LABORATORY STUDY OF A DYNAMIC BERM REVETMENT

u s Army C o r p s of E n g i n e e r s

TECHNICAL REPORT CERC-92-1

LABORATORY STUDY OF A DYNAMIC

BERM REVETMENT

.Hortioom Ditunca Irom BiAMsd (an)

by

Donald L. Ward, John P. Ahrens Coastal Engineering Research Center

DEPARTMENT OF THE ARMY

Waterways Experiment Station, Corps of Engineers 3909 Halls Ferry Road, Vicksburg, Mississippi 39180-6199

B I B L I O T H E E K Dienst Weg- en Waterbeuwkunde

Van der Burghweg Postbus 5044, 2600 GA Delft

Tel. 015 - 699111

January 1992 Final Report

Approved For Public Release; Distribution Is Unlimited

Prepared for DEPARTMENT OF THE ARMY US Army Corps of Engineers

R E P L Y T O A T T E N T I O N O F WESCW-R D E P A R T M E N T O F TH W A T E R W A Y S E X P E R I M E N T S T A T I O N , C O R P S 3 9 0 9 H A L L S F E R R Y R O A D V I C K S B U R G , M I S S I S S I P P I 3 9 1 8 0 - 6 1 9 9 AFIMY E MSI N E E R S <<IS . Sol 10 June 1992 E r r a t a Sheftt-No. 1

LABORATORY .STUDY OF A DYNAMIC BERM REVETMENT

^^l 1992

T e c h n i c a l Report CERC-92-1 J a n u a r y 1992

REPORT DOCUMENTATION PAGE

•

1_ AGPMCV I I ^ F O M I V i^f II II M r i "~ t~ -• i '

1. AGENCY USE ONLY (Leave blank)'

14. TITLE AND SUBTITLE

I 2. REPORT DATE

January 1992

3. REPORT TYPE AND DATES COVERED

F i n a l r e p o r t J u l 88 to J a n 91

Is. FUNDING NUMBERS

L a b o r a t o r y Study of a Dynamic Berm Revetment

I 6. AUTHOR(S) :

Donald L. Ward John P. Ahrens

I 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

USAE Waterways Experiment 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 Center 3909 H a l l s F e r r y Road

V i c k s b u r g , MS 39180-6199

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

US Army Corps of E n g i n e e r s Washington, DC 20314-1000

B t B l L t O T H E E K

Dienst Wef* en Wttertwiwkunde der Burghweg !|044, 2600 GA Delft 015-699111 Va* Postbus T( 8. PERFORMING ORGANIZATION REPORT NUMBER T e c h n i c a l Report CERC-92-1 10. SPONSORING/MONITORING AGENCY REPORT NUMBER

I 11. SUPPLEMENTARY NOTES

I n f o r m a t i o n S e r v i c e , 5285 P o r t Royal Road,

I 12a. DISTRIBUTION/AVAILABILITY STATEMENT •

Approved f o r p u b l i c r e l e a s e ; d i s t r i b u t i o n i s u n l i m i t e d

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

the e f f e c f o f

iLf^'^^^LT^"^

14. SUBJECT TERMS Berm Bulkhead Dynamic revetment 17. SECURITY CLASSIFICATION OF REPORT UNCLASSIFIED NSN 7540-01-280-5500 Revetment 18. SECURITY CLASSIFICATION OF THIS PAGE UNCLASSIFIED 19. SECURITY CLASSIFICATION OF ABSTRACT 15. NUMBER OF PAGES 78 16. PRICE CODE 20. LIMITATION OF ABSTRACT I

PREFACE

The i n v e s t i g a t i o n d e s c r i b e d i n t h i s r e p o r t was a u t h o r i z e d as a p a r t of the C i v i l Works R e s e a r c h and Development Program by Headquarters, US Army Corps of Engineers (HQUSACE). Work was performed under Work U n i t 32432,

"Design of Revetments and S e a w a l l s , " a t the C o a s t a l E n g i n e e r i n g R e s e a r c h Center (CERC), US Army.Engineer Waterways Experiment S t a t i o n (WES). The. HQUSACE T e c h n i c a l Monitors were Messrs. John H. L o c k h a r t , J r . ; John G.

Housley; James E. Crews; and Robert H. Campbell. Dr. C. Linwood V i n c e n t was CERC Program Monitor.

The study was conducted by p e r s o n n e l of CERC under the g e n e r a l d i r e c t i o n of Dr. James R. Houston, C h i e f , CERC, and Mr. C h a r l e s C. Calhoun, J r . ,

A s s i s t a n t C h i e f , CERC. D i r e c t s u p e r v i s i o n was p r o v i d e d by Messrs. C. E. Chatham, C h i e f , Wave Dynamics D i v i s i o n (WDD), and D. Donald Davidson, C h i e f , Wave R e s e a r c h Branch (WRB), WDD, CERC. T h i s r e p o r t was p r e p a r e d by

Messrs. Donald L. Ward, P r i n c i p a l I n v e s t i g a t o r , WRB, and John P. Ahrens, R e s e a r c h Oceanographer, WRB. The model was operated by Mr. W i l l i e G. Dubose, E n g i n e e r i n g T e c h n i c i a n , WRB. A s s i s t a n c e w i t h data a n a l y s i s and g r a p h i c s was p r o v i d e d by Mr. John M. Heggins, Computer T e c h n i c i a n , WRB. T h i s r e p o r t was typed by Ms. Myra E. W i l l i s , WRB, and e d i t e d by Ms. Lee T. Byrne, I n f o r m a t i o n Technology Laboratory, WES.

COL L a r r y B. F u l t o n , EN, was Commander and D i r e c t o r of WES d u r i n g r e p o r t p u b l i c a t i o n . Dr. Robert W. Whalin was T e c h n i c a l D i r e c t o r .

CONTENTS Page PREFACE I PART I : INTRODUCTION ; 3 Background 3 Problem 4 Purpose 4

PART I I : DEFINITION OF TEST PARAMETERS 5

Wave and S p e c t r a l Parameters 5

M a t e r i a l Parameters 7 Berm Parameters . 7

PART I I I : FLUME SETUP, TEST CONDITIONS, AND RESULTS 9

Flume Setup . . . . . 9

T e s t C o n d i t i o n s H

R e s u l t s ll

PART I V : DISCUSSION 16 C r i t i c a l Mass A n a l y s i s I 7

Wave R e f l e c t i o n and Energy D i s s i p a t i o n 22

PART V: SUMMARY AND CONCLUSIONS 24

REFERENCES 25 APPENDIX A: TABLE OF PROFILE SOUNDINGS A l

APPENDIX B: I N I T I A L AND EQUILIBRIUM PROFILES B l

APPENDIX C: NOTATION C l

• LABORATORY STUDY OF A DYNAMTH RKRM REVETMENT

PART I : INTRODUCTION

Background

1. C o n v e n t i o n a l revetments a r e designed to be s t a t i c a l l y s t a b l e ; t h a t i s , no motion of the armor stone i s a n t i c i p a t e d . Stones i n the armor l a y e r are s i z e d and p l a c e d such t h a t t h e i r weight and i n t e r l o c k i n g w i l l p r e c l u d e movement d u r i n g wave a t t a c k . I n c o n t r a s t , a dynamic revetment i s designed to a l l o w wave a c t i o n to r e a r r a n g e the stones i n t o an e q u i l i b r i u m p r o f i l e .

Because s t o n e s a r e a l l o w e d to move, a s m a l l e r stone s i z e i s used f o r the dynamic revetment than f o r the s t a t i c revetment, b u t dynamic revetments

r e q u i r e a l a r g e r q u a n t i t y o f stone to a l l o w f o r t h e r e s h a p i n g of the revetment i n t o an e q u i l i b r i u m p r o f i l e . The dynamic revetment i s e f f e c t i v e because the l a r g e mass of stone n e a r the s t i l l - w a t e r l e v e l (SWL) d i s r u p t s the wave a c t i o n and d i s s i p a t e s wave energy. Although dynamic revetments r e q u i r e a l a r g e r q u a n t i t y of stone, t h e s e c o s t s may be o f f s e t by the t y p i c a l l y lower c o s t of s m a l l e r stone, and, because s i z e i s l e s s c r i t i c a l , a more c o s t - e f f e c t i v e use may be made of q u a r r y output. I n a d d i t i o n , s m a l l e r stone i s l e s s expensive to h a n d l e , and, s i n c e i n i t i a l placement i s not c r i t i c a l , dynamic revetments may be dumped i n p l a c e r a t h e r than the stones b e i n g i n d i v i d u a l l y p l a c e d .

