o ^ ' ^ i a ' Ö ^ 1 / ó i B L I O T H E E K
W e i e r l o o p k u n d i q Laboraloriurr!
VELOCITY FORCES'ON
SUBMERGED ROCKS
MISCELLANEOUS PAPER NO. 2-265 April 1958
U . S, Army Engineer Waterways Experiment Station C O R P S O F E N G I N E E R S
i i i
. , ' PREFACE Y
The study described i n t h i s report was made under the Corps.of
-Engineers C i v i l Works I n v e s t i g a t i o n 80^1-; "Analysis of Hydraulic Experi- :; mental Data (Model and Prototype) and Development of Design C r i t e r i a . " : The Waterways Experiment Station i s assigned the r e s p o n s i b i l i t y o f
develop-ing "Hydraulic Design C r i t e r i a . " - ,.
A chart to he used as a guide f o r rock size c r i t e r i a f o r r i v e r j
closures and riprap i s included i n the seventh issue of Hydraulic Design; C r i t e r i a . The i n v e s t i g a t i o n and research that were necessary to develop; t h i s chart are summarized herein. ; i
The i n v e s t i g a t i o n was made by Mr. R. G. Cox^ Chief, Analysis Section, under the supervision o f Mr. F. B. Camphell, Chief, Hydraulic Analysis
COKTEWTS Page PREFACE i i i WOÏATIONS ,\ v i i SUMMARY i x PART I : IWIRODUCTION 1 Scope of Study 1 H i s t o r i c a l Background 1 PART I I : THEORY » 2 Transportation 2 S t a b i l i t y • • 3 Resistance • 5 PART I I I : DERIVATION OF DESIGN CURVES ,. 8
Hydraulic Design Chart 7 1 2 - 1 : River Closures
-Velocity vs Stone Weight 8 Slope Effect . . . . . 10
PART IV: CONCLUSIONS • H River Closures . • • H
Bank and Channel Protection . . . 1 1
Breakwaters ' 1 1 PLATES 1-3 ;
APPENDIX A : AMOTATED LIST OF REFERENCES A l
APPENDIX B: VELOCITY DATA ! • B l
NOTATIONS 2 A Cross-sectional area, f t - ' C-i „ Constants Cp Drag c o e f f i c i e n t s • , ' ' ! . d Depth o f flow, f t d Diameter of stone, f t ' g ' D Height o f cuhe, f t F Force, I h 2 g Gravity, 32 f t per sec
H Wave height, f t .
K' Constant i n modified I r i h a r r e n equation
Moment arm o f actuating force ' ^ • ' Moment arm o f r e s i s t i n g force
M^ Forcing moment, f t - l b ' M^ Resisting moment,- f t - l h
n Roughness c o e f f i c i e n t . Manning's s Slope o f energy gradient
V Mean v e l o c i t y , f t per sec
\ C r i t i c a l mean v e l o c i t y at v^hich movement begins, f t per sec Vg Velocity acting d i r e c t l y on stone p r o j e c t i o n , f t per sec
Approach v e l o c i t y , f t per sec W Weight o f rock, l b
y The Isbash constant, 1.20 and 0 . 8 6 f o r maximum and minimum stone, s t a b i l i t y . .
H Coefficient o f f r i c t i o n f t ^ '
.2 2 •
T Tractive force, l b per f t
C r i t i c a l t r a c t i v e force, l b per f t "
7 Specific weight o f water, 62.k l b per f t ^ 7g Specific weight o f stone, 165 l b per f t - ^ P . Density o f f l u i d , - , slugs per f t ^
& OC Angle o f repose
I , ' , ( - I '( ! " , ( , , , , ix SUMMARY
The development of interest in the hydraulic forces acting on a body in a moving fluid from the seventeenth century to the present time is traced. Various formulas pertaining to bed-load movement, rock-filled dams, break\'Taters, and drag coefficients are studied. The formulas are transposed to show their interrelationship.
Available data pertinent to the design of riprap and river cl~sures
are discussed and summarized. Suggested design curves are given. The ef-fect of bed slope on rock stability is considered.
VELOCITÏ FORCES ON SUBMERGED ROCKS
PART I : INTRODUCTION
Scope of Study .
1 . Modern use of rock f o r r i v e r closures, breakwaters, and r i p r a p has stimulated i n t e r e s t i n the hydraulic forces that act on submerged bodies. This i n t e r e s t l e d t o the development of a hydraulic design c r i
-t e r i a char-t f o r use by -the Corps of Engineers as a guide i n r i v e r closure and r i p r a p design problems. I n the development of t h i s chart m a t e r i a l
from many so\arces was compiled and i s l i s t e d i n Appendix A. I n a d d i t i o n , '• a study was made of various formulas commonly used i n the s o l u t i o n of these and similar hydraulic problems. The r e s u l t s of t h i s study are summarized herein.
• H i s t o r i c a l Background
2. Interest i n the hydraulic forces acting on a submerged body i n a moving f l u i d dates back t o the seventeenth centwy.^ l a t e i n the eighteenth century Dijbuat published the f i r s t r e l i a b l e data on the t r a n s p o r t a t i o n of s o l i d p a r t i c l e s by flowing water and derived an equation attempting t o de-f i n e the laws ode-f movement ode-f m a t e r i a l along the bed ode-f a stream. Study ode-f the movement of material i n canals and r i v e r s during the nineteenth century resulted i n many observations by independent investigators. Much of the data r e s u l t i n g from these t e s t s remains v a l i d today. I n I896, E. H. Hooker''"^ made a comprehensive summary of the data .and theories of these
early investigators.
