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UN IVERS ITY OF NEWCASTLE UPON TYNE DEPARTMENT OF CIVIL ENGINEERING

A STUDY IN THE ESTIMATION AND MP..ASUREMENT

OF BED LOAD DISCHARGE

by T.C. MUIR B.Sc.

A thesis submitted for the Degree of Doctor of Philosophy January, 1968. i

CONTAINS PULLOUTS

ACKNQl'ILEDGB ME N1'S

The author wishes to record his thanks to the Natural Environment Research Council which made this study possible by the award of a studentship during the years 1964-1967. Sincerethanks are offered to Professor W. Fisher Cassie for the provision of research facilities in the Department of Civil Engineering, and to

~~.

assistance during the this thesis.

P. Johnson for his supervision and

~seQ.rch

project and the preparation of

Mr. E. Armstrong and his technical staff who

built and maintained the equipment aro thanked for their valuable assistance. In addition, the author wishes to express his appreciation of the co-operation which he has received from within the University, from the Northumbrian River Authority, and from Lord Allendale, riparian owner of the Bywall reach of the River Tyne.

it

CONl'ENl'S Page ACKNOWLEDGEMENl'S

11

CONTENTS

iii

FIGURES

ix

NOTATION

xiii

SYNOPSIS

xix

1.

Geneml Introduction

1.1.

The Sediment Problem

1

1.2.

Investigations on the River Tyne

2

1. 3.

Aims and Objectives of Present Research

3

PART I

2. 2.1.

2.2.

ESTI~TION

OF BED LOAD DISCHARGE

The Sodiment Prccess and Bed Load Movement

The Sediment Proceos

5

2.1.1.

Erosion

5

2.1.2.

Transport

6

2.1.3.

Deposition

9

2.1.4.

Artificial interference

The Bed Load Transport Phase

10

12

2.2.1.

The bed load concept

13

2.2.2.

Critical conditions of movement

14

2.2.3.

Bed load discharge

18

2.2.4.

Applicability of bed load theories to rivers

20

2.2.5.

The regime approach

23

3.

The River Tyne at Bywell

3.1.

The River Tyne Catchment

26

3.2.

The Test Reach

28

iii

3.3.

3.4.

3.5.

Ptlge 31

Survey of the Reach 3.3.1.

lmin cross-sections

31

3.3.2.

Supplementary cross-sections

34

3.3.3.

Longitudinal profiles

35

Hydraulic Characteristics of the Reach

36

3.4.1.

Measurement of water-surface level

36

3.4.2.

Computation of water-surface and energy-surface slopes

39

3.4.3.

Variation of surface slopes with river stage

41

3.4.4.

Stage-discharge relationship

42

3.4.5.

Velocity distribution at tho cableway section

43

3.4.6.

Tractive force distribution at the cnbleway section

44

Bed

~mteriBl

of the Reach

~~thods

of sampling and analysing river bed

44 44

material

3.6. 4. 4.1.

3.5.2.

Location of sampling positions

48

3.5.3.

Bulk sampling

48

3.5.4.

.Il.real sampling

53

3.5.5.

Comparison of bulk and areal sampling methods

57

3.5.6.

Particle shape and roundness

59

3.5.7.

Petrographic analysis

64

3.5.8.

Specific gravity

66 66

Conclusions

Application of Bed Load Theories to the River Tyne at Bywell Determination of Bed Load Rating Curve

69

4.1.1.

Preliminary considerations

69

4.1.2.

Schields method

71

4.1.3.

Straub method

72

4.1.4.

Egia~roff

73

4.1.5.

Valin method

method

74 iv

Pago 4.1.6.

Schok1itsch method

75

4.1.7.

l~yer-Peter and MUller method

76

4.1.8.

Ka1inske method

80

4.1.9.

Einstein method

82

4.1.10.

Modified Einstein method

89

4.2.

Regime Theory

4.3.

Other Bed

4.5.

Lo~d

92

Theories

93

hvernge Annual Bed Load Discharge

95

Conclusions

97

Pi'.RT II

5.

MEl~SUREMENT

OF R'I<.:D L.1AD DISCH!.RGB

Measurement of Bad Load Discharge in Rivers

Methods of Measuring Bed Lond Discharge

5.1.

5.2.

5.1.1.

Bed load samplers

105

5.1.2.

River structuras

UO

5.1.3.

Tracer techniques

112

5.1.4.

Observation of dune movement

U3

5.1.5.

Other possible methods

114

Use of V.U.V. Bed Load Sampler on the River Tyne at Bywe11

5.3.

115

5.2.1.

The V.U.V. bed load sampler

116

5.2.2.

Sampling attempts

119

5.2.3.

Possible sampling methods

119

121

Conclusions 6.

105

Development of Apparatus for Lnboratory Investigation of the Acoustic Detection of Bed Load Movement

6.1.

~ims

of Lnboratory

Experim~nts

v

124

Page 6.2.

6.2.1.

6.3.

125

General descript10n

121

6.2.2.

Measurement of water discherge

6.2.3.

Measurement of channel slope

6.2.4.

Sediment

129

6.2.5.

Sediment feed device

l~O

6.2.3.

Measurement of sediment discharge

J24

Microphone and Recording Equipment

135

6.3.1.

r..iicrophone

136

6.3.2.

Amplifier

140

Frequency filter

141

Output circuit and recorder

141

6.3.4.

6.4.

125

Description of Sediment Channel

Conclusions 7.

143

Laboratory Investigation of the Acoustic Detoction of Bed I.oad Movement

7.1.

Preliminary Experhlents 7.1.1.

7.2.

7.3.

Location of microphone above the sediment bed

146

Area of sensitivity of microphone

1-:18

7.1.3.

Influence of channel sides

149

7.1.4.

Frequency spectrum

150

Calibration Experiments and Analysis

151

7.2.1.

Experimental procedure

151

7.2.2.

Time lag between microphono and weighing davice 153

7.2.3.

Abstraction of

d~ta

from experimental results

Theoretical Relationship batween Microphone Bed Load Dischnrge

vi

Si~na1

and

157 157

7.4.

nlscussion of Observed and Theoretical Relationships

Page 162

7.~.

Conclusions

166

I.

Acoustic Detection of Bed Load Movement in Rivers

3.1.

?rsvious Investigations

172

8.2.

Development of an Acouotic Bed Load Detector for use at 3Y\1ell Cableway Gauging Station

175

8.2.2.

8.~.4.

Design and Development of the bed load detector

175

Bed load detector

178

Amplifier

179

output circuit and recorder

leo

l-c

3.3.

Usa of Acoust ic Bed Load Da...ctor at Bywell Cableway Gaur;in~ S.at ion

180

8.4.

Conclusions

181 9.

Summary of Conclusions

9.1.

Estimation of Bed Lond Discharge

184

9.2.

Measu2'amant of Bad Load Discharge

186

9.3.

Raco~~ndationsfor

APPE}IDn~:

Further Research

Regression Analysis of Laboratory Experimental Data

189

191 200

REFERENCES

vii

FIGURES After page 2.1.a.

Annual solids deposition in the River Tyne estuary

2.1.1.>.

Hexham bridge on the River Tyne

12

2.1.c.

Haltwhistle bridge on the River South Tyne

1?-

2.1.d.

Haltwhistle bridgo

12

2.1.e.

Site of gravel extractions on River South Tyne

12

2.2 .. a.

Schie1ds entrai:lment function

16

Forcos acting on a particle

15

E:I.ver Tyne drainage area

26

Longitudinal profile of River Nortl, 1'yoo

23

Longitudinal profiles of River Tyne and tribuJ.;aries

23

Ri.;rer Tyne at Bywoll - location of main and s~pplementary cross-sections

2 'J"

Cross-sectional profile of scction AB

32

Cross-sectional prof1ls of section CD

32

3.1.a.

3.3.n. 3.3.c.

011

9

the River South Tyne

Cross-sectional profile of section EF (Cablesay soction) 32 32

Cross-sectional profile of section GH

3.3.e.

Cross-·:::ectional profile

3.3.f.

Aren-st5ge

~elr.tionships

ox

32

section JK

33

of main cross-sections

33

V!etted perimeter-stage relat ionships of main cross-sect ions

in pocket

3.3.h.

~iver

3.4.a.

Point gauge for measurement of water surface level

37

Water-surface profiles of River Tyoo at Bywe11

40

Relationship between stage and water-surface slope at Bywell

42

Relationship betwoen Rtage and energy-surface slope at Bywell

42

Tyne at Bywell - longitudinal profiles

StaGs-Discharge relationship for Bywell cableway section 42

3.4.f.

Velocity distributions at 3ywell cablewny section

43

3.4.1$.

Cbsarved and theoretical vertical velocity distributions

4'3

Tractive force distribution at Bywell cabloway section

44

3.5.a.

River Tyue at Bywsll - location of bed material sampling positions

48

3.5.b.

Bed mnterial at sampling position 1

48

3.5.c.

BGd material at sampling position 2

4J

3.S.d.

Particle size distributions of bulk sediment samples

49

viii

After page of bulk composite sample 7

,49

of areal sediment samples

57

3.5.e.

Particle size

distri~ution

3.tJ.f.

Particle size

distri~utions

3.5.g.

Particle size distribution of areal composite sample 7

57

Relationship between

-n 0,-,

3.5.i.

4.1.c. 4.1.e.

and d ' s :.> Relationship between nGGO and d 90 Ohart for visual estioation of particle roundness

61

Division of cross-sectional area of flow

71

Determination of Straub sediment parameter

71

Bed load rating curves by the Schoklitsch method

75

Rntio of critical shear to bed shear ofter

81

n

d~

"V

:~nli11s~t.e

Bed load rating curves by the Kalinske method

81

ki."Oa-stage relationship for representative cross-soction 83 4.1.~.

Wertted perimeter-stn3"O relationship for represcmtntiv,:) cross-sect ion

83

~~rface

35

drag correction factor

Lift force correction factor

85

Hiding correction factor

Gt)

3instein bed l03d

funct~on

95

4.1.1.

J)Gtorm:!.nation of bad sr,ape resistance

86

4.1. r,-••

Compllted ,bod load rating curves for the Rivor Tyno

!.l1

4.2.n.

Determination of zero bod factor

92

Cumulative flow frequency curves for the River Tyno at

95

4.4.n.

EYflell 5.l.n.

Hesper box type

sample.i.~

lOG

Polyakov pan typo sampler

100

SUIB pressure difference type sampler

lOG

Arnhom pressure difference type sampler

lOG

Sphinx pressure difforonce type sampler

108

V.U.V. bed load trap

in pocket

SuspenSion arrangement s fOl' bed lond sampler

125

Laboratory sediment channal General view of upstre:lm end

lnbora~ory

119

sediment channel from 125

6.2.c.

Location of orifice plate and flow straightener

128

6.2.d.

Orifice plate mater arrangoment

128

6.2.e.

Flow straightener

128

8.2.f.

Calibration of orifice plate meter

128

ix

6.2.g.

Gravel used in laboratory investigations

After page 129

6.2.h.

Particle size sediment

distri~ution

130

6.2.i.

Sediment feed device

132

6.2.j.

Calibration of sediment feed device

133

6.2.k.

Sodiment weighing device

134

6.2.1.

Calibration of sediment weighing

6.3.a.

Piezoelectric crystal

137

6.~.b.

Microphone for detection of sediment movement in laborntory channel

l3~

6.3.c.

E19ctrical circuit diagram - laboratory microphone

141

6.3.d.

La:)oratory microphone and recol'ding equipment

140

6.3.e.

Frequ3ncy response of laboratory amplifier

141

6.3.f.

Linear gain of laboratory amplifier

141

a.3.g.

:';;ffGct of time constant on laboratory micropl:'.ono siGnal

142

G .3.h.

Laboratory microphone signal with zero time constant

7.l.a.

Effect of microphone height on flow velocity near bod

147

7.I.b.

D3tsrmination of area of sensitivity of laboratory microphone

140

7.l.c.

Cooparison of decay Signals

149

7.l.d.

Frequency spectrum of inter-particle collision s01.:nd in laboratory channel

151

7.2.a.

Continuous record of microphone Signal and bed load discharge in laboratory channel

1~;2

7.2.b.

Samp13 trace of microphone signal produced by interparticle collision sound of sediment moving in laboratory channel

lj2

7.2.c.

Relationship between lne tinn and cross-correlation of microphone signal and ~od load discharge

154

7.2.d.

Relationship between lag of sediment weighing davics behind microphone and average bed load dischar~e

155

7.2.e.

Relationship between avera~e microphone signnl and average bed load dischar~a over 10 minute peTiod

- 157

7.2.f.

Relationship between avera~e microphone signal a:1.d average bed load dischnr~a over 20 minute peri~d

15?

7.2.g.

Relationship between average microphone signal and average bed load dischar~e over 30 minute period

15~

7.2.h.

Relationship between average microphone Signal and average bed load discharge over 40 minute period

157

8.2.a.

Early design of acoustic 1,)od load detector

177

8.2.b.

Latest deSign of acoustic 0sd load detector

178

:x

of laboratory channel

devi~e

135

,147

After ;>ago G.2.c.

Acoustic bed load detector

l7S

8.2.d.

Electrical circuit diagram - river microphone

179

Frequency response of amplifier of river microphone

1'79

Linear gain of amplifier of river microphone

179

Trace of signal from acoustic bed load detector in River Tyne at Bywell

181

8.3.0.

xi

NOTATION

I lid

a

for a aediment mixture

constant in the microphone equation 7.3.d. cross-sectional area of flow

A

cross-sectional area of flow pertaining to the bed At b

cross-sectional area of flow pertaining to the bed related to particle roughness

A" b

cross-sectional area of flow pertaining to the bed related to bed shape resistance total cross-sectional area of flow cross-sectional area of flow pertaining to the banks constant in the microphone equation 7.3.d.

b

c

s

c

velocity of sound in a sediment particle bed load charge, i.e. ratio of bed load discharge by dry weight to water discharge by weight concentration by weight of suspended sediment in fluid particle diameter

d

d d

a

e

arithmetic mean weight diameter of a sediment mixture geometric D1ef'.n of triaxial dimensions of a particle geometric mean weight diameter of a sediment mixture characteristic particle diameter used by Pantelupulos effective diameter of a sediment mixture used by MeyerPeter and MUller

d d

d d

n

w r

s

nominal diameter of a particle sedimentation diameter

~f

a particle

arithmetic mean of triaxial dimensions of a particle sieve diameter of a particle major axis of a particle intermediate axis of a partiole minor axis of a particle xii

d

5,10 •••

particle size than which 5,10 ••• % by weight of a sediment mixture is finer

d

median di&meter by weight of a sediment mixture

SO

d

n 5,

10

•••

particle size than which 5,10 •• % by number of a sediment mixture is finer median

diaD~ter

by number of n sediment mixture

dH

rate of rise of river stage

D

depth of flow, average depth of flow average depth of flow in area pertaining to the bed

e

the exponential number

E

average vibrational energy emitted by tnter-particle collision per unit time par unit area of bed energy-surface level A.O.D. at section AB anergy-surface level A.O.D. at section EF energy-surface level A.O.D. at section JK a function in the regime slope equation 2.2.e.

f

f

1, •• 7

c

a function of critical fluid force acting on a particle denotes function of M , a, b s

F

bed factor in regime equations

zero bed factor in regime equationa side factor in regime equations acceleration due to gravity

g h

e

stage at cableway section EF above staff gauge zero

(46.25 ft A.O.D.) H

stage A.O.D. stage A.O.D. at section AB

H

e

stage A.O.D. at section EF stage A.O.D. at section JK xiii

ib

fraction by weight of bed material in a given size range

ia

fraction by weight

ia~

bed load discharge in dry weight per unit width of a

of

bed load in a given size range

given size range bed load discharge in dry weight of a given size rang-e coefficient in regime slope equation 2.2.e. k k

r

s

k

t

k

1, •• 6

coefficient of particle friction with a plane bed height of surface roughness projections coefficient of roughness in Strickler formula constnnts in derivation of microphone equation 7.3.d.

K 1, •• 23

constants

1

coefficient in regime slope equation 2.2.e. time lag between laboratory microphone and

sedi~nt

weighing device m

coefficient in regime Dlope equation 2.2.e.

m 1, •• 7

exponents

M

uniformity modulus of a sediment mixture used by Kramer

M

average level of record of signal from microphone

s

phi mean diameter of a sediment mixture McIp

phi median diameter of a sediment mixture

n

coefficient of roughness in MAnning formula

n

w

coefficient of roughness for the banks in Manning formula

o

ratio of longest to shortest diameter of a particle

p

factor indicating the proportion of the bad aree taking fluid shear factor indicating the proportion of the bed area occut>ied by a given size range taking fluid shear

p

wetted perimeter wetted perimeter of bed

total wetted perimeter wetted perimeter ot banks dimensionless variables used by Yalin water discharge in volume per unit width water discharge pertaining to the bed in volume per unit width qB

bed load discharge in dry weight per unit width

Q

water discharge 1n volume

Q b

water discharge pertaining to the bed in volume

Q w Q B r

water discharge pertaining to the banks in volume

r(l)

cross-correlation ooefficient between laboratory microphone

bed load discharge in dry weight relative intensity ot turbulence

signal and bed load discharge for a time lag of I minutes R

hydraulic radius reSidual, difference between observed and predicted value hydraulic radius pertaining to the bed

a'b

hydraulic radius pertaining to the bed

rel~ted

to particle

roughness

a"b

hydraulic radius pertaining to the bed related to bed shape resistance total hydraulic radius hydraulic radius pertaining to the banks weighted reSidual, percentage difference between observed and predicted value ~eynolds

number related to the particle,

s

slope

ss

specific gravity of sediment

S

energy-surface slope

e

u*d/~

S

water-surface slope

w

(SR)

m

quantity obtai3ed by solving Keulegan equation for RS with a known mean velocity time taken for particle to move from microphone section

t

to end of sediment bed u

m

shear velocity equal to

Ar;(;;) J m

shear velocity shear velocity related to particle roughness u "

shear velocity related to bed shape resistance

u

instantaneous velocity of flow at grein level

U

-

time average of velocity of flow at

uc

critical velocity of flow at grain level

*

instantaneous

veloci~y

g~ain

level

of particle

time average of velocity of particle time average of velocity of particle during a step v

velocity of flow velocity of flow in area pertaining to the bed velocity of flow in area pertaining to the banks velocity of flow at height y above bed

w

width of bed width of laboratory channel

w

water-surface width

x

parameter for transjtion from hydraulically smooth to hydraulically rough flow

x

characteristic particle size of sediment mixture function of M , a, b, used in regression enalysis s

y

height above bed

y

pressure correction factor function of Ms' a, b, used in regression analysis

z

function of M , a, b, used in regression analysis s

xvi

acp

phi skewness mensure of a sediment mixture a logarithmic function, log a logarithmic function, 10g

l0 l0

10.6 (10.5 X

~ks)

phi kurtosis measure of a sediment mixture specific weight of fluid specific weight of sediment

CI m

thickness of laminar sublayer for U

*

thickness of laminar sub1ayer for u

I

m

Tlp

efficiency of bed load sampler on a fixed bed

'~

efficiency of bed load sampler on a movable bed

s

a

angle of repose of sediment particles

tD

characteristic of sediment mixture used by Straub

s

porosity of sediment, fraction of a volume not occupied by sediment particles dynamic viscosity of fluid kinematic viscosity of fluid circular circumference-diameter ratio hiding correction fnctor for a mixture of sediment particle sizes mass density of fluid mass density of sediment standard deviation of flow velocity fluctuations a.~

phi standard deviation of a sediment mixture

,.

critical fluid shear stress for initiation of motion of

c

a sediment particle T

o

fluid shear stress on solid boundary

T'

fluid shear stress on bed related to particle roughness

T"

fluid shear stress on bed related to bed shape resistance

T

dimensionless shear parameter

o

o

*

xvii

cp cp

phi particle size notation (-log2 diameter in mm) 5,10 •••

phi size than which 5, 10 ••• % by weight of a sediment

mixture is finer dimensionless intensity of bed load transport funct;ion dimensionless intensity of bed load transport function for a given size range dblensionless intensity of shear function 't'

I

dimensionless intensity of shear function for a representative particle

'f

m

dimensionless intensity of shenr function for n given size range in modified Einstein procedure

't'

*

dimensionless intensity of shear function for a given size range Subscript c denotes critical or threshold conditions of movement of sediment in flUid.

xviii

SynOPSIS The subject of the thesis is the estimation and measurement of bed load discharge, i.e. the rate at which coarse sediment particles are transported la a floVI of water, in particular in the River Tyne near Bywell. The first part of the thesis deals with the estimation of bed load dischorcre using empirical or theoretical formulae.

A

description of the collection of the necessary hydraulic and sediment data for the Bywell reach is followed by an account of the determination of the relationship between bed load disohnrge and river stage by several of the formulae available at present. Estimates of the average annual bed load discharge in tl'.e River Tyne at Dywell are given.

In the second part of the thesis, concerning the direct measurement of bed load

dischar~e,

attempts to use a trap-type

sampler from the !Jywell cablewny are

des~ribed.

An account of

the develop:nent of an experimental laboratory chllnnel for the investigation of an alternative technique, the detection of sediment movement by acoustic methods, is followed by a comparison of the oboerved and theoretical relationships between bed load dischar~e

and the sound emitted by inter-particle collision of

the moving sediment.

An acoustic bed load detector for rivers is

also described. Finally, a summary of concluSions, including reconmendations for further research, is given.

xix

Section 1 1.

General Introduction

1.1.

The Sodi.ant Probl••

The 1deal ceoloc1cal cycle oan be couid.red to coutat ot tb. upheaval at a land maa., ita eros10n to a plain near to aea-level, aDd a

au~equ.nt

upheaval j

as

part of

th1s cycle the aed1ment

procea. of erosion, tral18port and depos1tion ball played, and atill plays, a major role in the ahaping of the surface of the earth. Fro. the times of the ancient oivilisations of Mesopotamia, Chinn and Eeypt to the modern highly-developed, industrialised world of today sediment hall created multifarious economic, social, and acientitic problems.

Consideration of its importance in the fielda

of 80il conservation, reservoir development, water .upply, power development,

ir~igat10n,

stream erosion, flood control, navigation etc.

indicatea that there is a vital need for further reliable information concerning all three phasea of

t~~

proceaa.

Thia requires not only

a deeper understanding of the oomplexities of sediment mecbanics but the development of il18truments and methods which will facilitate

th~

collection and analysis of accurate field data. In the British Isles the magnitudG of the sediment problem is relatively small.

Occurrences of intense rainf all caUSing sovere

er08ion are extremely infrequent, while, even in the larger rivers, movements of substantial quantities of sediment are rare. the greateat problems are created

~

Perhaps

the movement of aands and silts

in estuaries where dredeing is requirGd to maintain a navigable channel (INGLIS and ALLEN, 1957 and GIBSON, 1933), although high concentrations of su.panded sediment in rivers are of soma concern to the water supply industry (INSTITUTION OF WATER ENGINRE3.S, 1961) and CaR cause cOllBidernble damago whea deposited in inundated araas

(UNITED NATIONf:!, 1953).

Publications dealing directly with the

movement of coarse sediments in the freshwater renches of English rivers are few (CLAYTON, 1951). 1

r~vertheless,

there are problems

facing river 8ni1neers today concerning bank erosion, shoaling, channel improvement, gravel extraction etc. which

far have

80

tackled only by mathods based on experience and empiricism.

baeD

It

1s evident that before n more sophisticatad scientific approach can

be attempted fUrther precise systematic sediment data i8 needod. 1.2.

Investigations on the River Tyne

Hydraulic investisations on the River Tyne have been restrlctGd mainly to the improvement of harbour facilities and, more recently, the pollution aspect. of the estuary.

The earlie8t sediment

measurement. were made in the estuary by RICHARDSON (1937) in an attempt to oompare the results of laboratory studies with obeervntions in the river.

SWAIN and NEWMAH (1952) carried out a hyclrograpblc

survey of part of the tidal reach of the river near Stella power station but the oollection of sediment data was not included.

A

study of tho estuarine hydraulics ot the TYfte was conducted by ALLEN (1962). while HALL (1864) invutllated the patterna of movement at aeclill8nt and produced a sodillllnt budget baaed on an examination of dredging records.

for the eBtW".ry

An account of thG

work of Allen and Hall ia included in two reports published by KING'S COLLEGE, UNIVERSITY OF

DUP~JM

(1960, 1961).

HALL (1964) a180 carried out the only previous aediment

investigations on the freshwater part of tho River Tyno.

AsseSslOCIllts

of upland catchment erosion waro mado from the results of a survey of the deposition in a reservoir on the upper reaches of a main tr1butary.

Attempts were mnde to measure bank erosion d1rectly

and information was collected on the variation of bed mnterial

siz~

over the whole length of tho river from source to mouth. Determinations at tho total solids discharge entering the estuary were made from measurements of suspended sediment and dissolved

2

solids at Bywell, about eight miles above the tidal limit.

The

only estimntes of bed load discanrga wore basad on the evidence of local gravel-extracting companioD. 1.3.

Aims and Objectivos of Present Research

One of the important topics of the investigations of HALL (1964)

which, through lack of time, received little nttention was tho transport of sediment as bed lond, i.e. the coarso material which moves on

O~ nen~

the river bed by rolling, sliding and saltating.

It was decided, therefore, that the subject of the prosent

rcso~,rch

would be rul investigation of bed load movement in the River Tyno near Bywoll cableway gauging station.

The mnin objectives

o~

tho

investigation worG to establish the applicability of existing methods of Gstimating bed load dischargo under the conditions preva11ine at Bywell, and, if necessary, to develop a suitable alternativo motnod. As an indirect approach to the problem it was decided to roviuw tho large number of bed load formulae which have been proposod during the past one hundred yearo and to uso

r~s

many as we:J."O

considered applicable to deriva n relationship between bed load discharge nnd rivGr dischnrgo

o~ st~go.

This part would involve

a comprehensive survey of the bydraulic and sediment

charnct3~istics

of the reach of thG River Tyno ncar Bywell. It was intended to check theso cstimatGs of bed lond dischargo by direct measurement nt Bywell.

Preliminary attempts using n

sampler designed for use on the River Danube in Czechoslavakia encountered financial and personnel difficulties.

It was decidod,

thereforo, to develop a different type of instrument which could be suspended in the river from the cableway and would detect and rooord the sound of inter-particle collision on the river bed.

3

Sixteen

months otter tho start of the research programme an exparimentnl sediment chnn17.01

WIlS

obtnined by the University of Newcastle upon

Tyne for the Hydrnulics Laborato:;:oios of the Dopartlilant of Civil Engineering.

It was then decided tI1nt part of the remnining

nvailnble time would

b~

devoted to an investigation of tho

relatfolls11ips between sediment dischnrse nl1d the magnitude and frequency of tho sound omittod by intor-particle collision 1:-1 tho controlled conditions of tho laboratory channel.

This part

0:::

tho

rosearch would il1cludo the devolopment and instnllation ot oquip:ncnt ncc~ssary ~or

the operation of tho flume and for the moasurement

of the relevant quantities.

4

Pi'~('T

I

Estimation of Bed Load Discharge

Section 2 2.

The Sediment Process and Bed Load Movement

2.1.

The Sediment Process

The sediment process forms a major part of the geological and involves three distinct phases;

~ycle

erosion, transport and deposition.

Each phase is extremely complex and closely dependent upon the other phases.

As a natural process it 1s delicately balanced and, as

history proves, interference by man can cause appreciable short-term and long-term changes in the equilibrium of one or more of its phases.

2.1.1.

Erosion

Erosion is the fragmentation of soils and rocks to produce sediment.

Water is the most powerful erosive agent with temperature,

wind, ice, gravity and human activities such as mining, construction etc. also acting as contributary factors. Detachment of the soil particles by raindrop impact and their subsequent removal to drainage channels is known as sheet erosion; this type of erosion, which coincides with the overland flow phase of the hydrological cycle, is witnessed in the more barren moorland areas of both the North Tyne and South Tyne.

In arid and semi

regions where vegetation is sparse and rainfall intensities arc considerably greater sheet erosion is a more serious problem.

As

overland flow concentrates into rills and gullies the increased energy of flow permits further erosion known as gully erosion. Gully erosion develops into bank erosion and becomes an integral part of the transport phase of the sediment process. . Much of the coarser material transported by the River Tyne is the product of bank erosion.

A petographic analysis (see section 3.5.7) of a

sample of the surface of the river bed near Bywell revealed a considerable number of stones from parent rocks in the Lake District and the Southern Uplands of Scotland. origin~ted

These particles must have

in the glacial drift which forms the banks of the middle

and upper reaches of the River Tyne and its tributaries. 5

1':10 o::'ooibUity of the rainfall and tho e::-osivity of the soil

gCI10rlllly dotO::'l;::i.nc tho phase.

qLl~ntity

01 s.odimcnt LlVolvod in tho orosion

TI1Q total quc.nti ty of o:("odeci m:1torinl which complotoD tho

journey f::'''O:!l oo:)1'ce to a catchmont outlet such no confluer~co w:Lt~"l

n main river,

that catcimcmt.

the son,

0 ...•

C\

reservoir, c

is knowr. as tho yield of

The annual yield :'"tc, usunlly exprossed ill to;.lS

pOl' squaro nile, doponda on:1)

P~lynical

conditions such aD catchment area, slope and drainage

pattGTn. 2)

S~.lCl1

:dyd:'ologic condi tions

ao procipi tatton and runoff

chc.racteristics. 3)

Gcolocric, pedologic ruld vogetative conditions of the catchment.

HALL (lS64) determined that the volume of SGdimont which hns lles~rvo:l.:·

accumulated in Cutc leugl:

on tho upper Rede over n pel'iod

of 54 yeura is in the order of 10 million cubic foet. bulk density of 80 lb/ft

mil~

3

AssuminG' a

the annuul sediment yiold of the 15.4 square

2 catchment can be calculated to be 420 ton/milo •

Based on tho

measurements of susponded sediment at Bywell by Hall And the this investigation an estimnte ot 1'10 ton/mile

2

resul~s

can be made for tho

The avo rage surface slopo and

River Tyne catchment to Bywell.

rainfall intensity aro lower ovo:: the largor catchment, thereby accounting fo:;.· the difference in yiolds. 2.1.2. c~~

Sedimect moving in rivers 1)

Origin of sediment.

ba classified in two wnys:-

Thnt part of the sediment load which

is composed of particles sizes found in oignificant quantities in the bed of the

1'1 ver

is known

M

tho bed material load.

T:lO finer

particles of the b(;!d material load may move continually in suspension while largor particlas Slide, :"'011 or saltate clong the river bed;

G

of

the total qunntity in motion depends entirely upon the transporting capacity of the flow.

Superimposed upon the bed material lond 1s

the wash lond conoisting of fine partjocles which nre found in the bed in only small amounts.

It mny be regarded as an additive to the

river, which is picked up on the dl'ainnga basin nnd passes in suspension without participnting in the formative prOCess of the river system.

T.le quantity of the wash load is thus controlled by

its availo.bili ty from the catchment. 2)

Mode of transport of sediment.

From the point of view of

sedimont transport theory and mansU:i. emcmt this is the more oonoJeniont, 4

and more often used, method of distinct modes of movoment. suspension,

l~opt

cl~sificntion.

There nrc two

Susponded load is material mov1nG 1n

up by the upward components of the turbulent currents

or by colloidal forces. moving on or nenr the bed.

Bed lond 1s materinl, usually coarse, A subcommittee on sedimant terminology

of the AME:UCAll GEOPHYSICAL UNION (1947) defined two other terms; contact load, mntorial which rolls or slides along the bed 1n substantially continuoua contact with tho bod, and saltation lond which bounces along the bed or 1s moved, directly or indirectly, by the impact

of

bouncing particles.

Bed load can thus be

considered to comprise contact lond plus snltation load. Suspended sediment conSists of both suspended bed material load and wash load nnd, due to the varinbili ty of wash load, 1s not n unique function of river dischargo.

At the beginning of a

storm more fine mnterial is availnble from sheat nnd gully

e~osion

and rainfall intansities nre higher than towards the end. Consequo":tly, aa has been observoo

011

soveral rivers (BENEDIOl', 1957

nnd KENNEDY, 19(4), including tho :l.iver Tyne, peak suspended seditlGnt discharge may prGcedo peak water discharge.

Tioe of year alao

affects suspended load since durillg surneer months there are l~~ 7

and drier intervals between storms and the supply of wash load is thus greatar.

The theory of the distribution and transport

o:f

suspended sedimont is based on tha nssumption that the settling velocity of n particle is counteracted by turbulent exchango, tho continual exctlange of fluid ootweon horizontal layors.