2. The concept o f a rubble breakwater h a v i n g a dynamic response to wave a t t a c k i s not new. Per Bruun has commented f r e q u e n t l y about the h i g h

s t a b i l i t y of "S"-shape p r o f i l e s of some v e r y o l d b r e a k w a t e r s i n Plymouth, England, and Cherbourg, F r a n c e (Bruun and Johannesson 1976), and the berm b r e a k w a t e r concept developed by W i l l i a m B a i r d ( B a i r d and H a l l 1984, H a l l

1987) i s an a d a p t a t i o n o f t h i s "S" p r o f i l e . The i d e a o f a dynamic revetment, however, seems to be o f more r e c e n t o r i g i n . Van Hijum and P i l a r c z y k (1982) and P i l a r c z y k and den Boer (1983) p r e s e n t d a t a and summarize some o f the Dutch e x p e r i e n c e w i t h g r a v e l beaches and c o b b l e - s i z e d revetments, and r e s e a r c h has been i n i t i a t e d i n England on the response of s h i n g l e beaches to wave a c t i o n ( C h a n n e l l , Stevenson, and Brown 1985; P o w e l l 1988). Recent r e s e a r c h i n The N e t h e r l a n d s and England i s m o t i v a t e d by a need f o r fundamental u n d e r s t a n d i n g of s h i n g l e beaches, how they might be n o u r i s h e d , and i f s h i n g l e

beaches c o u l d be used i n some s i t u a t i o n s i n s t e a d of a t r a d i t i o n a l s t a t i c a l l y -s t a b l e r i p r a p revetment.

3. I n the U n i t e d S t a t e s , Johnson (1987) found t h a t g r a v e l beaches and dumped r u b b l e a r e f r e q u e n t l y c o s t - e f f e c t i v e a l t e r n a t i v e s to u s i n g sand f o r beach nourishment and p l a c e d stone f o r revetments, r e s p e c t i v e l y . Johnson's

f i n d i n g s were o b t a i n e d from e x t e n s i v e e x p e r i e n c e on Lakes Michigan and S u p e r i o r , where f l u c t u a t i n g water l e v e l s c r e a t e d enormous problems f o r con-v e n t i o n a l s h o r e l i n e p r o t e c t i o n . T h i s e x p e r i e n c e i n d i c a t e d dynamic recon-vetments were n o t v u l n e r a b l e to toe s c o u r , overtopping, or f l a n k i n g . Advantages c i t e d by Johnson f o r c o a r s e m a t e r i a l on beaches i n c l u d e a long r e s i d e n c e time and an a b i l i t y to s t a y i n the v i c i n i t y of the water l i n e . Other advantages a r e

s i m i l a r to those noted by B a i r d and H a l l ( 1 9 8 4 ) , i . e . , ease of placement and lower u n i t c o s t .

Problem

4. Comprehensive r e s e a r c h e f f o r t s conducted r e c e n t l y i n The N e t h e r l a n d s r e s u l t e d i n d e t a i l e d and q u a n t i t a t i v e f i n d i n g s on dynamic s t a b i l i t y (van der Meer 1988) . Although the f i n d i n g s were based on e x t e n s i v e l a b o r a t o r y work and data a n a l y s i s , the d a t a a r e of l i m i t e d a p p l i c a b i l i t y i n the U n i t e d S t a t e s because van der Meer's t e s t s were conducted i n r e l a t i v e l y deep water, whereas most US Army Corps o f E n g i n e e r s (USACE) problems i n v o l v i n g s h o r e l i n e e r o s i o n and p r o t e c t i o n a r e i n s h a l l o w water. There i s no d e s i g n guidance on the use of dynamic revetments f o r c o a s t a l p r o t e c t i o n t h a t i s a p p l i c a b l e to the s h a l l o w waters t y p i c a l l y encountered i n USACE p r o j e c t s .

Purpose

5. The purpose of t h i s study was to determine how dtomped stone might p r o t e c t a v e r t i c a l bulkhead i n s h a l l o w water, and p a r t i c u l a r l y to determine a means o f c a l c u l a t i n g the minimum q u a n t i t y of stone n e c e s s a r y to p r o v i d e

adequate p r o t e c t i o n ( t h e " c r i t i c a l mass"). However, the i n f o r m a t i o n on r e s h a p i n g , e q u i l i b r i u m p r o f i l e , and dynamic s t a b i l i t y i s of g e n e r a l

PART I I : DEFINITION OF TEST PARAMETERS

6 . I n c o n s i s t e n c i e s among authors i n n o t a t i o n s , d e f i n i t i o n s o f parame-t e r s , and parame-the meparame-thods by which a v a l u e f o r a parameparame-ter i s obparame-tained g r e a parame-t l y

r e p o r t , n o t a t i o n s w i l l f o l l o w g u i d e l i n e s p u b l i s h e d by the I n t e r n a t i o n a l A s s o c i a t i o n f o r H y d r a u l i c R e s e a r c h i n i t s " L i s t o f Sea S t a t e Parameters"

(1986) where a p p l i c a b l e . A d d i t i o n a l parameters, d e f i n i t i o n s , and method used to determine the v a l u e o f c e r t a i n parameters a r e g i v e n i n the f o l l o w i n g

s e c t i o n .

7. Wave h e i g h t s used i n t h i s r e p o r t a r e the h e i g h t s o f the z e r o t h moment (H^o)* and a r e obtained as four times t h e square r o o t of the z e r o t h moment o f the p o t e n t i a l energy spectrum. The H^o'^ °^ i n c i d e n t s p e c t r a are s e p a r a t e d from t h e H^o's o f the r e f l e c t e d s p e c t r a by the method o f Goda and S u z u k i ( 1 9 7 6 ) , u s i n g a three-gage a r r a y . Two a r r a y s a r e used, one to measure t h e H^o'^ near the wave generator ( A r r a y 1) and one near t h e s t r u c t u r e toe ( A r r a y 2 ) .

8. Peak p e r i o d (Tp) i s the wave p e r i o d a s s o c i a t e d w i t h the h i g h e s t energy d e n s i t y o f t h e spectriom. T h i s was o b t a i n e d by d i v i d i n g the spectrum i n t o 256 bands and f i n d i n g the p e r i o d c a u s i n g the h i g h e s t energy d e n s i t y over 11 adj a c e n t bandwidths.

9. Peak p e r i o d was used to e s t i m a t e the d e s i r e d l e n g t h o f a t e s t r u n by m u l t i p l y i n g the d e s i r e d number o f waves by t h e peak p e r i o d .

10. R e f l e c t i o n c o e f f i c i e n t i s commonly d e f i n e d as the r a t i o o f

r e f l e c t e d wave h e i g h t to i n c i d e n t wave h e i g h t . T h i s i s c l e a r l y i n a p p r o p r i a t e when i n c i d e n t and r e f l e c t e d wave h e i g h t s a r e d e s c r i b e d by d i f f e r e n t s p e c t r a . R e f l e c t i o n c o e f f i c i e n t s were t h e r e f o r e determined by the energy o f t h e r e s p e c t i v e s p e c t r a , f o l l o w i n g the method o f Goda and Suzuki ( 1 9 7 6 ) .

* For convenience, symbols and a b b r e v i a t i o n s a r e l i s t e d i n the N o t a t i o n (Appendix C ) .

c o m p l i c a t e the t a s k o f comparing r e s u l t s from d i f f e r e n t s t u d i e s . I n t h i s

Wave and S p e c t r a l Parameters

where K^. i s the r e f l e c t i o n c o e f f i c i e n t and ER and Ej a r e the energy o f the r e f l e c t e d - a n d i n c i d e n t s p e c t r a , r e s p e c t i v e l y .

11. R e f l e c t e d wave h e i g h t i s obtained as the product of r e f l e c t i o n c o e f f i c i e n t and i n c i d e n t wave h e i g h t .

H, = K, ( 2 ) where Hj. i s r e f l e c t e d wave h e i g h t .

