WAR DEPARTMENT 

CORPS OF ENGINEERS, U. S. ARMY 

STUDIES OF RIVER BED MATERIALS 

AND THEIR MOVEMENT, 

WITH SPECIAL REFERENCE TO THE 

LOWER MISSISSIPPI RIVER 

PAPER 17 

OF THE 

U. S. WATERWAYS EXPERIMENT STATION 

VICKSBURG, MISSISSIPPI 

JANUARY, 1935 

MISSISSIPPI RIVER COMMISSION PRINT 

ST. LOUIS, MO. 1000. 5-35 
II 

PREFACE 

This paper presents the results of two closely related investigations which have been actively carried on by the U. S. Waterways 

Experiment Station since the summer of 1932. In August of that 

year, the Chief of Engineers, U.S. Army, directed that studies be undertaken to determine the force of flowing water required to move 

materials composing the bed of the Lower Mississippi River. In 

complying with this directive it was realized that much information 

was needed, not only concerning the tractive force required to move 

particles of different sizes and physical characteristics, but also concerning the actual composition of the bed of the Mississippi River 

from Cairo, Illinois to the Gulf of Mexico. Without accurate knowledge of the nature of the material composing the bed, it would be 

impossible to evaluate the forces required to move it. Consequently, 

the problem divided naturally into two phases. 

Part I of this report contains a resume' of results obtained from 

flume tests of materials moved by hydraulic traction. This work 

was begun under the immediate supervision of Lieutenant P. W. 

Thompson, C. E., designer of the special flume used throughout the 

investigation. At a later date this work was taken over by J. B. 

Tiffany, Jr., Junior Engineer, upon whom fell the task of correlating 

data, analyzing the results, and preparing the subsequent report. 

C. E. Bentzel, Junior Engineer, who performed most of the actual 

tests and who assisted in the study of the data, performed a great 

service to the Station through the development of the velocity meter 

which bears his name. The Bentzel Velocity Tube, which is described in the main body of this report, has largely supplanted other 

types of velocity-measuring devices in the hydraulic model studies 

at the U. S. Waterways Experiment Station. 

Part II of this report consists of a tabulation and discussion of 

data relative to the characteristics of the materials composing the 

bed of the Lower Mississippi River. Mr. Charles W. Schweizer, 

Engineer, of the Mississippi River Commission, in 1932 made a trip 

over the Lower Mississippi and several of its tributaries and procured about 750 small samples of bed material, which were analyzed 

in the soil mechanics laboratory at this Station, under the direction 

of Spencer J. Buchanan, Soils Engineer. 

Special credit is due to Lieutenant Herbert D. Vogel, C. E., 

former Director of the U. S. Waterways Experiment Station, who 

planned the scope of these investigations, and under whose direction 

most of the actual work was performed. Lieutenant K. D. Nichols, 

C. E., rendered valuable service in interpreting data and checking 

results. 

Acknowledgment is here made of the service and suggestions 

of Capt. Hans Kramer, C. E., whose work in Germany proved helpful as a basis for undertaking the study. Gratitude is also expressed 

to Prof. K. C. Reynolds and Mr. C. H. MacDougall of the Massachusetts Institute of Technology for their helpful cooperation, and 

to Profs. Henry V. Howe and R. Dana Russell of the Department of 

Geology of the Louisiana State University for their work in the 

petrographic analysis of the samples of bed materials. 
·-

iii 

It is desired to emphasize that the investigations conducted 

thus far by the U. S. Waterways Experiment Station cover a very 

limited field in the research on critical tractive force and rates of 

river bed materials. However, it is believed that this report will add 

much to the general fund of knowledge. For a complete bibliography on this subject, the reader is referred to "Sand Mixtures and 

Sand Movement in Fluvial Models", by Hans Kramer, Proceedings, 

Am. Soc. C. E., April, 1934, or to "Bibliography on the Subject of 

Transportation of Solids by Flowing Water in Open Channels", 

published by the United States Department of the Interior, Bureau 

of Reclamation, Denver, Colorado. Additional references are given throughout this report. 

FRANCffi H. FALKNER 

1st Lieut., Corps of Engineers 

Director, U. S. W atenvays 

Experiment Station 
iv 

STUDIES OF RIVER BED MATERIALS AND THEIR MOVEMENT, WITH SPECIAL 

REFERENCE TO THE LOWER MISSISSIPPI RIVER 

TABLE OF CONTENTS 

Preface 

Pnrt. I~ Flume Studies of lVIovement of River Bed Materials __ 

Preliminary Considerations, Apparatus, and Procedure ___ _ 

Authority for the Bed-Load Studies __ 

Program of Experiments 

Description of Materials Tested_ 

Collection of Samples __ 

Analysis of Samples ____ _ 

Ret.-up for Experiments, and Measuring Devices_ 

The Tilting Flume _______ _ 

The Weir Box and Weir Plate 

The Stilling Chamber ___ _ 

The Approach Flume ______ _ 

The SandtraP------··-

The Tailgate __ 

Pumps, Constant-head Tank, Return ChanneL 

Gages 

Flow Indicator __ _ 

Automatic Sand!eed __ _ 

Bentzel Velocity Tube_ 

Definitions and Symbols ____ _ 

Classification of lVIaterials in Transportation_ 

Bed-Load Movement __ _ 

Critical Tractive Force Riffles ______________ _ 

Symbols and Units_ 

Procedure of Experimentation_ 

Setting the Slope of the Flume __ 

Molding the Bed _________ _ 

Other Preliminary Steps __ _ 

The Test Proper_ __ _ 

Observations _________ _ 

Head on Weir __ 

\Vater-Surface Elevation_ 

Temperature of Water __ _ 

Velocities __________________ _ 

Character of Flow-Laminar or Turbulent_ 

Sand Movement_ ___ _ 

Riffles ____ _ 

Profiles ___ _ 

Presentation of Data from Experiments 

Explanation of Tables 

Explanation of Curves Showing Basic Data_ 

Du Boys' Expression for Tractive Force __ 

Results of Experiments ____ _ 

General ___ _ 

Critical Tractive Force_ 

Definition___________ _ __ 

Resume' of Previous Investigations __ 

Critical Tractive Force Curve ______________ _ 

Need for New Definition for General Movement, for Use in Models __ 

Suggested New Definition for General Movement_ ___ _ 

Evaluation of Critical Tractive Force _____ _ 

Rate of Bed-Load Transportation _______________ _ 

Resume' of Previous Investigations _____________ ·-_ 

Basis for Formulation of Rate of Movement _______ _ 

U.S. Waterways Experiment Station Formulation of Rate of Movement ______ _ 

PAGE 

ii 

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Turbulence Criteria_ 

Summary of HesulHL 

Part II-~--Studiet-J of Composition of Bed &:faterialH in l\:Iissjssippi Hiver System~ 

Se()pe and rroeedure_-

Purpose_ 

Petrograpllie Analysit-L 

Results of Analyses_ 

PreHentation of DaUL 

Plate .'58~ 

Plnte mL Plate 60~ 

Diticussion _ 

Table No. 

2 

a Critical Traetive Force __ 

TABLES 

Part I 

46 

47 

47 

47 

48 

54 

.'Jfi 

116 

116 

11\J 

120 

120 

121 

122 

122 

122 

12:l 

125 

125 

125 

126 

5 Sumnwry of Cornputed Values of 1\Iamting';., 11 48 

6 Value of Traetlve Foree at Appeur~1nce of HiffleB 50 

7 Values of H.eynolds' Number and VR:.--Turbulence Criterion af, Chang-e from Lanlinar lo 

Turbulent Flow_ 54 

8 ObHfH'Ved Data and C'omputed ResultN- :FlO\\' on Hnwoth Bottom- -Slope (t0005__ 57 

!l Ob,erved Data and Computed Hesuli,-~Fiow on Smooth Bottom ~~Slope 0.0010 58 

10 Obiserved Data and Computed Hesu]tf;--Flo\v on Smooth Bottom-~-1-'lope 0.0015~ .t5U 

11 Observed Data and Computed Results-~~Hand No. t~-Hiope 0.0010 60 

12 Observed Data and Computed Hesults~~~Sand No. 1~-~Siope 0.0015 (\1 

13 Observed Dat.a and Computed Results-~~Sand No. 1-~~Slope 0.0020~ 62 

14 Observed Data and Computed Hesulb~~-Sand No. 2-~~Slope 0.0010~ 6:l 

15 Obsened Data and Computed Hesults--~Sand No. 2~~-t'lope 0.0015 !l4 

10 Observed Dala and Computed Hesulls~Sand No. 2--Siope 0.0020~ 65 

17 Observed Data and Computed Hesults-~-Rand No. :3--~Siope 0.0010 ~ !l6 

18 Observed Data and Computed Hesuhs~~~-Sand No. :J~-~Slope 0.001.'5 67 
Computed -Sand No.~{- :-::.lope 0.00:20 

und Computed He~ult~"- i'4nnd No.4 ---Mlope 0.0010 

Snnd ~o. 4·· Slope 0.0015 

·Sand ~o. 4 · iilope 0.0020 

and ( 'omputed He;>·mlt:-:-- ~and No. 5 8lope 0.0010 

and Computed H.e~ults- Sand ~o. 5-- r;tope 0.0010 

Dntn and Computed Hesulis·- Salld ~o. 5---Hlop!~ 0.00:!0 

Dn1a and Cornputed ltc:·mlt;.;-- Kand No. ft---~ ~lope 0.0010 

Datn and Computed Hesult;-; ~and No. 6-- ~lope 0.0015 

and ('(nnputed Resu11s _._,und No. t)- -;-;lope 0.0020 

;mel Computt'd Results ):-::and No.7 Nlope 0.0010 

and ( 'omput<~d Result:-;--- ~alld No. 7 klope 0.0015 

and Computed Rc~·mlts- Sand No.7--- Hlope (L0020 

:md Computed He~ults -Sand No.8 ~lope 0.0010 

nnd Cumputed Hei-:uh,,- Pand No.8-- ~lope 0.0015 

and Compuied H.esult;-; ---~and No.8 ~lope 0.0020 

and Computed Hesult;-; ;-;and ::-.To.~~-- ;4lope 0.00:~0 

n~~ta and Computed Hesult~-- Sand No. f4lopc 0.0040 

Ob;-;Prvrd I bin nnd Computed He~uh:-; P.and No. H ~lope {}.0045 

Part II 

of Bed .\Iaterial of :.\-Ii...,sissiprJi Hiver and Tributtnie~ 

:\f{'<'hani(·:d .\nnlyses d :\Iaterial Bed of :\-iiHsiRHippi l{iver 

<{0 \Iedwnlt'al Analyse;..; of Alaterial frmn Bed of Tributary and Outlet Riven.; 

61'\ 

()H 

70 

7l 

7'2 

n 

74 

75 

7H 

77 

7R 

7H 

80 

1~0 

l28-i4:) 

144-14!1 

:md \'arious Com-;ttll1L'-' of ~\1aterial from Bed of fdississippi River lfi0-11)R 

Datn and Ynrlous ('onslan1s of :\Iaterial from Be-d of Tributary und Outlet 

1.'i!l-lfll 

PL\TES 

of Flume t:sed in Experimenlt-> 

Distribution of Originul :\Jateritds \)(~fore TeHting C\unulativ<' Ptol 

Njzp Distribution of Original :\iaterials before Ter:d iug ,t 

;:-;and ,·\nalyi-iis Curve ,1) 

:\I icrophot.ogrnph;.; of ~and firnin ;-:ihapes 7 

(~mwral Lnyout of Tilting Flume Vsed in Bed-· Load Studie'-' H 

of Flume 11 

of Lamin:tr anrl Turbulent F!ov.- 11 

Tube 

Ftn·ee in H.e1at ion 1 o Band Charaeteri~ti(·s, ·esiug Virma l C'rit erion 

in Hrlation In ~and C'haracteristi('s, l71-'ing: Yi:-:twl ( 'riierion 

Helation to ~and Charaeteristit'::-<, C;--;ing \'iswd and "?\lode!'' 

:\Innning's 11 in Hare-of-::\lovement 1·~valuntion 

to Depth, ;-::lope, and Houg-hne,"'" 

Dept b, ~lope. and Houghne.'-':--< 

of ~lovement of ~nuds T'e:-<ted~~-Logarithmi<· Plot 

Teeicd 

1:1 

l:i 

15 

1.'5 

21 

:lO 

:n 

:;;; 

:jg 

40 

41 
vii 

Vertical Velor>ity Curve.s ril 

:!4 ComparisoiJ of l\ilnnning':.; n and :\'lean Veloci1y for a Hand Bottom and 

Fixed Bottom of Neat Cement 0.0015 R7 

2f) Variation of r:.and DiH('harge, :VIean Velo(•ity, 2\'Imming'.s n, alld No.1, Slope 0.0010 

~Iean Grain Hize \Vith Depth No.1, Slope 0.0015 .SR 

2H Variation of Sand Dil·wharge, :\Iean Velo('ity, :VIanning'.s 11, and No.1, Slope 0.0020 

:Vlenn Crain Size with Depth No.2, Hlope 0.0010 xn 27 Varinlion of Sand Diseharl(e, Mean Velot'ity, :\fanning's 11, and No.2, Slope 0.0015 

::\lean Urnin t-lize with Dep1b ~o. 2. ;.-)love 0.0020 DO 

'28 Variation of Hand Difi.rharge, J.:Ienn Veloeity, :vranning's n, and No. :-L Slope 0.0010 

::\Jean Clrnin Size \dtlt Deptl! No. a, Hlope 0.0010 Hl 

2H Vnriation of Sand Di::i('harge, :\Jean Velocity, :Vlanning'~ n, and No. :5. ~Hope O.OO:W 

:\lean Grain ;)ize with Depth No.4, Slope 0.00!0 !12 

:JO Variation of Sand DiselJarge, :VIean Vel<H'ily, Manning's "·and No.4, Slope O.OOlii 

~Jeun Uraiu Size with Depth No. ·t Nlope 0.0020 !);{ 

:n Variation of Hand Discharge, Mean Veloeity, :\Janning's 11, and No.1\, Slope 0.0010 

:Uenn Crnin Size \\rith Depll1 No.5, Rlope O.OOV} 94 

:3:2 Variation of Hand Discharge, .:\'lean Vel(H'ity, )danning:'e n, and No. !1. Hlope 0.00:!0 

:\lean C:ntin Size with Depth No.6. Slope 0.0010 \15 

;~:i Ynriatiou of Sand Discharge, iVIean Velocity, :\Janning's n, and No. n. ~lope 0.001.1 

~lean Ur:tin Size with Depth No.6, Slope 0.0020 !Jt) 

:-}4 Variation of Hand Diseharge, 2\.'fean Velocity, :\'!arming':-; n. :md )Jo. 7, Hlope (},0010 

~Jean Urnin Size with Depth ~o. 7, Slope O.OOlfi H7 

;)f) Variation of Sand Diseharge, :\Jean Veloeity, :\Lanning's 11, nnd No.7. Slop<~ O.Oo::w 

"\1 ean Grain Size witlJ Depth No. 8. Slope 0.0010 H8 

:)(') Variation of Rand Disehargc, :\'lean Veloc·ity, ~Vlannin~'s n, aHd No.8, Hlope 0J)015 

:vienn Orain Size with Depth No.8. i:-l!ope {10020 9B 

:)7 Variation of Hand DiReharge, ~fean \relo('ity. ~Innning'R No.!), Slope O.OO::Hl 

:\lean (;rain Rize with Depth No. !1, Nlope 0.0040 100 

:18 Vttriation of Sand Discharge. :\Iean Velo('ity, :\'Ianning's 11, and 

,:\Jean Omin Size with Depth Sand ~o. (l, Hlope 0.0045 101 

!3D Longitudinal Profiles of Hand Bed, Hn11d No. 1 10:! 

40 Longitudinal Profiles of ~and Bed, 14ands Nos. 2 und :i lO:l 

41 Longitudinal Profiles of Rand Bed, Rand No.4 104 

42 Longitudinal Profilef' of Rand Bed, Rnnd No.5 105 

4:; Longitudinal Profile' of Sand Bed, Sand' Nos. 7 and 8 10() 

44 Lougit udinal Profiles of Hand Bed. Hand No. 0 107 

45 Progres:-;ivc Variation of Rir.e and Distribution of Grains in ~'iovement- ·Sand No. lOS 

46 Progressive Variation of Size and Distribution of Grains in lVIovement ·---Sand No.2 IOU 

47 Pro_gres~ive Variation of Hize and Distribution of Grains in :'vlovement-~--Snnd No. :1 110 

48 Pro,gre.-.:-:ive Variation of Size nnd Distribution of Grains in :'vfovement-~Rand No.4 lll 

4H Progressive Variation of Size and Distribution of Grains in :\:fovement---Hand No.5 112 

50 Progressive Variation of Size and Distriburion of Grain,s in l\tiovement--~-Snnd No.7 11>) 

[)1 ProgrcHsive Variation of Size and Di::-;triblltion of Grains in ::\:Iovernent 

52 Progt•e;.;Rive Variation of Size nnd Distribution of Urains in ::Vlovemcnt 

Part II 

Pr.ATE No. 

,5:1 \\'n ter,hed of I he i\liSHi"ippi River 

54 The Alluvial Valley of the C.Iis'i"ippi lli,'er 

,1)5 Permanent Container for River Bed P.ample 

,56 Sampler Used for Proeuring River Bed :\Iaterinl 

57 l\·Iethod of Using the Silt Sampler 

58 Variation in Compo:-;ition, :\'liKsissipJ)i River Bed ~Iaterials 

fin Variation ill .i\{cnn Grain Diameter;.;, l\JiRRis: .. ;ippj lliver Bed l\Iaterinl:-:; 

Hand No.8 

Sand ~) 

00 Vnriat\on in :\iet\Jl Orain Size of Sand Only, ~'lissisl-'ippi Hiver Bed 1\Iaterinls 

114 

115 

117 

118 

11\l 

121 

121 

!24 

126 

127 

PART I 

FLUME STUDIES OF MOVEMENT OF RIVER BED 

MATERIALS 

PRELIMINARY CONSIDERATIONS, APPARATUS, AND 

PROCEDUHE 

The ultimate purpm;e of the flume studies of bed-load movement described herein was to discover and evaluate laws to t be end 

that the riYer hydraulician might be able to calculate the action of a 

given bed material under given conditions. Inasmuch as this has 

been the subject of a great amount of research by both American and 

European experimenters during the past generation, the purpose as 

conceived is both far-reaching and ambitious. It was thought, howeyer, that advances might be made on the problem, and that even 

failing to attain a complete answer to the baffling problem of bedload movement, many data contributing toward the final solution 

might be obsf~rved and recorded. 

The original expectation was that, from the study of the distribution of materials in the river samples, in combination with the 

knowledge gained from the tests in the tiliing flume, an accurate determination could be made of ihe tractive force required to move the 

material at any point in the lower Mississippi !liver. Front this i1 

was hoped to ascertain the sta~e necessary to produce the critical 

force in any reach of the river. It now seems certain, however, 

that the present state of knowledge preeludes the immediate por-;sibility of making any such r-;weeping conclusions. Much more rer-;earch 

will be necessary before any satisfactory equations can be set up, 

to express the movement of Mississippi River bed material throughout an entire range of depth, slope, sizes of material, eurvahue of 

bends, bed configuration, etc. 

The more immediate purpose of the flume tests, which was satisfactorily achieved, was the discovery of many of the basie laws under·lying the subject of bed-load movement. In particular, emphasir-; 

was given to the study of the rates of movement of bed materials of 

various sizes, and of the trnctive forces necessary for the commencement of their movement. Information was also obtained on riffle 

formations, values of bed roughness, turbulence, velocity Yariations, 

etc. All the data are presented for referenee in tabular form at the 

end of Part I of thiR report. 

Authority for the Bed-Load Studies 

Authority to undertake a study of the bed-load of the Lower 

Mississippi !liver was contained in a letter from the Chief of Engineers, dated August 13, 1932, addressed to the President, Mississippi 

River Commission. This authority was transmitted to the Director, 

U. S. Waterways Experiment Station, in AuguR!, 1932. 

1 
o.o~n I 

0.0207 

o. own I 

(1.()1!l0 

!') 

7 0.0122 

O.OOSl 

0. 

the COUJ'Re of the i 11-

WaR varied small inereThe three main 

mixture. 

of bed and water surface. 

of the water in the flume. 