Many

workers have oxporimented in this fiold, notably HURST (1929), GRIFFIT.H (1933), VANONI (1941, 1944), DOBBINS (1943) and NAGY (1961),

snabling c1090 predictions of river conditions to be made.

FUl'thor

references and more detailed informntion are given by BROWN (1950), CHIEN (1954a) n..'ld the AMERICAN SOCIETY OF CIVIL ENGINEERS (1963).

Measurement of the suspended lond of

riv~rs

can be relatively eosi1y

effected by manns of depth-integrating, point-integrating or instantanoous typo samplers.

Theso snmplers and methods and analysis

of sampling nre described in reports I, 3, 6, 7, 8 and 13 of the UNITED STATES INTER-AGENCY COMMI'l'I'EE ON WATER RESOURCES, SUBCOMMITTEE ON SEDIMENTATION.

USing an instantaneous type samplor suspended at

0.6 depth at mid-channel at Bywoll oab1away gauging station on tha

River Tyne HALL (1964) produced a curve relating average suspended sediment discharge to water discharse.

By oombining this ourve

with a 5 year duration curve of moan daily flows he estimated the average annual suspended load at Bywoll to be in the order of 130, 000 tOnG.

The various theories, concepts and mothods of measuring bod load transport are treated elsewhere in this thesis.

On

the rtiver

Tyne a figure ot 20,000 ton/yenr has been given by two gra.vel firms as the average natural replacemunt of exca.vated material and tilis figure was aocoptod by HALL

(l9~)

to apprOXimate to the average

annual bed lond discharge at Bywell.

s

Duri:lg every phase of geomo:."phologlcal BcttV! ty c.

rivo~

,/i1l

try to obtain some form of equilibrium between sediment supply and sodiment 1)

tr~~spoTt.

th~

~ro

important variables involved nre:-

indopeudent variables of wnter dischargo,

discharge and 2)

The

effectiv~ sedi~nt

sedims~t

size.

the dopendant variablea of r1vor slope, maan depth to width rQt10 and the meander characteristic (KUIPER, 1965).

The whole process of obta1nillg eq\.1i1ibrium is obscured by several

such as variability of river discharge and sediment

facto~

supply nne tho chango of bod configuration and channel alignment with dii:f()l'ent sodiment tr3llSport intensities.

Much research 1

::>bservatioll Cond measurement has boon conducted in an effort to obtain the law13 of normal river oohaviour (GILBER.T, 1914, Mt..C~rnrJ 1948, LEOPC':':.D and MADDOCK, 1953, LEOPOID, WOUfAN and MILlEn., 1C(4). This dolicately balrulcad equilibrium of the transport phase of tho

sediment process is generally reforred to as the "regime" of the :fluid syston;

BLENCH

analagous to climnte.

(1957) considers the word "regilOO" to 00 Over m03t of tho length of tho Rivor Tyne

the regioo of the river is stable, except in the short reaches which have been affected by artificial interference. 2.1.3.

DepoSition

Depoait1on, the third phnso of the sediment process occura mainly when n river enters ito estuary.

In general, and especially

in the River Tyno, the river carries into the estuary not only n sediment load, but sewage, floating debriS and sp1l1agl';l froo shiploading wharveS. transported in the gale.

~ivor

Fie.

int~

Considerable quantities of sand and silt nro often the estuary from the sea;

this occurs

froquG~tly

Tynl';l, especinlly during a flood tide or north-easterly 2.1. a. which is basad on reports published

by :cnrG r 8

COLLEGE, UHrvE?SITY OF DURHAM (1960, 1961) shows the approximate 9

Sol ids in sewage eff luents.

27, 000 ton

Material carried

Freshwater sediment. Suspetlded load : 180,000 ton Bed load

25,000 ton

-

~

.

in from sea.

.~-

340,000 ton

Spillage from Mis c, d aneo l)

staiths etc.

f'CJ . tl oat inCj ,J ebris, 15,000 ton

l

n1rnos pher l(

pollution,

Fig. 2.1. 0 . ANNUAL SOLID S DEPOSITI O N

( Based

Bed load discharge

5,0 0( Ion

4· 2% of total disc harge

IN THE

RIVER TYNE

ESTUARY.

on Bulletin No 24 of th e Dept. of Ci vil Engineering, King's College, Unlv. of Durham .)

annual

of solids entering the River Tyne estuary.

to~~ag~

Move1llOnt

of sedimont within an estuary is extremGly complex (IPPEN, 1966), being affected by currents produced by the mixing of fresh water with salt water of a different density. can cause

&1t~er

These "density currents"

erosion or deposition in the estuary, depending

upon the state of the tide, the fresh water discharge and the shape of the estuary. All the solids deposited 1n the aiver Tyne estuary (it cnn bo seen from fig. 2.l.a. that bed load sediment constitutes only 4% of the total) must be removed if the river is to remain navigable by the shipping which uses the port. when the Tyne

Imp~ovement

Until just over 100 years ago,

Commission was formed, the River Tyne

estuary was a tortuous, shallow waterway with shoals, sandbanks and even islands presenting a serious hazard to ships attempting to use the harbour.

MACGREGGOR (1832), TAYLOR (18tH), GUTHRIE (l880),

SARGENT (1912) and HINDMARCH (1947) have described the prevailing conditions and the various plans for improvement which were proposed. Since then the TYNE IMPROVEMENT COMMISSION (1930, 1963) has removed many millions of tons of material in the clearinc and deepening of a navigable river channel.

Maintenanoe of this channel and the berths

along the quays requires a fleet of dredgers and hopper barges which every year raise about

It

million tons of material and deposit it far

out to sea. 2.1.4.

Artificial Interference

Artificial interference of the regime of a river can have appreCiable short-term and long-term effects.

In many areas of

the United States, for example, increased ereeion and hence increased sediment transport have resulted from the removal of large areas of vegetative cover (HUXLEY, 1945).

The oonstruction of reserVOirs, 10

bridges, weirs, river improvament schemas, flood control measures and gravel extractions 0.11 involvo sediment equilibrium.

0.

disturbance of the delicnto

Until recentl; the science of river

engineering was based largely on individuQl exporience and could predict only qunlitatively

th~

offact of enginoering works.

However, the recent publications of BLENCH (1966a),

HENDE~tSON

(1966)

and THOHlT (19Se) have enabled more quantitative approaches to bo made. A simple example of artificial intGrference is tho construction of a weir, possibly for flow-go.ug1ng purposes.

The backwater offGct

created upstream of the weir decreases the transporting capacity of the flow and the sediment load is doposited behind tho woir. Downstream, tho river is thus deprivod of its normal

sedim~nt

and erodes both bod and banks to make up the deficiency.

On

load tho

River Derwent at Rowlands Gill flood flows cause a largo gravel shoal to form just upstream of a compound crump woir.

The accumulation io

removed at regular intervals by tho Northumbrian River Authority.

A

model of tho reach including tho weil· was bu1l t in tho Departmont of Civil Engineoring at the Ullivcarsi'cy of Newcastle upon Tyne and tast results showod that orrors in discharge estimation of up to 10% are possiblca if the presence of the shoal is disregarded. Anotl1ozointerterence from whioh tho a1ver T1ne has sutfered considerably is the extraction of gravel from the river bad.

Upotream

of the workings the bed is lowered by increasod velocitiop while further areaion occurs downstr(3am duo to tho doficiency of sodimont load in the river. readily

obtain~,

company operators.

Riv(3r gravol is olean, well

sort~d,

durablo and

offering an attractiv(3 proposit1on to gravel Until reoent1y, however, practically

uncont~clled

oxtractions caused considerable damngo, especially to the foundations of bridges situated upstream of the workings. 11

Many thousands of

pounds hcvc boan spont by locnl authorities, the Northumbrian River Authority

fuid ~~avGl

companies on repairs to bridges at Ovinghanl,

Hexham (fig. 2.l.b.), Haydon (figs. 2.1.c, and 2.l.d.)

B~idgo,

Lardon Mill and Hnltwhiotle

Extraction of gravel about one nile

downstream of Bywell gauging station has altered the stage-discharge characteristics of the station and nacessitnted the sinking of a new float well,

Gravel extractions are also detrimental to fishery

interests by dostroying the spavming grounds of migratory froshwator fish, and may be aesthetically undesirable (fig. 2.l.e.) result

Rosn

As n

(1966), the Northumberland County Planning Officer, has

recommended that no further licencos for river gravol should be gl4Bnted;

extractio~

it was suggested that sufficiont gravel could be

obtained from glacial depOSits. Bank orosion in the River Tyne valley can be sevore, resulting in the loss of valuable agricultural land.

However, it has been

realised by river engineers that if natural bank erosion is provented at one place erosion will occur elsewhere due to the river to maintnin its sediment equilibrium. only where flood protection schemes or

e~fort

of tho

Consequently, it 1s

draina~

outlet works are

threatened that use is mode of remedial measures such as pitclling, stone-filled wire mesh crates, groynes and sheet-piling. 2.2.

The Bad Load Transport Phase

During the past hundred years a vast amount of literature concerning the transport phase of the sediment process has boon published in the English, French and German languages, and more recently the work of scientista and engineers in Russin and eantorn European countries has becomo available.

In the particular cana

of bed lond transport a wealth of figures and statistics have boen recorded, nuoerous contradictory statements modo, and n plethora 12

Fig.2.1.b. Hexham Bridge on the River Tyne. Extensive sheet. piling was found necea ry to proteot the bridge piers nd adj cent banka against erosion oau ed by gravel extr otion downstream.

Fig. 2.1.c. Haltwhistle Bridge on the River

~outh

Tyne.

extraction one mile downstream caused

ever

Gravel undermining

of the concrete apron between the bridge piers.

Fig.2.i.d. Haltwhistle Bridge on the River outh Tyne. Gravel extr ction one mile downstre m has low red the river bed nearly fiY8 feet.

Fig.2.1 ••

~ite

of gravel extraction on the River

outh Tyne

one mile downstream of Haltwhistle Bridge.

of theories developed.

It io not intended to giva hero n

detailed and comprehensive survey of this liternture since this in itself would require several volumos.

A general discussion

only of bad load movement is given in this sub-section.

lid of

descriptions of several bed lond theories and their application to tho reach of the River Tyne nt Bywell are given in section 4, following- all account of the colloction of thl3 nacessary sGdiment and hydraulic data in

sectio~

3.

Much of the avnil!\blG 11 t.:lrnturo

on bed load movement and associated top1cs hns boen DUllmmrisoa i:1 text

b')o!~:

LINSLEY, KOHLE~

nnd PAULHUS (1949), BROWN (1950),

LEr..:u..vm~

(1955), BLENCH (1957, 196Ga), EINSTEIN (1964),

HENDEaOOH

(laSS) and THORN (lOG.3).

Papers by ClIIEN (1954£1.), tho

AME!UC/J'r SOC!3'lY OF CIVIL ENGIl1F'...s:'J3 (1962, 1965, 1966) and B~1DI

(1965) include also substnntinl bibliography sGctiona.

For more detailed :I.nformation on. I'\ll.Y worle: mentiolled the orig1nnl referencos Silould be con;Julted. ~1e

Bed Load Concept

Due to the complexity of the movement of aedimant in rivars a universal thOOl'Y of bed load transport has yet to be formulated. Tho large number of

varinbleo involved, tho problems of defining

adequatoly soma variables, and tho complicated relationsh1ps between the variables have presented great difficulties.

Howevor,

the rational approach of eliminating sorno of thG variables and studying in detail Selected pnnuooters has producod valuable information.

The effects of channel alignment,

non-coh~siv\j

banks

and variations in size and shape of the particles, for exnmple, have baen olinunated by conduoting experiments with singlG-s1zed sediment in rectangular laboratory channels, where thG vnriables of sediment discharge, water dischargo, slope, depth and velocity may ba controlled.

ThG wide-ranging experimants and painstaking

observntions of GILBERT (1914) are classic in this rospGCt. 13

B~"

t:l<3se means the luws

and trnnsport

COAl

be obGcrved

govo~.·nillg

the mechllIlism of ontrnirunant

closel~r.

As the velocity of flow of

water ove::- a bod of sediment is illorcr-.ead individual particles to move whon n c·;)rtain velocity is reached.

be~ln

This critical volocity

is sot;lCwhat indofinite since tho initial movemont of the pnrtiolo3 dopends on tha loonl turbulent fluctuations at velocity IlIld tho arrangement at -th<3 particles 011 thc Durface of the bed. velocity i3 sufficiently great it

CIDl

llfuell the

bo soen that tho bod lond,

defined as that part of the sediment load which moves on or ncar the bed by rolling, sliding and saltnting, moves within n thin lnyor, called tho bed layer, 0111y

0.

fow grnin diameters thicl,..

(For dunad beds or for a wide rru1go of particle sizes such as nro found in gravel-paved rivers tho bod layer concept becomes vftgUe). KALINSKE (1342) has shown that the role of saltation ill the fluid transport of sedil1lOnt is of loss importance than in the aoo11(1;.1 transpol~

at sand (BAGNOLD, 1936).

It cnn be move from

t~e

~eneralised

that the froquency with whi ell partiolos

bed nnd the velocity at which they travel do ponds

mainly upon the velocity of flow 2.2.2.

ne~

the bed.

Critical Conditions of Movement

When the hydrodynamic force acting on a sediment partiole has reached a value such that, when it is increased, motion of the particle results, than critical reached.

01'

threshold conditions h"lfo ooan

Suoh quantities as de),lth, velocity and bed shea ..• stl'<3SS

then have their critical or competent values.

Tho problom of

determining tno critical conditions for the initiation of motion at sediment particles has received much attention, especially in tho ~esign

ot stable channels and oanals through both cohesive and non-

cohesive materials. threshold

co~ditions:-

Three main oritoria have been used to defino velocity, lift and shear stress. 14

C:-citical velocity, either

~4:~le

velocity near the bed or the

mean velocity of flow, was tho first 'i;o LELIAVSr~

bo

COllslderod.

(19f.5) mentions that in 17(;3 Brabms formulated the

woll-known one sixth power law, i.o. the critical velocity 10 proportional to the

on~

sixth root of tho woight of the particlu.

Th1s was rastated by AIRY (1005), and several tables giving critical velocities for sp€cific materials were produced by DU BUi'.. T (1815), SCHOKLITSH (1914) et ale

More recently,

FO~TI~~

and SCOBEY (1926), MAUVIS and Ll'... USHEY (1948), IPPEN and VERM/\. (1953), BCX1ARDI (1051) and NEILL and V/.IT DE:1 GIESSEN (1966) are among t110se who

hav~

attempted to derive practicable relationships.

The

principal disadvantage of the velocity criterion is that the moan velocity of flow does not

compl~toly

specify the scouring action of

the water at the bad and the depth itself must bo givon.

nlO

difficulty of defining the bottom volocity of flow has also loss consistent

l~d

to

results than those obtained using bod shear stress

as a criterion. The use of the hydrodynamic lift as a criterion for the initiation of motion has received comparatively little attention. The theoretioal considerations of JEFFREYS (1920) and EINSTEIN and EL SAMNI (1929), nevertheless, show that it can be of considerablo importance.

However, since in most cases 11ft depends upon the

same variables as bed shear stress or drag, it is thus implioitly included in experiments involving obBervation of shear stross. The oriterion which has received tho most attention is tho bod shear stress,

T

o

,

or the or:1tioal bed shear stress,

.,. • c

The most important work in this connection was carried out by SCHIEIDS (1936) who, by a rather devious method involving consideration ot the forces acting on a sodiment particle and tho 15

introduction of t!le Pradntl-VOD Knrman velocity distribution law, concluded that:1 C

=f

- yf)d

Iu.

,

1 ~

d

O \I

Ji









• •



2.2. a.

in which Ys' Y f are tho specific weights of tho sodiment and fluid respectivaly, d is the particle diameter, fl moans a fUllction of, \I

is the kinetlatic viscosity of tho fluid and u.

critical shoal' velocity;

P

~

c

1cl Pf is tho

f is the flu1d mass donsity.

Tho loft-

hand side is termed the dimensionless critical shear stross, and the rigilt-hancl side the dimensionless critical Reynolds number. of tho particle, ae. c •

Equation 2.2.0. can thus be writton:-

• • • •













2.2.b •

BLENC:] (196Gb), however, pointa out that for the simplo cnsa

considered (1a:f1nitely broad channel, uniform bed material) dimensional Malysis would requiro t:l0 inclusion on the rigllt-hand side of the above equation of two additional dimens1on1ess variables, Did and (Ss - 1), where 0 is the depth of flow and Ss is tho specific

gravity of the sediment. Data from laboratory experiments by the UNITED STATES Vlh.'I'fJ'.!....W/.YS EXPERIMENTAL STATION (1935), OHlJ1G (1937) t TISON (1948a, 1940b, 1933), PANTELUPULOS (1955, 1957, 1961), EGIkZAROFF (1957, 1959, 1965) and several Hungarian researchers

(BoruL~I,

Re. from 0.04 to 10,000 to be covered.

1965) have enabled a range of Fii. 2.2.a. iives a plot of (It can ba soen that bed

equation 2.2.b. as determined by this data.

configuration is also a function of 1. and Re.). Re. > 1000 the value of T. c is constant at 0.055; c can then be reduced to:1 0 ~

0.055(" - ~)d





16









For values of equation 2.2.b.



• •

• 2.2.c •

IO· r----------,----------,---------~----------,_--------~

5 suspen

fon

/

/

hed undu/oti on shor ten ond d epen

/

/

sholl ow

0·1 cr s

0-05

at

b

d

I e nq

b a

undulation

r:s=-_--------:--~~ ~ 0·055

/

turbulent flolN ot b d

thres holC' of m (,)V PJrnent

0 ·0 1L-----------~------------~----------~----------~----------~

10

0·,

Re-*

100

/000

10000

=-¥

Fig . 2.2.a . Schiel ds e ntrolnment

centre

i...- --l- - --

functio n .

of

gravity

angle of repose

----

point of supp ort number of port; ele

=4P/Tid

per unit Or

2

for equJ/ ibrlum:-

Tc =3{p( Y5 - Y,) d

Fig.2.2. b

Forces

acting on C1 part i cle

at R *>3' 5, (WH,"'c. 1940)

tane

a

This d'3110tes a hydraulically rough bed at which, in tho caso water

temperatu~e8

o:~

and specific gravities of sediment most

frequently occurring in nature, partj cle8 larger thr.m approximatoly 0.6 in.may be sot in motion. WHI1-r.s (1940) I who conducted exporiDlGnts with water flowing in

specially designed nozzles, cOl1Sidered the forces ncting on a particle on a horizontal bod.

Fo~

equilibrium of tho grain in

turbulent flow, i.e. Re.> 3.5, tho cl"iticnl fluid force acting on the grain (fig. 2.2.b.) is given by:-

where

e io

~~e

If p

angle of reposo of the sediment particles.

is the proportion of the bed taking fluid shear then tho number of grains PGr unit area of bed is 4p/n d

2

and tho fluid forco taltan

by each grain at critical conditions is:-

gi Vill€;

'T 0

= 2/3

P (y s -

Y f) d tan a

Diroct measurements of p p.nd tan 9 for single-sizod sands gavo values of 0.35 and 1, respectively.

White found that experimental

results indicated it was necessary to introduce a factor of about

i

since turbulenco in the ragion of the particle caused fluid forces The equation for tho actual

to fluctuate about the measured force.

critical shear stress required to initiate motion is thus glven by:'T

c

:.::

0.12 (y

s

-

'Yf)d











Experimental data from largo scale turbulent flow such as

2.2.d • occu~s

in rivers and laboratory channols show that tho actual shear stress on the bod can be twice the measured mean value.

Equation 2.2.d.

therefore agrees well with too Sohiolde diagram for Ro. > 3.5.

11

CAMP (1946) has a:lown how, by l.lBi~l~

Dlopa 01 tho onol'gy surf r.ce , f:rictiml cOGf:!iciont, as a

rest~:l;el"Jl;;j~'lt

~:;;

8.l1d

'r

0

10 tha

of tho Brahnw ono-s1:cth power law.

o! a bod of

:l0:c'~13fJCr101:,..~

e

is pOD.Jiblo to Intarpret oquation 2.2 .d.

is no truu definition of the motio~

1:

illtl-od'.lcing tho Darcy-WaisbA.cll

Duo to tho statistical natul'1'3 ot

of

'( .,DS , where S

o

cl·itic~J.

sodi~nt

'i.;~hl

outl'ab,m.:ll.lt procooO tho):'o

condition for the initintioll

particlcs.

Mrmy subjocti vo mo"thods

moveoont nuar tIln have baan

m'Ji.lIlCa (1934), for ~,amplo, defined three inten~i tic::!

?:;,-opoSGd;

of movement: -. includi~

woak, medium and g'onGl'al.

Schields, determined

c~itical

shear

str~os

as tho valuo

of shea:::- stroso at zero bed load dischara-o ootain..;;d by

Elxtrapo~,('.t~.on

of thJ G,;,-apr.. of sediment discha:rg<.1 against shear stross. confUSion

\L:'::o'cl~tably

explains to a cGrtain extent "i;:10 variation

in rosults of diffo:'Gnt workers in -;;h1s field.

predict the behavi0ur 01.. uniZor;;l aediml3nt particlas forrr.:i.llg r pIa.,) bed but theh' validity when applied to

GxtroiJ~na:~y

non-E:pharical

particles ~ m1;ttllres of particle sizes and duned beds ha;J not ooon provod.

2.2.3.

Bed

Loa~

Discharge

The first attdmpt at the formulation of a rational thoory of bed load transport was made by D'U BOYS (1879) when hv postulu'i;ed that the bed load discharge shoul.i be a. funotion of tU;3 d1fleronco betweon the b.3J. sllenr streus

e.n~ th~

crt tical shoal' s'.;ross of "tho

sediment pa:':"::ioles in the bed, 1.0. a fUnction of tho oxce.Js trac'l;i vo ferce.

!Io assuim that th3 propulsi vo movement of

me:~~l'ial

va:;,'ie3 gradur.lly and wliformly from a

surface

~o zu~o

maxhlUDl

at some dopth below the surfaoe.

10

th'-l grf\llula::.'

at tho bod

Basing his

analysis on a concept of sUding layers of bed mate:dal kept in motion by tho tractive forco of tho moving fluid Dy Boys proposed his now clasoioal bed load formule:CL ::: Ie

in which

~

,.

(T

loo

-,il

-

'T

is the bed load

c

)

dlacha~ge

in weight por unit time per

uni t width, and ;(1 is n constant dependiug upon the phys ical characteristics of the bed matorial. MF.UlY bod load formulae are modifications of tho bafJic Du B·')yc eqnatio:l;

Gove:-al experimenters have usod excess velocity or

diochargo raisad to soma power.

Although observation of the

movement of sediment in laboratory channels haa ahm'ln that tho

OV01'-

simplified picturo of sliding layers of aodlmont is dofinitely 'lot true, good agreement with obtained with

suc~

measu~od

formulae.

bed load dischargos haa bee;.l

JOlilmOn (1938) Dhows statistically

that they all fit exporimental flume data equally well. More recently, the problem has baen approached on a more thorough theoretical basis.

KALIlrG:m (1947), retaining the

concept of critical tractive forco, introduced the role of turbulent fluctuations and concludau:-

in which the function f2 involves the characteristics of tho fluid turbulence around the grain. The complex theory of EINSTEIH (1950) considered the probnl>ility of movement of individual particles to be a function of the hydrodynamic lift exerted on the particle.

nlis lead to the functional relationship

between two hydraulic parameters fro:n which the bed load discharge could be calculated, i.e.

19

k~\Ji (~3t .

o_~:

in which

tho dilllOnsionloss intensity of

bed load transport function. (8 and 'f -

s

- l)d

RS .e

MEYEa-PE~1

the dimansionless intensity of shaal" fUllction.

and MULLER (1940) dorivud a formula to fit the

results of a large number of flumG experiments, using tho Froudo law of similarity.

In its simplsot form it can bo written:-

in which q is the fluid dischargo in volumo per unit width pel' unlt time, and

!~2'

:C3 are constants.

CHIEN (1954b) showod that not only

could the above equation be mod1fiGd to give a relat10nship betwoen the Einstoin paramoters,

~

and

~

, but it could bu reduced to an

excess tractive force equation of tho Du Boy a type. From the above brief discussion it can be seOll thnt all approaches to the problem of bed load transport are in fnet related, t:le same dimensionless parameters occurring througho·,lt. In the past dGca.de considerablo Use haa been mndo in sediment research of tho technique of dimensional

analys~B

and GARDE and P.LBERTSON (1961), inter alia.

by YMJIH (1963)

USing this tecIllliQue

it has been possible to combine a large numbGr of variables into possibly significant dimensionless groups, many of which have bOGn found to be similar to the pazoamGters arrivod nt by n

considorntio.~

of the physical processes of sediment transport. 2.2.4.

Applicability of Bod Load Theories to Rivera

All "rationa.l" bed load theories have been devoloped USing the results of laboratory experiments.

In Boma cases data wero obtained

from certnin material under certnin flow conditions nnd an ompirical equation fitted (UNITED STATES WA'J."ERWAYS EXPERIMENTAL STATIon, 1935, 20

CHANG~

1D37);

other workers, in contrast, first evolved n theory

of the DlCchnnism of sediment unpredicted 1947,

cOG~~ficiel1ts

:?IlT8'l~r.lT,

1950).

tl~rulOpO:rt

and used this datn to provide

which occur--:od in the nnalysis (ImLIlTS:;C!:, Strictly, therefore, these fornn.llao nro

only applicable to the same

~te~ials

in tho sarno conditions,

i.e. straight, smooth-sided laboratory channels with beds of Wliform or well soTted sediments.

TIle incroasing use of dimensionloss

parameters has facilitated the npp1icction of these formulae to conditions such as those prevailing in river channels.

HOWOV0:;'~,

while tha :rango of values of man)}: of trleso parnnoters arc the

sn~no

in river and laboratory, some parnmeters, especinlly those referring to channel geometry,

n~c

of ton

The baoic

dif~oront.

variables of depth and wnter discharge are usually greater ill. rivers •

Extrapolation, therefore, bacomQo nocessary.

.liver conditions differ in several other rcapects.

Probably

the most important difforences nro the existonce of banks, tho shape of the bod surface and tho alignment of tho ri"o::- channal. Fully-devoloped dunes, bars

ann meanders (or a superimposed

meandering thalweg such as that in tha aiver Tyne nt Bywell, described in section 3.3.3.) represont another type of rooistnnce in addition to the roughneso ot the particles of which the bed is composed. and

Only the theories of EINSTEIN (1950) and MEYER-PETER

MULLER (1043) recognise the

effects on sediment trnnspol't of tho

turbulonco created by the two systems of roughness. macroturbulenco on the scale obsorved in rivers by

Also, b~TTims

(1947)

does not occur in laboratory flumes. For gravel-paved rivers the problems of size and a largo rnngo of sizes at sediment arise.

Few experimenters hnve used matorinl

21

other than sand, the largest sizG used in qurmtitntivo bed load laboratory oxporimants being 1.62 in by }:GIAZAROFF (1959).

l .. lthotlgh

SCHOKLI'l"SCH (1934) and KALINSKE (1941) suggested the computation of bed lond diBcI... a:;.'~e for individuC'.l sizo ranges of n sodimont mixture, and

~,IEYER-PETE~:

and

MULLER

(1943) usad a single size to ropresont

the mixtuTos usad in their experiments, only EINSTEIN (1950) attempted to account for the mutunl pnr~icles

of d1:ffGrGnt sizes.

~l

interfer~nce

tho

~ivGr

Gffects betweon

Tyne at Bywell

accumulatioas of small particles can froquently be observed immediatoly do,nwtroam of large stones. Nono of the theories allow:l

fOl'

thG effect of particle shape

to be directly and quantitative17 includod. beds of a

m~y

The surface of tIle

rivers with underlying sedimentary rocks often contain

preponde~nncG

of disc-shaped

pa~tic1esi

at Bywol1 about 60% of

the bed surface particles nrc disc-shaped (see section 3.5.6.). \'lith a large range of sizes this type of bad is pc.rticulnr1y suited to the forl!\ation of a "pavement" having n critical shonr stross tor the initiation of movement consldGrRbly greater than thnt indicated by the equations of SCIIIEIDS (1936) or WHITE (1940). Finnlly, the relationship bQtwocn sediment motion and streamflow in natural watercourses is extremely complex.

Not only docs

sediment discharge depend upon the hydrology, geology and pedology of the catchment but hydraulic characteristics such as depth, veloci ty I turbulence and shear, and honce the sediment trmwpo:.:'t chp.racteristics are likely to vary non-uniformly both latorally and longitudinally within the river. Where direct observation of bed load dischargo in rivers has been

posai~lG

for instance in the Danube in Hungary (K(iROLYI, 1957),

results have displayed considerable fluctuations, indicating that 22

bed loan movement in rivers is a non-steady prOCASS.

The "rational"

formulae, based on laboratory experiments in steady flow conditions, cannot then yield satisfactory predic'dons for rivers.

It would

seem that in ordar to further investigations of the relationship between actual and predicted sediment transport the development of an instrument for the continuous recording of bed load movement in both rivers and laboratory channels is necessary. The Regime Approach

2.2.5.

The concept of " reg i me " , or the equilibrium state of rivers and canals, has been referred to in section 2.1.2.

This concept and

the practical necessity of excavating stable channels in alluvial material has led to the formulation of a set of empirical design rules known as the regime theory.

Based on the observation of a

number of Indian canals KBNNEDY (1885) proposed the first quantitative rule that the "non-silting, non-scouring" velocity of a stable channel is proportional to some

pow~r

of its depth.

Further work by LINDLEY (1919), LACEY (1929, 1940) and many others led to the important concept of the three degrees of freedom of self-adjustment of regime channels, requiring three oquations for the complete determination of the ultimate stable breadth, depth and slope of the channel.

It is possible to consider that a

fourth degree of freedom exists in rivers or neglected canals where meandering has been allowed to take place. Recently, BLENCH (1955, 1957, 1961) introduced the bod load charge, C, the ratio of the bed load discharge by weight in air per unit time to the water discharge by weight per unit time. His equations are as follows:D

=

W=

V

2 IFb

3

v /F s 23

in

whic~

V is the mean velocity i1. the soction, D is the depth and

W is the width at mid-depth.

side

factol~,

BLENCH

and

respectively.

QU?.ESHI

...,

"'b

The

llJ.'ld

F

s are termed the bed and

lat~st

slope equation is given by

(1964) as;-



in which k, 1, and mare coefficiellta to allow for meandering, the definition of the representative discharge, Q, and miscellaneous other effects (e.g. suspended sediment), respectivoly. termed the zero bed-factor and is n function of d ~article

diameter by weight of the bed material.

50

Fbo

io

, the nwdinn

Q is the forontive

dischargo, usually taken in rivera as bankful discharge;

oxact

definition of Q is rendered unnecessary by the exponent 1/12.

The function, f"'(C), has been dorived by BLENCH and ERB (1957) from the results of GILBERT (1914) and other workers

f"'(C)

=

8S:-

0.12C)11/12 (1 + C/233)

(1 +

The theoretical lower limit of

f"'(C) is thus unity.

The regimo formulae have been developed with the immediate purpose of facilitating the design of stable channols in alluvial material;

the "rational" app:uach has boen formulated with the

specific intention of predicting bed load discharge.

However, it

is possible that the slope equation of Blench could be used to determine the bed load discharge of a river in which both water and sediment dischnrges fluctuate widely.

NIXON (1959) has been able

to establish regime relationships for several English rivers of this type.

24

Til':) tiost p:romising approach to a cOr.lplete solutio:a of bod lond transport, since this

i~

the

pal~

associated wit:! channel shape, is

of the sediment lond most closely prob~bly

of the "regirJU" and "rationnl ll theories. work of

LCKE~S

the ultimnte coohination In this connection tha

(1964) on small streams in alluvium and the derivation

of the rogime equations using the principle of minimum enorgy degradation rate by BREBNER and WILSON (1967) could prove to be valuable contributions.

25

Soction 3 3.

The River

~~ne

at Bywell

It has been seen in section 2 that a number of hydraulic and sediment parnmaters are necessary for the estimation of bad load dischnrga in a river. this

requi~ed

data for the reach of the niver T,yne near Bywell. 3.1.

Tbe

~iver

This section doscribes the collection of

The River Tyne Catchment

Tyne drains an area of about 1,140 square miles of

the counties of Northumberland, Durham and Cumberland in the north of Englenc and a sm11 part of the oounty of Roxburghnhire in scotland.

Tho catchment, roughly triangular in shapa, is bounded

in the south and west by the main Pennine block and in the north by the Cheviot dome (fig. 3.1.a.).

