01563
MISCELLANEOUS PAPER N O . 2-777
rIYDRAULIC DESIGN OF ROCK
by
F. B. Campbell
February 1966
Sponsored by
Office, Chief of Engineers
U . S. Army
Conducted by
U . S. Army Engineer Waterways Experiment Station C O R P S O F E N G I N E E R S
01563
MISCELLANEOUS PAPER N O . 2-777
HYDRAULIC DESIGN O F ROCK RIPRA
by f.B. Campbell February 1966 Sponsored by O f f i c e , Chief of Engineers U . S. A r m y Conducted by
U . S. A r m y Engineer Waterways Experiment Station C O R P S O F E N G I N E E R S
B i B L i C T H E E K
3 1 OKT. 1966 W a t e r l c o p b n J i g Lc':Dra!oriurr;
Raar^i 61-' - DZLFT
M I S C E L L A N E O U S PAPER NO. 2-777
HYDRAULIC DESIGN OF ROCK RIPRAP
F. B. Campbelli
oilöMii
February 1966
Sponsored by
Office, Chief of Engineers U . S . Army
Conducted by
U . S . Army Engineer Waterways Experiment Station C O R P S O F E N G I N E E R S
Vicksburg, Mississippi
FOREWORD
The d e c i s i o n t o prepare t h i s paper was reached d u r i n g a conference a t the U. S. Army Engineer Waterways Experiment S t a t i o n (WES) on l 6 March I965 attended by Mr. S. B. Powell, r e p r e s e n t i n g the O f f i c e , Chief o f Engineers
( O C E) , and s t a f f members o f the WES H y d r a u l i c s D i v i s i o n . The conference was conceived through the encouragement o f Mr. J.. H. Douma, OCE. The as-pects o f a r a t i o n a l approach t o the h y d r a u l i c design o f rock r i p r a p were discussed.
T h i s paper was prepared by Mr. F. B. Campbell, C h i e f , WES H y d r a u l i c A n a l y s i s Branch, w i t h the t e c h n i c a l assistance o f the A n a l y s i s S e c t i o n s t a f f under the s u p e r v i s i o n o f Mr. R. G. Cox. The treatment p f the s t a b i l -i t y o f r -i p r a p on a streaunbank as w e l l as o t h e r analyses was prepared by Mr. M. D o r l . The a n a l y s i s o f the f i e l d observations of v e l o c i t y d i s t r i b u -t i o n f o r -the Fea-ther River S i -t e 12, f u r n i s h e d by -t h e Sacramen-to D i s -t r i c -t , was performed by Pfc. J . S. Watkins. The graph on "Stable Rock Size" was based on an e a r l i e r study by Mr. Cox i n connection w i t h the p r e p a r a t i o n of H y d r a u l i c Design C r i t e r i a Chart 712-1. Numerous aspects o f the design
problems t r e a t e d are the outgrowth o f s t i m u l a t i n g discussions w i t h Mr. S. B. Powell who a l s o f u r n i s h e d numerous r e p o r t s on f i e l d i n v e s t i g a t i o n s o f r i p -rap which were not a v a i l a b l e i n the WES Research Center L i b r a r y .
This p r e s e n t a t i o n was prepared under the general s u p e r v i s i o n o f and w i t h the sympathetic i n t e r e s t of Mr. E. P. F o r t s o n , J r . , C h i e f , H y d r a u l i c s D i v i s i o n , and Mr. J. B. T i f f a n y , T e c h n i c a l D i r e c t o r . Col. John^R.
Oswalt, J r . , CE, was D i r e c t o r , WES, d u r i n g the p r e p a r a t i o n and p u b l i c a t i o n of t h i s paper.
r • CONTEOTS Page FOREWORD i i i GLOSSARY v i i SUMMARY i x PART I : HWRODUCTIOÏÏ 1 Purpose • 1
Scope o f This Paper 1 The Design Problem 2 PART I I : UNIFORM TRANQUIL FLOW WITH FULLY DEVELOPED TURBULENCE . . 3
S t r a i g h t Channels 3 Channel Bends 12 F i e l d Data Needed f o r Design l 6
PART I I I : HIGHLY TURBULENT FLOW l 8
Bottom Riprap 18 Bank Riprap • • • ^9
PART rV: CONCLUSIONS 22 LITERATURE CITED 23 PLATES 1-12
APPENDIX A: STABILITY OF CUBICAL RIPRAP ELEMENTS OF BANK SLOPES . . A l APPENDIX B: RIPRAP INVESTIGATIONS NEEDED . B l
/
IJ GLOSSARY A^ F r o n t a l area o f cube Drag c o e f f i c i e n t 2 1 /2 2 1 S t a b i l i t y c o e f f i c i e n t = ( n + l ) " / F^ - jj^ t a n ^2' ( s i n ^ + cos d Depth o f f l o w d-j^ Flow depth e n t e r i n g s t i l l i n g b a s i n
d T h e o r e t i c a l downstreajn depth f o r h y d r a u l i c jump
2 - „2
K
D Drag f o r c e = ^ p ^ f - ^ f 2g ' ^-l^o, stone diameter Isbash s t a b i l i t y c o e f f i c i e n t V K F P a r t i c l e Froude number P ^/gi F-j^ Froude number e n t e r i n g s t i l l i n g b a s i n g A c c e l e r a t i o n due t o g r a v i t y
H Observed wave h e i g h t from c r e s t t o t r o u g h s
K E q u i v a l e n t stone diameter
K Nikuradse's sand g r a i n diameter s
ê Length o f side o f cube M F a c t o r = [1 + s i n ( 2 ^ ) ] ^ / ^ n Cotangent o f slope angle Q Discharge
r Bend r a d i u s
R H y d r a u l i c r a d i u s s Water-surface slope T Overturning f o r c e ; a l s o t h i c k n e s s o f r i p r a p b l a n k e t V V e l o c i t y o f a f l o w p r o f i l e a t a d i s t a n c e from t h e boundary Shear v e l o c i t y o f f l o w a t a boundary V„ V e l o c i t y of f l u i d a t h e i g h t l/2. above cube t o p ; a l s o v e l o c i t y o f f near a boundary ( e q u a t i o n 2)
w Channel w i d t h a t water surface
W Weight of cube on side slope under f l u i d W^ Weight normal t o side slope
W^ Weight of cube on bottom -under f l u i d W^ Weight t a n g e n t i a l t o side slope
y Distance from f l o w boundary
Y Distance from center l i n e of stone r i p r a p p e r p e n d i c u l a r t o boundary Y^ Distance from t o p o f r i p r a p p e r p e n d i c u l a r t o boundary
7^ S p e c i f i c weight of f l u i d
7p S p e c i f i c weight o f p a r t i c l e i n a i r
7 Submerged s p e c i f i c weight of p a r t i c l e = 7 ~
s p 1
-0 Channel bend d e f l e c t i o n angle; a l s o angle o f r e s u l t a n t f o r c e a c t i n g '
stone on bank slope p F l u i d d e n s i t y
T Average w a l l shear i n a s t r a i g h t approach 1^ Highest w a l l shear caused by a bend
T Wall shear o
SUMMARY
This paper summarizes a study o f open channel f l o w c o n d i t i o n s a f f e c t i n g r i p r a p design and suggests a design procedure based on h y d r a u l i c p r i n -c i p l e s r a t h e r than on rule-of-thumb formulas. Riprap design i s i d e a l i z e d by study o f the s t a b i l i t y o f a c u b i c a l element. F i e l d and l a b o r a t o r y i n v e s t i g a t i o n s r e q u i r e d f o r t h e development o f f i r m design c r i t e r i a are recommended.
HYDRAULIC DESIGN OF ROCK RIPRAP
PART I : INTRODUCTION
Purpose
1. The serious need f o r v a l i d c r i t e r i a f o r the h y d r a u l i c design o f
r i p r a p has been apparent f o r some time and the Waterways Experiment S t a t i o n (WES) has been working on v a r i o u s phases o f the problem f o r the past e i g h t years a t the request o f the O f f i c e , Chief o f Engineers (OCE). This r e p o r t i l l u s t r a t e s the a p p l i c a t i o n o f the r e s u l t s t o date o f the WES i n v e s t i g a -t i o n s i n -t o p e r -t i n e n -t -t h e o r y , experimen-tal work, and f i e l d experience -t o the problem o f designing r i p r a p f o r v a r i o u s channel c o n d i t i o n s . Much more l a b o r a t o r y work and f i e l d observations are needed before f i r m c r i t e r i a can be e s t a b l i s h e d . However, i t i s b e l i e v e d t h a t s u f f i c i e n t i n f o r m a t i o n i s a v a i l a b l e from s c a t t e r e d sources, and modern f l u i d mechanics concepts have 'advanced t o a p o i n t where t e n t a t i v e design c r i t e r i a can be o u t l i n e d .