0.4:\88 

0.4:!84 

of Materials Tested 

were 

minute quantities 

mostly from 

some rounded 

chamct 

T.\BLE 1 

lo 

Berlin. 

were 

of tlw 

''~\'Iodellgesehiebe und 
"'' ~~l:;3"" 7/; :.-> -------~~p=-

~ J. /~;; ~/~v I I v 1 1 /}/~/ · r I 0 .,)1 ~ 

I i/ /~ '/ 

I .,, ·Q f!, 

J I J tj r 1 I 

/; I 0 

I t r1 ~1 7 li ·- ........... ·~· 

/; r;, ~~ 

. . --

I Jl 

• I 

o I I 

I /l II' I 

50 II 1 ffl 

!7 I 'II I 

6 I If II 

1t 

-· 

f 

I !'I 

I • ~1/ I . 

i 

1 I JIll 4 : 1 r I' it i 0 

I if!i i , 0 

I I I I I I!! 0 

- If~ !!: J 

1// 

r li/ :I I 

I i I I. 

/l I 

I 

1 I~ ! i 

f ! If ! I 

. / I I 0 

~/ 11// I 

1? /1 

~k~?~~,/ -~-~-~ 

l,/ -'---·- .., 'It <t .... <!> "' ~ .... 0 '<t 0 "' 0 - - l\1 "' !II d 0 0 0 d 

110 G) l'l 

'<t "' Ill Ill 

0 d d - ~ieve ~ize~--1\'Jillimeters 

P:r~ATl•: 1 

-

"' 'I! 

: 

i 

I 

I 

/ 

I 

If 

I 

0 

G.ILUN ~rzg J)c.;;,THIBFTWN OF OuHHNAL :'\IA'r'ERLH ... i'4 lhworn: T.I<;.-rriNO 

.. 

! j ·····-· 

I 

... 

I 

l I 

i 

SAND 

NO. LEGEND 

I -

2 ---- ·- 3 -----

4 --- ·-·- 5 ······-········ 

6 -·-·- 7 -o-o6 -o-o-

!I -t>-.t>-

0 "' !II "' II) N 1'1 ., : 'It ,.; '¢ tli 
0 

SAND IM£!'J'!GMIN UNIFORMITY LEGEND NO SIZE dg MOOUUJS M 

i 1 0.5861 0.2796 -- 5 2 0.5409 0.4388 --- -

i . 3 0.5246 0.5385 -·-·-·-

4 0.5056 0.4063 -··-··-··- j'\ 5 O.i4828 0.4384 ................... 

0 6 0.3470 0.6428 I . -+-+-+ I 7 0.3104 0.5246 -o-o- II j i 8 0.2053 0.5597 -0--{Ja\ 9 4.0769 0.5661 -'1>--l>-

I ~ 1 l 

\ ·i 

I 

f· \ . I 

r i I \ 

6 Cl 

I l I \ \ • I 0 t \ 1\ r \ J I i 5 0 

~, I\ J \ ~ I \ 0 I· I \ I ~ \ i\ \ r ... f 

5 

5 

4 

4 

r ~ I ott·- \ 

f, ~\ r 1 I I I. I []' ! I \ \ "' I 0 f I io ' \ \ I 0 I !I \ 

5 

J 1 I I i .·~ ~I I I . \ I 

J 1 ! I, \ . 

0 ! \ i Jl. j \ \ /I' I \~,1 \ \ 

~ 1 j di: I I\\ ~~! ' ;if . '.I 

I I 1 !\( 

5 

/'' \l r:l f l 

i)1/i1 '\• 0 \ \~ ! t I l :·~, "' I r I ~ '\\. I 0 ? 

1/ I I 

~ 0 \ v t 0 

~ I .\ f' I I I 

~ \~ \ I ~ I / ~\ II \\ <1 I 

~~il \\ I~ 

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t p~. I \ ~ 

·~ .~ \ ~-- ~ ;:>: ~- )~<--~<!" .... _, ~--.:::'· 0) "' .... lll "' 0) ;;; "' 0 .., 0 <I" 0 "' "' ~ j (\1 "' .. (\1 

N N "" "' ., ! "' lil 0) ,.. d ;::; d 0 0 d 0 .,; ... .0 ClOi 

2 

Sieve Size-!vlil1ilneters 

PLATE 2 

Brz1:: DrH'l'RIHUTION OF OnrtnNAL :\1A'l'I1HIALS BEFOUE 'I~J'JR'l'ING 
The mean grain diameter, dg, is a value often tuled by Krey in his 

experiments coneerning bed-load movement, and was adopted later 

by Kramer, in his study of critical tractive force. Referring to Plate 

3, which shows the grain sizes plotted as nbscissa and the cumulative 

per cent passing as ordinates, dg is simply the mean abscissa of the 

curve, and represents a weighted average size of particle. 

The uniformity modulus, :VI, has been proposed by Kramer as a 

convenient expression for the distribution of sizes of the particles in 

a sand mixture. Expanding upon a scheme devised by Hummel to 

express the strength of concrete from the gradation curve of the 

aggregate, Kramer divided the area between the gradation cune 

Reference line for 

:mbdivision of area. 

Crain Diameter 

PLA'J'E :5 

HYPOTI-H~TJCAI· SAND ANALYSis CunvE 

:vfnximum 

grain size 

(see Plate 3) and the vertical axis into two parts, above and below 

the 50-per cent line. The uniformity modulus, :vi, is the ratio of the 

area below this line to the area above the line. This value, which 

has been found convenient when it is necessary to evaluate the distribution of particles within a mixture, has the following charaeieristics: 

(1) For a uniform grain size, its value is 1.0. 

(2) For a uniform distribution, its value is L 3. 

(:3) The addition of fine or coarse materials to a given mixture 

tends to reduce its value. 

( 4) It therefore is a meHsure of the voids ratio. For a uniform 

material, which has the largest possible percentage of voids, 

its value is the maximum of 1.0. With the addition of 

finer or coarser materials, the voids rai io decreases, as does 

the value of ::VI. 

The value of :vr can be determined from the plot ted sieve analysis 

curve, or it can be computed directly from the sieve analysis dnta. 

The shapes of grains are classified according to a chart prepared 

by Dr. H .. Dana Russell, Assistant Professor of Geology at the Louisiana State University. This ehart, composed of micro-photographs 

of sand grains of various shapes, with the designation assigned to 

these shapes by Dr. Russell, is reproduced in Plate 4. It should be 
definii e effect of wear. The 

form and the faees are 

and the corners have 

the bet wPen faces 

or corners 

curves; flat areas 

may he sngfrom the bed of the 

of the U. 8. 

and to the 

from creek beds and 

sand within fiO miles of 
WR- LL 

R 

SAJ'L\'1'10 4 

:\IwHOPHOTO(i!L\PHI<\ oF ~.\ND GHAIN Sn \PI·:~ 

:\f:t!!llifiPd ):J. 

7 
for and Measuring Devices 

All the bed-load tests were conducted in a tilting flume, which is 

located on the main floor of the laboratory building. The water was 

from a circulating system, composed of an underground 

two centrifugal pumps for elevating the water to a conon the second floor of the building, piping connections to the entrance of the weir box, weir box with measuring weir, 

the flume itself, and the return channel. 

Flume: 

The flume itself, illustrated pictorially in the frontispiece, and 

in Plate Ei, is a wooden structure, lined with cona smooth surface, and supported by two 12-inch 

in cross-section, its approximate inside dimensions : length, 48 feet; width, 2.3 feet; depth, 1.3 feet. The 

I-beams are supported at the upper end on horizontal pins, a.nd at 

the and lower end on jack screws, through the proper manof which it is possible to set the flume to any desired slope, 

to a maximum of 0.015. At the top of the flume, as shown in 

6, are two adjustable wooden straight edges, one on each side, 

which ean be set to any slope desired. In aetual operation, these 

rails have the same slope as the water surface and the bottom of the 

and are used as a base for the various sliding measuring devices. 

The W et:r Box and Weir Plate: 

The water was admitted through an 8-ineh pipe, eontrolled by 

from the constant-head tank into the weir box; the latter is 

structure 10 feet long, 4 feet wide, and 3,!/z feet deep (see 

This box is equipped with baffles which effectively 

before the water discharged over the weir plate, and 

with a well and hook gage, which were used to measure the 

head over the weir. The weir itself, of the 90° V-notch type, is made 

of a steel plate, with a 60° bevel on the downstream face 

and a 16-inch flat edge; it was carefully calibrated for all heads 

means of a volumetric measuring tank. The rating curve for 

was found to check very closely the curve of King's equation 

H 2.47 ; all discharge quantities, however, were taken frmn 

experimental rating eurve. 

The Chamber: 

From the weir box, the waier was diseharged into a stilling 

chamber shown in frontispieee), 4 feet wide, 6 feet long, and 

about 1 deeper than the flume. This chamber contains a system of of various types, which served to quiet the water and 

allowed it to enter the flume in a smooth flow, free from waves and 

surges. 

rnrm11·.n Fhtrne: 

approach flume is simply a wooden trough which connects 

chamber with the upper end of the flume proper. It is nnr»•,·nn on stationary foundations, and cannot be tilted with the 

flume. 
e-j 

" " 

r Frorn Tonk Hook 

TdhtHj 

PLAN 

Movablt Sond 

LONGITUDINAL SECTION 

R(ll! 

GENE 

Jack Sc.n"" TIL

D-

TYPICAL CROSS SECTION 
movement of the sand under test 

at the downstream end of the 

COnSiStS Of a ouuu'"''.Y 

flume itself. The sudden 

water caused the sand in transTo facilitate the removal and urr.nf11An box lined with sheet metal was 

This with 

snnd iH 

was found to be too small to catch the fine 

trap with a much more enuse while this sand waR 

water were taken from the overand the rate of load mon;ment 

water surface at the lower end oft he flume 

The existence of 

means of the 

solution into the water, 

colored stream. The 

of a 

in the flume was deof a stream of perand observation of the eourse 

solution was inserted into the 

as 

The 

in use, and 

stream lines extheir in srnall 
Top, 

Top, 

Bottom: 

PLA1'E 6 

UsE oP TILTING FLUME APPUH'l'ENANCF:s 

l\1Iolding the sand bed with the sliding 

l\!lea:-;uring an elevation with the slidinp; 

Hemoving the snnrl box from the sandtrn p 

PLAT>> 7 

DB'l'ERMINA'L'ION oF LAMINAH AND TnunuLENT PLow 

""'""'""'"" pcrmangannte solution 
which were 

was used for this 

of the solution was 

elenttion of the containing; the liquid. It was necessary 

flow so as to obtain the same velocity as that of the 

With this thread-like lines of as long; as 

the necessary conditions in an the 

of bed-load is that there be no in the 

of the bed the course of a test. In order to 

insure !hat this condition is necessary to seeure balance 

R 

~-\U'J'OMA'TIC HANDFEl!JD 

amount of sand which is in 

carried out at the lower end of 

added at the upper end. 

occasional manual addition of is 

condition at the head of the flume which 

riffle formation and may render the test 

it is desirable to install some kind of autocan be adjusted to discharge sand into the 

the same rate at which it is extruded 

to devise a machine following; the 

* and later used with suceess 

m operation adjustment 

of Gi I bert's. This dey ice con6 inches divided into two 

.S. ProfeHsionnl Paper 

of Kedimmli Tmn;.;portation". 
compartments which were separ·ated by a vertical sliding partition. 

The box was piYoted about the center of the smaller compartment, 

which was used for the storage of sand, and was shaken at the open 

end by means of a pair of cams operating against a pair of rollers at 

approximately 165 r. p. m. The cams had an eccentricity of }i inch; 

a bumper was constructed on a rmlid block under the open end of tlw 

box, and caused a sharp blow to be delivered i o the box. In operation, the box was set at a predetermined angle, dry sand was placed in 

the small compartment, and the sliding partition was set to an opening corresponding to the largest grain size existing in the sand under 

test; the rapid shaking of the box caused the sand to move in an 

evenly distributed layer down the slope and to drop through the 

slot in the base into the flume below. A piece of smooth plate glasR 

on the bottom of the box inRured a plane surface at all times. 

5.0 

~ / ----r--....---

- ~ / 

---------- I I 

/ 

------ 4 '/ 7 

4.0 

v VL ~ '~-- oAND No.3 

--- SAND No.4 

v / / SAND No.5 

2.0 / / / I 

I / 

/ v 

/ j_ 1.0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 

Sand Di1-wlwrp;e- ---Pound;.; Per ivlinute, Dry \\"eight 

E·L\NDI<'EED HATING Ct'HVI<:S 

The rate of feeding was varied by an adjustment of the slope of 

the bottom of the box. As can be seen in Plate 8, the shaft on which 

the box was pivoted had a vertical range of movement of about (i 

inches. A seale was installed on the vertical adjuRtment to facilitate 

the duplication of setting. In order to keep the rollers directly over 

the cams on which they ran, a horizontal movement of the entire box 

waR pro\·ided. 

The Randfeed waR calibrated for each sand mixture for which it 

was used (Ree page 22) before the mixture was teRted, and a eune 

was drawn Rhowing the variation of the rate of feed with the vertical 

Reale setting. Three of theRe curveR are shown in Plate 9. During 

the course of the test, the m aehine was set after each nm to the position corresponding to the rate of movement found for that run. Hence 

there was a lag of one run in the adjustment of the quantities. Sinct> 

the water discharge through the flume was increased in very small 

increments, however, and since the upper 22 feet of the flume were 

used as an entrance ehannel, with observations eonfined to the lower 

portion, this lag was considered to be of no importanee. Furthermore, bed profileR were taken periodically, to insure ihat no progri'sRiYe altPrations w!'re occurring in the slope of the bed. 
incidental rmmHR of l his inof suitable instrurnent for measwater. This instrument has been 

velocities from about 0.10 feet 

5 per second. It has been found 

measuremerrt.s at the where it has 

the use of the Pitot tube and other current-measwhich the meter works is as follows 

rises until it 

When water 

it 

within the 

of the float 

trials 

effect 

water must. be 

in of a few CU>O'N't>Q 

In Plate 11 are shown the calibrations for 

used in thP conduct of the bed-load tests. 

Definitions and 
10 

-~~ I I O.!l 

FLOA~ .. B~ v -

0.8 I 

I 

1-------- '--~--

0.7 !--~- -t1 

0.6 -- -- j 

1 

0.5 ~--~ ~-- r 0.4 

1 0.3 1 

i f 

It / 

0 0.2 0.4 

PLATl'J 10 

TuE Rm•;·rzra ... \"EI .. OCI'I'Y TuHE 

- ~~ 

: I 

F~op:f P.' tv-v - ---v~ 

vf-~t---

/ 

I -

I i 

i/ 

/I NOTE• rtON WITH 

1/ I~MI"U<>\IVR<. 

I ;::,.:.lsRATtOI FLOAT 

DATED ~:~7;~:~~RE 

/I 

1/ I 

/1 

0.6 0.8 1.0 1.2 

Veloeity~~Feet Per Reeond 

PLATE 11 

BENTZEL 

I 

I~ 1.6 

"A" 

I 

lh 

I ~ -

--- !--~~~ 

--!----

1.6 2.0 
load: That portion of the stream load whieh is bein)!: 

ed by flotation (e. g., trees and drift). 

load: That portion of the stream load which 

is transported by colloidal suspension or in 

solution. 

RPdimPntary load: That portion of the stream load which is being transported by hydraulic traction or hyclraulie suspension (e. g., clay not in colloidal 

suspension, silt, sand, gravel, boulders, organic 

material). 

load: That portion of the sedimentary load whieh 

is not in contact with the bed of the stream. 

BPd-load: That portion of the t~edimentary load which is in 

eon tact with the bed of the stn~am. 

Rnltation: ~Vfovement by "jumping"; particles in saltation or 

particles moving intermittently as suspended 

load and aB bed-load. (No sharp dividing line 

is intended for this type of movement). 

Rt rPam hed: The non-moving (not necessarily non-movable) 

material underlying the stream. 

S<'din1ent: Fragmental material deposited by water. In general, both that which has been deposited and 

that which is still being transported. Specifically, that which has been deposited. 

Consolidai ed material: Material which cannot be transported 

without first being disintegrated (e. g., m:umnry 

liningH, beds of rock). 

Red-load Jl!Iovernent: 

The definitions suggested by Kramer were tentatively adopted 

for uRe at the Experiment Station, and throughout the experiments 

eh of movement waR elassificd according to his definitions. 

The encountered by Kramer and other investigatorR in 

an accurate classification of movement by visual 

however, were found to be so pronounced in the early 

1 eRts that additional definitions were eRsential. The use of aetual 

meaRured quantiti('S of material moved \Vas found practicable, since 

the tilt flume was equipped with a sandtrap which efficiently 

the material extruded at the lower end of the flume. 

All the rates of movement, therefore, have been computed in terms 

of foot width of flume per hour, dry weight, and this 

l iR all the tests. 

For purposes of reference, Kramer's definitionR of rates of bedlmHI movement are quoted below: 

"thnl 

"1. 'None' refers to that condition in which a bsoluiely no 

particles are in motion. 

"2. '\Veak' movement indicates that n few or several of the 

smallest sand particles are in motion, in isolated spotR, and in 

numbers. countable is meant that by confining; 

the field of observation to, say 1 em , the particles in motion can 

be counted by the obsern~r. 

tlH• eon<'ise (;ermnn word eorreHJ)(mding: !o ''hcd-lond''; li1erally, 
]7 

"3. 'l\!Iedium' movement is used for that condition in 

which !!;rains of medium size are in motion in numbers too large 

to be countable. Such movement is no longer local in charaeter. 

It is not yet strong enough to affeet bed configuration and <loes 

not result in transportation of an appreeiable amount of geschiebe. 

"4. 'General' means that condition in which sand grains 

np to and ineluding the largest are in motion. Sinee in these 

experiments, as in general laboratory praetice, sand grains above 

a certain size have been sifted out, this designation has a definite 

significanee. This movement is also not local but general. It 

is sufficiently vigorous to ehange the bed configuration, although at lower sta11:es this action takes place only slowly. 

There is an appreciable amount of material transported with 

this conclit ion of movement. This condition is termed in this 

paper the lower limit of usefulness of the sand. 

"No higher stages of movement are designated, although increasing intensity might be based upon the quantity of geschiebe 

movement. Interrm~dia1<' stagPs are denoted by ) plus or 

minus signs." 

Critical Tractive Force: 

Critical tractive foree is that traciive force which bringR ahoul 

general movement of 1 he bed-load mixture. 

R~ffles: 

Local riffles are those riffles which appear first in isolated seelions. 

General riffles are approximately uniform in height and length, 

and are distributed throughout the entire area of the flume. 

No attempt will be made to designate riffle stages by size. 

Kramer bases his riffle classification on I he height of riffle as compared with the depth of water which forms it, and classifies as excessive any riffle which is more than 8 per cent of the depth of the 

water. It has been found at the Experiment Station, however, that 

all sands of mean grain diameter about 0 .. 5 nun m· less have a strong 

tendency to riffle greatly in excess of this 8-per eent limit. In fact, 

for some of the finer sands, very little downstream movement of the 

particles was obtained until the formation of riffles was as high as 20 

to 25 per eent of the water depth. 

It should be noted, however, that frequent profiles of the bed 

were taken throughout these experiments, and are shown in Plates 

;)g to 44. Frorn these plates the size of rifflps at any time ean be 

found. 

Symbols and Units: 

With the exeeption of the size of sand grain, which is expressed 

in millimeters, the English system of units was used throughout these 

experiments. The use of millimeters for the grain size resulted from 

the faet that the openings in the sieves used in the analyses of the 

sands nre commonly expressed in these units at the Laboratory. 

Equivn.len1 sizes, in inches, are given throughout this report, however. 
of not ntion for of 1 hiR 

who haR worked 

his own set of 

when an effort iR made 

TABLE 2 

:\OMID!>iCLA'I'l'IUC AND l:X!Tf4 

because of a lack 

nomenclature in 

Occasional devia 1 ionH 

invE'si 

JWr . width 

" 

Non-dimenHional 

Ft. 

Lb. pPr sq. ft. 

Lb. pPr sq. fi. 

Non-dimPnRionnl 

Ft. ~ .. 

Non-dimensional 

· Ft. per sec. HOe. 

Lb. per ft. per hr. 