Both main tributaries, the River

North Tyne and the River South Tyne respectively, are considorab1y varied in oharaoter throughout their lengths; rivers meo:.ldar freely

th~augh

in soma parts, the

large banks of gravel, locally t0rr.13d

haughs, in corked contrast to the fast-flowing, rocky reaches in other parts.

F .."'om the confluence of the two rivers the lower

River Tyne flows eastwards, past Bywol1 gauging station, for about thirty miles to enter the Horth Sea at Tynemou"th.

1'ho

tidal influence extends upstream no far as Wylnm. PEEL (1941) has demonstrated thnt the longitudinal profile of the

~lver l~e

is of considerable interest.

On the bas 1s of

many measurements, mainly on the North Tyne, he waD able to produce tho thnlwegs of the River Tyne and its main tributaries, as shown in figs. 3.I.b. and 3.l.c.

The profiles revenl features out1roly

consistent with topography except for a break, at which tho River North Tyne suddenly steepens, just below Bellingham at n height of about 350 A.O.D.

Peel suggested that this "knick-point" and

similar breaks on other tributaries are the result of river rejuvenation.

Assuming a semi-logarithmic equation for the 26

RIVER TYNE DRAINAGE

AREA,

N '\\;"',

-(-'Y 'I.

',0 /

/

e ....\

~

..... - - _ ....,

Catcleugh" "Res . \

/

......

r'<:' / v /

I

-, \

,

I

......

--,

\

I

/

/'

'I

I tterbut>l1 I

J

/

I I

I

North Seo

"

~/

\

\

/

(

.....

......

'\

\I

,_-

............ -,

J

I

------

I

........ I

I

I

I

,,---.......

/ /

) ,/

I

/ I ( J

.... _ /

/"

,;/~---""----..-

/'

/

//

Gotesheod

/

......

(

\

/

./

_/

/

/

/

\

/

\ \

\

~.

J

.

/

Conseltl _/

\

\

A I s ton

\

I

I

I I

,- ...... -,,/

/"'-,_",r-..-..

-

,,_-,,""

---

I

I I

\

Fig.3.1.a.

/

\ \

Cross Fell

miles 0

5

10

15

20

25

, 30

35

40

I

45

I mile~ 50

feet A.O.D.

- - - Actual longitudi na I prof i Ie ------ Logarithmic profile

900

800 700 600

Tyne confluence

River Rede

I

500 4 00

-.. _. _ 350ft AD.D.

300~

-------

Bellih 9 ham

100

100

0'

I

I

I

I

5

10

15

20

Fi9.3.1.b.

I

25

I

30

I

35

I

I

40

.15

J

miles

Longitudinal profile of River North Tyne (PEEL,1941)

feet

A.o.D. 1500

1000

500

Tynemouth

I

o

, 10

I

20

I

I

30

40

~ ---~ - : --- J -,-~150ftA.O.D. 50

60

70

80

fig.3.1.c. Longitudinal profiles of River Tyne and tributaries (PEEl, 1941)

90

m'es

mature profile he showed that the central part of the Rivel' North Tyne is graded to a base level about

l5~

ft above the present level

while the lowor part is still in a stage of youth, being unadjusted and irregular. The geology of Northern England has been comprehensively doscribed by EASTWOOD (1963) and ROBSON (1965). River Tyna

cat~;ment

coal measures

The underlying rooks of the

are mainly sandstones, limestones, shales and

the Devonian and Carboniferous period;

o~

the

o~ly

igneous rocks are those of the Cheviot volcanic extrusion ru1d a number of dykes and sIlls of quartz dolerite. to 200 0ver

Glacial drift, up

ft. thicl:: in places, has been deposited by ice which flow3d

north-ea~t

England from

Scand~~avia

during the period of maximum glaolation.

and

the Lake District

The main mass of the

drift is usually a tough dark deposit containing boulders, mostly of local

above this is a

ori~in;

t~re

sandy, brownish clay

containing smaller boulders and pGbbles of material foreign to tr.;3 region

(HIC~CL!l!G

et aI, 1931).

Thin, acid soils in upland areas of the catchment support moorland vegetatioll, rough pasture and, especially in the North Tyne region, considerable expanses of forest;

in the valleys and lowland arena

loams and clays, mostly originating from glacial carboniferoUG till, provide large areas of good moadowland and permanent pasture (NOa'n-l-EAS'J.' DEVELOPMENT ASSOCIJi.l'I01;, 1950 and NORTHUMBERU.1rD COUnTY comiCIL, 1952). The greater part of the River Tyne catchment is sheltered from the prevail1ne south-west winds by the mountain barriers of the Northern Pellninel3 and the Cheviot

I~ills.

Annual average rainfall

varies from noarly 80 in. on the South Tyne area near Cross Fell to about 26 in.

0:1

Hewcastle upon Tyne (METEOl10LOGICAL OFFICE, 1931). 27

According to Hf.LL (1964) runoff amounts to about 64% of rainfall on the catchT!lQnt.

Concentration of direct runoff on the

its tributaries is often extremely rapid.

~iver

Tyne and

During the present

investigations the river level on the River Tyne at 3ywell was hou:4~s.

observed to riso 9 feet in Ii occurrence of serious flooding

This effect has caused the

severnl occasions, especially in

011

1771 (PALr:iEU lCB2) and more :recently in 1954 (BlACK, 1957). 3.2.

The Test aeach

The 3ywcll cableway gauging station (grid reference NZ/038.617) is situated on the aiver Tyne

Ii

miles upstream of Bywell B:ridge,

Northumberland and 8 miles upstream of the tidal limit at Wylam (Fig. 3.2.a.). and Tyneside

It was constructed in 1956 by the Northumberland

~iver

Board (now pn:rt of the Northumbrian River

Authority) on l&.d owned by Lord Allendale.

The area of the

River Tyne catchment to the station 1s 834 square miles. The gauging station, which.ls easily accessible, consists of a cnbleway for current-meter gauging and a wooden hut located over a float well on the left bank of the river. the

dist~.ce

A wire cable spans

between two stanchions, 12 feet high, situated on

opposite banks about 30 feet above low water level.

A small

trolley mounted on this wire can be manoeuvren to any position across the river by means of a continuous cable which passes round one drum of a hand-operated winch unit in the hut.

Another cable,

for suspending an instrument from the trolley at any depth in the river, can be manipulated by means of a second drum on the winc..'1. The suspension cable is of a coaxial type, with a single core insulated from the outer braiding, and is used for carrying electrical signals to or from the suspended instrument.

The

station is equipped with a Lea Recorder vertical-drum recorder

28

Scale: 6 inches to 1 mile.

b'

'11C£O--=r

hJ

I

9

2000

Feet. - BYWJ:.LL "1'AJ
~:::::::~::.:.;f

_ .!" -

:1- --

..... main cross-section

supplementary cross-section

Fig.3.2.a. River Tyne at Byrrell--Location of main and supplerr.entary cross-sections.

producing weekly continuous charts of water level.

A teletone

audible warning device has been incorporated and proved to be extremely useful.

By dialling n special number from any public

or private telephone the river stage can be obtained from series of pips.

In October 1965

Q

Q

coded

Fisher and Porter instrument

was installed, which, at intervals of 15 minutes, records stage to the nearest one hundredth of a foot in a binnry code form on punched tape;

water levels can be read at any time on a cnlibrated

disc. The right bank of the cableway section has been pitched with stone while the left bank adjacent to the hut is fairly densely covered with bushes and trees.

Regular flushing of the float-

well in recent years by the River I:..uthority has minimised trouble due to silting of the intake pipG. Downstream of the cableway the river bed gradunlly widens, water depth decreases and flow velocity increases.

At a distance

of about 1000 ft., just upstream of a line of ancient

~imber

pile3,

placed in the river for some forgotten purpose, the bed gradient suddenly steepens.

This section acts as the control section for

the gauging station and is usad at low flows for current-meter measurements by wading.

Until 19G1 the section provod. quite

stable and a stage-discharge calibration had been estnblisllGd by the River Board.

In 1960 permiSSion was granted for Lord. l.. llendale

to extract gravel from the river downstream of the timber piles and upstream of Bywell Bridge (see fig. 3.2.a.).

Between June 1960

and July 1962 a considerable quantity of material was removed. The main purpose of the scheme was to reduce flood levels by improving the alignment of the river channel and, in this respect, it proved to be very successful.

However, it was noted in 1961

that the level of the control section had fallen causing a change 29

in the low-flow part of the

stng~-discharge

could be detected at high flows. time the

~iver

intake were started.

curve;

no change

In September 1964, by which

bed had regained stability, the float-well and

~econstructed

and a new calibration of the station

It should perhaps be noted that periodic fluctuations

of the lower ends of the ratincr curves of cableway stations on the River Tyne and other Northumberlwld rivers have been observed where gravel extractions have not

tak~n

place.

EINSTEIH (1964) has emphasised the importance of the concept of the test reach which should adequately describe the overall characteristics of the river

c;~nnnel.

One of the greatest

difficulties in applying hydraulic equations, especially those concerning sediment transport, to a natural river is the basically irregular flow pattern in such a channel. different from all other cross-sections.

Each cross-section is In the application of

all but one of the methods mentioned in section 4 for computing bed load a knowledge of the average water-surface or energy-surface slope is necessary.

Only one method requires a number of cross-

sections in the reach to be averaged.

The nature of the

longitudinal profile of the River Tyne near Bywell made the determination of these average conditions even more difficult. Observation of the river channel showed that the profile consists of a series of deep slow-flowing "pools" separated by shallow "bars" which at low and medium flows

to~

rapids.

This undulating

"pool-bar" configuration occurs frequently in gravel-bed rivers; LELIAVS:CY (1955) describes how some aussian rivers have been found to be of this type.

Bed irregularities have little effect on

water-surface prOfiles at high discharges but are closely reflected

30

in low or medium flow profiles.

The cableway gauging station at

Bywell 1s located in a "pool", while the "bar" downstream acts as the control section. It was decided to survey several sections on the fairly straight reach of river which extends from rapids about

i

M1le

upstream of the cableway to just downstream of the control section The total longth of tho ronch is about

3.3.

~

mile.

Survey of the Reach

In li!ay 1955, permission to survey the river rea.ch near nywell was obtained from the Northumbrirul River Authority and the riparian owner, Lord Allendalo. 3.3.1.

Main Cross-sections

After inspection of the reach it was decided to sound in detail five cross-sections AB, CD, EF (the cnblewny), OH and (fig. 3.2 .a.) •

Jr~

A peg and nail had already been located at the

cableway on onch bank;

the other four cross-sections two ups t::oo a.;l

and two downstream of the cableway, were fixed by driving a peg and nail into tho left bank at a suitable posit:l.on.

Equipment and

p3rsonnel were organised such th:lt all five cross-sections could be sounded in one day at a convenient low flow.

SoundiDG' was

carried out from an eight foot long fibre-glass dinghy by means of a ton foot long pole graduated in tenths of a foot. cableway it was possible to USe the pulley and traversing cable to locate the

din~hy

in the requ!:i."ed position.

The lef-: banlt peg, E,

was taken as zero chainage and soundings made every 10 feet the section.

I ..t the other four sections

Q

ac~oss

1000 feet line, ma.:rl:ed

at 5 feet intervals by coloured tags, was stretched across the

31

~ivor

from the left bank and secured to n peg and nail driven into tho right banIt.

':.'he dinghy wns t:l011 manoeuvred across the section

and soundings made at 10 feet

interv~ls.

At all sections the elevations of the left nnd right bank pegs above the water-surface wore measured using an surveying level.

ordinal~

Water-surface slope across each section wns

assumed to be zero and the level of the right bank peg and all soundings -.rare related to the level of tho left bank peg.

The

banks of each section were surveyed, relating all levels to tha left bank psg. It was then necessary to reduce the levels of the left banIt pegs of each section to a common datum. of the

gau~il1g

During the constructiO:l

station the Northutloorlnnd and Tyneside ;Uver Board

had used a temporary bench mnrk on the corner of the concrete plinth of the stanchion beside the gauging hut.

Using this mark

the left benlt peg, E, at the cableway wns established as a T.B.M. (66.91 ft. A.O.D.) for the survey.

The elevations A.O.D. of the

other left bank pegs A, C, G and J were determined by careful levelling from peg E.

All cross-sections were thon related to

O.D. ns shown in figs. 3.3.a., 3.3.b., 3.3.c., 3.3.d. and 3.3.e. Attempts were made to check the assumption of zero crosssectional water-surface slope but sighting distances proved too great for the equipment used. In order to detail further the bed and, later, to be able to apply the various bed load formulae it was decided to divide the "channel" total wetted perimeter, P , into "bed", that part of t the perimeter cOmnnAed of gravel ote. P b" and "bank" -,.of the perimeter composed of bushes, grass etc., P • w

32

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Aocordingly, field observations of the elevation and chainaga of the bed-bank divisions were made at each section.

The elevations

of the bed-bank divisions were found to be almost equal on each side of each section and it was possible to ascribe to each section a particular water-level at which the "bed" was jU8t submerged, i.e. at which Pt equalled Pb •

This level is indicated in

f1gs. 3.3.a. to 3.3.e. and 1s given 1n the following table with the corresponding wa.ter-8urface width or

"bed"

width, the mean

level and. the wetted perimeter of the "bed", P • b

"bed"

Mean "bed"

level was obtained b1 dividing cross-sectional area by watersurface width and subtractine this mean depth from the watersurf ace level. Table 3.3.a.

''Bed'' details at main cross-sections

Section

"Bed" width

Water level

Mean bed level

Bed" ftttad perimeter P

b

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(ft)

(ft. A.O.D.'

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47.71

141

43.81

149

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193

45.83

199

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203

44.29

211

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244

46.19

24a

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49 .. 00

270

46.50

272

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crce.-aectiona1 areas at one foot intervals of water level were measured by planimeter on sections drawn to a large distorted scale, 10 horizontal to 1 vertical. a map measurer.

Wetted perimeters were measured USing

Figs. 3.3.f. and 3.3.g. show the variation of

total cross-sectional area, At' and total wetted perimeter, P t respectively, with water level, II, for all five sections. A form of tacheometric traverse, usine a theodolite and vertical levelling staff to measure distances nnd horizontal angles, was carried out to fix the positions of the main cross-sections relative to each other.

Arbitrary co-ordinates were assigned 33

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1_

to peg K and the co-ordinates of all other pegs calculated.

As

a chock on the accuracy of the survey the pegs A and J were located on a 25 inches to the mile Ordnance Survey map of the area using fences etc. and the line AJ measured on the map as 2755 ft. calculated from their co-ordinates tho distance between

~

Vfnen

and J

was 2761.4 ft. The d!otance between the sections was taken to be the distance between the mid-points of the river "bed" at each section.

'.:'hese

mid-points weTe easily calculated from the survey details and the distances determined as follows:AB

Section

EF

CD

Distance between sections (ft)

1123.2

GU 535.3

J .:.. "

321.8

The total distance between sections AB and JK was 2750.8 ft or 0.520 miles. 3.3.2.

SupplemGntary Cross-sections

From figs. 3.3.0. to 3.3.e. and table 3.3.n. it can be seen that thore is considerable variation in the shapes, "bod" widths, mean

"bed" levels etc. of the five main cross-sectiol13 AB, CD, EF,

GH, JK.

To obtain a more complete picture of the rivor reach it

was docided to supplement theso sections with a number of intermediate sections.

A further eighteen sectiOns, about 150 feet apart, were

located by pegs and nails driven into the left bank;

3 sections

upstream of lJ3, 13 betweon AB and J!{ EU"1d 2 downstream of J:{. Distances between sections were

n~DSured

by tape along the left bank

and proportionately adjusted such that the distances between trls five main sections agreed with those determined in the tncheometric survey.

Peg elevations

wer~

fixed by levelling from the T.B.M,

peg E, at the cableway. 34

Inspection of the five main cross-sections showed that the mean JIbed" level of each section could be obtained by the addition

ot 0.36 tt to the mean of the

"bed"

levels at distances across the

"bed" of 1/5, 2/5, 3/5 and 4/5 of the "bed" width.

In this way

detailed surveys of the bed and banks of all eighteen sections could be avoided, and it was decided to sound at these four positions and

at the mid-point of the

"bed".

The poSition and depth at the

deepest point were also noted at each section.

Sounding was

effected in a manner similar to that used with the fige main sections except that the line was secured to a steel rod temporarily driven into the right bank.

At each section the water level was related to

the corrccponding ~height, the

"bed"

of the sounding poSitions determined.

9Wth noted and the location Mean "bed" levels and the

Itbed" levels at the deepest point and mid-point of the "bed" were then

calculated • 3.3.3.

Longitudinal Protiles

Details ot the bed at all 23 cross-sections are given in fig. 3.3.h. (in pocket). The plan view, drawn with

tl

straight centre line to facilitate

plotting of the protiles beneath it, clearly shows that the bed width increases gradually downstream over the length of the reach.

The

thalweg profile is uneven and tends to meander within the bed, the deepest parts occurring near the banks.

It can be seen that the

highest point on the thalweg ~ the "bar" torming the control section of the gauging station (or the outlet ot the preceding "pool") is located at JK while the higheat point of the mean "bed lt love1 profile occurs further downstream. An attempt was made to assign an average bed slope to the whole

length of reach between sectiOns 1 and 18, a distance of 3531 feet or 0.73 miles.

The method of least squares was used to determine the 35

best stra1gb.t line through the mean "bed" levels of all 23 sections plotted against distance downstream of section 1.

was calculated to

this liDe

-3

be 0.171 x 10

The slope of

upwards in a downstream

It is evident from this result that it is impossible to

direction.

describe the river channel by its bed slope over a reach of this ;ength.

POSSibly, the bed slope of a "pool-bar" typo river could

be taken as the average slope through the tops of two or more

successive "bars", but the physical significance of this slope is doubtful when applied to a single cross-section in hydraulic calculations involving, for example, sediment transport or flood If the slope of a river at a single cross-section must

routing.

be described then the water-surlace (or energy-surface) slope

would have to be used;

this, however, will vary considera!)ly

wi th stage, especially in "pool-bar" type rivers. 3.4.

Hydraulic Characteristics of the Reach

In order to apply the bed load theOries described in section 4 it was necessary to determine the relationship between stage, discharge and the water-surface and energy-surface slopes.

r~le

velocity distribution and tractive force distribution at the cableway section were also investigated. Measurement of water-surface slope within the reach involved the determination of water-surface levels at three sections (the cableway section) and 3.4.1.

l~,

EF

~{.

Measul·ement of Water-surface Level

Measurement of the water-surface levels at EF presented little difficulty.

The Fisher and Porter punched tape recorder housed in

the cableway hut indicated to one hundredth of a foot the river stage above staff gauge zero.

This datum was determined by leve2ling

from the T.B.tl., peg E, to be 46.25 ft A.O.D.

36

The height of water-

surface A.C.D. could then be obtained easily from the reading of the recorder. For the measurement of

wate~-sur!ace

levels at sections AD and

JK staff gauges located on the banks would have been insufficiontly accurate, would have been required to be robust and elaborately anchored and might possibly have beon aesthetically undesirable. To overcome these difficulties a modified point gauge arrangement as shown in fig. 3.4.a. was designed.

The tip of the point gauge

could be moved over a range of 3 inches inside a 2 inch internal diamotel' porspex tube.

The tube was partially blanked off o.t the

t

lower end by a perspex cap with a central

inch diameter hole,

thus considerably damping surface ripples. provided at the upper end of the tube.

Air vents were

The location of the point

of the gauge wns indicated by tho position of a disc on the top end of the moving stainless steel rod relative to long metal scale.

0.

fixed 3 inch

By means of a button and keyhole slot arrangement

the point gauge could be attached to one of nine, numbered positions, 3 inches apart, on a flat aluminium support.

In the top position

the level of the top of the aluminium support coincided with that of the top, or zero, of the 3 inch scale.

The aluminium support

itself could be fixed by two button and keyhole slots to any of several 6 foot lengths of rust-proof painted angle iron driven into the river bank.

Ii

in x

Ii

in x

i

in

The range of water level

covered by each length of angle iron was thus

21

feet.

For ease of access to the water-surt ace the left banlt was chosen for the location of the measuring points and eight numbered lengths of angle iron were positioned at the required height, allowing a small overlap, at both

sectiol~

AB and JK.

The hoight

A.O.D. of the top of the aluminium support when fixed to each angle 37

7'

6ft. length In x

/ 1'2 In x

1'6?

V4

In

angle Iron

I I

'I 'I

U-

but to,., keyh':l/e

:. I

an d slot

I

,II'I

~

'I

I,

_

spa ced

I

,Ii

I

II I

I I

ke yho/e

I I' ': 1 \ I

reod i n

disc

,

I I

bu tton keyhole

16

, ....

"

"

rlA..a-+----

33 in. leng t h in . flot 31n .x 3 [.,..---a lum lnlum sup po rt

,

and slot

I I

,,

r,

,d II II II

,

'I

II II

I'

water level

gra d uated 31n . scale

t-

D'I ,I I

I I I

I

~~:~ ! ,I II

I....

"

I

I, ""

I

I I

I,I I I

lOin . length l - - 2 ,n. Internal diame ter tube P erspe x

I

' I ., t I II v ' I I I,

perspex

7~ In .

endcap.

dl ameter hOI;--'

".

11 (",( 1

I' ~ I

,

I'

I

II

,

II

I

I: \?: I

bu tton bA-J--ke/hole

I~ O I II U I I

an d

li e I

slot

I;

I

II

, ,I , I

I 7"77 7 77~··b-r17""""/-+-[/-7"" ' /-r"1'/'-T7--?T

.' evel

,,, ,

lL.-

c

'-

~I

, -

Fig 4 · 3 . p Oin t

g -::t L.lg e

for

measuremen t

a... o f

slo ts 31n. ap art

o \NQt e r-surface

l ev e l.

was detormined by levelling from the appropriate peg, A or J. (These levels were later checked after several high flows and found to be unchanged.)

Knowing the length between point and

disc it was then possible to draw up a table for each section giving the level A.O.D. of tlle point, when tho reading on the 3 inch metal scal. was zero, for any angle iron and any position

of tho gaug3 on the aluminium support.

In this way the

measurement of the water-surface level was reduced to tho simple procedure of notlng:number of the angle iron,

1)

t~c

2)

tho number of the position of the gauge

011

the aluminium

SUPPo:i·"t, and 3)

tho reading of the d:"sc against the 3 inch metal scnle to t:18 nearest 1/20 inch.

The accuracy of the levels detorminad by this method depends UPOi.l the accuracy of the levelling.

i'.t high flows macroturbulenco near

the banks caused surface levels to su::,"ge and it was found nocessary to take the moan of three or four readings of the point gauge. TIlo

~~iver

Tyne at Bywell is subjeot to rapid changes of stage

and the following procedure was developed to enable the water levelS at A, E and J to be measured by one person wi thin as a period of time as was possible.

~hort

Advantage was taken of the

Fisher and Porter instrument which recorded the level at E on punched tape at 0, 15, 30 and 45 minutes past each hour.

A few minutcD

before the instrument was due to record, the water level at 1'.. was measured.

The observer then moved as quickly as possible to J

(a vehicle could be used for part ot the distance) to mensure the level thel"e.

The time between the two measurements was usually

about 7 minutes during which time the level at the 38

eablcway section,

EF, had been recorded.

~lis

level was noted together with the

preceding and succeeding punched tape recordings which were

used

subsequently to determine the rate of rise or fall of stage. Thirty-seven sets of readings were made (table 3.4,a) over a range of stage at E above staff gauge zero from 1.76 ft 13.01 ft.

~o

Four longitudinal profiles are shown in fig. 3.4.b.

Profile No. 1 was determined on the day that the five main crosssections were sounded, during which time flow conditions remained steady.

It included water levels measured at C and G, which can

be seen to lie on straight lines AE and EJ, respectively.

'flle

water-surface profiles in the reach were therefore considered to consist of two straight lines whose slopes become more nearly equal at higher stages. Computation of Water-surface and Energy-surface Dlopes To determine the energy-surface levels at each section, discharge

values corresponding to each of the 37 sets of water level measurements were obtained from the stage-discharge curve of fig. 3.4.e,

Mean

velocities, V, at each of the sections AB, EF and JK were calculated using the area-stage curves of fig. 3.3.f.

Assuming a Coriolis

coefficient of unity, the velocity head, ~/2g, was calculated and added to the water-surface level to give the energy-surface level (table 3.4.a.). Surface slope at the cableway section, EF, was calculated as the geometriC mean of the slopes from AB to EF and from EF to JK. Examination of a number of laboratory channel drawdown profiles, to which the reach profiles apprOXimated, showed that the assumption of the geometrio mean rather than the arithmetic of the upstream and downstream slopes should be more accurate.

39

The geometric mean was

in all cases Ie•• than the arithmetic mean;

since the flatter

slope extended over the greater length of the reach (fig. 3.4.b.) this was considered a justifiable bias. Water-surface elopes, SWI and energy-surface slopes, So' for the 37 profiles are given in table 3.4.a. Table 3.4.a. h

e

= stage

at section EF above staff gauge zero (46.25 ft. A.O.D.) (ft)

Ha

= water-surface

level at section AB (ft. A.O.D.)

H

e

= water-surface

level at section EF (ft.

Hj

= water-surface

level at section JK (ft. A.O.D.)

S

=

w

~.O.D.)

water-surf ace slope at section EF

E a

= energy-surface

level at section AB (ft. A.O.D.)

E e

= energy-surface

level at section EF (ft. A.O.D.)

Ej == energy-surface level at section S

JI{

(ft. A.O.D.)

energy-surf ace slope at section EF e ==

dH=

rate of rise (+) or fall (-) of stage at section EF (ft/hr)

Distance between sections AJ3 and EF

= 1894

Distance between sections

==

roile

Eli' and

.II{

857 ft.

lYater-surface h

H

0

a

H

e

Hj

8.80 48.63 47.9

ft.

Energy-surf ace 3 Xl0

w

E

a

E

e

Ej

0.259 48.83 48.65 48.06

1

2.30

2

6.62

53.88 52.8

3

5.62

52.57

4

11.93

5

4.11

6

4.03 ,51.73,51.0

7

3.:'4 150.42149.99 49.1

8

4.36

~51'32150'61149'S

50.53 50.07149.37 51.49 50.74 49.95

9

1.76

40.11;48.01 47.5

)48.12 48.02 47.55

1.07 1/48.28148.12 47.6

48.29,48.14,47.70

1 10

51.6

0.860 54.39 53.24 52.28

0.692 52.94 52.10 51.22 61.50 59.77 58.60

59.88 58.24

i 51.04 I

51.19 50.46 49.69

50.36 49.4 50.1

51.96 50.43

40

~.43

55-

_ f..-_

Table 3.4.a. (cont.) Water-surface

IJ?ro~i1e ~o.

h

e

:1

a

Energy-surf ace S x10

H

dH

3

E

w

e

a

11

2.19

43.61 4S.44 47.86

0.247 48.63 4S.46 47.92 0.235

O.OOG

12

2.00

48.38 48.25 47.71

0.208 48.39 48.27 47.7G 0.174

0.000

13

6.12

53.28 52.37 51.23

0.799 51.70 52.67

51.7~

0.773 -0.16C

14

5.93

52.90 52.18 51.04

0.711 51.32 52.45

51.5~

0.702 -0.220

15

5.52

52.54 51.77 50.65

0.729 52.S6 51.99 51.07 0.702 -0.320

16

2.83

49.36 49.08 48.43

0.335 49.41 49.11 48.54 0.324 -0.040

17

7.50

54.87 53.75 52.46

0.943 55.63 54.26 53.21 0.007 -O.lSO

IS

7.16

54.50 53.41 52.07

0.949 55.12 53.87 52.80 0.908 -0.400

19

6.76

54.05 53.01 51.85

0.862 54.59 53.40 52.57 0.780 -0.440

53.63 52.67 51.51

0.828 54.11 53.01 52.09 0.79d -0.360

20

6.

42

1

21

6.17

, 53.39

52.42 51.24

0.840 53.71 52.73 51.64 0.811 -0.420

22

3.25/ 49.86 49.50 48.77 3. 51 1 50.14 49.76 48.97

0.402 49.93 49.55 48.99 0.362 -0.040

0.430 eO.2ft 49.82 49.28 0.378 -0.120 • 7.55,I 54.94 53.80 52.551 0.937 55.61 54.32 53.31 0.896 +0.820

23 24

;

26

8.58! 5S.11154.83 53.50' 1.024 57.05 55.54 54.44 1.011 +0.420 6.B9 54.22 53.14 51.84 0.930 54.78 53.55 52.51 0.838 -0.320

27

6.76

54.07 53.01 51.74

0.911 54.60 53.40 52.36 0.B69 -0.220

28

6.66

53.94 52.91 51.63

0.902

29

6 .. :)1

53.76 52.16 51.52

0.874 54.Z6 53.ll 52.:1.2 0.831 -o.J..80

30

6.43

53.64 52.68 51.46

0.850 54.12 53.02 52.03 0.819 -0.080

31

7.50

54.99 53.75 52.39

1.019 55.63 54.26 53.15 0.963 -0.480

32

5.93

53.06

~2.18

51.02

0.793 53.46 52.45 51.52 0.751 -0.380

33

13.01

61.02 59.26 57.85

1.236162.05 61.07 59.70 1.259 -1.060

7.18, 54.24 53.43 52.15 5.03 51.99 51.28 50.26

0.800 54.90 53.89 52.86 O.SOO +0.540

25

34 35

I

54.~6

53.29 52.27 o.GSa -0.200

0.667 52.25 51.45 50.62 0.639 -0.lS0

I

9.011 56.69 55.26!53.93j 1.°,157.68156.05,54.944.1.056 +0.120 I 8.0"/1 56.35 54.92i 53.55; 1.09 52.27155.64154.5 1.070 -0.680

36 37

I

:l

I

:

I

;!!i

I

1



I

-----~--~------~----~----~----~--~~--~----~--.~~--~

3.4.3.

"lariatlon of Surface Slopes with River Stage

For correlation of surface slopes with river stage a standard multiple regression programme was used on the KDF9 computer of the University of Newcastle upon Tyne Computing Laboratory.

By means

of this programJllEl trial correlations of several variablos could be 41

obtained rapidly together with the oorrelation coefficient and significance level of ellch vn:rioble. kftex several trials i t was found that the best correlations were obtained by plotting the surface slopes against the logarithm of the stage at E above a certain datum.

The resulting equations

were:-

n nt Cor • cooff .:: 0.983 n

Cor • cooff

nt



= 0.990

~~ese

equations and the observed data are plotted in figs. 3.4.c

and 3.4.d. respectively. 7hc

:rate of rise or fall of river staae, dB, was introduoed

into the regression programme as a third variable to determine whether any improvement of correlation could be obtained.

~le

above equations were modified to:3

Sw x 10

S

e

= 1.497

loglO Gore - 45.55) - 0.012dH - 0.444 n nt Cor • cceff • = 0.983

1.865 loglO CIe - 44.35) - O.OO4dH - 0.915 n nt Cor • coeff .:-: 0.990

The t-value significance levels of the variable dH in these equations were only 35% and 15% respectively.

It was concluded

that, with the observed information, evidence of the effect of rate of rise or fall of river stage on water-surface or energy-surface slope could not be detected. Stage-discharge Relationship The l10rtaumbdan River Authority have established a rating curve (fig. 3.4.e) for the cableway section from gaugings oarried out since January, 1965, two years after the cessation of gravel extracting operations downstream of the cableway. to the ourve 1s:42

The equation

16 Stoff

74

gouge zero: 46'25 It A.O.D.

• 72

70

8

Stage at c ableway abov~

45,55 ft A.D.D••

He- 45'55

6

~

(ft)

S

w

><70

3

=

1·504 log

,0 CH-45'55) e

• 4 ~

2'L-______

o

~

______

~

________L __ _ _ _ _ __L_ _ _ _ _ _

0 ·2

0'4

~

________

~

______

Rei ationshi p

_ _ _ _ _ _ _ _L __ _ _ _ _ __L_ _ _ _ _ _

0'8

0'6

Water-surface

Fig.3. 4.c.

~

between

~

________

~

1·0

______

~----

__

'2

slopf!!'. Sw.(X103 )

stage

an d

wo t e r-surf ace slope

.::t Bywell.

~

-0'449

Staff

gaugf2' ze ro:

46'25 ft A.O.D.

12

10

8 Stage at above

cableway

44-35 ft A.O . ...., .•

He- 44 i 35

6



(ft)

~SXI03= e

I' 869 log (H 10 e

44 ,35) -

0 · 918 .

4

21~

o

______

~

______

~

0-2

______L -______

~

____

0 '4

~

______-L______-L______- L______

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between s';oge

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.