3. I n the f i r s t h a l f of the twentieth century many studies r e l a t i n g to specific problems vrere undertaken, l/hile major e f f o r t s were d i r e c t e d toward the study of the mechanics o f sediment transportation, the problems of r i p r a p and revetment design as w e l l as of r i v e r closures and breakwaters received considerable a t t e n t i o n . The advent of the airplane and the r e
-s u l t i n g aerodynamic re-search contributed much t o the knowledge of f l u i d forces acting on bodies. •
PARTJI: THEORY
h. The study of the hydraulic forces that act on bodies submerged i a f l u i d i n motion can be divided i n t o .three general categories.. F i r s t , t h movement or transportation of material i n a stream i s o f i n t e r e s t i n the study of natural r i v e r phenomena such as the formation of sand bars, cros ings, and deltas. Second, the s t a b i l i t y of a rock structure or an individ-u a l stone i s important i n the design and constrindivid-uction of rock dams, revet-ments, r i p r a p , and breakwaters. Third, the form resistance of a body or
structure t o flow i s important i n the design of p i e r s , b a f f l e blocks, and h y d r o f o i l s . Ifliile the general phenomena i n each case are the same, d i f f e r ent approaches have resulted i n numerous d e f i n i t i o n s and formulas. How-ever, since each case involves common actuating forces, the r e s u l t i n g equa-t i o n s can ofequa-ten be i n equa-t e r r e l a equa-t e d . •
Transportation
5. Submerged material transported by a f l u i d moves either along the boundary or i n suspension. Movement of p a r t i c l e s along the boundary i s more commonly defined as bed load i n a natural stream. The movement i s re
l a t e d t o the shear force of the f l u i d boundary i n which the material moves Duboys recognized t h i s phenomenon i n I879 and introduced the term t r a c t i v e force. The formula f o r t h i s force i s ( f i g . l ) :
E N E R G Y G R A D I E N T ( S ) T '= yds
(1)
W A T E R S U R F A C E
19
• ' • • S T R E A M B E D •••.•''.>•.••;:••:
Studies by L. G. Straub, by A. Shields, and others have determined t h a t the c r i t i c a l trac. t i v e force f o r p a r t i c l e s o f 0 . 0 3- f t diameter or greater can be expressed as:
Fig. 1 = 0.C6 (7g - 7 )
The Manning equation f o r twodimensional open channel flow i s
-„ 1.1.86 s l/ 2 d 2 / 3
|i:'ged i n ' | t , the the cross- fidivid-i-evet- • ir 1 and l i f f e r - low-5 equa-ig the i s is' re-;c-( /e ( 1 ) |:, and t r a c -|;eter ( 2 )
The investigations of Chang and others indicate t h a t the l4i,nning n f o r a movable bed can be expressed as a function of the mean grain-size diameter of the bed material. Straub's 19 expression f o r t h i s r e l a t i o n s h i p i s :
1/6 /
n = O.0I+32 d
g
The t h e o r e t i c a l c r i t i c a l mean v e l o c i t y a t which bed material w i l l begin t o move was obtained by Straub by s u b s t i t u t i n g equations 1, 2 , and k i n t o equation 3. The r e s u l t i n g equation i s :
1/6
8.1+5 ^s - ^
7
(4)
( 5 )For specific weight of stone and water of 165 l b per f t ^ and 6 2 .l . lb per f t > respectively, equation 5 can be reduced t o
1/6 1/2 V = 1 0 . 8 d„ c g ( 6 ) . 1 / 6
The term (d^/d)"^''" appears t o be a v e l o c i t y d i s t r i b u t i o n f a c t o r which translates the meaji v e l o c i t y t o the shear v e l o c i t y acting on the p a r t i c l e s at the boxmdary.
