s) Te = 1.534 (-) N = 3000 ( l ) d = .157 (degr) 0 _{= 0} Dn50 = .007 D85/D15 = 2 d e l t a = 1.65 Hs =.1141 T l = 1.534 N = 3000 d = .157 9 = 0 INITIAL SLOPE x l = 0 x2 = .7926 x3 = 1.0287 x4 = 0 x5 = 0 x6 = 0 x7 = 0 yl = .2698 y2 = .2698 y3 = 0 y4 = 0 y5 = 0 y6 = 0 y7 = 0 RESULTS H5/dDn50 = 7.0 HoTo = 404 Hs/Li = .022 I r = ,248 he = .161 l e = .215 hs = .091 I s = .627 tanB = 1.189 ht = .091 tanV = .567 RESULTS Hs/dDn50 = 9.9 HoTo = 567 Hs/Li = .031 I r = .338 he = .209 l e = .285 hs = .051 I s = .351 tanB = 1.474 ht = .051 tanY = .802

BOUNDARY CONDITIONS NoBinal d i a i e t e r Grading Rel. l a s s d e n s i t y Have height Have period St o n duration Hater depth Angle (norial=0) ( l ) _{Dn50 = .007} (-) _{DÖ5/D15 = 2} (-) _{d e l t a = 1.65} ( l ) Hs = .0415 (s) T l = 1.458 (-) N = 4576 ( l ) d = .1478 (degr) 0 _{= 0} Dn50 = .007 Da5/D15 = 2 d e l t a = 1.65 Hs = .0561 T l N d 0 = 1.458 = 4576 = .1562 = 0 RESULTS INITIAL SLOPE xl = 0 x2 = .5507 x3 = .8213 x4 = 0 x5 = 0 x6 = 0 x7 = 0 yl = .2577 y2 = .2577 y3 = 0 y4 = 0 y5 = 0 y6 = 0 y7 = 0 Hs/dDn50 = 3.6 HoTo = 196 Hs/Li = .013 ll" = . 137 he = .097 l e = .124 hs = .106 I s = .449 tanB =1.081 ht = . 106 tanY = .486 Hs/dDn50 = 4.9 HoTo = 265 Hs/Li = .017 I r = .176 he = .123 l e = .159 hs = .119 I s = .536 tanB = 1.127 ht = .119 tanY = .521 V E R I F I C A T I O N W I T H A H R E N S - T E S T

C O

J

Burcharth, I n f l u e n c e of wave height

— LnltLaL • -Hs-0.13 m . ---Hs-0.15 m A -Hs-0.20 m Distance (m) BOllfflflRY CONDITIONS N o i i n a l d i a i e t e r ( i ) Grading (-) Rel. l a s s d e n s i t y (-) Wave height (•) Wave period (5) S t o r i d u r a t i o n (-) Water depth (•) ftngle (norial=0) (degr)

Dn50 = .0169 D85/D15 = 1.7 d e l t a = 1.65 Hs = . 1 3 T l = 2 = 3000 = .5 = O N d 9 Dn50 = .0169 D85/D15 = 1.7 d e l t a = 1.65 Dn50 = .0169 D85/D15 = 1.7 Hs = .15 _{Hs = .2} T l = 2 _{T l = 2} N = 3000 _{N = 3000} d = .5 d _{= .5} 9 _{= 0 9 = 0} V E R I F I C A T I O N W I T H B U R C H A R T H I N F L U E N C E O F W A V E H E I G H T D E L F T H Y D R A U L I C S H 9 8 6 _{F I G .}