2. Optimum use o f c u r r e n t knowledge should r e s u l t i n lower
construc-t i o n cosconstruc-ts and should reduce mainconstruc-tenance cosconstruc-ts necessary construc-t o replace r i p r a p damaged and removed by f l o o d s . However, no s i n g l e s p e c i f i c a t i o n f o r r i p r a p can be employed t o cover a l l cases. Furthermore, h y d r a u l i c engineers
should g a i n an "understanding o f modern f l u i d mechanics p r i n c i p l e s i n v o l v e d and seek l a b o r a t o r y and f i e l d i n f o r m a t i o n a p p r o p r i a t e t o t h e s p e c i f i c s i t u -a t i o n f o r which r i p r -a p i s t o be designed.
Scope o f This Paper
3. The treatment o f t h e design o f r i p r a p presented i n t h i s r e p o r t '
w i l l f o l l o w the o u t l i n e g i v e n below. I t begins w i t h t h e s i m p l e s t problem w i t h the l e a s t number o f independent v a r i a b l e s and progresses through a sequence o f problems o f i n c r e a s i n g complexity.
a. Uniform t r a n q u i l f l o w w i t h f u l l y developed t u r b u l e n c e
(1)^ S t r a i g h t channels
(b) Bank r i p r a p , appreciable side slope
(2) Channel bends
b. H i g h l y t i x r b i i l e n t f l o w (Example: Immediately downstream from energy d i s s i p a t o r s )
(1) Bottom r i p r a p (Example: Downstream from s t i l l i n g
b a s i n end s i l l s )
(2) Bank r i p r a p
(a) Wave a c t i o n e f f e c t
(b) Side r o l l e r or bank eddy e f f e c t
The Design Problem
k. The designer needs t o determine the e f f e c t i v e s i z e of r i p r a p which w i l l be s t a b l e f o r the v e l o c i t y a c t i n g on the r o c k . I n order t o determine t h i s v e l o c i t y , he must estimate the v e l o c i t y p r o f i l e normal t o the bottom. For t h i s purpose, f i e l d measurements o f v e l o c i t y d i s t r i b u t i o n over r i p r a p o f known s i z e and g r a d a t i o n are needed. I n a d d i t i o n , the prob-lems of e f f e c t i v e s i z e o f graded r i p r a p which w i l l e s t a b l i s h the roughness dimension, and the e f f e c t i v e size f o r s t a b i l i t y c o n s i d e r a t i o n s r e q u i r e f u r t h e r study i n the l a b o r a t o r y and the f i e l d . However, considerable ex-p e r i m e n t a l i n f o r m a t i o n has been c o l l e c t e d f o r the ex-p r e ex-p a r a t i o n of H y d r a u l i c Design C r i t e r i a Chart 712-1. The shape of the r o c k , whether rounded as w i t h cobbles or angular as w i t h rock b l a s t e d from a q u a r r y , and the method of placement are f a c t o r s which c o n t r i b u t e t o the s t a b i l i t y .
* Raised numerals r e f e r t o s i m i l a r l y numbered items i n L i t e r a t u r e C i t e d a t end o f t e x t .
PART I I : UNIFORM TRANQUIL FLOW WITH FULLY DEVELOPED TURBULENCE
5. I n t h e development o f a design procedure, t h e l e v e l bottom o f a
channel w i l l be considered f i r s t . The increased weight o f stone needed f o r s t a b i l i t y on t h e channel bank and i n bends w i l l t h e n be r e l a t e d t o bottom r i p r a p i n a s t r a i g h t channel.
Bottom r i p r a p
6. The f o l l o w i n g a n a l y s i s does not apply t o nonuniform f l o w where
t h e r e i s r a p i d a c c e l e r a t i o n o r d e c e l e r a t i o n o f f l o w . I t i s a p p l i c a b l e t o n a t u r a l stream channels where t h e w i d t h i s n o r m a l l y more than f i v e times the depth.
• 7. V e l o c i t y p r o f i l e . The f i r s t step i n the a n a l y s i s i s t o estimate
the v e l o c i t y p r o f i l e which w i l l e x i s t a t a given normal t o the boimdary d u r i n g t h e design f l o o d . This problem i s t r a c t a b l e by use o f modern con-cepts o f f l u i d mechanics. I n h i s c l a s s i c a l paper on "Law o f Turbulent
2
Flow i n Open Channels," Keulegan used Nikuradse's research on pipe rough-ened w i t h u n i f o r m sand g r a i n s and developed the f o l l o w i n g e q u a t i o n : *
where V i s t h e v e l o c i t y of a p r o f i l e a t d i s t a n c e y from the boundary, V^ i s t h e shear v e l o c i t y a t the boimdary, and i s Nikuradse's sand g r a i n diameter. I t should be emphasized t h a t nondimensional equation 1 a p p l i e s e q u a l l y w e l l t o the p r o f i l e r e g i o n near the boundary o f an open channel as t o the boundary r e g i o n near the w a l l o f a c i r c u l a r p i p e . Some a u t h o r i t i e s c a l l t h i s r e l a t i o n t h e i n n e r law and t h e r e l a t i o n f o r the f l o w near the center o f the pipe the outer law. This treatment i s concerned o n l y w i t h the i n n e r law.
o. More r e c e n t l y . Rouse has p u b l i s h e d another dimensionless S t r a i g h t Channels
(1)
* See equation 23, page 732, i n reference 2. See equation 102, page 103j in''ref er ence 3.
e q u a t i o n which i s a l s o based on research by Nikuradse. The Rouse equation i s :
^ = 0.68 iog(^] + 1 (2) f = 0.68 l o g f f
where V„ i s a v e l o c i t y near the boundary and K i s t h e same as i n equa-t i o n 1. I equa-t should be noequa-ted equa-t h a equa-t i f equaequa-tion 1 i s d i v i d e d by 8.5 and equa-the v e l o c i t y r a t i o s equated, then:
f = 8 . 5 f (3)
E l i m i n a t i n g the v a r i a b l e V , the f o l l o w i n g r e l a t i o n r e s u l t s :
I n t h i s paper, V^r w i l l be considered t o be the v e l o c i t y a c t i n g on an Jv
i s o l a t e d piece o f rock.
9. Dimensionless v e l o c i t y p r o f i l e . Rouse's curve^ f o r a rough
bound-ary v e l o c i t y p r o f i l e has been adapted f o r t h i s treatment as i n d i c a t e d i n p l a t e 1. The v e l o c i t y p r o f i l e i n p l a t e 1 i s a p l o t o f equation 2. I t
should be noted t h a t when y/K = 1.0, the term 0.68 l o g (y/x) = 0, and s
V/V^ must then be 1.0. This i s a convenient device f o r i n t e r p r e t i n g l a b -K y - K
o r a t o r y and f i e l d o b s e r v a t i o n s . I n t h i s paper, V„ i s assumed t o have a
S
10. F i e l d measurements. There i s a s c a r c i t y of b o t h l a b o r a t o r y and
f i e l d measurements o f the v e l o c i t y p r o f i l e f o r a known roughness value. Extensive f i e l d t e s t s on an a r t i f i c i a l channel w i t h known r i p r a p size below Dorena Dam were r e p o r t e d i n 1952.^ The main t e s t reach was l60 f t l o n g , the bottom f a i r l y steep, and the f l o w nonuniform. Average v e l o c i t i e s increased from h.3 fps t o 11.^ f p s i n t h i s reach. However, v e l o c i t y
measurements were inadequate t o develup good v e l o c i t y p r o f i l e s .
11. F i e l d measurements on Feather R i v e r . * The U. S. Army Engineer
* Unpublished data on r i p r a p i n v e s t i g a t i o n s f u r n i s h e d by t h e D i s t r i c t Engineer, U. S. Army Engineer D i s t r i c t , Sacramento, i n I96O.