S t a b i l i t y
6. Adequate design of r i p r a p , revetments, breakwaters, and r o c k - f i l l dams requires knowledge of the s t a b i l i t y of large
size material i n f l u i d s i n motion. Two of the better known investigators i n these f i e l d s are S. V. Isbash"'"^'•"''^ and R. I r i h a r r e n Cavanilles.''"'^
I n 1932 Isbash published the r e s u l t s of h i s ex- Fig. 2
tensive experiments on the construction of rock
dams i n flowing water. His basic equation f o r stone s t a b i l i t y i s ( f i g . 2 ) :
y¥ 2 g
V cos a - s i n a y d
3
( 7 ) s " I - 7
Equation 7 can be f u r t h e r s i m p l i f i e d f o r 165 l b per f t ^ stone and on a hor i z o n t a l surface i n fresh water t o :
•h
and ,
1/2
= 8.85 dg ' (nonbedded stone) ( 9 )
7. The I r i h a r r e n formula f o r the design of rubble-mound
hreak-vaters was published by Prof. Ramon I r i h a r r e n Cavanilles i n I938. The co-e f f i c i co-e n t i n thco-e I r l b a r r co-e n formula as dco-etco-erminco-ed from obsco-ervations on a c t u a l breakwaters was dimensional. I n I952, R. Y. Hudson"'--'- published a more general form of t h i s equation which i s dimensionally homogeneous. The I r i h a r r e n formula as modified by Hudson i s ( f i g . 3 ) :
K' y 7^ ^3 ^3
W= x - j-^ (10)
(7„ - 7) (n cos a - s i n ay
F i g . 3
8. Mr. P. T. Bennett of the Omaha D i s t r i c t , CE, demonstrated some years ago that the I r i h a r r e n formula could be transferred i n t o the Isbash type formula by making t'ne f o l l o w i n g s i m p l i f y i n g assvmptions:
Let: W = D^ 7^ = 2gH | i = 1 . 0 Then K'
H-(
73 - 7 D = (cos a - s i n a)3 ^ f K ^ H 7 (cos a - s i n cc) 7 - 7 seoid (9) 1'eak-The co-is on .ished a leous. The _ D (cos g - s i n a ) ~ ^ 2 g = 3 ^ 7 V = 1
Eq.uation 11 compares w i t h equation 7 when
y _ y - ~ , r ~ \ cos a - s i n a ^ D (11) (10) ( • ied some le Isbash and d = 1.2lf D •
9. The modified I r i b a r r e n formula can also be w r i t t e n f o r a sphe-r o i d a l stone on zesphe-ro slope as:
or n 73 ^ K' 73 7^ (Vg^gg)^ ( 7 3 - 7 ) 3 1/2 (12) ir _ o O ^ — i .\
The average value o f K' f o r n a t u r a l and a r t i f i c i a l breakwater rock has been determined aa O.OI7. Equation 12 thus becomes
V = 18.2 d
s j
1/2 (13)
Resistance
10. The l o n g i t u d i n a l force-on an immersed body i s equal t o :
. . 2
F = A p —
The cross-sectional area of an embedded stone on which the force F acts can be expressed as ( f i g . 1+):
6
The moment a m o f the force F acting on the emhedded stone i s a function o f
the-stone diameter:
I.
2 ^g
F i g . k
Therefore, the f o r c i n g moment cam he -v/ritten as*:
^ 2 „ 2
2g ^ ^2^g (15)
The r e s i s t i n g moment of the stone t o overttirning depends upon the r e s i s t i n g moment arm {t ) which i s a function o f the stone diameter (C^ d^) and upon
the submerged weight of the stone. 3
d
M (73 - 7) C3 dg (16)
I n c i p i e n t overturning o f the stone r e s u l t s when the f o r c i n g moment equals the r e s i s t i n g moment: or. S ^ l - ^ ^ . ' ^ o ' ^^2 2g It d d = (17) V = 2g (7s - 7) C3
For a specific condition l e t :
2g C,
7 t i n g on ,f the be •written] (15) r e s i s t i n g and upon ( 1 6 ) i t eq.vial3
For 7 = 165 l b per f t ^ and 7 = 6^2 A l b per f t ^
1.28 (19)
D
11. I t has been shown t h a t y i n the Isbash equation i s the same as
. • i n the I r i b a r r e n equation when d = 1.2i*- D (paragraph 9 ) . This
relationship can be extended t o incl\ide the function of the drag c o e f f i c i e n t of equation I 8 . '4^ ' 4 ^ or D A JK ^ = y and (17) 0', = V ^ = ^
The r e l a t i o n s h i p between the Isbash, I r i b a r r e n , and drag c o e f f i c i e n t • formulas i s also shown by equations "J, 13, and 19. These equations can be related t o each other by proper manipulation of the c o e f f i c i e n t s .
XXX.. « - - ^ ^ ^ ' ^ ' ^ C l o s u r e s - v e l o c i t y ve 1 l i e D e e i s n C h a r t 7xa-l: ^ ^ « ^ ' ' ^ ^ ^ ^ . ^ a v a i l a b l e d a t . , " r t t e x T s - - - " ^ " " ^ ' ^ e . o « O. t . i e p e r t a i n x n g ^^^^ ^ost r e l x ^^r: tl p r e s e n t ti»e. t i o n s fron. 1786 independent i n v e a t i g a
Easic_tóta l^^te 1 al<i ^ . j t b o u l d e r s i n -" . d . o . Pe..xes i n _ used « o n s . M a t e r r a l s - ^^^^^ ^^^^^^ ,55 1. p ^^^^^ ^„ l^lSh r i v e r v e l o c r t r e s . A P ^^^^^^ ^be pXotted ^^^^^^^^ t o s i m p l i f y comparison, i'orty ^^^^^ ^ o r n t s ^^^^^^^ Tottom v e l o c i t y - - - ^ a a t a p l o t t e d on t . e c h a r t t e s t s hy s i x a-T4- -From tes-ot^ UJ
on i=°l=^*='l *°f===it,e v e l o c i t y " „eral agreement r n -e i g h t i h S t a n c -e = . J ^ ^ ^ . H o « « ^ ' ^ ^ c f m most c a s -e s , f o r t h e " - « " m " l i o c i t i e s were observe ^ , e n t y - s i x o h s e r v f - t s t o n e _ . a s ^
i a i H ^ ^ n
r
i ^ - o r - o i " : i;;se n ^ e ^ „ - X c l S e sbfan^to^SS-nt^f
t S ^ - ^ ^ ^ ^ ^ ^ ^ ^ ^^^^ r e s u l t i n g xn dxspx ^^^^ measured. ^ T w e n t y - f o u r - i n c b q u a r r y ^ , H i l e C l q s } H £ ^ . H t H v e l o c x t x e s e^^^"^^ ^ ctiannel Bonrievxxi:e__^ii--T^^ w x t n n o r t h it^a^" + T T -• fe^^^^^^^^oï^A?e of a b r e a c h xn t h ^^^^^a t h a t 11 per Bec ^--iX^^^le Dam. f ^ ^ f / . e / d a m i n the backc o f f e r d a m a t Bonnev ^^^a.ed. c o f t e ^ g ^ . i , . boulderB -n^^^^3,^extxeB estxmated a t 9 ^ ^ ^ ^ , , t o n e
. e r 9 A
-n^yXlf
v S e l u b o e ^ -d.9
Movement of the ^l-OO-lb stone occurred w i t h average veloc-i t veloc-i e s of 16-18 f t per sec.