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f ,.. •



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100

"

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' j

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(c:rsrct ·

I

567891

500

..l-

2'



F i g . 3 . 4 .e · Stage-d i scharge

3

"5

L7

5.000 re l a f io n sh ip

for

i

or

...

J

)i.J

.--.

.

I' .. I

,

yw~

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4'1

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10.000

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section .

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1

100.000

Q _ 233(h

e

- 0.37)1.974

or Q = 233(H - 46.62)1.974 e in which Q is the river discharge in cusecs and h

and H are tile e e stage in feet above staff gauge zero and A.O.D. respectively. 3.4.5.

Velocity Distribution at the Cableway Section

In the application of several bed load formulae assumptions have to be made concerning the uniformity of flow conditions within the section.

Fig. 3.4.f. shows how mean velocity varies across the

cableway section at four discharges.

It can be seen that as

discharge increases the influence of the deeper part of the section near the

le~t

bank becomes more noticeable.

At high discharges stage changes rapidly and few measurements of more than two velocities in a vertical were available.

Fig. 3.4.g.

shows four measurements of velocity in a vertical 130 feet from the left bank peg, approximately mid-cllannel, at a discharge of 12,200 cusec (h

e

= 8.73

ft.).

According to the Pral'.dtl-Von Karman

theory the velocity distribution is given by the equation:-

where V is the velocity at a height y above the bed, k is the y s roughness of the bed and

~.

~

is the friction velocl ty equal to

D is the water depth and S

e

is the energy-surface slope.

Taking D • 10.35 ft. from the cross-section profile, fig. 3.3.c., and S

e

~

-3

1.000 x 10

stage, fig. 3.4.d., suggests that ks

u.

= d65

MULLER (1948) take ks

from the graph of energy-surface slope against becomes 0.577 ft/sec.

EINSTEIN (1950)

of the bed material, while MEYER-PElER and

= d 90 ,

where d

65

and dgo are the particle

sizes than which 65% and 90%, respectively, by weight of tho sediment is finer.

From the particle size distribution curve of

the material composing the bed of the River Tyne near Bywell (fig.3.5.e.) d

65

= 0.196

ft. and d 90 43

= 0.350

ft.

10 9

8

6 Mean

5

ve/ocit y

(It/sec)

4

3

2 800 CUStZc

,"

,, ,,

", ,,' ", ,,' ," ,,,

,

I

,

I

I

! ': I"

:~ ~

Height

55

A.O.D. Ct t)

45

o

Staff gouge

Fig. 3.4.'.

50

100

DistonctZ

trom left

zerc: 46'25

Velocity

't

150

200

250

bonk pe'd (ft)

A.D.D.

dis.tributions

at Bywell

c(Jblewoy section

300

surface

wat~r

6 Height above bed,

y

observed velocity

distributIon

5

(f t)

. , theoretical -- ve loc /' ty di $tributions

o,~~~~~~~~==~--~--~~--~--~--~ o

5

3

:2

Velocity,

Location:

130 ft

Stage: 8'73 It

frofTI

above

(eft

bank

staff

vy

6

7

9

' (It/sec)

peg.

gau~e

zero(46'25 ft A.OD.)

Disch arge = 72,200 cusec. Dept h, 0

:

10·35 ft.

Energy-surf ac e

Prondtl-Von

slope. Se: 1'000

Karman

where u.=J90S

e

Law:-

V

Y

C'577

X 10-3

= 5'75u*log10 (30ylks ftls.ec.

ks /s the roughnes.~ height,

Fig.3.4.t;}.

Observed and

)

~5

theoretical

=0'196

ft

vertIcal

or

d 90 --

velocity

0'350 ft •

diStributions.

10

,,

The resulting theoretical velocity distributions for each value of k

are

s

&~own

in fig. 3.4.g.

The discrepancies between the

theoretical

~,d

observed distributions indicate the extent to which

river banlw

~~d

bed configuration offer additional resistance to

flow. 3.4.6.

Tractive Force Distribution at the Cableway Section

The average tractive force acting on the bed in a depth D of water with an energy-surf ace slope of Se is 8 iven by (CHOW I 1959) where

"0

=

Y f is the specif ic weight of water.

Y fDS e

The

tractive force acting on the bed in a given flow is thus proportional to the depth of flow above the bed.

Fig. 3.4.h. shows the

theoretical tractive force distribution across the section at a discharge of 10,850 cusec.

The measured velocity distribution is

also shown and illustrates that the actual tractive force distribution is modified by the shape of the cross-section. 3.5.

Bed Material of the Reach

A detailed sediment sampling programme was necessary for the comprehensive description of the material which constitutes the bed of the River Tyne at Bywell.

As will be described Inter in

section 4 properties such as particle size distribution nod specific gravity have a direct application in the determination of the critical conditions of movement, sediment discharge etc;

other

properties such as particle roundness, shape and petrography are mainly of intarest to geologists and sedimentologists but have been included to provide a complete description. 3.5.1.

Met~ods

of Sampling and AnalYSing River Bed Material

The sampling and analysis of river bed sand presents little difficulty, since only small quantities are required to produce n representative sample.

Several instruments, which may be grouped

into three classes of drag-bucket or scoop, vertical pipe or cylinder, 44

0'8

mean

Vi' OCit> 6

,.---- ..... .....

Mean

overage forc

~

Y,

.

tructi ve

on

R

b

S

. bed' 0'6

e

I

vel ocit y (ft/sec)

I

<4

I

s.tress 2

O·~

I

Ublft )

I

I

0·3

I

I I

2

I

I

I

- 0'1

I

I

I UL------~--------

____________________________________

~~----~O

6

He ;ght55

A.O.O (ft)

~5

~o

o

50

700 Oi st once

Staff gouge zero:

Fig.3.4. h .

Tractive

~6'25

200

'50

from

left ban k

pe g

250

(ft)

It A.a.O.

force

distribution

at

Bywe/l

cab/eway

section.

300

and clam shell, have been designed for this purpose and are described in 3.eport 14 of the UNITED WATER lESOURCES,

S~Y~ __'ES

SUBCOMMIT~J~E

mr

FEDERAL INTER-AGENCY SEDIMENTATION.

COMMI'J.'TEE ON

However, -;:he wide

range of size and shape and the variable areal distribution of particles in a gravel-bed river makes sampling considerably more I' is probably for -:11is reason that there exists

difficult. compara~ively

little recorded information on such rivers.

There are basically four methods for sampling and analysing coarse sedimant:1)

Volumetric sampling and sieve analysis by weight

2)

f~real

sampling, measurement of a representative diamoter,

and frequency analysis by number 3)

Areal sampling and sievo analysis by weight.

[~

mochod

used by IANE and Cf.. ~~LgOJ:T (1953) in which all stones exposed in an area of one square yard were collected and sieved as a bulk sample. mo~hod

The main disadvantages of this

are its inapplicability when patches of sand are

present and the difficulty in finding a representativQ and reasonably small sampling area, particularly in very coarse material. 4)

Photography of a small area of the bed either through a grid or with a measuring scale placed on the bed.

Representative

diamoters of the surface particles can then be estimated from the photograph and a frequency analysis by number plotted. Methods I and 2 were used in the sampling investigations ai: Bywell and are described in greater detail in sections 3.5.3 and 3.5.4. All of these methods raise the problem of ascribing a representative diameter to a sediment particle.

Despite attempts

to sl,;andardise nomenclature by authorities such as the I.!vIER.ICIUI GEOPHYS ICf..L

lliHON

(1947) there are several dimensions in conunon usage:45

d d d d

1 2

3

· major axis intermedia;;e axis

three mutually perpendicular axes

mino!" axis

• arLhmetic mean of major, intermediate and minor axes r •

de

geometric mean of major, intermediate and minor axes

d

nominal diameter, i.e. the diameter of the sphere of the

n

same volume as the sediment particle d

s

sieve daimeter, i.e. the length of the side of the square sieve opening through which the particle will just pass.

d

w

sedimentation diameter, i.e. the diameter of "i:he sphere of the same _pecific gravity and the same terminal uniform settling velocity as the sediment particle in the same sedimentation fluid.

For a equal.

perfec~ly ~e

spherical particle all eight diameters are, of course,

nominal

diamete~

has little Significance in sediment

transport but is sometimes useful in discussing the nature of sediment deposits.

Silt and clay sizes arc usually

d~scribod

by

the sedimentation dillmeter which COLBY (1963) has shown to be easily related to the sieve diameter.

~epresentative

diameters involving

any of the three axes of the particle are often used in frequency analysis by number and are discussed in more detail in section 3.4.4. Sieve analysis is the most convenient and most commonly used method of treating most sediment samples;

the grade scalo given in

table 3.5. a. is recommended by the AMERICAN SOCIE'IY OF CIVIJ. . ENGINEEnB (1962) and is based on sediment sizes described by the sieve diameter.

46

Table 3.5.a.

Sediment grade scale Particle size range

Class nama

in Very lal'ge bou Iders LaTge boulders Medium boulders Smnll boulders Large cobbles Small cobbles

160 - 80 80 - 40 40 - 20 20 - 10 10 - 5 5 - 2.5

Very coarse gravel Coarse gravel Medium gravel Fine gravel Very :line gravel

2.5 1.3 0.6 0.3 0.16

-

Very coarse sand Coarse sand Hodium sand Fine sand Very fine sand

- 2040 - 1024 - 512 - 256 - 128 64 -

64 32 -

16 8 4 1.000 0.500 0.250 0.125

Coarso silt silt !"ine silt 'lery fine silt clay Ucdium clay Fine clay Very fine cln.y

1.3 0.6 0.3 0.16 0.08

4096 2048 1024 512 258 128

32 16 8 4 2

2.000 - 1.000

-

0.500 0.250 0.125 0.062

0.062 - 0.031 0.031 - 0.016 0.016 - 0.008

l/Iedi um

Coars~

nun.

0.008 .. 0.004

I I

0.004 - 0.002

0.0020 - 0.0010 0.0010 - 0.0005 0.0005 - 0.00021

---------------------~~----_ _ _ _ _ _ _ _ _ _ _ _L__ _ _ _ _ _ _ _ _ _ _ _ _ _~

For purposes

of

size classification by means of the above table

and in investigations concerning channel roughness and sediment transpor~

it is common practico to describe a particle size

distribution by a single

diamote~.

The arithmetic maan, geometric

mean, and median diameter are thODe most frequently used;

these

measures are applied to frequency distributions by weight and nUlnber in sections 3.5.3. and 3.5.4. diameters aro not equal.

~or

most natural sediments these

This has led to a certain amount of

confusion since in many papers and reports the "mean "diameter of a particular sediment is given without stating exactly which diameter has been measured. 4'1

3.5.2.

Location of Sampling Positions

Severa: factors mate~ial

dicta~ed

the locations at which the river bed

at 3ywell could be samp10d.

Only those accumulations of

gravel expooed at low flows were sampled, since no method for takincr bulk samples from underwater was available.

Examination of the

reach showed that, in order to obtain sufficient samples, gravel deposits upstream and downstream of the test reach would hav0 to be conoidered.

It

was necessary tha.t the sampling positions were

easily nccessible and that the accuDlulations were natuTal deposits. OUring tho extraction of gravel downstream of the test reach nn artificial roadway was const:'ucted along the left bank of the river near BYVlell

:I~ll.

been er:'oneous.

Sampling' of thesa accumulations would thus have The gravel

n(3~r

the right bank became

p~ogressi vely

coarser dovl!lStrerun of section J!C, eventually including boulders of 4 to 5 fC0t diameter.

There are several explanations for the

presance oi these boulders; by

IC!UMBEIN

and LIEBLEIN (1956) have shown

the tileory of extreme values thnt they can form part 0:Z the

normal gravel population of the river.

However, it was considered

that a sample of this extremely coarse deposit would not be representative of the majo:." part of the bed material of the river reach. With these points in mind six sampling positions were selected 0.0

shown in fig. 3.5.n.

The deposits at positions 1 and 2 ere shown

in figs. 3.5.b. and 3.5.c. 3.5.3.

Bul~

S ampl1ng

Few refercnces to the bulk sampling of coarse river bed material could be found in the available literature.

JONES (1959) describes

how nine samples of about 4 cwt. each were taken from a 10 mile rench of a Hcw Zealand river and XETJ,p,:mALS (1967) mentions that samples of 40

t

Scale: 6 inches to 1 mile.

o

''-=

I

1000

I

I

I

2000

Feet HYWI:.LL

.--: ==:--=i:: :~ : ::

~ig.3.5.a. River Tyne at Bywell--Location of bed material s ampling positions.

Fig.3.5.b. Bed material at sampling position 1.

Fig.3.5.o. Bed material at sampling position 2.

I cubic matre each and totalling 90 tons were taken from the HasliAare 2iver in Switzerland. STANDLJ.DS

~l!ST!T~ION

Extrapolation of a graph in the B3ITISH

(1960) publication dealinG' with concTete

aggregates showed that when the maximum size present in substantial proportions is 4 inches then the minimum weight to be talten for sieving

s~ould

be 220 lb.

In order to be representative of the

sediment being transported the depth to which the sample is taken should be equal to the depth of

t~s

arbitrary depth of about twice the 1 foot,

wa~

mOVing layer of sediment. ~oximum

An

size present, i.e. about

considered sufficient in this respect for the bed moterial

at Bywell. 'l'he sampling procedure adopted at Bywell utilised four bins, 14 in. diameter and 30 in.

d~p.

mct~l

At each samp1in5 location n

2 ft. square area of the gravel surface was randomly choson and the

four bins half filled with gravelJ about

~

ovrt. nnd could

in this way each bin weighed

be carried by one person.

ThA total sample,

therefore, woighed approximately 220 lb. and the deptl1 of tIl':: resulting hole was about 1 ft.

Each sample was taken to thG Materials

Testing Laboratory of the Department of Civil Engineering where it was spread on a clean concrete floor, allowed to dry and then Sieved. Sizes up to

i

in. wemmechanically shaken, between! in. and 3 in.

manually sieved and for sizes greater than 3 in. each stone was passed through a specially constructed square opening. TIle weights and particle size distributions of all six samples are given in table 3.5.b. and plotted on logarthmic-probnbil!ty paper in fig. 3.5 .d.

The six s::unplos were combined to produc0 the

composite srunple, no. 7, details of which are given in tabla 3.5.b. and fie. 3.5.e.



o

Ut

....... .,_

N

...

o

..

. . ., -

...

....,

o ;..

'1'-

'1'

N

,

• 1 "

. .=-:-r·. 1. ;

~

~



;

~

o

,

...o

. .. .,

. -... . - .. - : :,. . ...0-,



~

, -l_

.... ..., _

.• -

·

.

·, ~

~ •• ..j

.- +

~

• --,

~

....

.- "

1 '1 •

1 ! 'i't- _.+ ••• -,.. ,..-....... +!.4 , • -t _. , .. , .j. '.' I, .... ,,-i .: t.~ .. ~: '. i !.:"'" .11:, .+~~! •

~......

. o

...o

...

o

...

o

f'

~.j.,

,.

• 1

jl,

" i"1

.,

to

o



...-.. ,- r

.. ·1-

..

1-

'"

t

l-t'

.



1 ,

i

I ....

.,

'tf

•r

;...

..

!.

H

.. ',

.. I

I _.

~,

..

«>

o ;.

... .....

.'

.

""PT' '. !"'

:

l

~_

,

...

.

... ! >;1 ~tlJ . .·e ,I • :~ l~n i: .,..1 ,.L-t- t .;~ tt. !!ifi~1 , .1. lilt ~ II" I ~:; ... '~l .:1 :: .f:! ...... ~j: 11t I ::)1 ':: ; .~ ., I,ii! 1 . '1'

.

• ..• , +

to

WI

o

, ";• 1,1"·· it.:. mjll~' t:t .,,' I' .1",!tJ!1 t· 'Hi 'i • f 1'1, .--+, ,.'.."m' .....

CD

-

~



., ...,

.. -

UI



..,



to -

. ..

..

. . -o

(,

...

Table 3.5.0.

Sieve analysis of bulk samples

-.

. ...

% f lnej,' by weight

Sieve Opening (in)

Sample 1

Sample 2

Sample 3

Sample 4

Sample 5

Sample 6

8

100.0

100.0

100.0

100.0

100.0

100.0

100.0

7

91.6

100.0

100.0

100.0

100.0

100.0

98.6

6

aG.6

100.0

100.0

95.3

100.0

100.0

97.0

5

71.1

100.0

100.0

95.3

100.0

94.9

93.5

4

61.0

100.0

91.9

91.6

100.0

87.7

83.4

3

53.1

99.6

16.1

CS.O

73.2

67.7

76.3

2.5

45.0

97.0

65.5

76.9

62.5

54.5

6'1.4

2.0

40.7

89.7

57.3

59.0

50.9

41.2

58.6

1.5

33.7

79.9

49.7

59.6

40.6

29.1

49.2

1.0

26.4

64.1

41.3

48.9

29.9

20.3

33.9

0.75

22.7

55.5

35.7

43.1

25.7

16.5

33.8

0.50

10.4

44.7

31.0

35.7

20.3

12.8

2"'.5

0.375

15.7

38.0

27.6

31.0

17.1

10.9

23.7

0.250

12.9

30.9

24.0

26.2

13.6

9.2

19.8

0.188

11.3

26.8

21.7

23.1

11.5

8.5

17.,1

0.125

9.5

22.1

19.9

20.4

9.4

1.9

15.2

0.0945

C.G

19.9

19.1

19.2

8.4

7.7

14.1

0.0472

6.1

15.2

17.5

15.9

6.4

7.3

11.7

0.0236

3.2

8.5

12.5

9.G

4.4

6.2

7.6

0.0118

1.3

2.7

3."

2.9

1.8

2.6

0.0059 Sample Woi,ht (lb)

0.5

0.81

0.7

0.0

0.8

0.8

263.5

266 6 •

187.4

275 • 7 1

COmpositE Sar.tplo 7

I

2.5 0.7

1

250.0

263 3 1 •

i

1

1504.5

i

The 65% and 35% finer by weight sizes of the gravel extracted at Bywe11 between 1960 and 1962 were given by the company concorned as 1.50 in and 0.19 in, respectively. From the size classification table 3.5.a. and the particle size distribution curve of the composite sample, fig. 3.5.0, it can be seen that about 30% by weight of the bed material consists of cobbles and about 50% by weight is in the medium coarse to very coarse gravel range. 50

I.

I I

t

;

In order to describe adequately the particle size distributions in a quantitative manner it was found necessary to consider measures used in the field of sedimentology.

It is recommended practice in

this field (r:lUMBEIN, 1934 and IHl'.1AN, 1952) to describe particle size in Cf' (phi) notation, where


Tables are available

(PAGE, 1955) for the rapid conversion of particle and sieve Dizes to phi-notation, and vice versa.

FOUC (1966) has recently reviewed the parameters often usod to descri.be sediments.

Some of the moasures were used directly

in the application of bed load formulae to the reach (section 4), while others, such as sorting and skewness measures, wore included because t!ley are characteristico closely associated with sedimont movement and deposition.

Tne following measures were calculated

for the size distribution of all samples, including tho compooite sample, ruld are given in table 3.5.c. d

a

:

Ari~lmetic

mean diameter, which describes the centre of

gravity of the distribution when size is plotted to an arithmetic scale.

It was obtained by the method of

moments using the mean sizes of 10% ranges. d

g

Geometric mean diameter, corresponding to the centre of gravity of the distribution when size is plotted to a logarithmic scale, or in phi-notation.

It is equal to

the phi mean diameter, l-ilf, expressed in inches McCAMMON (1962) gives:r,fCyl

= (CP 5 +

+········ ...+

'Pl5

51

Cf' 85

+cp

95>jiO

CPUS' etc. are the phi size. than which


where

5 J 15 etc.

d

50

~

by weight of the sediment is finer. The size than which 50% by weight of

: r.fedian diameter.

the sediment is finer.

When expressed in phi notation

it is termed the phi median diameter, Md cp • o~

: Geometric, or logarthmic, phi standard deviation, and is a mBaSUre of the spread or sorting of the distribution. McCAMI«>N (1962) gives:-

= ( CP3

oep Q'Cf'

+ eplO + <4'20 + 'P 30 - 'F97 - 1f90 - Cf'80 - Cf'70>/9.1

Phi sltewness measure, which describes the extent of departure of the distribution from the log-normal distribution Q'Cji

=

=0

Q'Cj)

(Mcp

-

Mel, >/ocp

for a symmetrical distribution

0< 0''1' < 1 for a distribution skewed towards fine sizes -1 < O''f'
: Phi kurtosis measure, which represen1B the peakedneas of the distribution.

~


~'f'

Table 3.5.c.

-

q>

95) -

oj /oq>

0 for a normal distribution

~'1'

> 0.65 for a distribution lass peaked than normal

~~

<0.65 for a distribution more peaked than normal. Descriptive measures of bulk samples d

Sample number

(in)

(in)

SO (in)

ocp

1

3.15

1.63

2.82

2.10

0.38

0.79

2

0.60

0.39

0.84

2.21

0.33

0.59

3

1.75

0.63

1.50

2.60

0.48

0.63

4

1.56

O.GO

1.0e

2.55

0.34

0.64

5

1.93

1.13

1.99

1.98

0.41

0.76

6

2.38

1.24

2.35

1.94

0.47

1.40

7

1.97

0.88

1.55

2.37

0.36

d

a

i

g

d

I; ,

I

~~

Q''1'

0.74 !

II I

! I I

From the above table it can be seen that, while de and d correspond fairly closely, d

g

is always smaller;

50 the need for

specifying exactly which mean diameter has been measured is evident. All distri buttons are skewed towards the fine sizes and most nre

slightly less peru
BLENCH (1952)

found that nearly

all river bed sands exhibit a log-normal distribution.

As is Dhown

by the S-shaped curves of figs. 3.5.d. and 3.5.e. and the values of in table 3.5.c. this is not so for the bed material at Bywell.

It is

probable that at high flows fine material in the bed will go into suspension and it seems likely, therefore, that the bed material may then approximate to a log-normal distribution.

With phi standard

deviations varying from 1.94 to 2.50 the sediments would be dascribed in sedimentological terms as "poorly sorted" (FOLK, 1966). 3.5.4.

Areal Sampling

A procedure for sampling coarse river bed material involvine the collection of a random sample of particles from the surface bed has beGn proposed by WOLMAIT (1954).

As will

be

of

tho

seen later, aroal

sampling methods based on this procedure require less effort and equipment 8I."1d produce samples more amenable to shape and roundnoss analysis than bulk sampling methods.

It was decided, thereforo, to

supplement the six bulk samples described in section 3.5.3. with areal samples taken from the same locatiOns. Several methods can

be

used to obtain the areal sample and it

was decided to test each method at sampling positions 1 and 2 to determine which produced the most consistent results in the most convenient way.

The methods tested were as follows:-

1.

3 ft. line transect at right angles to the direction of flow.

2.

5 ft. line transect at right angles to the direction of flow.

3.

7 ft. line transect at right angles to the direction of flow. 53

4.

3 ttl line transect parallel to the direction of flow.

5.

5 ft. line transect parn11el to the direction of flow.

G.

7 ft. line transect parallel to the direction of flow.

In theso methods a length of string, marked the necessary length, was stretched in the appropriate direction from a randomly chosen point on the bed.

All the stones exposed on the surface

of the bed and over which the string passed were collocted. 7.

9 in. x 9 1n. quadrat.

8.

U! in. x 12 in. quadrat.

9.

IG in. x 18 1n. quadrat.

In these methods a square of the appropriato size was marked out around a randomly chosen point on the bod.

All stonos

exposed on the surface within the square WilrG collected. 10. Paced grid This wns

the method '..lsad by W,)I...Mh.N (1054).

A grid was pacoC:

out .such that the number of stonos taken from tile intersoct:t.ons of the grid totalled a predetermined number;

for the purposos

of testing the methods 40 stonos were collected.

Subj3ctivity

in sampling was suppressed by refraining from looking at the bed as each pace was made and by taking the required stone from undor the tip of tho toe of the boot. Dmall particle sizes cannot be measured in the field so an arbitrary minimum size of

1

in. intermediate diameter was assumed.

Three sampleo were taken by each 01 the ten methods at posi tiona I and 2.

Each sample was weighed in air and in water, and the

number of stonos counted.

It was

~len

a simple calculntion to

determine the nominal diameter of the mean volume stone for each sample.

This measure was of little practical significance but

served as n menns of comparing sampling methods. positions 1 and 2

is given in table 54

3.5.d.

The r09ul ts for

~able

3.5.d.

Comparison of areal sampling methods Section 1

Number of Nom. dial Average Number of Nom. dial particles of mean of threo particles of mean volume samples volume particle particlel (in) (in) (in)

Method number

1

2

3

4

5

6

7

17

3.41

26

2.88

21

3.32

28

3.42

26

3.97

27

3.89

34

4.20

45

3.21

I

1.30

29

1.65

30

1.54

29

1.64

43

1.68

43

1.80

44

1.67

20

1.55

19

1.43

19

1.74

25

1.70

32

1.51

4.08

16

4.26

2';-

3.28

25

3.17

24

3~Z6

34

1.50

29

3.38

48

1.65

28

3.28

40

1.86

31

3.51

42

1.84

20

2.91

17

2.83

14

3.03

, I

I

!

40 40

3.66

3.23

3.39

,

2.92

II

33

1.35

30

1.44

II

36

1.47

57

1.38

I

50

1.41

3.28

3.10

I

!I

45

1.57

3.32

I

II

98

1.47

I

81

1.64

Ji

82

1.75

40

1.72

3.55

,

3.95

I

3.11

I!

I

3.07

3.46

37

40

I

3.73 t

22

14

60

10

I

1.68

3.52

42

I

3.76

22

14

35

I

3.20

1.75

3.79

22

8

I

19

29

20

9

Section 2

3.34 3.67

I

3.30

I

I

I

'!

. i

'\

3.52

d

40

;1 40

I

U

I

55

1.63 !

1.88

Average of threE samples (in)

1.50

1.61

1.74

1.57

I 1.57

1.78

I 1.42

1.47

I

1.62

I Ij I ,I I

1.74

I ,.,

The main disadvantage of both the line transect and quadrat methods was the difficulty in determining which stones were exposed on the surl ace of the bed.

In the latter method, especially, many

stones wore taken from just below tha surface resulting in the inclusion of a number of small stonss;

this is reflected in the

results of methods 7, 8 and 9 in table 3.5.d.

No differenoe could

be detected in taking line transect samples at right angles to or parallel with the direction of flow.

The paced grid method shows

less variation than the other methods and has the advantage of greater area of coverage and constant sample size.

It was decided I

therefore, to use the grid method, selecting 50 stones at each of the sampling positions to give a compoSite sample of 300 stones. If the sediment particle is spherical, or nearly spherical, then each of the diameters listed in section 3.5.1 can be considered aqual. Since the bed material at Bywell contained mdny non-sphorioal particles it was first necessary to determino which diameter was the most consistent

measur~

of stone size.

It was decided to measure tho

nominal diameter (d ), sieve diameter (d )' and the major (d ), l n s intermediate (d ) and minor (d ) axes of 75 stones whose nominal 3 2 diameters raIl300 from 1.15 to 7.19 in.

The arithmetic mean Cd ) r

and geometric mean (d ) of the triaxial dimenSions of each stone were e also calculated.

From this test it was found that on average d

2

was

2.12% larger than d , while d ,d and d were 2.47, 6.40 and 8.19%, n res respectively, smaller than d • n

GRANT C195S) have used d

2

aD

BLENCH and QURESHI (1964) and

tho stone size.

In the sample of

75 stones, however, the percentage differences of d

displayed more scatter than those of d

r from dn •

2

from d

n

The arithmetic

mean of the triaxial dimensions, dr' would thus appear to be a more consistent measure of size than the intermediate axiS, d , alono. 2 55

Accordingly, the major, intermediate and minor axes of each stone of the six areal samples were measured and the arithmetic mean of these dimensions taken as particle size. stone was also recorded.

The weight of each

Particle size distributions by number

frequency are given in table 3.5.f.

~~d

figs. 3.5.f. and 3.5.g.

Particle size analysis of areal samples

%finer

d

r (in)

by number

Sample 2 Sample 3 Srunp1e 4 Sample 5 Sample 6 Composite Sample 7

Sample 1

7

100

100

100

100

100

100

100

6

92

100

100

100

100

100

99

5

S4

100

96

100

98

94

95

4

72

100

84

92

90

90

8a

3

50

96

60

72

68

56

68

21-

36

90

54

62

44

36

54

2

24

80

42

50

30

24

42 I

1;

4

1

0

52

24

28

14

16

4

0

0

0

0

I

I

I

0

3.5.5.

II

I

Comparison

0

0

0

0

J

of

0

23 2

I !' )

0

Bulk and Areal Sampling Methods

BUlk sampling is a means of obtaining a particle size distribution by weight of the sediment composing the river bed to a certain depth; samples obtained by areal methods are analysed on a number frequency basis and represent the areal distribution of sediment sizes on the surface of the river bed. The main disadvantage of the bulk method when applied to coarse sediments is that each sample tlUSt weight several hundred pounds in order to be representative.

Considerable effort and eqUipment,

often unavailable, are required to collect, dry, sieve and waigh each sample.

Areal methods enable many samples to be taken by one

person with simple equipment in a oomparatively short time, all measurements being recorded in tho fiold.

Each areal samplo is

representativo of a far larger area than a bulk sample and can be 57

¢

0

....

.

.. ..

.. ..

...

!D

c.

....C" C,

'"

... 0>

....

.

?

•01» N

III

.

...

...

III

<;

..

.. C

~

..,...

....

.

•O

C-

.II

0

0

0

g

.

'" ... 0

0

0

IS

.

..

0

0

0

.. I r<::)

0

p 0

t-

r I

--..r-.~

--

Fj~..L5...g.

F!.D.rti.cl ot or

?

I:

;ze

a ll

I

II r

..

! I

------ ------

L..:

1 ....

o

..

o

. o

...

o

.. o

...,

..... ....



.......,,.

.



..

obtained from underwater if necessary.

Probably the major

limitation of the areal method is that it has a lower limit of particle sizt3 which can be sn:.1pled.

The absence of finas, however,

results in a good approximation to a log-normal size

dist~ibution

(fig. 3.S.g.). In the comparison of th'S size distributions of the bulk and areal samples it should be

rer~~bered

by quito different procedures.

~~le

that they have been obtained bulk samples hava been sieved

and weighed, while the average of the trixial dimensions of the particles of the areal samples have been measured and plotted on a number of Irequency basia.

Table 3.S.g. shows that tho medinI'.

diameter of the areal samples, ndSo' is always laraar than tho median dinmeter of the buIlt

s~les I

dso '

Comparison of median diameters of bulk and axenl samples

Table 3.5.g.

Sample number

d

ndSC (in)

~'d.Sot50

SO (in)

1

3.00

2.82

1.01

2

1.4S

0.64

2.27

3

2.34

1.50

1.56

4:

2.00

1 08

5

2.66

1.99

6

2.81

2.3S

7

2.34

0

,

1.55

I I I I

1.85 1 0 34

1.20 1.Sl

I

hrea1 samples could possibly be of considerable use in tho estimation of the bed roughness coefficient for use in hydraulic formulae Duch as the Manning fortlU1a o

EINSTEIN (1950) Buggestod

that the effootive roughness size of a sediment mixture should be d

6S

' the size than which 6S%

MEYE..'1-PET::?

and

Mlli.LER

Qy

weight of the

sed1~nt

(1948), in cO:ltrast, proposed d

representative gravel size for roughness estimation.

is finar; SO

os the

Figs. 3.5 h.

and 3.5.i. show ndSO plotted against d 65 ond d 90 raspectivoly. 50

0

1.88.~ 5





~5 of



bulk

••

sample (i n.)

2



oL-____

~

____

~

______

~

____

o

~

____

~

______

Fig

3.5.11.

dIameter

Relation~hip

____

~

____

_ L_ _ _ _ _ _L __ _

3

2 Median

~

of areal

between

sample, nd50 (In.)

d

n 50

and

~

7



6

2'22

d gO

n

d

50

-

7-22

5

• 4

d ~,

90



bul k



Sample (in.)

3

2

OL-____

~

_____ L_ _ _ _ _ _L __ _ _ _

o

~

____

~

2 M ed/an

Fig 3.5. i

______

~

____

~

3

between

~~

n

d

n

d

50

50

( ; nJ

and

__

~

5

4

diameter of areal sarnple/

Rtl at/onship

_ _ _ __L_ _ _ _

d

90

While some relationships are indicated, the number of samples and range of size data are insufficient to enable definite oonclusions to be drawn.