12. Wave h e i g h t s and p e r i o d s a r e f r e q u e n t l y r e p o r t e d i n o t h e r i n v e s t i -g a t i o n s i n terms of s i -g n i f i c a n t wave h e i -g h t (H^) and avera-ge wave p e r i o d (T^,) , where i s the average o f the o n e - t h i r d h i g h e s t waves. Both and a r e i n c l u d e d i n the data i n t h i s r e p o r t to s i m p l i f y comparison w i t h o t h e r i n -v e s t i g a t i o n s . Because the measured i n c l u d e s both i n c i d e n t and r e f l e c t e d wave energy, the i n c i d e n t i s e s t i m a t e d from the r e f l e c t i o n c o e f f i c i e n t as

^ s ( t )

( 3 )

where ^sd) i s the i n c i d e n t s i g n i f i c a n t wave h e i g h t and H^j^) i s the

combined i n c i d e n t and r e f l e c t e d s i g n i f i c a n t wave h e i g h t . i^sit) ^ ^ s determined as the average from the t h r e e gages i n the a r r a y . Average wave p e r i o d s i n t h i s r e p o r t were determined as

( 4 )

where m^ and mg a r e the z e r o t h and second moments of the i n c i d e n t p o t e n t i a l energy spectrum, r e s p e c t i v e l y .

13. The s p e c t r a l width or peakedness determined from the wave r e c o r d i s g i v e n as Qp , d e f i n e d by Goda (1970) as

Qp = -r\i f" f [ s ( f ) ] ^ d f

where f i s frequency and S ( f ) i s the wave s p e c t r a l d e n s i t y f u n c t i o n f o r the g i v e n frequency.

M a t e r i a l Parameters

14. S m a l l s i z e s o f stone, such as those used i n the c u r r e n t study, a r e f r e q u e n t l y measured by s i e v e a n a l y s i s . L a r g e r stones a r e d e s c r i b e d by t h e i r nominal diameter djj d e f i n e d as

where W i s the weight o f the stone and Wj. i s the s p e c i f i c weight o f the m a t e r i a l . The nominal diameter of the median stone weight i s d^^^o) •

Berm Parameters

15. F i g u r e 1 i l l u s t r a t e s the major berm parameters p r i o r to a t e s t run. Berm w i d t h Wg i s the h o r i z o n t a l l e n g t h o f the berm as i t was c o n s t r u c t e d a t the b e g i n n i n g o f a t e s t . Berm h e i g h t hg i s the average v e r t i c a l d i s t a n c e from the SWL to the h o r i z o n t a l berm s u r f a c e a t the b e g i n n i n g o f a t e s t .

16. A t y p i c a l a f t e r - t e s t p r o f i l e i s shown i n F i g u r e 2. Berm c r e s t h e i g h t \ and berm c r e s t l e n g t h 1^ a r e the v e r t i c a l and h o r i z o n t a l d i s -t a n c e s r e s p e c -t i v e l y from -the i n -t e r s e c -t i o n of -the SWL and -the e q u i l i b r i u m pro-f i l e to the conspicuous berm c r e s t pro-formed by the wave runup. E r o s i o n depth hg and e r o s i o n l e n g t h lg a r e the depth and h o r i z o n t a l d i s t a n c e , r e s p e c -t i v e l y , o f -the reve-tmen-t -toe from -the i n -t e r s e c -t i o n of -the SWL and -the e q u i l i b r i u m p r o f i l e .

17. Revetment Response Category (RRC) i s a s i m p l e e v a l u a t i o n o f the performance o f the revetment d u r i n g a t e s t where "F" i n d i c a t e s the revetment f a i l e d , "S" i n d i c a t e s the revetment was s a f e , and " I " i n d i c a t e s an i n t e r -mediate c o n d i t i o n . F o r t h e s e t e s t s , a f a i l u r e was d e f i n e d as exposure of the bulkhead, whereas a s a f e c o n d i t i o n i n d i c a t e d t h a t n e i t h e r sand nor water overtopped the bulkhead. These PRC's a r e d e s c r i b e d i n more d e t a i l i n paragraph 30.

100 90 80 H 70 60 50 40 LEGEND B Concrete slops + Pre-test profile SWL -T i 1 i 80 100 —T" r ₁₂₀ — i — 140 "T f— 20 40

—

Horizontal Distance from Bulkhead (cm)

F i g u r e 1. Berm parameters from the p r e t e s t p r o f i l e

100 90 80 70 H 60 -A 50 40 1 r LEGEND O Concrete slope O Posl-test profile 3000 Waves 20 40 60 80 100

Horizontal Distance from Bulkhead (cm)

120

~i 1— 140

PART I I I : FLUME SETUP, TEST CONDITIONS, AND RESULTS

Flume Setup

18. Model t e s t s were conducted i n the USACE C o a s t a l E n g i n e e r i n g R e s e a r c h C e n t e r ' s (CERC's) 0.46mwide by 0.91mhigh by 45.73mlong g l a s s -w a l l e d -wave flume ( F i g u r e 3) u s i n g an u n d i s t o r t e d Froude s c a l e ( S t e v e n s e t a l . 1942) o f 1:16 ( m o d e l : p r o t o t y p e ) . I r r e g u l a r waves r e p r e s e n t i n g J o i n t North Sea Wave P r o j e c t (JONSWAP) s p e c t r a (Hasselmann e t a l . 1973) were generated by a h y d r a u l i c a l l y a c t u a t e d p i s t o n - t y p e wave maker. Wave d a t a were c o l l e c t e d f o r each run u s i n g two a r r a y s , each c o n s i s t i n g o f t h r e e e l e c t r o n i c a l l y d r i v e n r e s i s t a n c e - t y p e wave gages. Wave s i g n a l g e n e r a t i o n and d a t a a c q u i s i t i o n were c o n t r o l l e d u s i n g a DEC MicroVAX I computer, and d a t a a n a l y s i s was performed on a DEC VAX 750 and 3600,

ARRAY 1 ARRAY 2

a 9.1 K a 6.1 >

'1 1 WAVE GAGES H i ^

PISTON-Pl'PE ^ - ^ ^ ' ^ ^ ^ ' ' ' ^ ^ VI/AVE GENERATOR 30.o ^

q 21,0 • • ^ J4.J

^

Note: Distorted scale: 1V = 5H

All measurements In meters.

F i g u r e 3. G e n e r a l l a y o u t o f wave flume

19. The t e s t s e c t i o n s were p l a c e d a p p r o x i m a t e l y 35.4 m from the wave board. F i g u r e 4 shows a t y p i c a l i n i t i a l and e q u i l i b r i u m p r o f i l e f o r a dynamic

revetment. A l l i n i t i a l p r o f i l e s except f o r T e s t 4 had a h o r i z o n t a l berm and a seaward f a c e on a s l o p e o f 1:1 ( v e r t i c a l : h o r i z o n t a l ) . T e s t 4 used the

e q u i l i b r i u m p r o f i l e from T e s t 3 as a s t a r t i n g p r o f i l e to determine how s e n s i t i v e the e q u i l i b r i u m p r o f i l e was to i n i t i a l c o n d i t i o n s ( s e e paragraph 25), A bulkhead was s i m u l a t e d i n the model u s i n g a pljwood board to

terminate the r u b b l e on the landward s i d e , l o c a t e d a t 0.0 on the h o r i z o n t a l a x i s i n the p r o f i l e f i g u r e s .

E O E O c O m E 3 J3 < 100 90 -00 70 60 50 Plan 1 Test 1 LEGEND Q Concrete slope + Pre-tesl profile 0 Post-test profile 3000 Waves SWL 40 G •-• a-c-oa-n-D-o-a-D-a-o-n-. 20 40 60 80 100

Horizontal Distance from Bulkfiead (cm)

— I —

120 140

F i g u r e 4. T y p i c a l p r e - and p o s t t e s t p r o f i l e s

s u r v e y s t a k e n a l o n g the l e n g t h o f the t e s t s e c t i o n . Surveys were made by t a k i n g soundings w i t h a r o d a t t a c h e d to a 15-mm-diam d i s c by a b a l l and s o c k e t c o n n e c t i o n . Soundings were taken every 3.05 cm along the l e n g t h o f t h e t e s t s e c t i o n . Very l i t t l e a c r o s s - t a n k v a r i a t i o n i n the p r o f i l e was observed d u r i n g t h e s e t e s t s .

21. A dense l i m e s t o n e was used f o r t h e r u b b l e i n t h i s study. Because of i t s s m a l l s i z e , the stone was graded by s i e v e s i z e . Table 1 summarizes the g r a d a t i o n s and s p e c i f i c g r a v i t y o f the stone used.