D i s t r i c t , Sacramento, measured v e l o c i t y p r o f i l e s a t a number o f s i t e s on the Feather River where r i p r a p o f known g r a d a t i o n had been placed. Although most o f t h e s i t e s were a f f e c t e d by bends i n t h e r i v e r , s i t e 12 was l o c a t e d on a s t r a i g h t reach and measurements a t t h a t s i t e were s e l e c t e d f o r f u r t h e r study. A c r o s s - s e c t i o n a l p l o t o f the v e l o c i t y d i s t r i b u t i o n a t s i t e 12 i s shown i n p l a t e 2. I n a p r e l i m i n a r y examination, i s o v e l s were c a r e f u l l y sketched. These showed i s o l a t e d peaks o f h i g h v e l o c i t y which c o u l d have been t h e r e s u l t o f a mound o f r i p r a p upstream or some other such l o c a l d i s
-turbance. The i s o v e l s i n p l a t e 2 have been normalized, and t h e values scaled f o r corresponding i s o v e l s a t t h e f o u r s e c t i o n s drawn p e r p e n d i c u l a r
t o t h e boundary. The v e l o c i t y p r o f i l e s a t these s e c t i o n s are p l o t t e d i n a dimensional s e m i l o g a r i t h m i c graph ( p l a t e 3 ) . A s i n g l e s t r a i g h t l i n e can be drawn t h r o u g h t h e p o i n t s which c l o s e l y approximates the v e l o c i t y p r o f i l e o f the f o u r s e c t i o n s .
12, E f f e c t i v e roughness. Several assumptions as t o the stone d i a
-meter r e p r e s e n t i n g the e f f e c t i v e roughness K were made f o r study on a dimensionless s e m i l o g a r i t h m i c graph. I n f o r m a t i o n from t h e Sacramento D i s t r i c t i n d i c a t e d t h a t ' t h e average r i p r a p stone diameter a t s i t e 12 on
the Feather River was approximately k.6 i n . , o r O.38 f t . The c o o r d i n a t e o f Y = K on t h e dimensional graph ( p l a t e h) w i t h a depth c o r r e c t i o n o f
0.19 f t , o r h a l f the K dimension, i n d i c a t e d a value V,^ o f 2.k6 f p s .
Dimensionless graphs f o r k.6-, ^-, and 6-in.-diameter stones were drawn u s i n g the corresponding values o f K and V^^ . A l l o f t h e curves were
Js.
v e r y close t o g e t h e r , and t h e average stone diameter o f k.6 i n . was adopted as r e p r e s e n t i n g - t h e proper dimensionless p r o f i l e .
13. The g e n e r a l equation f o r the dimensionless p r o f i l e i s :
As noted i n paragraph 7j Keulegan's constants f o r A and B u s i n g shear v e l o c i t y are 5.75 and 8.5, r e s p e c t i v e l y , whereas Rouse's constants u s i n g Vj^ i n s t e a d o f are 0.68 and 1.0. • I f the K f o r Feather River s i t e 12
i s 0.38 f t , the Vj^ i s 2.k6 f p s ( p l a t e k). From t h e corresponding dimen-sionless p r o f i l e , the slope o f t h e l i n e o f best f i t gives constant A
+ B
as 0.95. Although i t departs c o n s i d e r a b l y from the value A = 0.68 based on Nikuradse's u n i f o r m sand g r a i n , s i m i l a r departures f o r v e l o c i t y d i s t r i b u t i o n were found i n comparing dimensionless p l o t s i n l a r g e f l o o d -c o n t r o l t u n n e l s . ^ These departures are b e l i e v e d t o be t h e r e s u l t o f a mixed roughness size as c o n t r a s t e d t o the ixniform g r a i n size o f Nikuradse.
ik. E f f e c t o f depth. The Feather K i v e r s i t e 1 2 t e s t s were made a t a low stage on t h e r i v e r and cannot be expected t o a p p l y t o the design stage. The shear v e l o c i t y f o r an open channel can be w r i t t e n :
where E i s t h e h y d r a u l i c r a d i u s , s i s t h e surface slope, and g t h e g r a v i t a t i o n a l constant. I f i t i s assumed t h a t t h e g e n e r a l slope o f t h e stream a t t h e low stage o f measurement i s t h e same as t h e slope f o r t h e design f l o w , t h e f o l l o w i n g r a t i o can be w r i t t e n f o r shear v e l o c i t y :
where s u b s c r i p t s L and H r e f e r t o low and h i g h stages and d i s t h e depth o f f l o w along t h e v e l o c i t y p r o f i l e normal t o the boundary. F u r t h e r -more, since i s p r o p o r t i o n a l t o V;^ , t h e f o l l o w i n g r a t i o can be
w r i t t e n :
An e s t i m a t i o n o f depth f o r design f l o w i s n o t simple i f t h e bottom i s an a l l u v i u m which scours deeply d u r i n g f l o o d s . Measurements from e x i s t i n g b r i d g e s o r cableways can sometimes g i v e an i n d i c a t i o n o f depth o f scour upon which t o base an estimate. Obviously, t h e manner i n which the bank r i p r a p r e s t r a i n s erosion a t i t s t o e can i n f l u e n c e t h e l o c a l w a l l shear i f bottom scour i s deep. I n any case, t h e depths should be measured normal t o the boundary i n the a n a l y s i s o f the f i e l d data. V e l o c i t y p r o f i l e s measured t o o close t o the water's edge have no p r a c t i c a l s i g n i f i c a n c e i n
a t t e m p t i n g t o r e l a t e shear or bottom v e l o c i t y a t low stages t o these
(Rsg) 0.5 (5)
(6)
q u a j i t i t i e s a t a h i g h e r design stage. C e r t a i n stream dynamics aspects o f the problem have been analyzed r e c e n t l y by Lundgren and Jonsson.
15. E f f e c t of surface slope. Equation 5 f o r shear v e l o c i t y i n d i
-cates t h a t the l o n g i t u d i n a l water-surface slope s i s an independent v a r i a b l e e q u a l l y as important as depth d i n d e t e r m i n i n g t h e design ve-l o c i t y . I n order t o account f o r the e f f e c t of ve-l o n g i t u d i n a ve-l sve-lope o f t h e water surface on the design v e l o c i t y V^^ , the f o l l o w i n g r a t i o s are a p p l i c a b l e :
I f v e l o c i t y p r o f i l e s and depths are measured a t t o o low a stage, the stream surface slope w i l l p r o b a b l y be s u b s t a n t i a l l y d i f f e r e n t from t h a t which i s t o be expected a t design stage. Streams i n n a t u r e a t low stage
w i l l be l e s s than a t f l o o d stage i n the pools and g r e a t e r t h a n a t f l o o d stage over the c o n t r o l s . I t i s t h e r e f o r e i m p o r t a n t t o set slope stakes and measure the slope a t the time the v e r t i c a l v e l o c i t y d i s t r i b u t i o n and depths are measured. F i n a l l y , the h y d r a u l i c engineer must have s u f f i c i e n t i n f o r m a t i o n t o estimate the slope and depth a t design stage.
16. E f f e c t o f r i p r a p size g r a d a t i o n . On any one r i v e r , t h e f i e l d
measurements o f v e l o c i t i e s , depths, and water-surface slopes should be made a t s i t e s where r i p r a p has been r e c e n t l y p l a c e d . The most economical r i p r a p a v a i l a b l e f o r the l o c a l i t y i s commonly used, even though i t may not have an i d e a l g r a d a t i o n . S u f f i c i e n t i n f o r m a t i o n i s n o t a v a i l a b l e t o d e t e r -mine the i d e a l g r a d a t i o n , and w i t h the present s t a t e o f the a r t t h e r e i s no b a s i s f o r making an economic study i n v o l v i n g f i r s t cost and costs o f maintenance and r e p a i r . However, c e r t a i n b a s i c f a c t s should be recognized
i n regard t o g r a d a t i o n . I f the span o f the stone sizes i s very g r e a t , say from the s i z e t h a t 10 percent o f the stone i s smaller t o t h e s i z e t h a t
90 percent o f the stone i s s m a l l e r , i t may be c h a r a c t e r i z e d as a broad
size span. At the o t h e r extreme i s the narrow s i z e span i n which t h e r e i s l i t t l e d i f f e r e n c e between the s i z e o f t h e 10 p e r c e n t smaller and 90 percent smaller stones. From the h y d r a u l i c design s t a n d p o i n t , a n e a r l y -uniform
(8)
r o c k s i z e , or narrow s i z e span, i s i d e a l , but would h a r d l y be r e a l i z e d except i n the l o c a l i t y o f l a r g e t a l u s d e p o s i t s a t the f o o t o f rock c l i f f s or p a l i s a d e s vftiere t h e l a r g e rock i s a t the toe and the s m a l l rock a t t h e t o p o f the slope.
17. I t i s understood t h a t some Corps o f Engineers D i s t r i c t s p e r m i t
t h e use o f a broad s i z e span as f o l l o w s :
^100 ^ ^30
where D-J_QQ i s t h a t s i z e o f which 100 percent o f the stone i s smaller.
