International Conference on
FLEXIBLE A R M O U R E D REVETMENTS
I N C O R P O R A T I N G GEOTEXTILES
2 9 - 3 0 March 1984
The Institution of Civil Engineers, London
Deiegates intending to speak should hand in a completed dis-cussion slip at the Reception Desk not later than 10 minutes before the start of the relevant session.
No tape recording or shorthand record of the Conference will be taken.
Delegates taking part in the discussion on any paper must give a concise written version of their contribution, together with any relevant figures to the Conference Editor as soon as possible after the session concerned.
Delegates for whom there is insufficient time to speak may also hand in written discussion.
No discussion contributions can be accepted after the Conference.
British National C o m m i t t e e of
F L E X I B L E A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G C E O T E X T I L E S
D C h a r a c t e r i s t i c dlmenaion o f armour elements. Diameter o f porous c e l l d Sediment g r a i n s i z e , n7. f i n e r than t h i s v a l u e (by w e i g h t ) S h i e l d s ' parameter g G r a v i t a t i o n a l a c c e l e r a t i o n H Wave Height K S t a b i l i t y c o e f f i c i e n t L Normal l e n g t h o f porous c e l l P P o r o s i t y o f armour l a y e r 5 Shear f o r c e S^ R e l a t i v e d e n s i t y T T e n s i l e f o r c e Shear v e l o c i t y V V e l o c i t y W Weight = angle o f slope r e l a t i v e t o h o r i z o n t a l B d i r e c t i o n o f streamtube r e l a t i v e t o h o r i z o n t a l T d e n s i t y 6 angle o f p a r t i c l e motion r e l a t i v e t o h o r i z o n t a l p c o e f f i c i e n t o f f r i c t i o n T shear s t r e s s
15. Theoretical basis and practical
experience-geotextiles in hydraulic engineering. M. WEWERKA 16. Bidding procedure and placing operation of
geotextile filter layers. H.-U. ABROMEIT
.. 13. Experiences in the use of geotextiles in the water construction field in finland. J. JUVONEN
17. Case histories using filter fabric underneath revetments in lower Louisiana. L E. DEMENT and
J.
fOWLER18. The use of geotextiles impregnated with
bitumen in situ as bank revetment completion of a section of the Milano-Cremona-Po inland waterway. G. DELLA LUNA, D. A. CAZZUffl and M. CEPORINA
19. Profix mattresses-an alternative erosion control system. W. H. TUTUARIMA and W. van WIJ K T4. Some recent developments in the field of flexible
armoured revetments in the Benelux.
J.
NOMESand T.
J.
LUPTONT5. Revetment construction at Port of Belawan
Indonesia. E. LOEWY, A. C. BURDALL and'
A G. PRENTICE 209 221 227 231 245 259 273 285
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Flexible revetments-theory and practice
C. T. BROWN. BSc(Eng). MICE, MIEAust. Tillotson B.rown and Partners. and
Seabee Deve!opments, Australia .
SYNOPSIS. Flexible revetments are defined as revetments that maintain an intimate contact with the underlying Boil during any gradual settlement, and protect the slope from realignment by wave and current action. A brief summary is made of various failure modes before a comparison is made of the comtemporary theories of hydrodynamic failure due to waves and currents. Developments of the theory as regards armour geometry and porosity are made and some recent experimental results presented, which are particularly germane to the effect of currents on revetments. The practical applications of this are briefly touched upon.
INTRODUCTION
1. Since 1976, the Author has undertaken investiga-tions into the behaviour of rip-rap, gabion and Seabee armoured revetments, mainly under orthogonal wave attack. Contemporaneously a review and reworking of the momentum theory was undertaken by considering the effect of a rotat-ing jet of fluid instead of the usual fixed direction. The envelopes of the theoretical stability curves were found to bear strong similarities to the empirical relationships found by experiment for both uplift and sliding failure modes.
2. Further consideration of the similarities between initiation of erosion under currents demonstrates the strong kinship between the Shields parameter and the various stability numbers and coefficients to be found in coastal engineering.
3. This suggests that perhaps the onset of erosion in streams depends upon the generation of sufficiently large rolling eddies at the movable boundary.
4. In considering flexible revetments, the considers this term to include all revetment systems elements can maintain intimate contact with settling
..,.... ,,, I ~ 1 , 1 (\0 1
author whose
under-F L E X I B L E A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G C E O T E X T I L E S
layera without rendering the revetment unstable o r allowing erosion to o c c u r .
5. F l e x i b l e revetments i n c l u d e r i p - r a p , d r y l a i d
b l o c k s as w e l l as gabions and t i e d b l o c k systems and a s p h a l -t i c c o n c r e -t e l a y e r s . Impervious c o n c r e -t e s l a b sys-tems do not f a l l w i t h i n t h i s c a t e g o r y .
6. F a i l u r e Modes. T y p i c a l l y , revetments may f a l l by one o r more o f the f o l l o w i n g :
1. Vandalism, t h e f t and f a u l t y c o n s t r u c t i o n .
11 A b r a s i o n , w e a t h e r i n g and chemical d e c o m p o s i t i o n . 111. Environmental hazard.
i v . S t r u c t u r a l f a i l u r e .
V . Scour a t the edges o r t o e .
v i . Understreaming and l o s s o f u n d e r l a y e r m a t e r i a l . . v i i . E x t r a c t i o n o r u p l i f t o f the armour l a y e r by
c u r r e n t s o r waves.
v i l l . S l i d i n g o f t h e revetment f a c e . I x . Slope f a i l u r e .
7. F a i l u r e mode 1 . i s hard t o p r e v e n t and revetment systems should i d e a l l y be r e s i s t a n t t o p a r t i a l v a n d a l i s m y e t c l e a r l y demonstrate t h a t such has o c c u r r e d , so t h a t the need f o r r e p a i r s I s o b v i o u s . F a u l t y c o n s t r u c t i o n i s t h i a c a t e g o r y .
8. F a i l u r e mode l l . I s a r e s u l t o f I n a p p r o p r i a t e m a t e r i a l s and/or e x p e c t a t i o n s , and I t s avoidance r e q u i r e s
the e x e r c i s e o f sound e n g i n e e r i n g judgement based on experience and experiment. I n A u s t r a l i a we have found t h a t r e s i s t a n c e t o s a l t c r y s t a l g r o w t h , t h e r m a l shock and t r a n s i t of boats and t r a i l e r s are t h e main agents o f w e a t h e r i n g and a b r a s i o n .
9 . A revetment may a l s o f a l l by b e i n g an environmen-t a l hazard, by h a r b o u r i n g noxious vermin o r by being decep-t i v e l y s a f e . P o o r l y f i n i s h e d gabions I n a back beach revetment may be p r e s e n t a f a c e o f r u s t i n g wire-ends which can cause h a r m f u l c u t s . Rip-rap and o t h e r l a r g e v o i d e d revetments may harbour r a t s . Other systems nfay become v e r y s l i p p e r y and dangerous t o walk on.
10. S t r u c t u r a l f a i l u r e o f i n d i v i d u a l elements i s most
f r e q u e n t l y found where o t h e r c r i t e r i a , p a r t i c u l a r l y h y d r a u l i c performance, have been c a r r i e d t o o f a r and l a most u s u a l l y a s s o c i a t e d w i t h s l e n d e r non-redundant elements. The I d e a l element i s one t h a t can f a l l s t r u c t u r a l l y and e i t h e r s t i l l f u n c t i o n I n the revetment o r disappear c o m p l e t e l y , w i t h o u t damaging t h e a d j a c e n t elements o r r e n d e r i n g them u n s t a b l e .
2
B R O W N
11. Many revetments f a l l due t o scour a t t h e edges o r
a t the t o e , and d e t a i l d e s i g n o f these p a r t s i s o f t h e utmost Importance. The a b i l i t y t o accommodate p e r i p h e r a l scour i s one o f the c h i e f advantages o f t e n s i l e f l e x i b l e revetments such as gabions. However, t h i s t e n s i l e c a p a c i t y needs t o be an u l t i m a t e c a p a c i t y , as o t h e r w i s e t h e revetment may span over s u b l a y e r scour h o l e s w i t h o u t much s i g n o f d i s t r e s s , vhen e a r l y i n d i c a t i o n would a l l o w an e a r l y remedy.
12. The d i r e c t r e s u l t o f l o s s o f c o n t a c t between the revetment system and i t s u n d e r l a y e r s i s understreaming which a l l o w s and causes the r e g r a d i n g o f the u n d e r l a y e r m a t e r i a l to a p r o f i l e o t h e r t h a n t h a t designed. T h i s w i l l u s u a l l y ft r e s u l t i n p r o g r e s s i v e r e a d j u s t m e n t o f t h e slope and p o s s i b l y
a s e r i o u s slope f a i l u r e .
13. S i m i l a r r e s u l t s can occur w i t h l o s s o f u n d e r l a y e r m a t e r i a l due t o i n c o r r e c t d e s i g n o r c o n s t r u c t i o n .
14. Although t h e modern use of f i l t e r f a b r i c s has
overcome the problems a s s o c i a t e d w i t h m u l t i l a y e r g r a v e l f i l t e r s , o t h e r problems a s s o c i a t e d w i t h t h e f a b r i c s can ocur, namely unseen damage i n c o n s t r u c t i o n ; inadequate l a p p i n g ; d e t e r i o r a t i o n due t o U.V. l i g h t ; a b r a s i o n by sand; and f a t i g u e due t o w o r k i n g by wave a c t i o n when I n s t a l l e d t o o c l o s e t o the s u r f a c e o f t h e revetment. F i g u r e 1 shows a revetment under wave a t t a c k . The f i g u r e shows the d i f f e r e n -t i a l pumping -t h a -t can occur a -t -the face o f -the f i l -t e r c l o -t h a t t h e p h r e a t i c l e v e l .