9
L' Zuider Zee.-^ Ihe data on the Zuider Zee closure indicate stones 1.77 f t i n diameter on fascine mattresses were stable i n currents of 9.85 f t per sec.
g- Passarnaquoddy.^ Tests were made on a l:50-scale model o f the Passarnaquoddy r o c k - f i l l dam at the Alden Hydraulic laboratory. Stone sizes varied from O.O62 t o O.I67 f t i n
diameter. , ,•
28
h. S t i l l i n g Basin. Tests were made on a 1:36-scale model a t the Waterways Experiment Station on 0.028- t o 0.083
-ft-diameter crushed rock i n a channel inmediately below a s t i l l i n g basin. V e l o c i t i e s were measured one prototype ' foot above the bottom when stone movement occixrred.
28
1 ' Channel. These data were obtained i n conjunction w i t h h above. Observations were made downstream from the area o f " s t i l l i n g basin turbulence.
2k
j . ' McHary Dam. This, observation i s based on a general com-ment on the action o f concrete tetrahedrons i n the model closure study.
Design curves
ik. Three design cvirves are shown i n p l a t e 1. The Isbash cvtrve i s considered applicable t o conditions where turbulence i s not excessive and the stones are embedded. I t was derived from equation 8 i n the f o l l o w i n g manner:
« d 3
then
Let stone weight (w) = ^ ^ 7^
165 rt d 3 W = ^ — = 86.5 d ^ 6 ^ g and / *g - WJ^ Equation 8 V = 12.35 d g
10 o r ,. V 12.35 and W = 2.kh X 10"^ (20) 29
15. The USER curve ^ i s the t e n t a t i v e design curve recommended hy the Bureau of Reclamation f o r r i p r a p design helow s t i l l i n g hasins. I t i s considered applicable \mder conditions of excessive turbulence. The Isbash formula (equation 9) f o r minimum stone s t a b i l i t y approximates the Bureau's t e n t a t i v e design curve.
16. The t h i r d curve on the graph shows the v e l o c i t y required to overturn an i s o l a t e d cube. This curve was developed from data presented " i n Wind Tunnel Studies of Pressure D i s t r i b u t i o n on Elementary Building Forms- The pressure d i s t r i b u t i o n and the pressure resultants obtained on the f i v e exposed surfaces o f the cube used i n t h i s i n v e s t i g a t i o n are shorn i n plate 2. The i n c i p i e n t overturning moment i s the summation o f the moments on the upstream, top, and downstream faces of the cube. The r e s i s t i n g moment i s the submerged weight o f the cube times one-half the cube height. For 165 l b per f t ^ rock, the equation of i n c i p i e n t over-t u r n i n g on a l e v e l bed i s :
W = 1.2 X 10"3 (21)
Slope E f f e c t
17. The data sho™ i n plate 1 apply t o h o r i z o n t a l or gently sloping surfaces. V/here steep slopes w i t h uniform flow are encountered, the e f f e c t of slope on the s t a b i l i t y of the structure should be considered. The curves i n plate 3 i l l u s t r a t e t h i s e f f e c t . A constant depth and an Isbash c o e f f i c i e n t of 1.20 was assmed i n the development o f these curves.
11 \
PART IV:\ CONCLUSIONS
18. Considerable data are available t o a s s i s t i n the design of r i v e r clostires, breakwaters, and bank and channel protection. However,
f i n a l design, t o a large extent, depends upon p r a c t i c a l experience and ex-perimental studies. Local conditions and a v a i l a b i l i t y of material may
c o n t r o l the type of structure t o be b u i l t . ,
River Closures ƒ
19. Model studies of planned r i v e r closures are often desirable t o determine v e l o c i t i e s t h a t w i l l be encountered during d i f f e r e n t stages o f closure. They can be used f o r planning closure construction methods and
schedules. •
Bank and Channel Protection
20. The degree of tvirbulence expected i n an open channel i s an im-portant factor i n selection o f the size of r i p r a p f o r bottom and side pro-t e c pro-t i o n . The selecpro-tion of pro-the proper blankepro-t pro-thickness and gradapro-tion pro-t o protect the underlying m.aterial i s important i n designing r i p r a p .
Breakwaters
21. Present-day knowledge i s adequate f o r the design of conventional breakvfaters where stone size, shape, specific weight, and method o f
place-12
ment can be r i g i d l y c o n t r o l l e d . However, extensive research i s now m progress t o provide data t o meet the need f o r more economical designs.