It would seea, however, that areal samples could be

used to determine the representntive roughness size of a sediment The following table shows how nd50 could possibly bo

mixture.

taken to equal d Table 3.5.h.

65

, the roughness size suggested by Einstein.

Possible use of areal samples for roughness sizo estimation

.....

% by weight of

Areal sample median dial d 11 50 (in)

Samplo number

bulk sample finer than nd

..

1

3.00

52.0

2

1.45

78.0

3

2.34

63.0

4

2.00

69.0

5

2.G6

65.0

6

2.81

63.0

7

I

2.34

I

5C

I

65.0 i

There is, in feet, no need for extreme accuracy in deiining the representative roughness sizG of a gravel surface, since it is known that

~n1n

roughness on a plfu.e bed (representod by the

Manning coeffiCient, for instance) is proportional to the sixth root of this sizo.

Hence, if the gravel size is overestimated by

100% then the roughness coefficient itself will have been overestimated by only 10.5%. 3.4.6.

Particle Shape and Roundness

Although there are no provisions for the inclusion of measures of particle shape and roundness in any bed load formulae they are most probably important factors in the consideration of bod formation, ini tiation of movement and sediment transport (BLENCH, 196Gb). was decided, therefore, to record these characteristics for each particle of the six areal samples tru{en from tho surface of tho 59

It

river bed at Bywel1.

Few reierences

wo~e

found in civil engineering

Ii terat'..ll'o on tho measurcment of these propertios

(BaITrS1~

S'. :'AEi)1U1DS

INSTI'...'J:::;:~)IJ, 1950, and MACKAY I 19(5) and i t was necessary once again to refe:;:- to mansures devised by sedimolltologists. The \vo"4d "shape" describes t:::.o fOl'm of the particle wit:lOut reference to the sharpness of its edcres.

To measure this

charnctexistic it was decided to use the KRUMBEIN (1941) approximatior. 1,'!Jillm~LL

to the

(1935) definition of sphericity as the cube root of the

ratio of the volume of the circumscribing sphere. apprmrimntcd by Krumbein as

3J (d2d3 )/

d

2

~-,

This is

where d , d , and d 2 1 3

are the major, intermediate, and mino14 axes, respectively, 01 the 'rable 3.5.i. gives the distribution of sphoricitie:J

particls.

and average sphericities of eac!l areal sample and of tho composite sample, numbal' 7. Ta.ble 3.5.i.

Distribution of particle

Sample Number 0.300.3D

1

-

2

1

3

-

4

I-

5 G

7

,

-

I

1

1

f

Sphericity range 0.50- O.SO- 0.700.7f) 0.59 0.69

0.400.49

0.800.89

"' Il.verage 0.90:- 8phoric1. t· O.Da

-

5

14

19

9

3

-

12

22

12

3

1

5

22

19

3

-

2

11

20

13

2

2

14

16

14

2

-

13

22

6

-

19

2

4 2

,

in areal samples

sp~ericities

I

I

14

69 "

t 121

!

1

7

I 74 I

I

I,I

0.C3

O.SG t

I, I

I

I

:\

O.GG

O.SS 0.63 0.64

0.65

I'

III conjunction with the sphericity measure each particle

was

classified according to the four types proposed by ZINGG (lD35) as follows:-

60

I

;'2

Class

d 2 /d l

d3

Disc

~'2/3

< ?/3

Gphere

~2/3

?- 2/3

Blade

<2/3

< 2/3

i?od

<2/3

~2/3

Table 3.5.j. gives the distribution of shapes in each of the samples Shape classification of areal samples

Table 3.5.j.

shape class Sphere Blade

Sample number

Disc

1

27

4

12

7

2

34

5

6

5

3

33

9

5

Zing~

Rod

3 I

31

4 5

29

6

31 185

7

The word

11

10

4

II

I

S

i

5

14 7

I ! I

!

,

4

3 4

I

40

,

49

26

,

roundness " describes the shnrpness or radius of

curvature ot the edge of the particle and reflects the aQrasion resulting from the transport of the particle along th\J river bed. POvm~

(la53) proposed a new roundness scale for sedimentary particles

but the visual method of KRUMDEIlT (1941) has proved to be the most convenient for many workers in the field.

Krumbein defined

roundness as the ratio of the average radius of curvature of the edges and corners of the image of the particle to the radius ot the inscribed oircle and produced

0.

chart (fig. 3.5.j.) snowing

calculated values of various particle outlines.

Each particle of

the areal samples was classified by means of comparison with tZle chart;

table 3.5.k. gives tho distribution of roundness within each

sample and that of the composite sample.

61

-,

(]

o .8 Fil'?;. 3.5.j. Chart f'or visual estilP.ation of particle roundness. (KRUMBEIN, 1941-)

Distribution of pa:;.·ticle roundness in areal srunples

Table 3.5.k.

Roundness class

~ample ~umber

0.2

0.3

0.4

0.5

1

1

2

5

S

2

-

-

2

3

-

-

3

-

-

'I

5

G

..

4

-

5

-

6

1

7

,i

,,

I

I

2

I

I! :

2 17

I

0.6

0.7

0.8

0.9

Average ftoundnes::

6

4

2

0.53

4

21 I 15

11

13

4

0.68

9

10

21

4

3

0.65

5

5

0.67

4

3

C

I 45

!

I

I

11

15

II I

I I

16

15

I

!

17

! i

15

I 96 !

I

,

Btl

!

I

5

3

1i 35

I

20

O.G;'i·

I

I

0.64

,

0.64

i

In tables 3.5.i and 3.5.j. the distributions among tho shap':; classes of all samples follow much tho some pattern;

the largo:;,-

differences in the roundness distxibutions of table 3.5.k. arc probably due to subjectivity involved in the use of the visual chart. Plots of t!le sp:lorici ty and

~ess

distributions of the cor;lpoa1 to

sample on arithmetic-probability paper yielded almost straight lines, indicating n no::.-mnl distribution of these properties in tho rtvor bod material. Shape plays an important part in the formation of the bad in gravel-bed rivers (lANE nnd CARlSOn, 1954). reach of the

Ziv~r

3urfac~

Examination of the

Tyne at Bywe1l revealed that the bed surface

partic10S were arranged with their flatter faces sloping upwards in a downstream direction.

This imbricated arrangement, which occurs

in most rivers of predominately disc-shaped particles (from tablo 3.5.j.,

611~

of the surface particles at Bywell are discs), is tho

result of the tendency of these particles to assume their most stable position under tho forces exerted by the flow of water. particles are usually washed away

fro~

Finer

the top of the largor,

flatter particles and accumulato between, underneath, or in the oddy immediately downotream of them.

This action leads to a form of 62

armouring or p:;.,'-otection of the bed sUrfaco;

such "bed pavements"

have been observed in rivors in Russin (LELIAVSKY, 1955) and Canada

(ImT,IIi<:~IALS,

1967).

A gravel bed oL flat-shaped

is

pa~icles

~herefore

ablo to

resist much higher shear stresSOD than a bed of uniform-sized spherical particles.

The use of a tractive force formuln such as

equation 2.2.a (SCHIELDS, 1936) on tha rivar reach at Bywall is thus likely to underestimate the critical shear stress required for the initiation of movement for two reasons:-

i)

the coarser particles

of the bad tend to occupy the surface layer nnd i1) no provision is indluded 1n tho formula for the relativoly high stability of d1soshaped particles in nn imbricated position.

The influence of shape

on the susceptibility to movement of sediment particles at Bywoll was clearly demonstrated in the following simple observation carriod out at sampling position 1 (fig. 3.5.a). from as

nen~

Ten stones were selected

mid-chennel as possible, their triaxial dimansiona

measured and then they were replnced on the bed with their orientation marked by yellow paint.

The arithmetic menn of the triaxial

dimensions varied from 3.1 to 0.4 inches.

After the passage

of a short flood of about 17,000 ousec it was noted that, while the smaller disc-shaped particles had remained stationary, most of the largel' stones had moved at least some distance;

two of tlle

more spherical particles, about 5 inches in diameter, had travelled over 100 feet. The influence of shape on the rate of transport of sediment as bed load is not so immediately evident.

It is possiblo that

particlos moving as contact lond, i.o. in more or less continuous contact with t11e bad, tond to maintain their most stable orientations, with the result that flnt particles travol more

63

slowly

thfu~

spherical particles of the same size.

Disc-shaped

particlos, however, have a lower settling velocity than spheres so that flnt, snltating, particles probably travel further bafore being deposited.

Saltation load is relatively unimportant in

fluvial sediment trnnsport

(KALnrs!~,

1942) and hence it mny be

expected that bed load formulae applied to the Bywell reach will overestimate bed load discharge (assuming that the formulae will predict accuratoly bed load discharge for spherical particles of the same size). Petrographic Analysis

3.5.7.

A

petro~ca~lic

carried

o~t;

Table 3.5.1.

analysis of onch of the areal samples waG

tabla 3.5.1 gives the results. Petrographic analysis of areal samples Sample !lu;nbor

Rock typo



~I

1

2

3

4

5

~bndl3tOl1e

33

3S

24

28

21

2-/

169

56.3

~it!Jo9tona

2

-

-

3

2

-

7

2.3

preywacke

4

3

9

6

15

15

52

L .3

1

-

-

-

1

0.:;

1

-

-

-

-

1

0.3

-

-

1

0.3

4

1.3

-

2

0.7

-

10

3.3

5

1.'1

B

2.7

1

0.3

~inte14

-

Ironstone

Ganistel' ~hert

1

-

-

1

1

2

~uartzite

-

2

-

/Volcanic ash

2

3

-

-

2

3

1

1

-

1

2

ole rite

1

-

2

abbro

-

-

1

6

1

11

II -

-

-

-

salt

f

~ndeSit. :lyolite

I

1

2

I

5

6

-

-

rsels1ta

-

-I -

-

Syenite

-

1

~ranite Phyllite

1

- i I

I

-

I

II !

-

I i

I

,

.I.

I

-

1

f'

-

- I 3 I I - I! .1 5

-

I -

I -I - -

-

i

I':1

~I I"

II ·1-,

1

f

I

!

!

%

.

3f':" 11 1.3 1

j

0.3

1

-)

I

; 1 ,I

.!

1

0.3

1

0.3

1

0.3

,I

1

0.3

!

I, !

I

I.. s would be expected the sedimentary rock, sandstone, form c major part of t!'lC bed population;

its presence is reflected in the

preponderance of particles in the Zingg classification of disc-shaped The presence of a considerable number of andesite

(table 3.5.j.).

and graywacke particles which

havo originated from parent rockD

r.~st

in the Lalee District and the Southe:rn Uplands of Scotland indicntes that much of the coarse bed material of tho River Tyne at 13ywell has been

eroded f:;:-o:n the glacial dl'i1t which forms the banks of the midtlle

and upper :i."Elnches of the Ri VOl" Tyne.

It is not possible to

distinguish bemoen particles from the aivers North and South Tyno. The sparsity of limestone in the bed indicates a high solution load. 3.5.8.

Specific Gravity

The specific gravity of the bod material, required in section 4 for the application of bed load formulae to the reach, was obtaincd by weighing a srunple in air and ia water according to tho method described by the BRITISH

STAND.~1DG

INSTITUTION (1960).

that the specific gravity of thG sediment, S

s

It was

foun~

= 2.60, IJence the

3 specific weight, 'I = 162.3 lb/ft • s The specific weight of a fluid-sodiment mixture is equal to:-

Y - C (y -'V) s s s f

whGra

'If'

'V

s

respectively and C

S

fluid.

are the specific weights of the fluid and sediment, is the concentration by weight of sediment in

L~e

AS9uming the specific weight of water to equal 62.42 lb/ft

3

and the maximum concentration of suspended sediment to bo 1500 p.p.m. then the maximum value of the specific weight of the water-sediment 3

mixture can be calculated to be 62.47 lb/ft •

The differancG

between the specific weight of the clear water and that of the mixture is less thnn i%;

it was decided, therefore, that tho

specifiC WGight of the river

wat~r

3 to 62.42 lb/ft • 65

at Bywell would be assumed equal

3.6.

Conclusions

The longitudinal bed profile of the River Tyne at Bywell exhibits the undula:;ory form characteris-;;ic of most rivers with gravel-paved beds.

This "pool-bar" configuration, while providing convenie~1t

control

sec-~iO:1S

the

selec~10n

for cableway gauging stations, greatly complicated

of a suitably straight and uniform test reach.

Twenty three cross-sections in the

!

mile reach which included the

cableway section at Bywell displayed considerable variations in shape and it was found impossible to determine an average bed slope over the length of the reach.

Soundings showed that a meandering

thalweg is superimposed on the relatively straight length of river. Examination of tbe horizontal and vertical velocity distributions at the cableway section showed that this complex bed configuration offers resistance to flow in addition to that of the particle roughness of the bed and affects the distribution of tractive f.orce on the bed. The inst!"Ument and procedure developed for the measurement of the water surface slope by a single observer proved successful although a recommended improvement would be the simultaneous measurement of water level at each end of the reach by two observers. At low flows the water-surface and energy-surface profiles above the cableway are fairly flat, becoming steeper downstream of the cablewaYi

at higher stages the upstream and downstream slopes

become more nearly equal.

The geometric mean of the two surface

slopes was taken to represent the actual slope at the cableway section and wan found to vary from 0.2 x 10-3 1.2 x 10 at just below bankful stage.

3

at low flows to

Good linear correlations

ware obtained between the logarithm of stage above a given datum and the water-surface and energy-surface slopes.

No improvement in

the correla-::ion could be detected !Jy the introduction of the rate of chango of stage into the reg:;:oessioi:i analysis.

SG

There are, at present, no standardised methods for the sampling and analysis of coarse river bed material;

recent papers by

CAMPBELL and C[J)DIE (1964) in Haw Zealand and NEILL and GAIAY (1967) in Canada have emphasised the need for systematic collection of river da"i:a.

The two basic methods of sampling, bulk sampling and

areal sampling, were both car:;'4ied out on the River Tyne at Bywell. Six bulk samples, with a total weight of 2/3 ton, were collected and sievedj

about 75% by weight of the bed material can be

classified according to the Al\1E...'UC1.Il SOCIETY OF CIVIL ENGIIlEEl1S (19(32) grad~

Gcale as cobbles and coarse gravel.

The particle size

distribution curves are not log-normal, being skewed towards the fine sizes.

A certain amoun-;; of confusion has been caused ill

sediment transport studies by the large number of measures usod to describe a size distribution.

In order to faciH tr.te compn:dson

all of the following properties have been calculated for

sample collected at Bywell:-

eac~l

bulk

arithmetic mean diameter, geometric

mean diameter, median diameter and measures of

sortin~,

skewness

and kurtosis. Three methods of obtaining areal samples of tho bed material were tested;

sUl~ace

the most convenient was found to be the paced

grid method suggested by WOU1t.lT (1954).

Particle sizes were

defined by tho arithmetic mean of the triaxial dimensions and plotted on a number frequency basis. For the description of particle shape the sphericity

T~asuro

of KRUMBEIE (1941) and the ZINGG (1935) classification were used, since only the triaxial

dimensiol~

of the particles were required.

Shape probably plays an important role in bed formation, initiation of motion, and sediment transport, although there is no provision for the quantitative inclusion of this property in any existing bed load formulas;

it 1s most likely of particular importance nt 67

Bywell whe:oe over 60% of the bed surface particles can be classLlied as disc-shaped.

Roundness was fOU:ld to be most easily lOOasurod using

the viGual Cl1::":--;; produced by K2,JUBIUH (1941). Compa:L'ison of the particle size distributions of the bulk samplos with those of the areal samples indicates that the latter could possibly be used to obtain eGtimates of the representative roughness size of the gravel bed. Areal sampling was found to have several advantages

ove:;,~

bulk

sampling:1)

TI10

equipment and personnel required are minimal;

bul!~

snnpling of coarse mate:dal requires heavy equipmont

!o~

oollection, drying and siaving. 2)

The

n~thod

is quick and Simple, enabling several samples

to be collected and

3,

a~alysed

in a considerably shorter timo.

Samples are representative of larger areas (underwnter, .if necessary).

4)

f~ll

ooasurements are made in the field.

5)

Descriptions of particle shape and roundness are

facilitn~ed.

A pctrog:raphic analysis at the bed surface particles nt ilywell showed thnt, while predominantly sruldstone, much of the matorial originated from outside the Tyne Catchment, and must therefore be the result of erosion of the glacial drift which forms the banIce of the

P.ive~

Tyne for most of its length.

60

Sec~1on

4.

4

Application of Bed Load Theories to the River Tyno at BYV/Gll

The gGncral concept of bed load movement has been discussed in section 2 and t:1C colltlction of data required for the appl1catior. of bed load

t~eories

section 3.

to the Bywell test roach has been detailed in

This section describes the application of the bod load

theories to the River Tyne at rating river

cu~~e,

sta~~

used to

Byw~ll

to determine the bed load

i.e. the relationship between bed load discharge

(or river discharge).

obtni~

~~d

The resulting rating curves are

estimates according to each theory of the average

annual bed load discharge of the 3iver Tyne at Bywell.

4.1.

Determinatiol: of Bcd Load Rating Curve

Almost thirty theories and formulae for the prediction of bed load

dischar~e

Only nir.. c

wore found in the available literature.

of these theories, including tho modified Einstoin method, coulJ possibly be considered suitable for application to the River Tyuo at Bywelli

nevertheless,

consider~ble

extrapolation and estimation

were required by some of the methods due to the sediment

a~d

stroam

flow conditions at Bywell. Each method was applied to determine the bed load dischargo the cableway section at 1 foot intervals of stage

f~om

:::~t

48 ft. to

61 ft. A.O.D. 4.1.1.

Proliminary ConSiderations

To avoid unnGcessary repetition the essential data required by all the methodo are noted in tJ:.:i.s section. o

0

River tGmperature at Bywel1 was observed to vary from 0 C to 20 C. Study of rocorded river temperatures in the north of Engla!1d

smv.J:Y,

(HERSCHY I 1965 and SURFACE Wt..'.i'E:t o

1966) showed that a

temperature of a.bout 8 C could be a:3:::rumed.

Henco:-

Speoific weight of river water, Yf

= 62.42 lb/ft

Mass density of river water,

= 1.94

69

~r

ll1O~m

3

slug/ft

(section 3.5.8.) 3

Viscosity of river water at Kenamatic viscosity of at

eoc,

~

-5

= 2.843

x 10

slug/ft. soc.

wnter

rive~'

aoc,

\i

-5

= 1.465 x 10

2 ft /soc.

Details of the river bad material are obtained from section 3.5 as follows:Specific grnvity of bad llk'1.terial,

S

Mass density of bed material,

Specific weight of bed mnte:rial,

Ps = 5.04 slug/ft 3 'Va = 162.3 lb/ft

Arithmetic mean weight diameter,

d

mean weight diameter,

Geomet~ic

d

Median weight diameter,

2.60 s =

a g

d SO

= 1.97

in

= 0.88 = 1.55

in in

2

= 0.164 .ft. = 0.0733 ft. = 0.129 ft.

All the methods which were used, except the Einstein method, were concerned solely with the cablewny section, EF.

Table 4.l.n.

summarises the physical and hydraulic properties ot the section at 1 ft. intervals of stage. slopes have

Oee~

The water-surface and energy-surface

calculated frou the equntions determined in

section 3.4.3:S

3

w

x 10

ae x

3

1C

= 1.504 loglO (Iie - 45.55) - 0.449

= I.S69

logIO (He - 44.35) - 0.918

where He is the stage in feet A.O.D. The total oross-seotional area of t1ow, At' the

water-Sul~aco

width, W, and the total wetted perimeter, P t' have been determinad Mean depth of flow, D

in section 3.3.

= At/wand

the totnl hydraulic

The total water discharge through the section,

Q, is given by the equation (section 3.4.4):Q

= 233

(r·!

e

-

46.62)1.974

and mean volocity in the section,

V =

70

Q/Ae

T. \.BLE 4.1. a.

AW 2

(ft )

R

P

W

W

Q

V

W

Q

Vb

b

W

P

Db

(ft) (ft) (ft/sec) (cusec) (cusec) (ft/sec) (ft)

Rb

b

(ft)

(tt)

~

'fO

(ft/sec) (1b/ft

2

-_.

0

440

0.58

3.76

209

3.61

0.124

0.0298

0.43

1.7

1289

1.35

4.71

211

4.54

0.219

0.0935

1.00

0.82

9

2570

2.21

5.71

211

5.50

0.294

0.168

14

1.50

1.21

25

4276

3.14

6.71

211

6.46

0.359

0.250

17

1.88

1.53

49

6405

4.09

7.71

211

7.42

0.419

0.340

45

20

2.25

1.76

79

8959

5.06

8.71

211

8.38

0.474

0.436

60

23

2.61

2.14

128

11920

6.05

9.71

211

9.34

0.526

0.538

77

25

3.08

2.49

192

15290

7.03

10.71

211 10.30

0.576

0.645

96

29

3.31

2.70

259

19080

8.02

11.71

211 11.27 . 0.625

0.757

119

34

3.50

2.94

350

23280

9.02

12.71

211 12.23

0.671

0.872

144

39

3.69

3.07

442

27880

10.01

13.71

211 13.19

.

0.715

0.991

175

43

4.07

3.36

588

32860

11.01

114.71

211 14.15

0.758

1.115

211

55 j3.84

3.30

696

38300

12.01

115 • 71

211 15.11

0.800

1.240

260

70 I13 • 71

3.29

855

44100

0

0'

0

0

4

8

0.50

11

11

21 32

I

I i

i



I

! 13.00 Ij16.71 i

..

j

I

I

211116.081 0.841

I i

1.371

I

I

Table 4.1.a.

Physical and hydraulic properties of cableway section, EF.

For explanation of notation

and determination of values see text.

h

W D P R At w t t 3 (ft2) 3 (ft) (ft) (ft) (ft) Cft A.O.D' (ft) (X10 ) (s10. ) H

G

S

e

S

e

Q ~cusec)

48

1.75

0.133

0.136 755.0

201

3.7Ei 209

3.61 439.9

49

2.75

0.330

0.360 960.7

209

4.6C 219

4.39

50

3.75

I 0.488

0.526 1117

212

5.52 222

5.27

51

4.75

0.620

0.658 1384

214

52

5.75

0.734

0.768 1598

53

6.75

0.833

54

7.75

55

A b 2 (ft/sec) (ft , V

0.583

755

1291

1.34

957

»~79

2.20

1160

6.46 225

6.11 . 4301

3.10

1363

215

7.43 228

7.01

6454

4.03

1566

0.862 1814

217

8.36 233

7.7E

9038

4.98

1769

I 0.922

0.945 2032

219

9.2E 234

8.6e 12050

5.93

1972

8.75

1.002

1.018 2252

221 10.19 236

9.54 15480

6.88

2175

56

9.75

1.075

1.083 2474

224

240 10.31 19340

1~12

2378

57

10.75

1.142

1.143 2699

227 ll.SS 245 11.02 23630

8.75

2581

58

111.75

1.203

1.198 2928

230 12.73 250 11.71 28210

9.67

2784

59

12.75

1.261

1.248 3161

236 13.3S 254 12.44 33440

10.58

2986

60

13.7511.314

1.297 3401

245 13.88 266 12.79 39000

11.47

3190

61

14.75 I 1.365

1.339 3653 1260 14.05 281 13.00 44950 J J

12.30

13393

I

i

f

!

11.~

t

1

In section 3,3 the total cross-sectional wetted perimeter, P , t was divided into "bed" 1 that pal-t of the perimeter composed ot g ravel etc., P , and " ban kIt , tt.,•• at part of the perimeter oompoaod of b bushes, grass etc., P ,

Bed load

w

co~putations

were mado only for the "bed" and in an nttempt to eliminate the effect of t:10 banks it was decided to assign part of the crost3sectional aTea of flow to the "bod" and part to the "banks". was effected as shown in fig. 4,1.0.;

This

tho area of flow pertain:1.ng to

tho "bed", A , is bounded by thG "bed", tho we ter-surl ace and two b

verticals from the "bGd-bank" division to the water-surface. area of flow pertaining to thG banlcs is given by I.i.

w

= J\ -

Tho

l:"b'

l!'ro.n table 3.2. a, 1 t can be svon that the leval of thG "bod-ba!ll-::" dlvisiol~ at Eloction EF in 48.21 i t f .• O.D., the w:1.dth of the "bed", W =:

203 ft n:1d the wetted perimtc:" of the "bed", Pb = 211 it,

hydraulic :;"odius of the "bad", :!, :-: l~l/P ,)

the "bunks" 1 ~"t "banks" I nw

:=

w

= f. \'IIPW .

IJ

b

Tho

and the hydraulic radius of

i ..ssunrlng a Manning coefficient for tho

0.040, the menn voloci ty in the area pertaining to the

"ba:lks If is given by:-

R ?/3

vw

n

w

w

se i

nnd tho discharge in the area pe:..·taining to the "banks", i'1w = fl.. V • ww The discharge in tho area pertaining to the "bed", Q b

= 0-0 ... "'w

maan velocity in the area pertaining to the "bed", Vb

= Q/fl.. b ,

mean depth of flow in the area partaining to the "bed'·, Db The

averng~

velocity

u*

tractive force on tho bod,

T 0

=

Yf~bSe

and the

= j\.,li'VI.

and tho shear

=,f"-rjp'; = .jgRbS e •

Sohiolds Method SCHIEI.;")S (1936) used the r0sults of his own experiments and those of

GIL~1T

(1914) on uniform materials of diameter 1.5G to

2.47 mm and specific gravity 1.06 to 4.25 to produce the dimension1esD oquatlon:'/1

The

Area

pertaining

Area

per taining

to

th~

to the

'bed' . Ab

'banKs', Aw

'b ed'-' bank' division

Fig,4.1.a.

Division

of crosS-sectional

area of flow .

5

TO Straub sed i ment

parameter,

8s

rlb/ft3 sec) 75"00 Ib/ft 3 sec

" ~ 0'129 ft

103 L-______________ 10-4

~~

______________

10 -3

________________

10 -2 Particle

Fig. 4. T. b.

~

size

Determin-ation of Straub

~

_______

10 -1 (ft)

sediment

parameter,

lO{T

T

)

*c

= _ y

f

- T ) 0

C

(8

- l)d

s





4.1.n •

where qB is th<3 ood load dischnl'go by weight in air per unit width per unlt tilllG, qb is the water discharge p::Jrtaining to the "bod" by u~it

volume par

dinn~ter.

width per unit time, nnd d is the sediment M~YE1::-PE'rnB and MULLER (1948)

From tllC results of the

<3xparimonts

it appears that for sediment mixtures the representativ0 diametor, U

m

I

(see section 4.1.8) should bo used in the Schields critical t?nctivQ

T

== C. 055 (y

c

3 10 :-

>

f.orce equrrtio:l for Re*

- Y f) d

s

u d For

tb~

bed material at Bywell d

m

= 0.151 ft and using 3

it 1s fOU1:d tha&;R~* varies from 1.27 x 10 ~..

= 61

at H e

ft.

Hence

T

QB :: (D -l)d

s

in whic:l and Q

b

~ ...

b

(T

m

- Y f)d

= 48

= 0.829 m

=

>I<

v 3

ft to 8.6S x 10 2

lb/ft •

rewritte~-;,:-

Equatio::1 4.l.n. can be IG(;bS e

= C.055ty s

c

at He

fio*

-T

)

c

o

is tile bed load discharge by weight in air per uni -:; t:!.me

is the wat<31' discharge pertaining to the "bed II in voluoo t-l:J:: ~

Values of

unit time.

were calculated for 1 ft intervals of

stage and the reeults plotted in fig. 4.1.m. No r<3ferences concerning the actual application of this fOl'1llu1a. were found but

its dimension1es13 homogeneity and the inclusion of

sp~cific

gravity are to be noted.

4.1.3.

Straub l'4ethod

S'i'FAUB (1939) proposed a load

discha:~ge

fo:..~mula

for the determination 01 bed

based directly Oll th<3 Du Boys theory.

materials in the range of fin<3 sands and grave1s:-

e

Q.-.

-B

= 'y-s2 f

To

rr 0

-

Tc>







• 4.2.b.

m

where

®n

is a sediment parameter.

Combining the results of his own

experimentn on uniform msterials with those of GILBERT (1914) at al he produced a table giving valueD of T for use in the above equation c for particle sizes

C.125 to 4.0 mm,

fro~

Comparioon of these vulues

with th0se given by the Schields critical tractive force equatio;} showed that the representative sizo of a mixture would have to be somewhat si:1alle:::- than the Meyer-P.)ter and MUller representativo dinmctE;l', d , m givLlg

T

Accordingly, the roodian diameter, d

2 lb/ft,

= C.1De

c

50

, wns usod,

St):au:) also produced a graph giving

values of ®;3 fo:- sizes from 0.125 nun (0.00041 ft) to L! mm (0.0131 ft); fig. 4.1. b. shows the extent of extrapolation required to obtai:l

9

s

= 7500

l~/ft

to calculate HUBBEL.""~

river in

3

sec for d

n = wqB

Q

and

dlsch~xges

= 0.129

ft.

Equation «\.l.b. was usod

and tha results plotted in fig. 4.1.m.

MATEJKt~

lIe~ras:!::a,

50

(1959) applied this method to a sa:ld-bod

United Statos and found that it gave bod load

of necrly twice the total load measured at a specially

constructcd tu:;:bulence flume in rivsr could 00 p'.l-:; Llto

VI~licil

s\;.spei.l;~:i.on

the w!'lolo sediment lond of the

and

m'3ar:mr~d.

Zgiazaroff Method Combinir:.c; a t::le:>ry based on the elcmcmts ot dimenaional analysis with the resulta of experiments by GILBERT (1914), the mTITED G'fArmS WATERl'IAYG EXPEl:HBNTAL STATIOl'! (1935) and several Russian

worl~rs 011

sediment sizes ranging from 0.21 m:.n to 40.5 mm, EGIAzt.3.0FF (1057, 1953) established the following relationship for fully developed twrbulence:(T

o

-

T ) C

= 0.0225 (S -1) T s c

• • •

The c=q>el'imantal data shor/ed

f.





cczotnin amount of scatter which

Egiazaroff attributed to non-hOOOaell;)ity of supposedly UnifOl'h. sediments, t!lC i:1fluence of pal"tic1e shape, and the impossibility of defining the critical conditions

73

ot movement with precision.

The Schields criterion of critical tractive force was used in the development of the equation so it was decided to calculate T for c the bed sediment at Bywell from d

m

= 0.151

T

c

= 0.055

Y (S -l)d , in which m f s

Hence T = 0.829 lb/ft2.

ft.

c

y

S

iQ

(

feb

T

o

(S. - 1)

-

T

C

Rewriting equation 4.1.c.:-

)

T

o

substitution of the appropriate values gave the bed load rating ourve shown in fig. 4.l.m. In later investigations

EG~OFF

(1965) extended the

th~ory

to include all ranges of flow, i.e. turbulent, transitional and laminar, as well as for hydraulically smooth and rough boundaries.

This

involved tho inolusion on the right-hand side of equation 4.1.c. of a coefficient dependent upon the velocity distribution near the bed. 4.1.5..

Yalin Method

Combining a mathematical oonsideration of the saltation paths of sediment particles in water with the results

of

dimensional analysis

YALIN (1953) derived an expression for the bed load discharge producec' by a steady, turbulent flow over a plane bed composed of grains of equal size and shape.

Experimental ooefficients were obtainod

using the results of experiments by GILBERT (1914) and MEYER-PETEil and MfJLLER (1948) with sizes ranging from 0.32 to 28.6 nun. equation

CWl

be written:-

qB = 0.635 Yfd in which P1

The

=IT o ~ and T0

].

u.Pl (1

-



4.l.d •

P2

The application of the formula to a river bed with a large range of sizes is questionable;

indeed, the role of saltation in the fluid

transport of sediment particles is considered by KALIUSKI!: (lD42) and EINSTEIlT (1941) to be of negligible importance. NORDIN and

~1h~~GE

(1964) the median diameter d 74

As suggested by 50

= 0.129

ft, has

been uood to oalculate T

c

from the Schields equation.

dimensionless critical shear parameter,

T. c = 0.055,

The giving

lJubsti tution of the appropriate values in equation 4.1.d. and multiplication by tho bod width, w, produced the rating curve shown in fig. 4.1.m. Schoklitsch Method

4.1.6.

SEUL!TS (1935) has discussed

oo~prehensively

a formula for the

prediction of bed load discharge proposed by Schok11toch in Germany in 1934.

The two basic assumptions are that the bed material will

begin to move at some critical value of water discharge and that the bed load discharge is a function of the work done by that part of the tractive force in excess of that roquired to overcome the reSistance of the wetted parimeter.