Lb. per eu. H. 

in. 
19 

Procedure of 

Before placement in tho flume, each of the materials (with the 

of Sand No. 1, which was U8Cd in its natural state) was 

thoroughly washed, to remove all traces of silt, clay, and other extraneou8 material, and screened through a 4-mesh sieve, to removo 

the particles than 4.699 mm in size. In the case of the tests 

on the small gravel, the particles ranged in size from 0.208 mm to 

6.680 mm, with about 98 per cent larger than 1.168 mm. 

the of the Flume: 

The flume was adjusted to the desired regulation of the 

jack screws on which it is supported. After main structure itself 

had been set to the proper slope, the adjustable rails on the sides of 

the flume were set very accurately to this same slope. In thiR operaRhots were taken with a level at 2-foot intervals the 

to insure that no humps or hollows exist <>d; nn accuracy of about 

0.002 foot was obtained. 

the Bed: 

The sand or gravel surface was molded to the exact slope 

means of a 'Vertical template so constructed as to slide along the 

mils. The material was first thoroughly mixed, to insur<> a 

uniform distribution of the particles, then was placed in the flume to 

a of about 2 inches. At the upper and lower end of the flume 

cement sills had previously been constructed to this same depth, the 

upper one arranged to provide a smooth transition section from the 

approach flnme. These Rills arc shown in the longitudinal scet ion 

of the flume, Plate 5. 

The bottom ed~e of the sliding template was adjusted to the eleYation of the eement sills, and then was worked back and forth over 

the material (all molding was done under wa.t until a Rmoot h surface of uniform slope was obtained. Care was taken that no ridgeR 

or furrows, or isolated large particles, remained on the surface, since 

they would start the formation of riffles at an unnaturally early 

in the test. A series of phot ogmphs showing Ruch unnat urn! 

development is presented in Plate 12. Th<> process of molding is 

illustrated pictorially in Plate 6. 

Other Steps: 

At this stage in the procedure, small samples of material were 

taken from three locations in the flume, and RU bmitted to 1 he soil 

meehanics laboratory for mechanical and microscopic analysis*, and 

for a specific gravity teRt. The average of these analyses was used 

as.the original on which all traeti\'e foree and rate-of-movement caleulahons were based. 

After the holes from which these samples had been takm1 were 

filled in and the surface again made smooth, a longitudinal profile of 

the bed was taken, to provide a cheek on the molding of the bed and 

to meaRure the bottom elevation. These original profiles are shown 

in Plates ~19 to along with the profiles taken later after the formation of riffles. should be noted that in theRe plates the 

slope of the bed is plotted as a straight, horizontal line. 

The mel hods of analyzing the materials are deseribed in detail in Part ll. page 122. 
The Te8l 

To Rtart the test, the flume was flooded slowly from the lower 

after which tlw inlet valve a boYe the weir box was opened 

nnd a Rmall quantity of water bef!:an to flow through the 

chamber and into the flume. The tailgate was then manipuntil it was found that uniforrn flow prevailed throughout the 

h of the flume. This condition was attained when the needle 

H('l'\·aJi0!1R". 

on the water surface were the same at all points. After 

of flow conditions had been reached and held for seyeral 

e set of obseryations was made and recorded. A 

obserYations will follow, under the heading "ObAt ilw eonelusion of the first run, after all neeessary data had 

lwPn 1 he diseharge was increased slightly by an adjustment 

of tbe inlet thP tailgate was again manipulated until uniform 

flow waH obt as evideneed by like readings of the sliding needle 

at all and another complete Ret of data was reeordt>rL 

>vas repeated, the discharge being increaHed in sucC:PSHin• Hmall increments, until the maximum eapacity of the supwas reaehed. After the conclusion of the test, the flume 

waH sPt another slope, the bed was remolded to that Harne slope, 

and another independent test was made in a similar manner. 

ThP firHt run in each and seYeral subsequent runs, were 

wit b laminar flow in the flume. During this period in which laminar 

flow was obtained, t lH' discharge in the flume was increased in very 

Hmall in order to provide complete data on the transition 

1wtwren laminar and turbulent flow. The type of flow, whether 

or turbulent, was determined by observation of the course 

tlw solution of potassium permanganaLe whicb was ininto the water with the instrument d.eseribed on page 10. 

the flow had passed well into the turbulent range, no further 

obHenat ionH were made with the permanganate Holution. Typical 

sf ream lim•s indicating laminar flow are shown in Plate 7. 

the first several runs of eaeh test, the sand bed remained 

Hmooth, practically as it had been molded at the commencement of 

t lw teHi. After the first ten or so runs, however, the number deupon the type of sand, slope of bed, etc., small riffles into appear at isolated points in the flume, and gradon~r the entire sand bed. It was preferred to have 

Rtart at the upper end of the flume and work themselves 

downstream. The riffles frequently appeared simultaneously at 

several however, and developed in all directions. Tbe genPml was not to interfere with or attempt to control their 

""'"'"'""' but to let the riffles deyelop themselves. It was imt o seeure uniform conditions of flow while these riffles were 

for t be reason 1 hat the gradually inereasing roughness 

eaused the same cliHeharge 1 o be carried at gradually inlienee, no attempts were made to reeord simulof depth, velocity, etc., until this riffling period had 

In most of the teHts this deYelopment required from 

during whieh the diseharge was kept constant and 

was manipulated as often as was neeessary to maintain 

of the walt>r surface parallel to the original slope. 
PL.\Tl<l 1:2 

Puo(mt<::!:'SIVN Dicvl·;u)P:\m~T OF HIFFLgR, BY OnKTHU('TION ON Jhm 

21 
and 
23 

constant check on the bed means of the 

to end the test whenever it was seen that any 

taken 

Observations 

Head on Wc'ir: 

the 

The head on the weir was deriYed from a hook-gage reading on 

water surface in a manometer cup, which was attached to an 

in the weir box rubber tubing. The corresponding diRt his head was from thC' weir rat CUJ'VC'. 

Elevation: 

The elevation of the water surface was read with the sliding 

previously described. BC'fore the rC'ading was the tailwas manipulated to a position where the slope of the water surwas the same as that of the bed; the gage of the 

water-surface elevation was the same at all points in the flume. From 

the water-surface elevation, the mean eleYation of the bPrl was subtracted to dt~lermine the depth of flow. 

Water: 

In the last fiYe series oft the temperature of the water was 

read for each run, from n Centigrade thArmometer suHpended in the 

water just above the approach flume. The temperntureH in the other 

those on Sands Nos. 1, 2, 6, and 7, were estimated later from a 

study of air temperature records of the U. S. vVeather Bureau at 

Vicksburg, and a few temperature records of the reservoir at the ExStation. Inasmuch as these sands were tested during the 

summer of 1933, when the air temperature remained fairly consistbetween 80° and 95° F, no serious errors entered the results 

from the assumption that the air and water temperatures were the 

same. 

Velocities: 

The water-surface velocity was obtained from the measurement 

of the time necessary for a small float to travel a distance of 20 feet 

in the flume. In ease, this velocity was taken as the 1werage 

of about fiye trials. must be noted that surface velocities WPl'P 

not observPd in the tests on Sands Nos. 1, 2, 6 and 7. 

~Iean velocities were computed from the discharge and crosssectional area. 

In the test on Sands Nos. 4, 5, 8, and 9, a complete set of velocobservations was made wit the Bentzel tube. Most of these 

were made with the tube directly o\'er the downstream 

cement an inch or two below the end of the sand section. The 

use of the tube over the sand itself was found to be impracticable because of the scour which immediately resulted when the tube 

proached the sand bottom. Velocity measurements were made 

the bottom, and at one to three other depths, depending upon the 

of flow. 
Turbulent: 

or in the transition 

from the 

intotlw 

with occasional refer-

' whose exact would 

source of data on the 

to which show the 

in Paeh test. 

of the bed were 

ofthe and 

Presentation of Data from 

Tables; 

alwater tem-

, actually the tests on Sands 

and for the tests on Sands Nos. 1, 2, 6, and 7, 

bureau records. The mean vcloeit y, in 
2il 

C~olumn (7), was computed from the discharge and the area of crosssection; the surface velocity, in Column (8), was computed from the 

measured time interval required for a small float to tntYersc a 20-foot 

course; and the bottom velocity, in c:olumn (9), was read from the 

rating curve for the velocity tube, the <trgument being the scale reading of the tube when in its lowest position. The velocity measured 

at this lowest point was actually that at a distance of 0.02 foot above 

the bottom, this distance being half the diameter of the glass tubing 

of which the instrument was constructed. 

The value of Manning's n, in Column (10), wail computed from 

the formula V = 48~ V and R being t.a ken from Columns 

n 

(7) and (5), and S being the slope used throughout the test. Reynolds' number for open channels, in Column (12), is equal to 

V R h · h ff . f I . . . . Th l v , w ere v 1s t e coe JCJent o GnematJc v1scos1ty. e va ue 

of v was taken from a viscosity curve, the water temperature being 

used as argument. It must be noted again that these values for 

Reynolds' number are aceurate for the tests 011 Sands Nos. :3, 4, 5, 

8, and 9, in which the water temperature was measured, but that 

the values for the other tests are accurate only so far ac; the estimate 

of water temperature was correct. 

The wave velocity, in Column (1:5), corresponding to Ow velocity 

at which flow ehanges from streaming to shooting, was computed 

from i he accelerat.ion of gravity and the depth. In the tabulations 

for Sand No.8, the rates of suspended load rnovement, as determined 

from the turbidity analyses, are listed, in addition to the usual 

bed-load rates. The mean size of the trapped sand, and the uniformity modulus, in Columns (16) and (17), were computed in 

the manner described on page 5. The tractive force, in Column 

(18), is the product of the depth, slope, and unit weight of water. 

The nature of flow, in Column (19), was based on observation of the 

behavior of the dye injected into the water, and the nature of sand 

movement, in Column (20), is the visual description of the movement, in conformity with Kramer's rate classification. 

It will be noted that in Tables 8 to 10, presenting the results of 

the flow experiments conducted on the cement bottom, all of the 

columns concerning the movement of sand have been omitt eel, but 

that the column numbers have been made consistent with those in 

the other tables. 

E:rplanation of Curveo 8how1;ng Basic Data: 

The complete history of developments of the tests is presented 

in the curves on Plates 24 to 38. On these plates are shown the calculated values of mean velocity, the roughness coefficient n from 

:V[anning's formula, the mean size of the grains in motion, and the rate 

of movement of the sand particles, all plotted against simultaneous 

values of the depth. (In Plates 3.5 and ;)6, the rate of suspended load 

movement is also shown.) At the top of each plate is the Yisual history oft he test, showing the development of the riffles, and the pointi-3 

at which the flow changed from laminar to turbulent, through the 

transition stage in which the flow was partly laminar and partly turbulent. The depths at which general movement was observed, ac-

error in its value. The use of mean 

from 

tion i hat the mean 

the bottom velocity, the 

in the 

Consider uniform flow of water of 

If no resistance were offered 

of water 1 foot 

differentials of n 

dE m (,· 

dE= 

where m is the mass of the of water. 

the increasE' in 

feel in 

, would 

(l) 

Since it is that uniform flow hence that there is no 

increase in kinetic t hiR increase must bn ted 1 he 

action of a force T, t h0 distn nee v 

v dt, the force is 

T = mg; S 

D 

p for m, this force is seen to be o· 

,.., 

the ener11;y 

manners: 

T 

Internal friction and turbulence. 

2. Friction of the bed. 

;{. Friction of the air. 

~V[ovement of the 

of H. 
While it does not appear reasonable to asRign the entire value 

of the traetive foree to the laRt of these four, it does seem reasonable 

that with bed material, itR movement will be in 

to the value of t be traetive foree, whieh 

thrn as a measure of the bed movement. As will be 

out later in I his report, it has been demonstrated in these 

that there is a definite relationship between the traetive 

ll·ee and the bed movement. Furthermore, the assumption of this 

is as reasonable as any attempt to correlate bed movement with velocity or unit discharge, where it must also be assumed 

that the movement is in some way proportional to the value of theS(' 

elements. 

RESULTS OF EXPERT:VmNTS 

General 

purpose of these experiments, as originally outto discover and evaluate, if possible, the laws controlling 

the movement of bed materials in flowing streams. The two prinwhieh grew out of this original purpm;e were: 

Determination of the value of the tractive force at which 

movement of a ~iven bed material starts---i.e., "eritica! 

tract i \"C force''. 

2. Deterrninntion of the rate of movement of a given material 

nt all values of tractive force within the ran!!:e of values 

which can be reached in the experiment flume. 

i hese two problems are quite intima! ely related, and 

in all studies pertainin~ to either, it was necessary to keep constantly 

in mind the importanee of the other. Also, the assumption wns 

made that the existing tractive force value was the faetor 

the movement of the bed-that is, that for a given value of 

acting on a given bed material, there was a resultant 

type and of movement, which, after the eompletion of the 

st eonld then be predieted with fair aceuraey from the value of 

tlw tractiYe foree. It will be shown below that this assumption 

was at least within the range of the values of slope, depth, 

and ratios which were used in these experiments. At 

t however, no attempt will be made to extrapolate 

1lw:·w results beyond this range, and it must remain for further 

studies determine whether the same verifications ean he made for 

tntehve forces equivalent to those found in full-scale rivers and for 

flumes of different width-depth ratios. :Vloreover, it must be kept 

in mind that these experiments were condueted under 

ideal conditions of uniform flow in a straight ehannel, and 

that their results nrc not necessarily direcily applicable to eurved 

channels of varying eross-seetion. 

The diseuRsion of the results will be didded into three general 

Critieal truetive force; (2) rate of mo\·ement; (3) misal results. Included in the latter discussion, 

L Ya ria iion of ~VI roughness eoefficienl 

2. Hiffle 

:3. Veloeities. 

Turbulence criteria. 
2\1 

Critical Tractive Force 

Defi niho n: 

Critical lractive force is that tractive foree whieh brings ahont 

p;eneral movernent of i he bed-load mixture; general movement is thai 

condition in whieh sand grains up to and including the lnrg0~1 arC' in 

motion. 

Resnme' P re1rio 11 s I nvestiuations: 

Since NiacDougall* has presented a thorough summary of the 

work clone by earlier inve~tigators on the subject of sand movement, 

it is not deemed necessary to inelude here a duplicai ion of hiR diseu~­

Hion. H will be sufficient to :,;ay that, while investigation~ of erilieal 

tractive force ha,·e been made by SehoklitReh, Eisner, Schaffcrnak, }{ramer, and others, only the latter haR dev0loped a practieal 

formula for eritical eonditions in terms of the Rand Rize and di~1ribution. :VIost of the formulaR developed by the ol her experimenters 

contain eertain con~taniR, who~e determination iH almost impo~~ible 

without first eonducting a teRI on the individual Rand in queRtion. 

Kramer'H experiments, made in Berlin in 1931-32, ineluded leRtR 

on three ~and mix! ureA, hiR general proeedure being closely similar I o 

that uRed at thiR Station. After analyzing the results of his experimentH to determine the general behavior of the mixtures, and n~rifying 1 he "law of constant critical force" (according to this law, 1 he 

critical tractive force for a giv0n :,;and mixture iH a eonslant, not :1 

function alone of either depth or Rlope), he deY eloped the following 

formula for critical tractive foree in termH of the phyHical charaeteriRtics of the Rand: 

in which T,. is in grams per square rrwter, dg in millimeterR, and Pl 

and pare in gramH per eubic centimeter. In EngliHh units t hiR equation reduees lo the forrn, 

1\ = 0.00138~h (Pl -- p) ( 4) 

in which Te iR in pounds per ~quare foot, dg is in ineheR, and Pl and p 

are in poundR per cubic foot. His method of e\'aluating dg and :VI is 

explained on page 5, this paper. 

Critical Tractive Force Curve: 

On Plate 13 are shown 1 he valneH of i he critieal t.mctive forees 

of SandH Nos. 1 to 8, plotted ap;ainst the eornpute(l values of the expreHRion (p 1 - p). On the same plate are Rhown Kramer'R 

eune for critical tractive force and tho plotted data from which his 

eurve was drawn. In order to follow more cloHely the plotted pointst, 

the pambolie eurve marked ":vr odified Cune'' has been drawn, and 

"An Experimentnl Investigation of Bed Sediment Tnumportalion". by C. H. :\IaeDoui(:Jil. 

i· Kr:tmPr cousid~·rf' only points A. ,01, N. P. Q, as eomparable with his O\vn vnlues. 
Pl ~- P ( ) 

(()) 

PLATr·: 1:{ 

I'AND ( 'HAILH'Tl'JHT:-l'!'ICS, 
all close to the 

bPd his one was H<'leeted 

four were bet ween the laHt smooth-bed run and tlw 

first run with riffles, and the seven were selected within 

the laHl two or three nms with smooth ; this faet was used as n 

to the selection of the point of moYement in tests where 

a Yisual determination produced unusually inconsistent reFmHs. 

The point at which the critical tractiYe force waR acto thiH method of spotting mon~ment, iR noted in 

the tabulations of ob10erved :md computed Tables 11 

The corresponding h D 11 is noted on the C' 

Plates 24 to and t critical tractive force ntltH'H are 

smnmarized in Table :3. 

PLATE 14 

C'mTH'AL TnAC'l'J\'E FoncB rN 

Need New Oeneml Fse in 111 odels: 

In attempting to apply to model design tlw critical tractive 

force valueR for fine Hands found in the study deReribed 

cral obstaeleR were encountered which made it apparent that a 

limit should be placed on the sand sizeH to which the visual method 

of mo\'ement determination should apply. St udiPs of the 

data aYailable from theRe experiment:'\ indicate that this lowPr limit 

may tentatively be placed at a mean grain Rize of about 0.6 mm. 

The following data tend to support this belief, and lead to the conclusion that a new criterion for genNal movement be advisable for 

finer materials, if they are to be used in becl hydraulic 

rnodels: 

L With Hands of size less than 1 his limiti 

rate of mon;ment at the point of movement" 

to apprPeinblr. 

the 

small 
\Vii h Rome fine sa even though 1 be rate of movement 

tlw of moYement" iR apprnciable, riffle formationR 

at tractin• forces greater than thiR "critical" value :so increase the 

of the bottom and retard the that there it' a sudin the rate of mon•ment. In the caRe oft be finest san ell' 

rat of mon;ment frequently became z<>ro at tractin• 

"critical" This point, as well as the first one, is 

out in Table :i, colun:m (20), and on the graphs on Plates 

where it ean be Reen that the rate-of-mon;ment emTe dropl' 

when t hP riffles to form. 

:3. In thP case of all snnds excc>pt No.s. 1 and 9, the sand 

the point of "general movement" waR 

i\·e of the material of which the bed wa,.; molded. 

n size of the Rand in motion was much larger than that of 

sand. The exception in th<~ case of Sand No. 1 may be 

the content in 1 he mix! ure; Sand No.9, the small 

the range where this condition ob1 ainl'. 

the curves showing i he analyseR of 1 lw 

Plates to 52, where it can be Reen that it waR 

until after a uniform riffling condition had been reached that the 

of 1 be tra ppP<l sand approached that of the original. The 

change in the mean grain size, and its relation to the rifstagP, are shown on the graphH on Plate:s 24 to >l8. fn other 

it would appear that at the point at which, aecording to th<' 

general movement of the bed material was obi ained, 

i he rna 1 erial in mot ion was not representative of the mixture 

1 lw bed waR originally molded. 

Thi:-< fmmewhat paradoxical condition, in which 1 he mn !erial 

firHt moYer! the flowing water was larger in size than the original 

mat was confirmed in every i CRt of Sands Nos. 2 to 8 by visual 

ohsPrvat oft he individual particle;;; in mot ion. ln en;ry instance 

it was notieed that the first partieles to begin moving were the larger 

mws, and that aR the depth was increased, more of the smaller began 

to be movetl. It is belie\'ed that the explanation for this phenomenon li<>s in the fact that the larger part ieles, which protrude a small 

diHtanee ahon; the generalle\'el of the bed, are acted upon by greater 

\'Ploei t iPH t ban are the finer particles, whieh fill the interst iceR bet WP('n t larger particles. \Vhile this vertical diHtance is very small, 

tlw in veloci at the bottom of the flume is very rapid, and a 

:-<mall in \'erticalloeation causPs a relatively great difference in vdocity. At !J;reater depthR, however, the increased velocity 

the aided by the inc reaRed condition of t urbnlcnee, is 

suffieien t to reach and renwve the finer particles. Hence, it may be 

eonclm!Pd that mo\'C'ment of a fine Hand on a smooth bed is a sorting 

proeesR, and that only after the format ion of riffles doeR the moveuwnt hPeonw general in the sense that all the partielcR are mo\'ed in 

a bou I t hp of their oecurenee in the mix! ure. 