D O W N S T R E A M F A C E B A S I C E Q U A T I O N S U P S T R E A M F A C E PRESSURE P A T T E R N (cp C O N T O U R S ) 2 W H E R E : Cp= P R E S S U R E C O E F F I C I E N T 6p= D I F F E R E N C E I N P R E S S U R E B E T W E E N A N Y P O I N T O N C U B E A N D T H A T IN T H E U N D I S -T U R B E D F L O W I N L B P E R S Q I N . V = V E L O C I T Y U P S T R E A M F R O M C U B E , F P S e= D E N S I T Y O F F L U I D I N S L U G S P E R C U F T F = F O R C E O N F A C E I N L B R = R E S U L T A N T O F A V E R A G E Cp F O R F A C E A •= D I M E N S I O N O F C U B E I N F T N O T E ' . D A T A F R O M " W I N D T U N N E L S T U D I E S O F P R E S S U R E D I S T R I B U T I O N O N E L E M E N T A R Y B U I L D I N G F O R M S " . N . C H I E N , Y. F E N G , H . J . W A N G , A N D T . T . S I A O , I O W A I N S T I T U T E O F H Y D R A U L I C R E S E A R C H . , R E Y N O L D S N U M B E R O F T E S T F L O W • A P P R O X 4 X 1 0 " ' PRESSURE R E S U L T A N T S ( A V E R A G E Cp V A L U E S )
FORM RESISTANCE OF SINGLE CUBE FLOW N O R M A L TO FACE
A l
APPENDIX A: ANNOTATED LIST OF REFERENCES,
American Society of C i v i l Engineers, Review of Slope Protection Methods, Report of the Subcommittee on Slope Protection of the • Conmittee on Earth Dams of the Soils Mechanics and Foundation
D i v i s i o n . Vol 74, No. 6, June 19^+0. ' "A summary of available information on p r o t e c t i o n of slopes of
dams against the d i s r u p t i n g e f f e c t s of waves and the erosive e f f e c t of r a i n , wind and f r o s t . " A r t i c l e evaluates various wave height formulas i n terms of current v e l o c i t y . No experimental data tabulated.
Blanchet, Ch., "Formation and. destruction of stone masses by a water current" ("Formation e t destruction par un courant d'eau de massif, en p i e r r e s " ) . La Houille Blanche, New Series No. 2 (March 19^6), p i t l . U. S. Army Engineer Waterways Experiment Station Translation No. 50-5, 1950, t r a n s l a t e d by W. W. Geddings.
Part I of three p a r t s . Discusses e q u i l i b r i u m of stones i n • flowing water. Equates forces acting on stones f o r various' condi-t i o n s of flow and scondi-tone posicondi-tions.
, "Technique f o r the construction of r o c k - f i l l dams i n flowing water" ("Technique de l a construction des barrages en pierres lancees dans 1'eau courante"). La Houille Blanche, v o l 1
(November-December 19^-6), pp 393-l|-05. U. S. Army Engineer Waterways Experiment Station Translation No. 52-1, 1952, translated by Jan C. Van Tienhoven.
J _ J L C t O U X C i - O O V X \JLJL.^^K^^i-t.l.^i.X V J . l ^ i i . . - j VJ. w...v j . w w — — —
dams. Chapter 1 gives equations for'computing the configuration o f , a dam under construction. Phenomena observed i n the construction of dams. Chapter I I discusses flow conditions, seepage, etc., during construction. This i s apparently Part I I of item 2.
, "Technique f o r the construction of r o c k - f i l l dams i n flowing water" ("Technique de l a construction des barrages en pierres lancees dans 1'eau cotirante"). La Houille Blanche, v o l 2
( January-February 19hj), pp hl-kj. U. S. Army Engineer V/aterways Experiment Station Translation No. 52-1,' 1952, translated by Jan C.
Van Tienhoven. • Chapter I I I and Part I I I of items 2 and 3. I l l u s t r a t i v e
ap-p l i c a t i o n of theory and design t o a ap-prototyap-pe ap-problem.
Chang, Y. L., "Laboratory i n v e s t i g a t i o n of flume t r a c t i o n and trans-p o r t a t i o n . " Transactions, American Society of C i v i l Engineers, v o l
loi. (1939). • ,
Paper presents r e s u l t s of a laboratory i n v e s t i g a t i o n of t r a c t i v e and transportation f a c t o r s determined f o r numerous sizes of bed
6. Chien, Ning, Feng, Yin, Wang, Huang-Ju, and Siao, Tien-To, Wind Tunnel Studies of Pressure D i s t r i b u t i o n on Elementary Building Forms. Iowa I n s t i t u t e of Hydraulic Research f o r the Office of Naval Research, ^
1951.
Experimental i n v e s t i g a t i o n of wind forces on various simply . shaped objects simulating b u i l d i n g s . Piezometric pressures measured on.surfaces of buildings and pressure contours developed. For use on Chart 712-I, the pressure data on a cube were evaluated i n terms of the overturning force. The required size of a stable cube having a s p e c i f i c weight of I65 l b per cu f t was computed f o r various v e l o c i -t i e s . The r e s u l -t i n g curve i s shown on Char-t 712-1 as the i s o l a t e d cube curve.
7. G i l b e r t , G. K., The Transportation of Debris by Running Water. United States Geodetic Survey Professional Paper Ö6, 1914.
P r i n c i p a l i n t e r e s t i s discussion of bed load and suspended load
e. motion. No basic data tabulated.
8. Gontcharov, V. N., "Flow arovind a cube f i x e d t o bottom o f f l m e . " Transactions, S c i e n t i f i c Research I n s t i t u t e o f Hydrotechnics, v o l 17
(1935)J PP 77-112. Translated from Russian by Dr. A. Lukseh, Associate Research Engineer, Iowa I n s t i t u t e o f Hydraulic Research, University of Iowa.