The nocessary experimental coefficients

were derived by Schokl1tsch from tho results of flume measurements Although the

by GILBERT (1914) and additional data of his own.

sediments used were uniform-sized (0.31 to 4.9 mm), Schok1itsch suggested that the formula could be used to compute

th~

dlschnrgu

of individual size ranges of a mixture, the total load being tho summation of the individual discharges.

Hence if d, in feet, is

the geolllOtr1c mean of a size rangt3 and ib is the proportion by weight ot that size range in the bed material, then the bed load dl:Jcharge of that size range,·

iB~'in

lb/a8c, where iB is the

proportion by weight of that size rango in tho bed load, is given by:i S 3/2«(,' - Qbc} • b e "h

where Q

bc

is

t~e

critical value of

• 4.1.0 •



wat~r

discharge in cusecs

pertaining to the bed and is given by:Q

bc

= 0.0638

wd/s

e

4 3 / •











in which w is the width of the bad, in feet. discharge, Gn

=

L i

Q B B• 75







Tho total bed load

Since the cumulative particle size analysis distribution bed material (fig. 3.5.e.) is open-ended it was deeided to the bad load discharge of the particl'J sizes between d and d

l

= O.
99

tho

compu~e

= 7.20

Table 4.1. b. gi vas the size rangea into

in.

o~

in

whic~l

the bed material was divided. Bsd material size rangos

Sizo range (1n)

Geometric Geometric tlizQ mean of moan of siz~ ra:1go range (in) (ft)

ib (xlO2)

< 0.0034

1.0

0.0004 - 0.020

0.0103

0.000862

5.2

0.000

- 0.040

0.02SS

0 .. 00236

4.6

C.040

- 0.080

0.05-33

0.00472

3.0

o.eoe

-

0.16~

0.113

0.00944

2.6

C.IGO

- 0.32'0

0.223

0.0183

5.4

0.320

- 0.640

0.452

0.0376

10.0

0.G40

- 0.904

0.'161

0.0'134

3.2

1.290

1.073

0.0894

10.C

1.280

-

1.80B

1.521

0.1267

10.0

1.80G

- 2.560

2.1<10

0.1733

1-1.0

2.560

-

3.613

3.C4?'

3.618

- 5.120

4.22~

I

I

0.3576

B.G

5.120

- 7.200

6.071

4.7

7.200 <

I

0.5060

:

O.D~

II f

I

t

I

I

! I

0.2534

i

!

16.5

i,

1.0

I

I t

Since Se variod with Q for the Bywe11 reach it was necessary b to solve equation 4.1.f by grnphical means to obtain Q

bc

value of d.

for a given

USing equation 4.1.0. the individual discharges of ench

size rru1ge WG-.:a then ca.lculatod and aUI:l.mted as shown in tn!)la 4 .1.c. and plotted in fig. 4.1.c. This !OOthod of application to sediment mixtures mog1acta th:l hiding

ef~3ct

of small particlaa in t!1c la.miaar sublayer and behLid

larg~r pal~iclas,

bed

rive~ Wi~1

an influancc which could be significant in gravel

a large range of sizes. 75

It also 813sumes an unlimited

T.kBLE 4.1.0.

·range of sediment size, d (ft)

Q B ~ [iSQB

;

Q B using d

0.0894

0.1267

0.1788

0.2534

0.3576

0.5060

-

-

-

-

-

-

-

-

-

-

-

-

0.14

-

-

-

-

-

1.25

-

-

-

-

-

-

4.01

-

-

-

-

9.14

-

-

-

17.54

-

29.59

-

0.74

-

-

-

46.16

7.75

1.94

0.76

-

68.12

19.83

95.46

35.55

, 130.84

54.63

171.91

77.54

-

220.85

104.39

-

11276.94

135.28

-

.

-

I

-

I

-

-

-

3.48

1.97

0.31

-

5.37

3.48

2.62

0.54

7.63

5.31

4.66

2.41

10.29

7.47

7.13

4.69

9.96

9.94

7.36

13.34

I,

I

-

I -

I!

-

I I I

I, I

I

I

-

I -

I 0.81 :

I

-- (lb/sec)-

I 1.93

I

I

I

I

:l

4C

(ll¥',JIecl •..

Table 4.1.c.

Bed load discharca computations bf the Schokl1tsch method

1B~

H

(lb/sec) for each

e

(ft A.O.D' 0.000862 0.00236

0.00472

0.00944

I

0.0188

0.0376

0.0634

-

-

-

-

-

-

-

48

-

-

49

0.14

-

-

50

0.85

0.32

0.08

51

2.39

1.08

0.40

0.14

-

52

4.95

2.39

0.97

0.46

0.37

-

53

8.70

4.35

1.85

0.97

1.06

0.61

-

54

13.81

7.03

3.06

1.68

2.05

1.78

0.18

55

20.37

10.49

4.64

2.62

3.37

3.39

0.54

56

28.57

I 14.83

6.61

3.81

5.07

5.50

1.03

57

38.46

20.08

9.01

5.25

7.15

8.81

1.64

58

50.03

26.24

11.83

6.96

9.61

11.78

2.38

59

63.59

15.15

8.97

12.52

14.95

3.27

60

79.l2

41.72

18.94

11.27

15.87

19.24

4.30

61

96.72

51.10

23.24

13.89

119 •89

24.29

5.48

i

23.45

,

-

-

-

I

62

using

representative

60 d i am e fer,

58

Stag

sumrnat on

c

size

A.O. O. ( f t )

of

r'lnge

individual disch a

r ges

54

5

5

480~1~~~~-------::·co 50 300 750 200 250 Bed

Flg.4.1.c.

Sed

load

load

rating

disrharg e

curves

by

the

(Ib/sec)

SchoklltSch

method

supply of fine material from the bed. and

KRESG~a ~~

According to SHULITS (1935)

LASZLOFFY (1964) the results of bed load

measurements on the Rivers Danube and Terek agree reasonably well with the Schoklitsch formula when d diameter of a mixture.

is used as the representativQ

40

From fig. 3.5.e. d 40

= 1.05

in

= 0.0875

ft

for the Bywell bed material, and this value was used in equations 4,1.0. and C.l.f. as shown in table 4.l.c. nod plotted in fig. 4.1.c. Since the method. as applied to mixtures neglects some important factors it was oonsidered that bed load discharges computed using a single representative diameter were more reliable. bed load rating curve obtained using d

40

Therefore, tho

has been plotted

ill

fig. 4.l.m. for comparison with the results of other bed load formulae. Meycn-Peter and MUller Hethod MEYER-PE~~t and

MULLER (1948) described the development of rul

empirical bed load formula which

Crul

be shown to obey the .roudian

The results of pzoelim1nary laboratory experiment.;

law of similarity.

with uniform materials of natum! specific gravity were found to

agre~

with the following equation:q 2/3 D.... ___ e _ d

in which

I~

TI'

+



''2

and

~























Further tests were carried out

are constants.

with mixtures and, although it was found possible to represent a sediment mixtUro by a single diameter, d

m

= ~dibl

satisfactory

agreement with equation 4.l.g. could not be obtained.

A series of

special tests concerning the commencement of motion indicated thnt for most cases tho value of YfDSe/d conditions, i.e.

T

c

m

was a constant at critical

Cod , which oonfirmed the Schields equation for m

fully developed turbulence.

Since

co~~ncement

of movement was

dependent upon a limiting shear stress Meyer-Peter and MUller 76

concluded that the bed load dischargo should also be a function of shear stress.

Accordingly, equation 4.I.g. was altered to:qB d

2/3



m









in which K4 and K5 are constants.

A large number of tests with mixtures of various sizes

W3TO

carried out but it was found that bed load discharges occurring with ripples, dunes or shoals gave very poor agreement.

It was evident

that the shoal' stress on the bed was taken by two distinct resistances:1)

Form resistance due to the unevenness of the shape of the bod.

2)

Grain resistance due to friction on the individual particlos of the bod.

Meyer-Peter and Mijller therefore divided tho total energy slope into two

co~"rosponding

L~owed

formula

partial slopes a.nd by n;8ans of the Stricklor

that the pure frictional slope was equal to (kt )·

k

2~

'.)0

r

where k

t

is the coefficient of totnl roughness in the Strickler

equation, V

= IttD2/3s e !,

and k

friction with a plane bed.

r

is tho coe!f laient of particlo

SincQ only the energy dissipateu by

resistanc3 is effoctive in the transport of bad load, S equation 4.1.h. should be roplacod by

tk~2s . kJ

e

gra~n

in

However, evaluation

e

of test results and other consido::."ntions indicated that the exponont

Of(:t) should be adjusted to 3/2, with equation 4.l.h. rewritten on:r

2/3

qB

d

in which Ka and

r~7

are constants and

m (i, Q

b

and Db have been introduced

to account for the effect of bank friction ill open channel flow.

77

Further experiments with materials of different densities enabled a tinal dimensionless form of the equation to be propoaGd:-

I

ty

yf

- y

J~-. (k~3/2 ...!



D 8 ~

,~k

d

....

= 0.047

+ 0.25 d

m

IY~1/3(~_ y /3~ )2/3 ....! s B Y f

m

- Y

c



f

4.1.i.

Flume experiments on which tIle fornrula was based covered tho following ranges:Particle size

0.016 to 1.15 in

Specific gravity

0.25 to 3.20

0.033 to 3.80 ft

Slope

O.4XlO-3 to 2OXIO-~

At zero bed load dischargo on a flat bed in a flow without bank friction equation 4.l.i reduces to:-

which agrees closely with the Schields equation for the critical tractive torce in fully turbulont flow. that the rO}Jrosentative diameter d sediment mixtures;

m

=

It can be concluded thon

!. d ib f"lould be used for

its v2lue depends on

th~

whole particle size

distribution, Equation 4.1.i was applied to the Bywell test reach aD Show.l in table 4.1.d.

The required valuas of Q, Qb, D and 8 b

in table 4.l.a.

e

From table 4.l.b. the representative

bed material, d

m

a

are listed diamete~

t di , was oalculated to be 0.151 ft.

b

of the

The

coefficient of roughness in tho Strickler formula was calculated at each stage from:"

k

t

b

= p'

2/3

··b

8 ei

l 3 and has the units of ft / /sec,

From test results Meyer-Peter

a~d

MUller noted that the coarse particles of a mixture are most effoctive in determining the grain roughness of a sediment mixture.

They

suggested that the coefficient of particle friction with a smooth bed, kr

= 38.64/dgO1/6 ,where

d 90 is expressod in feet and kr has 73

t~e

units ft

1/3

lace.

From the particle size distribution curve of the

bad material, fig. 3.5.e., d 90 Total bed load discharge, Q B

=0.350 ft.

= WCln'

giving kr

= 46.03

ft~3/sec.

was computed at one foot interv.1ls

of stage and plotted in fig. 4.1.m. Table 4.1.d.

Bed load discharge computations by tho and

H

e (ft. A.O.D.)

Q b

Q

Meyar-Peta~

MUller method

(:f2

k

t 3 (ftl/ /see)

S

Qn Db qB (ft) (lb/sec.ft) (lb/soc'

e 3

(x10 )

48

1.000

21.61

0.321

0.133

3.76

49

0.998

27.09

0.451

0.330

4.71

50

0.997.

32.10

0.582

0.483

5.71

51

0.994

36.36

0.702

0.620

6.71

52

0.992

39.67

0.800

0.734

7.71

53

0.991

42.66

0.892

0.833

8.71

54

0.898

44.92

0.964

0.992

9.71

-

-

-

55

0.983

46.91

1.029

1.002 :"0.71

-

56

0.987

48.71

1.088

1.075 11.71

0.1766

57

0.985

50.26

1.140

1.142 12.71

0.6150

58

0.985

51.74

1.203 13.71

1.269

59

0.983

[,3.02

I

1.192

35.8 I 124.8 i , 257.6

1.261 14.71

2.092

424.1

I,, 1.2771 1.314 15.71

3.095

62s:1.7

1.365i16.71

4.299

872.7

60

0.982

54.17

61

J 0.981

55.26

I

I

I I

1.236

I

I 1.3151 :

,

-

and VOLKER, 1959), Nigeria

(NEDECO, 1959) and the United States of America (HUBBELL and W\Tl'Jn-l., 1959).

GEMAEHLING, GINOCCHIO and CHABERT (1957) reported that the

total quantities of coarse material (median diamater about 2 in) transported during several floods in the central portion of the River Rhone agreed well with those computed by tho formula.

BAUER (1965) also found good agreement with bed load movements in the River Danube with sediment of representative diameter of 0.75 79

I

! I, I

has been found to describe closely bed load discharges in soma sandWE~mLSFELDER

I

I

The Mwyer-Peter and M{ll1er formula, with slight modifications,

bed rivers in Holland (TOPS,

I I

~.n.

II ...

Kalinske Method

4.1.8.

KALINSKE (1947) accepted two basic concopts in the development of a bed load transport formula.

The first concept is that there

is some minimum fluid force which will cause a sediment particle to move, and the second concept is that the shear stress on the partie}'...; may not be constant but will f luctunto duo to turbulenco about a m.:"n For an estimate of the critical shear stress required to

value.

start movement Kalinske accepted the conclusion of WHITE (1940) (see section 2.2.2.) that:-

,.



c



4.i.k.



From an analysis of data on pebble move,1I0nts the velocity of a particle at any instant was assumed to be equal to U

~ingle

g

=u

- u

c'

where U is the instantaneous fluid velocity at grain levol and U is c the critical fluid velocity.

As shown in soction 2.2.2. tho number 2

of particles per unit area of bed is 4p/ TId , where p is the proportion of the hed taking fluid shear.

Hence the bed load

discharge in dry weight per unit width of bed is given by:s dUg

qB = 2/3 P Y

where U

g







is the mean particle velocity.

If velocity fluctuations

due to turbulence are in accordance with the normal error law then U can be obtained by integrating the error function for U = U - U g g c between the critical fluid velocity, U , and infinity:c -2

co

-(U - U)

r

U

g

=

J (U

- Uc )

20-2

1

rrJf'ft • e

dU

U

c

in which U is the menn fluid velocity at grain level and~ is the standard deviation of the velocity fluctuations. division by U it can be shown that intensity of turbulence r:::

(J

/V

UgiV

After

is a function of the relative

and the ratio of U to c 80

F-··).:= v(U - u)·

u.

Since

shear stress varies with the square of velocity, then U IU can be c

/

written as

T

c

IT 0 and:•

















4.1.1 •



Kal1nske stated that for turbulent flow near the bed r had been found to equal

i

an~

he described equation 4.1.1. by the graph shown in fig. 4.l.d. According to Kalinske U is approximately equal to

ll~

which

enables equation 4.l.k. to be written:-





1.l.m •



If the formula is to be applied to a mixture then the bed load discharge per unit width of a given size range is:•











in which Pi is the proportion of the bed area covered by grains in a size range and is given by pib/ad, where d is the geometric moan of the size range, ib is the proportion by weight of the size range in the bed material, p is the praportion of the bed taking fluid shee. (=

0.35 according to White) and a

= t(i~d).

using the data of table 4.l.b. a was calculated to be equal to 98.64 enabling 'i to be calculated for each size range. Equation 4.1.j. was used to calculate

T

c

for each size range and

values of f t:.( T IT ) were taken from fig. 4 .l.d. for each value of ,. • ~ c 0 .0 Bed load discharges of each size range over the whole width of section, iB~

= win~'

were calculated from equation 4.l.n. and ara given in

table 4.1.e. with the summated discharges, QB

= ~ inQB"

As with the Schoklitsch method, the application of the Kalinske method to mixtures neglects the mutual interference effects of particles of different

sizes and assumes an unlimited supply of the finer sizes.

81

relative of

0·'

intensity

turbulence,

r=0'25

0'01

O'OO'~----------~----------~------------~-----------L--------~~

o

Fig.

64

TO

0·5

4·7. d.

Ratio of

summation size range

of

critical

1-5

shear

2·0

to bed

shear after Kalinske.

indiviaua/

discharges

60

~

"'",

Stage uSing

A.O.o.

representative

ciiarn eter

(f t )

d

SO

48U-------~--------~--------~------~---------L--------~------~~-500 GOO 200 70C 300 100 400

o

Bed

Flg.4.1.e

load

Bed loa r !

discharge

rating

(lb/sec)

curves

by

the

Kalinske

method

Kalinska suggested that the median diameter could be used as a representative diameter.

Bed load discharges were therefore

computed using equation 4.I.m. with p

= 0.35

and d

= d 50 = 0.129

Total bed load discharges across the section are given in table

ft. 4~1

•••

and plotted in fig. 4.l.e. for comparison with the summated discharges of the individual size ranges. For the same reasons as those given in the discussion of the Schoklitsch method the bed load rating curve obtained using the median diameter of the bed material is considered more reliable and is plotted in fig. 4.l.m. The principal merits of the Kalinske method are that it introduces the concept of fluid turbulence statistically and that it dOGE: not utilise the empirical results of any beu load experiIOO1.ts, However, the validity of certnin assumptions such as p

ug

=u

- uc , and

U

= llu

,~.

is uncertain.

= 0.35,

Accordtng to

ELZERMAN

and FRISLINK (1951) measurements of bed load transport in Holland indicate that the constant 7.3 in equation 4.l.m. mny in fact be as low as 5. 4.1.9.

Einstein Method

EINSTEIN (1941, 1950) presented a complex method for the computation of the bed material discharge of an alluvial channel, i.e. the summation of the bed load discharge and suspended bed material discharge.

This section is concerned solely with the part

of the theory concerning bed load. The method was developed for application to an average crosssection of a reach of river in which several cross-sections have been surveyed.

It was necessary, therefore, before making any

sediment computations to determine the physical and hydraulic properties of the representative cross-section of the Bywell rench, using the five main cross-sections AB, CD, EF, GH and JK. 82

Each

cross-scction has been described by the two curves of stage against total cross-sectional area (fig. 3.3.f.) and stage against total wetted perimeter (fig. 3.3.g.).

The

corresponding curves for the

representative section were obtained by sliding the curves of each section along an average slope into the plane of the cableway EF.

sect~on~

Since the water-surface slope of the Bywell reach varies ~

~

at H = 61 i t A.O.D. e 3 it was decided to use an average slope of 0.75 x 10- • The curvez

0.136 x 10

at H = 48 i t A.O.D. to 1.339 x 10 e

fro~

thus obtained were averaged directly to give the variation of At and P

t

with H for the representative section (figs. 4.l.f. and 4.1.g., e

respectively).

Since the plane of the cablewny section, EF, was

used as a common datum, H was taken to denote st?ge A.O.D. at the e

average section. fit

= At/Pt

Values of At' P and total hydraulic radiUS, t

are given for oevera1 values of HE:: :a table 4.1.f. together

wi th water discharge, Q, and energy-surface from table 4.1.n.

slo~,

S , taken

e

direct~.y

(PreliJainary calculations indicated that bed ·loa r \

movement was unlikely to occur below H e

= 55

ft., and

~or

this reaso/'.

only 2 ft. intervals of stage have boon considered below this 1evol)., The elimination of the influence of bank frictil'Jn was effectEld in a manner similar to that described in section 4.1.1.;

it was

assumed that the level of the "bed-bank" division on the representative cross-section was 48.00 ft. A.O.D. and that the slope of the banks was 1 vertical to 3 horizontal.

Calculated propert ies are given :'.:.

table 4.1.f. An important concept in the Einstein method is that the resistance to flow over a sediment bed is composed of two distinc'j; types:1)

nesistance due to the shape of the bed;

the part of the

flow energy which corresponds to shape reSistance is transformed into turbulence at some distance from the bed 83

~-------------------------------------------------------------------------------------

~

---:

Table 4.1.f.

H

At

e

(ft f.,O.D) (ft2)

Physical and hydraulic properties of representative section

P

R t

t

S

e

A

Q

P

w

(ft)

(ft)

3 (X10 ) (cusec) (ft2)

b

P

w

a

v

w

Q

Q

w

w

b

Vb

Ab

I I

(ft)

(ft)

(ft) (ft/sec) (cusec) (cusec) (ft2) (ft/sec)

I

48

580

211

2.75

0.133

440

0

211

0

50

1010

225

4.49

0.448

2580

12

211

14

0.86

52

1460

237

6.16

0.734

6450

48

211

26

54

1930

248

7.78

0.922

12050

108

211

55

2160

255

8.47

1.002

15480

147

56

12410

262

9.20

1.075

19340

57

\2670

269

9.93

1.142

276

10.62

3190

282

3470

288

0

440

500

0.76

0.74

9

2570

998

2.58

1.85

1.52

73

6380

1412

4.52

37

2.92

2.30

248

11800

1922

6.48

211

44

3.34

2.62

365

15480

2013

7.50

192

211

51

3.77

2.95

566

18774

221B

B.46

23630

243

211

58

4.19

3.26

792

23630

2427

9.41

1.203

28310

300

211 ,

65

4.62

3.57

1071

27239

2630

10.36

11.31

1.261

33440

363

211

71

5.11

3.31

1419

33440

2827

1l.33

12.05

1.314

39000

432

211

77

5. 61 1

4.25

lS36

, 37164

3038

12.23

I

4.31

3243

13.16

t

0

0

I

58

\ 2930

59 !

i

GO I

61

I ~

!

I i

._-

1

3750

296 \12.67 ~

1.365

44950

I 507

I

l I i

!

211

85

5.96\

I

I

I 2237

I

I, I

-

44950

-'---

I .

:

,! I

and hence does not contribute significantly to the bed load transport of sediment particles. 2)

Resistance due to the bed particles;

the flow energy

whL~.:,

is dissipated by turbulence in the immediate vicinity of i;he particles has a large effect on bed load movement. MEYEU-PETER and ~illLLER (1940) also noted this distinction (see section 4.1.6.) and assigned a part of the energy-surface slope tc each resistance.

Einstein, however, extended the principle of ttl'.!

distribution of total cross-sectional area of flow between "bed" (A ) and "bank" (Aw) and divided Ab into b

Ab

and A~ , areas

corresponding to grain resistance and shape reSistance, respectively. Both types of resistance are distributed over th<3 entire "bed" surface and hence act along the same perimeter, P • b S

e

R~

is held constant in the drag expression, =

t4b /Pb

T

In this way 1

=

a

becomes the hydraulic radius whIt respect to the

particles and a~ = A~Pb becomes the hydraulic rediu~ with respect to channel shape, such that:R

b

= RIb

+ R" b

,." = Y R ItS

u." =VI gRItS b t;>

T

u - u'

o

f



..

b e

2

=T'+T"

000

-

4.1.0

2

According to Einstein the mean velocity in a vertical is given by the Keulegan Equatlon:R'x b 5.75 loglO(12.27 -k---) s

• • • • • •







4.Lp •

where ks is the representative roughness diameter of the bed and considered by Einstein to equal d

65



The value of the corrective

parameter x is dependent upon whether the flow is hydraulically 84

rough, transitional or hydraulically smooth; k

s

/6~

as shown in fig. 4.l.h., where

it is a function of

6' is the thickness of the

laminar sublayer calculated from:6' = 11.6 v /u;





4.l.q .



The derivation of the final Einstein bed load equation for sediment mixtures is lengthy and complex, and will be described By equating the number of particles being

only briefly here.

eroded from unit area of the bed in unit time to the number being deposited in unit area per unit time Einstein was able to express the probability that a given sediment particle would move as a function of the bed load discharge and physical properties of the Laboratory experiments indicated that this

fluid and sediment.

probability depended upon the size, shape and weight of the

postulating that tho

Aft(_~,

and upon the flow pattern near the bed.

particl~

probability was a function of the ratio of the instantaneous hydrodynamic lift exerted by the flow to the submerged weight of th,-, particle, Einstein concluded that the bed lOf-ld equation representing the general relationship between bed load discharge, flow condition9 and bed material is given by:-

~ * = f7 {'¥ .} where ~ * = the dimensionless

r~ (

= 18 ib _Y s and

Y'

= the



y• 'Y s - 'Y f

't'

=

(8

s RIS

r( J





1 )

gJ.3



4.1.1'.



4.1.~"

dimensionless intensity of flow function

= S y(~2/~x 2) where

intenSity of bed load trnnsport function.

'±'



















-)d

, the intenSity of shear on a single particle

b e

85

18r----------,----._--------~----._--------_T--~

16

12

X 10

08



04 01

',0

10

05

I

0

ks/b' Fig.4.1.h. Surface drag

correction factor.

100 :>0

10

y

5

I~~------~~~----~

10

ks/f/

a

5

Fig.4.1.i. Lift force correct ion factor. I

'J

{J'

UI

djx Fig.4.1j. Hiding correction factor.

100r------,-------r------._----~~----_r----~

10

01~----~------~------~----~------~--

00001

(J

001

o

1

10

__~

Fig.4.1.k. Einstein bed load function.

lUO

= 10glO (10.6) • ~x

x

= 10glO =a













(lO.6XX/ks )













• •









reference particle size for a given bed.



4.l.u •

Laboratory

experiments have shown thot:-

x = 0.77

k

Ix

S

if k

& if k

X = 1.39

s

S

Ix >

Ix <

1.80 0 I

1.80 6 I

Y = a lift force correction factor necessary for mixtures with dlfferen·t

roughness conditions.

It is given as a functiol.

of k/o ' in fig. 4.1.1. s

s

= a correction factor for the effect of small particles which

tend to hide between larger particles or in tho laminar sub1ayer.

It is given as a function of d/x in fig. 4.l.j.

Recent research (EINSTEIN, 150(4) indicn"tl3s that, for values ot d/x smaller than that at whicL rem~ins

~dj\l

= 9,

the factor

constnnt.

USing the results of his own flullle experim,mts GIL3E~T

E~_nstein

~md

those of

(1914) on uniform materinls between 0.315 and 28.6 mm

produced a curve of the

relationsh:j.p~ ~.

* = f,,( 't *} as

shown in fig. 4.l.k. Before applying the bed load equation to the Bywell test reach further hydraulic calculations were made for the representative cross-section.

In his paper EINSTEIN (1950) assumed that a stage"

discharge curvo for the test reach would not" b'1 aV£1ilnble and proposed that it should be obtained by the following procedure. It was suggest ad t hat f or most rivers the va 1ue

0

f

" I u*'

V~

whi c h

can be consiuered to be a function of the coefficient of resiotnace due to bed shape, should be a function of the flow intenSity function for n representative particle size,

The

curve shown in fig. 4.1.1. is the results of iuvestigatlons on several rivers in the United States of America with values of d 86

35

100

10

4567891

0 '1

f.

5

0'5

Fig. 4.1· 1.

6

y

50

10

Determination

of

bed

shape

9

1

TOO

resistance .

l

5

500

6

7



9

1000

between 0.00052 ft and 0.0033 fti

the establishment of this curve,

which purports to give the normal amount of shape resistance encountered in rivers, has been described in detail by EINSTEIN and BARBAROSSA (1951). S

Einstein recommended that an average value of

should be determined for the reach and, with an assumed value o!

e

b,

R

equation 4.1.p. should be used to calculate Vb.

From fig. 4.1.1.

u; could then be calculated and by USing the relationship of equation 4.1.0. the value of R , and hence stage, corresponding to b Q = AbVb could be obtained.

b

Although a staga-discharge curve was available for the Bywell reach an attempt was made to follow the complete Einstein method. However, it was found that values of

R~

obtained by the above

procedure were extremely large and it was decided to compute the

V/u;

relationship between

and 'f' using the ,!·.~ta of table 4.1.f.

'I11e results of thesa comput ations are given

iiI

tc.ble 4.1. g., togetheL'

with other hydraulic calculations required for the computation of Assuming hydrau 11cally rough flow, i. e. x

load discharge. with ks

= d 65 = 0.196

= 1,

ft, equation 4.l.p. wac used to obtain

knowing Vb and Se for each value of stage.

b·)cl nn~l.

Rb '

Equations 4.1.0. and

t

4.l.q. enabled u;, 6

and It /6 s

to be calculated and since k,/6 r > 10

for all values of stage the assumption of x

=1

proved correct.

Using equation 4.1.0. V1I'u; was calculated and with d 35 If

I

=

/RbSe.

(Ss - 1)d35

= 0.0683

ft,

These calculations enabled the curve fo? the

River Tyne at Bywell to be added to fig. 4.1.1.;

the deviation from

the Einstein and Barbarossa curve would seem to indicate that the importance of channel shapa resistance as part of total resistanco to flow is considerably less in gravel-bed rivers.

BROOKS (1955)

at al also found that observed shape resistance in both laboratory flumes and rivers differed from the recommended curve.

87

The remaining hydraulic calculations in table 4.Z.g. were necessary before direct computations of bed load discharge could be made.

Since ks /x>1.800 ' then X

= 0.77

ks/X

= 0.77

d

65



The

value of Y was obtained from fig. 4.1.i. and (fV~ )2 obtained from x equations 4.I.t. and 4.I.u. Bed load discharges were computed for each of the thirteen size ranges given 1n table 4.I.b., taking d equal to the geometric mean size of the range. and

.~

For each size

'" calculated from equation 4.l.s.

of fig. 4.1. k.,

~.

~

was taken from fig. 4.l.j, Using the 9", -

r '"

curve

was obtained and the bed load discharge per unit

width for that size range was calculated from equation 4.l.r., rewritten as:-

The total transport rates for each

S~_ze

range (Ner the whole section

The curve of total bed load discharge of all

(table 4.1.h.).

sizes 1s plotted against stage in fig. 4.l.m. Although the concept of bed load movelll6lli: embodied in the Einstein theory is more realistic than that of Du Boys or Valin, the dependency of the method upon strictly empirical relationships such as figs. 4.l.i. and 4.l.j. and the definition of X tends to detract from its validity. hiding factor, uncertain; than about

S

I

In particular, the evaluation of the

for a very large range of uizes is extremely

the results of table 4.l.h. show that particles smaller

!

inch are stated by the theory to remain stationary

even at high tractive forces.

It would seem, then, that the metho1

is likely to predict only minimum rates of bed load transport. Another limitation of the method as proposed by Einstein is indicated by comparison of the shape resistance curve for the River 88

Table 4.1.g.

H e (ft A.O.D' 48

Hydraulic calculations for the Einstein method

R'

b (ft)

u'

0'

• (ft/sec)

3 (ftxl0 )

k s /6'

a"

u"

(ft)

(ft/sec)

b

*

1.19

0.071

2.38

82.3

1.56

0.081

50

2.68

0.205

0.839

234

2.05

0.179

52

4.45

0.324

0.524

374

2.24

54

6.35

0.434

0.391

501

55

7.45

0.490

0.347

56

8.48

0.542

57

9.51

58 59 60 61

Vb

/ u"

'f

X

t

Y

*

9.37

~x

(\f

691

0.1509

0.54

0.91?

1.263

14.4

83.6

"

"

"

"

0.230

19.7

33.5

"

"

"

"

2.29

0.261

24.8

18.7

"

"

"

"

564

2.09

0.259

29.0

14.6

"

"

"

"

0.313

626

2.03

0.264

31.9

12.0

"

"

"

"

0.591

0.287

683

1.99

0.270

34.8

10.1

"

II

"

"

10.60

0.641

0.265

739

1.86

0.268

38.7

8.6

"

"

"

"

11.73

0.690

0.246

797

1.66

0.259

43.7

7.4

"

"

"

It

12.75

0.734

0.231

848

1.65

0.264

46.3

6.5

"

"

"

"

903

1.43

0.250

52.7

5.7

"

"

"

It

13.94

0.783

0.217 I



Table 4.1.h.

Computation of bed load discharge by the Einstein method iB~

H

(1b/sec) for each size range of sediment, d (ft)

e

1ft

A.O.D) 0.000862 0.00236 0.00472 0.00944 0.0188 0.0376 0.0634 0.0894 0. 1261

-

-

52

-

-

54

-

-

-

55

-

-

-

-

57

-

58

-

-

59

-

-

-

-

- 1 -

48 50

56

60

61

I

-

-

-

-

-

-

-

-

-

- I

-

-

-

-

-

-

-

-

-

I I

-

-

-

-

0.80

-

Q B -,.. iBQB -" 0.1788 0.2534 0.3576 0.5060 (lb/sec) _..... ..-. ,

-

-

-

-

,

-

-

I 20.52

-

-

-

-

-

-

-

0.40

-

2.83

1.99

!, 10.17

9.55

-

-

3.15 iI 21.48

26.53

7.65

-

I -

7.37 141.82 ,

55.11

24.27/

-

II

-

0.06

13.39 168.95

92.85

52.781

3.11

-

0.13

-

-

I

i 18.75

190~:3 ~24.69

I

79. 16

-

I

I

i

!