15. A p a r t f r o m the s t r u c t u r a l s t r e n g t h o f the u n i t ,
the l a s t two f a i l u r e cases are the o n l y two cases, u s u a l l y analysed m a t h e m a t i c a l l y , a l t h o u g h a l l t h e d e r i v a t i o n s t o date have r e q u i r e d e m p i r i c a l c a l i b r a t i o n o f t h e c o e f f i c i e n t s i n the r e s u l t i n g e q u a t i o n s .
THEORY
16. The s t r o n g s i m i l a r i t i e s between t h e d e r i v a t i o n s
f o r c u r r e n t and wave e r o s i o n ( S h l e l d s C l J , I r r l b a r r e n [ 2 ] and Hudson[3]) are due t o the common b a s i c f o r c e s , t h e d i s t u r b -ing f o r c e b e i n g d e r i v e d f r o m t h e momentum o f t h e water f l o w v i a the dra.'j and l i f t f o r c e s , w h i l s t t h e r e s t o r i n g f o r c e s are e s s e n t i a l l y those due t o the w e i g h t o f an armour element, a l t h o u g h some have i n c l u d e d t h e e f f e c t o f i n t e r -u n i t f o r c e s s-uch as f r i c t o n , t e n s i o n and shear.
17. The I r r i b a r r e n and Hudson d e r i v a t i o n s f o r the
e f f e c t o f waves s t a r t w i t h t h e water v e l o c i t y I n the break-ing wave, t r a n s f o r m i n g t h i s t o an e q u i v a l e n t wave h e i g h t , the s i m p l e r and more u s u a l d e s i g n parameter. I t should be remembered t h a t i t t s t h i s s i m p l i f i c a t i o n t h a t causes t h e e f f e c t s o f wave p e r i o d t o be l o s t .
F L E X I B L E A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G C E O T E X T I L E S
B R O W N
18. The r e l a t i o n s h i p s compare as f o l l o w s : S h i e l d s : Fa - U»/(Sr-l)gD -to/1f(Sr-l)D
I r r i b a r r e n : W « KTH*/(Sf-l)* (iiCo8«^ S i n " ? - Cy.yO* Hudson: W - TrH'/KoiSr-D* Cot« - Cv-'TD* 19. These may be reduced to a common form r e l a t i n g t y p i c a l armour dimension with Incident v e l o c i t y . I n both the I r r i b a r r e n and Hudson cases, we take the reverse step from wave height to water v e l o c i t y .
S h i e l d s : D - Ui/Fg.CSr-Dg
I r r i b a r r e n : D - H/CCy/K)^^ (Sr-l)(uCoa« - S i n - ) - VVCi.(Sr-l).g.(|JCoa« - Sln«) Hudson: D » H / ( C V / K D) ^ ^ * . ( S r - l ) C o t «''^
- V»/CH(Sr-l).g.(Cot-''» ) A l l equations are of the form:
— = C.(Sr-l).(Cot-='> ) gD
20. I n 1978,79 Brown (4,5,6) reworked the momentum rflux d e r i v a t i o n as a vector problem, allowing the j e t to rotate on an element of a revetment. The b a s i c f o r c e s a r e :the d i s t u r b i n g f o r c e :
Fj, -pAV «nd the r e s t o r i n g f o r c e :
Fj^ - W + S + T
21. The d i r e c t i o n a l i t y of these forces was s p e c i f i c a l -l y considered and then reso-lved f o r two cases - u p -l i f t movement and s l i d i n g movement - t o give the following r e s u l t s : U p l i f t : R ( l - p ) > ^ C o s * ( 6 - B ) / C ( S r - l ) S l n 6 2g S l i d i n g : R ( l - p ) > — {Ki Sin 2(«+B)+K2Sln* («+B)-[f!llï]l 2g gPwA (Sr-l)(uCos« ±Sln«)
FLEXIBLE A R M O U R E D R E V E T M E N T S INCORt>ORATlNG C E O T E X T I L E S
By s u i t a b l e assumptions, these d e r i v a t i o n s may be c o n v e r t e d to e i t h e r the Hudson o r the I r r i b a r r e n e q u a t i o n .
n e g a t i v e = downwash p o s i t i v e = upwash
22. I g n o r i n g t h e shear and t e n s i l e f o r c e s i n t h e
revetment, t h e envolopes o f these t h e o r e t i c a l equations are i n c l o s e agreement w i t h the e m p i r i c a l forms d e r i v e d from l a b o r a t o r y t e s t a .
U p l i f t : J
R ( l - p ) > - I /CBu(Sr-l)Cot '
D o w n s l i d i n g : ^
R ( l - p ) > J- I Cgg(Sr-l)Cot «
23. I t can be seen t h a t these formulae have i s o l a t e d
the p l a n shape o f a revetment element from t h e s t a b i l i t y e q u a t i o n s . This enables s u i t a b l e revetment elements t o be designed f o r p r o d u c t i o n and placement economy w i t h o u t a f f e c -t i n g reve-tmen-t s -t a b i l i -t y . They have a l s o i n -t r o d u c e d -t h e p o r o s i t y o f the revetment as an independent v a r i a b l e .
24. The values o f these c o e f f i c i e n t s have been d e t e r
-mined by experiment f o r the cases o f gabions and Seabees exposed t o wave j e t s .
TABLE 1
STABILITY COEFFICIENTS FOR BLANKET REVETMENTS
For H = W 2 g Gabions Seabees
U p l i f t 4 5 - 6.5
S l i d i n g 7 U p l i f t
dominates
25. The membrane and shear f o r c e s have been i g n o r e d on the b a s i s t h a t t h e area o f concern i s l a r g e r t h a n an i n d i v i d u a l element and t h a t t h e f o r c e s do n o t come i n t o p l a y I n p r e v e n t i n g i n s t a b i l i t y o f the revetment l a y e r s . However, they are m o b i l i s e d d u r i n g the f a i l u r e process and may serve t o l i m i t the amount o r c o n t r o l t h e r a t e o f d e f o r m a t i o n o f the revetment.
B R O W N
TABLE 2
TESTER HANSEN & KEATS PAGE
GRADING Fine Graded 1mm 2mm P o o r l y W e l l
Sand Sand Sand Sand Graded Graded
•^15 0.24 0.29 0,59 1,22 0.28 0.26 PARAMETER d^^ 0.32 0.47 0.71 I 1.55 0.30 0.51 0.41 1.55 0.98 1.82 0.41 1.10 L D Stage A B C E F 0 1 <.21 <.22 <.27 <.37 <.21 1 .35 .45 .51 .56 .32 .44 0.8 2 .49 .55 .67 ,75 .49 .52 3 .60 .70 .82 1.19 .61 .67 1 .48 .63 ,66 .81 .44 1.2 2 .56 .71 .82 1.09 ,55 3 .68 .80 ,95 1.40 .66 1 .63 -78 .83 1.06 ,62 ,78 1.6 2 .74 .88 1.01 1.34 .75 .88 3 .80 .97 1.20 >1.4 .85 .90 1 .73 .89 .95 1.33 .67 2.0 2 .93 1.07 1,13 >1.4 .92 3 1.03 1.17 1.32 ,99 1 .74 .98 2.4 2 i 3 1 1.36 1.23 1,27 >1.0 1 4.0 2 >1.40 3
1
RECENT WORK26. Recent l a b o r a t o r y work has I n v e s t i g a t e d t h e
behaviour o f u n d e r l a y e r s under c u r r e n t a c t i o n . Two s e r i e s of flume t e s t s by Page and Hansen & Keats (7, 8 ) have been undertaken t o examine the e f f e c t upon t h e e n t r a i n m e n t o f a n a t u r a l sand bed under a porous revetment w i t h o u t an i n t e r -mediate f i l t e r l a y e r .
27. For t h e most p a r t , the p o r o s i t y was normal t o t h e
bed b u t i n one experiment a z i g - z a g h o r i z o n t a l p o r o s i t y was p r o v i d e d by u s i n g two staggered l a y e r s o f armour. i
F L E X I B L E A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G G E O T E X T I L E S Stage ID 1-4 1-2 1-0 0-8 i 1 1 1 1 t- J 0-5 0-8 1 0 1-2 1-6 2-0 2 4 4-0 UD F i g . 2 Mean V e l o c i t y vs C e l l Aspect R a t i o O O^b-^-a^A 0-6 0-8 1 0 Vb •'SO
F i g . 3 R e l a t i o n s h i p between C^^ and Median Grain Size
28. The apparatus c o n s i s t e d o f a t i l t i n g g l a s s flume w i t h a r a i s e d f a l s e f l o o r c o n t a i n i n g the sediment bed p r o
-t e c -t e d by -the armour l a y e r and a sedimen-t -t r a p .
29. Three d i s t i n c t phases o f m o t i o n o f t h e sediment were observed b e f o r e s i g n i f i c a n t e n t r a i n m e n t o f sediment o c c u r r e d . These were:
Stage 0 - No movement.
Stage 1 - H e m i s p h e r i c a l d e p r e s s i o n ocurs under v o i d c e l l , but no sediment e n t r a i n e d . Stage 2a - L i g h t e r p a r t i c l e s suspended i n lowest
v o r t e x I n v o i d c e l l .