m i N = 3000 WAVES H = O 15 m .3 D > (D

Burcharth, LnfLuence o f wave perLod

• LnltlaL - - Tp=L8 s Tp=aO s Tp-2.2 s — s Distance (m) BOIMWRY CONDITIONS N o i i n a l d i a i e t e r ( i ) Grading (-) Rel. l a s s d e n s i t y (-) Wave height Wave period S t o r i duration Water depth ftngle (norial=0) ( I ) (s) (-) ( I ) (degr) Dn50 = .0169 D85/D15 = 1.7 d e l t a = 1.65 Hs Tl N d 9 = .15 = 1.44 = 3000 = .5 = O Dn50 = .0169 Dfl5/D15 = 1.7 d e l t a = 1.65 Hs Tl N d = .15 = 1.6 = 3000 = .5 = O Dn50 = .0169 D85/D15 = 1.7 d e l t a = 1.65 Hs Tl N d = .15 = 1.76 = 3000 = .5 = O Dn50 = .0169 D85/D15 = 1 . 7 d e l t a = 1.65 Hs Tl N d 0 = .15 = 2 = 3000 = .5 = O V E R I F I C A T I O N W I T H B U R C H A R T H I N F L U E N C E O F W A V E P E R I O D D E L F T H Y D R A U L I C S H 9 8 6 _{F I C . 7}

N = 9000

O

Burcharth, Influence o f number of

waves InltloL - -N-SOOO ••••N-6000 •--N-9000 1.5 Distance W ' • ' I I I ! 2.5 BOUNDARY CONDITIONS N o i i n a l d i a i e t e r ( i ) Grading (_) Rel. l a s s d e n s i t y (-) Have height Have period S t o r i duration Hater depth Angle (norial=0) (I) (s) (-) ( I ) (degr) Dn50 = .0169 D85/D15 = 1.7 d e l t a = 1.65 Hs Tl N d 0 •• .15 ^ 1.44 3000 .5 0 I^nSO = .0169 D85/D15 = 1.7 d e l t a = 1.65 Hs Tl N d = .15 = 1.44 = 6000 = .5 = 0 Dn50 = .0169 D85/D15 = 1.7 d e l t a = 1.65 Hs Tl N d 9 = .15 = 1.44 = 9000 = .5 = 0 V E R I F I C A T I O N O F B U R C H A R T H I N F L U E N C E O F N U M B E R O F W A V E S D E L F T H Y D R A U L I C S H 9 8 6 _{F I G . 8}

35 30 ' 25 LU 15 10 22.5 ₄₅ Distance ( m ) 67.5 ₉₀ BOJNDflRY CONDITIONS N o i i n a l d i a i e t e r ( i ) _{Dn50 = 1.65} Grading (-) _{D85/D15 = 1.15} Rel. l a s s d e n s i t y (-) _{d e l t a = 1.68} i ^ v e height ( i ) Hs = 6.5 Have period ( s ) T l = 13.2 S t o r i duration (-) _{N = 1640} Water depth ( i ) d = 21 Angle (norial=ö) (degr) 0 = 0

Dn50 = 1.65 D85/D15 = 1.15 d e l t a = 1.68 RESULTS INITIAL SLOPE y l = 32 y2 = 32 y3 = 24 y4 = 24 y5 = 14 y6 = 14 y7 = 0 V E R I F I C A T I O N W I T H D H I , C A S E S K P T E S T 1 8 D E L F T H Y D R A U L I C S Hs/dDn50 = 2.5 HoTo = 81 Hs/Li = .026 I r = 19.413 he = 4.193 l e = 5.807 hs = 4 . 7 8 4 I s = 18.524 tanB = .488 ht = 4.784 tanY = .170 H 9 8 6 _{F I G . 1 0}

- - - - ^ e s t ^ - D I - l !