T a b l e 1

C h a r a c t e r i s t i c s o f Stone Used i n T h i s Study T e s t s T e s t s Cumulative 1-22 23-26 P e r c e n t S i e v e S i z e S i e v e S i z e P a s s i n g mm mm 2 4.8 3.1 15 5.6 4.3 50 8.1 5.6 85 11.2 7.3 98 12.7 9.3 S p e c i f i c g r a v i t y : 2.68 2.72

T e s t C o n d i t i o n s

22. I n i t i a l t e s t c o n d i t i o n s were generated to s i m u l a t e wave a c t i o n s i m i l a r to t h a t found on Lake Michigan near a s i t e i n Chicago a t Devon Avenue. The i n i t i a l berm width approximated t h a t o b t a i n e d by s u b s t i t u t i n g t h e s e

i n i t i a l t e s t c o n d i t i o n s i n t o the Dutch equations (van der Meer 1988). As t e s t i n g p r o g r e s s e d , more s e v e r e wave c o n d i t i o n s were r u n i n t h e wave tank to f u l l y - t e s t the range o f c i r c u m s t a n c e s f o r which a dynamic revetment would be s u i t a b l e . L a t e r t e s t s examined a s h o r t e r wave p e r i o d t h a t may b e t t e r r e p r e -s e n t the c o n d i t i o n -s f o r a -s t r u c t u r e on a body of water -s m a l l e r than

Lake Michigan.

R e s u l t s

23. Water depths and wave data c o l l e c t e d during the wave flume t e s t s a r e g i v e n i n Table 2, and data f o r the dynamic revetments a r e l i s t e d i n T a b l e 3. Soundings from the t e s t s a r e g i v e n i n Appendix A, and i n i t i a l and e q u i l i b r i u m p r o f i l e s a r e i l l u s t r a t e d i n Appendix B.

24. I t was found t h a t the i n i t i a l p r o f i l e a d j u s t s r a p i d l y to i n c i d e n t wave c o n d i t i o n s . F o r t e s t s w i t h Tp = 2.5 , there was l i t t l e change i n t h e p r o f i l e between 3,000 and 5,000 waves, and f o r t e s t s where Tp = 1.75 , t h e r e was l i t t l e change between 3,000 and 4,000 waves.

25. The Dutch found the shape o f dynamic p r o f i l e s a t e q u i l i b r i u m were not v e r y s e n s i t i v e to i n i t i a l c o n f i g u r a t i o n (van der Meer and P i l a r c z y k 1986) V e r i f i c a t i o n o f t h i s f i n d i n g was made i n a p a i r o f e a r l y t e s t s . F i g u r e 5a shows t h e i n i t i a l p r o f i l e s o f T e s t s 4 and 5, which can be s e e n to be q u i t e d i f f e r e n t . The i n i t i a l p r o f i l e f o r T e s t 4 i s the e q u i l i b r i u m p r o f i l e a t the c o m p l e t i o n o f T e s t 3, and the i n i t i a l p r o f i l e f o r T e s t 5 i s t h e s t a n d a r d s t a r t i n g p r o f i l e used i n t h i s study w i t h a h o r i z o n t a l berm and a 1:1 seaward f a c e . Wave c o n d i t i o n s f o r T e s t s 4 and 5 were n e a r l y i d e n t i c a l , and the e q u i l i b r i u m p r o f i l e s t h a t were produced were a l s o almost i d e n t i c a l , as shown i n F i g u r e 5b. A p r e l i m i n a r y c o n c l u s i o n i s t h a t the f i n a l p r o f i l e i s indepen-dent o f the i n i t i a l p r o f i l e as long a s the volume o f stone remains c o n s t a n t . T h i s i s a v e r y important f i n d i n g because i t would reduce the c o s t o f c o n s t r u e t i o n by a l l o w i n g rough placement o f the stone berm. T h i s c o n c l u s i o n p a r a l l e l f i n d i n g s from s t u d i e s o f sand beach p r o f i l e development. The c o n s e r v a t i o n of

T a b l e 2

Water Depths and Wave Data f o r P h v s i c a l Model T e s t s

Test No.

Water R r r a y 2 Depth R r r a y 2 Water Wave No. a t Wave Water Depth Height Waves Generator Depth a t Toe Hmo

N cm cm cm cm Array 2 Wave P e r i o d Tp s e c R r r a y 2 Wave Height Hs R r r a y 2 Wave P e r i o d Tz Wave Height a t t o e Hmo R e f l e c t i o n C o e f f i c i e n t Kr Wave Height a t t o e Hmo Deep Water Wave Length Lo-1 3000 60.96 37. 19 14.81 6.73 2.505 1 5000 60.96 37. 19 14.81 6.83 2.526 2 3000 60.96 37. 19 14.81 13.31 2.516 3 3000 57.91 34. 14 11.77 6.81 2.597 3 5000 57.91 34. 14 11.71 6.92 2.570 4 3000 57.91 34. 14 11.71 13.25 2.516 5 3000 57.91 34. 14 11.71 13.03 2.516 6 3000 60.96 37. 19 15.30 13.62 2.649 7 3000 60.96 37. 19 15.30 6.86 2.505 7 5000 60.96 37. 19 15.30 7.02 2.500 e 3000 60.96 37. 19 15.58 14.07 2.643 8 5000 60.96 37. 19 15.58 13.61 2.500 9 3000 60.96 37. 19 13.66 7.07 2.542 10 3000 57.91 34. 14 10.61 6.90 2.474 11 4286 57.91 34. 14 11.51 11.62 1.813 12 4286 60.96 37. 19 14.56 11.49 1.849 13 4286 57.91 34. 14 10.61 11.43 1.762 13 7143 57.91 34. 14 10.61 11.52 1.737 14 3000 67.06 43. 28 15.23 13.46 2.535 15 3000 67.06 43. 28 15.23 11.44 1.752 16 3000 67.06 37. BD 15.91 13.51 2.557 17 3000 60.96 34. 14 13.62 12.07 1.745 17 4576 60.96 34. 14 13.62 11.45 1.749 18 3000 57.91 34. 14 10.92 13.44 2.494 19 3000 57.91 34. 14 10.47 5.56 1.774 19 4576 57.91 34. 14 10.47 5.61 1.774 20 3000 60.96 37. 19 13.52 5.71 1.73 20 4576 60.96 37. 19 13.52 5.64 1.741 21 3000 60.96 37. 19 13.52 13.38 2.488 22 3000 60.96 37. 19 14.60 5.75 1.792 22 4576 60.96 37. 19 14.60 5.65 1.73 23 2160 60.96 37. 19 14.60 12.38 2.505 24 3000 60.96 37. 19 14.60 6.42 2.516 25 3000 60.96 37. 19 14.60 10.97 1.709 25 4576 60.96 37. 19 14.60 10.78 1.849 6.64 2.030 4.85 0.4541 297 979 6.85 2.028 4.93 0.4539 299 995 13.78 1.724 9.59 0.3550 298 988 6.75 1.973 4.65 0.4750 276 1052 6.80 1.971 4.71 0.4670 272 1030 13.62 1.683 9.03 0.3602 266 988 13.48 1.689 8.88 0.3540 266 988 13.72 1.737 9.92 0.3876 320 1095 6.81 2.028 5.00 0.4590 302 979 7.01 2.011 5.12 0.4598 301 975 14.29 1.734 10.31 0.3855 322 1090 13.74 1.774 10.00 0.3799 304 975 6.86 2.011 4.95 0.4909 290 1008 6.80 1.950 4.54 0.4442 249 955 11.47 1.404 8.01 0.2998 188 513 11.37 1.413 8.37 0.2755 215 533 11.34 , . 1.392 7.67 0.2820 176 484 11.43 1.393 7.75 0.2749 173 471 13.91 1.790 9.30 0.3768 305 1002 11.41 1.421 8.12 0.2845 207 479 14.04 1.753 9.93 0.3773 314 1020 11.70 1.401 8.86 0.2966 196 475 11.30 1.414 8.40 0.3217 196 477 14.01 1.682 8.93 0.3658 255 970 5.45 1.456 3.71 0.3470 176 491 5.56 1.455 3.75 0.3393 176 491 5.53 1.456 4.07 0.3318 193 467 5.50 1.465 4.02 0.3327 194 473 13.83 1.688 9.34 0.4222 282 966 5.69 1.449 4.20 0.3271 208 501 5.61 1.455 4.15 0.3223 200 467 12.99 1.741 0.88 0.4271. 295 979 6.41 2.002 4.60 0.4980 296 988 11.00 1.408 8.05 0.2982 198 456 10.72 1.417 7.86 0.2990 215 533

Table 3

Revetment Data f o r P h v s i c a l Model T e s t s

T e s t No.