B R O W N
Stage 2b - P a r t i c l e s i n motion throughout height of void c e l l , but no l o s s occurs.
Stage 3 - V o r t i c e s i n c e l l r i s e above top surface of armour l a y e r and entrained p a r t i c l e s are l o s t from i n d i v i d u a l c e l l s . Rate of l o s s i n c r e a s e s with increased flow. Stage 4 - U n i d i r e c t i o n a l flow occurs i n void
c e l l s , u p l i f t i n g sediment from beneath armour l a y e r and removing. (Understream-ing and/or r a p i d settlement o c c u r ) . 30. The onset of each stage was found to be r e l a t e d to the non-dimensional aspect r a t i o of the void c e l l and the gradng of the sand. The a c t u a l height of the armour l a y e r does not appear to a f f e c t the s t a b i l i t y of the u n f i l t e r e d bed m a t e r i a l . The r e s u l t s obtained are shown i n Table 2.
31. An e m p i r i c a l r e l a t i o n s h i p of the form: V = C i ( L / D ) ^
was found best to describe the r e l a t i o n s h i p . C l was found to depend on the grading curve of the bed m a t e r i a l with a r e l a t i o n s h i p :
T y p i c a l graphs are shown i n Figures 2 & 3.
32- The f i n a l equation f o r the stages of motion were found to be:
Stage I : V = 0-63 dJ^O (L^O.S
Stage I I : V = 0.82 d^J^S (L)0.75
Stage I I I : V = 1.08 d^'^ (i)°-'
A t t h i s t i m e the second dlmensionless parameter c o n t a i n i n g d has n o t been p r o p e r l y I d e n t i f i e d and t h e n u m e r i c a l c o e f -f i c i e n t has t h e dimensions:
T - l
3 3 . The occurrence o f macro t u r b u l e n c e o r o b s t r u c t i o n s a t the bed Increases the l o c a l v e l o c i t i e s so d e c r e a s i n g t h e
FLEXIBLE A R M b U R E D R E V E T M E M t S i N C Ö R P O R A T ( N C C E O T E X T I L E S
scout p r o t e c t i o n p r o v i d e d . The hótlzöhtal p o r o s i t y a l s o decreases the bed s t a b i l i t y . Although v e l o c i t i e s approach-i n g 1.5 m/sec were achapproach-ieved, 5 gm and 10 gm armour elements were n o t e n t r a i n e d i n the f l o w , even a d j a c e n t t o c o l l a p s i n g scour holes due t o bed o b s t r u c t i o n s .
34. For p r a c t i c a l purposes, the onset o f Stage I I I I s
the i m p o r t a n t case and an adequate f a c t o r o f s a f e t y must be p r o v i d e d a g a i n s t i t . Stage I I may be i m p o r t a n t when con-s i d e r i n g a b r a con-s i o n o f an I n t e r m e d i a t e f i l t e r c l o t h .
35. I t i s hoped t h a t work may proceed . t o c o n s i d e r
cases where the armour l a y e r can be rendered -unstable b e f o r e the u n d e r l a y e r s , ( i . e . by u s i n g v e r y coarse m a t e r i a l i n t h e u n d e r l a y e r ) b u t t h i s w i l l r e q u i r e s u b s t a n t i a l l y improved water f l o w s compared t o those p r e s e n t l y a v a i l a b l e .
PRACTICAL APPLICATIONS
36. I n A u s t r a l i a , a p p r o x i m a t e l y 1.3 km o f revetments
u s i n g gabions have been designed i n accordance w i t h t h e b l a n k e t t h e o r i e s o u t l i n e d here and d e s c r i b e d i n d e t a i l i n r e f . 5.
37. The Seabee armour u n i t , the p r o g e n i t o r o f a l l t h i s
t h o u g h t , has been taken through successive stages o f development form model 10, 28 and 85 gram u n i t s t o p r o t o t y p e ceramic u n i t s o f 10 t o 20 kg, and p r o t o t y p e concrete u n i t s f o r 0.5 t o 4.0 tonnes mass. This armour u n i t a l l o w s the use of v a r i a b l e p o r o s i t y b o t h normal and p a r a l l e l t o the plane o f t h e revetment as w e l l as mass range i n t h e o r d e r o f 40:1 f o r any p a r t i c u l a r i n s t a l l a t i o n . I t can a l s o s u r v i v e extremely poor q u a l i t y c o n t r o l , p r o v i d i n g a 'tough' design i s u t i l i s e d . The p r a c t i c a l a p p l i c a t i o n s o f t h i s system a r e d e s c r i b e d i n r e f . 8 and some examples shown i n the p l a t e s .
CONCLUSION
38. The g r e a t s i m i l a r i t y between t h e elements o f
t h e o r i e s o f i n c i p i e n t m o t i o n due t o c u r r e n t and wave a c t i o n are seen t o d e r i v e from t h e common d e s c r i p t i o n o f the a c t i v e f o r c e s . What d i f f e r e n c e s t h e r e are i n n a t u r e a r e s t i l l locked up i n our c o e f f i c i e n t s . N e v e r t h e l e s s , by e x e r c i s i n g a degree o f o b j e c t i v i t y i t i s p o s s i b l e t o g a i n more c o n t r o l of t h e m u l t i t u d e o f v a r i a b l e s i n v o l v e d i n t h e design o f c o a s t a l works.
39. I t i s hoped t h a t , wheress i t was u s u a l t o d e t e r
-mine the s i z e o f r o c k s t o be o b t a i n e d ( i f p o s s i b l e ) from the q u a r r y , i t I s now q u i t e f e a s i b l e t o manufacture revetment p r o t e c t i o n i n any s u i t a b l e s i z e a c c o r d i n g t o p r o d u c t i o n and c o n s t r u c t i o n c r i t e r i a , w i t h o u t s a c r i f i c i n g m a t e r i a l economy. I t i s a l s o p o s s i b l e t o design v a r i o u s s e r v i c e c r i t e r i a a t
BfeOWN
thë öamè t i m e , b u t I would recommend t h a t we e r r on t h e s i d e o f s t r u c t u r a l I n t e g r i t y r a t h e r than h y d r a u l i c e x c e l l e n c e , i f e r r we must.
REFERENCES
1. STREETER V.L, Handbook of F l u i d Mechanics, Section 18.7, McGraw H i l l , London, 1961i
2. HUDSON R.y„ S t a b i l i t y of Rubble-mound Breakwaters, W.E.S. Vicksburg, T.M. 2-365, June 1953. 3. HUDSON R,Y, Rubble-mound Breakwaters, Laboratory
I n v e s t i g a t i o n s of Proc. ASCE, Waterways & Harbours D i v i s i o n , Vol. 85, No. WW3, Sept. 1959.
4. BROWN C.T. Blanket Theory and Low Cost Revetments. Chap. 151, 16th ICCE, Hamburg 1978. 5. BROWN C.T. Armour-Units, Random-mass or d i s c i p l i n e d
A r r a y ? ASCE S p e c i a l t y Conference, Coastal Structures 79, Alexandria V i r g i n i a , March, 1979.
6. BROWN C.T. Gabion Report. The Water Research
L a b o r a t o r y o f t h e U n i v r s i t y o f New South Wales, Research Report No. 156, Oct 1979
7- PAGE R. E r o s i o n C o n t r o l u s i n g Seabees.
Under-graduate T h e s i s , N.S.W, I n s t i t u t e o f Technology, Jan. 1983.
8. HANSEN S, I n v e s t i g a t i o n o f Seabees as an E r o s i o n
& KEATS J . C o n t r o l S t r u c t u r e - Undergraduate t h e s e s , N.S.W. I n s t i t u t e o f Technology, Dec.
1983-9. BROWN C.T. Seabees i n S e r v i c e . ASCE S p e c i a l t y .
Conference C o a s t a l S t r u c t u r e s '83, Washington D.C, March 1983. NOTATIONS A Area o f element C C o e f f i c i e n t ^ " b - exponent C Volume C o e f f i c i e n t V Cj,Cjj V o l u m e t r i c c o e f f i c i e n t s f o r I r r i b a r r e n and Hudson t r a n s f o r m a t i o n s
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The Permanent International Association of Navigation Congresses as a body does not accept responsibility for the statements made or for the opinions expressed in the following pages
Published for the Permanent International Association of Navigation Congresses by Thomas Telford Ltd, 26-34 Old Street, PO Box 101, London ECl P lJH
Contents
1. Flexible revetments-theory and practice.
C. T. BROWN
2. Loads on beds and banks caused by ship
propulsion systems. H. U. OEBIUS
3. Proposals of flexible to~. design of revetments.
G. HEERTEN and W. MUHRING
4. Design of bank protection of inland navigation
fairways. H. G. BlAAUW, M. T. de GROOT,
F.
C. M. van der KNMP and K. W. PIIARCZYK5. Geotextiles as filters beneath revetments.
T. S. INGOLD '
n.
Influence of the filtration opening size on soilretention capacity of geotextiles. Y. FAURE,
J.
P. GOURC, and f. SUNDIAS6. Development parameters for integrated flexible
revetment systems. E. G. WISE
7. Technical and economical design of modern
revetments. H.-U. ABROMEIT and H.-G. KNIESS
8. Stablity of Armorflex revetment system under wave
attack. C. van den BERG and
J.
LINDENBERG9. Tubular gabions.
C.