1 7.07 i

-

i

I

1

0.40 4.82

58.81

I

1129.17

.123 1.14 ~i

:1320.23

,

I

Tyne at Bywell with that given by Einstein and Barbarossa (fig.4.l.l.). If a stage-discharge curve is available the evaluation of channel shape resistance is still dependent upon an accurate determination of the energy-surface slope of the reach. COLBY and HEMBREE (195fi) and HUBELL and MATEJKA (1959) reported that total bed material discharges computed by the Einstein method for two sand-bed rivers in the United States compared poorly with suspended sediment loads measured at specially constructed turbulent sections at which all sediment was brought into suspension.

The particle sizes

transported were also found to be considerably

differ~nt

from

predicted Sizes, a result which has been confirmed by STALL, RUPANI and KANDf.SWAMY (1958). 4.1.10.

Modified Einstein Method

Studies of total sediment load measured in a contracted, natural rock section of a sand-bed river in the Ullited States of America have led to the d'3velopment by COLBY a:ld HEMBREE (1955) of a modified Einstein procedure for the material discharge.

There

1U'13

comp~i;ntion

of total bed

four modif:1cf'tions to the orlginul

procedure for calculating bed load discharge:·1)

Computations are made for a single cross-section at whicb the channel shape nnd stage-discharge curve are known. For application of the method to the Bywell reach the cableway section, EF, was used.

2)

The maan velocity oquation 4.l.p. is modified to:-

u

xDb 5.75 loglO(12·27 k -).

s

m

in which u

m



is a shear velocity equnl







to~g(SR) m,

(Sa)

~

being the quantity obtained by solving equation 4.l.v. _:c.1' SR with a known value of Vb" replaced R~. 89

The mean depth, Db' has

3)

Both the dimensionless intensity of shear function for a single particle,

t.,

and the function for a representatiw'!

particle, 1'1, have been replaced by 'i' , which is computod m

for each size range, d, l'

from~-

d m = 0.4(S s - 1) (Sa)

d 35 or 'i' = (Ss - l)(Sil) m m 4)

d> 2.5d

if

m

S5

• if d < 2.5d



4.1 •••

35

The dimensionless intensity of bed load transport ~*'

function,

determined from fig. 4.l.k. USing

'f =

m

'i'>i<' is

divided by 2 "to make computed sediment discharges agree better with measured total :ilediment discharges".

The

bed load discharge per unit width for each size range is thus given by:-

• The hydraulic calculations necessary discharges are given in table 4.l.i.

bef~re



computing bed load

Values of Vb and Db were

obtained from table 4.1.&. and, assuming hydr"'_l1.lically rough flow, i.e. x

= I,

equation 4.l.v. was solved for u

the laminar .ublayer, stages eks x

=1

= d65 ),

6

m = 11.6\1/um•

e

m

The thickness of

Since k,/ 6 m > 10 at all

then according to fig. 4.l.h. the assumption of The value of (SR)

J

was given by U = g(Sn) • m m m Bed load computations' were made for the t!,irteen sizes ranges of was correct.

table 4.1 ••• , USing fig. 4.l.k. and equations 4.l.w. and 4.l.x. Discharge over the whole section for each size range, iBQB = wiBqB' and the summated d lscharge,

~

=

Z i13Q-B' are given in table 4.1. j

The lesulting bed load rating curve of the cableway section is plotted in fig. 4.l.m.

90



Table 4.I.j.

Computation of bed load discharge by the modified Einstein method lB~

(lb/sec) for each size range of sediment d (ft)

Q

H

e

ft A.O.D) p.OOO862 0.00236 0.00472 0.00944 0.0188 0.0376 0.0634 0.0894 0.1267 0.1718 0.2354 0.3576 0.5060

-

-

-

-

-

-

-

0.26

-

-

-

-

0.49

1.10

1.85

2.14

-

-

-

6.10

0.68

3.55

5.98

10.47

1.12

-

23.99

2.20

1.54

8.06 13.59

25.54

6.35

-

-

57.80

4.05

2.83

14.83 24.99

48.32 18.80

6.69

4.68

24.50 41.30

, 84.a6 38.10

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

0.01

0.04

0.03

0.15

0.01

0.05

0.30

0.21

0.01

0.03

0.18

0.97

0.02

0.03

0.07

0.42

0.01

0.03

0.05

0.13

0.77

0.01

0.05;

0.09

0.22

1 1.27

52

-

-

-

55

-

56

-

-

57

-

-

-

58

-

0.01

59

-

60

i

-

-

-

-

-

-

61

-

-

-

50

-

-

-

-

54

-

-

-

-

I

{lb/sec)

-

-

48

B = E l BQ B

--

0.86 3.6S ~

-

115.86 204.79

I

Table 4.1.i.

Hydraulic calculations for modified Einstein method

H e

V

(ft)

(tt/sec)

b

ioI

(ft)

(ft/sec)

•3 (ftxl0 )

m

48

0.58

3.76

0.042

50

2.21

5.71

52

4.09

54

k

6

Db

s~

(RS)



m 3

(ftxlC )

0.151

4.045 1 48 • 14 1.125 I 174

0.708

7.71

0.265

0.641

306

2.18

6.05

9.71

0.378

0.449

436

4.44

55

7.03

10.71

0.432

0.393

498

5.79

56

8.02

11.71

0.487

0.349

561

7.36

57

9.02

58

10.01

59

11.01

60

12.01

61

12.00

I

I

0.055

I!.

12.71

0.540

0.317

618

9.04

13.71

0.593

0.287

682

10.90

!

14.71

0.646

0.203

745

I

15.71

I I,

0.698

0.243

807

12.95 I 15.10

,!

0.748

0.227

863

.! II

I

16.71

:

I

!

I

The major attraction of the part of the procedure concerned with bed load

I

diccharg~

~ified

11.38

Einstein

i5 that the difficulty

of accurate measurement of energy-surface slope is avoided; data required is 1io1ted to the size

distri~utlon

grav! ty of the bed material and the variatiC':>l velocity, depth and width at a single

the

and specific

vn th

stage of mean

cross-see~ion.

A further

advantags is the simplicity of the necessary computations, only three. equations and one graph being required.

The important

effect of the hiding of small particles is st.ill included, although it can be seen from table 4.1.j. that a

sl!g~tly

wider range of

particle sizes has been calculated to be in notion.

However,

th~

modified procedure haa been developed for the computation of total sediment discharges in sand-bed rivers and the VA,lidity of

modif~.r.e.t1C'r.s

3 and 4 for coarse ,ravel-bed rivers such as the River Tyne is uncertain.

SClmOEDER and HEMBREE (1956) found gooe agreemant

between measured and computed sediment discharges in several sand-bed rivers in the United States of America. 91

------_._-

-

Although the regime theory has been developed with the i-.ediate purpose of facilitating the de.ien of stable channels in alluvial . .terial it is possible that the slope equation given by

BLBNCH and QURESHI (1964) (equation 2.2.e.) could be used to

.

determine the bed load discharce of a river, such as the River Tyne, in which both water and eediment discharge. fluctuate

w~de1y.

An attempt was made, therefore, to calculate the bed load disoharge at the Bywe11 cableway section at a stage of 61 ft A.O.D. usina the regime theory. Bquation 2.2.e. can be rewritten:-

flll(C)

=

kl

F

1/12



• • •



m bo

At the cableway section, EF, Q = 44,950

C.lSQC

at the near

baakful1 stage, H = 61 ft A.O.D. From thB g-ra~ of surface-energy e slopa against stage Cfig. 3.4.d.) S = s = 1.365 x 10-3 • The e product kIm was arb! trarily assumed equal to 1.3. From the crosssectional profile (fig. 3.3.c.) W was found to be 220 ft.

The

terticle size distribution curve of the bed material (fig. 3.5.e.) gave 450

~

gave P

= 4.50.

ao

0.129 ft, for which fig. 4.2.a. (BLENCH and QURESHI, 1964) Substitution of the appro9riate values in

equation 4.2.a. J.ielded fillce) :: 0.947,

whic:~.

indicates zero bed

load DIOvement. It would appear, therefore, that the regime theory 1s not

y~t

8ufficient1y developed for the unsteady conditions of cravel-paved rivers.

92

4.3.

other Bed Load Theories

In addition to the nine bed load theories applied to the River Tyne at Bywell many more were found in the available literature. Although they wore not used for bed load computations at Bywe11 , mainly because various coefficients (IO and exponents (m) could not be evaluated, they are mentioned briefly in this section.

From the results ot a series of tests on various materials

GILBERT (1914) proposed several bed load formulae, one of which stated that for a particular material under given cond1tions:qB

= K7 (q

- qc)

CHANG (1937) conducted laboratory experiments on three different materials and concluded that:-

CIa

n

T (T

= KS -2

o

T

0

-T

c

)

C

in which n 1s the Manning roughness coeffiC'i.ent nnd

where

0

i8 the ratio ot the longest to the

~~o~test

T

c

is given by:-

diameter ot a

Chang also mentioned formulae attr1l-;uted to:-

particle. Chyn:

'I B

=KV~(T 9 0

-T)

Fabre:

qB

= KloSe 3/ 2 (Q

- Qc)

c

3 2 where qc = K1I(Ss - 1)7/9d/Se / Casey:

Qn

where q

c

=

m

1(12 5 e 3 ('I - qc'

= K13 di/S e 5/4

93

The UNITED STATES WATERWAYS EXPERIMENTAL STATION (1935) tested nine sands in laboratory flumes and concluded:-

t

m

T

a.-=-n1 -B

in which

-

T )

0

It17 Y1.

5

c

.--.------

= O.013ajy f (S :J - l)d/M, where M is the KRAMER (1934) c

T

uniformity modulus of a mixture. O'BRr~N R1v~r

(1936) analysed material dredged from the Columbia

and suggasted:-

qB

=n

TP

18

m (V/al/3) 5

SHULITS (1955) mantioned that Haywood developed the followlng:-

qB

= K

19

d~(S c q2/3/d~3

- K ) '20

The regional report from Japan in the procceGings at the

INTEHH!..TIONAJ.. ASSOCIATION FOR IiYDP.AUL lC aESE..'!.RCH (1959) stated ·~nat

t.:l1.lbnki anaJ.ysc.d dat". from the ...:xperioonts of GI:J:umT (1914)

to obtaln:-

PANTELUPULOS (1955, 1957, 1961) considered the importance of turbulence and the velocity distribution near the bed:-

where d

k

is a characteristic grain size.

B~~DI

(1965) attributes the following formula to Levi:-

Bogardi also mentions tho experiments of Pedro11 with bed load movement over a smooth inerodiblo bod giving:T

o

8/5 3/5 l/5 d g

3/5 \11/5

- 23.2 Y

Ys

94

s

\I

ROTTNER (1959) applied the technique of dimensional analysts

to the results of several experimenters to obtain:-

LAURSEN (1958) introduced the ratio of the shear velocity to the fall velocity of the bed particles 1n an attampt to predict tl:·.<;;; total sediment load of rivers. Probably the most sophisticated, though as yet insufficiuntly Although too

developed, approach is due to BAGNOLD (1954, 1957).

conc.:3pt of bed load movement postulated 1.>y Bagnold is one in whicl . the w!lole bad 1s "live" and moves as a thick grain-fluid mixture ~he

variables deduced are the same a3 the 4.4.

In

erd~r

~

and l of

EI?~T.EIN

(1900).

Average Annual Bed Load Diocharge to calculate

th~

averagG annual b3d load dischnrbo at

ByweJJ. according to each of the nine methods of soction 4.1. i t was first necessary to establish the distribution of river discharge (or stage) above

1~J050

cusec (04 ft. A.O.D., 7.75 ft. flbove staff

ge1Jge zero) over as long a pr.riod of time as possible.

The 1.6a

Recorder instrument at Bywell provided a continuous record of Vlat~r

level for the ten year pe:r:'.od 1956/66 but the time scale of

the weekly charts was too small to enable an accurate determination of the duration of high flows to be made.

Rocords were available,

however, for the year 1965/66 from the Fishar nnd Porter

Inatrumer.'~

which recorded the stage above staff gauge zero on punched a binary code form at intervals of 15 minutes.

possible to plot the hydrograph

o~

ta~e

in

It was thus

each flood greater than

12,050 cusec during 1965/66, determine the duration of flow abov0

any given discharge and summate tor the whole year to produce tho cumulntive flow frequency curve (curve 1 of fig. 4.4.n.). 95

Recorr.r3

~--------------------------------------------------------------------------------

~--------------------------------------------------------------------

of mean daily flow were available for the ten year period 1965/66

~nd,

had it been po.:sible to deacribe tho c.i3tributicn of flow withln a single day I theG3 recorda cculd have b..}on used to dei:rH'mine tho cumulative flow frequency curve

fo~

that time.

of the punched tape records fo:...· the dC".ys in rive!:" dischnrg'J

WAS

Howover, examinr>t.i.o••.

I9G~/66

during whicni;he

greatt3r thn.n 12,050 cusoc showod that tho

distributiuns of flow wit;lir. each of these dayn wore not normal. and thflt !.Juak rli::.:chargc in a alngle dr.y varied from 1.2. 'co 4.3 moan tlow for that day.

til!J~:J

ih.

Hence, the requirod cu!'vc could not UJ

obtained 'zroUi the ten year record of mean dO-ily flows by stp:ti3tical mathu~s.

curves of

It was decideu to plot the Clear.. d~ily

flow fQj', both

l,~p!>er p~!"ts

1~o5/66

01 the

d~ratlon

and 1955/Ga (curves 2 and S,

J:'oJl3p0ctiv;ly, in fig. 4.4.a.) anel th,;;,n ootimHt., tho cumulativo flow fre(Juency cUt"ve for 1956/66 (curve <1 in fig. '1,£loa.) by

cOnlpf,'I:":~:1·)r..

The calculationo of p.verage a:u'!ual bed 10&_\ dIscharge ar3 (;i vell in ta.ble 4.4.a.

Tha average length of timo-1 par y ... ar dUl'ing wh:lch the

rlv0T discharge (or stage) is curve 4 of fig. 4.4.n.

~';.thi.n

n given range waD obte'.ined from

The bed lond discharf,'l in that range of rtvcr

discharge (or stage) according to each of the nine methods was taken from fig. 4.1.m.

Multiplicntion and summation for all ranges then

gnve the average annual bed load discharge.

The corresponding bed

load discharges for the yoar 1965/66 hnve been comptltGd from curvo 1 of fig. 4.4.0.. ac:d show toot the esti mnted cumulative flow froquenc> cm've for 1956/66 \\QuId have to be

substantln~.ly

nlt0 roc1. to produ-:;',3 a

significantly different total bed lond discharge. As would be Qxpected the discharges vary greatly;

calc~llltecl

averago annual bed

10::.\~;.

if the Meyer-Peter nnd MUller method i:3 to

96



Kal1nske

I

ton

ton/hr

Einstein tOrVhr

Mod. Einstein ton

ton/hr

ton

4.83

141.4S

18.51

379.4f

33,81

625.4E

2.41

44.5E

51.52

695.52

5.95

80.3~

80.50

805.ex

10.46

104.6C

3.05

30.50

134.46

1176.91

22.54

191.5S

7.56

64.26

204.41

1226.4E

45.08

270.4E

12.88

77.28

280.14

1260.e;i

77.28

348.6E

25.76

115.92

365.47

1279.H 115.92

405.72

46.69

163.41

470.12

1527.8S 167.44

544.U

75.67

245.92

590.87

1181.74 244.72

489.44

109.48

218.96

724.50

1267.8'3 326.83

571.95

156.17

'73.19

909.65

1364.41 404.11

606.16

220.57

330.85

090.77

545.3S 479.78

239.89

293.02

146.51

).3478.43

1884.90

3897.57

1.3.480

3 1100

22 1 210

6,260

llSS<>.

t

2 530

1



ton/hr

I

Ya1in

Egiazaroff

ton

ton

ton/hr

tOn/hr

I

Meyer-Peter and MUller tOn/hr ton

Schokl1tsch ~ -~

171.58

17.71

327.63

2.41

44.5fi

27.37

369.49

35.42

478.11

3.54

35.40

37.03

370.30

85.33

853.3C

12.88

109.48

6.76

57.46

49.91

424.23

157.78

1341.13

101.43

605.58

13.68

82.08

64.40

386.40

251.16

1506 .9El

204.47

-920.11

25.76

115.92

SO.50

362.25

354.20

1593.9<:

326.83

1143.90

41.86

146.51

96.60

338.10

474.95

1662.32

473.34

1538.35

53.13

172.67

115.92

376.74

605.36

1967.42

652.05

1304.10

85.33

170.66

135.24

270.48

759.92

1519.84

843.47

1484.82

110.09

192.65

157.78

276.11

922.53

1614.42

1054.55

1581.82

141.68

212.52

180.32

270.48

1107.68

1661.52

1324.22

662.11

174.68

87.34

205.27

102.64

1308.12

654.06

t. 9353.271 ~1350

+ ~1060 ,

8.37

I,

I

1273.21

-1,2702,040

4046.43

!

1419~

4,050

--1-

~

!

14897.61

6 1 710

25_1 09,?.

Table 4.4.a.

Computation of annual averasa bed load di80harse of the River Tyne at Bywe11

(19~~66)

Staff gauge zero : 46.25 it A.O.D. Range of discharge (cusec)

Range d. DUration stage (ft A.O.D.) (hours/year)

Schie1ds toD,/hr ton

12,050-13,710, 13,710-15,480,

54.0-64.5

29.50

54.5-55.0

20.50

15,480-17,360

55.0-55.5

18.50

17,360-19,340

05.5-56.0

13.50

19,340-21,430

56.0-56.5

10.00

21,430-23,600

56.5-57.0

8.50

17.71

23,600-25,930

57.0-57.5

6.00

~,

Straub toD,/hr

, I

ton

I

I ,

I

I 150.53

97.74 I 370.30 I 602.14 :

7.24 37.03



70.84

579.60

109.48

1238.89

152.95

656.88 688.21

25,930-28,310

57.5-58.0

4.50

96.60 275.31

28,310-30,830

58.0-58.5

3.50

439.53

1538.35

199.64

698.14

30,830-33,440

58.5-59.0

3.25

656.88

2134.86

252.77

821.50

33,440-36,160

59.0-59.5

2.00

914.48

1828.96

316.56

631.12

36,160-38,910

59.5-60.0

1.75

1151.15 1t 2014.51

381.57

667.74

452.41

.678.61 1266 • 86

38,910-41,940

60.0-60.5

1.50

,41,940-44,930,

60.5-61.0

0.50

discharge (ton)

I

, 111576.19 I 2384.28 '

: 2376.19 11188.10 ,j

;j Averago annual bed load

I

:

'13031.08 ,

533.71

~179.90

~!

"

I' ~

:





, I I

j

6 1 180

13 1030

~

Bed load discharge 1965/6 (ton)

!,

I

20,220

10 510 1

I

be

cons~dered

the most reliable ·(section 4.1.11) then a figure of Accordtng to IAn and

15,000 ton could be accepted tentatively.

BORLAND (1951) i t has been suggested by Mnddook that for grnvel rivers with suspended sediment concentrations of loss than 7500

p.~

m

then the average annual bed load discharge amoul,ts to between 5% anu 12% of the suspended sediment discharge.

HALL (1964) has given

130,000 ton as the F.verage annual ouspended sodiment discharge at

Bywe:Ui

tak:.i.ng an aV6rage of C!% gives an annual LIJd load dinc!uu;::,.

of about 11,000 ton.

Since Hall used the duratlon curve of moun

daily flows for the five slighly drier yoars 1956/61 i t is likoly that a more accurate estimate of th::: average

m~nunl

load would be somewhat greator than 130,000 ton.

suspondod Comparison wi til

other rivors is difficult due to tho scarcity of field measuraments of hod lond discharge in gravel-bed rivors.

Howovl3r, KRESSER. nnd

LASZLOFli'Y (1964) have heen able to stnto that tho r:lver Iech, with

catchment area to its of the

~iver

confluenc~

with the River Danubo equnl to thflt

Tyne at Bywell, has nn annual bed load

di9~!harge

about 15,000 ton (11% of the susPGnded sediment dischargo) of up to 4 inches in diameter.

of mn'~erifll

The foregOing figures appoar to

corroborate the results of the Moyer-Peter and MUller method. 4.5.

Conclusions

The main conclusions drawn from the application of

0.

number of

bed load theories to the aiver Tyno near Bywe11 can be discus sod in r~lation

to the nature of the bed material and the hydraulic

characteristics of the reach. 1.

Bed material Most bed load formulae utilise the concept of n criticnl tractiv0

force or critical bed shear stress for the initiation of motion of tho sediment

particl~s.

This has caused n certain amount of confusiol!, 97

mainly due to the difficulty of defining precisely these cdticnl conditions.

Some researchers have taken it to mean conditions at

weak, medium, or general movement of the bed particles, while others have used the conditions prevailing at zero bed load discharge, obtained by extrapolation of experimental date.

For a singlu

particle size the equation or diagram (f1g. 2.2.a) of Schields, who accepted the latter definition, can be used to obtain tho criticnl pertaining to that size;

for a sediment mixtUre such aD

that at Bywell, however, the concept of critical conditions of movement is rather vague, since a to represent the range of siZes.

MEYER-PETER

and

MULLER

sin~le

size

At zero

b~d

~ust

then bo

soloct~u

lond dischargo the

(1948) formula reduces to n for~ agreeing

closely with the Schields equation for fully developed turbulent flow.

It might seem, therefore, that the MI?Y,1r-Pcar and MUller

representative diameter, d , should be used in tho Schields equat"lon m

Account

to obtain the critical tractive force of a sediment mixture. must be taken, however, of the natural accumulation of larger

Also,

particles on the surface of the bed of most sravel rivers.

:"'l

described in section 3.5.5., particle shape can play an important part in the susceptibility to movement of the sediment.

At Bywoll

the bed surface particles are predominantly disc-shaped (table 3.5.j.) and rest on the bod in such a way as to increase their resistance to Hence, if it is required to estimnte the stn,e or water

movement.

discharge at which movement of a coarse-grained, disc-shaped bed material will commence a particle size slightly larger than the representative diameter, dm' (for tae bed material at Bywoll, possibly d

55

or d

SO

of the composite bulk sample) should be used

in the Schields equation.

99

Ft·.,.

the computation of discharge rates by some bed load formulae

it was necessary to select n single Size, such as the medium diamvter, d

50

, or d , to represent the sediment mixture. 40

It would seem thnt

the Meyer-Peter and f.tUller representative diameter r d , is more m appropriate in this respect since it has been found by

experim~nt

to

describe sediment mixtures in movement and its calculation involve:: the whole size distribution curve. r-ome

bej

load theories

reco~nJ!Je

the dubiot;snoDs of asslgJ1L-.g a

single particle size to a large range of sizes.

P-illj

di13cll:.uge ratas for individual

sediment

Com~nrison

siz~

ranges of

p.

attempt tv

~~:i vt"

ralx·i;cLi.~e.

of tables 4.l.c. (Schok!Jtsch methocl.j r.nd 4.1.0. (Kalinol,;:a

method) with tables 4.l.h. (Einsteln mothod) and ( . l . j . (modifi.Jd Einotcin procedure) illustrates

cl~arly

interference between particles of

that 11og10.>;; of the

dL~fcrent s~ %)u

large predic-t;,'3d loads of fine material.'

:;'uncts to

r.lutll:11 eY..trcrn'~ I y

The Ein!:!toir. t'.nd modi!.!:;-.;

Einstein methods include & correction factor for this important influence, but for

the~r

application to the River Tyne it was

necessary to extend the validity of this factor to the large size and range of sizeS prevailing at Bywell. All nine bed load formulae applied to the Bywell reach were developed using empirical constants or fUnctions obtained by observation of the behaviour of certain sediments, usually of uniform size, in certain flows along laboratory channels.

Tho

size and range of sizes of the bed material at Bywall were found to be greater than those of any of the material used in these experiments

and in this reSpect extrapolation, sometimes considerable, was necessary.

99

2.

Hydraulic characteristics The rational theories consider bed load movement to be a

steady, uniform flow process and use shear or stream power (product of shear and velocity) as a measure of the trancporting ability of the flow. D_ll these

theor~_es

pr~dur0

EXC0pt for the modified Einstein

require the accurate determinr..tion of

~nergy-

slope for the evaluation of these menRurCA.

su~face

in scction 3.6., flow conditions 1.n most natural rivers, (lspd.;ially thoG0 with the "p::>ol-bar" configuration of tho Riv~r Tyno, rnr~ly

uniform or steady.

(fig~.

3.3.a. to 3.3.e.).

Cross-se~tional

anrl !!lay be affected by wind or of

~lope

t:l:~_ns'/erse

s!u'.pe3 vary

cUI'rents.

n1'e

con:~in,jl"~

t.ly

Mensurernun~;

over a long reach may overcome some tlH:!:tculties,

bu~

enc-:-[,-y-surface gradients thus obtc_inod may not be repre:Jen-:;p.tlv:: of the single cross-section at which bed load di schar-go is to b-: Thus, measurements of bod shear usIng

estimated.

ener8'y-surfD~e

slope are unlikely to be accurate, especially in gravel-bed rivers. Accurate estimates of slope are of particular importance in tho application of the MEYER-PETER and

MULLER

(1948) and EINSTEIN (1950)

methods, which divide total bed shear into that due to particle friction (effective shear contributing to the movement of the sediment) and that due to bed cOl)figuration. and

b~ller

With the Meyer-Peter

equation effective bed shear is obtained by multiplying

total bod shear by the reduction factor (kt/kr)3/2j k

t

evnluation of

requires the use of the Strickler uniform flow equation. In tho

Einstein method the !{eulegnn equation is used to divide total hydraulic radius into a certain

cn~es

,

II

and R •

(Einstein proposed that in

the curve of EINSTEIN and BARBAROSSA (1951), shown

in fig. 4.1.1., should be used to effect this division; 100

data

from the Bywell reach, however, indicated that the curve may not be applicable to all types of rivers).

It c&, be seen that the necessity for accurate measurement of energy-surface slope is the main stumbling block of noor1y all bod load formulae.

In the development of the modified Einstein

procedure COLBY and

HE~mREE

(1955) overcome this difficulty by

using the solution of the Keulegon equation for (RS)

m

for a

known mean velocity as a measure of effective bed shear.

More

recently COLBY (1964) suggested that mean velocity nnd depth together are a sufficiently accurate, and certainly more conveniont, measure of the transporting ability of flow in a sand-bed river. From the abovQ considerations on the nature of tho bed motorial and hydraulic characteristics of thoUver Tyne at Bywell i t can bu seen that methods available at present for the estimation of bed load discharge are likely to give only approximato results.

For

computation of discharge rates of coarse-grained disc-shaped sediment thero is clearly

0.

need, not necessarily for

l)ut possibly for the development of existing methods.

0.

new formula, In the

same way as the Einstein procedure hns been modified to give bed load discharges in sand-bed rivers, so it may be possiLle to extend the procedure, or more likely the Meyer-Peter and MUller equation, for application to gravel-bed rivers.

This further

development must deal with the three prinCipal drawbacks of present methods:1.

Accurate evaluation of energy-surface slope.

It mny be

possible that where effective bod shear is to be used as a measure of the transporting ability of the flow, then current meter observations of velocity near to the bed could be used to obtain shear directly proportional to

101

the square of this velocity.

Alternatively,

me~.

velocity

in the total depth may be measured and a relationship such as the Keulegan shear.

equatio~1

used to determine effective bed

In this way, a complete

progranm~

of current

meter observotions could yield the variation of shear both across the section and with river stage. 2.

'!'be influence of particle shape.

More information is

needed on the shear strosse. required to initiate movement of the coarse disc-shaped particles observed to fore n natural pavement on the surface of most gravel-bed rivers. The effect of particle shape on transport rntes also requires attention. 3.

Mutual interference between particles of different sizes. If the new method is to estimate bed load discharge rotes of individual size fractions then more must be known about the "hiding" of smaller particles in the laminar sublayer and between larger particles, especially for the largo ronges of sizes occurring in rivers such as the River Tyne.

The bed load rating curves for Bywell computed by nine of the methods available at present (sections 4.1.2. to 4.1.10) are shown in fig. 4.1.m.

At a near bankfull stage of 61 ft A.O.D. calculated

bed load discharges vary over n very wide range from 120 lb/sec by the Ynlin method to 1350 lb/sec by the Sehiolds method.

Calculoted

values of critical stage at which bod load movement begins can be seen to lie between 54 ft and 57 ft A.O.D., or 7.75 ft and 10.75 ft above sta.ff snuge zero.

The discrepancies between tho rating

ourves are most likely due to the various degrees of extrapolation of parameters such as particle size, water depth etc. and also to the different concepts of bed load movement and the pertinent assumptions embodied in each method. 102

If one of the methods in sections 4.1.2. to 4.1.10 is to be considered the most reliable then the

MEYE~-PETER

method hils several points in its favour.

and MfiLLER (1948)

It is basod on a

theoretical foundation, the Froude low of Similarity, and utilises a wide range of experimental hyuruulic and sediment data.

This

data includes the results of experiments on sediment mixtures. The formula is relatively 8imple to use, and has been found to desc~ibe

the movement of bed load in certain European gravel-bad

ri vera.

For these reasons the Meyer-Peter and MUller method is

considered to yield the moat reliable estimate of the bed load ratine curve for the River Tyne at Bywell.

However, conSiderations

of the influence of particlo shape (section 3.5.6.) indicates the

mct~lod

th~t

mtly somewhat overestimnte discharge rates of the

predominantly disc-shaped sediment at Bywell.

Also, due to the

natural paving of coarse material on the bed surface and the resistance to entrainment of the disc-shaped particles, critical stage is probably slightly higher than that given by the rating curve, i.e. at about 56 ft A.O.D. (9.75 ft above staff gouge zero). Using the Meyer-Peter and MUller rating curve with a flow frequency curve for the ten year period, 1956/66, the average annual bed load discharge of tho River Tyne was calculated to be about 15,000 ton, approximately 10% of the average annual suspended sediment discharge.

nle results of other workers on similar rivers

corrobOrate these figures.

Experience gained in this research

programme indicates thnt if any future investigation should require eBtimation of only the annual average bed load discharge of n particular river, then a figure of 10% of the average annual &~spendeci

sediment discharge (as suggested by LANE and

BORLt~ND,

1951) will be as accurate as, and more easily obtuined than, the result of application of any bed load formulae to the river. 103

~ART

II.

Measurement of Bed Load Discharge

Seci:ion 5 j.

Mens"itrcment of Bed J,ona ;)isch:'\rgc in :avera

5.1.

Methods of Measuring Bed Load Discharge

Although the measurement of suspended sediment discharge in rivers can be relatively easily effected there exists at present no single apparatus or procedure which has been accepted as being completely adequate for the determination of bed load dischnrge over the wide range of sediment and hydraulic conditions occurring in nature.

The majority of literature in this field has been

published in the German, Russian and East Europcc.n languages and, nlthough some translations are available at

variou~

estnblishments

1n the United States of Amorica, only Reports 2, 8 and 14 of the UNITED

ST1'4TJS

INTE1-AGENCY COMr.IITTEE ON WATER nESOURCES -

SUBCOMHITTEE ON SEDIMENTATION and HUBBELL (1964) have revillwod existing techniquos and apparatus at length in English.

A largo

number of methods for measuring bed load discharge have been devised and are classified here a8:-

.amplers or traps, river

etructllrf,lS, trncer techniques, dune movement, and miscellantlous possible methods. with particular

They are discussed in sections 5.1.1. to 5.1.5.

rofore~ce

to their applicability in the range of

conditions prevailing in the River Tyne at Bywell. Bed Load Samplers The simplest and most direct method of measuring bed load discharge is to plaoe some kind of trap or sampler on the river bed and weigh the quantity of sediment collected ill n given time. Ideally, the bed lond sampler should:1)

not alter the distribution of water velOCity and bed load discharge in the vicinity of the sampler.

2)

collect the largest and smallest particles in motion.

3)

sample a definite width of bed, trapping all the materinl which passes through that width. 105

4)

be stable on the river bed

5)

be

correctly orientated both horizontally and vertically

on the river bed 6)

be

designed such that the height of the opening is at

least twice the maximum particle Size, and its width about 150 times the average particle diameter (NOVAK, 1957). 7)

have a leading edge which conforms to the shape of the river bed.

All the above criteria cannot be completely satisfied and each sampler should be calibrated to determine its sampling efficiency, i.e. the ratio, expressed as a percentage, of the weight of bed load collected during a given sampling time to the weight of bod load that would have passed through the sampler width hod it not Generally, the efficiency can most easily be

been there.

determined by laboratory flume tests;

however, even under the

controlled conditions in a flume, two main difficulties arise. Firstly, due to the size of most bed load samplers, scale models must be uoed to avoid nlteration of the flow conditions, thus producing the problems of similarity inherent in most 8ediment modol studies.