Paper presents r e s u l t s of extensive studies of pressures on cubes f i x e d t o the bottom of a flume. Various patterns of cube ar-rangements vrere investigated from the i s o l a t e d cube to completely f l o o r i n g the flume bottom w i t h cubes. The e f f e c t s of various cube spacing were studied. The r e s u l t s are presented i n terms of average pressures on the faces of the t e s t cubes.
9. Grimm, C. I . , and leupold, Norbert, Hydraulic Data Pertaining t o the Design of Rock Revetment. U. S. Army Engineer D i v i s i o n , North
P a c i f i c , CE, 1939.
r\.; c ^ n o c j Q Q (-vn-^von-t- -rA-irp^+.7npn+. T i T - a p t i ceR. Tabulates and n l o t s available laboratory data of movement of solids by flowing water. Evaluates Bonneville, Passamaquoddy, Isbash, WES, Groat, and Hooker
data. Includes observed prototype data on Columbia River, Zuider Zee, and i n the Los Angeles D i s t r i c t .
10. Hooker, E. H., "The suspension of solids i n flowing water." Trans-actions, American Society of C i v i l Engineers, v o l XXXVI (1896)^ "
H i s t o r i c a l review of knowledge on movements of solids i n f l u i d s . Describes types of movement. Discusses experiments and r e s u l t s of numerous investigations. Major p o r t i o n l i m i t e d t o sand -'studies. Page 3O8 tabulates r e s u l t s of e a r l y Investigators f o r
observed bottom v e l o c i t i e s i n which various materials including ; boulders 2.7 f t i n diameter were moved.
1
A3
11. Hudson, R.Y., "Wave forces on breakwaters." Transactions, American Society of C i v i l Engineers, v o l l l 8 ( 1 9 5 3 ) , P 6 5 3 .
Reviews common theories f o r computing wave forces on v e r t i c a l , walls and sloping rubble-mound breakwaters. Compares and evaluates various formulas. Gives a dimensionless form of the Irxbarren formula and c o e f f i c i e n t values which vary w i t h slope f o r n a t u r a l rock. The
Isbash curve-shown on Chart 7 1 2 - 1 i s s i m i l a r t o Iribarren's equatxon w i t h K' = 0 . 0 1 7 . : - - - . ,
12 , Laboratory Investigations of Rubble-mound Breakwaters.. , p i i i F ^ ; n t i d ^ > r J^ ^ 5 R I 9 5 7 American Society of C i v i l E n g x ^ r s Meeting, B u f f a l o , New York. WES MP 2 - 2 2 4 , June 1957..
Paper describes laboratory i n v e s t i g a t i o n at the Waterways"Ex-periment Station, Vicksburg, M i s s i s s i p p i , t o < i f f^^^^J^^^^^^f f o r the design and construction of rubble-mound breato^aters'. A new formula i s derived which i t i s believed w i t h new ^ ^ P f i f „ • e f f i c i e n t s w i l l increase considerably the accuracy of the design of rubble-mound breafa/aters.
13. Isbash,-S. v . . Construction of Dams by Dumping Stones i n t o Flowing Water,
translated
by A. Doujikov. Corps of Engxneers, U. S. Army, Eastport D i s t r i c t , Eastport, Maine, 1935 "-• - Complete design i n v e s t i g a t i o n of rock dams b u i l t i n flowing _
water including study of forces acting on i n d i v i d u a l f , t y of percolation, overflow discharge, requxred cross sectxons.
De-sign c r i t e r i a developed mathematically and v e r i f x e d experxmentally i n laboratory w i t h models of d i f f e r e n t scales. Numerous charts and graphs
L r dLign
of rock dams. No basic laboratory data tabulated. \k , "Construction of dams by depositing rock i n runnxng* ^:?^r." Transactions, Second Congress on Large Dams ( 1 9 3 0 ) .
summarizes experiments f o r construction of dams by «^^P^^iti^S rock i n running water. Author b r i e f l y reviews f ^ ^ ^ - y / ^ ^ J ^ ^ ^ ^ ^ f
small-scale experiments^ and gives equatxons applicable t o varxous. stages of construction. Riprap composed of 1 5 - t o f ^ - f
Larle rock not moved. No basic data given i n report. A tentatxve-l y Recommended curve f o r r i p r a p design appears to ctentatxve-losetentatxve-ly f o tentatxve-l tentatxve-l o w data discussed i n item 10. ' • Mo^Ha T? T Tiu T. Y., and Soucek, E., The Transportation of
u n i v e r s i t y of Ï S r a i ^ t S m T s i i t e m b e r continuation of work discussed i n item 16. Studies extended sizes of solids but sizes and v e l o c i t i e s r e l a t x v e l y small.
16. MavisTF.- T., and Tu, Y. C, T t e T r a n s ^ o r t ^ ^
1935-Reviews and e v a l u a t e s p r e v i o u s work on bed l o a d t r a n s p o r t a t i o n . D i s c u s s i o n i s r e s t r i c t e d t o some of the problems of t r a n s p o r t a t i o n o f s o l i d p a r t i c l e s w h i c h a r e r o l l e d or dragged a l o n g the hed of a c h a n n e l i n t r a c t i o n . I n c l u d e s i n v e s t i g a t i o n of Ho and Tu a t U n i v e r s i t y o f Iowa. Data l i m i t e d t o s m a l l g r a i n s i z e s and v e l o c i t i e s .