Such a s p e c i f i c a t i o n f u r t h e r s t a t e s i n regard t o f i n e s t h a t :
D^5>0.25D5Q
I n other D i s t r i c t s , the smaller s i z e span i s s p e c i f i e d as f o l l o w s :
\00 ^ 3 or to^Q
These d i f f e r e n c e s p r o b a b l y i n d i c a t e the most economical r i p r a p a v a i l a b l e a t s p e c i f i c l o c a l i t i e s . The r i p r a p w i t h t h e smaller s i z e span would no doubt be more s t a b l e because t h e r e are fewer small stones t o be l o s t d u r i n g f l o o d
stage. Experiments w i t h t h e e f f e c t o f g r a d a t i o n can best be accomplished i n the l a b o r a t o r y because s y n t h e t i c g r a d a t i o n i s l e s s c o s t l y on a s m a l l s c a l e .
18. E f f e c t o f r i p r a p t h i c k n e s s . The t h i c k n e s s o f the r i p r a p b l a n k e t
and the g r a d a t i o n are i n t e r r e l a t e d . With a broad s i z e span, i s o l a t e d
pieces o f l a r g e rock w i l l p r o t r u d e i n t o the f l o w . The f l o w w i l l a c c e l e r a t e around t h e l a r g e stone and remove the s m a l l e r p a r t i c l e s . This phenomenon i s s i m i l a r t o t h e deep scour alongside and j u s t downstream from b r i d g e p i e r s . As a general guide, under the present s t a t e o f t h e a r t , the t h i c k
-/
ness o f t h e b l a n k e t T should be
T = 1.5D
max;
where D i s the s i z e o f which 100 percent o f t h e stone i s s m a l l e r , max ^
19. S t a b l e rock s i z e . To estimate the r e q u i r e d s i z e o f r o c k which
i s s t a b l e f o r a given v e l o c i t y , t h e 50 percent size i s used. The A i r y
7 8 9
law ' s t a t e s t h a t the weight r e q u i r e d f o r s t a b i l i t y v a r i e s as t h e s i x t h power o f the v e l o c i t y a c t i n g on the rock. I n the Transactions o f the Second Congress on Large Dams, p u b l i s h e d b y the Government P r i n t i n g O f f i c e i n 193^, S. V. Isbash"^^ presented experimental c o e f f i c i e n t s t o be used v/ith A i r y ' s law. Other experimental i n f o r m a t i o n used f o r H y d r a u l i c Design C r i t e r i a Chart 712-1 (paragraph k) confirms the Isbash
recommenda-t i o n s i n g e n e r a l . A c o e f f i c i e n recommenda-t Eg = 1.20 i s used as recommenda-t h e b a s i s o f recommenda-the Isbash curve i n p l a t e 5- Because cobbles are used f o r r i p r a p i n some l o c a l i t i e s , an a r b i t r a r y curve t o the l e f t o f the Isbash curve i s p r e -sented f o r use w i t h cobbles. Another t o the r i g h t o f the Isbash curve i s marked f o r use w i t h quarry r o c k . I n g e n e r a l , cobbles approach a s p h e r i c a l
shape and r o c k b l a s t e d from a quarry approaches a c u b i c a l shape. More e x p e r i m e n t a l i n f o r m a t i o n i s needed f o r quarry rock and cobbles.
20. The method o f placement o f t h e r i p r a p can be expected t o a f f e c t
the s t a b i l i t y . Random dumping o f r i p r a p i s t h e most common placement meth-od. Hand-placed r i p r a p , as placed by t h e New England D i v i s i o n u s i n g WPA funds, has been shown t o be v e r y s t a b l e d u r i n g f l o o d s . Tamping r i p r a p w i t h a heavy s t e e l p l a t e , as i n a few instances i n the P o r t l a n d D i s t r i c t , can be expected t o wedge the rock t i g h t l y i n t o p l a c e . The curves i n p l a t e 5 are considered a p p l i c a b l e o n l y t o random-dumped r i p r a p .
Bank r i p r a p
21. The preceding c o n s i d e r a t i o n s are a p p l i c a b l e t o the bottom o f
a s t r a i g h t channel. C e r t a i n a n a l y t i c a l procedures can be used t o r e l a t e s t a b l e stone s i z e on t h e bottom t o the corresponding size on a bank o r l a t e r a l s l o p e . The a n a l y s i s can be made w i t h an i d e a l i z e d shape such as a sphere ( r e p r e s e n t i n g well-worn cobbles) o r cube ( r e p r e s e n t i n g rock b l a s t e d f r o m a q u a r r y ) . As most r i p r a p i s p r o b a b l y q u a r r y r o c k , t h e i s o l a t e d cube was selected f o r a n a l y s i s . D e f i n i t i o n sketches are shown i n p l a t e 6 and the complete a n a l y t i c a l treatment i s i n c l u d e d as Appendix A.
22. P l a t e 6a i n d i c a t e s a cube having weight r e s t i n g on the
bottom and a l a r g e r cube w i t h weight W r e s t i n g on the bank. The objec-t i v e o f objec-t h e design problem i s objec-t o esobjec-timaobjec-te objec-the r a objec-t i o o f objec-t h e weighobjec-ts W/V
f o r any given weight W , v e l o c i t y V.^ , and side slope n . P l a t e 6h o K
i n d i c a t e s t h a t . t h e cube on t h e slope has a component normal t o t h e slope W and one down the slope W, . P l a t e 6c shows t h a t the g r a v i t y component
n t
and the drag component D combine t o form a r e s u l t a n t T a t a s p e c i f i c angle ^ t o the d i r e c t i o n of f l o w . These general concepts were noted by Lane and Carlson. The a n a l y s i s i n Appendix A assumes t h a t the cube i s dislodged by r o t a t i n g over a hinge l i n e normal t o the r e s u l t a n t f o r c e
caus-i n g the caus-i n s t a b caus-i l caus-i t y .
2.3. The a n a l y s i s i n Appendix A i n d i c a t e s t h a t the s t a b i l i t y of a cube on a slope i s a f u n c t i o n of the Froude number F^ of the p a r t i c l e
s i z e :
where V„ i s the v e l o c i t y a c t i n g on the stone and i i s the l e n g t h o f a Jv
side o f the cube. The s t a b i l i t y i s a l s o a f u n c t i o n o f the side slope n These tw
f o l l o w s :
These tvro f u n c t i o n s can be combined i n t o a s t a b i l i t y c o e f f i c i e n t C as s W o C = — 1 _ (10) ^ F^ {n + l)°-5 P
P l a t e 7 shows t h e r e l a t i o n between C and a f a c t o r M i n the f i n a l s
equation y i e l d i n g t h e f o l l o w i n g r a t i o o f weights.
2^- I n t h e a n a l y s i s , i t i s necessary t o assume a drag c o e f f i c i e n t . For t h i s purpose, the curve f o r quarry r o c k i n p l a t e 5 i s used. This i s not a pure drag c o e f f i c i e n t b u t i n c l u d e s any v e r t i c a l l y upward or down-ward f o r c e on the cube. The r e s u l t i s a c o e f f i c i e n t which combines drag and l i f t .
25. From equations 10 and 11, i t can be seen t h a t t h e r e are two
separate f u n c t i o n s o f t h e side slope n . The f o l l o w i n g t a b u l a t i o n p e r t a i n -i n g t o s-ide slope f u n c t -i o n s -i s -i n c l u d e d f o r the conven-ience o f t h e des-igner,
, Slope, n 0.5
( )
3/2 2 3 2.2k 3.16 k.12 2,15 i.Uo 1.21 5 6 5.10 6.08 1.125 1.085This t a b u l a t i o n t o g e t h e r w i t h p l a t e 7 can be used t o detennine the weight r a t i o wA? .
Toe p r o t e c t i o n
26, One o f the most troublesome problems p e r t a i n i n g t o r i p r a p
b l a n k e t s on stream.bahks i s the design, c o n s t r u c t i o n , and maintenance of the t o e . The h i g h e s t boimdary shear on the bank i s near the bottom
I f the bed i s an a l l u v i u m (sand and f i n e g r a v e l ) , i t i s n a t u r a l f o r the t o e of t h e b l a n k e t t o be -undercut d u r i n g h i g h water. There are two design con-cepts o f t o e p r o t e c t i o n e x t a n t i n the Corps o f Engineers, each w i t h i t s own advantages and disadvantages. These schemes are designated t h e "toe t r e n c h " and t h e "thickened t o e " i n t h i s paper and are shov/n i n p l a t e 8. This p l a t e does not show dimensions or slopes, as each design must be assigned i t s own dimensions dependent upon the l o c a l a n t i c i p a t e d bed scour and the character o f the r i p r a p a v a i l a b l e . More f i e l d i n f o r m a t i o n i s needed on the behavior of these designs d u r i n g f l o o d passage.