This t ion, as stated a bon~, was not observed in the t e,.;ts on 

thP ,.;mall in which at the very commencement of mo\"ement 

I rrwan in motion was approximately equal to mean size of the original material. The rea.son for this probably 

fact that a resistanee to motion varies as the cube 

while the diRtance the particle prot rudeR above the 

on the particle, vary as a mueh smaller 
probably lesR i han unity. Hence, there must be some limiting 

particle at which the larger Rizes no longer move firRt, and 

a bon~ which the finer matnialR are the first to be placed in motion. 

While no data vvere recorded in these experimentR which would tend 

I o locn leI his limiting sizP, it is bPlievc'd that its \·nhw is in I hn \'ieinit v of 0.6 rnm. · · 

New Definition for Oeneral Jl!fovernent: 

To answer the need for an Ewaluation of critical i racti n~ forc0 

which can be used in model design, and which has a real meaning 

through the range of sand Rizes smaller than 0.6 mm, the following 

tentative new definition for general mo\·emEmt has lwen work<•d 

out at this Station. 

General movement is obtaiued when both the fo1lowing eon- eli! ions are attained: ' 

1. The material in transportation is reasonably similar in composition to the material composing the original bed. 

2. TrH~ rat El of movement is equal to or excePds onP pound 

weight) per foot width of channel per hour. 

The critical tractive force is still defined as that Yalue of 

tractive force existing at the time of the commencement of genPral 

movement. 

It £s desired to ernJJhas?:ze the fact that tlu:s 

1rwvement ·is intended 8olely joT use ·in conne<:tion 

where sands of mean grai11 size less than about m.m are 

in no case is it meant to be e:rtended to include bed-load movement in 

full-scale streams, or sands larger than the limit stated. It is fully 

realized that the two spen.jications do not a condition of nwvernent tohich is e.rcu:tly the same for a 1~{ mean size say 

0.3 mm, as for another of mean grain size of, say ·rnm.. fl behowever, that with·in the assiuned l?:m:dat·ions, it defines a r'onrhtion is neu.rly umJorrn, and which 1m:ll prove useful 'i·n 

model design. Further studies will be made of this snbject, and it ·i8 

hoped that a better de.finit?:on for general which will 

stn:Ct theoretical as well as practical mn be developed. 

It is understood that this clefinitiou can not be applied to a gm \'el 

or small Rtone mixture because of the faet that the movement of 

only a few isolated large particles might be sufficient to satisfy t hP 

1-pound requirement, even though the movement waR not at all 

general. Through the range of sizes with which this Station is usnally concerned, however, it is believed that thiR condition leacb to a 

usable definition for critical tractive force. The value of 1 pound 

was derived from experience recordR at the Laboratory, when• it 

has been found that in a 12-hour cycle of operation of a model oft he 

:\[isRissippi H.iver, which averages about 4 feet wide, a minimum of 

about ;)0 pounds of sand muRi be moved to secure Ratisfactory developrneut of the model bed. 

The fulfillment of the first condition-that the moving material 

must be similar to 1he material composing the bed-insures that the 

value chosen for the critical tractive force iR greater than that neeest-mry to produce riffles, and com;equently, that there is no retardation 

in the rate of moYement at tractive forces greater than critical. Thifl 

point is eYident from nn inspection of the upper curve on the com-
be seen that the cun'e 

mo\'Nnent 

thai of the 

of tlw ri fflPs, 

t hPn comin column 

and (he 

forces abon~ critical wen: recorded in colunms 

ntlues from colmnn wen• then 

values of Pl- p), and the result 

on which arP also shown the curve representing 

<'qnation and i revised cmTe this 

erii nion mon>cment, 

ic; apparent that l he procluet of depth and ic; a 

for critieal condit inasmuch aH the ntlues dethe three were the same for en>;ry 

tlw curve iH 

r;, arP too fpw 

p) of more than 5, Tlw evidence 

out, how<'\'Pr, thnt there is a minimum ndue of critical 

this to a mean grain size of 

and thai this there is an 

ieal t force, This size of particle 

to thnt ;-;ize bPlow which riffles become apthat tlw rate of sand HlO\'Cment at the time> of 

mO\'ement of Sand X<L 2 was about fLO 

hour, while that of the ot lwr sands was 

tionofthisis hat the 

factor in the detennination 

in all the others the 1-pound 

t lw finer the the smaller 

henee at the ( ime when 

t ion to the molded 

parap-
;£ 

2 

"L 

~ 

" p. 

~ 

11 

" c 

q, 

~ ;;::; 

.:: '" 

~ 

d 

~ 

:,... 

·c 

G 

r:; 

The increasE~ in the critical tractive force values for the finer 

according to this criterion for geneml movement, is the exact 

reverse of the trend indicated the Kramer formula, which >vas 

deriyed from tests of sands than those teflted at this Station. It is believed that the explanation for this phenomenon 

lies in the matter of the riffle development. As can be seen from the 

Plates ;)9 to the finer the sand, the greater wa.s the height 

riffles in comparison with the depth of water forming them, and, 

uenily, the greater the roughness of the bed. At a given depth, 

of the water, then, was less for the fine materials than 

fur the coarse, and the movement oft he part iele::; was correspondingly 

les::; brisk. The value of tractin; foree at which lhe 1-pound limit 

was satisfied increased then~fore with grain and sinee 

the 1-pound limit was the controlling factor locating the of critical tractive foree fort he finer ilw critical value also increaseed 

in this manner. 

0032 

0028 

0016 

0012 

10 

' d .• value of \I (p,· p) 

J?J~ATE 15 

CmTICAr~ TnACTIVE Fonnc IN 

The scattering of the points on the curve of Plate 15 is not eon-

::;idered to decrease the useful ness of this evaluation, for I he10e reasons: Sands Nos. 4 and 5, which have higher critical Yalues than 

seem consistent with the curve, were composed of grain::; which wc-n~ 

much more angular than those composing the other and it is 

believed that the interlocking effect of the angular grain;:; cau::;ed a JT'-

tardation in their movement. The low valnr of Sand No. which 

was also angular, or rather, the high values of Sands NoR. 6 7, can 

he attributed to the probability that some of thP moving material in 

the tests on the latter sands was lost over the> tailgat n, and that tlw 

tractiYP force corresponding ton 1-pound rule was higher ihan it::; 

true value. This argument is borne out by the fact that the c-nlargPd 

sancltmp used in thP tests on Sand No.8 caught, at all stag<>s of mo\'Pment, an appreciablP quantity of the sand, whieh on'r tlw 

in the other tests. The posRibility is suggm:~ted that this 

the critical force relationship should 

two or three parallel eun·n::;, enrh cmTe joining tlw 
JZ~fl 

UllJf\ 
pointE' corrm;ponding to sands of thr 8amc angularity of grains. Although the data from t he8e ex peri mrnts arc not numerous enough to 

establish this theory, future studies may sene to pron' or dispro\·r 

its mrrits. 

Rate of Bed-Load Transportation 

A knowledge of the rate of transportation of bed-load is as irnportant in calculations concerning changes in the configuration of 

stream beds as is the knowledge of the stage at which bed monmwnt 

begins. In the operation of hydraulic models with montble beds, for 

im;tance, it is essential that the material composing the bed of thP 

moc!Pl bP moved at all stngps corresponding to thoRP during which 

thPre is mon;ment in nature, and it is likPwise important that tlw 

movement in the model be qmmtitatiyely in :mme known proportion 

to the rate of movement in thr full-scale stream. Hence, sornP 

knowledge of the laws governing the rates of movement of both tlw 

model stream bed and the natural stream bed is essential to the pmper intPrpretntion of modfJl r\?fmlts. LikewisP, in the dPsign of rpgulatory works for ri\'ers, the subject of sedimentary load transportation 

sometimes is as important as the hydraulics of the problem. 

Resume' of Previous I nvest?:gut~ions: 

Several investigators, including du Boys, Schoklit sch, Gilbert, 

Eisner, and :VIae Dougall have contributed to the knowledgr of I he 

subject of ilw rate of bed-load movement, but none has as yet succeeded in so formulating the movement of sand that a mechanical 

and physical analysis of the material is sufficient to pn:dict accurately its behavior wlwn acted upon by a flowing stream. 

:vracDougall* has contributed t hP latest information on the su hjecl, as a result of his experimPnts at the :VIassachui::letts Institute of 

Technology, and has arrived at an approximatP method for prPdicting the mon~ment of bPd-load from an analysis of the material. 

His eonelusions are based on observations of only three sand mixtures, however, and his final muvos are drawn from only three points. 

Bas~£s for Formulation of Hate of Jv[overnent: 

There is a not ice able similarity in the general form of the equations derived by various experimenters to exproi::ls the rate of movement 

of bed-load in terms of the hydraulic elPmentR. Almost all of them 

attempt to relate the rate to some function of slopP and excess discharge or excess depth, with an experimrntal constant to lake eare of 

thP variation in the sand mixtures. Gilbert has attempted to show 

the individual effect of each of the factors, velocity, slope, and discharge, by keeping the other factors constant, and hai::l presented seYeral expressions which show these relationships. Eisner has included 

in his formula a factor to exprei::ls the friction on the bed. :VIae Dougall 

has derived three similar equations in terms of dii::leharge, one for <'ach 

of his sands, and has then attempted to <:waluate his eonstants in 

terms of 1 he physical charaeteristies of the materials. 

U. 8. vVaterways E.Tperirnent Station Formnlution of Rate Movement: 

After a thorough study of the ratP-of-rnovement data accumulated in the experiments, it was found that the following empirical 

* "An Experimentnl Inve~iiga1ion of Bed HPrlimeu1 Tram-<por1ntinn", hy C. H. }'lni'J)ougall. 
between th0 

bed-load movement after the formation of 

Dt'·-·fPeL 

PLATE 1() 

\L\NNf"Nn's 11 IN lV.rrF:~oF<Hon;:MF:NT r,L\J>uxn• 

Snnd ~o. fi 

stagP of 

derived 
As will be shown 

constant. The 

lirnits, is of c>vlr.r<>rn 

effectR on bed-load rate 

tion of grain sizes, voids 

of material, density of 

width-depth ratio of 

m is very 

Within ntlJTOW 

the 

The nine logarithmic plottings of Wn DS Do ), 

from which equation (7) was derin~d, are Plates 17a 

to 19c, and the range of of k and rn, as well as 

those of nand DoSo are summarizeed in Table The nine curvrs 

are Rhown iogether on Plate 20. 

TABLE 4 

v ALUIG OF CONSTANTS IN EXP!U<:SSION IV 1 

1 

to 

to 

to 

a 

to 

to 

4 to 

to 

to 

to 

7 

8 
b. 

(Wn) 

;-.:and i'-Jn< 

(\Yn) 

Sand )J(). 2 

(Wn) 

('. r-:nnd ~o. 

PLA1'E 17 

01' OF ;-iAND .\'lOVEl\H~NT TO DE:PTH' ~LOPE, AND H./HTGHNESR. 
0 

70 

1 0.00010 

·1:: 

8 

;;: 

d 

I 

m 

8 

;} 

d 

! 

m 

8 

(Wn) 

Nand Nn. 4 

(Wn) 

b. Hand No, 5 

(Wn) 

t'. ~and No, () 

Pr"'"'" 18 

HF.:L\TION or BATI<; OF ~.\ND .\1oYg?o.tENT TO DF::PTH, i-4LOPE. AND l{OC(iHNI<.:SH 

4] 
OF 

(\rn) 

f-iand No. 7 

(Wn) 

b. Sand No.8 

(Wn) 

(". Sand ~<J. 0 

PLATl': 1\1 

TO DJ·:Pnr, ~LOPE, AND HouGHN1,:ss 
It will be noticed from Table 4 that lhc values of the expon0nt 

m nrc confined to a narrow range, from 1.5 to 1 

is evidenced in the composite logarithmic plot e 20), where it 

can be seen that all nirw of the lines are Yery nearly parallel. Furthermore, the values of k 1 fall within the small range from 0.00046 

to 0.00110, and with tlw omission of Sands Nos. 6 and 7, fall between 

0.00046 and 0.00066. It is believed possible that the same explanation may be offered for these high values of k 1 for the two sandR 

that waR offered for the high values of eritical tractive force for the 

Ramp Rands--i.e., that not all of the sand waR caught in thP trap, and 

1 hat actual valueR of \V Rhould be Romewhat larger than 1 heir reeonlc>d ntlueR. It will be Re('n that an incrPaRe in each \V-\·a.lue, 

with its corr('sponding effect on Wn, would ~Pne to move the logarit hmie eurve down and to the right, and would reduce Hw n1lue of k 1 • 

w 

e 

(Wn) 

PLA'l'l'J 20 

('oMPAIUSON oF HATES OF :\loviG.:-.IEN'r OF' ~ANDH Tlt:WJ't<:D- LooARJ'rnMic Pun 

Whether the effect on k 1 would be largp enough to bring the \'alueK 

for Sands Nos. 6 and 7 into the range of valueR for the other RandR 

cannot be Raid, but it can be said that thP effect would be in the 

proper direction. Hence, it may be found pm;sihle, with furl her 

study, to express the rate of movement for all Ramb by an equation 

similar to (7), in which the valuPR of m and k 1 will he conRtant, and 

the only variableR will be the valueR of Do S" and n. 

Little eonsisteney haR been found in the manner of variation of 

the DoS 0 -valueR. An atiempt waR made to plot the values againRi 

cmTeRponding valueR of ( p1 p), a procedure parallPl to that 

uRed in the Rtudy of critical tmclive force, but no more than a general 

trend eould be diseovered from the Rome what RcatterPd positionR of 

the plot! ed points. It must be rpa.lized, however, that theRe \·alueR 

have little real meaning, and are only the points determined from thr 

extension of the rate curves to the horizontal axiR. Tlwir prima.ry 

use is in the equation, and it iR not intended to mean that their vahws 

to the actual commencement of moyement of 

load. ually there iR n rat her wick Real of i he plotted point K 
of movement, and the value of DoSo can 

a nuiation of as much as 15 per cent. 

however, t there is a definite relatiorwhip beyahws of DoSo and the phyRical of the Rand 

that later studieR will disclose The preliminary 

.~,~~'"""~" in the paragraph show<:'d a close Rimilarity 

form to the curn~ (Plnte lf>) for critical tractive force 

t tlw "model" criterion for general movement. H seernR 

that there should be such a similarity, since there is a cloRe 

ween the limit for general movement and the 

the main r('ason for the cliRcrepancy betwo eurvm; is the critical tractive force values were 

the tabulated rate va]w,s, which tend to disperse ai the 

curyes, while the DoRo values were taken from the 

enrn~s ihemseln;s. 

ean be 

s from the 

in the following form, which insands and the Rmall gravel: 

1.5 lo 1.8 

tlw omisRion of the resultR from the Rmall gravel, equation 

U\ to 1.8 

w 

II 

The rate-of-mm·ement curves on the composite graphs, Plates 

been drawn to conform with the logarithmic plots on 

to 19c. The value of Wn corresponding to each selected 

as read from the logarithmie eurve, was divided by the 

to thai ntl ue of DR, as read from the comvalue of vV waR used in determining 

the location of the curve on latter Rheet. From an inspeetion of 

it will be seen that they follow the pointR n~ry closely. 

No. 2 at 0.002 prm;entR the inconsiRtent 

R heentire in theyalueof islessthnnthatof 

, and the curve does not closely follow the plotted pointR. The 

first is the fact that De was chosen from 

t lw rate while Do was determined from the averTn 

for all The probable explanation for the 

is that the experiment waR conducted too ra.pidequilibrium between riffle eondit ions and diRreaehed. 

demonstrate the method suggeRted for using the 

of moYement, a hypothetical example will 

that it is cleRirecl to determine the rate of 

at a of 0.0012 and a of 0.417 

S is 0.0005. 

eorresponding at 

From Table 4, m 

0.00049. 

0.001 to a DSseen to be l 

these vnlnes in 
4i} 

s~~-o dg M 6 

\ 1 0.5861 0.2796 

2. I 

2 0.5409 0.4388 

811 3 0.5246 0.5385 

4 0.5056 0.4063 84 

I I 

I 5 0.4828 0.4384 

10 

I I 

6 0.3470 0.6428 

711 l 7 0.3104 0.5246 

7 I 8 0.2053 0.5597 

2.1 

I 9 4.0769 0.5661 

66 

I I 

4 I 

i I 

/ I 

0 I 

I ---

l 

6 I 

I / ':J 

52 

I A ( I 6 

4 

2-V; ~ i 0 

/I/ t ? 

6 / /6 -·- il ~ 3 [o ;. frll 

2 I ·---- T! 7 J l .8 I 

I i 0 .,/ I I 5 I "~' : 

0 l I J ~./ 

l i ... ~ !fr· ,/! /' II ' I i if/ I / " / : ~ 

12 / t! I / ,y/ "-6 

. /¢ I I I II I .· if; ~I 

i /./ q/ 4 I I· ~;.~ ~<1 ~.jf.~ 

2 

0 0 0.0002. 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.00111 

DS .... Feet 

PLATE 21 

CoMPAiusoN OF HATI>Jr. oF ?dovr•Jl\II<.:NT OF NANDR. TEHTIDD 

Average (~urvcs dnnvn from plotted vnlueK ~-;eeured nfler the formation of riftle~ 

T 1 0.0005 - 0.0003 ]7 v\ == ----:;~ ( -- ~----------- .. ) O.Olt>a 0.00049 · 

or, \V 14.1 lbs. per foot width per hour. 

The experimental values for the three slopes, at corresponding DSvalues, are 14.6, 11.3, and 11.2 lbs. foot width per hour, respce-
nccurntc. 

ion 

and 

results which MG 

The n Yalm's for 

and had 

lower Yalne for 

been closer to the 

sand rlifwith 

bebe limited, of course, to sand mixof l:lizes covered by the materinlK 

these to slopes not different from 

between 0.001 and 0.002. Further, the value8 of 

which were obtained were about and it is 

1 hat the results be extrapolated value. 

of this then, for computations involving fullIn a ri\·er like the ~VIis8issippi, 

the lowest slope U8ed in the experiis Kufficiently to produce a depththe \'alue Further, while 

measure of bed-load mm·ement through 

used in the ts, it remains to be 

flat or extremely slopes is 

remembered that theRe rewlt s 

flow in a straight flume, and that the 

between bed-load movement under these ideal concHand under the usual conditions of cuned channels of vary-

·sectiom; has not been established. 

Yariation Ho.te with Size: 

the rat CK of mo v~c•nwn i of all the 

are shown in Plat 21. h will 

that thP mie of movement is greater with the larger 

in dw cn;.;e of Sand No. 9, the small 

ion for this condition liefl in the riffle 

fine t i he of tracii ve force 

1 he riffles were of appreciable , were retarded in 

, white the eoamer retarded to a lm::ser exat rates. 

m 

\'alues 

to enms 

rates of movement at 
Coefficient 

The value of :V!anning's roughness co0fficient as computed 

from the formula for open chanrwl flow, has recorded 

for each run in 8 to and all the ntlnes ha \'<' bcPn 

1 ed depth on 1 he e graphs, Plat Ps 24 1 o :is. 

of the Formula: 

The fact thai the formula can be used to adnmtage in 

lhe,;e studies i:s well demonstrated from the of the }fanning':.; 

n curTes on Plate:.; 24 to 38, and especially tho,;e on Plate when•in 

are data from the flume both with sand bottom and with 

cement bottom. On the latter it can he seen that the eomed value of n remain:.; at a nearly con,; I ant value n~ry cloRC to 

throughout the complete range of depths which were UR('tl. For 

the sand bottom, on the other hand, n remained nearly constant :-:o 

long as tlw bolt om remained smooth, at a :sli12:htly higher ntlue 1 han 

1 he 0.01 found for the cement bottom. 

Some caution muRi be applied to the use oft he actual YaluPR of 11 

computed in these experiments, for the reason that the side roughnCRH waR not the same as the bot1 om roughne,;s. The sides of the 

flume had a smooth surface of neat cement, exactly like the bottom 

in the teAts made without sand in the flume, and it was not belim·pd 

practicable to roughen the sideR to conform to the roug;hnesH of the 

sand bed. ThiR equal mughneRR would ha \·e been CApecially hard to 

achieve after the formation of riffle,;. \Vhile the u,;ual conception 

of Manning's n iR that it representR the roughneRH of the bed, actually 

it iH a resistance factor which must indude Huch other factors in addition to roughness as curvaturm;, eddies, ancl change:s in bed configuration. In these computation:s, therefore, it muAt be con,;idered 

that the n-values repn•sent the resist a nee to flow of a channel with 

a Rmooth side :surface and a bottom of variable roughne:s,;. 