1 7 . O f f i c e o f the C h i e f of E n g i n e e r s , Slope P r o t e c t i o n . C i v i l Works E n g i n e e r B u l l e t i n 5 2 - 1 5 , 2 June 1952.
B u l l e t i n g i v e s d a t a f o r d e s i g n o f s l o p e p r o t e c t i o n f o r dams, r a i l r o a d and highway embankments, and c h a n n e l s .
18. P e i x o t t o , E . D., and Roherge, R. A., S i m i l i t u d e of I n c i p i e n t Motion. Master o f S c i e n c e T h e s i s , M a s s a c h u s e t t s I n s t i t u t e of Technology,
1956.
T h e s i s i s a l a b o r a t o r y i n v e s t i g a t i o n o f c o n d i t i o n s c o n t r o l l i n g i n c i p i e n t motion o f graded r o c k p a r t i c l e s composing the bed of a t u r b u l e n t stream. A r e s i s t a n c e c o e f f i c i e n t was o b t a i n e d f o r v a r i o u s s i z e d m a t e r i a l and p l o t t e d a g a i n s t R e y n o l d s nimiber. 1 9 . Straub, L. G., "Dredge f i l l c l o s u r e o f M i s s o u r i R i v e r a t F o r t R a n d a l l . " P r o c e e d i n g s , Minnesota I n t e r n a t i o n a l H y d r a u l i c Conference, lAHR (September 1 9 5 3 ) . D e s c r i b e s a c t u a l p r o t o t y p e c l o s u r e vrith i l l u s t r a t i o n s . D i s -c u s s e s b a s i -c p r i n -c i p l e s of d e s i g n of -c l o s u r e i n v o l v i n g -c r i t i -c a l t r a c t i v e f o r c e , c r i t i c a l v e l o c i t y , and s u r f a c e roughness of f i l l m a t e r i a l . C l o s u r e made by h y d r a u l i c f i l l . • Maximum s i z e b o u l d e r c a p a c i t y of dredge was ik i n .
20. Torpen, B. E . , "Large r o c k s i n r i v e r c o n t r o l works." C i v i l E n g i -n e e r i -n g , v o l 26, No. 9 ( S e p t 1 9 5 6 ) , pp 5 7 - 6 1 . (Mr. Torpen was f o r m e r l y w i t h North P a c i f i c D i v i s i o n , CE.)
A r t i c l e d e s c r i b e s c l o s u r e o p e r a t i o n s a t McNary, C h i e f Joseph, and A l b e n i F a l l s Dams and B o n n e v i l l e • c o f f e r d a m r e p a i r s . D u r i n g C h i e f •Joseph Dam c l o s u r e v e l o c i t i e s a p p r o a c h i n g 20 f t per s e c occurred-,and_ o n l y s e l e c t e d r o c k s o f 15 t o 20 t o n s vrould r e m a i n i n c l o s u r e gap. C a b l e s were f a s t e n e d to l a r g e r o c k s t o a s s i s t i n s t a b i l i z i n g s m a l l e r r o c k s . I t i s t o be noted the e q u i v a l e n t d i a m e t e r s o f 15- and 20-ton r o c k a r e 7 and 7 . 7 f t . These v a l u e s e x c e e d the l i m i t s o f C h a r t 712-1
b u t would p l o t c l o s e t o the i s o l a t e d cube c u r v e extended.
2 1 . U. S. Army E n g i n e e r D i s t r i c t , P o r t l a n d , CE, Report on Channel P r o t e c -t i o n a g a i n s -t High V e l o c i -t y Flow ( C i v i l W o r k s ~ P r o j e c -t ) . 1 J u l y 1951.
S t u d i e s of v e l o c i t i e s a l o n g t e n major revetments on r i v e r s i n Idaho and Oregon. F i e l d o b s e r v a t i o n s showed t h a t an l 8 - i n . l a y e r o f dvunped stone graded from 50 t o 3OO l b was g e n e r a l l y adequate w i t h maximum o b s e r v e d v e l o c i t i e s o f 10 f t p e r s e c p r o v i d e d no undermining o c c u r r e d or u n d e r l y i n g m a t e r i a l washed out through the v o i d s of the r i p r a p .
22. ' , Report on High V e l o c i t y Revetment T e s t s . CWI kd^, • ;
1 January 1952. ; ,
Prototype t e s t s on dumped graded r i p r a p i n a s p e c i a l l y h u i l t c h a n n e l below Dorena Dam. F o u r c l a s s e s o f graded rock, 20 t o kOO l b , were p l a c e d i n b l a n k e t s 12-21+ i n . t h i c k and t e s t e d under v e l o c i t i e s o f 7 t o 20 f t p e r s e c . Study p l a n n e d f o r revetment f a i l u r e r a t h e r t h a n movement of i n d i v i d u a l r o c k s . No s p e c i f i c d a t a r e c o r d e d f o r . r o c k movement. E x p e r i e n c e d f a i l u r e s r e s u l t e d from removal o f f i n e s a c t u a t i n g f a i l u r e r a t h e r t h a n d i s p l a c e m e n t o f l a r g e s i z e r o c k b y v e l o c i t y f o r c e s ,
23. U. S. Army E n g i n e e r D i s t r i c t , P o r t l a n d , CE, B o n n e v i l l e H y d r a u l i c L a b o r a t o r y , The D a l l e s Rock F i l l Model, Memorandum r e p o r t 2-2, 27 October 1954, ~ "
D e s c r i b e s r e s u l t s on model c l o s u r e u s i n g q u a r r y r u n r o c k ( l/ 2
t o n and s m a l l e r p r o t o t y p e ) and 3-ton r o c k on h i g h e r l i f t s . No s t u d y made o f independent stone a c t i o n . G e n e r a l procedure s a t i s f a c t o r y .