27. Toe t r e n c h . The t o e t r e n c h shown i n p l a t e 8b i n v o l v e s
excava-t i o n and preplacemenexcava-t o f r o c k below excava-the low-waexcava-ter bed o f a l l u v i u m . I excava-t has the advantages of p o s i t i v e knowledge o f the l o c a t i o n o f the toe p r o -t e c -t i o n s-tone, and a side slope s -t a b i l i -t y designed -t o w i -t h s -t a n d -the h i g h boundary shear estimated f o r f l o o d stage.
28. A disadvantage o f the toe t r e n c h i s t h e requirement f o r
under-water excavation o f the t r e n c h i n a l l u v i u m . Another disadvantage i s t h a t the angle o f repose o f t h e toe t r e n c h i t s e l f may be f a i r l y f l a t so t h a t a l a r g e q u a n t i t y of rock may e v e n t u a l l y be r e q u i r e d t o f i l l the t r e n c h . Also, i n t h e case o f a narrow stream, the toe t r e n c h type o f c o n s t r u c t i o n
f u r t h e r narrows the cross s e c t i o n a t f l o o d stage. I f appreciable narrowing and i s approximately equal t o t h a t a c t i n g on the adjacent bed ( p l a t e 8 a ) .
r e s u l t s , the l o n g i t u d i n a l water-surface slope would be increased, causing increased bed shear and deeper scour.
29. Thickened t o e . The thickened toe ( p l a t e 8c) design a n t i c i p a t e s
t h e scour l i n e of the a l l u v i a l bed and purposely p r o v i d e s f o r a steeper slope near the toe so,that the rock can r o l l down over the eroded bed beyond. I t s p r i n c i p a l advantage i s the e l i m i n a t i o n of an underwater
t r e n c h , but i t does assume t h a t the bank on the steeper back slope w i l l be t e m p o r a r i l y s t a b l e l o n t i l the rock i s p l a c e d . The t h i c k e n e d toe type o f design would r e s u l t i n a minimum c o n s t r i c t i o n o f the stream cross s e c t i o n d u r i n g f l o o d and reduce the excessive scour caused by such c o n s t r i c t i o n .
30. The disadvantage o f the t h i c k e n e d toe design i s t h a t the smaller
s i z e rock woiild probably wash outward i n t o t h e stream and t h e i r f u n c t i o n as a v o i d f i l l e r would be l o s t . A l s o , i t i s d i f f i c u l t t o estimate the percentage o f l a r g e size rock needed; however, i t seems d e s i r a b l e t h a t the
s i z e span o f the g r a d a t i o n should be narrow. Furthermore, o p p o r t u n i t i e s f o r o b s e r v a t i o n of the f i e l d performance o f the t h i c k e n e d toe d u r i n g f l o o d s are l i m i t e d . P o s t f l o o d i n s p e c t i o n would r e q u i r e subaqueous hand excava-t i o n , p o s s i b l y by J e excava-t excava-t i n g .
31. Complete f i e l d i n f o r m a t i o n on t h i s aspect o f the r i p r a p problem
should be obtained as i n d i c a t e d i n paragraphs 2 and k. I n a d d i t i o n , s o i l mechanics engineers should be consulted i n e s t i m a t i n g the s t a b l e s a t u r a t e d
slope o f both the i n s i t u a l l u v i u m and the bank m a t e r i a l . Most n a t u r a l stream channel r i p r a p i s i n v o l v e d w i t h bends or curved reaches which are discussed subsequently.
Channel Bends
Bend problems
32. I n n a t u r a l stream channel s t a b i l i z a t i o n , r i p r a p -is most commonly
used i n the v i c i n i t y o f bends. The f o r e g o i n g d i s c u s s i o n o f s t r a i g h t channels considered f i r s t the problem of the channel bottom which was t r e a t e d essen-t i a l l y as a simple essen-two-dimensional problem i n v o l v i n g essen-the v e l o c i essen-t y p r o f i l e and the roughness as r e l a t e d t o the d i s t a n c e from the bottom. The e f f e c t s o f t o t a l depth and l o n g i t u d i n a l water-surface slope were a l s o discussed.
The s t a b i l i t y o f r i p r a p on the bank o f a s t r a i g h t channel i n t r o d u c e d the l a t e r a l dimension o f bank slope. One of the g r a v i t y components o f bank-slope r i p r a p r e s i s t s movement, w h i l e the other must be coupled w i t h a drag-type f o r c e t e n d i n g t o d i s p l a c e the r o c k s . I n a d d i t i o n t o the considera-t i o n s p e r considera-t a i n i n g considera-t o a s considera-t r a i g h considera-t channel, considera-t h e banks o f a channel bend i n v o l v e other v a r i a b l e s , t h e e f f e c t s o f which have not been f u l l y e x p l o r e d .
33. One o f the simpler g e o m e t r i c a l approaches t o the bend problem
i s t o assume a u n i f o r m , t r a p e z o i d a l cross s e c t i o n . The geometry o f the bend can t h e n be d e f i n e d i n t h e f o l l o w i n g terms:
n , — , 0 , and — ' w ' ' d
where n i s the r a t i o o f the h o r i z o n t a l t o the v e r t i c a l dimensions of the side slope, r i s the r a d i u s t o the center l i n e o f the channel, w i s t h e channel w i d t h a t the water s u r f a c e , 0 i s the c e n t r a l angle, and d i s the depth o f f l o w . L a b o r a t o r y experiments conducted on bends o f t r a p e
-12
z o i d a l channels a t the Massachusetts I n s t i t u t e o f Technology ( M I T ) , t h e Bureau o f Reclamation (USBR),'^^ and the U n i v e r s i t y o f Iowa"'' are discussed belov;.
L a b o r a t o r y experiments
3*+. T e s t s . Tests were conducted on smooth channel bends a t MIT,
USER, and Iowa. I n a d d i t i o n , MIT made l i m i t e d t e s t s on rough channel bends. I n t h e l a t t e r t e s t s , the channel was roughened by f i x i n g 0.l8- by
0.10 by 0.10in. p a r a l l e l e p i p e d s t o the boundary i n a random manner, r e
-s u l t i n g i n a roughne-s-s h e i g h t o f 0.10 i n . I n a l l t e -s t -s , Pre-ston tube-s'*"^ were used t o measure boundary shear d i r e c t l y . A comparison o f t e s t condi-t i o n s and r e s u l condi-t s i s given i n condi-the f o l l o w i n g condi-t a b u l a condi-t i o n .
Type Side I n v e r t
L a b o r a t o r y Channel Slope Width, i n . r/w 0, deg w/d MIT Smooth 2:1 12 3.^5 60 10.0 ^ 8.0 2.50 7.0 2k 1.67 12.0 1.37 8.8 (Continued) 1.25 8.0 13
Laboratory Type 'channel Side Slope I n v e r t Width 5 i n . e, deg w/d USER Smooth 1-1/2:1 2h 3.76 15 . 5.7 Iowa Smooth 1:1 72 1^.18 h.OQ 3.99 3.99 3.73 90 19.0 ih.0 13.7 13.7 10.0 MIT Rough 2:1 2h 1,^9 1.25 60 10.0 8.0
The p l a n o f the 2if-in.-wide MIT t e s t channel i s shown i n p l a t e 9. Those of t h e USER and Iowa channels are given i n p l a t e 10. The p r i n c i p a l d i f -ference i n the geometry o f t h e MIT 1 2 - i n . and 2i4-in. channels was t h e i n v e r t w i d t h .
35' R e s u l t s . The l i n e s o f equal boundary shear are presented i n
p l a t e s 9 and 10 i n terms o f t h e r a t i o of w a l l shear a t the p o i n t t o the average w a l l shear T i n t h e s t r a i g h t approach. I t can be noted t h a t
a
the h i g h e s t w a l l shear caused b y t h e bend occurs downstream from t h e o u t s i d e o f t h e bend i n t h e USER and MIT t e s t s . Another area o f h i g h w a l l shear i s l o c a t e d a t t h e i n s i d e o f t h e bend. I n the Iowa t e s t s , o n l y t h e shear w i t h i n the bend was measured. For purposes o f c o r r e l a t i n g t h e r e -s u l t -s , the meiximiim w a l l -shear ha-s been r e l a t e d t o the average approach w a l l shear as ^ A and p l o t t e d a g a i n s t the r e s p e c t i v e r a t i o s o f r/w
D a
( p l a t e 11). The equation o f the graph i s f o r t h e l i n e of b e s t f i t u s i n g the smooth channel d a t a p o i n t s . Even w i t h a l i m i t e d range o f values o f r/w , t h e r e appears t o be a power law r e l a t i n g these values t o '^-./'^ Although o n l y two measurements are a v a i l a b l e f o r rough channels, t h e r e
-s u l t -s p l o t t e d i n p l a t e 1 1 i n d i c a t e t h e -same -slope o f curve a-s f o r t h e smooth channel d a t a . The shear v e l o c i t y i s commonly expressed i n terms o f w a l l shear as f o l l o w s :
V,. = (-yp) ° ' 5 ' (12)
where p i s the f l u i d d e n s i t y and i s assumed here t o have a value o f 1.9^ slugs per c u f t . C o n s i d e r i n g t h e p r o p o r t i o n a l i t y expressed i n e q u a t i o n k,
the r a t i o o f e f f e c t i v e v e l o c i t i e s a c t i n g on the rock can be w r i t t e n :
(13)
T h i s equation i s v a l i d o n l y f o r a case where the V,
Ka i n t h e s t r a i g h t approach i s based upon an average w a l l shear f o r the s e c t i o n .