D. Hall10. Geotextiles for bank protection in relation to causes of erosion. F. G. CHARLTON
11. Experience with a flexible interlocking revetment system at the Mittellandkanal in Germany'. since 1973. G. HEERTEN, H. MEYER and W. MUHRING
T2. The ACZ-DELTA mat.
J.
C. DORR, A H. M.BARTELS and P. SCHUlT
12. US Army Corps of Engineers experience with filter fabric for streambank protection applications. M. P. KEOWN and N. R. OSWALT
13. Prototype tests of slope protection systems. K. W. PIIARCZYK
14. Yugoslav experience in constructing revetments incorporating geotextiles. M. BOZINOVIC, M. MILORADOV and E. CIKIC
1 ·13 25 39 59 71 85 99 109 123 131 145 159 171 183 199
2
Loads on beds and banks caused by ship
propulsion systems
Dipl.lng. H. U. OEBIUS, Versuchsanstalt fiir Wasserbau und Schiffbau, Berlin
SYNOPSIS, Using l a t e s t r e s u l t s from i n v e s t i g a t i o n s concern-i n g t h e v e l o c concern-i t y d concern-i s t r concern-i b u t concern-i o n concern-i n p r o p e l l e r j e t s w concern-i t h and w i t h o u t v e l o c i t y head an a t t e m p t i s made t o deduct a l s o loads t o be expected from s h i p p r o p u l s i o n systems l i k e water j e t s and p r o p e l l e r j e t s a c t i n g on beds and embankments o f p o r t s , channels and r i v e r s .
INTRODUCTIOH
1. One o f t h e most i m p o r t a n t p r e s u p p o s i t i o n s f o r t h e e s t i -mation o f t h e degree o f d e s t r u c t i o n o f beds, embankments and revetments i n h a r b o u r s , channels and r i v e r s caused by ma-n o e u v r i h g o r c r u i s i ma-n g v e s s e l s , except t h a t from c o l l i s i o ma-n , i s t h e mathematical d e s c r i p t i o n o f those c u r r e n t s which a c t as c a r r i e r s o f t h e e s s e n t i a l and r e s p o n s i b l e k i n e t i c energy. There are two sources f o r such energy c a r r i e r s , i . e . t h e p r i -mary wave system o f any v e s s e l as w e l l as t h e induced secon-dary wake f i e l d , and t h e p r o p u l s i o n j e t as product o f t h e necessary impulse system t o push t h e v e s s e l i n t h e d e s i r e d d i r e c t i o n , i n c l u d i n g bow t h r u s t e r s and s i m i l a r p r o p u l s i o n s y -stems.
2. I t i s obvious t h a t wave and wake f i e l d s as r e s u l t from the surmounting o f t h e blockage r e s i s t a n c e o f t h e water body a g a i n s t i t s displacement by t h e moving s h i p a r e t h e r e f o r e c a u s a l l y connected w i t h t h e displacement speed o f t h e v e s s e l r e l a t i v e t o t h e s u r r o u n d i n g water body ( n o t r e l a t i v e t o t h e bed!) and are t h e more s i g n i f i c a n t t h e h i g h e r t h e speed o r the blockage e f f e c t a r e . Under normal c r u i s i n g c o n d i t i o n s the i n f l u e n c e s . f r o m these c u r r e n t s exceed t h a t from t h e p r o -p u l s i o n system by f a r . U n f o r t u n a t e l y u n i v e r s a l s o l u t i o n s f o r the loads t o be expected have n o t been f o u n d , y e t , a l t h o u g h these e f f e c t s have been s u b j e c t t o d i v e r s e i n v e s t i g a t i o n s ( r e f . 1 ) . . .
3. B a s i c a l l y t h e degree o f d e s t r u c t i o n due t o t h e i n f l u -ence from p r o p u l s i o n systems i s t h e more d i s t i n c t t h e h e a v i e r t h i s p r o p u l s i o n system i s loaded ( i . e . t h e g r e a t e r t h e imp u l s e o f t h e system i s ) , t h e e a s i e r t h e revetments can be r e -moved by t h e impact o f t h e j e t and. t h e l o n g e r t h e t i m e o f a t t a c k i s , i . e. t h e lower t h e s h i p speed r e l a t i v e t o t h e
FLEXIBLE A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G G E O T E X T I L E S
a t t a c k e d area i s . Indeed t h e g r e a t e s t d e s t r u c t i o n s occur a t those p l a c e s , where v e s s e l s are s t a n d i n g , s t a r t i n g o r ma-n o e u v r i ma-n g w i t h low speed, i . e . i ma-n f r o ma-n t o f p i e r s , i ma-n b a s i ma-n s , at t u r n i n g b a s i n s , a t o u t e r harbours i n f r o n t o f l o c k s and docks, e t c . That t h e y can reach enormous dimensions has been demonstrated by a t e s t w i t h an i n l a n d s h i p accomplished by the Bundesanstalt f i i r Wasserbau, K a r l s r u h e , i n a d e s e r t e d channel ( r e f . 2) (see F i g . l ) .
.Fig. 1 Scour induced by i n l a n d s h i p
PHYSICAL BACKGROUND OF PROPULSION SYSTEMS
h. P h y s i c a l l y seen t h e p r o p u l s i o n system's t a s k i s t o a c c e l l e r a t e a i r o r water i n such manner t h a t an impulse o f d i s t i n c t f o r c e and d i r e c t i o n i s produced, which from modern p r o p u l s i o n systems g e n e r a l l y w i l l be a j e t from e i t h e r submerged nozzles o r f r o m p r o p e l l e r s . Due t o i n t e r n a l f r i c t i o n between t h i s j e t and t h e s u r r o u n d i n g f l u i d w i t h i n c r e a s i n g d i s t a n c e from t h e o r i f i c e t h e diameter o f t h e j e t i s i n c r e a s i n g t o o , a c c e l l e r a t i n g p a r t s o f t h e s u r r o u n d i n g f l u i d , a t t h e same t i m e consuming k i n e t i c energy from t h e core v e l o c i t y o f t h e j e t , r e s u l t i n g i n a decrease o f t h e maximum v e l o c i t y . Due t o t h i s s p r e a d i n g t h e j e t e v e n t u a l l y reaches t h e water s u r f a c e and/or t h e bed and w a l l s o f t h e b a s i n , where t h e j e t d i s s o l v e t r a n s f e r r i n g i t s k i n e t i c energy t o t h e boundary. Loads from these energies are t h e r e f o r e d i r e c t l y connected w i t h t h e ac-t u a l a x i a l and ac-t a n g e n ac-t i a l v e l o c i ac-t i e s nx,y,z a-nd yx,y,z a ac-t ac-t h e l o c a t i o n x,y,z i n t h e i n t e r f a c e . I n r o t a t i o n a l symmetrical j e t s y^ + = r ^ . The d e t e r m i n a t i o n o f t h e v e l o c i t y d i s t r i -b u t i o n i n a plane o r c i r c u l a r water j e t and a p r o p e l l e r j e t w i t h and w i t h o u t v e l o c i t y head (which r e p r e s e n t s t h e c u r r e n t
O E B I U S
o f t h e f l u i d o r t h e t r a n s i t i o n speed o f t h e s h i p ) w i l l t h e r e -f o r e be t h e -f i r s t step towards t h e d e -f i n i t i o n o -f t h e a c t u a l loads from p r o p u l s i o n systems.
5. V e l o c i t y d i s t r i b u t i o n i n j e t s w i t h o u t v e l o c i t y head.
From i n v e s t i g a t i o n s by Kraatz ( r e f . 3) and Wiegel ( r e f . h) we know t h a t g e n e r a l l y t h e v e l o c i t y d i s t r i b u t i o n i n j e t s f o l -lows GauB's law o f t h e normal d i s t r i b u t i o n o f e r r o r s o f ob-s e r v a t i o n ( r e f . 5 ) . T h i ob-s law fix) =-rj==:' e x p [ - ^ ( | ) ' j ( 1 ) can be t r a n s f o r m e d w i t h f ( x ) = u , = u and x = r ' (see F i g . 2) t o ""'^ C5 ^ 2 ^ '^^'^ r 1 r ' ^-1 u = u • exp - — ("TF-) , ( 2 ) x , r max 2 J ' ^ ' which i s v a l i d f o r a l l k i n d s o f j e t s and a l s o f o r a l l s o r t s o f v e l o c i t y heads a f t e r d e f i n i t i o n and adjustment o f t h e main parameters
\ a x ' ^ 0 ' ^ ' ' ^ = ^('^O'
a c c o r d i n g t o t h e i n d i v i d u a l f l o w c o n d i t i o n s o f t h e f l u i d .