Case SKP, a f t e r t e s t 19E 22.5 ₄₅ D i s t a n c e ( m ) 67.5 BOUNDARY CONDITIONS Grading Have height Have period S t o r i duration Hater depth Angle (norial=0) ( l ) Dn50 = _1.&5 (-) D85/D15 = _1.15 (-) d e l t a = IM ( l ) Hs = _b (s) T l = 13.2 (-) N = ₁₆₄₀ ( l ) d = ₁₉ <degr) 0 = ₀ Dn50 = 1.65 D85/D15 = 1.15 d e l t a = 1.68 Hs T l N d 0 = 7 = 13.2 = 820 = 19 = 0 INITIAL SLOPE x l = 0 x2 = 8 x3 = 24 x4 = 44 x5 = 54 x6 = 74 x7 = 102 yl = 32 y2 = 32 y3 = 24 y4 = 24 y5 = 14 y6 = 14 y7 = 0 RESULTS Hs/dDn50 = HoTo Hs/Lm I r hc I c hs I s tanB ht tanY 70 • o a e 19.881 4. 653 4. 653 4.659 £1.785 . 695 4.659 .£•51

0.0 C 0.<^ OVJER. H L * S ) i - L S - , I Tp . ( i . L i li-2.> Hi-ix 5-^, T , _{\ = 15 bs} dansk hydraulijk ^ Inslitut t o ^ .... (Qtib.MM -l-.aoo .... MfAAv

c .3

I

T e s t s DHI t e s t c a s e GL^^ 30 25 20 15 10 5 O — Hs-1.0 m •--Hs-L5 m Hs-2.0 m - Hs-2.5 m -i ! L _{•I I I l„.} O i I—L 10 ₂₀ 30 Distance (m] 60 BOUNDflRY CONDITIONS Nominal d i a i e t e r ( i ) Grading {-) Rel. l a s s d e n s i t y (-) Have height (•) Have period ( s ) S t o r i d u r a t i o n (-) Hater depth d ) Angle (norial=0) (degr)

Dn50 = .3 D85/D15 = 1.95 d e l t a = 1.69 Hs T l N d 0 = 1 = 7 = 1500 = 24 = O D85/D15 d e l t a Hs T l N d 0 = .3 _{Dn50 = .3} = 1.95 _{D85/D15 = 1.95} = 1.69 _{d e l t a = 1.69} = 1.5 _{Hs = 2} = 8.5 _{T l = 9.9} = 1250 _{N = 1000} = 24 d = 24 = 0 0 _{= 0} Dn50 = .3 D85/D15 = 1.95 d e l t a = 1.69 Hs = 2.5 T l N d 0 = 11.1 = 900 = 24 = O INITIAL SLOPE xl = O x2 = 30 x3 = 52.5 x4 = O x5 = O x6 = O x7 = O yl = 25 y2 = 25 y3 = O y4 = O y5 = O y6 = O y7 = O V E R I F I C A T I O N W I T H D H I , C A S E G L R D E L F T H Y D R A U L I C S

-it a '•^(JM £ / £ ) E F T E R F O R S 0 G 1 , M s : O E F T E R F O R S O G 2 . H g : 1 E F T E R F O R S 0 G 3 , H s ; 1 ( E F T E R F O R S O G u. H a T 2 , E F T E R F O R S B G 5 , H s , 3 S I G N I F I K A N T B O L G E M O J D E • P E A K " B Ö U G E P E R t O D E F O R S f f l G S V A R I G M E D T p : 1 3 S, T p : 13 S, T p . 13 s . T p I 13 S, T p : 13 S.

SSI,^®-,°H\cr^^s^ c a s e EID BOUNDARY CONDITIONS N o i i n a l d i a i e t e r ( i ) Dn50 = .15 DnSO - i s Grading (-) De5/D15 = 3

mm'^-f

0 n 5 0 = . 1 5 D n 5 0 = . 1 5 Rel. l a s s d e n s i t y (-) d e l t a = 1 68 ? .a ^'^^^ " ^ ^^^^^ = ^ Have height (,) Hs - 7 ^ ^ t a = 1.68 d e l t a = 1.68 d e l t a = 1.68 Wave period ( 5 ) T i = 9 i rl ~ i , = = 2-3 S t o r i duration (-) N = 600 H - I ' '^'^ ^' ='^'^ W a t e r d e p t h (,) d = 10 4 H " N = 400 N = 400