A p p l i c a b i l i t y of experimental r e s u l t s
36. An examination o f the research r e s u l t s on w a l l shear d i s t r i b u t i o n
i n a channel bend i n d i c a t e s t h a t f u r t h e r extensive i n v e s t i g a t i o n needs t o be accomplished. Laboratory s t u d i e s have been concerned m o s t l y w i t h smooth w a l l s because the use of a Preston tube has been considered a p p r o p r i a t e i n the past f o r o n l y such boundaries. However, a m o d i f i e d Preston tube was used s u c c e s s f u l l y i n the MIT rough channel t e s t s . The a c t u a l p a t t e r n o f w a l l shear d i s t r i b u t i o n appears t o be s i m i l a r f o r b o t h smooth and rough boundaries ( p l a t e s 9, 10, and l l ) . However, a v a i l a b l e data i n d i c a t e h i g h e r shear r a t i o s f o r rough boundaries. Lacking the proper experimental simula-t i o n o f r i p r a p , one can use simula-t h e e x i s simula-t i n g r e s u l simula-t s as a guide simula-t o judgmensimula-t. Of g r e a t e s t p r a c t i c a l importance i s the f a c t t h a t a t i n i f o r m , t r a p e z o i d a l cross s e c t i o n around t h e bend d e v i a t e s g r o s s l y from the geometry formed i n a n a t u r a l stream w i t h an e r o s i v e a l l u v i a l bed. I t has l o n g been recognized t h a t a n a t u r a l streambed w i l l develop a b a r on the i n s i d e
of t h e bend and a deep scour h o l e on the o u t s i d e . Extreme examples o f t h i s phenomenon are experienced on the Lower M i s s i s s i p p i River where scour holes may reach a depth o f 200 f t . However, f o r streams o f l e s s t o t a l shear v e l o c i t y and bed a l l u v i u m more r e s i s t a n t t o e r o s i o n , no such extreme scour hole depths should be expected. I t may be t h a t a l a b o r a t o r y channel o f t r i a n g u l a r cross s e c t i o n w i t h a s h o r t , steep bank a t the o u t s i d e o f the bend and a l o n g , f l a t l e g a t t h e i n s i d e would approximate t h e n a t u r a l c o n d i t i o n . F i e l d measurements o f cross s e c t i o n s are needed as a guide. Pending f u r t h e r l a b o r a t o r y s t u d i e s , the designer should consider the
e f f e c t i v e r a d i u s t o the mean c u r v a t u r e o f the thalweg o f a n a t u r a l stream. I t appears reasonable t o use a smaller value o f top w i d t h than t h a t measured i n n a t u r e i n u s i n g p l a t e 11.
Reconmended cur-r e n t design p cur-r a c t i c e
37. I t i s apparent from the c o n s i d e r a t i o n s discussed ahove t h a t
any-comprehensive l a b o r a t o r y study be c o s t l y and time consuming. I n t h e meantime p l a t e s 9 and 10 can be used as guides t o the general l o c a t i o n o f h i g h -wall shear on t h e o u t s i d e o f the bend, and p l a t e 11 can be used t o
supplement judgment as to t h e r e l a t i o n o f maximum shear values i n the t a n -gents t o those o f the bends.
F i e l d Data Weeded f o r Design
38. The most p r e s s i n g c u r r e n t need i s f o r f i e l d measurements o f
depths and v e l o c i t i e s a t s e l e c t e d l o c a t i o n s where new r i p r a p o f known g r a d a t i o n and shape has been placed. Observations on b o t h s t r a i g h t and curved reaches are needed. I n view o f the h e t e r o g e n e i t y o f the independent v a r i a b l e s o f the problem as found i n t h e f i e l d , m u l t i p l e cross sections should be observed. Analyses s i m i l a r t o t h a t described p r e v i o u s l y f o r Feather E i v e r s i t e 12 should be made.
39. The v e r t i c a l v e l o c i t y p r o f i l e s should comprise a t l e a s t seven
v e l o c i t y observations i n a s i n g l e v e r t i c a l w i t h s p e c i a l a t t e n t i o n g i v e n t o the bottom h a l f o f the depth. A l a r g e r range i n v a r i a t i o n o f the q u a n t i t i e s measured can be expected i n the bends than I n the tangent reaches. I t i s
t h e r e f o r e important t o have a l a r g e r number o f observations i n the bends s e l e c t e d f o r o b s e r v a t i o n . The o b j e c t i v e s o f the v e l o c i t y measurements are t w o f o l d : ( a ) t o o b t a i n average v a l u e s , and ( b ) t o o b t a i n extreme values. Average values are o f i n t e r e s t i n e s t a b l i s h i n g the constants f o r the general
laws o f r i p r a p behavior, and extreme values are o f i n t e r e s t i n c o n s e r v a t i v e design. The t u r b u l e n t nature o f natural streamflow w i l l cause b o t h s h o r t -p e r i o d and l o n g - -p e r i o d v a r i a t i o n s i n the v e l o c i t y a t a given -p o i n t . To o b t a i n a r e l i a b l e average v e l o c i t y a t a p o i n t , t h e c u r r e n t meter r e v o l u -t i o n s should be recorded f o r from 1 -t o I - I / 2 min.
l+O. As mentioned p r e v i o u s l y , s y n t h e t i c s i z e g r a d a t i o n i n the f i e l d i s a c o s t l y procedure. However, t h e r e i s a wide range o f s i z e spans and shapes i n t h e most economical, a v a i l a b l e r i p r a p used by the v a r i o u s GE D i s t r i c t s . Reasonably accurate measurements o f size gradations and
photographs o f t y p i c a l rock shape are an important p a r t o f t h e r e c o r d . A comparative study o f t h e f i e l d data from v a r i o u s l o c a l i t i e s (both t h e e f f e c -t i v e roughness size f o r a given average v e l o c i -t y p r o f i l e and -t h e e f f e c -t i v e size f o r s t a b i l i t y ) could y i e l d much i n f o r m a t i o n o f value t o f u t u r e design. F i e l d r e s u l t s have a d u a l r o l e i n g u i d i n g f u t u r e l a b o r a t o r y studies and i n
a f f o r d i n g i n f o r m a t i o n f o r immediate use i n c u r r e n t design.
kl. F i n a l check on the e f f e c t i v e rock size on r i p r a p t e s t sections r e q u i r e s a record o f t h e sizes o f stone which have been d i s p l a c e d d u r i n g f l o o d s . Samples o f i n - p l a c e stones o f three size groups l a r g e r than t h e estimated average stone i n t e s t i n s t a l l a t i o n s should be p a i n t e d w i t h d i f f e r e n t c o l o r s . These stones should be numbered and t h e i r l o c a t i o n s recorded so t h a t the s i z e o f rock displaced by a subsequent f l o o d can be determined. Photographs o f t h e observation stones should be made. Pre-c i s i o n i n e s t i m a t i n g t h e stone size and weight i s n e i t h e r p r a Pre-c t i Pre-c a l nor necessary i n view o f the present s t a t e o f the a r t . P o s t f l o o d examination need n o t determine how f a r t h e observation stone has been t r a n s p o r t e d , b u t o n l y what size groups have been dislodged.
PAET I I I : HIGHLY TURBULENT FLOW
h2. The preceding d i s c u s s i o n i s a p p l i c a b l e o n l y t o the normal t u r -bulence found i n n a t u r a l stream channels. A s p e c i a l s i t u a t i o n e x i s t s
down-stream from energy d i s s i p a t o r s , a t a severe r e s t r i c t i o n of a down-stream channel which causes a l a r g e head drop, and a t other places where man-made s t r u c t u r e s cause h i g h l y t u r b u l e n t f l o w . As i n d i c a t e d i n paragraph 3b, two problems e x i s t : one i n v o l v e s the bottom r i p r a p , and the other the bank r i p r a p .