F i g . 2 Schematic o u t l a y o f t h e v e l o c i t y d i s t r i b u t i o n i n a p r o p e l l e r j e t
F L E X I B L E A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G G E O T E X T I L E S
By e x t e n s i v e t e s t s i n t h e VWS, B e r l i n , these parameters have been d e f i n e d e m p i r i c a l l y and l e a d t o t h e e q u a t i o n s u„ _ = e x p [ - - ( ) J ( 3 ) x , r 0 0 f o r t h e c i r c u l a r water j e t and r - [ 0 . 3 B,- (f-)-°-^J U = 'O-n' S X p x , r 0 ^ r _ l ( 0 ) ' ] (h) f o r t h e p r o p e l l e r j e t i n t h e zone o f e s t a b l i s h m e n t (O-^-X.<£.XQ; Xp = 2 DQ; see F i g . 2 ) , as w e l l as n = — exp - ^ ( ^ r ) ( 5 ) 2[ | 0 + 0. 0 8 0 7 (X - X Q ) J 2 | O + 0 . 0 8 0 7 ( X - X Q ) ^ f o r t h e c i r c u l a r water j e t and , ^ ,x , - 0 . 6 r 1 , ° ( 6 ) • exp - -X ;: „ _n ^ ^ ^ 1 0 + 0 . 0 8 7 5 ( X - X Q ) - [ 0 . 3 D Q ( ^ ) ° - ^ ] - ' f o r t h e p r o p e l l e r j e t i n t h e zone o f d i f f u s i o n [x^^ x .cco ). The parameter Do r e p r e s e n t s t h e f r e e n o z z l e o u t l e t a t c i r c u -l a r water j e t s o r equa-ls DQ = 2 ( 0 . 6 7 Rp + Rjj) ( T ) a t p r o p e l l e r j e t s , t h e parameter U g r e p r e s e n t s t h e maximum core v e l o c i t y i n t h e zone o f e s t a b l i s h m e n t . I t can be com-puted a c c o r d i n g t o p i p e f l o w approaches i n t h e case o f water j e t s and a c c o r d i n g t o I s a y ( r e f . 6 ) o r Lerbs ( r e f . 7 ) i n case o f p r o p e l l e r s . For t h e l a t t e r one computer programs a r e a v a i l -a b l e . Comp-arisons o f computed -and me-asvired d-at-a f o r c i r c u l -a r water j e t s (see F i g . 3 ) and p r o p e l l e r j e t s (see F i g . k) show t h e a p p l i c a b i l i t y o f t h e e q u a t i o n s ( 3 ) t o ( 6 ) .
6 . V e l o c i t y d i s t r i b u t i o n i n j e t s w i t h v e l o c i t y head. Here o n l y experiences w i t h p r o p e l l e r j e t s a r e a v a i l a b l e . But i f t h e v e s s e l s are s a i l i n g a t low speeds V Q = 0 . 5 k t s , t h e equa-t i o n s ( 3 ) and ( 5 ) may be used f o r c i r c u l a r water j e t s w i t h v e l o c i t y head, t o o , w i t h o u t c a u s i n g t o o g r e a t e r r o r s . From t h e l a t e s t i n v e s t i g a t i o n s t h e v e l o c i t y d i s t r i b u t i o n i n a p r o p e l l e r j e t w i t h v e l o c i t y head can be w r i t t e n a c c o r d i n g t o e q u a t i o n (2) 16 O E B l U S
F i g . 3 Computed versus measured v e l o c i t i e s i n a c i r c u l a r water j e t w i t h o u t v e l o c i t y head
T • I I I I I B I '• I I I I I t I I I ' B
0,5 1.0 1,5 — ^ U j , 2.0 m / s
F i g . It Computed versus measured v e l o c i t i e s i n a p r o p e l l e r j e t w i t h o u t v e l o c i t y head
FLEXIBLE A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G C E O T E X T I L E S r - - ( x ) 2. r 1 2' ^ , r . = "0- L - 2 ^ D . D , ^ ) J ( 8 ) f o - | ( x ) i n t h e zone o f e s t a b l i s h m e n t (O / ^ X Z X Q) w i t h xp = 2 • D ; . exp [1.265 (9) and \ n o ^-0.3 ( 1 0 ) - ( x ) = 0.3 D Q ( P ^ ) , DQ b e i n g = 1.15 • • u ^ ° 5 5 ( „ ) According t o e q u a t i o n (2) t h e v e l o c i t y d i s t r i b u t i o n i n t h e zone o f d i f f u s i o n (XQ.<^ x.<i°o) f o l l o w s t h e b a s i c l a w f- . r - f ( x ) 2 w i t h -max= ^-5 • -0 ' (13) fi b e i n g = 0.6 • exp [ - 1.2 ^ ] ( l U )
t h e diameter o f t h e core zone (zone o f hub v o r t i c e s ) equiva-l e n t t o e q u a t i o n ( 1 0 ) , t h e geometric p o s i t i o n o f t h e p o i n t s o f i n f l e c t i o n o f t h e Gaufi-curve
<5j^ = |o - §(x) + O . O T ( x - X Q ) (15)
and x ^ a c c o r d i n g t o equ. ( 9 ) . A comparison o f computed and measured v e l o c i t y d i s t r i b u t i o n w i t h v e l o c i t y head i s g i v e n i n F i g . 5.
LOADS ON BEDS AND EMBANKMENTS
T. There a r e t h r e e modes o f t r a n s f e r o f k i n e t i c energy t o beds and embankments, i . e . by shear s t r e s s i n case o f t h e a x i s o f t h e j e t b e i n g p a r a l l e l t o t h e s u r f a c e o f t h e bounda-r i e s , by mixed f o bounda-r c e s fbounda-rom sheabounda-r s t bounda-r e s s and v e bounda-r t i c a l dynamic pressure (and p e r c o l a t i o n f o r c e i n form o f drag f o r c e and v i s cous s k i n f r i c t i o n ) i n cases where t h e a x i s o f t h e j e t s i s i n c l i n e d t o t h e embankments(per d e f i n i t i o n t h i s does n o t o r v e r y seldom occur a t t h e beds) and by mere hydrodynamic p r e s -sure (and p e r c o l a t i o n f o r c e s ) i n cases where t h e a x i s o f t h e j e t a c t s n o r m a l l y t o t h e embankments (see F i g . 6 ) . 18 O E B I U S 0 , U m -r _ luga£0,25 m / s
1 -
O m e a s u r e d1
0 , 1 0 -0,75 m / s u „ = 1.0 m / s V c o m p u t e d - u ^ 0 , 5 m / s I. \ « n P r o p - N o . 1187 ^ 5 ^ x = 0 4 5 m , np=.1000 1/min 0 / ) 5 -<a:^rop.No.1119 ^ ^ ^ ' * ' * < < : > „ ^ = Q S ^ X 3 0 i 3 0 m ^ X ^ ^ 0 / ) 5 -• P r o p . - N a I I B T A xaOlSOm y j n p « 5 0 0 Wmir^Xr j cf h A x « 0 , 1 5 m < ^ " " " "—I—»—1—1—1—1—i—
0.5 1,0 1,5 — ~ U x 2,0 m / sF i g . 5 Computed versus measured v e l o c i t i e s i n a p r o p e l l e r j e t w i t h v e l o c i t y head
F i g . 6 Schematic p r e s e n t a t i o n o f t h e v e l o c i t y f i e l d s i n w a l l j e t s , i n c l i n e d and i m p i n g i n g j e t s
Loads induced by p a r a l l e l j e t s
8. The d e t e r m i n a t i o n o f t h e sought a f t e r shear s t r e s s
en-sues from c u t t i n g t h e j e t w i t h t h e s u r f a c e area i n t h e g i v e n i n d i v i d u a l d i s t a n c e o f t h e j e t from t h e s u r f a c e o f t h e bed o r embankment p a r a l l e l l y t o t h e a x i s o f t h e j e t . I n t h i s case t h e s a t i s f a c t i o n o f t h e boundary c o n d i t i o n s r e q u i r e s t h a t t h e s y -stem has t o be r e f l e c t e d a t t h e b o u n d a r i e s . As moveable boun-d a r i e s - except t h e water s u r f a c e - behave l i k e r i g i boun-d w a l l s under t h e i n f l u e n c e o f shear s t r e s s e s ( r e f . 5 ) , a t o t a l r e f l e c -t i o n o f -t h e c u r r e n -t s can be expec-ted, h e r e , r e s u l -t i n g i n a d o u b l i n g o f t h e v e l o c i t y i n t h e r e f l e c t i o n p l a n e . T h e r e f o r e t h e determined l o c a l v e l o c i t i e s i n t h e c u t t i n g p l a n e have t o be i n c r e a s e d by a f a c t o r 2, and so have t h e shear v e l o c i t i e s
U j j . W a l l shear s t r e s s and f i c t i v e shear v e l o c i t y a r e combined
by ( r e f . 8)
T o = ^ J. • u | . (16)
For rough boundaries t h e shear v e l o c i t y and t h e l o c a l v e -l o c i t y U/ ; a r e combined by a -l o g a r i t h m i c t r a n s i t i o n -law o f t h e form^'''''^
u, V 2.3 r„
_ k ^ = _ _ , o , ( _ ) . B ( I T )
* s
w i t h k = Karman c o n s t a n t = 0,k, ~ mean roughness diameter ~ D 5 0 , k = Nikuradse roughness ~ 0 . 5 -D C Q and B = 8.5 f o r com-p l e t e l y rough b o u n d a r i e s , u^ s u b s t i t u t e d by equ. (16) t h e n f o l l o w s t o
'^0 = ^ F • < x , r ) - (5.75 l o g ( ^ ) . 8 . 5 ) - ' . (18)
s
I f t h e c r i t i c a l w a l l shear s t r e s s f o r t h e e r o s i o n o f a boun-dary i s known, equ. ( i T ) can be reduced t o
- ( x , r ) c r i t = " * c r i t - l o g ( ^ ) . 8.5 (19) w i t h u ^ ^ ^ . ^ = (T ^ ^ . ^ / ^ F) ^ ^ ^ - Equs. ( 3 ) , ( M , (5) o r (6) r e -duced t o r and u, s u b s t i t u t e d by u/ ^> ^ ^ ^ r e s u l t i n t h e geometric p o s i t i o n ' o f c r i t i c a l w a l l sheaf S t r e s s a l o n g t h e j e t a x i s . Loads induced by i n c l i n e d j e t s