C r o s s

-Benm s e c t i o n Berm Berm Height Rrea Revetment C r e s t C r e s t Berm Above Revetment S t a b i l i t y Response Height Length Width SWL At Number Categnry he l c

cm cm cm''2 Ns RRC * cm cm

P e r c e n t Beach Beach Energy E r o s i o n E r o s i o n S l o p e S l o p e D i s s i p a t i o n

Depth Length B e l o u Above by he l e SWL SWL Revetment cm cm h e / l e h c / l c P e r c e n t D 1 54.86 10.77 1623 3.56 I 18.44 1 54.86 10.77 1623 3.62 I 19.04 2 54.86 10.77 1623 7.05 F NA 3 54.86 13.82 1624 3.41 S 17.56 3 54.66 13.82 1619 3.46 s 17.07 4 54.86 13.82 1619 6.64 I 21.12 5 54.86 13.82 1619 6.53 I 21.61 6 70.10 11.28 2061 7.29 I 21.43 7 70.10 11-28 2061 3.68 s 18.50 7 70.10 11.28 2061 3.76 s 19.51 8 77.72 11.15 2253 7.58 I 23.26 8 77.72 11.15 2253 7.35 I 24.20 9 24.38 1G.93 862 3.64 F NH 10 24.38 13.98 862 3.34 I 16.73 11 54.86 14.25 1637 5.89 s 17.43 12 54.86 11.20 1637 6.15 I 17.89 13 24.38 13.98 862 5.64 I 15.52 13 24.38 13.98 862 5.69 I 16.73 14 77.72 11.27 2230 6.84 I 24.05 15 77.72 11.27 2230 5.97 s 17.74 I S 92.96 11.24 2652 7.30 I 24.51 17 24.38 11.04 865 6.51 F Nfl 17 24.38 11.04 865 6.17 F NA 18 24.38 14.09 882 6.56 F Nfl 19 24.38 14.09 861 2.73 s Nfl 19 24.38 14.09 861 2.76 s NA 20 24.38 11.04 861 2.99 I 13.69 20 24.38 11.04 861 2.96 I 13.62 21 24.38 11.04 861 6.86 F Nfl 22 54.86 10.99 1624 3.09 S 14.20 22 54.86 10.99 1624 3.05 5 14.48 23 54.86 10.63 1596 9.22 F NR 24 54.86 10.63 1596 4.78 I 20.33 25 54.86 10.63 1596 8.36 I 18.99 25 54.86 10.63 1596 8.16 I 19. 11 26 54.86 10.63 1596 4.15 S 14.72 26 54.86 10.63 1596 4.08 s 15.79 29.79 15.58 52.50 0.297 0.619 79.4 26.71 15.35 52.54 G.292 0.713 79.4 Nfl NH NH NH NA 87.4 26.75 12.53 40.30 0.311 0.656 77.4 26.23 12.66 45.40 0.279 0.651 78.2 37.14 12.66 49.73 0.255 0.569 87. G 37.78 12.29 46.05 0.267 0.572 87.5 36.28 15.88 62.78 0.253 0.591 85.0 28.29 15.76 52.48 0.300 0.554 78.9 31.31 15.61 52.51 0.297 0.623 78.9 39.87 15.BB 59.19 0.268 0.583 85.1 42.51 16.09 62.55 0.257 0.569 85.5 Nfl Nfl NH Nfl NA 75.9 24. DB 11.37 36. BB 0.308 0.695 80.3 26.87 12.71 50.86 0.250 0.649 91.0 28.75 15.85 61.12 0.259 0.622 92.4 25.64 11.35 45.99 0.247 0.644 92.0 28.60 11.64 46.08 0.253 0.585 92.4 41.73 15.68 54.28 0.2B9 0.575 B5.8 30.70 • 16.00 57.69 0.277 0.578 91.9 40.48 16.28 57.05 0.285 0.605 85.8 Nfl NH NH NH Nfl 91.2 Nfl NA Nfl NH NH 89.7 NR NA NH NH Nfl 85.6 19. IB 11.32 40.26 0.281 Nfl 88.0 19. 17 11.32 40.27 0.281 Nfl 88.5 19.68 14.38 48.90 0.294 0.695 89.0 19.54 14.38 49.05 0,293 0.697 88.9 Nfl NA NA Nfl Nfl 82.2 22.11 15.45 49.52 0.312 0.542 89.3 21.67 15.45 49.95 0.309 0.668 89.5 Nfl NA Nfl Nfl Nfl 81.8 30.56 15.35 50.22 0.305 0.665 75.2 26.91 15.50 56.00 0.277 0.705 91.1 27.87 15.45 54.50 0.283 0.586 91.1 18.69 15.42 48.36 0.319 0.788 86.1 22.49 15.45 48.00 0.322 0.702 85.3

1 0 0 9 0 8 0 7 0 H 6 0 - { 5 0 4 0 2 0 T 1 r LEGEND M Concrete slope

+ Pre-test profile, test 4 O Pre-test profile, test 5

~i 1 1 1 1 r 4 0 6 0 8 0 1 0 0 H o r i z o n t a l D i s t a n c e f r o m B u l k h e a d ( c m ) a. P r e t e s t p r o f i l e s 1 2 0 1 4 0 1 0 0 9 0 H 8 0 7 0 6 0 H 5 0 4 4 0 _{1 1 \ 1 \ r} 0 2 0 4 0 LEGEND H Concrete slope -t- Post-test profile, test 4 O Post-test profile, test 5

1 ^ — 1 0 0 6 0 8 0 H o r i z o n t a l D i s t a n c e f r o m B u l k h e a d ( c m ) — I i 1 — 1 2 0 1 4 0 b. P o s t t e s t p r o f i l e s F i g u r e 5. P r e - and p o s t t e s t p r o f i l e s f o r T e s t s 4 and 5

stone p l a c e s an important c o n s t r a i n t on t h i s g e n e r a l i t y s i n c e f o r s e v e r e wave c o n d i t i o n s a t t a c k i n g a s m a l l revetment, a l a r g e p o r t i o n o f the stone can be thrown landward beyond the bulkhead and l o s t to the system. L o s s o f stone can cause a n o n r e v e r s i b l e d e t e r i o r a t i o n o f the revetment and u l t i m a t e l y f a i l u r e .

26, Other i n t e r e s t i n g f e a t u r e s o f both the Dutch and CERC dynamic p r o f i l e s a r e a pronounced beach c r e s t and a v e r y steep s u b a e r i a l beach f a c e . During the CERC study, the dynamic p r o f i l e would t y p i c a l l y r e a c h a s l o p e of about 45 deg seaward of the beach c r e s t . The s t e e p e s t beach f a c e segment observed d u r i n g t h i s study was 52 deg. The angle of repose f o r s h a r p - s i d e d stone or g r a v e l i s approximately 45 deg, and t h i s v a l u e i s assumed to be about the l i m i t i n g v a l u e f o r the beach f a c e s l o p e .

PART I V : DISCUSSION

27. One development from v a n der Meer's (1988) r e s e a r c h i s a method to c a t e g o r i z e " s t r u c t u r e s " from b r e a k w a t e r s to sand beaches ( T a b l e 4 ) . The method i s based on a s t a b i l i t y number s i m i l a r to the one used e x t e n s i v e l y by Hudson and Davidson (1975) i n t h e i r study o f breakwater s t a b i l i t y . F o r i r r e g u l a r waves, the s t a b i l i t y nxomber i s d e f i n e d as

N „ = ^ . o r

-^ - l l w-^/-^

\ ( 7 )

where w„ i s t h e u n i t weight o f water, w i t h w„ = 1.000 g/cm^ f o r f r e s h water and w„ = 1.025 g/cm^ f o r seawater. When stone s i z e s a r e r e l a t i v e l y s m a l l , as i n t h i s study, d n ( 5 0 ) i s determined by s i e v e a n a l y s i s . Energy-b a s e d wave parameters a r e used i n t h i s study so the z e r o t h moment wave h e i g h t H^o (measured a t A r r a y 2) i s used i n E q u a t i o n 7 r a t h e r than Hg . F o r t h i s study, the range o f s t a b i l i t y numbers i s from 2.7 to 9.2. S i n c e CERC t e s t s a r e r u n i n s h a l l o w water where H3 i s t y p i c a l l y g r e a t e r H^^, , t h e s t a b i l i t y numbers from t h i s study w i l l be somewhat lower than van der Meer's.