D i f f e r e n t h y d r a u l i c and s t a b i l i t y phenomena are encountered i n the separate areas. The problems are so complex i n h i g h l y t u r b u l e n t f l o w t h a t l i t t l e or no a n a l y t i c a l approach e x i s t s a t present. Model s t u d i e s are thus r e q u i r e d f o r s o l u t i o n o f the r i p r a p problem i n h i g h l y t u r b u l e n t areas. Flow j u s t downstream from a s t i l l i n g b a s i n i s used as an example of design of r i p r a p f o r h i g h l y t u r b u l e n t f l o w by means of model s t u d i e s .
Bottom Riprap
1+3. A t e r m i n a l s t r u c t u r e f o r a s p i l l w a y or o u t l e t works may be a
f l i p bucket, r o l l e r bucket, or s t i l l i n g b a s i n . The s t i l l i n g b a s i n i n v o l v e s numerous independent geometric v a r i a b l e s such as l a t e r a l spread of the e n t e r i n g f l o w ; the s i z e , shape, l a t e r a l spacing, and l o n g i t u d i n a l l o c a t i o n o f b a f f l e p i e r s ; and the h e i g h t s , shape, and l o n g i t u d i n a l l o c a t i o n o f the end s i l l . The bottom upon which r i p r a p i s placed beyond the b a s i n may be l e v e l or sloped upward or downward. I n a d d i t i o n t o the innumerable combina-t i o n s o f geomecombina-tric v a r i a b l e s are combina-the h y d r a u l i c v a r i a b l e s of Froude number of t h e e n t e r i n g f l o w and t a i l w a t e r depth. Not o n l y do the many combinations o f these independent v a r i a b l e s have an u n p r e d i c t a b l e e f f e c t upon the bottom v e l o c i t y , but the i s s u i n g f l o w does not have a t u r b u l e n t boundary l a y e r
which can be p r e d i c t e d . I n a d d i t i o n t o these v a r i a b l e s , the l a r g e t u r b u l e n c e p u l s e s create unknown v e r t i c a l pulses on the bottom r i p r a p . I t i s t h e r e f o r e obvious t h a t h y d r a u l i c model studies o f f e r the b e s t means f o r determining t h e s t a b l e s i z e of bottom r i p r a p .
kk. I n the cases o f o u t l e t s from c u l v e r t s or other small s t r u c t u r e s where model s t u d i e s are not j u s t i f i e d , the two dashed l i n e s i n p l a t e 5 can
be used f o r e s t i m a t i n g r i p r a p s i z e . These c r i t e r i a should not be used i n l i e u o f model s t u d i e s f o r l a r g e energy d i s s i p a t o r s f o r reasons s t a t e d p r e v i o u s l y . The curve' f o r s m a l l t u r b u l e n t s t i l l i n g basins should be used f o r minimum design type basins having l e n g t h s o f 2.5 times o r l e s s the t h e o r e t i c a l l y r e q u i r e d t a i l w a t e r depth d ^ and a design t a i l w a t e r depth l e s s t h a n t h e o r e t i c a l dg . The curve f o r small s t i l l i n g basins i s con-s i d e r e d a p p l i c a b l e t o bacon-sincon-s w i t h a l e n g t h o f Sdg or g r e a t e r and a decon-sign depth equal t o t h e o r e t i c a l d g .
Bank Riprap
k^. Whereas the bottom r i p r a p s t a b i l i t y problem i s v e r y complex, bank r i p r a p below energy d i s s i p a t o r s i s more troublesome because of the combined e f f e c t o f wave a c t i o n and side r o l l e r s . Waves generated i n a s t i l l i n g b a s i n c o n t r i b u t e t o t h e i n i t i a l dislodgement o f the rock and the side r o l l e r t r a n s p o r t s the m a t e r i a l i n t o the main c u r r e n t of f l o w below the s t i l l i n g b a s i n . There are numerous cases o f severe bank e r o s i o n below s t i l l i n g basins which has formed r o u g h l y s e m i c i r c u l a r i n d e n t a t i o n s on each side o f the o u t l e t channels. The p e r i o d i c replacement o f bank r i p r a p i n these s i t u a t i o n s i s , no doubt, a c o s t l y i t e m .
Side r o l l e r s
k6. The ' S i d e r o l l e r s are more l i k e l y t o be intense i n t h e case o f an
abrupt t e r m i n a t i o n o f the v e r t i c a l s i d e w a l l s o f a s t i l l i n g b a s i n a t an o u t -l e t channe-l o f t r a p e z o i d a -l cross s e c t i o n . The suppression o f side r o -l -l e r s by wing w a l l s i s d e s c r i b e d i n t h e Engineer Manual on h y d r a u l i c design o f r e s e r v o i r o u t l e t structures,'''^ s p e c i f i c a l l y paragraph-25i and p l a t e 37 t h e r e i n . I t has been demonstrated i n the l a b o r a t o r y t h a t a w a l l w i t h a c i r c u l a r quadrant extending t o the channel side slope i s e f f e c t i v e i n suppressing the side r o l l e r .
1+7. The appearance o f t h e side r o l l e r on t h e surface i s t h a t o f a simple eddy or v o r t e x w i t h a v e r t i c a l ax:is o f r o t a t i o n . However, the toe o f the side slope i s n o r m a l l y i n l i n e w i t h the base of the s t i l l i n g b a s i n w a l l so t h a t the eddy a x i s must curve away from t h e bank and the diameter
of the v o r t e x decreases w i t h increased depth. So f a r as i s known, t h i s
phenomenon w i t h i t s s p e c i a l boxmdary geometry has not been f u l l y explored e x p e r i m e n t a l l y . Regardless o f t h e complexity o f the problem, the h y d r a u l i c model study o f f e r s v a l u a b l e a s s i s t a n c e i n d e s i g n i n g t o minimize the e f f e c t o f t h e side r o l l e r upon t h e bank r i p r a p below energy d i s s i p a t o r s .
Wave a c t i o n
k8. Superimposed upon t h e side r o l l e r e f f e c t are s u b s t a n t i a l waves generated by the t u r b t a e n c e o f a h y d r a u l i c jump or the impingement o f a j e t from a f l i p bucket. The f o l l o w i n g d i s c u s s i o n i s concerned p r i n c i p a l l y w i t h waves generated i n a s t i l l i n g b a s i n . I t can be expected t h a t such waves from a jump w i t h a h i g h i n i t i a l Froude number would be g r e a t e r than those from a jimip w i t h a lower Froude number. Furthermore, waves i n a jump f o r e -shortened by b a f f l e s and an end s i l l shoixld be l a r g e r t h a n those from a simple jump on a f l a t f l o o r .
i+9. The h e i g h t o f waves below a simple h y d r a u l i c jump on a f l a t
17
f l o o r was measured by Abou-Seida a t the U n i v e r s i t y o f C a l i f o m i a , Berkeley. The Berkeley t e s t s were reanalyzed and p l o t t e d i n p l a t e 12
w i t h e n t e r i n g Froude n-umber F, versus H /d , where H i s the observed
-L S J- S
wave h e i g h t measured from c r e s t t o t r o u g h and d.^^ i s t h e depth o f the f l o w e n t e r i n g the h y d r a u l i c jump. A r e l a t i o n was determined by l e a s t squares, e l i m i n a t i n g the parameters where t h e sequent depth r a t i o dg/d-^ was g r e a t e r than 10 percent o f the t h e o r e t i c a l v a l u e . For reasons mentioned
subse-q u e n t l y , the r e g r e s s i o n l i n e was e x t r a p o l a t e d from the upper l i m i t o f Abou-Seida' s t e s t s (F ^ = 5.0 t o F^ = 10.O).
50. The USER measured wave h e i g h t s i n a model study o f the s t i l l i n g l8
b a s i n f o r Paonia Dam. The p l a n and p r o f i l e o f t h i s s t i l l i n g b a s i n are a l s o shown i n p l a t e 12. I t should be noted t h a t the wave h e i g h t s were mea-sured near the water's edge. The maximum wave h e i g h t observed i s shown as a s i n g l e p o i n t a t F^ = 10. The dashed l i n e through t h i s p o i n t i s drawn p a r a l l e l t o the Abou-Seida r e g r e s s i o n l i n e . Although such a l i n e has l i t t l e meaning because i t i n v o l v e s a double e x t r a p o l a t i o n and a s i n g l e s t i l l i n g b a s i n , no o t h e r guide i s known f o r the problem o f e s t i m a t i n g wave h e i g h t s i n such a s i t u a t i o n .