9. The loads from i n c l i n e d j e t s a c t i n g on beds and
embank-ments r e s u l t from two h y d r o d y n a m i c a l l y d i f f e r e n t procedures which can be d e s c r i b e d as impingement and as w a l l j e t e f f e c t . Whereas i n t h e w a l l j e t zone a g a i n o n l y loads from shear s t r e s s e s o c c u r , i n t h e impingement area t h e loads upon t h e boundary s u r f a c e are dominated by dynamic p r e s s u r e ( F i g . 6 ) . The e f f e c t s i n t h e impingement zone are t h e same as from j e t s a c t i n g normal t o w a l l s due t o t h e f a c t , t h a t t h e a x i s o f i n -c l i n e d j e t s seems t o bend t o d i r e -c t i o n s normal t o t h e boundary
2 0
s u r f a c e ( F i g , 6 ) , B e l t a o s ( r e f . 11) found a r e l a t i o n s h i p b e t -ween t h e maximum p r e s s u r e and a r e s u l t i n g w a l l shear s t r e s s due t o t h e d e f l e c t i o n o f t h e v e r t i c a l c u r r e n t t o be
"^Omax = • Ps • '^^'^ (20) w i t h c^ = 0 . 1 6 6 , t = angle o f i n c l i n a t i o n and p = t h e
mo-mentum, due t o t h e c e n t e r v e l o c i t y o f t h e j e t , a c t i n g on an area w i t h t h e diameter D , which i s d e f i n e d hy DQ a t f r e e wa-t e r j e wa-t s and D, , a wa-t p r o p e l l e r s i n wa-t h e d i s wa-t a n c e H from t h e o r i f i c e
<2,F JT. 2
= _ _ . _ _ . ^ ^ ^ ^ . ( 2 1 )
The maximum a c t u a l shear s t r e s s i n t h e impingement zone t h e n f o l l o w s t o
T „ = 0,166 • . u ' • s i n t . (22)
Omax F h xmax
10. As from experiments i t has been f o u n d t h a t f o r angles
g r e a t e r t h a n ^ = t h e e r o s i o n i n t h e impingement zone i s s i g n i f i c a n t l y g r e a t e r t h a n i n t h e w a l l j e t zone, f o r e s t i m a -t i o n s c o n c e r n i n g l o a d s from p r o p e l l e r s o n l y equ, (22) should be used. I n a l l cases where }5° ^ ^ h5°\ t h e w a l l shear s t r e s s T ^ ^ ^ s h o u l d be computed a c c o r d i n g t o B e l t a o s ( r e f . l l ) :
V x • ° - 0 9 8 R ; ° - ' , ( 2 3 )
'^max t h e maximum r e f l e c t e d v e l o c i t y a t t h e p o s i t i o n x', equal t o t h e c e n t e r v e l o c i t y o f t h e j e t a t t h e d i s t a n c e x from t h e o r i f i c e , and R ^ b e i n g t h e Reynolds number a t t h e o r i f i c e
Loads induced by i m p i n g i n g j e t s
11. Erosions by j e t s a c t i n g n o r m a l l y t o t h e boundary s u r
-f a c e r e s u l t -from two e -f -f e c t s which have t o be superponed (see F i g . 6 ) , i . e . an impingement impact due t o dynamic p r e s s u r e o n l y and a shear e f f e c t from t h e d e f l e c t i o n o f v e r t i c a l t o r a d i a l v e l o c i t i e s . While t h e impingement e f f e c t i s s t r o n g l y dependent on t h e r e l a t i v e d i s t a n c e o f t h e o r i f i c e from t h e boundary H / D Q, t h e shear e f f e c t i s o n l y dependent from t h e development o f t h e v e l o c i t i e s p a r a l l e l t o t h e boundary s u r -f a c e and reaches i t s maximum a t t h e r e l a t i v e o r i -f i c e Z (see f i g u r e 6) i n t h e d i s t a n c e r^. from t h e s t a g n a t i o n p o i n t S.
12. The dynamic p r e s s u r e i n t h e impingement area has been
-d e s c r i b e -d by Kobus, L e i s t e r an-d W e s t r i c h ( r e f . 12) by
Ps = S • -^r/ • 5T exp [ - l i l t (£-)2] (25)
FLEXIBLE A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G C E O T E X T I L E S and I Q r e s u l t i n g from = • = 0.07 • P3 ( 2 6 ) The shear s t r e s s i n t h e w a l l j e t r e g i o n , s t a r t i n g a t t h e s t a g n a t i o n p o i n t , i s d e s c r i b e d by B e l t a o s ( r e f . 11) ( 2 7 ) w i t h r b e i n g t h e diameter o f t h e j e t a t t h e d i s t a n c e x from the o r i f i c e . £ i s a f u n c t i o n o f t h e r e a c t i o n t i m e T g c r i t i c a l s h e a r v e l o c i t y u,^^^^^ and ^•^'S o f t h e o r i f i c e from t h e b o u n d a r y ' ^ s u r f a c e . SCOURING 13. The e r o s i o n the v e l o c i t y u, the d i s t a n c e r ^
F i g . 7 g i v e s an example f o r t h e development o f scours as func-t i o n i f func-these paramefunc-ters. I func-t can be seen func-t h a func-t aboufunc-t 50 % o f the f i n a l e r o s i o n depth i s reached w i t h i n h a l f an hour, a r e l a t i v e l y l o n g t i m e compared w i t h t h e r e a l r e a c t i o n t i m e . T h i s means t h a t t h e r i s k o f damages i n r e g i o n s o f low d e n s i t y o f t r a f f i c i s low, b u t extremely h i g h i n areas which are v e r y near t o t h e p r o p u l s i o n system o r where t h e sequence o f i n d i -v i d u a l e-vents i s -v e r y s h o r t t h u s p r o -v o k i n g l o n g t e r m e f f e c t s . 0,15m em 0.10 i 0.051 F i g . 7 E r o s i o n depth £ as f u n c t i o n o f r e a c t i o n time T r m c 22 O E B I U S CONCLUSION
1I4. The equations mentioned above are d i m e n s i o n a l l y c o r r e c t and g e n e r a l l y p h y s i c a l l y based but have t o be regarded a t as rough e s t i m a t i o n s o f t h e loads t o be expected. The formulae do not s a t i s f y h i g h s t a n d a r d s , because t h e y r e p r e s e n t i n nearl y a nearl nearl cases s i m p nearl i f i c a t i o n s f o r p r a c t i c a nearl reasons. Those i n -t e r e s -t e d i n more d e -t a i l s are k i n d l y r e f e r r e d -t o -t h e o r i g i n a l papers.
15. The developed equations enable t h e engineer t o e s t i
mate damages a t beds, embankments and revetments from p r o p u l -s i o n -sy-stem-s a l t h o u g h t h e d e f i n i t i o n o f t h e c r i t i c a l -shear s t r e s s e s f o r t h e b e g i n n i n g o f e r o s i o n w i l l be d i f f i c u l t i n many cases. They are known p r a c t i c a l l y o n l y f o r l o o s e sedim-ments.
REFERENCES
1. SCHUSTER,S. Untersuchungen über Strömungs- und
Wider-s t a n d Wider-s v e r h a l t n i Wider-s Wider-s e b e i der F a h r t von S c h i f f e n a u f beWider-schrank- beschrank-tem Wasser. Jahrbuch der STG, 1952, 1*6, 2l*l4-280.
2. FELKEL, K.; H. STEINWELLER. N a t u r - und Modellversuche
über d i e Wirkung der S c h i f f e a u f F l u f i s o h l e n aus Grobkies ( B r e i s a c h e r Versuche). Die W a s s e r w i r t s c h a f t , 1972, 62, 8, 2h3 - 21*9.
3. KRAATZ, W. Strömungsverhalten und V e r t e i l u n g h o r i z o n t a l
an der Oberflache e i n g e l e i t e t e r Beckenzuflüsse. Wasserwirt-s c h a f t - WaWasserwirt-sWasserwirt-sertechnik, 1972, 2 2 , 3, 102 - IOU; 1972, 22, 5,
171 - 175.
1*. WIEGEL, R.L.; J . MOBAREK; Ï. YEN. Discharge o f warm
wa-t e r j e wa-t over s l o p i n g bowa-twa-tom. H y d r a u l i c Eng. Lab., U n i v e r s i wa-t y o f C a l i f . , B e r k e l e y , 196O.
5. OEBIUS, H.U.; S. SCHUSTER. A n a l y t i s c h e und e x p e r i m e n t e l
-l e Untersuchungen über den E i n f -l u B von Schraubenprope-l-lern a u f bewegliche Gewassersohlen. V e r s u c h s a n s t a l t für Wasserbau und S c h i f f b a u , 1919, VWS-Report No. 8U8/79.
6. ISAY, A. P r o p e l l e r t h e o r i e . S p r i n g e r V e r l a g B e r l i n
-Göttingen - H e i d e l b e r g , 196I».
7. LERBS, H. Ergebnisse der angewandten T h e o r i e des S c h i f f s
-p r o -p e l l e r s . Jahrbuch der STG 1955, i»9, 163 - 206.
8. SCHLICHTING, H. G r e n z s c h i c h t t h e o r i e . G. Braun V e r l a g ,
K a r l s r u h e 1965.
9. OEBIUS, H.U. Shear s t r e s s and hydrodynamic pressure
mea-surements a t sea beds. Proc. o f Oceans '83, San F r a n c i s c o ,
1983.