R e g a r d l e s s o f d i f f e r e n c e s , t e s t s from t h i s s t u d y f a l l i n t o v a n d e r Meer's "berm breakwater and S-shaped p r o f i l e s " and " d y n a m i c a l l y s t a b l e r o c k s l o p e s " c a t e g o r i e s ( s e e T a b l e 4 taken from v a n der Meer and P i l a r c z y k ( 1 9 8 7 ) .

T a b l e 4

S t r u c t u r e C l a s s i f i c a t i o n Based on van der Meer and P i l a r c z y k (1987) S t r u c t u r e Range o f S t a b i l i t y Number S t a t i c a l l y s t a b l e breakwaters N3 = 1-4

Berm breakwater and S-shaped p r o f i l e s N^ = 3-6 D y n a m i c a l l y s t a b l e rock s l o p e s Ng = 6-20 G r a v e l beaches N = 15-500

S Sand beaches N3 > 300

28. Johnson (1987) remarks about the i m p r e s s i v e a s p e c t o f waves b u i l d -i n g h -i g h , steep beach f a c e s on Lake M-ich-igan, and t h -i s f e e l -i n g was s h a r e d by l a b o r a t o r y o b s e r v e r s watching the r a p i d development o f the beach f a c e d u r i n g s m a l l - s c a l e t e s t s . The r e a s o n f o r these beach f e a t u r e s r e l a t e s to t h e h i g h p o r o s i t y o f the r u b b l e , e s t i m a t e d to be about 45 p e r c e n t . I f the waves a r e l a r g e enough to m o b i l i z e the r u b b l e , then runup w i l l c a r r y some o f i t upslope, but the r e t u r n flow w i l l not c a r r y a l l o f i t downslope u n t i l the p r o f i l e has r e a c h e d e q u i l i b r i u m . T h e r e f o r e , the s u b a e r i a l beach f a c e i s about e q u a l to the angle o f repose l a r g e l y because the runup flow d r a i n s away so q u i c k l y . The e x t e n t o f p a r t i c l e m o b i l i z a t i o n i s measured by the s t a b i l i t y momber Ng d e f i n e d by E q u a t i o n 7. Height o f the berm c r e s t i s a conspicuous f e a t u r e t h a t can be e a s i l y i d e n t i f i e d and a c c u r a t e l y measured. The berm c r e s t h e i g h t i s a t the approximate upper l i m i t o f wave runup ( P o w e l l 1988). V i s u a l o b s e r v a t i o n s of the t e s t s i n d i c a t e t h a t the "mature" c r e s t i s only o c c a s i o n a l l y overtopped. T h e r e f o r e , berm c r e s t h e i g h t i s a good measure o f extreme wave runup h e i g h t .

C r i t i c a l Mass A n a l y s i s

29. To e v a l u a t e economic f e a s i b i l i t y o f a r u b b l e s t r u c t u r e , i t i s c l e a r l y n e c e s s a r y to determine the minimum amount o f stone t h a t w i l l p r o v i d e the d e s i r e d p r o t e c t i o n . T h i s minimum q u a n t i t y (volume p e r u n i t l e n g t h o f revetment) i s r e f e r r e d to i n t h i s study a s t h e c r i t i c a l mass.

30. A l l o f the t e s t r e s u l t s were c l a s s i f i e d i n t o one o f t h r e e revetment response c a t e g o r i e s . When wave c o n d i t i o n s were s e v e r e i n r e l a t i o n to the q u a n t i t y o f stone i n the revetment, wave a c t i o n eroded the r u b b l e , u s u a l l y by c a r r y i n g i t over the bulkhead, u n t i l waves impacted d i r e c t l y a g a i n s t the bulkhead. T h i s c a t e g o r y was d e s i g n a t e d f a i l u r e , denoted by "F" i n T a b l e 3. When the amount o f stone i n a revetment was l a r g e i n r e l a t i o n to wave

c o n d i t i o n s , development o f the berm c r e s t had enough room so t h a t n e i t h e r stone nor water was c a r r i e d over the bulkhead. T h i s c a t e g o r y was d e s i g n a t e d s a f e , denoted by "S" i n Table 3. The t h i r d c a t e g o r y f e l l between s a f e and f a i l u r e and o c c u r r e d when the berm c r e s t b u i l d u p extended f a r enough landward to r e a c h the bulkhead and t h e r e was a t l e a s t some overtopping o f the bulkhead by both water and s t o n e . T h i s category was d e s i g n a t e d i n t e r m e d i a t e , denoted by " I " i n T a b l e 3. The t h r e e PRC's a r e i l l u s t r a t e d i n F i g u r e 6,

100 E Ê O O CQ 0 ) e L L ? O < C O ro > LU 90 H LEGEND d Concrete slope + Pre-test profile RRC's O 'S" Safe X "I' Intermediate V "F- Failed 40 60 80 100

Horizontal Distance from Bulkhead (cm)

120 140

F i g u r e 6. T y p i c a l e q u i l i b r i u m p r o f i l e s i l l u s t r a t i n g the s a f e i n t e r m e d i a t e , and f a i l e d revetment r e s p o n s e c a t e g o r i e s

31. To c a l c u l a t e c r i t i c a l mass, i t i s n e c e s s a r y to e s t i m a t e t h r e e c h a r a c t e r i s t i c dimensions o f a dynamic revetment, i . e . , berm c r e s t h e i g h t , ] berm c r e s t l e n g t h 1, , and e r o s i o n l e n g t h 1, . R e g r e s s i o n a n a l y s i s was ' employed to determine the f o l l o w i n g equations, which d e f i n e these c h a r a c t e r -i s t -i c d-imens-ions a s f u n c t -i o n s o f l o c a l wave s t e e p n e s s H^^Lp , where -i s the wavelength determined by l i n e a r wave theory f o r the depth a t the toe and the peak p e r i o d . H, ° - 0 . 2 7 0 * ' ^ ' -0.645 '0 1 TO_{, = 0 . 9 6} 2 _ r _{( 8 )} 0 . 6 7 7 * Hmo -0.521 , R 2 = 0 . 9 2 ( 9 )

^ = e x p

E q u a t i o n s 8, 9, and 1 0 a r e based on a n a l y s i s o f T e s t s 1 through 2 2 .

v a l u e s g i v e the p o r t i o n o f the v a r i a n c e e x p l a i n e d by the r e g r e s s i o n a n a l y s i s . T e s t s 2 3 , 2 4 , 2 5 , and 2 6 were conducted w i t h somewhat s m a l l e r stone ( s e e T a b l e 1 ) and were w i t h h e l d from a n a l y s i s . F i g u r e s 7, 8, and 9 show observed d a t a w i t h r e g r e s s i o n t r e n d s f o r Equations 8, 9, and 1 0 , r e s p e c t i v e l y .

Although the s m a l l e r s t o n e was not i n c l u d e d i n the a n a l y s i s , i t has been i n -c l u d e d i n F i g u r e s 7, 8, and 9 to i l l u s t r a t e the a p p l i -c a b i l i t y of the equations to o t h e r stone s i z e s . Stone s i z e s a r e denoted by sjmbols i n t h e s e f i g u r e s , w i t h "L" i n d i c a t i n g the l a r g e r stone and "S" i n d i c a t i n g the s m a l l e r s t o n e .