51. I t can be concluded from the f o r e g o i n g study t h a t wave h e i g h t
observations i n s t i l l i n g b a s i n model s t u d i e s are v e r y much needed. The
l a b o r a t o r y measurements can be accomplished w i t h modern e l e c t r o n i c appa-r a t u s . Pappa-repaappa-rations have been made by t h e WES i n coopeappa-ration w i t h t h e F o appa-r t Worth, Kansas C i t y , and L o u i s v i l l e D i s t r i c t s t o measure wave h e i g h t s i n t h e p r o t o t y p e when t e s t flows are a v a i l a b l e . However, t h e l a b o r a t o r y o f f e r s a b e t t e r o p p o r t u n i t y t o o b t a i n i n f o r m a t i o n on a wider range o f h y d r a u l i c and bovindary geometry v a r i a b l e s . I f t h e designer has i n f o r m a t i o n on t h e
approximate wave h e i g h t s t o be expected, t h e m a t e r i a l on rock s t a b i l i t y
19
i n t h e Engineer Manual on design o f breakwaters sn-d j e t t i e s may be u s e f u l .
/
I
5 -PAPS IV: CONCLUSIONS I
52. F u r t h e r i n f o n n a t i o n needed f o r r i p r a p design i s o u t l i n e d i n J Appendix B. However, c e r t a i n conclusions can he dravm from the study I presented i n t h i s r e p o r t , and are presented as f o l l o w s .
a. The o n l y known sound p h y s i c a l p r i n c i p l e f o r s t a b l e r o c k design i s the A i r y law'''~9 which r e l a t e s the weight o f the stone t o the s i x t h power o f the mean v e l o c i t y a c t i n g on the rock.
b. Only knowledge o f the v e l o c i t y p r o f i l e near the bottom can be expected t o y i e l d a reasonable average v e l o c i t y a c t i n g on the rock. The s i z e o f rock i n t u m a f f e c t s the v e l o c i t y d i s t r i b u t i o n .
£. The mechanics o f the s t a b i l i t y o f a given s i z e r o c k w i t h -i n a w-ide span o f s -i z e g r a d a t -i o n needs more study. F u r t h e r i n v e s t i g a t i o n may r e v e a l t h a t i t i s economical, where l a r g e q u a n t i t i e s o f r i p r a p are t o be p l a c e d , t o screen out the
smaller s i z e rock f o r other uses, l e a v i n g a narrow span o f s i z e g r a d a t i o n .
d. The e f f e c t o f f l o w i n channel bends on r i p r a p needs f u r t h e r study i n the l a b o r a t o r y . I n t h e meantime, the measurement o f h y d r a u l i c v a r i a b l e s i n the f i e l d on b o t h tangents and curves should y i e l d e a r l y design i n f o r m a t i o n f o r a given s i z e g r a d a t i o n .
e. The e f f e c t i v e n e s s o f d i f f e r e n t designs o f toe p r o t e c t i o n ~ f o r r i p r a p b l a n k e t s needs t o be i n v e s t i g a t e d .
f . Riprap problems i n connection w i t h energy d i s s i p a t o r s are so complex t h a t they w i l l r e q u i r e s o l u t i o n b y the use o f h y d r a u l i c models.
g. I n g e n e r a l , the problem o f the s t a b i l i t y o f r i p r a p i n v o l v e s such an i n t e r r e l a t i o n o f independent and dependent v a r i a b l e s t h a t much more f i e l d and l a b o r a t o r y i n v e s t i g a t i o n i s needed t o p e r m i t development o f the most economic design.
LITERATURE CITED
1. U. S. Army Engineer Waterways Exp'eriment S t a t i o n , CE, H y d r a u l i c Design
C r i t e r i a . Vols 1 and 2 ( p u b l i s h e d s e r i a l l y by i s s u e s ) , V i c k s b u r g , Miss.
2. Keulegan, G. H., "Law o f tiorbulent f l o w i n open channels." U. S. Bureau o f Standards, J o u m a l o f Research, v o l 21, No. 6, RP-1151
(Washington, D. C , December 193Ö), pp 707-7UI.
3. Engineering H y d r a u l i c s , Proceedings o f the F o u r t h Conference, June 12-15, 1949, Hunter Rouse, ed. John W i l e y & Sons, I n c . , New York, N. Y.,
1950, 1039 pp.
k. U. S. Army Engineer D i s t r i c t , CE, P o r t l a n d , Oregon, Report on High V e l o c i t y Revetment Tests ( C i v i l Works I n v e s t i g a t i o n 485). 1 January
1952.
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Characteri s t Characteri c s Characteri n F l o o d C o n t r o l Tunnel 10, F o r t R a n d a l l Dam, H y d r a u l Characteri c P r o t o
-type TestsT T e c h n i c a l Report No. 2-626, V i c k s b u r g , Miss., June I963. 6. Lundgren, H., and Jonsson, Ivan G., "Shear and v e l o c i t y d i s t r i b u t i o n
i n shallow channels." ASCE H y d r a u l i c s D i v i s i o n J o u m a l , v o l 90, HY 1 (January 1964), pp 1-21.
7. S h e l f o r d , W i l l i a m , "On r i v e r s f l o w i n g i n t o t i d e l e s s seas, i l l u s t r a t e d
by the R i v e r T i b e r . " Proceedings, I n s t i t u t i o n o f C i v i l Engineers, v o l 82 (1885).
8. A i r y , W i l f r e d , d i s c u s s i o n o f paper, "On r i v e r s f l o v r i n g i n t o t i d e l e s s
seas, i l l u s t r a t e d by the R i v e r T i b e r , " by W i l l i a m S h e l f o r d . Proceedings, I n s t i t u t i o n o f C i v i l Engineers, v o l 82 (1885), p 25.
9. Hooker, E l o n H . , "The suspension o f s o l i d s i n f l o w i n g water."
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Cambridge, Mass., January I962.
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V E L O C I T Y P R O F I L E R O U G H B O U N D A R Y
SITE LOCATION
V E L O C I T Y D I S T R I B U T I O N F E A T H E R R I V E R S I T E 12
1 2 3 4 5 6 7 8 V E L O C I T Y , F P S D I S T A N C E F R O M S Y M B O L W E S T B A N K , F T O 26 0 39 O 47 A 56 V E L O C I T Y V E R S U S Yf F E A T H E R R I V E R S I T E 12 P L A T E 3
D I S T A N C E F R O M K = 4.6 IN., 0.383' S Y M B O L W E S T B A N K . F T y = 2.46 F P S K O 26 0 39 / 0 47 A 56 V E L O C I T Y V E R S U S Y F E A T H E R R I V E R S I T E 12 P L A T E 4
S T A B L E R O C K S I Z E
A. S C H E M A T I C VIEW L O O K I N G U P S T R E A M
F O R C E S A C T I N G O N B A N K R I P R A P
3.0 2 . 5 a. O y-u < ll. 2.0 1.5 1.0
-/
1 1 1 1 l l l l l l l l l l l l 1 I l . l 0.00 0.05 0.10 0.15 S T A B I L I T Y C O E F F I C I E N T C . 0.20 0.25 Vk + 1 - 1, , 3 / 2 M = [ l + S1N(2<^)] N O T E : S E E P L A T E 6 F O R D E F I N I T I O N O F (f). S T A B I L I T Y O F B A N K R I P R A P P L A T E 7A . M I T ROUGH B O U N D A R Y T E S T S
( S T A 1, F I G . 20 IN R E F 9 - S T R A I G H T C H A N N E L )
B. T O E T R E N C H
LOW WATER
LOW-WATER BED
• HIGH-WATER BED SCOUR
C. T H I C K E N E D T O E
R I P R A P T O E P R O T E C T I O N
I A . SMOOTH C H A N N E L I B. ROUGH C H A N N E L N O T E : F I G U R E S R E P R O D U C E D F R O M R E F 12, C H A N N E L B E N D E X P E R I M E N T S M I T . P L A T E 9 L.
U. S. B U R E A U O F R E C L A M A T I O N B E N D (SMOOTH C H A N N E L , R E F 1 3 ) U N I V E R S I T Y O F IOWA B E N D (SMOOTH C H A N N E L , R E F 14) C H A N N E L B E N D E X P E R I M E N T S U S B R A N D I O W A P L A T E 10
E L E V A T I O N J U M P ON H O R I Z O N T A L B E D (Pjg.p ,.7) P A O N I A S T I L L I N G BASIN ( R E F 18) z . 0 1.5 1.0 ©, ^ B E R K E L E Y T E S T S ( R E F 17), é = P O I N T S F O R W H I C H < l „ / d . V A R I E S F R O M T H E O R E T I C A L B Y L E S S T H A N 10% U S B R T E S T S ( R E F 18) M E A S U R E D MAXIMUM W A V E ( R E F 18) 0.5 0 . 0 " 10 W A V E S B E L O W H Y D R A U L I C J U M P S P L A T E 12