10. ZIPPE. H.; W. GRAF. T u r b u l e n t boundary-layer f l o w over
permeable and non-permeable rough s i i r f a c e s . J o u r n a l o f Hy-d r a u l i c Research 1983, 21, 1, 51 - 65.
11. BELTAOS, S. Oblique impingement o f c i r c u l a r t u r b u l e n t
-j e t s . J o u r n a l o f H y d r a u l i c Research 1976, l l * , 1, IT - 36.
12. KOBUS, H..; P. LEISTER; B. WESTRICH. Flow f i e l d and
s c o u r i n g e f f e c t s o f steady and p u l s a t i n g j e t s i m p i n g i n g on a moveable bed. J o u r n a l o f H y d r a u l i c Research 1979, 17, 3,
175 - 192.
OEBIUS CONCLUSION
li». The e q u a t i o n s mentioned above a r e d i m e n s i o n a l l y c o r r e c t and g e n e r a l l y p h y s i c a l l y based b u t have t o be regarded a t as rough e s t i m a t i o n s o f t h e loads t o be e x p e c t e d . The f o r m u l a e do not s a t i s f y h i g h s t a n d a r d s , because t h e y r e p r e s e n t i n n e a r l y a l l cases s i m p l i f i c a t i o n s f o r p r a c t i c a l reasons. Those i n -t e r e s -t e d i n more d e -t a i l s a r e k i n d l y r e f e r r e d -t o -t h e o r i g i n a l papers.
15. The developed e q u a t i o n s enable t h e engineer t o e s t i
mate damages a t beds, embankments and revetments from p r o p u l -s i o n -sy-stem-s a l t h o u g h t h e d e f i n i t i o n o f t h e c r i t i c a l -shear s t r e s s e s f o r t h e b e g i n n i n g o f e r o s i o n w i l l be d i f f i c u l t i n many cases. They a r e known p r a c t i c a l l y o n l y f o r l o o s e sedim-ments.
REFERENCES
1. SCHUSTER,S. Untersuchungen über Strömungs- und Wider-s t a n d Wider-s v e r h a l t n i Wider-s Wider-s e b e i der F a h r t von S c h i f f e n a u f beWider-schrank- beschrank-tem Wasser. Jahrbuch der STG, 1952, h6, 2l*lt-280.
2. FELKEL, K.; H. STEINWELLER. N a t u r - und Modellversuche
über d i e Wirkung der S c h i f f e a u f F l u f i s o h l e n aus Grobkies ( B r e i s a c h e r Versuche). Die W a s s e r w i r t s c h a f t , 1972, 62, 8, 2U3 - 2l»9.
3. KRAATZ, W. Strömungsverhalten und V e r t e i l u n g h o r i z o n t a l
an der O b e r f l a c h e e i n g e l e i t e t e r Beckenzuflüsse. W a s s e r w i r t -s c h a f t - Wa-s-sertechnik, 1972, 22, 3, 102 - IOU; 1972, 22, 5,
171 - 175.
h. WIEGEL, R.L,; J , MOBAREK; Y. YEN. Discharge o f warm wa-t e r j e wa-t over s l o p i n g b o wa-t wa-t o m . H y d r a u l i c Eng. Lab., U n i v e r s i wa-t y o f C a l i f . , B e r k e l e y , 196O.
5. OEBIUS, H.U.; S. SCHUSTER. A n a l y t i s c h e und e x p e r i m e n t e l
-l e Untersuchungen über den E i n f -l u f -l von S c h r a u b e n p r o p e -l -l e r n a u f bewegliche Gewassersohlen. V e r s u c h s a n s t a l t für Wasserbau und S c h i f f b a u , 1919, VWS-Report No. 8148/79.
6. ISAY, A. P r o p e l l e r t h e o r i e . S p r i n g e r V e r l a g B e r l i n
-Göttingen - H e i d e l b e r g , 196U.
7. LERBS, H. Ergebnisse der angewandten T h e o r i e des S c h i f f s
-p r o -p e l l e r s . Jahrbuch der STG 1955, ^9, l 6 3 - 206.
8. SCHLICHTING, H. G r e n z s c h i c h t t h e o r i e . G. Braun V e r l a g ,
K a r l s r u h e I 9 6 5 .
9. OEBIUS, H.U. Shear s t r e s s and hydrodynamic p r e s s u r e
mea-surements a t sea beds. Proc. o f Oceans '83, San F r a n c i s c o , 1983.
10. ZIPPE. H.; W. GRAF. T u r b u l e n t b o u n d a r y - l a y e r f l o w over
permeable and non-permeable rough s u r f a c e s . J o u r n a l o f Hy- • d r a u l i c Research 1983, 21, 1, 51 - 6 5 .
11. BELTAOS, S. Oblique impingement o f c i r c u l a r t u r b u l e n t
j e t s . J o u r n a l o f H y d r a u l i c Research 1976, ll<, 1 , IT - 36.
12. KOBUS, H..; P. LEISTER; B. WESTRICH. Flow f i e l d and
s c o u r i n g e f f e c t s o f steady and p u l s a t i n g j e t s i m p i n g i n g on a moveable bed. J o u r n a l o f H y d r a u l i c Research 1979, I T , 3,
Proposals of flexible toe design of
revetments
Dr Ing. G. HEERTEN, Naue Fasertechnik, Espelkamp and
Dipl.lng. W. M Ü H R I N G , Neubauamt Mittellandkanal. Osnabrück, West Germany
SrNOPSIS. Revetments a r e f r e q u e n t l y damaged by s c o u r a t r e v e t m e n t t o e . I f they a r e c o n s t r u c t e d by t r a d i t i o n a l methode, s c o u r a t the toe i n e v i t a b l e r e s u l t s I n l o s s o f s t a b i l i t y . S c o u r i s n a t u r a l l y more l i k e l y to o c c u r a t the t r a n s i t i o n between the p r o t e c t e d and u n p r o t e c t e d p a r t o f the c a n a l bed.
C o n s e q u e n t l y , adequate toe p r o t e c t i o n i s h i g h l y i m p o r t a n t f o r the e n t i r e r e v e t m e n t . T h i s p a p e r w i l l p r o v i d e t h e i n f o r m a t i o n on the f u n d a m e n t a l s o f r e v e t m e n t toe d e s i g n , the f i n d i n g s o f t e s t s on d i f f e r e n t t y p e s o f f l e x i b l e toe c o n s t r u c t i o n on the M i t t e l l a n d C a n a l i n Germany, and new recommended t o e c o n s t r u c t i o n s .
INTRODUCa?ION
1. One the c o n s t r u c t i o n o f c a n a l s i n C a t e g o r y IV, the C o n f e r e n c e o f E u r o p e a n T r a n s p o r t M i n i s t e r s recom-mends a waterway c r o s s - s e c t i o n a l a r e a a t l e a s t ^ t i m e s the c r o s s - s e c t i o n a l a r e a of a f u l l y l o a d e d t y p i c a l v e s s e l . Depending on l o c a l c o n d i t i o n s , c o n s t r u c t i o n i s c a r r i e d out i n t h r e e t y p i c a l c r o s s s e c t i o n s f o r t e c h n i -c a l and e -c o n o m i -c a l r e a s o n s ( s e e F i g .1 ) . A2.00 —
1 1
! 0.00 mi i
, - *.ÓÓm- - ^ f ^ ^ T —
Fig.1
FLEXIBLE A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G C E O T E X T I L E S
BAM PfiOTECTION
Bevetment c o n s t r u c t i o n 2. The p r i n c i p l e s u s e d i n t h e d e s i g n and c o n s t r u c t i o n o f r e v e t m e n t s i n e x p a n s i o n work on c a n a l s a r e based on e x p e r i e n c e s accumulated i n p r a c t i c e . I n t h e c o u r s e o f e x p a n s i o n , d i f f i c u l t i e s a r o s e because i t was accompanied by a s t r u c t u r a l change i n i n l a n d s h i p p i n g brought about by the r e p l a c e m e n t o f t h e o l d towed b a r g e s by s e l f -p r o -p e l l e d s h i -p s w h i c h i n c r e a s e d t h e s t r e s s on r e v e t m e n t s and had u n f o r s e e a b l e e f f e c t s on t h e i r d u r a b i l i t y . 3. Growing e x p e r i e n c e a c q u i r e d d u r i n g many y e a r s of work on t h e M i t t e l l a n d C a n a l , f o r example, l e d t o the development o f s t a n d a r d r e v e t m e n t c o n s t r u c t i o n methods w h i c h g u a r a n t e e d f a r l o n g e r l i f e f o r aprons and s i m i l a r bank p r o t e c t i o n c o n s t r u c t i o n s . T h i s work had t o be done w i t h o u t d i s r u p t i n g s h i p p i n g and i n v o l v e d placement o f a l o n g - l a s t i n g f i l t e r l a y e r c o v e r e d by an apron t h a t p r o t e c t e d the r e v e t m e n t a g a i n s t t h e e r o s i v e e f f e c t o f s h i p p i n g and w a t e r .4 . T e a r s o f p r a c t i c a l development work, f o r eyample, have shown t h a t heavy m u l t i - l a y e r g e o t e x t i l e f i l t e r s c o v e r e d by bonded r i p - r a p o r f l a t composite m a t e r i a l s ensure adequate p r o t e c t i o n ( s e e P i g .2 ) .