.2k. , McNary Dam--Second-step Cofferdam C l o s u r e , May 1956.
D e s c r i b e s model t e s t s made i n c o n j u n c t i o n w i t h a c t u a l r i v e r c l o s u r e b y u s e o f 12-ton t e t r a h e d r a l s , Most o f r e p o r t concerned v,rith methods o f making c l o s u r e . L a b o r a t o r y t e s t s i n d i c a t e d t e t r a h e d r a l s
s t a b l e f o r v e l o c i t y o f 20 f t p e r s e c b u t moved from c r e s t o f f i l l w i t h v e l o c i t y o f 29 f t p e r s e c . P r o t o t y p e c o n f i r m a t i o n o f model
c l o s u r e p r o c e d u r e . ;.
25. U. S. Army E n g i n e e r D i s t r i c t , V/alla W a l l a , CE, R e p o r t on C l o s u r e o f the Second-step Cofferdam--McNary Lock and Dam, J u l y 1951'
Report on a c t u a l c l o s u r e procedure and r e s u l t s . No d a t a on i n d i v i d u a l t e t r a h e d r a l s .
26. U. S. Army E n g i n e e r V/ater^rays E x p e r i m e n t S t a t i o n , CE, E x p e r i m e n t s t o Determine t h e E f f e c t i v e n e s s o f T e t r a h e d r a l B l o c k s a s Revetment. T e c h n i c a l Memorandum No. 26-2, J a n u a r y 1933.
I n v e s t i g a t i o n o f s i n g l e course o f t e t r a h e d r a l s f o r revetment use. I n v e s t i g a t i o n c e n t e r e d on removal o f f i l l e r m a t e r i a l from be-tween and under b l o c k s . No s t u d y made o f bottom v e l o c i t i e s r e q u i r e d t o move t e t r a h e d r a l s . T r a c t i v e f o r c e measured on i n d i v i d u a l t e t r a -h e d r a l s .
27. ^ C r i t i c a l T r a c t i v e F o r c e T e s t s o f Coarse M a t e r i a l . . . T e c h n i c a l Memorandum No. 59-1, J a n u a r y 1935*
Measurement o f t r a c t i v e f o r c e s on s o l i d s from sand g r a i n s up to 2 . 3- i n . s t o n e . No bottom v e l o c i t i e s measured. D r i f t o f m a t e r i a l meas\ired.
A6
29.
Model t e s t s \rere made on graded dvmiped r i p r a p below a s t i l l i n g b a s i n and i n t h e c h a n n e l downstream. B l a n k e t t h i c k n e s s v a r i e d from
1 t o 2 f t ( p r o t o t y p e ) . Bottom v e l o c i t y measurements observed a s m a t e r i a l moved.
U. S. Bureau o f R e c l a m a t i o n , S t i l l i n g B a s i n Performance--An A i d i n
D e t e r m i n i n g R i p r a p S i z e s . H y d r a u l i c L a b o r a t o r y Report No. HYD-409
23 F e b r u a r y I 9 5 6 . ' '
D i s c u s s e s and compares model and p r o t o t y p e r e s u l t s o f impact-type s t i l l i n g b a s i n s on r e l a t i v e l y s m a l l c a n a l - t y p e s t r u c t u r e s . Com-p a r a t i v e Com-photograCom-phs o f f l o w and s c o u r c o n d i t i o n s below P i c a c h o Arroyo C o n t r o l , North Branch Dam. P r o t o t y p e r i p r a p d e s i g n e d f o r v e l o c i t y o f
30 f t p e r s e c . Prototype v e l o c i t i e s computed t o be 37 f t p e r s e c .
30. , H y d r a u l i c Model S t u d i e s o f R o b l e s D i v e r s i o n Dam S p i l l w a y . H y d r a u l i c L a b o r a t o r y Report No. HYD-427, Ö November I 9 5 6 .
A l : 1 2 - s c a l e s e c t i o n model o f R o b l e s D i v e r s i o n Dam S p i l l w a y was - t e s t e d t o determine d i s c h a r g e c o e f f i c i e n t s o f r o c k b l a n k e t s p i l l w a y s
of v a r i o u s s i z e d r o c k . F l o w c o n d i t i o n s and r o c k s t a b i l i t y were checked.
3 1 . Webster, M. J . , "The D a l l e s d i v e r s i o n made w i t h r o c k - f i l l dam." C i v i l E n g i n e e r i n g , v o l 99 ( F e b 1 9 5 7 ) . '
A r t i c l e d i s c u s s e s c l o s u r e u s i n g end-dump method. E x t e n s i v e use was made o f a l : l| 0- s c a l e model t o determine the b e s t c l o s u r e procedure. The c o n d i t i o n s t e s t e d i n t h e model showed a v e r y c l o s e c o r r e l a t i o n w i t h t h e p r o t o t y p e .