Angle (norial=0) (degr) 0 = 0 ' 1 d = 10.4 d = 10.4

INITIAL SLOPE x l= 0 y l = 11.4 xa = 25.8 y2 = 1 1 . 4 x3 = 39.9 y3 = o x4 = 0 y4 = 0 x5 = 0 y5 = 0 x6 = 0 y6 = 0 x7 = 0 y7 = 0

c .s > — LnLtLaL — Dn50-0.12 m ••- Dn50-0,15 m — • Dn50-0,20 m 20 _ 30 DLstance (m) c O -p D T e s t s DHI t e s t c a s e ns=l.b, v a r i a t i o n of EID _m 20 30 DOsiance (m) V E R I F I C A T I O N W I T H D H I , C A S E E I D I N F L U E N C E O F D . S Q A N D T ^ D E L F T H Y D R A U L I C S H 9 8 6 _{F I G . 1 6}

- P R O F I t C - C F o r s 0 g s 0 s t - m o l e V e s t - m o l e B 0 l g e - ~ No V a r i a n t V a r i a n t r e t n i n g H T V a n d s t a n d W (b) (m o v e r mid-d e l v a n mid-d s t a n mid-d ) S e r i e 6 S e r i e 7 237 238 239 240 241 242 243 244 245 246 247 248 249 R20 R20 R4V R5V NN0 NN0 2 12 _+0,7 3 12 II 4 12 II 5 12 II 6 14 II 7 14 II 3 12 _+0,7 4 12 II 5 12 fl 6 14 II 7 14 tl 8 16 II 7 14 _-0,7 V E R I F I C A T I O N W I T H D H I , C A S E S L V D E L F T H Y D R A U L I C S

c > JS 20 15 10 — After 242 •--After 249 actual initial slope 20 _{30 40 50} DLstance (tn) 60 70 80 BOUNDflRY CONDITIONS N o i i n a l d i a e e t e r ( i ) Dn50 = 1.45 Brading (-) D85/D15 = 1.29 Rel. l a s s d e n s i t y (-) d e l t a = 1.68 Wave height ( i ) Hs = 7 Wave period (5) T l _{= 10.8} S t o r i duration (-) N = 840 Water depth ( i ) d = 15.7 Angle (norial=0) (degr) 0 = 0

Dn50 1.45 D85/D15 = _1.29 d e l t a = _1.66 Hs = 8 T i = 12.3 N = 2000 d = _14.3 0 = ₀ RESULTS RESU.TS INITIAL SLOPE x l = 0 x2 = 4 x3 = 11.5 x4 = 31.5 x5 = 42.5 x6 = 57 x7 = 73 y l = 24 y2 = 24 y3 = 19 y4 = 19 y5 = 8 y6 = 8 y7 = 0 Hs/dDn50 = 2.9 Hs/dDn50 = _3.3 HoTo = 81 HoTo = ₁₀₅ Hs/Li = .038 Hs/Li = _.034 I r = 16.385 I r = _19.767 he = 3.698 hc = _3.714 l e = 5.474 I c = _8.039 hs = 6,001 hs = _7,447 I s = 24.418 I s = _30.109 tanB = .430 tanB = _.654 ht =6.001 ht 7.447 tanY = . 143 tanY = _.255 V E R I F I C A T I O N W I T H D H I , C A S E S L V D E L F T H Y D R A U L I C S H 9 8 6 F I G . 1 8

Wave h e i g h t Hs ( m ) s l o p e a n g l e : c o t a = 1.5 1.5 l e a n H a v e p e r i o d ; _{T l = 9.6 12.8} n u i b e r o f w a v e s : _{N = 650 650} p e r i e a b i l i t y ; _{P = .5 .5} l a s s o f s t o n e ; W50 = 4250 4250 l a s s d e n s i t y o f r o c k ; r h o - a = _{2800 2800} l a s s d e n s i t y o f H a t e r : r h o = _{1000 1000} V E R I F I C A T I O N W I T H T j 2 ) R U M D A M A G E C U R V E F O R S T A T I C S T A B I L I T Y D E L F T H Y D R A U L I C S