It must also be noted that the Manning formula applies only to 

turbulent flow. The values of n h:.we been computed for the laminar 

flow range, and han been plotted, to illustrate the point that they 

are meaningless in this range. A dashed line is drawn through t he,;e 

points, to distinguish them from t lH• poin 1R computed from t urhulent 

conditionR. 

Fariation in Values u: 

The range of n-\'alue,; encountered in these experiments is summarized in Table 5. The average value for the cement bottom, 

eheeks very elosely the value of 0.010 l!:in~n for a 

neat cenwnt surface under best conditions. The twPrage for 

all the sands for a smooth bottom is 0.0107, eloRe to the ya]uP of 

(Ulll given by for a neat cenwnt surface under good eon <lit ions. 

The \'nine of O.OHi the small is rwarly tlH• ,;anw as tIt<: v:duP 

for a eement-ruhbh; Rnrface. 

a riffled bottom, ihe 11.-Yalnes ,;ho1v n 

a minimum of 0.0112 in tlw ea,;e of Sand No. 

for 8. It iR 

variation, from 

maximum of 
trend followed by the riffle sizes-----i. 

ihe percentage of fines in the 

In the ease of Sands Nos. 1 and 2, 

riffles were verv the n-ndues on the riffled bed wern only 

aboui 0.001 ·than on the smooth bed. \Yith the finer matcrhowe\-er, the n-value for the riffled bed frequently waR more 

than double il ude for the smooth bed. 

Ne!ation 

The 

value of 

s n and Rate of Sand Jl1overnent: 

e of movement of the sand is very closely related to the 

of the 

n, which is determined prinei pally by the Rize and 

This fact was brought out in the diReuRsion of 

I<' of BPd-lond Transportation, where it waR Rhown that thn in0.0102 

0.0115 

0.0117 

o.ouo 

0.0110 

0.0099 

0.0100 

0.010:3 

0.0160 

TABLE f) 

0.0112 

0.0120 

0.0207 

0.0270 

0.0243 

0.02:1:) 

0.0254 

0.0287 

0.017:3 

~vraximurn 

Change in n 

0.0010 

O.OOOfi 

0.0090 

0.0170 

0 .()1:3:~ 

0.()1;34 

0.0154 

0.0184 

0.001:3 ~~~-~~-cc=---------~----~-~-----~--------

elusion of n in the rate formulation tended to reconcile the rates at 

to tlwR<l at lower discharges. In general, the rate of 

movement ntries inversely with the value of n. Lacking enough 

information to determine what power of n should be uRed, i1 was 

aRRmned thai the first power sufficient covered the effect of the 

of 1 he flume. 

Riffle Development 

The r:;eyeral manners in which sand is transported by traction 

been described in detail Gilbert*, who has conduetecl the moHt 

ion the subject, and by :VIaeDougall**. 

modeR of transportation are: 

ovcrnent on a smooth bed. This rnorement begins 

stage when the tractive force reacheR a certain value, del he of the bed material. 

Debri:-: by Bunning \Yater", by Grove Karl Cilbert, S N. Pro~ 

InvE"stig:dion of Bed Hedimcnl Trmtspnrtidion'' 1 by C. H. ,:\ltJ('DougalL 
Movement in "dunes'', or riffles which downthis of the particles are 

oft he dune, are rolled over its 

are deposited the foot of the Rlope, resulting; in the typieal 

stream movement of the riffle. With increasing; depth, these riffles 

until the beginning of the next stage of movement. 

distributed in which the riffles 

state are smoothed out, and the bed bePLATE: 22 

TYPICAl~ HIFFLE FonMATIONH 

Upstream Views 

comes approximately plane, although somewhat irregular in 

ance. This stage is reached at a point close to that at which 

changes from streaming to shooting. 

Movement in "anti-dunes", in which, as the term implies, there is an upstream progression of riffles. In this stage of 

there is a scouring on the gentle downstream of the 

and a deposit on the steeper upstream face of the next riffle. 

This anti-dune stage occurs only with Rhooting flow, and is seldom 

observed in nature. 

Most of the movement in i hese experiments fell in the first two 

classifications, with a tendency at the highest toward the third 

(see Plate 43, Sand No. 8). None the tests extended 

into the anti-dune stage of transportation. 

Variation in R1j.fle Size with of Bed Jfaterial: 

the 

it was found that the size of the riffles increased as 

of fine matPrial in the mixture increased. Rands NoR. 
insi ancc, i he 1 wo coarsest sand mixtures 

and their effect on the roughness of 

noticeable. This fact can be verified from an 

where the values of n increase very little 

The actual size of the can be rnemmred 

ted on Plates ~jg and 40. Sands Nos. 6, 7, and 

on ihe other cleYeloped riffles which 

imes as as ;jQ per cent of depth of wai er forming 

which more than doubled the roughness value of the bed. 

riffle formations for four of the mixtures are pietured in 

and the exact profiles for all i he mixturPR are plotted on 

44 

Yalue at ppeamnce 

Table 6 the average lracti\·e force value existing on the lmd 

Rmooth run, before the appearance of riffles, has 

liRted for each of the Each of these values is the average 

three but it was found that the individual values were 

from the average. According to the table, the 

the small gravel), was the slowest to 

8, was the quickest, and between these exwas for a more rapid riffle development 

size decreased. This fact was verified in case by 

from which the conclusion was by the 

assistants in charge of that the fine sands more 

then the coarse. 

TABLE 6 

VALUE OP THA("l'lVE F'OIH'_f.j AT A.PPKAHANCBH OF RIFFLES 

.:\ verage of Yalu(~B for Three Slopes 

Velocities 

serieR of Ydoeity ineluding 

and bottom and \'elocities at ntrious depths, 

the course of these experiments, and the data are 

r form in Tables 8 i o 37. The mean veloeities 

the corresponding depths on Plate's 24 to 

the \·ertieal distributions arC' shO\vn in 

veloeities are best illustrated in the 

Plates 24 to in which have 

each one of curves it will be 

exists between and 
51 

SLOPE 0.0010 SLOPE 0.0015 SLOPE 00020 

I [ 1 I i ~- -

-~---t----- 0.1 - -- 1- I ____, ~~-~-I 

o I I i boi 

R N 15 () RUN "21 o Ei o"" RlJNU 

~~ 12! ~ .. - H 13[ b 0.1 E 01 t ~~-- I RUN 19 

~-·- f-·-

~= 0 I I ..... I i·h ~ 0 +-

0 RUN Z6 o I ol ~ RUN Z3 ID I E\ '0 11 i lo 

IE .£: 0.1 I cn1 I _QLI({) Ill 4-

j I<UHll 

0 ~-- --=-r 1 71 0 J E 0 0 ({) R N 27 0 j •.t· RUN 24 

I "31 - Ll "'i 0.2 0.1 _., 0 ~r-- 1 s~ rt.,-· 01 /, 0 RUN 28 0 _sl RUN 25 

0 I RNZZ 0.1 l 0.1 _.J., ~ /I I 0.3 - ---9 0 I R<JN Z9 0 RUN 26 

t -

r-r -r 

0.2 o:z 01 

0.1 f 0.1 IJ: I 0 I RUN 28 

I RJN 24 I I o:z -·· 0 0 RUN31 --

..Qi_ - i) h 0.2 11' 0.1 1 

"' t I .::: </) / 

...QL iY 0.1 0 "' <I) - • Rl,IN 30 

"' ''pi> '+- L. 0 c ;;:: &I .,_ 

~ L 0 RUN 32 o:z. "' rx c L .~ OJ 

0 cs 0 L 

Ql 0."3 L -

17- ... 0.1 "' c 

) R N28 

c "' ~~N 31 

., 

(!) l9 

0 o:z. 0 

i v !7 04ii I 01 J 0.2 

I ----------' 

0.5 1/Rl)N 34 I 0 0.1 

0.4 I 0.4 t--r 0 c{UN 32 

03 I J 0.3 j 0.3 

02 I o.z / O.Z -r-r 

J 

Ql I 0.1 J _QI __ --r--r--- v ------.:..----

0 /gt;N30 0 I/ Rl)N 3€> 0 ~UN33 0 1.0 l.O 0 1.0 2.0 0 1.0 20 

Vehwity~"Feet per Necond 

PLA'I'l'l 2:3 
line and the 

transition between 

break in the 

commeneed to form. 

of turwas 

which were 

there wns 

in the rate of inof the break at this 

"u"'""'"' which occurs in the 

the size of the 

is not 

which 
Veloi'1Jies · 

:vrc~mmrernents were made of surface velocities, in addition to 

bottom veloci I ies, in tlw 1 ests on Sands Nos. :3, 4, 5, R, and 9. These 

values were all plotted against Rimultaneous valuPs of mean velocity, 

and it was diRcovered that a Riraight line could be drawn through 

th0 pointR, for all the tml1R on smooth sand beclR or cement bottom. 

The equation of thiR line was approximately Vm = 0.90V,. After 

the formation of riffh~R, ilw relationRhip was not RO ddinite, although 

an equation of the form \Tm = 0.8fi V, would Rat moAt of t hr 

pointA, within a reaA<mable pPrcentag(' of error. 

Vertical Distrib11tz:on 17 el on'ties: 

In Plate 2:), a serieA of vertical velocity distribution curn'R is 

given for Sand No. :3, with point A ReJected from sen~ral runA both 

before and after the format ion of riffleA. The general shape of all t lw 

cun·es is the mune, with a nearly uniform increaAe in the ,·elociiy 

from bottom to 1 op. A 1 the i ime of riffle formation, the AtHne phenomenon is obAerved for the velocities at all depths---a marked deerease occurs, followNl a gradual inerease as tlw depth beeomes 

inereased. 

Turbulence Criteria 

In eaeh of the tests exenpt those with SandA Nos. 1 and G, obAerYationA were made of the type of flow, wlwther laminar or turbulent, 

and special attention was paid to the tranAition stage betwel'n theRe' 

two types. As explained in detail under Procedure of Experimentation, 1 heRe determinai ions were made from ohRen·ationA of 1 he 

path taken by a stream of potassinm permanganate Rolution whieh 

was injected into the water. 

The ndues of Reynolds' number for open channel flow and of 

the YR-criterion for turbulence (the latter value is similar to t lw 

}teynoldA' number, lacking only the factor for ehange of viscoAi t y 

with temperature, and iA conveniently uAed when the temperature 

is nearly conAtant), defining the tmnAition from laminar to turbulent 

flow, are given in Table 7. The \·alueA ginn in the table were talwn 

from the laAt run in which the flow waR partly laminar. It was found 

impracticable to uAe the values for the first turbulent run, AincP they 

sometimes were too far into the turbulent rangP to define i I R lower 

limit. 

The maximum value of Reynold's number for open channelR a( 

which some laminar flow was obsened waR 1970, and the correAponding nclue of VR was 0.024. From theRe obAervationA it may tentatin~ly be concluded that turbulence will exist in a flume if the value 

of Heynolds' number iA about 2.500 or more, or if the corresponding 

\'R-value is about o.mo (aRtmming the coefficient of kinematic YisCOHit at an average value of 1.2 x 10 5). 

previously Alated by this Station, turbulence in a hydraulic 

model is inAured if the product of depth and velocity iA greater than 

0.02. The criterion of depth and velocity iA very similar to that of 

hydraulic radiuA and velocity, inasmuch aA the hydraulic radiuA iR 

almost equal to the depth. The two values, 0.02 for the VD-produel in a model, and ().03 for i he VR-procluet in a flume, ru·fl not 
TABLE 7 

1810 

:no 

1170 

0.012 

0.016 

O.OlG 

0.011 

O.OlH 

0.011 

0.010 

0.024 

0.010 

0.012 

(),024 

0.015 

run in whi(•h flow \Yas partly laminar. The next nm in each cn~-;e waf-1 

ll3ABLl': FTrrUIU; STUDIES OF BED-LOAD 

~V!OVE:VCENT 

be on i he fact that i hese studies are not 

the final answer to the problem of bed-load movement. 

rnade at the I'~xperirnent 

continuation these experiments, i he hope that 

information will be obtained and made available to hvdraulic 

concerned with this subject. ~ 

aff members at the Station are of the opinion that the rate 
nation of the critical tractive force of the material composing i he 

bed is not so important as a knowledge of its rate of movement at 

all An exception to this condition may occur in some inhowever, and the critical tractive force may become the 

important factor. An example of this is found in certain upper 

reaches of the Savannah River in which there is little or no movement of the bed at low stages. higher stages, however the movement is appreciable, and the determination of the which the 

movement begins is essential 

One of the aims of the future studies will be the elimination, or 

partial elimination, of riffles in movable bed models. While the formation of riffles in the sands in use in models at the Station has been 

troubleRome at timeR, it iR not believed that they have been FlO severe 

as to vitiate the results of the studies. NeverthelesR, the elimination 

of large riffles will make for easier operation of i he models, and will 

to some extent reduce the element of judgment necessary in the interpretation of the resultR. The present Rtuclies have indicated that 

there is little riffle formation with sands of about 0.6 mm mean 11:rain 

size, and that the critieal tractive foree, uRing the "model" criterion 

for general movement, is a minimum at about this same grain size. 

the first efforts will be be to mix a sand of about thiR size, 

having a very small pereentage of fine 

Another step that must be taken is the study of the relation betv•leen the flume results and the results under corresponding conclitions in a model having the complieating faetors of bends, ehanging 

erosR-seetions, ete. Until sueh a time as this Rtep is taken, flume 

reRults must be taken as indieations only, comparable only \Vithin 

themselveR, and applicable only with careful judgment to hydraulic 

models. 

The finallogieal problem to be faced is that of the determination 

of rates of movement and critieal tractive forces for materials composing the beds of full-scale rivers, and the relation between theRe 

full-seale phenomena and the results of flume observations. Some 

work haR been done on this subject, by the NiiRsiRsippi River Commission and various others in this eountry, and by several observerR 

in Europe, but no measuring devices have been perfeeted with 

which quantitative reRults can be obtained. A strong impetuR will 

be given to the study of bed-load movement whenever a satisfaetory 

method is devised for measuring itR rate and determining itR critieal l ractive foree in nat ural riverR. 

SU~L\IARY OF HESUI/l'S 

Nine sand mixtures, ranging; in mean grain size from 0.205 mm 

(0.008 in.) to 4.077 mm (0.161 in.) \Vere tested in a tilting flume at 

the U. S. Waterways Experiment Station, to determine their eritical 

tractive forees and their rates of movement eorresponding to 11ll 

values of traetive force within the range obtainable in the flume. 

Eaeh sand was tested at three different slopes, 0.0010, 0.0015, and 

0.0020, with the exeeption of the coarsest mixture, whieh was tesh'cl 

at slopes of 0.0030, 0.0040, and 0.0045. 

The basic data derived from the experiments, along with emresponding calculated data, are tabulated in Tables 8 to 37, are 

shown gmphieally on Plates 24 to 38. The du for 
and unit weight of water, 

the resuHR. 

which cht>cked Krawithin a reasonable percentage of error. A slight 

ion of his curve was in order that the ted 

be followed more closely, and it was ;;uga lower limi of applicability (for model be placed 

to a mean grain size of cmnd mixture 

For sands of mean gn{in size smaller i han a 

movement (the "model" criterion) wm; 

e., thai movement be said to obtain when, (1) 

motion aR bed-load iR reasonably similar in composition 

material of whieh the bed was formed, and when, 

movement m· exeeedR 1 pound per foot width pPr 

t. 

w 1 

waR deri\·ed empirically for trw rate of 

mixiureR. 

the~ rate of movement in pounds per foot width per 

) , n is the :\:I anning roughnesR coefficient, D;.:; is t lw 

1 he in feet and the slope, Do So is the depth-slope 

which the linear plot of W against DS meet At he DS-axiR, 

m and k 1 are dimensional conRtants obtained from a logarithmic 

of t data. The range of values of each of theRe fact orR iR 

Rummnrizecl in Table 4. 

Rt was made of the YalueR of ~\:fanning's n Pneountered in 

llw and it was found I hat for flow on a smooth sand 

before 1 he formation of riffles, the values differed very lit I le 

from an average of 0.0107. After the formation of riffles, however, 

1 here variation in the values, the maximum being 0.0287. 

I finer the sand mixture, the larger waR the riffle 

the the value of n. 

abo that the finer sands commenced to riffle 

:ll Rmaller \'a.lues of traeti\"P force than the value at whieh the coarser 

material::; riffled. The tractive foree values at which rifflcoR apnre Rmnmarized in Tnble 6, and actual bed profiles are Rhown 

Plnt :39 to 44. 

:Vlean, butt and surface velocities were obsened, and are 

reeonled in Tables to :37. \Yhile thev were not used aR a basis for 

the RtudieR of bed movement, signific1;nt changes in their variation 

h were found at pointR corresponding i o the change from 

to t urbnlent flow eonditionR and the change from ::;rnooth 

riffled RmHl bed. 

st of the turbulence conditions in the experiments, 

nded that turbulent flow in a straight flume was as8ured 

for open channels was 2.~00 or 

on the faei that onlv a limited field wns coved in 1 his papc:r. An extension of the 

R is now under way at thP 
TABLE 8' 

On sERVED DATA :\.::ND RESt:LTs:! 