3 2 . C h a r a c t e r i s t i c dimensions determined by E q u a t i o n s 8, 9, and 1 0 may be used to determine a p s e u d o - c r o s s - s e c t i o n a l a r e a of the mature revetment A^ where

A3 = + h,) * ( 1 , + 1,) ( 1 1 )

T h i s e q u a t i o n i s e s s e n t i a l l y j u s t l e n g t h times h e i g h t . Water depth a t the toe of the revetment dg i s s e l e c t e d based on d e s i g n c o n s i d e r a t i o n s . The t o t a l volume of the revetment per u n i t l e n g t h i s then determined from Ag f o r the d e s i r e d degree of p r o t e c t i o n . T o t a l d e s i g n volume i s denoted At (cm^/cm) , which i n c l u d e s v o i d s p a c e . F i g u r e 1 0 shows the revetment response c a t e g o r y v e r s u s the r a t i o of At to Ag . The two s o l i d l i n e s i l l u s t r a t e v a l u e s of At/Ag o f 0 . 6 7 and 0 . 4 6 , and i n d i c a t e t h a t i f

A t > 0 . 6 7 Ag ( 1 2 )

the revetment i s s a f e , and i f

A t < 0 . 4 6 Ag ( 1 3 )

the revetment w i l l f a i l . V a l u e s o f At/Ag between 0 . 4 6 and 0 . 6 7 a r e i n the i n t e r m e d i a t e revetment response c a t e g o r y . T h i s guidance i s based on l a b o r a -t o r y -t e s -t s w i -t h a range o f s -t a b i l i -t y numbers ( E q u a -t i o n 7 ) from 2.7 -to 9 . 2 .

3 3 . Johnson's ( 1 9 8 7 ) c r i t e r i a f o r p r o t e c t i n g e r o d i n g p o r t i o n s of the Lake Michigan s h o r e l i n e was 3 6 m e t r i c tons/metre. Assuming a p o r o s i t y of 3 5 p e r c e n t and a u n i t weight of 2 . 6 4 g/cm^, t h i s guidance i s e q u a l to 2 1 m^/m. F i g u r e 1 1 compares t h i s guidance w i t h the d e s i g n volumes determined by

2.24 *

-0.143

0 . 0 1 4 _{0 . 0 1 8 0 . 0 2 2 0 . 0 2 6 0 . 0 3 0 0 . 0 3 4} LOCAL WAVE STEEPNESS, H m o / L p

0 . 0 3 8 0 . 0 4 2 0 . 0 4 6

F i g u r e 7. C a l c u l a t e d and observed r e l a t i v e berm c r e s t h e i g h t s as a f u n c t i o n o f l o c a l wave s t e e p n e s s 7.0 o £ r \ 6 . 5 -A 6 . 0 L L O z a: o 2 UJ m OC 5 . 5 H 5 . 0 4 . 5 H 4 . 0 3 . 5 H 3 . 0 \ LL , LL L L -1 I I i 1 p S L L - | 1 r 0 . 0 1 4 0 . 0 1 8 0 . 0 2 2 0 . 0 2 6 0 . 0 3 0 . 0 3 4 0 . 0 3 8 0 . 0 4 2 0 . 0 4 6 LOCAL WAVE STEEPNESS, H m o / L p

F i g u r e 8. C a l c u l a t e d and observed r e l a t i v e berm c r e s t l e n g t h s as a f u n c t i o n of l o c a l wave s t e e p n e s s

F i g u r e 9. C a l c u l a t e d and observed r e l a t i v e e r o s i o n l e n g t h s as a f u n c t i o n of l o c a l wave steepness

F i g u r e 10. T o t a l a r e a of berm, , v e r s u s c a l c u l a t e d A^ , w i t h w i t h observed RRC. S o l i d l i n e s i l l u s t r a t e t h a t f o r At < 0.46 as

1 0 0 E \ 10 ( E O tn 9 0 8 0 7 0 H 6 0 5 0 4 0 3 0 2 0 -10 O — 0 . 2 0 . 6 D F o i l / I n t e r 1.4 1.8 1 1— 2.2 D e p t h o f B u l k h e a d T o e , ds ( m ) + I n t e r / S a f e ' T r 2.6 C. J o h n s o n

F i g u r e 11. Comparison o f stone volume c a l c u l a t e d i n t h i s r e p o r t v e r s u s guidance i n Johnson (1987) f o r Great Lakes storm w i t h

Tp = 10 s e c and H„„ = 0.6 * d^

E q u a t i o n s 8 through 13. F i g u r e 11 assumes d e s i g n c o n d i t i o n s o f Tp = 10 s e c and H„„ = 0.6 * d^ .

Wave R e f l e c t i o n and Energy D i s s i p a t i o n

34. The r e f l e c t i o n c o e f f i c i e n t i s d e f i n e d as the square r o o t o f the r a t i o o f r e f l e c t e d wave energy to i n c i d e n t wave energy (Goda and Suzuki 1976). Wave r e f l e c t i o n from dynamic revetments appears to be a f u n c t i o n o f two

v a r i a b l e s , wave s t e e p n e s s and r e l a t i v e v o i d s i z e . R e f l e c t i o n c o e f f i c i e n t s can be p r e d i c t e d w i t h the f o l l o w i n g equation: 1. 0 1.0 + CO * ^ ( 5 0 ) 01 * exp C 2 Hmo/LoJ (14)

where L^ i s the deepwater wavelength. D i m e n s i o n l e s s r e g r e s s i o n c o e f f i c i e n t s a r e g i v e n by,

CO C l C2 = 23.4 = 0.312 = -0.00374

E q u a t i o n 14 e x p l a i n s about 97 p e r c e n t of the v a r i a n c e i n a sample s i z e o f 30, i . e . , R'^ = 0.97 and N = 30 . T e s t s i n the f a i l u r e response c a t e g o r y were not i n c l u d e d i n t h i s a n a l y s i s s i n c e a t f a i l u r e a s u b s t a n t i a l p a r t o f the

r e f l e c t i o n i s from the v e r t i c a l bulkhead. Percentage o f i n c i d e n t wave energy d i s s i p a t e d by a dynamic revetment c a n be e s t i m a t e d by u s i n g E q u a t i o n 14 and the r e l a t i o n ,

%D = ( 1 . 0 - Kr) * 1 0 0 % (15) where %D i s the p e r c e n t energy d i s s i p a t i o n . Observed d a t a g i v e r e f l e c t i o n

( c o e f f i c i e n t s between 0.27 and 0.50, i n d i c a t i n g t h a t dynamic revetments d i s s i -pate between 75 and 92 p e r c e n t o f the i n c i d e n t wave energy. By d i s s i p a t i n g over t h r e e - q u a r t e r s of the i n c i d e n t wave energy, dynamic revetments make good wave a b s o r b e r s .

PART V: SUMMARY AND CONCLUSIONS

35. A s e r i e s of l a b o r a t o r y t e s t s were conducted to i n v e s t i g a t e the response of dynamic revetments to shallow-water wave c o n d i t i o n s . Most t e s t s from t h i s study f a l l i n t o the category " d y n a m i c a l l y s t a b l e rock s l o p e s " based on the Dutch c l a s s i f i c a t i o n system (van der Meer and P i l a r c z y k 1987). For t h i s study, the r a t i o of the wave h e i g h t to stone dimension i s i n the range of roughly 5 to 16. T y p i c a l l y , zero-damage on a c o n v e n t i o n a l r i p r a p revetment o c c u r s when the wave i s about two and a h a l f times l a r g e r than the stone dimension.

36. I t was found t h a t the e q u i l i b r i u m dynamic revetment p r o f i l e was not s e n s i t i v e to the i n i t i a l p r o f i l e . T h i s f i n d i n g means t h a t c o n s t r u c t i o n c o s t s can be lowered because s p e c i a l c a r e i s not r e q u i r e d i n the placement of the stone. The berm c r e s t i s a conspicuous f e a t u r e of the p r o f i l e and p r o v i d e s a good i n d i c a t i o n of the extreme wave runup.

37. The concept of a c r i t i c a l mass f o r a dynamic revetment i s

i n t r o d u c e d . C r i t i c a l mass i s the q u a n t i t y of stone r e q u i r e d to p r o t e c t a u n i t l e n g t h of a v e r t i c a l bulkhead f o r a given water depth a t the toe and g i v e n wave c o n d i t i o n s . T h i s q u a n t i t y i s found to i n c r e a s e w i t h i n c r e a s i n g water depth, z e r o t h moment wave h e i g h t , and p e r i o d of peak energy d e n s i t y .

38. The i n f l u e n c e of the i n i t i a l berm width and berm h e i g h t above the s t i l l - w a t e r l e v e l were two of the major v a r i a b l e s i n v e s t i g a t e d i n t h i s study. I t was found t h a t t h e s e parameters p l a y a major r o l e i n determining how much stone i s r e q u i r e d to p r o t e c t a v e r t i c a l bulkhead from d i r e c t wave a t t a c k .