Fig.2
Rem^eoble revefment 5 . Without g o i n g i n t o t h e d e t a i l s o f t h e s e g e o t e x -t i l e f i l -t e r s and -t h e p r o -t e c -t i v e r i p - r a p l a y e r , i -t c a n be s a i d t h a t t h i s method o f p l a c i n g permeable r e v e t -ments h a s r e a c h e d a s t a n d a r d t h a t promisee l o n g - l i f e d u r a b i l i t y .DESIGN OP HEVENTMENT TOE G e n e r a l e x r i e r i e n c e s
6. D u r i n g t h e develpoment o f t h i s new type of
r e v e t m e n t , a t t e n t i o n was f o c u s s e d f o r a l o n g time on the c o n s t r u c t i o n o f t h e elements on t h e a c t u a l s l o p e . 26 H E E R T E N and M Ü H R I N G Although I t was g e n e r a l l y r e a l i s e d t h a t " a r e v e t m e n t i s o n l y a s good a s i t s t o e " , no s p e c i f i c c o n s i d e r a t i o n was g i v e n to i t s d e s i g n . 7 . I n i t i a l l y , t h i s was u n n e c e s s a r y anyway,as t h e need f o r a new approach i n r e v e t m e n t c o n s t r u c t i o n
a r o s e a u t o m a t i c a l l y a s a r e s u l t o f n e g a t i v e e x p e r i e n c e s i n bank p r o t e c t i o n ,
8. The need t o g i v e c l o s e r a t t e n t i o n t o t h e d e s i g n
of t h e t o e s i n r e v e t m e n t c o n s t r u c t i o n o n l y became a c u t e a f t e r the r e v e t m e n t on t h e s l o p e had r e a c h e d an a c c e p t a b l e s t a n d a r d . There were two r e a s o n s f o r t h i s .
9 . P i r s t l y , s c o u r had p r e v i o u s l y been d e l a y e d o r l e f t u n d i s c o v e r e d because the toe was n o r m a l l y o v e r -c o v e r e d by s t o n e s s l i d i n g down the s l o p e from unbonded r i p - r a p .
1 0 . Underwater e x c a v a t i o n i s t done m a i n l y w i t h s u c -t i o n c u -t -t e r - d r e d g e r s . Depending on -t h e p r o p o r -t i o n o f f i n e s i n t h e s o i l , p a r t of t h e s p o i l i s h e l d i n s u s -p e n s i o n and c a r r i e d away from t h e w o r k -p i t by t h e c u r r e n t from s h i p p i n g i n t o s t i r r o u n d i n g a r e a s . I t s u b s e q u e n t l y s e t t l e s a t t h e b r e a k p o i n t between t h e b£tnk and c a n a l bed, c o v e r i n g t h e stone p i t c h i n g o f the t o e .
1 1 . T h i s sediment i s t r a n s p o r t e d f u r t h e r by c a n a l c u r r e n t s and t h e wash from s h i p p i n g u n t i l i t r e a c h e s a r e a s , l i k e t u r n i n g p o i n t s o r w i d e r s t r e t c h e s o f t h e waterway, where the l o w e r v e l o c i t y o f t h e c u r r e n t a l l o w s the suspended m a t t e r t o s e t t l e permanantly. As soon a s t h i s sediment r e a c h e s a c r i t i c a l h e i g h t , i t i s e x c a v a t e d . 1 2 . A f t e r s e v e r a l y e a r s the t r o u g h p r o f i l e formed by t h e s e t t l e m e n t o f suspended m a t t e r a g a i n becomes a t r a p e z o i d a l p r o f i l e . 1 5 . Under f u r t h e r s t r e s s from c u r r e n t s i n t h e w a t e r -way, eroded c h a n n e l s and scotir o c c u r on t h e caneQ. bed, and especiauLly a t the t r a n s i t i o n from t h e s t o n e p i t c h i n g of t h e t o e to t h e u n p r o t e c t e d s e c t i o n o f t h e bed
(see P i g ,5 &• 4 ) .
!0.00ni
Rg.3
Measured profile in conol bed Cross secJion
FLEXIBLE A R M O U R E D R E V E T M E N T S I N C O R P O R A T I N G G E O T E X T I L E S
iaOOm
-UDOm,
Length of scour
Fig.
A
Measured profile in canal bed Longitudinal section at the toe
1 4 . P i g . 4 shows the t y p i c a l t r a p e z o i d a l p r o f i l e o f an eroded hed w i t h i r r e g u l a r c h a n n e l s a t the s i d e s and sediment i n the c e n t r e .
1 5 . The s i t u a t i o n becomes c r i t i c a l f o r the toe and, i n d e e d , the e n t i r e r e v e t m e n t when s c o u r s p r e a d s beneath the toe i n the d i r e c t i o n o f i t s b r e a k p o i n t w i t h the bank. When the s c o u r r e a c h e s a l e n g t h , such as t h a t d e s c r i b e d i n P i g .' 4 . the inadequate d e s i g n of the t o e s c a u s e s i t s end to cave i n . Subsequent damage i s
i n e v i t a b l e whenever the m a t e r i a l from the c o l l a p s e d t o e -end f a i l s to f i l l c o m p l e t e l y the d e p r e s s i o n c r e a t e d by s c o u r i n the c a n a l bed. And t h i s i s n o r m a l l y the c a s e , s i n c e the d e s i g n of the toe (depending on t h i c k -n e s s , w e i g t h a-nd type of bo-ndi-ng) g e -n e r a l l y c a u s e s
c o l l a p s i n g m a t e r i a l to b r e a k away i n clumps, which o f t e n encourage f u r t h e r s c o u r .
16. The h i g h e r the bending moment of the toe apron, the g r e a t e r i s the h a z a r d to the whole revetment be-cause the s c o u r can t h e n r e a c h a s f a r a s the b r e a k p o i n t of the bank, c a u s i n g p a r t s of the r e v e t m e n t to c o l l a p s e a l o n g w i t h the t o e .
1 7 . R e p a i r work on the damaged r e v e t m e n t and i t s toe i s not o n l y troublesome b u t a l s o e x p e n s i v e .
C o n c l u s i o n s
18. Up to now f i e l d c o n d i t i o n s have made i t too d i f f i c u l t to o b t a i n an a c c \ i r a t e d e s c r i p t i o n of c u r r e n t s i n the a r e a of eroded beds, so t h e r e has been no way of c a l c u l a t i n g the e x p e c t e d depth and development of s c o u r a s a b a s i s f o r d e s i g n of toe approns.
1 9 . Moreover, i n s t a l l a t i o n of a toe apron c a u s e s v a r i a t i o n s i n the f r i c t i o n and s t a b i l i t y c o e f f i c i e n t s
H E E R T E N and M Ü H R I N G
o f the c a n a l bed, which u n f a v o u r a b l e i n f l u e n c e bed deformation, e s p e c i a l l y i n the a r e a o f the toe apron. U n l i k e ' c o n v e n t i o n a l ' s c o u r , the oncoming f l o w d i r e c t s i t s angle of a t t a c k not v e r t i c a l l y but p a r a l l e l to the p r o t e c t e d end o f the revetment, w h i c h a c t s as a b a f f l e .
2 0 . The o n l y way of f i n d i n g a s o l u t i o n t o t h e s e problems, t h e r e f o r e , i s to a s s e s s the degree of e r o s i o n u n t e r a s p e c i f i c volume o f s h i p p i n g o v e r a g i v e n time and u t i l i s e t h e s e parameters a s e m p i r i c a l g u i d e l i n e s i n d e s i g n work. 2 1 . One i m p o r t e n t p o i n t t h a t s h o u l d be noted i n t h i s c a s e i s t h a t on waterways w i t h the c r o s s e c t i o n a l a r e ^ of the M i t t e l l a n d C a n a l , f o r example, i t h a s been e s t a b l i s h e d t h a t bed deformation i s caused more by c u r r e n t , i . e . the wash from s h i p p i n g , t h a n i t i s by the a c t i o n o f s h i p ' p r o p e l l e r s . These f i n d l i n g s have been confirmed by measurements c a r r i e d out by the B u n d e s a n s t a l t f i i r Wasserbau i n K a r l s r u h e ( I ) .
T h i s f i n d i n g a p p l i e s o n l y to the open waterway and n o t , of c o u r s e , to mooring a r e a s where the a c t i o n of s h i p s ' p r o p e l l e r s i s an e s s e n t i a l f a c t o r i n the d e s i g n o f aprons on c a n a l beds.
2 2 . Another p o i n t t h a t needs c l a r i f y i n g i s whether the sediment i n t h e s e a r e a s i s m e r e l y d i s t r i b u t e d o r whether i t i s c a r r i e d away by the c u r r e n t and c a u s e s permanent d e p r e s s i o n s i n the waterway bed. I n the l a t t e r c a s e , e i t h e r the e n t i r e bed s h o u l d be paved or the waterway c r o s s - s e c t i o n a l a r e a s h o u l d be i n c r e a s e d c o n s i d e r a b l y .
2 3 . Consequently, i t i s e s s e n t i a l to ensure t h a t t h e r e i s no l o n g i t u d i n a l movement of suspended m a t t e r when the c a n a l bed i s n o t p r o t e c t e d a g a i n s t e r o s i o n .
2 4 . When c o n s t i r u c t i o n work i s done ' i n the d r y ' , the problem i s e a s i e r to s o l v e , e i t h e r by e x t e n d i n g the revetment a l o n g i t s a x i s i n t o the c a n a l bed to the e x t e n t of the assumed d e p r e s s i o n ( s e e P i g .5 ) .
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( Composite materal 1
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