Flow on Cement Bottom, Tei't No, 0-0,0005, i'lope 0,0005, Decemb
~~~•c=~oo=o~~~•~~~oo=o~~~~~=~oooo-~ 

---~----~~~NNNNNNNNNM~~ 
TABUc 10 t 

0HBEHvEn DATA AND CoMPUTI<:D RERULTH 2 

Flow on Cement Bottom. Test No. 0-0.001.5. Slope 0.0015. Dece
L 0 .. )8fl1 1-0.001
0 j Zt 

;:; § I 

2 0,017 0,020 0.048 

:3 0,0;)5 O,O:JO 0,078 

4 0,066 0,042 0,102 

5 0,101 0.054 C\.1:31 

6 0,1:34 0,062 0,150 

7 0,169 0,071 0.172 

12 t 

OnsEnVED DATA Co),fPGTBD HESULTH 2 

Sand C'{o, L :\lean Crain ciize 0,5861 lllllL Uniformity :\Iodulu> lU796, Test C'{o, 1-0,0

:..:::-

;::;r.£, 

w > "'" 

::: 

0,22 0,0170 0,004 410 

0,020 27,0 0,:35 0,0120 0,007 770 0,029 27,0 OAS 0,0114 0.014 1520 

0,041 27,() 0,65 0,0107 0,027 :!SilO 0,052 27.0 0,77 omo:l 0.040 4:370 

0,05\J 27.0 0,8\J 0,00\JS 0,058 57:30 

0,067 27.0 0,\JS 0,00\17 0,066 7160 

0.0101 

0,0100 

2 

a 

4 

6 

6 

TABLE 14 

OnsEHV:E:D DATA AND C'OMPUTED HEsuurs 2 

No. 2. ::\Iean Grain Size 0.5409 Hll1L Uniformity :\Iodulm; 0.4:388. Test No. 2-0.001

0.034 0.014 0.044 0.018 

0.07.5 O.o:J:i 0.11:3 0.045 0.152 0.060 

0.17\l 0.070 

0.210 0.081 

0.2:32 0.0811 

0.288 0.108 

0.:317 0.118 

o.:365 0.1:34 0.416 0.151 0.466 0.166 

0.018.5 0.002 0.0004 0.006 0.0125 0.013 0.010\J 0.025 0.010!! 0.040 0.011:5 0.050 0.01 1() 0.061 

" i 0.011:3 0.074 .g i 0.0114 0.100 

grain size in millime1 

220 

670 

BiJO 

2680 

42\lO 

.5400 

6580 

8060 

10\JOO 

12700 15600 18500 

21700 
0)\10\l 

grain :-:izE' in millimeters, 

15\ 

Ow-<EHYED 

l-niformi1)-' 
2 

:l 

4 

.s 

I) 

7 

8 

() 

10 

11 

12 

1:3 

14 15 

16 17 

18 

18 

20 

:21 

2:3 

24 

0.007 0.012 0.02\J 

0.010 o.cn:> o.o:n 0.015 0.017 0.041 

0.01 \) 0.020 0.048 

0.024 0.025 0.060 

O.o:l7 0.0:32 0.077 

O.OHH 0.054 0.1:30 

0.125 0.064 0.155 0.150 0.072 0.174 

0.187 

0.241 

0.287 0.379 

0.456 0.14tl 0.35:3 

0.5.50 0.10.5 0.3(;\) 

0.660 0. HJ:3 0.466 

0.7.50 0.210 0.508 

0.820 0.22:3 

O.rl24 0.235 

0.\J\18 0.248 

1.080 0.264 1.238 0.287 

1.2ns o.a02 

L\ BLE 16' 

OnsEHYED DATA AND 2 

:-:.<.md ::-.Jo. ).Jenu Graiu :-lize 0.5400 mm. Uniformity :\lodutus 0.4:188. Test No. 2-0.002

0.077 27.0 

0.085 27.0 

0.0\)5 27.0 

0.116 27.0 

0.24 

0.32 0.37 

0.40 

0.40 

0.48 

0.76 0.81 

0.86 

0.130 27.0 1.2\J 0.145 27.0 1.38 

0.167 27.0 1.42 

0.17\l 27.0 1.48 

0.188 27.0 1.5:3 

0.197 27.0 1.63 

0.206 27.0 1.66 0.217 27.0 1.6\J 

0.2:12 27.0 1.79 

0.242 27.0 1.78 

X 

E 

'"" 0 

X 

§ 

iil 

:8 

0 

z 

X 

"' 

;::: 

'" 

"'3 ...0;-::,..,.. 

::· 

o.OH:> o.om 0.0111 0.004 

0.0118 0.006 

0.0124 0.008 

0.0138 0.010 0.0138 0.015 

0.0121 0.040 

0.0128 0.049 0.0128 0.05\J 

0.0127 0.07:3 

0.0118 0.0\)2 

0.0120 0.10\J 0.0128 0.142 

0.0132 0.168 O.OU2 0.200 0.0142 0.236 0.014:3 0.264 0.014:3 0.287 0.0108 0 .. 121 o.o140 o.a4a 0.0142 0.:368 0.0140 0.415 0.0145 0.401 

ex{·ept grain in millimeter;;;, 

:no 

460 

680 

860 

1040 

1620 

4:300 

5350 

6370 

7880 

10000 11000 1.5400 

18:300 

21700 

25700 28700 

:l1200 

.34800 

:37200 

:)D900 

45100 46800 

TABLE 18 J 

OnsEHVED DATA Co::v:rPtJTED HgsrLT:-; 2 

... .. "' •. 
0.0187 0.002 

0.0157 O.OO:J 0.01:)6 0.004 

0.0126 0.005 0.0114 0.006 

0.0121 0.006 0.011\J 0.007 0.0116 0.008 0.0117 0.009 

0.0120 0.010 

0.0118 0.012 0.0125 0.015 

0.0116 0.015 0.0117 0.017 

0.0120 0.020 

0.0110 0.028 0.01:24 0.025 

o.on!l o.o:n 

0.011:3 O.D:i!l 0.0111 0.046 0.010() 0.0106 0.061 
TABLE 20 r 

OnsEHYED DATA AND HE:-srLTH 2 "' 

,.;and Xo. 4. :\lean Grain t'ize 0.5056 mnL Lnifonni1y :\Iodulu" OA06:J. Te"' No. 4-0.00

TABLE 22 

DATA AND CoMPL:T:rm 

L\BLE 

0BSEHVED DATA AND CO:\!PCTED 

Sand 2'\o. 5. ,}Iean Grain ;:-}.ize 0.4828 nun. Unifonnity :\1odulus 0.4.384. Test 5-0.0015
f 

:s 

4 

fi 

13 

7 

8 

\) 

10 

11 

12 

]:) 

14 15 

Hi 

17 

18 

Hi 

20 

21 22 

2:5 

24 

25 

26 

27 

28 
TABLE 21l 1 

0HSEHYED DATA AND C'OMP'CTJ<::D HBSULTS 2 

Sand No. 6. :\lean Urain Size O.H470 mnL Uniformity :\Iodulus 0.6428. Test No. 6-0.001

7 

8 o.:J:Js 0.17.'i 0.42:) 

!) 0.420 0.207 0 . .500 

10 0.510 0.2:10 0 . .577 11 0.576 0.2.54 O.Gl:J 

12 0.661 0.267 0.645 

l:J 0.742 0.27U 0.675 

14 0.8:18 0.3Q:l 0.73:3 

15 o.n27 0.818 0.76\3 16 17 

18 

1() 

20 21 

TABLE 281 

OnsEnvEn DATA AND CoMPUTgn HERULTs 2 

eland No. 6. :\Ienn Urnin ciize 0.:3470 mm. Fnifonnily :\Iodulus 0.6428. Tes! No. 6-0.002

;;.;; 0.158 0.80 " 0.02:38 0.122 12200 2.:-37 0.8 

0.177 0.84 ·§ 0.0250 0.14\l 14900 :34 

0.200 0.88 > 0.0257 0.177 17700 :Ja :;;; z 

i; 0.210 0.\14 :£ 0.024\J 0.1\JS Hl800 :w "" " 02HJ 1.02 5 0.02:15 0.225 22500 80 " 1 

0 0.227 1.10 0.022.'i 0.24\J 24000 :30 '£ 

0.24:3 1.14 z z 0.0226 0.278 27800 :;o 0.252 1.21 0.021\l 0.:304 :)0400 Hl "" ;,; "" g 

'L-\llLE :lO 1 

0HSEHYED DATA AND Co:.IP'CTED TtEsULTs 2 

Sand Xo, 7. :\lean Grnin 8ize o.:no4 lUHL Uniforruity ::\lodulus 0.5246. 'Te;:;t No. 7-0.00

0,013 0.030 0.013 

0.014 O.o:J2 0.014 

0.016 0.037 0.016 0.017 0.03\J 0.017 

0.01\) 0.044 0.01\J 

0.020 0.046 0.020 

0.022 0.051 0.022 

0.024 0.056 0.028 

0.034 0.07\J O.o:l:3 

0.041 0.0\!5 0.040 0.0.50 0.116 0.048 

0.056 0.120 0.053 

0.061 0.141 0.058 

0.068 0.157 0.064 

0.075 0.17:3 0.070 0.082 0.18\J 0.076 0.217 0.502 0.183 0.2:14 0.540 0,1\14 

0.255 0.58\l 0.200 

0.276 0.637 0.222 

o.:no 0.716 0.244 

TABLE 021 

0HHEHVBD DATA AND CoMPUTED HJGs-cLTs 2 

No_ 8. .\lean Grain 0.205:3 mm. Uniformity .\Iodulus 0 . .55H7. Te;.;t No. 8-0.0010

'" 

·;::: 

"' " ?1 

15.0 0.18 0.0141 0.002 1DO 15.1 0.20 0.01:l2 O.Oo:3 220 

15.8 0.22 0.0128 0.004 :iOO 

16.2 0.26 0.0118 0.004 :360 16.4 o.:n 0.0105 0.006 4\JO 

16.5 o.:3s 0.008\J 0.007 6:10 16.7 0.47 0.0078 0.010 870 16.7 0.53 0.0072 0.012 1040 16.8 0.51 O.OO\l5 0.017 1±40 16.8 0.5:3 0.0102 0.021 1810 

16.0 0.55 0.0112 0.027 2210 16.7 0.64 0.0105 0.034 2880 

Hl.\l 0.67 0.0104 0.03\J as:Jo 

16.() 0.75 0.0100 0.048 4100 16.0 0.81 O.OODH 0,057 4840 

17.0 0.87 0.00\17 0.067 5750 

18.0 0.50 O.o:J04 0.091 8080 18.1 0.57 0.027\J 0.110 0740 18.1 0.62 0.026!) 0.12\J 11400 

18.0 0.67 0.0258 0.148 1:noo 18.0 0.71 0.0260 0.172 1.5200 

O.!l1 

1.12 1.22 

1.58 

TAni,E 341 

0BSli1HVBD DATA CoMPUTED ResuL'l'S 2 

Sand 8. :\lean Grain Size 0.20.;:3 mm. Uniformity :\Iodulns 0.5597. Test 8-0.002

exeept grain size in millimeters, 

0.002 0.006 0.014 

0.021 

0.040 

0.051 

0.062 

0.078 0.105 0.164 

0.268 0.362 

0.548 

0.701 

180 

480 

1200 

1780 

3430 

4390 

5400 

6780 

1)220 

14400 

23700 

;!2100 

48500 

62500 

0.037 

0.046 

0,055 

0.072 0.0!)7 

().l20 

0.143 0.176 0.21:3 

0.2,52 

0.2H1 

0.342 0.3\l:J 0.441 

0.517 

TABLE 36l 

0HSEHYED DATA AND CO:VIPUTED H_T!:fHJLTS 2 

Sand No. ll. 1\Iean Grain Size 4.0769 mm. Uniformity :\Iodulus 0.5661. Test No. n-0.00

0.016 18.5 0.14 o.:J5 0.0416 0.002 100 I 0.72 I 

0.020 18.4 0.17 0.44 0.0406 o.oo:J 21)0 

0.02;) 18.2 0.25 0.4D 0.0:304 0.006 5:1o 

0.030 18.2 o.:l6 0.61 0.0253 0.011 !l70 

0.041 18.8 0.47 0.75 o.oz:l7 0.019 1700 

0.050 19.0 0.59 O.H2 0.0216 0.029 2680 

0.05!1 l!l.1 0.74 1.08 0.01!)3 0.044 :3()60 0.071 HJ.l 0.87 1.24 0.0184 0.062 5640 

0.085 HJ.O 1.01 1.45 0.0180 0.086 7830 

0.100 10.0 1.16 1.5\l 0.0174 0.115 lO.'iOO 0.114 HLO 1.:32 1.7!1 0.0166 0.150 13700 

O.r:ll 19.0 1.48 2.02 0.0163 0.19;) 17600 

0.148 Hl.O 1.64 2.15 0.0160 0.142 22000 0.164 1!1.0 1.74 2.:10 0.0162 0.284 25800 

0.187 18.,5 1.86 2.41 0.0166 o.:l47 :nooo 

OEPTH-FC:ET 

SLOPE - 0.0010 

OtPTH-fEET 

SLOPE- 0.00!5 

Ph-\'l'E 24 

C'o;~,1P,\nrsoN OF :,\IANNINd~-' n AND :VfEA~ V1<.:LOOITY FOH A fhND BoTTOM AND "F'IXED 

BoTTOM OF C'EMENT 

H7 
SAND NO< t- SLOP£ tWOl 

NO.1- SLOPE 0.0015 
SAND NO, 1- SLOPE 0.00? 

SAND NO 2 SLOPE 0.00! 
SAND NO.2- SLOPE 0,001"-

SAND NO, 2- SLOPE 0,002 

OF DI<::PTH 
0 

z 

§ 

~ 

" 

~ > 

z 

< 

w 

, 0 

z 

~ 

SAND .NO.3- SLOPE 0.001 

SAND NO.3- SLOPE 0.0015-

PLATE 2H 

\VI'l'I-1 D~<;P'l'H 
SAND NO.3- SLOPE 0002 

SAND NO.4- SLOP f. {toOl 

0 

z 

0 

0 

Q 

0 

" 

~ 0 

a 

~ 
SAND NO, 4-SLOPE 0.00!5 

"' 0 

0 

X 

''i---C-t-t--~--~-7~--'~-----~~-c~-~~---~-----~------4-------!---·----r-------e---------•~~ 

SAND NO.4- SLOPE 0.002 
$,>.NO N0.5-SLOF'E 0.00\ 

::! 

~I 1/, ,\I 
-~~-----~--!-~-------J~~-----~-i-~----~~~ 

~ 

SANO NO.5- SLOPE O.OOZ 

" 0 

" 0 

oc > < 

X 

< " 0 

" co< 0 

z 

< 

SAND NO 6- SLOP[ Qf\f\l 

VAHTATTON OF Hx:-a> DrHCHAHG~i. l\tEAN \'IDLOCJTY, ~JANNrNn's rt, AND 1\IEAN UnATN 8rzg WI'rn DIJJP'I'r-r 
SAND NO. a- SLOPE 0..0015 

:vf ANNING ';;.; 
!)7 

oc 

0 

0 

r 

. 

0 

~ 

. " w 

E 

> 

~ 

u 

~ z 

< 

~ 

SAND NO 1 -SLOPE 0,00! 

DEPTH-fEEl' 

SANO NO.7- SLOPE 0.0015 

VAlUATION oF HAND DrRCHAHGI<J, .\ND 1\IEAN (iRAIN NJZE WT'!'H 

SAND NO. 8.- SLOP£ tl00J5 

SANP NO, 8 -SLOPE 0002 

PLA1'E :l6 

VAHTATION SANn Drt'>n-rArtGE, :\h;,\N 'l/ruLOCITY 1 ;vfANNIN01

R n. AND \:fR·\N CHAT~ 

lOl 

SAND N0.9 (PEA GRAVEL) SLOPE 0.()04~5 

lO~i 

VAr--------;-------,--------,..-------,-----,w'"'ss:-:-,.-,,-,-·-.·· 

0 21···---- ----- .. RUN 13 -! 

'~ " 0.4h·--· -~--- ---.:;:~ ----,::_- "-~--·" --··--------1---

2 0.2 ---v ~ !·-··· 

" 0 z 0.2 ·-- .. -

0.2 -·---

- RUN 23 1 I - ·w: 5:, -· 

0.41·------·---·-----·· . 

8tation:c;~ FeE>t 

P!u\T@ 40 

LoNCHTUDT~AL PHOFILEB OF HAND Bli:D 

:-lnnds No,-.:< and 
------ R IN 24 --w=--1 ------- -

~ ~ A - ----------- ----A 

()• -v _If_ __ ::______ v ' 

-----IWN--3! 

O.E ---------- ---------- -

0 

A ~ ,.,... t 0 

'\.-' \:::;? """ ,__ " / d Q2 

-------- w 

CL 

0 ---- RUN 32 J 

""-~- <II 

0. 

'" Mn, r 

0.~- /""' ..----. ,...., ~- /\ / " / 

, __ .....- /...-' / \ 

""" 

~~ I 

f--

;a .. ,~, 

nn 'r' r 

"' v-v v.~ 

I 

RUN 24 

- OAi------------- A A • .hA 

0.2 v y_v "VV"V' '- ~ "'V"' V" vv vv 

"' RUN 26 0 

0 

d 

0.4 

"' --- ( ~ ·~~ w -v v '-/V v "V v v v V" CL 

0,2 0 

..J 

Ill 

RUN 31 

0.6 

0. .r -- 0.2 

~- / ~ ......... .._. 

0 

V" ---- - .. _ '" RUN 25 

tL 

.A. A { ~_;.,;,: 1\j 

0. 'v""V v \..-\. v V"'-''V \.-,/ v w-v V v iVV v "V 0 0 

d 

w 

0.8 RUN 32 fl. 

W~'> 0 

..J 

<II 

- 0.4 

~ - .rC RIGINAL ~ROFILE 

- --- - '\.. "'----

-/ .... - 0 I 0 15 20 ~tal inn;-:; 

,.;~tnd ::\o. 
08 -- . !--- r---- +----· f------------f----------- . ------ -------·--- -----------.:j.{~!f"iO.GI-----·--------+----------+----"R\LtL?.J __________ . ----_,..--c,-.r:--:,"-,·-l--P,-IRO--F'tt_L_-E----l 

0.4~~~~~~~~~~~~~~~~-~~~~~---;-~~--~~~2\~~~~~~~~~~-~~~~~~ 0.2-- fVV "' -- -----------l--------1 

------·--+------·--------- ---------------·----- ·-----------------

0 ---------··---+------·-------------------- -----·- ------- ----------·--w-:c,·---

0.8-

-------------+-------------c-------------1---------- -----------

1------------j------------------f-----,R,.. 'J"N-c2~!-8..--+-------------------

0.61------ --·-------·------1-------- ---- --i ---------''-'~'"--""-''-----t---------------r-C~l--=Ruc.-::cGifc-ct>,-:-L- -PRO--F--1--L-E_ -~= 

o.l::::;_,_;;:;---;:::;;c;;~-::;;...;...'t· ;:,;;:::;;;;;:~.;::;;;;;:;;:;::~~~~~;=;;~~~~-~-:-;,.~ .. ""';:;;JiJ:=~~::::$""~!.;;,_ ~~. ~~---~-~~~;;~'\../_~--~ 

0 .. 21------·-------- +----·-··----------·----j-----------·-------r--·-·--------- -·------ -------- ----

---------- ·------------·-··-----f--·-------------j----·----·----·-----·---- ----

ob---------~----------~----------~----------b---------~.~ 0 5 10 15 20 ?.5 

Ptnfion~ --Feet 

PLA'J'J:i_) 

f,ox(aTrDIXAL Pnovu .. gs OF N .. \ND BED 

,..;;and .\:o. 
R IN 24 

0. t;;::A·-j, RJN 

/'-'\. / A r-> A ~v vv v '--.1 :vv 0 

0.8 

0.6 R IN 25 ····;·· 

0.4 

-~ 

.L-________ ()• ::;;;,..: ,_., 

.....• '/. ~ '-../ 'i../\/ "-.,/_ 

Mr l-···-··=RUNl4 1·-

0.21····--

~.~ 

~ ----~-- --~lNAt;;~pR~~---. ~ 

WO• .• ~ 

. --- u' 

A-" -~ v 

..._,_ T "" "' 

0 R N 5 n A ~A 

10 15 20 25 
QB,~-----~-~-~~-~~--~-1------

1=:: 

~~~ 

04-~-------------+---------------~-----------------[--------------------~·----- l-----~--------r--------------------~---

~--------- -------~-~-

5 10 

:4i:ltiou:-:, :fi\•(.•t 

PLATI<: 44 

l,ONOfTUDl?>l.\L PHOFlLEA OF 

~:wd \1 

15 20 

~~~ ~~ 

- ~~~ -~-

--
OF IN 

.J 

0 

!L 

w 

"' 

0 

0 

ID 

" 

Ul 

.J 

0 

!L 

w 

0 

0 

0 

0 

Ul 
1----

I 

! 

I 

~voro 
mmli :] i'l' I' i'i' 

UlntlOjJNr~~~~~~~~~ ~!~~~~~~~~~~~~~~~~~ 

:\fOVE:MgNT 
'";: 

Q 

:n 

:; 

?1 ..-: 

0 

"' ;!-

" ;:::: 

:.:; t;;l,... 

"' 

0 

z 0 

"' 

" " :;;: 

z 

0 "" 

< 

" 

8 

--

l ci 

" " Cj'U :l;:!; "' " z.:, 5 ..J <N 1J,. 0 ... " ... "' ii' Iff r--

0 

" 

"' " 

" g 

:> 

0: 5 

Ori ina! 0.506 

0.406 None lOri lnal 0.506 0.40

i9 0.661 0.-110 

20 0. 727 0.4-87 " 21 0.697 " 

17 0.656 0.44

!8 0.159 0.462

19 o. 717 0.41

22 0.686 0.#9 20 O.b7a 0.50

23 0.693 0,4-14- " 21 0.630 0.411

24 0.481 0.·4-51 General 

25 0.478 O . .<f.+Z 

0.49> 0.361 

0.+68 0.4-1

" 26 0.483 0.4-50 " ··r- I I I I I I I L 21 0.4-80 0.4-6+ " 28 0.+43 0.44-7 " 

29 0.415 O.#T " 30 O.S!Z O."f6Z " 

zs 

o.soz 0.427 

zs 0.48f 0.4+2 

26 0.475 0.456 

Z1 0.39

I Ia 0.4-56 0.395 

Jl o. 505 0.464 31 0.531 0.4f2 " 

29 0.473 0.46

50 0.458 0.501 

Sl OAM 0.475 

l---" I 

.. 1\ I 

I \I \ 

1 .. [l>;; I , :tr{ Kl\-+· 

25 ' 1::::- . I \ 

!···l·" 7 r·0 \ u I 1 ... ,. 

r ,_ · ,\ \-·· .. 

;; bi '1\ I / Ll"·" 

Jli H -- ... -(jj LL •• 1- 

!IIi i T 

& .\:' '/l 

17 "· 

0 -N 1"- 01 0 f"' 

:\Iillimcter:-: 

SLOPE 0.0010 

Size--- '""'mctnN 

SLOPE 0.0015 

PLATl•) ;)0 

PnonHEHHn·g \·.\HL-\'f'ION OF Nrzl< AND DIH'l'HIIHJTlOX ov c; H:\T;'-;S IK :\IoVB.:\IE:XT 

:-l;md ~o. 7 

...1 

0 

0. 

w 

"' 

0 

0 

"' 

(f) 

...1 

0 

0. 

w 

0 

0 

0 

(f) 
j~~ ~~~-~ -~~ 

r-~~ 

1--~~ 

r 

- ~~ 

:\JOVf<lME:ST 
(Jl '£ 

r ;;:;· 

0"' 

1l 

[!ly 

og 

o s· 0 ~ 

"'(p 

0;; 

9: 

7/. 