REFERENCES B a i r d , W. F., and H a l l Q u a r r i e d Stones TX. •• P r o . . ^- ^'

^l^""-

Port and Harbor

R l L ' ^ h ^ l L t S ^ i ' S n i r i f

f ^ ' R a n L ; Wave'H^p"iJ„ta'"proc;fai""'"^? o f I n c l d s n t a n . R e f l e c t e d Waves Honolulu, H a w a l i . ' v o l I sfffg-^ ^ " " " " ' ' ' ^ Fuptnor-rlnp Conf.ren.,,

":i=;

A;^oï^;rBr"Lre?s"^°pt:ie^in"s"c"r"

°^

^ e r l c a n S o c i a l , „f

C i : i r E ; , l n ^ ° r : ! ' ' ê ; t ^ ; : t S f " ^

Enke K Rwi^,^ b a r n e t t , r . P., Bouws, E. , C a r l s o , H. , C a r t w r i g h t D C

North Sea Wave P r o j e c t (JoSswIpT • D e u t Ï h r H 7

Hamburg, Germany. ^''""'"AP), Deutshes Hydrographlsches I n s t i t u t ,

w a t ^ r s t a b l U ^ y C e i r ' ^ P r ^ c s e d " - " " ' " " " " ' y Rubble-Hound Break-S o c i e t y of

cJnltXi^rrSfS^riT ""^^^

S r

: : e t : J : ? ^ ^ * ; ; j : : : L " t

„ t i ; S i n i e "

^ r " " "

-c:ng:;:;c^„!-.i!!!^

^-g^-

1983, D e l f t , The Netherlands S r i Lanka: a l s o D e l f t H y d r a u l i c s Laboratory'Report 293,

S t e v e n s , J . C. , B a r d s l e y , C. E., Lane, E. W., and Straub, L. G. 1942

" H y d r a u l i c Models," Manuals on Engineerinpr P r a c t i c e No. 9S American S o c i e t y of C i v i l E n g i i i e e r s , New York.

van d e r Meer, J . W. 1988. "Rock S l o p e s and G r a v e l Beaches Under Wave

A t t a c k , " Ph.D. T h e s i s , Dept. o f C i v i l E n g i n e e r i n g , D e l f t T e c h n i c a l U n i v e r s i t y a l s o D e l f t H y d r a u l i c s Communication No, 396, 1988, D e l f t , The N e t h e r l a n d s . van d e r Meer, J , W,, and P i l a r c z y k , K. W, 1987, "Dynamic S t a b i l i t y o f Rock Slopes and G r a v e l Beaches," Proceedings 20th Conference nn C o a s t a l

E n g i n e e r i n g , T a i p e i , Taiwan, Nov 1986; a l s o D e l f t H y d r a u l i c s Communication No. 379, 1987, D e l f t , The N e t h e r l a n d s .

van Hijum, E . , and P i l a r c z y k , K. W. 1982. " G r a v e l Beaches: E q u i l i b r i u m P r o f i l e and Longshore T r a n s p o r t o f Coarse M a t e r i a l under R e g u l a r and I r r e g u l a r Wave A t t a c k , " D e l f t H y d r a u l i c s L a b o r a t o r y P u b l i c a t i o n No. 274 D e l f t The N e t h e r l a n d s .

Average E l e v a t i o n Above Tank F l o o r (cm)

P l a n 1 P l a n 1 P l a n 1 P l a n 1 P l a n 1 P l a n 1 P l a n 1 P l a n 1 T e s t 1 T e s t 1 T e s t 2 T e s t 3 T e s t 3 T e s t 4 T e s t 5 T e s t 1 A f t e r A f t e r A f t e r A f t e r A f t e r A f t e r A f t e r

Concrete Before 3000 5000 3000 3000 5000 3000 5000

H o r i z . Slope T e s t i n g Waves Waves Waves Waves Waves Waves Waves

D i s t . Avg. Avg. Avg. Avg. Avg. Avg. Avg. Avg. Avg.

(cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) 0.00 48 .96 71 .73 71, .73 71, .73 71, .73 71, .73 71. .73 71. .97 72.16 3.05 48 .99 71, .97 72, .58 72, .70 66, .37 72. ,19 72. .07 73. .35 73.38 6.10 48, .87 72, .07 73, .22 73, .01 65, .39 72. .13 72. .07 73. .83 74.66 9.14 48 .75 72, .10 73. .50 73, .88 64, .02 72. .22 72. .19 75, .27 75.39 12.19 48, .69 72, .00 73, .92 74. .55 62, .92 72. ,28 72. .31 75, .81 75.78 15.24 48, .60 72, .10 74. .78 75, .27 62, .10 72. .46 72. .40 76, .67 77.16 18.29 48, .60 72, .10 76. .58 76. .94 60, .51 72. ,34 72, ,28 77. .46 77,89 21.34 48, .47 72, .10 77. .67 78. .97 59, .17 72. .46 72. .40 78. .53 78.92 24.38 48, .41 72, .13 79. .75 80. .34 58, .17 72. .28 72. .52 79. .38 79.87 27.43 48, .32 72, .13 79. .44 79. .62 57, .19 72. .55 72. .34 78. .41 78.89 30.48 48, .32 72. .13 76. .64 76. .66 56, .28 73. .10 72. .67 75. .33 75.94 33,53 48, .23 72, .13 73. .47 73. .67 55. .24 73, .68 73. .28 72. .98 73.53 36.58 48, ,08 72. .13 71. .27 71. .72 54, .63 74. .72 74. .08 70. .69 71.24 39.62 47, .99 72. .07 69. .05 69. .05 53. .87 75, ,81 75. .33 68. .71 68.93 42.67 47, .93 72, .10 66. .98 67. .48 53, .05 74. .63 74. .20 66. .79 67.19 45.72 47, .74 72, .10 65. ,70 63. .65 52. .13 72. .37 71. .21 65. .15 65.39 48.77 47, .68 72, .10 63. .74 62, .25 51, .49 68. ,41 68. ,65 63. .59 63.38 51.82 47 .65 72, .13 62. .25 61. .01 50, .82 65. .85 66. ,40 61. .82 62.10 54.86 47 .47 72, .13 61. .03 60. .11 50, .27 63. .96 63. .90 60. .76 60.97 57.91 47 .35 71 .00 60. .18 59, .09 50 .03 62. .04 62. .19 58. .56 59,51 60.96 47 .25 68 .04 59, .14 58, .34 50 .03 60, .39 60, .48 58, .47 58.65 64.01 47 .19 65 .12 58, .59 57, .51 49 .75 59, .11 58, .87 57, .31 57.65 67.06 47 .07 61 .95 57, .47 56, .72 49 .42 58, .01 57, .86 56, .40 56.73 70.10 46 .95 58 .75 56, .89 56, .21 49 .27 56, .95 56, .86 55 .42 55.94 73.15 46 .89 56 .06 56, .09 55, .51 48 .99 55, .88 55, .79 55 .06 55.18 76.20 46 .77 53 .20 55, .18 54 .51 48 .78 54 .87 54 .87 54 .20 53.96 79.25 46 .65 50 .36 54, .42 53 .83 48 .53 54 .11 54, .11 53 .47 53.66 82.30 46 .58 48 .02 53, .87 53, .09 48 .14 53 .32 52 .95 52 .62 53.02 85.34 46 .49 46, .49 53, .08 52 .27 47 .83 52 .47 52 .16 51 .74 52.16 88.39 46 .37 46 .37 52, .22 51, .34 47 .04 51, .67 51 .46 50 .97 51.49 91.44 46, .31 46, .31 51, .37 50, .61 46 .49 51, .19 51, .06 50 .58 50.46 94.49 46, .22 46, .25 50. .67 49, .84 46 .25 50, .21 50, .24 49 .88 49.81 97.54 46, .00 46, .04 49, .33 48, .41 46 .04 49, .14 49, .54 49, .05 49.33 100.58 46, .00 46, .00 47, .93 47, .38 46 .00 48, .05 48, .50 48, .20 48.38 103.63 45, .91 45, .91 46, .95 45, .94 45 .91 47, .19 47. .22 47, .01 47.50 106.68 45, .73 45, .73 45. .73 45. .60 45, .73 45, .73 46, .34 46, .28 46.25