O

Torurn, t e s t 31,2, profLLes 1-4 S t a t i c stoblLLty, damage profLLes

5 O J 1 I L 10 - J — ^ — ^ —\—\ i I I I 20 30 DLstance (m) 40 ₅₀ BOMWRY CONDITIONS N o i i n a l d i a i e t e r ( i ) Dn50 = Grading (-) D85/D15 = Rel. l a s s d e n s i t y (-) _{d e l t a =} Have height ( i ) Hs = Have period (s) T l = S t o r i duration (-) N = Hater depth ( i ) d = P e r i e a b i l i t y (-) P = 1.19 1.48 1.8 2.9 9.6 650 20 .5

INITIAL UNIFORM SLOPE

height of slope ( i ) = 30 length of slope ( i ) = 4 5 RESULTS S = .56 cota = 1.50 Hs/Li = ,0202 HoTo = 37.32 h r = 2.263 hd = 2.263 h i = 3.063 hb = 11.085 V E R I F I C A T I O N W I T H T 0 R U M - D A M A G E P R O F I L E S F O R S T A T I C S T A B I L I T Y ( P R O F I L E S I - 4 ) D E L F T H Y D R A U L I C S H 9 8 6 _{F I G . 2 1}

c O 40 50 Distance (m) N o i i n a l d i a i e t e r Grading Rel. l a s s d e n s i t y Wave height Have period S t o r i duration Hater depth Angle (norial=0) ( I ( -( ¬ ( I (s (¬ ( I (degr) Dn50 = 1.19 D85/D15 = 1.48 d e l t a Hs T l N d 0 1.8 = 6.2 = 9.6 = 650 = 20 = 0 Dn50 = 1.19 D85/D15 = 1 . 4 8 d e l t a = 1.8 Hs T l N d Dn50 D85/D15 d e l t a 1.19 1.48 1.8 = 7.1 Hs = 7.9 = 9.6 T l = 9.6 = 650 N = 650 = 20 d = 20 = 0 0 = 0 Dn50 = 1.19 D85/D15 = 1.48 d e l t a = 1.8 Hs = 8.6 T l = 9.6 N = 650 d = 20 0 = 0 INITIAL S L C K xl = 0 x2 = 12 x3 = 30 x4 = 48 x5 = 84 x6 = 0 x7 = 0 yl = 30 y2 = 30 y3 = 24 y4 = 24 y5 = 0 y6 = 0 y7 = 0 V E R I F I C A T I O N W I T H T , 0 R U M P R O F I L E S 4 - 7 D E L F T H Y D R A U L I C S H 9 8 6 F I G , 2 2

c .s > Torum, t e s t Bl,2, p r o f i l e s 7-11 10 20 30 _{40 50} DLstance (m) 60 70 80 90 BOMWRY CONDITIONS N o i i n a l d i a i e t e r ( i ) Grading (-) Rel. l a s s d e n s i t y (-) Have height ( i ) Have period (s) S t o r i duration (-) Hater depth ( i ) Angle (norial=0) (degr)

Dn50 = 1.19 D85/D15 = 1.48 d e l t a = 1.8 Hs T l N d 0 = 8.6 = 9.6 = 650 = 20 = O Dn50 = 1.19 D85/D15 = 1.48 d e l t a = 1.8 Hs = 8.6 T l = 9.6 N = 4540 d = 20 0 = O Dn50 = 1.19 D85/D15 = 1.48 d e l t a = 1.8 Hs = 8.6 T l _{= 9.6} = 8090 = 20 = O Dn50 = 1.19 D85/D15 = 1.48 d e l t a = 1.8 Hs = 8.6 T l _{= 9.6} = 10460 = 20 = O V E R I F I C A T I O N W I T H T 0 R U M P R O F I L E S 7 - 1 1 D E L F T H Y D R A U L I C S H 9 8 6