"' UJ ~ 

b ~ 1J cy 

ll1 

"' 0 ~ 

0 s 0 ::::· .,. ~ 

0 0 

r; 

7, 

·ol\: puu::; 

.1N~IJ".(riA01\: SNIYHL) JW NOLLilUIH.f .. I:H([ GNV ;>tZl';j ,•10 NOIJ.VIliVA tiL\I8H3.HDOHJ 

;:;g 

Per ( Hei ained 

0.074 !)' 0 c: 0 (; 0 ~ 

'"'' i::--1, 0 ).104 f---+----~---+-----+-----+--- +-----j----f---f--Cl (Q ~~~[IJ)iG~, RUN NO. 

OJ47 --c-~~~~~~~~~~~~~~ MEAN GRAIN 

0206 ~~i<O; ~~~~ SIZ_E_d9 

i !uNJFORMITY 

0 295~----+--------+-----·+------f---·---~.--------i-------f------- .(;:; MODULUS- M 

. . "' - 0

·

417 :; .:1 : ;;: ~ R!FFLES 

I ' 

0589 1 

oa33 ~' I 

WB \'~~>- 'f I 1-------+ ·---+--1-----\------J-----

IBSI .f~Kt,.J:JJ : I 

n•2 -o;,;;~-- -- ~ I~ 

3.327 1 ~ lk'";:J>J,'i) I 

.,-1··~ I 

4.699 "'"'~"'~0 ~ : .~ a.eao 

9.423 i ~ 0.104 (;; (;:;~~~0; <:;;~ RUN NO. 

0.147 I~ eo;!<>; !§;!<:; ORAIN 

I~ ~~ ~~:~SIZE - dg 

:::: I I~~~~~~ ~1~ UNWORMITY 

0417 i tl ,[ •I '~ RIFFL£5 

0.589 I "I I 

i 

o.a»H-------~-----+ -----+------+--------1-------+-----+----+-------+-------+-------1---------

'"" ;\ i I 

1651 <::'~s,-;.-.. ~ . ·-:::::: ===== ---- r 1 

3.327 ·-·-- - I ~:.::.~ 

4.699 - -- !_ ~ ~ E ~:: ~ 

ll 
PART II 

OF COMPOSITION OF BED MATERIALS IN 

MISSISSIPPI RIVER SYSTEM 

~COPE D PROC'EDHHE 

years HiYPr 

restricted ofmanw up he of the stream. that 

tiered obsen·ations had been made from time to time, no thorYC survey had e\·er been undPrl a ken lo deterrnirH' 

the various materials throughout the lengl h of the 

all the t lwory has been held 

there is a progres;-;i,·e downs! ream decomposing the bed of the lower :\lissufficient data to prove or disproYP I his 

of bed materials of 1 he :vfissisHivN was conduct under superYision of :vrr. Charles \V. 

oft he :VIissiRsippi Ri\·er Commission. Bet Wf~<'ll 

Louisiana, ;);:U were I a ken 

In addition Ramples were' 

of l he Ohio, Old, Black, and Hcd 

furl her infmmal ion being desired as to tlw 

below New Orleans, a not her seriPR of ta!weg 

betwePn that point and the Gulf of :vrexieo. 

were obtained from the :Vfississippi, including 

the prineipal passes and Re\·eral of l he minor out 

and meehanieal are prPfollowed Rueh eonelusionR as 

sun-ey has been slaried 

inclucled in 

of the Lower 

ion", printed in 

Station, for a eomplete 

River and its tribut its 
I 

1-u 

)> 

II o 

> 

t;J 

c. I I 

"' " 

() 

0 

() 

" 

() 

'\'\ 

)7 TEXAS 

WATERSHED 

OF THE 

MISSISSIPPI RIVER 

D A 
92'00' 91"00' 

il:i THE ALLUVIAL VALLEY 

OF THE 

MISSISSIPPI RIVER 

10 s 0 10 

Scale: 20 

NOTES 

30 40 50 MILES 

River mi s are noted in red. 

Mississipp iver mileages measured from 

Cairo, Ill. 

---- bi~I ges measured from Cairo, 

Ill. 

. 

....... 

....... 

(X) 
119 

physical characteristics, hydraulics, met hods of transporting sediment, etc.; and to "Sedimentation in the :\Iississippi River Between 

DaYenport, Iowa, and Cairo, nlinois", by Alvin L. Lugn, published 

in 1927 by the Augustana College and Theological Seminary, Roek 

Island, Illinois. This latter publication presents the results of the 

investigation of sediment and bed material made by ;'vlr. Lugn in 

1925. Referenee is also made to Papers H and U of the Station, 

in which are presented the results of studies made prior to 1932 to 

determine the quantity and distribution of sediment in suspension in 

the :VIississippi and several tributaries. The results of a similar 

:-:;ediment investigation, made during the Spring high water of 19:32, 

will be printed in a later paper of the Waterways Experiment Station. 

LoCATIOX: ML '76.50 MISSISSIPPI 

STATIOX: Talweg depth.J7feet 

GAGE AT NEW MADRID Reading 7:8 ft. 

How \Vith bucket sampler 

Consider·able coal. 

RIVER 

El.Z6S.76fL 

Yes 

Sizes: 1.17 to 6.68 mm. 

PeHMA~t-;NT ('oNT.UNER FOJt HIVEH Br:n i'4A.\fPLJ:'l 

Purpose 

As stated in Part I, the purpose of the entire :-:;erie:-:; of invefitigations of river bed ma.tPrials was "to discover and entluate laws to 

1 he end that the riYer hydmulician mi~~:ht be able to calculate the 

action of a giYen bed material under gi,·en conditions.'' The morP 

immediate purpose of this portion of the investigation, however, 

was to determine the composition of the material in the bed of the 

Lower .:Vlississippi, and its progressive variation throughout the 

course of the river. The information presented in the tables and. 

curves in thifl part of the report may be considered as one step toward 

the realization of this goal. H should be noted here that authority 

has recently been given for a further invefltigation of the bed materinl of the :VIississippi Hiver and its tributaries, which is planned to 

include such streams ail the :\'1 issouri, Illinoifl, Ohio, Arkansas, White, 

Ued, and other rivers. 
the Samples 

were taken by a field party on specially schedDepartrnent towboats. In general, each 

»V'""v'~ for supplying the floating equipment necesto procure within the part of the river in its jurisTable 38 shows the dates when the various portions of the 

along with the number of samples secured in 

and Plate 54, a map of the Lower :Vlississippi 

to which the samples are referred. Plate 

of the :VIississippi, is included for general 

TABLE m.S 

BED :VIATEIUAL oy :vrrssrssiPPI RrvEn AND TnmuTAIUEs 

Ohio Loui;,;ville 

chafa- 2nd 

New Orleans 

:VIile 

0-400 

below Cairo 

400-610 

below Cairo 

610-977 

below Cairo 

977-Gulf 

0-1 

aboYe Cairo 

0-148 

below head 

0-7 

of 

Samples 

209 

217 

105 

84 

2 

110 

12 

Date 

Sept. 10-17, 19:32 

Oct. 20-25, 19:32 

Aug. 23-30, 19~32 

:Vlay 1-5, r9:H 

19:32 

NoL 9-17, 19:32 

NoY. 9-17, 1932 

9-17, 19:32 

9-17, 19:32 

of experimentation with various types of 

in Plate .56 has been developed, and has 

It is to pick up Bamples of mateand is expected to produce only qualitaThe sarnpler consistB ;,;imply of n 

inches in diameter and 4 feet long, closed at one 

at the other end to a diameter of about 8 inehes. 

attaehed means of a bail to a 1 rope, with 

from the boat. 
121 

[ 'se of the Sampler: 

Practice haR Rhown that the ;.;ampler operates beRt when it iH 

dragged along the bottom in a dowrml ream direction, as indicated 

in Jlw Hkelch of Plate 57. The reaHon for thi;.; i:-; that when it i:-; 

upRtream, the force of the current lendH to belly llw roJW in 

:-;uch a manner as to pull I he mouth of t be sampler off the bottom of 

the stream. When it i;.; dragged downHtream, on the other hand, 

I he sag of the rope keepH the mouth in contact with the bed. When 

a sample iH being taken, the speed of the boat iR reduced until there> 

iR practically no mol ion with respect to the current. The sampler 

i;.; then dropped overboard, and sen,ral hundred feet of line are paid 

DIRECTION OF FLOW 

lf/'MANILA ROP£ 

:\I }<;']'HOD OF n HJNU 'l'Hl!.l Sn.'l' ~AMPLli:H 

out, to allow the deYice to remain on the botiom, after which it i:-; 

pulled along at the approximate speed of the eurrent by the drifting 

boat, until a sufficient q uaniity of material has been o btainecl. The 

pipe is then pulled in, the contents emptied by dropping the open end 

of the pipe on a board, and n Hample of the mat erial is plaeed in a 

properly ean. 
of the bed material retained at the U.S. 

in 1 he soil mechanics laboratory, 

the various sized grains, the absolute 

of the grains, and the presence of such 

nnd iron oxidf'. 

has yielded most of the basic informaof the when studied as a bedwere all prepared for testing by being 

oven, which maintained a constant 

were then allowed to cool to room 

and were with a sample splitter until reproof approximately 200 grams was obtained. The 

material (grain size larger than 0.074 mm) 

ed to a sieve A set of standard Tyler sievcR 

machine were used, the latter equipped with a Stopto insure uniform shaking of all samples for the 

of time (20 The remaining details of this 

arc standardized and uRed universally; hence no further 

is deemed necessary. The samples of cohesive material 

the hydrometer method. For this test a density 

having a range of 0.995 to 1.040, and 

and details of this test as described in 

hod of Mechanical of Soils and other 

were followed. 

Tlw method of determining the specific gravity of 

used because of its reliability and simplicity. The values 

determined for the sand were found to be fairly constant, 

but those for the and silt varied from this to a maxi2.80. The air in voids of the soil was released 

the mixture of soil and water in the pycnometer bottle. 

study of bed samples from the 

of the mineralogical composiin the material effected by transprocedure which is being followed in 

Soils the 11assachusetts InstiProft\.<;;;;-;or of Ceology at the Louisiana f-Hnte "Fni-
12~} 

:sentative samples taken from the river between Cairo and New 

Orleans. This phase of the study includes percentage determination 

of minerals, and of rounding in every grade size, as far as possible, 

with the expectation that a legitimate basis of compariRon for all the 

samples will be discovered. The procedure used in this detailed 

study consists of the separation of the whole sample into grade sizes, 

the further separation of each grade into a light and heavy fraction 

meam; of bromoform, and a percentage determination, by count, 

the mineral:;; in both the light and heavy fractions of each grade 

size. The percentage of well-rounded, rounded, sub-rounded, subangular, and angular quartz grains in each grade size is also det('rmined by count, using photographs of type grains for comparison 

Plate 4, page 7). 

Second, with a legitimate basis of comparison established by i he 

detailed work outlined above, the rnajority of the samples will then 

be studied in a similar fashion, with the exception that only one or 

two representuti\·e gradP sizes will he separated from each sample for 

comparison. 

RESULTS OF ANALYSES 

Presentation of Data 

The data from all these samples are summarized in Tables 39 to 

42. In Tables :39 and 40 iR given the complete size distribution of 

each sample of material. The samples are designated mile munber in the first column (see Plate 54), and each of the successive 

figures in the rows across the page represents the percentage of the 

Rmnple which is finer than the arbitrary size heading the column. It 

will be noted that the U.S. Bureau of Soils classification of materials 

has been bracketed above the sieve sizes, in such a manner that the 

percentage of the samples falling within the clay, silt, sand, or gravel 

range can easily be calculated. It must be understood that the exact points of division between the Bureau of Soils designations are 

not obtainable from this table, owing to the fact that the sizes heading the columns correspond to the sizes of the openings in the sieyes 

which were used in the analyses. The Bureau of Soils classification 

follows: Clay-up to 0.005 mm; silt--0.005 to O.Oi) mm; very fine 

sand-0.0.5 to 0.1 mm; fine sand-0.1 to 0.25 mm; medium sand--

0.25 to 0.50 mm; coarse sand--0 .. 50 to 1.0 mm; fine gravel-1.0 to 

2.0 mm; medium gravel---2.0 to 10.0 mm; large to 

100.0 mm. 

It should be noted that the values in the silt and clay range are 

interpolated; J.he arbitrary sizes heading the columns in these ranges 

were chosen close to the sizes dividing the classes. This interpolation was made necessary by the fact that the hydrometer method of 

analysis does not lead to the sorting of the particles into definite size 

classifieations, as dot'S the sieve analysis. Hather, the tabulation of a 

hydrometer analysis leads to a series of simulianeous values, size, and 

percentage finer than that size, with no regularity between any two 

samples as to the sizes shown. Renee, in order to simplify the tabulation of a large number of samples, it became necessary to 

interpolate each sample into the finer than the chofien 

;;;izes. 
'"' 

'" 0/J 

NOTE 

U.S Bureau of Soils Classifications 

C!ess of Material 

Clay 

SilT 

Very Ft'ne Sand 

Fine Sand 

MedtumS.and 

Coarse Sand 

Fine Or.ave/ 

Medium Or.-ve! 

L .ar!?t!! 6r.,;;vel 

Grain Size ih Mrn, 

0.001 0.005 

o.oos-o.os 

o. os -o.ro 

o.to -o. Js 

0. 25-0 . .50 

0 . .50 -/.0 

1.0-2.0 

2.0-10.0 

/0.0-/00.0 

MISSISS

BED A

SHO

VARIATION IN 

AVERAGED BY 

Mile 0 to Mile 10

615 Samples Collected A

Analysis by Waterwa
12ii 

Tables 41 ancl42 contain the physical data for the same sample:.;;, 

with the ri,·er mileage again the distin!!;uishing de:.;;ignniion. The 

method used in computing the mean grain size, median grain 

and uniformity modulus are discussed on page 5 of this report. 

fn the "locality" column are given the g0ogrnphicnl location:,;; from 

which the sampl0s were taken. 

In addition to the complete prei'ientation of data in Tables :39 to 

Plates 58, 59, and 60 are ineluded, showin!!: the results of the 

studies which ha\·e been made to date of the systematic ntriation in 

the com position of the rnaterials in t hP :VI iRsissippi Hi ver. The 

manner in which t hesf' plate;:; wPre prep a rf'd is expla i nf'd in the following paragraph;.;: 

Plate :)8: 

ThiR illni'il rat ion show;.; i he steady decrease in the percentagt' of 

lar!!:e materials in the samples, and the corresponding increase in the 

percentage of fine sands and silts. In calculating 1 he data fm this 

diagram, the sieve sizes nearest to those dividing th0 U.S. Bureau of 

Soils elasses were selected for Rtudy. For the values plot ted at :vl ile 

12Yz, for instance, all the samples between :VIiles 0 and 25 were incluckd in the computation, and the average percentage pa;.;sing each 

oft he arbitrary sizes was determined. The same averages were cktermined for the samples between :VIiles 25 and 50, and the valw:s 

plotted at ~\!rile 37Yz; this procedure was followed for each 25-milP 

rPach from Cairo to tlw Gulf, following Soutlnvest Pass below i he 

HPad of Passes. 

To interpret the curve, the vertical distance between adjacent 

jagged lines represents the percentage of the material fallin!!: in the 

class noted between the lines. At :Vfile .'500, for example, the percentage of coarse ;.;and is about 76 minus 29, or 47 per cent, that of 

fine sand is 29 minm; 3, or 26 per cent, etc. At Cairo it is evidPn1 

that nearly 50 per cent of the mat erial is coarse sand or gravel, and 

that 1 here is only a small percent age of silt and clay. At New Orleans, on the other hand, 1 he material is almost all fine sand, silt, or 

clay. Between these points there is n steady, though irregular, increase in the pro port ion of fine parhcles, while below New Orlnans 

there is a rapid increase in ilw percentagP of silt and clay. 

Plate 5.9: 

The mean grain diameters have been averaged by 25-milP 

reaches ancl plotted on this diagram. The extremely high peaks in 

the dashed line are due to 1 he occasional oecurrence of large gra n;l 

samples, and their influencp is seen in tbe solid line, presenting the 

an~rage for all the samples. The dash-dot line was drawn to show 

the general variation of the materials other than the extremely large 

graYels, and fits in consistently with the trend noticed in Plate 5R, 

showing a ddinite downstream decrease in the size of the materials. 

Plate 60: 

It was de:-;ired to determine the variation in the size of the sand 

portion of the samples, eliminating from consideration the portion of 

eaeh sample on tside this classification. Aceordingly, the average 

size of the sand portion of of the samples was computed in ilw 
described in Part I, 5, and these means were 

and 10-mile reaches. same downward trend in size is 

from the cmTes, with fewer and less violent 

in tlw 25-mile averages. 

DISCUSSION 

locations ha \·e been noted on each of 

Care should be taken that no 

con elusions are drawn from the coincidence of certain of I heBe 

loea 1 h in the eurves. In Plate for instance, 

k in 1 he mean at about Mile just below 

moui hs of the Rivers. The hasty eonclusmade that this sudden increase in size is caused the 

these tributary rivers. Actually, this 

of three large samples, one from a 

the mouth of "White River, and two 

bar about 3 miles below the mouth of the Arkansas. 

these bars were built up from materials discharged by the 

rin~rs is a that cannot be determined from this 

near mouth of the St. Francis River is caused 

5 miles above the mouth, the possible conclusion 

caused frorn the discharge of large material by the St. 

fallacious. Similarly, eare should be in intercurves, to the data in the tables before draweonclusions as 1 o the cause of the 

should also be remembered that these samples were all taken 

the of the river, and do not the 

which was in were scooped off the 

Further, at low of the 
PLATli.: 60 

VAHJA'riON rN :\,h~AN GnAIN Nrz1;: OF RAND ONLY 

(lUl74-l.Hl8 mm) 

Averap;ed by Heaehef' 

Other l\TnteriaiR in f.;atnples Eliminated from CakulntionA 

f.~J<JOTDND 

127 

river, and the material found may be different from that which would 

be taken at other stages. 

These studies, then, while they represent a long step forward in 

the aceumulaJion of knowledge of the materials composing the beds 

of streams, can be considered only preliminary in nature. The 

of the investigation should eventually be enlarged to inelude 

taking of samples from all points in many representative transverse 

sections of the river, at stages varying from the 0xtremely low to the 

extremely high. Also, instruments must be perfeeted with which 

samples oft he moving materials can be talwn, from which 

hve as well as qualitative results can be obtained. 

TABLE Continued. 

::\lECHANICAL ANALYSES OF ::\IATEHIAL FHOM BED OF ).I!ssi;;;srP

_.\eeumulative Per C'ent Finer 

Large Gravel ).Iedium Gravel 

1)8.8 il6.2 fl4.0 

97.8 ULO 87.5 

1)8.5 97.9 97.0 

100.0 nn.:l il8.6 

U!L7 IJ7. 7 116.1 

60.7 62.6 50.:3 

\ltl.6 98.8 97.6 

HILS H7. 7 06.2 

2:3.4 18.6 17.6 

100.0 il9.9 

83.9 77.0 72.2 

1)5.0 Hl. 7 8\LS ()7.2 87.8 82.6 

98.6 !l6.3 \l3 

tlO.l 84.5 80 

51\.8 48.4 46.3 

ilU.1 98.2 il6.6 

100.0 9!) . .') \J9.1 

O\L6 \J8.7 98.2 

60.2 67,0 53.6 

\)f) .4 !!8.1 !!6.8 

86.6 7ll.5 74.\l 

na.n ilLS 8(). 6 

84.7 66.8 57.8 

100.0 nn.s un.5 

\)().4 D6.!J D4.3 

84.8 80.5 78.3 

HH.2 il5.0 no. 7 

HS.:l 05.il 94.1 

06.2 fJ3 

9.5.:l 04.7 n4. 

\)7.6 \!6 .4 95 

!lil. 4 !!7.6 H5 

I I I 8:1.7 I 

au J I 8.1 I 

80.4 I .!O . .'i 

I 

97 .] I I 46.0 

lVI ·> •)R 1 I 

TABLE Continued. 

J-lECH.ANICAL ANAL,YRES OF :=\lATEHL-\L FHOM BEn OF 

A<·cumulative Per Cent Finer 

Large Ora \·el :1Iedium Gravel 

TABLE 

:\IFJCHANICAL ANALYSEs o:v ::\IATEIUAL FHOM BBD oF .:\In:-sissr

Aecumulative I'er Cent Finer 

.:\ledium Gravel 

TABLE 

::\li<JCHA)JICAL ANALYSES Ol? l\IATEIUAI, FHOM J3I<·m OF ".\hSRlBS

Af'eumulatiYe Per Cent Finer 

:\lediur:n Gravel 

6 

:z 

T. 

'l: 

 

"' 

,..., 

0 ~ .,; A ~ 

"' d3 ~ 

.e ;;', § q 0 G .c 

"" 

"' a "' "" .., ~ 

" " " .::: ;,:: ,.. ~ ~ ,_:; ~ 3 X ..-. 

""' "' [i f-< 

'h 

0 

.1i 

z 

<! 

"" 

,., 

" 

T. 

" 

,:_;, 

~ 

z 

"' 

"' 

""' 

ril 

,..., 

TABLE Continued. 

:\lECHANICAL ).NALYSJ<;S OP FIWM BED OF 2\IrssiSBI

Arcnmulative Per Cent Finer 

:.\Iedim:n Gravel 

TABLE Continued, 

OF :\lATEHL\I.J FHOM BED OF :UJ:-JflTi';::;

_-\('cumulative Per l'"'iner 

Large Gravel ::\I cdi um Gravel 

Tc\ BLE 8!l- -C:ontinued. 

::\JECRANICAL _\NALYSES OF 1\IATERLAL l:'llOM BED OF :\11:':\HISf·H

AcrumultitiYe Per Cent Finer 

:\Iedium Gravel 

Loeality 

Pass A L'Outre 

106fl% 1 72 m!le bclo\Y / I I I 100.0 no.n 1 no.o 1 

I 

I head ___ - 1 - J- 1- r- I 'lo I 

1060;1 

1 1 mile below I I 100.0 H\J .s I • I I , head ........ 1- 

I I 

106\J% j I% miles belo'' 

I I I 100.0 D9.U m1.s I ua.B 

Cubits Gap 

1066)4 U mile_ east of l I I I 

\!8.8 U8. 1 

1066% I I i I 

- -1100. () I I 1- !J\J. 6 U\J.3 

I I I· I I 

1066% I I I 100.0 1 !J!J.S 1 9!U5 98.\J I I· 1066% I I i I I 

8 \HI. 1 ns.n 

1066%' I 

\ I I wo.o I \)!). s \l\1.6 !J\).4 

I I 

1056% I I I I i 100.0 DO.D OO.H 

I 1- I' I' 1066%' I I I 

08.8 D7. 2 

\ mile_ eas_tof \ I 1066% I I I 

1oo.o I 9!) 2 

The ,Jump 

J05UPi I 

I 

L 

I 

I 

! 100.0 i 09.2 ! !J7 

7 I !15.5! 

l05ilM 

Baptiste Collette <:anal 
2 

:3 

4 

72 

'\Iedium Gravel 

}!edium Gravel 

*See nl;-;;o 'fable 42. 

Ohio River. 

Bbu:k River. 

Red River. 
of 

*See also T'abJe ·42. 

TABLE Continued. 

::\lECHANIC.U. AxALYSES OY FHOM BED OF TruHUTAHY AXD 

A(·rmnulative Per Cenr Finer 

Red 

:\Jedinm GraTel 

Old Rive•·· 

TABLE 40 Continued. 

:\1ECHANICAL oF ).Lvi'EIUAL FHO:vt B:rm OF TmH1ITAHY AND 

Per Cent Piner 

Gravel 

Atd1afalaya Continued. 

Little Atd•afalaya River. 

HU D nu.7 !)!),;) 84 10.6 

Vpper (iraml Rh·e•·· 

lAnver Grand River. 
3 

ai 

·~ 2 

" 5 

" 

= 2 

" 

"' " ~ ~~ 

~ 

" .::: i3 

""' 3 

~ 

::; 

8 

""' 

h 

~ " 

::z; 

~ 

"' 

'1:1 

-~ 

.~ 

~ 

""' 

v 

C) 

~ 

" ,., 

~ 

~ 

c:: 

0 

"' 2 

ai 

j 

-~~---'---~~---~·------~-----~~-----·'-··-'---:-c-ci~ 

~ 

" f-; 

----~---~-------~-'-~-'-~----'--~--'---

'" 'j_; 

~ 
TABLE 

ANALYSEK OF ::\IATEIUAL FJ-tO),f BEn OF TnrnLTA.HY AND 

Aeeumuluti-ve Per Cent Finer 

::\Tedium Gmve1 

Atchafalaya Ba,in.-- Continued. 

(Bayou L'Embnrras. Lake FnuHse Point, ;Htd Grand Lake 

*Bee abo Table 4:!. 
TABLE 4! 

See Tab1P >Hl for s.ize dlstribulion. 
lfil 

TABLID 41~~-Continued 

PnYsrc.u. D.vr.\ AND VAHIO'l.:JS ( 'o;-;;.:;;'!'ANTH oF :\lATEHJAL FHO:\t 1-:h:n oF l\IlRHLSHlPPI R1vE:H* 
TABLE 4!~Continued 

2.60 o.n:Jo 0.5:)6 0.25:lll 2.65 0.50:l 0.480 o .. 5!lOU 

2 ()5 o.:l85 o.:362 O.G:H\1 

2 {\.5 ·o.:147 o.:J:J7 O.M28 2 t)f) 0.!156 0.5.50 0.:?!)1)4 ,, M 0.20!1 0.1!18 0. 0452 2 t35 0.55:1 0.5:32 O.tl850 2 65 o.:m; 0.271 0.415.') 

2 65 0.\l.OO 0 . .'140 0.27\l:l 

2 65 0.448 o.:3n.5 0.50:1[) 

2 Of) 0.:3.50 o.:Hr 0Jl444 

2.65 0.681 0 . .5.5~ 0.47();) 

:C.65 0.64.5 0.:360 ()' :lt\18 2.65 0.575 0. 51!1 0.4\108 2.65 0.770 0.500 0.28Hl 

2.W2 fi.\)48 6.112 0.20\14 

:2.60 0.577 0.548 0.6()52 

2.65 0.47() 0.4()11 O.t\6Gl 

2.65 o.:H1 0.2!1:1 0.5:3HD 

2.65 0 . .5.'3:l 0.48!1 o.:J55:J 2.62 1.00.5 0. 707 o.:l6!l7 

:! .6.5 0.282 0.251 0. 611:3 2.65 o.:ar o.:lOs 0.5821 2.6fi 0.:3:34 o.:n2 O.i\.5:l4 

2 ().5 0.25~) 0.250 0.6!!:)4 

;! .6:3 1.617 1.004 (), 17!)1 

:2.0f5 0.486 o.:l57 o.:l785 

2.62 6.71:3 6.78\1 0.1614 2.65 0.411 ().,'388 0.646 2.65 0.621 0.520 0.5:;:;7 

2.05 0.:322 o.:lOS O.tl:380 

2 .6.5 0.502 0.422 0.4!14!) 

:! 65 0.!127 O.ti:ll o.:H7t~ 

2 o:l UJ41 0.6:3!1 O.l:JM 

2 ti5 ().4:32 0.282 o. am1 2 66 2.976 0.885 0.0800 

2.65 0.510 0.45:3 0.476:3 

:!.66 0.:101 0.267 0 .. 5570 

2.65 0.:386 0.:5.56 0.5761 

2.65 0.508 0.451 0.44\1\) 

2.6t) 0.277 0.2:30 0.4414 2.65 0 .. 568 o.:3r,:; 0.1()00 

2.6:1 1.721 0.44() 0.088!1 

2 6:3 1.2!!0 0.54.5 0.1:ll4 

2.65 0.2!10 0.271 ()..')6.50 

2.65 0.858 0.4!16 0. 2:584 :!.()5 0.268 0.242 0.5005 

2.65 O.:Wl 0.200 o.:;san :2.6."5 0.247 0.20.5 0.4!l!l4 

2.65 0.264 0.248 0. 5127 

2.66 2.141 1.052 o.1:mJ 

2.65 0.4\lH 0.471 () .. 5~08 

2 .6.5 0.4\J:l 0.475 0.5:22\J 2.6:l 1. !158 0.757 0.15:36 ().5 21 .41.5 27.0:32 o.:ll52 

65 0.219 (). 18:3 O.M05 2.6o o.:J07 0.2\11 0.6104 2.65 0.647 0.414 0.:!454 2.61) 0.60:) 0.5Q:J 0.5170 2.65 0.256 0.228 o.:J:n:l 2.65 0.422 o.:ms 0.627\J 2 .6,3 0.257 0. 2:3!1 0.605\J 

2.65 IJ.2:J2 0.22.1 0.6:)60 

2.65 o.:l!l6 o.2:m 0' 26fi7 2 60 16.668 16.711.5 0. 21:!0 2 62 8.420 6.20!1 0.1G7fl 2 on 2:3.77:3 27' 100 0.4585 2 f\:l 1.04\1 0.481 ().2122 

2 65 o.:Jn 0.:!24 0.6887 2 65 0.2.56 0.244 0.5867 

2 62 t t t 2 65 0.28!! 0.26D o.n:l:lo 2 o:l 7.858 1.541 0.0:32 2 62 ().5:36 1. 57:3 0.058\J 2 65 0.748 0.4:38 0.246!) 

~eE' T<1ble ::w for sizP dif-'trihn1imL 
TABLE 41-Continued 

TablP :~9 for f:izP di;-;tribntiou. 
TABLE 41 ~~Continued 

\'AnHnr:-. CoNs·r.\N'['s oF :vL\TmnrAL FnoM I-hJu oF :\IJsstssrPPr Hrvtm* 

~ G5 0 ~ 287 0~205 0.411!) 

~ 62 0.472 :>.174 0 ~ 0!157 

2 62 6~ 816 :3.0:12 O~Ofi06 

2 6.5 o.s:w 0.4:l\i 0.2082 

2 65 o.:J:l\J o.:no 0.642:) 

2 65 0.577 o.:Js2 0.:3044 

2 u.s 0.268 0.241 0.4845 

2 ().5 o.so:; o.5:m o.:J5:n 2 60 8. 7\!7 :ui52 ().04\!2 

2 65 0.511 0.475 0 . .5.')54 

65 0.46:3 o.:Jm 0.4654 

65 0.44\l O.:Jiil O.:l784 65 O.:i:>7 o.:n!l o.57:m 

65 0.566 0.41)4 0.4727 

65 0.455 o.:.JD7 0.55:3:5 

65 0.271 0.25:3 0.506:5 

65 0.:!5:3 0.246 0.62\)5 

61 27.601 27.806 0.6752 6() 7. HJ2 0.405 0.0222 

65 0.476 0.:362 0.4:3\l5 

6:l 1.018 0.287 0.1142 

2.6:J 1.181 0.565 0.2068 

2.6:3 1. 763 0.568 0.1:307 

2 65 0.:36\J o.:J56 0.6Hl0 

65 o.:1:n 0.:!82 0.5600 

65 0.40<1 o.:J77 0.5544 

66 0.246 0.17:3 o.:nzs 65 o.42n 0.:357 0.4212 

2.65 0.278 0.252 0.6212 

2.65 0.:!.55 0.241) 0. 70!)\) 

2.65 0.281 0.258 0.052.5 

2.65 o.:n2 0.2\JO 0. rJ477 

2.65 0.280 0.25\J 0.5\J4 

2.6.5 0.241\ 0.241 O.Ot\70 

2.66 0.:380 0.2()6 0.4440 

2.65 0. 5:31 0.461 0' 4681 2.67 5.t;:J.5 0.610 O.o:lM 

2 05 0.484 0.46:) 0.5786 

2 5.5 0.564 0.4:)1 0.42:)0 

2 o:J 1.016 0.486 0.12!)7 

2 65 0. 705 0.482 0.:1541 

2 6b 0.287 0.268 0.6052 

2 6.5 0.2!12 0.276 O.U04:l 

2 65 0.212 0.180 0.54:J:l ()5 0.465 0.4:12 o .. 'i711 r.:J 1 '7:1:3 0.501 0.1245 

0.85:3 0 551 0.:!410 

0.252 0 247 0.6\l:l6 

0.2:18 0.241 0 . .5276 

o.4m O.:J\JO 0.6:)20 

0.408 o.:l!l2 0.6620 

0. 768 o.:;M 0.20:l!J 17.25:3 20.465 o.:lo41 

1.47a 0.478 o.J:J:Jo 

o.:>:Js o.:;:l7 0.641!! 1 '.58!) 0.6:38 0.1676 o .. o:H 0.512 0.60H2 

4.1!7\J 0.68() o.o.s:Js o.:-::41 0. 27:l 0.4:176 

0.408 0.3.56 0.4:321 

0.:376 o.:Jo:; 0.4728 0.42!) 0.:):35 0.4:J4(j 0.624. 0.480 0.41)07 

1.400 0.55!) 0.184!1 0.441 o.:l!JO 0.5645 l.oti6 0.582 0.2401 0.600 o.:J:J7 0.2\!4.5 

t t t 0.406 0.40:1 0. 5G.15 2 :;oo 0.554 0.1021 22. 5~);) 22.o::w 0. 7264 17.8:32 20.484 0.28:32 

See Table :-H) for size distribution. 
15f) 

TABLE 41~-Continued 

1.2:10 0.571 0.402 o.:l7u 0.444 0.;{.57 

0.4\l:J 0.45il 12 .40() 11.081 2.65 0. fl1\J 0.508 2.()2 6.685 0.7fl7 :!.62 :LJ64 0.;3\JO 

2.6:) LH!l 0.44:) 2.65 0.752 0 . .'504 2.62 7 .ti14 0.810 2.65 0.414 o.:l\JO 2.fl0 ·j· t 2.65 0.470 o.:174 2.65 o.:Jss o.:120 2.65 O.tl4\J 0.4!):3 

2.6:) 1.27:l 0.:3()7 

2.(3:) 8.512 0.8\JO 2.66 2.072 0.200 2.64 20.14(\ 2:3. Oll 6.5 0.17\J 0. l?:l 2 62 6.291 0.625 2 62 18.4\J:l 18.010 2 65 0.6:Jti 0 .• 522 2 ()5 o.:l48 0.:1:{5 

2.6.:! 5.127 0.472 2.65 0.186 0.181 2.6:3 1.1()8 0. 748 ., 65 o.:l5!J o.:Ha 2 65 0.250 0.2:)5 2 62 :).6.5() 0. 721 2.0:1 1.452 0.508 2.65 0.2:3\l 0.210 2.6:l 1.478 0.422 2.(35 0. 2ll 0.1!14 2.0[) 0.8\l6 0.581 2.6.5 0.402 o.:Js6 2.65 o.:l68 0.:128 2.65 0..1:18 o.:1!J8 2.()5 0.4:16 0.400 2.65 0.277 0.261 65 0.26:1 0.2;)2 

2. 6.5 0.2\J!J 0.:!{)\) 2.65 0. l!JO 0.17:1 

2.62 l(J.(){)() () .161) 

2.H5 0.565 0.50.5 2 66 0.258 0.251 2 05 0.2:):) o.n.s 2 l):; 0.524 0.50\J 2 65 0.248 0.246 2 65 o.:l7!J o.:>o5 2 65 0.21:; 0. l!J8 2 65 0.414 o.:H5 2 6.5 0.440 o.:J76 2 ()5 o.:l24 o.:m7 2 65 0.268 0.2.'18 2 ()f) 2.062 0.467 2 65 0.42:) o.:l5!! 2 65 0.:.177 o.:J58 2 6:; 1.05!) 0.54:1 2.6.'i o.:·HJii o.:;:;:; 2.65 0.422 0.400 2.!\5 0.220 0. 2:!5 

2.{)5 0.1:J!J ll.085 0.1587 

6L'i 2.65 0.401 o.:Js4 0.56:3:) 

617 2.6.'> 0.4:)2 o.:l!J:l 0.4!J77 

61\l 2.67 5.:100 0.581 o.o:ws 620 2 6() I t t 625 2 o:l 1.5:)7 0.6!J5 0.187\l 

628 2 6fi 0.164 0.152 0.5628 

6:l0 2 65 0.687 0.47:1 o.:1an 681 2.65 o.:ns 0.205 0.6022 

6:HA 2.65 0.416 o.:1no 0.6171 

6:13 2.65 0.2\J!J O.l!J4 0.:1218 

of bed materialli~ted in Table .1H. 

See Table :-w for ;.:;ize dif;tributimL 
TABLE 41~Continued 

oF :\L\TEHIAL Yl-WM BEn OF :\lrssl.SSIPPI Hrvr•::n* 

Tahl<' :l\J di;..;;trihution, 
TABLE 4!-Continued 

South l'ass 

South Pass Bar 

o.1:n 

0.121 

APe Table !1\l for ?-;iZP disi rihulion. 

1G7 
VAruous 

Loeality 

1 O\l0~2 I 

TABLE 41~-~Continued 

}f.A'rlilHTAL FHOM BEn OF :VIJSSikFHPPT Hrvgn* 

Southwest Pass 

Southwest Pass Bar 

2.08 

l.'ass a L'Outre 

Cubits (,\ap 

2 5() 

2 57 2 67 

2 64 2 65 2 64 2 ():2 

2 {)t) 

The .Jump 

I 

Raptis t" Collette Canal 

0.0.'57 ().024 

o.osr, I 0.068 I 

O.l:l5 

0.168 

0.188 

0.022 

0.010 

0.048 

0.141 

0. 

0. 

0. 

0.142 

0.010 

0. ()()l 

Hec> Table :m for Kizf': distribution. 

t 

t 

t 

0 .. 55l\ 

t 

t 
TABLE 42 

FHOM Th;n OF Tnrnr·rArtY 

Lneality 

Ohio ltiver. 

T~<wality 

Ilia!'!< River. 

Red River~ 

i 

I 

j· 

i 

t ·i· 

j· 

0 05\J 

I 0. 1.54 0.061 

0.107 

0.174 

0.120 

0.284 

0.0!)4 

Loeuliiy 

Old Riv(~r., 

2.6.5 0.757 2.65 0 .45(\ 

2. 78 t 2 u:J o.:J74 

2 65 o.:J:J2 

2 65 0.26tl :!.65 0.462 2.6.5 0.5:50 

2.65 0.15V 2.65 0.218 2.70 t 

2.05 0.2:l2 

H('c Table 40 for Rize distribution. 
t 

t 

() 407 0.472 0. fi72~J 

Hee Table '10 for ;;;iz<' di,c.:lrihution. 
104 

107~2 

llO% 

114 

liD 

TABLE 42--Continued 

PHYSICAL DATA AND VAHIOUN 

2 

4 

Chopin Chute Bay Natehez_ Belle River 

Bayou JJong 

Bayou Long Ji'lat Lake_ 

Ben\'id( Bay 

Loealiiy 

L<nver (~rand Jlh'er .. 

:!.65 

2.68 

Atebafalaya River. 

(Lower Grand Hiver Houie) 

:2.71 

:!.67 

2. 7:3 

2.42H 

2.65 

2.60 

2.()8 

0. 

t 

i 

t 

t 

t 

t 

t 

0.151 

t 

i 

t 

t 

t 

t 

t 

t 

(Bayou La Rompe, Lake Chi('Ol, and (h·und Lake lloute) 

6.') 

65 

65 

()5 

65 

fJ5 

65 

65 

65 

65 

65 

5.0 

71 

44tt 

olH 

.62tt 

70 

6() 

70 

o.:>M 

o.:J54 

1.083 

0.41~ 

o.:l!J7 

o.:;sz 

o.:Js9 

0.258 

0.28:1 

0.256 

0.262 

0.217 

t 

t 

t 

t 

i 

t 

t 

t 

t 

t 

t 

t 

i 

t 

t 

t 

t 

(Bayou L'Embnrrn:;, Lake Fam;se Poiut, nnd (;rand l,ake Hout.e) 

Bayou 1. 'EmbarraR, Yz mile bclo\v Bayou Hompe ________ ._ _____ . ___ _ 65 0.4:l5 0.421) 

L'Embarrar;, 1 mile below 05 0.401 615 o.:l02 6!1 t 65 0 25:3 

62i't t t 

62tt t t 

66 O.l:H 0. 15:3 

65 0.158 0.166 

C:ee Table 40 :-:ize distribuiion. 

I 

I 

i 

i 

t 

t 

t 

HJI 

0 6072 0.64!J:l 

0.6604 

t 

t 

t 

I 

t 

t 

O.G27fl 

t 

t 

0. 'l!\47