Secondly, the unsteady temporal distribution

(JOHNSON, 1939) and the lateral distribution due to side effects of bed load movement in laboratory channels render determination of

actual bed load discharge through the sampler width difficult.

ex~eedingly

According to HUBBELL (1964) calibratioD3 of certain

samplers have been carried out in flumes with

fi~~d

beds by

Ehrenberger in 1932 and in flumes with movable beds by Einstein in 1937.

The latter method more closely reflects conditions in

natural streams.

NOVAK (1957) conducted a comprehensive series

of tests on sevGral samplers using both methods. 100

The accuracy of the total bed load discharge in a river as determined by a particular sampler is 1)

affe~ted

The estimate of the efficiency of the

by three factors:snmpl~r.

Apart from

difficulties involved in the calibration of the sampler undor the controlled conditions of a laboratory flume, tho efficiency of the sampler may vary with any or nIl of the following:depth of flow, particle size, magnitude of bed degree of filling, and bed configuration.

lo~d

water velocity, discharge,

Sinco all of these

factors vary in natural streams, estimates of efficiency should therefore 00 considered to be highly variable and llD('ertain. 2)

The spatial and temporal distribution of

in tha river.

sedin~nt

transport

Not only must a sufficient uUmOer of samples be

taken across the section to

o~scrve

the lateral distribution of

bed load discharge but each sample must be taken over a length of time sufficient to account for the OSCillatory or unsteady character of bed load movement. Ehrenberger

(HUBBEL~,

From lOOasurements made with bed load samplers 1964) concluded that variations in the River

Danube and Inn could be characterised by constant periods of oscillation of 18 minutes and 7 minutes, respectively.

KAROLYI

(19~7)

also observed similar fluctuntions on rivers in Hungary and postulated that, while these variations may have boen to some extent due to the inaccuracy of the bed load saoplers, the fluctuations were the result of pulsations of

wat~r

discharge and

v~locity

helicoiaal currents, bods and tha reflection of

lnr~~

from various obstacles such as islands, banks etc.

due to water mnsoes It can be seen,

therefore, that maximum accuracy would be achieved by sampling at n few verticals over a long period of time;

on rivers with rapidly

changing stage this may prove to be impossible.

101

3)

Methods of suspension of the snmpler in the river.

Bec:l.use

of the hydraulic resistance of most samplers an elaborate system of suspension and retention cables may be necessary.

As the sampler is

lowered into layers of progressively decreasing velocity it achieves an upstream motion due to its own weight and the elastiCity of the cables.

In this way the sampler, on reaching the bod, may scoop up

bed material not in movement.

MEYER-PETER (1937) has suggested that

a form of rieid suspension would minimise this elfect.

In addition.

when the samrler is on the bed, fluctuating drag forces may cause the sampler to oscillate and possibly scoop sediment from the bed. In general all bed load sample.cs can be classified according to one or more of the following types:-

box or basket, pan or tray,

and pressure-difference. Box or basket type samplers operate by retaining sediment that is deposited by a reduction of the flow velocity in a box which is open at the front and top, or in a basket which 1s screened by mesh on all sides except the front.

According to Report 2 of the UNITED STI.TES

INTE3-AGENCY COMMITTEE ON WATER RESOURCES - SU'BCOMUITTEE ON SJ4]DIMENTATION

one of the earliest devices was used by Davis in 1898 in the Nicaragua Canal and LAHAYE (1948) mentions a trap used by Schatfernak in 1908. In the 19308 soveral more sophisticated basket type traps using rudders to improve stability were developed for use on European rivers by MUhlhofer, Ehrenberger, Nesper (fig. 5.1.a.) and tho Federal

A~thority.

Swis~

All these samplers were of a sirnLi.ar deSign, the

latter three hc.ving leadine:;

~d;;es

conformed to the shape of the bed.

of loosely woven iron rings that Experiments by Ehr"311berger and

and Einstoin showed thnt their sampling efficiencies varied from 30% to 80%, figures which were later verified by NOVAK (1957).

The usc

of tho Ehrenberger sampler to meaS".lrc coarse hod lOud diGcharge on:::1H"> 103

Fig.5. T.a . Nesper

Flg. 51 b .

box

Po/yakov

type

pan

s amp/ er.

type

sampler.

~

...

Fig. 5.1. c.

0.3 mrn

SRI H

me s h

press ure

differ ence

t ype

bag

Sa mpler.

60crn

90crn Fig.5. 1.e.

175 cm

Fig . 5 .1. d .

Arnh ern

differenc e

type

pressure sampler

Sphinx

difference

type

pressure Sampler.

River

D~nube

has been referred to by KRESSER and LASZLOFFY (1964)

and TSCHOCHNER (1964), while BOOA::.oI (195l) described a wire-mesh basket type sampler used on the River Tisza in Hungary.

Because

of their large capacity these types of samplers are more suitanLe for the measurement of the discharge of coarse bed load, but they cause considerable disturbance of flow and are subject to selectivity of sampled particle size. Pan or tray type samplers, which have been uEod principally in Russia, are usually wedge-shaped in longitudinal section with the pointed end of the wedge facing upstream.

They operate by retaining

the sediment particles which roll or slide up an entrance ramp into n transverse slot or series of slots.

HUBDELL (1964) described

th~

samplere designed by Losiebsky and Volyakov (fig. 5.l.b.) which havo been shown by Shamov to give

effi~iencies

as low DB 30% and 46%,

respectively, mainly due to the accumulation of sediment in fro;.t of the adverse slope of trie entrance ramp.

This type of sampler io

only suitable for low velocities in smooth, sand-bed r:tvers. In the operation of ordinary basket and pan type

samplo~s,

tho

resistance to flow of the sampler causes an undesirable disturbance of the water and sediment regime at the sampler entrance.

The

pressure-difference type sampler has been designed so that entrance velocity and stream velocity are maintained equal by constructing the sampler walls so that they diverge towards the rear, thus creating a pressure drop at the sampler exit.

Report 10 of the UNITED STATES

INTER-AGENCY COMMITTEE ON WATER RESOURCES - SUBCOMMITTEE ON SEDIMENTATION described two trapo based on the pan or tray type designed by the [;cielltific Research Inotitute for Hydrotehnics (fig. 5.1oc.) in Russia and by the United States Corps of Enginoers, Little Rock.

The Arnhem bed load sampler (fig. 5.l.d.) descrlbeti uy

SHAANK (1937), has been developed to collect mo.terial in the 109

&-'-ZC

range C"l5 to 5 mm in a fine mesh bag flexible attacherl to a rigid rectangular entrance.

According to MEYER-PETER (1937) the effioiancy

of the sampler is about 70%.

Its use on the Dutch part of tho

River 1binc has been rofered to by ELZERMAN and FRIJLINK (1051) nnd TOPS, WEMEL'3FELDEtl and VOLKER (1959) and on the River Niger by

NEDECO (1959).

Another pressure-difforence type trap, called the

Sphinx sampler (fig. 5.1.e.)Jhns been

~evloped

in Holland by

VINCKEaS, BIJKER and SCHIJF (1953) for grain size:.> smaller than 0.4 mm. Tn this sampler flow enters through a rectangular g~nQually

no~zle

that

becomes circuiar, passes through a series of sottling

chambers and then out a wide a«it at the rear.

BOOARDI (1951)

described how Karolyi modified the wire-mesh sampler used in Hungary into a pressure-d1fference type sampler wHh n horizontal, curved divili,ing wall about midway between top and bottom of tho roar of the sampler.

NOVliK(l957) found from laboratory tests that

this sampler, which was used to measure coarse sand and gravel discharges, has nn efficienty of only 45%

After

eD

~xhoustive

series

of laborai;ory 'tests on sCllle modnls of several bed lond samplers FIt the Vyzkumny URtav Vodohospodarsky (v.U. V), Prague, NOVAK

(19G'l ~

1959) developed a new pressure-difference type trap, known as the V.U.V. sampler, for collecting bed loati. in the size range I to 100 mm nnd in water velocities of up to 3 metre/soc.

The efficiency of this sampler,

which is desci':"hed in greater dotnil in Section 5.2, was det.ormined by model tests to be 70%.

HUBBELL (1964) tncntions two traps of

..l

s1.milar type designed by Uppal and Gupta for use in Indian Cnnule bui; no information concerning their efficiencies 1a available. River Structurea According to Report 2 of the UNITED STATES INTEll.-AGEN CY COMMITTEE ON WATER PJ!:SOURCES - SUBCOMMITTEE ON SEDIMr!:NTATION MlJhlhoffor in 1:)33 trapped bed 10ac4 in a series of boxes placed in the r;i.ver bod with 110

their t,ps flush with the bed surfaco in order to determino tho partlc1e size distribution of the material moving nlong the rivol' bed.

Ot.her in'JGstigntiors hnvo extend;;d this idea to the

determination of bed load dischru'ge by measurinG the time requi:l.'od for a slot, pit or trench of known volume to fUI. eJ.nborntG installation, which

~las

The most

been described by JOHNSON and

DOBSON (1910), was constructed by '. .'he United E;tutes SolI Conservation Servi~G

on the Enoree P.iver, South Carolina.

Thw .:Intire 100 feet

wi.dth of the river was concreted and divided by piors into 14 cha;muln, eA.ch havj.ng a grated s lot which could be ope nod and closed. tl~rough

load wilich dropped into the slota wns pumped 01lt

BIJd

n pj.pe

beneath the concrete floor to a hopl>':i!' on tho bank for weighillS MGnsureroc:nts of suopendcd load w(n'o also made and cOllt1nu~:Js

~.n

8

this wny n

r.:cord of total sediment dischargo could be made (EINSTEIN,

ANDEHSON and JOHNI:SO!~, 1940).

EINGTEIN (1944) described n semi-·

portnble slot type structure usod by the United States Soil ConscH--vation Service in Mountain Creek, South Carolina, operating on the sam') principle of wi thdrav';\l of tho trapped s()cHment UlCas:Jremcn~

by weighing.

u~1d

HUBBELL (1964) proposed Il similar pit

sampler but its use is probably restricted to sand-bed strealllB of low velocity. It is possible that the devices constructed for tho exclusion O~~

oediment froti, irrigation, power Ilnd m'h:icipel

considered for the measuroment of bod lond

can~ls

dls;::hc:cge~

could be ROBINSON (.i.960)

improvod upon the vortex tube saud trap devised by Pn=ohllli which we::.: observed to 1>0 vm·.y effectiv\3 in th'7 removal of conl'se matorinl up to "(le instrumGut consisted of a tube wi"\;h u slot

the size of cobbles.

nlc.I1g the 'I::)P plncCtd in the stream bed c.t an anglo 0:Z 45 di rection of flow;

0.

vortex

motio~l

J.11

o

to the

was thus inducet! inside tho tub<),

washing the trapped sediment out at the downstream ond.

Efficiencies

of between 80% nnd 100% are possible with these slot or pit samples. Another type of structure, working on a difforen1: principle, is the turbulence flume constructed on the Middlo Loup River, noar D~nning,

Nebraska (SERR, 1951).

A specially designed series of

br-.ffles were installed in the dver to induce turbulence sufficient to hring the total sodimcnt load oi the sand-bed rivor into sucp.:nsion.

Conventionai

ware used to IThjllsuro the suspend"',l

m~thods

r.Kl.terial and these observations ware compared with suspended s~dimont

dischargQ

mC~Gurements

(SCHnO~DER

at an upstream section to give the bod lond and

HEMEk~~E,

195G).

thE major disadvantage of all such structures is the excessivo cost of both construction and operation. Trncer Techniques During the last decede severnl investigations have been cnrried out

alon~

the connt and in estuarios using tracers to determine the

direction of movement of sand and silt in marine Th~

~nd

tidal currents.

various methods by which sodLmant particles cnn bo

been dese-tbed by KIDSON

nn(~

CARR (1962).

labol~od

hnvo

The HYDRAULICS HESEf.;lCIf

eTATION (1961), ZENKOVI'roIJ (1960) and Rl!:ID and JOLLIF}t'E (1961), using

fluoresc0~t

tracers Duch nc rhodamine , primuline, anthracone

and 1 imogene , have obtainod useful qualitative results. however, no direct

m6llsure~:nts

beGn made with fluorORcent Similar coastal nnd

of bed lond

di~charg~

in

At present, ri~ers

have

trace~s.

t..;r.·~;u~rjne

investigations h'lvtl been conductuJ

with radioactive tracers in Japan (INOSE and SMlRAISHI, 19n.s), France

(G:i~RMAIN,

KINGDOM ATOMIC

FOREST and JAFFRY, 1957), Great Sri tatn (UN lTED

ENERGY AUTHC!UTY, 1957) and Hollllnd (ARLMP.N, SVASEK

and VERrGlRK, 196C).

In France est:l.mates of total bed load 112

dischf1"~oE'

occurring during several floods on the River Rhona near Lyons were made by RAMETTE and HEtrlAL (1962).

At the Hydraulics Research

Station, Wallingford, England, research has been carried out (DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH, 1960 to 1965) on tho usa of radioactive tracors for the determination of sand transport rates in a 5 ft wido, 350 ft long laboratory flumo.

Two

techniques, similar to those used in dilution techniquos of water dischnrge measurement, hnvG been dove1cpod.

In the space-

integration method (CRICKMOaE nnd LEAN, 1962a) the bod load diachnrgo was deduced from observations of the activity distribution downstrOI'.m of tho point of injection of the irradiated sand

particl~s.

nlO

time-integration method (CRICKMORE nnd LEAN, 1962b) involves the determinn'~ion

of the time variation of activity at a fixed point

downstream.

These mothodo have been applied to the sand-bod

River Idle, in Nottinghnmshire, but tho accuracy of the results cannot be evaluated.

Similar experiments have been carried out in

the United States of America by HUBBELL and SAYRE (1964; who, assuming n

Lagrangian probability concept 0! sediment transport, derived

distribution

functions of concentration and discharge similar to those

of EINSTEIN (1950). Results of the British and American research indicate that tracer techniques aro feasible in laboratory flumes and sand-bod rivers. Their major restrictions are that

maasuro~nt

must be made over an

extended period of time during which conditions must romnin steady, and that a sltil1ed team of operntors is required. Observation of Dune Movement The possibility of determining bed load discharge from the diroansions fUld speed of movement of dWl3S and ripples in chnnnels was realised over seventy years ago (HUBBELL, 1964). 113

However, it is

only rerently that technicnl advances in portablo electronic equipment have enabled rapid and reliable determinations of bed configuration over large areas of the bed of a channel to be made.

SIMONS, RICHARDSON and NORDIN (1965) proposed a bed lond

equation based on the mean forward velocity and mean height of ripples and dunes.

Good agreement with measured sediment discharges

was obtained when this equation was applied to the observations from a sonic depth recorder in laboratory flume experiments with four uniform sands from 0.19 to 0.93 mm.

Although dune movement is a

promising line of research, the proposed equation requires soveral assumptions concerning uniformity of sediment and flow conditions nnd is only applicable to dune and ripple forming sedimento. 5.1.5.

Other Possible Methods

Several other poasible mothods which havo been investigated nro mentioned by HUBBELL (1964).

Kennody and Mundorf independently

proposed bed load samplers for collecting small particles that are composed wholly or partly of magnetic minerals.

However, since

the specific gravity of such particles can be as high as 5.2 they are unlikely to be representative of the behaviour of tho majority of particles in a river bed. Taniguchi developed a method for computing total sediment load using a tiltmeter, conSisting of a Z8llner pendulum suspension and recording equipment, which measures variations in ground tilt duo to the passage of different weights of water and sediment through a channel.

Several important assumptions are necessary and it seems

likely that the tiltmeter method could only be applied to rivers with large variations in sediment discharge and which flow through u~consolidated

materials. 114

A device using ultrasonic waves has been developed by Smoltczyk for use on beds of fine sand.

It consists of an open-ended

rectangular tube with a transducer and reflector housed in opposite sides of the tube;

the transducer transmits and receives the

reflected high-frequency sound waves enabling the amount of acoustic energy absorbed by the sediment water complex to be calculated. Several important, unverified assumptions are necessary to relate the absorbed energy to bed load discharge. Some attempts have been laade to photograpn bed. load movemaHc but a number of technical and practical difficulties were encountered. It appears that the use of photography would be restricted to streams of low suspended sediment concentrations and transporting bed load particles greater than

t

inch.

Several attempts have been made to detect sediment movement by recording the sound emitted by coarse bed load particles.

This

promising possibility is discussed in greater detail in sections 7 and 8. 5.2.

Use of V.U.V. Bed Load Sampler on the River Tyne at nywell It can be seen from the literature review of section 5.1. that thv

portable trap and permanent structure are the only techniques of bed load discharge measurement applicable and sufficiently developed for the flow and sediment conditions of the River Tyne at Bywell.

However,

the construction and operation of a permanent structure was impossible due to a lack of finance and personnel.

The development of an entirely

new sampler was also precluded, for two main reasons.

Adequate,

precise knowledge of the size, distribution and rates of movement of bed load at Bywell would first have been necessary for the design and testing of a new sampler, and existing laboratory facilities were inadequate for the determination of the stability, performance and efficiency of a new sampler.

Correspondence with the 115

lIydrauUo~

Research Station, Wallingford, England and the Federal Inter-Aaency Sedimentation Project, Minneapolis, U.S.A. indicated that no research on samplers of coarse bed load discharge was being conduoted in Great Britain or the United States of America.

It was decided, therefore,

to try to use the V.U.V. sampler designed by NOVAK (1957,

19~9)

at the

Hydraulics Research Institute, Prague, for the following reasons:1)

The V.U.V. trap was designed to sample particles of up to

4 incheD diameter in flow velocities of up to 12 ft/sac, oonditions similar to those expected at Bywell.

EXamination of the Northumberland

and Tyneside diver Board gauging records showed a maximum recorded velocity just below the surface of 13 ft/sec and it was considered from inspection of gravel shoals in the Bywell reach that the

Qu~'tity

of material In motion greater than 4 inches diametor would not be significantly large. 2)

The trap had been subjected to an exhaustive series of

laboratory and field tests. 3) 5.2.1.

The trap has a relatively high sampling eff icJ.ency of 70% The V.U.V. Bad Load Sampler

The V.U.V. bed load sampler, which was developed by NOVAK

(19~7)

from the Karolyi pressure-£ifference sampler, is 2.8 metres long, hns D.

50 em x 20 cm opening and can collect a sample of about 30 Kg

(fig. 5.2.a., 1n pocket).

The principal features of the instrument

are the horizontal curved dividing wall which separates the lower sediment-retaining part of the sampler from the upper direct flowthrough part, and the rear door which was designed to improve the stability of the sampler while covering the 5.5 cm high slit at the rear of tho lower part.

During lowering and raising, the tenSion

of the suspension cables maintains the rear door In a closed position, the water flowing through the sampler and out the wire mesh in the top renr part of the sampler.

When the trap is located on the river 116

bed the suspension lines slacken and the flow of water causes the rear door to open until the top of the door rests on the rudder. The shape of the sampler and the position of the wire mesh wore designed such that with the rear door open, sufficient pressure drop is created at the exit to overcome the flow resistance of the sampler.

Experiments showed that the hydraulic efficiency (the

ratiO, expressed as a percentage, of the water discharge through the sampler to the product of the undisturbed mean velocity of flow at the entrance and the area of the entrance) of the sampler is 100%. Novak carried out comprehensive studies on the V.U.V. sampler and four other types of sampler in laboratory flumes of 60, 100 and 250 cm width and with sampler models of scale ratios of 1:1, 1:2,

1:4 and 1:8.

Determinations of sampler efficiencies were made with

the samplers placed on fixed beds (Ehrenberger method) and on movable beds (Einstein method), with particle size mixtures and individual size fractions ranging from 0.1 to 100 mm, and with mean water velocities from 0.6 to 2.2 metres/sec.

The model scales, particle

size ranges, and velocity ranges wore selected in each test so as to obtain approximate similarity with the flume size.

Sampling

efficiencies of the V.U.V. sampler were calculated from the ratio, expressed as a percentage, of the weight of sediment retained by the sampler to the weight of sediment which would have passed through the sampler width, for fixed beds (

np ) and

for movable beds (~ ) as

s

shown in table 5.2.a. From the results of laboratory tests Novak also concluded that the efficiency of the V.U.V. sampler increases only slightly, if at all, with particle size nnd water velocity.

It was found that the

sampler retained particle size distributions that agreed, in general, with the size distributions of the actual bed load, and that the 117

efficiency is independent of the degree of filling so long as it does not exceed 30% of the sampler capacity. Table 5.2.a.

Sampling efficiencies of model V.U.V. samplers

Sampling efficiencies scalel Ratio of flume in indicated flume r.tl~ width to sampler I (mode width in 250 cm 100 cm 60 cm to I indicated flume "roto- 250 cm 100 cm 60 cm 11 11 p Tl p 11 Tl lls p s s .. ype) 82 52 5 1:1 1:2

10

4

1:4

-

-

8

4.8

I

I -

1:8

- I!

16

70

64

-

-

aecommended overall efficiency

-

-

75

40

-

-

93

61

72

58

I 83

55

-

-

70

Details of the V.U.V. bed load trap were obtained from Dr. Novak and a prototype sampler constructed from 16 s.w.g. brass.

Particular

care was taken to ensure the correct dimensions, especially those of the horizontal curved partition.

A eecond hinged door was provided at the

rear of the lower part to enable the samplor to be emptied of collected For ease of

material.

transpo~t

the sampler was constructed such that

it could be dismantled into box and rudder.

The weights of these two

parts were 86 lb and 60 lb, respectively, giving a total weight of 146 lb.

(A

test of the suspenSion cable of the Bywell cnb1eway

showed that it had a tensional breaking load of 0.77 ton, i.e. ten times the weight of the sampler).

Five

S in

diameter cables were

attached to the sampler by small brass shackles and their lengths adjusted so that the sampler could be suspended from a Single point at o

an angle of about 20

to the horizontal with the entrance uppermost.

This ensured that, on immersion of the sampler, the rudder would enter the water first and correctly orientate the sampler to face upstream.

118

Sampling Attempts It was decided initially to observe the stability of the sampler when suspended by a single cable from the Bywell cableway. The first tests were made at a low stage of about 2 ft above staff gauge zero (600 cusec) and it was found that, despite very slow flow velocities, there was considerable resistance during raising and lowering, and that correct orientation of the sampler on the bed could not be guaranteed.

Two further trials were made at

stages of 7.8 ft (12,000 cusec) and 6.0 ft (7,IOO.CU80C).

Several

attempts were made on each occasion to place the sampler on the bed at a distance of 50 ft from the left bank where surface velocities would be about 8 ft/sec.

\Vhen the trap was let down on to the water surfnce

the rudder entered first and, as expected, the trap turned to point upstream.

However, the pressure of the flow of water on the

underneath of the sampler caused it to move downstream, but remain on the water surface, as the suspension cable was paid out. 15 ft downstream of the cableway the trap entered the sudden increase of load on the suspension cable.

At about

w~ter

causing a

As the sampler sank

to the bed it became extremely unstable and correct orientation on the bed could not be ensured.

(It should be recorded that no material

was colleoted by the sampler on the river bed at the 7.8 ft river stage). It was obvious from these preliminary trials that either a rigid suspension or a system of suspension and retention cables would be necessary to ensure both the accuracy and safety of the sampling procodure. 5.2.3.

Possible Sampling Methods

The use of a rigid suspension of the bed lond sampler would obviate the need for an elaborate system of cables and also improve the accuracy of the instrument (section 5.1.1.).

Some preliminary calculations were

made for a twin-hulled boat moored to the cnbleway as shown in fig. 5.2.b. 119

c ablewoy

Winch

_ - - w inc h

- tWin-hulled boot flow 4--

flow

ret en tic.' n

anch or

coble

"

~

/'

FIg. 5,2. c.

Fif:!..5.2.b . l'T'l ain

ca b/eway

up tream c ob/ewllJY

cobLeway

r reten t ion ca bl e

suspension cable

I

_flow flow

I

fix ed (1( cht..1r

--~~~==========~~

elevation .

ret entio n cable ~

-

fl o w

flow winch

winch

plan

plan

winch

Fig . 5,2. e.

Fig. 5 . 2 . d . Cdbleway

winCheS

t wo

cab /eway

l ef t bank winch

fl ow

suspension cable -

reten tion - - c a bles

right bonk ---anchor

_ _ flow

elevation

e/evot ion

lelt

bank pulley

n c h or

___ flow

plan

winch

winch

---flow

winch

w inch

plan

Fig. 5 . 2.g. Fig. 5.2. f.

suspension arrangements for be d load sampLer "

However, on tentative enquiries to the Northumbrian River Authority the scheme was rejected as the cableway was not designed to take lateral loading. Fig. 5.2.c. shows the method of suspension used by Novak for measurement on the River Danube in Czechoslovakia.

There were two

main objections to using this type of flexible suspension at Bywell:1)

The material of the bed was too large to ensure that an

anchor would remain fixed when dropped on to the bed. 2)

It would be impossible to manoeuvre sufficiently in high

velocities. An alternative method, similar to that used on the Danube, is shown in fig. 5.2.d. where the retention cable is anchored permanently to the bed some distance upstream.

Tho major disadvantage

is that there would be only one position of the sampler nt which the retention cable would be parallel to the direction of flow.

With

a 1000 ft long retention cable the sampler would be inclinod at an angle of 9

o

to the direction of flow when placed near the bank.

The retention cable could bo attached to a travelling pulley on a second cableway upstream of the gauging station as shown in fig. 5.2.0., enabling sampling to be carried out at any point across the section. The distance between the cableways would have to be considerable sinco the retention cable would be inclined to lift the londing edge of the sampler off the bod. Another possibility would be the use of two retention cables attached to winches at the top of each bank (fig. 5.2.f.).

Using

the winches it would be possible to maintain the sampler vertically below the cableway. The system shown in fig. 5.2.g. could also be used.

With this

system the retention cable would be nDchored near low water level on 120

the right bank, passed through a ring on the front of the sampler, round a capstan or pulley near low water level on the left bank and wound on to a winch at the top of the bank. The Northumbrian River Authority were approached with the possibility of using a suspension system similar to either fig. 5.2.f. or fig. 5.2.g., although it was realised that these methods would require at least three operators and could be costly.

However,

permission could not be granted and ettempts to make direct measurements of bed load discharge were therefore abandoned. 5.3.

Conclusions

The most accurate method of measuring bed load discharge is the slot or pit type structure which traps all of the sediment moving along the whole width of the river bed.

By means of withdrawnl by

pumping and then weighing of the collected material a continuous record of bed lond movement can be obtained.

However, the oost

of construction and operation of such struotures will usually be prohibitive, especially in larger rivers. Since all portable bed load traps affect the ambient flow and sediment regime by their presence on the bed, each trap must be calibrated to ascertain its sampling efficiency under given conditions.

This can only be effected in laboratory flumes with

sampler models, thereby introducing similarity problems nnd detracting from the reliability of the determined efficiencies.

In addition,

the efficiency of any sampler is likely to vary with water volocity, particle size, bed loed discharg€, degree of filling and bed configuration, and since these factors can vary considerably in a single river, the true efficiency of the sampler must be rather uncertain. Due to the oscillatory, or unsteady, nature of bed load movement a ~l

single short-term measurement is not necessarily representative of the mean bed load discharge;

to determine the total bed load

discharge in a river each point in the section should be measured for a considerable time. For the measurement of the discharge rates of fine sand and sand the Sphinx and Arnhem samplers are probably the most suitable although precise information concerning their efficiencies is not av£ilrble.

The V.U.V. pressure-difference type saI:lpler, which was

sQlected for use on the River Tyne at Bywell, is the most advanced sampler of coarse bed load for the following reasons:1)

It has been subjected to a comprehensive series of

laboratory and field tests to determine its stability, performance nnd efficiency. 2)

It has a relatively high efficiency of 70%, which varies

little, if at all, with particle size and wnter velocity. 3)

It samples sediment sizes from 1 to 100 rum and generally

gives a good representation of the Size distribution of the bed load. 4)

It can be used in water velocities up to 4 metre/sec.

The techniques involving readioactive tracers and dune tracldng by sonic recorders are promiSing, but are not yet suffiCiently developed.

Several other methods such as a magnetic sampler,

tiltmoter, ultrasonic device and underwater photography have been used with limited success. Preliminary experiments with the V.U.V. bed load snmpler suspended by a single cable at the Bywell cableway gauging station indicated that a system of suspension and retention cables would be

necessary to ensure correct orientation and stability, nnd hence

accuracy and safety.

Several suggested alternative arrangements

were rejected by the Northumbrian River Authority and all 122

att~mpts

to

measure bed load discharge at Bywell had to be abandoned.

These

investigations have shown that the measurement of bed load discharge in rivers under nny conditions is, at present, likely to be

cxtre~ly

costly and that the use of a bed load trap at n cab1ewny gauging station would require at least three winches and a team of three operators.

123

Seotion 6 6.

Development of Apparatus for Laboratory Investigation of the Acoustic Detection of Bed Load Movement

6.1.

Aims of Laboratory Experiments

After the attempts to make d1rect measurements of bed load discharge using the V.U.V. sampler at Bywell had been abandoned, wit was decided to consider further a possible means of detecting coarse bed load movement which hitherto had been investigated by only a few research workers. The method, mentioned briefly in section 5.1.5., involves the recording of some measure of the intensity of sound emitted by moving bed load

particles either during collison with an object placed on the river bed or during inter-particle collis10n.

S1nce most of the other methods of

measuring bed load discharge described in section 5.1. have been found to be either unsuitable or impractical in the sediment and flow conditions of the River TYne at Bywell, it was decided that the method of acoustic detection warranted further investigation.

Plans were

therefore made for the design and construction of a suitable instrument which could be used at the cableway gauging station near Bywell.

The

development and use of this instrument is described in section 8;

a

survey of existing literature on the acoustic detection of sediment movement is also included in sect10n 8 since all previous work in this field has been concerned solely with river observations. Soon after the decision to develop an acoustic bed load detector the Hydraulics Laboratory of the Civil Engineer1ng Department of the University of Newcastle upon Tyne received from ....................,., 11................. some equipment intended for use

sediment channel.

a8

an experimental

It was then decided that, at the same time as field

investigat10ns were being carried out, a series of controlled laboratory experiments would be conducted to evaluate the potential of the method as a means of not only detection but accurate tneasurement of bed load discharge~

The aim of the laboratory experiments was, therefore, to

investigate the relationship between bed load discharge in the 124

laboratory channel and the intensity and frequency of the sound emitted by the moving bed material. The sediment channel, in the condition received from the manufacturers, could not be used immediately for the planned experiments.

Considerable modifications had first to be carried out,

and the eqUipment for the measurement of sediment feed rate, sediment discharge, water discharge, etc. had to be

develo~ed.

The deSign,

construction and testing of the necessary apparatus proved to be n considerable task, occupying much of the available time, and is described in this section;

the experiments, their analysiS and the

resulting conclusions are described in section 7. 8.2.

Description of the Sediment Channel

The 40 ft. long, 18 in. Wide, tilting, glass-sided sediment channel with a self-contained circulatory water system was located in the basement Hydraulics Laboratory in the Stephenson Building of the University of Newcastle upon Tyne. General Description The general arrangement of the sediment channel and the associated equipment is shown in figs. 6.2.8. and 6.2.b. The water supply for the system was stored in a 10 ft x 6 ft x 3 ft deep galvanised steel sump tank;

it was found necessary to

raise the sides of the tank near the channel outlet and to extend the channel outlet chute to avoid splashing.

Approximately 60 lb of

sodium nitrite were added to the 1250 gallons of water in the system to give a 0.5% by weight solution for protection against corrosion. Water could be extracted from the tank by a 10 in axial flow pump, running at 1470 r.p.m. and powered by a 20 h.p., 3 phane, a.c. motor.

(The 12 h.p. motor supplied by the manufacturers was 125

~iment Wdr~ng

sediment weghing device

-

lSin. wide sediment

-

channel

sediment

feed 10ft x 6ft x 3ft sump tonk

lOin. pipe

-

10in. diameter axial flow pump

onflce

p lot~-

butterf 'y valve

meter

PLAN

sediment woeighing manometer

adj ustable outl et wei r

--s ump

sedime nt feed

3m. deep sed iment bed

It
L

tonk

sediment trap 40ft . c hanne l l enath .

ELE VATION

1="1g. 6.2 a

Laboratory

sed im e nt

c hann e l.

' •• :':.

heade r tank



.0

• C\I •

\D



bO

oM

found to be overloaded when pumping low water discharges, and took 5 months to be replaced).

It was also found necessary to replace

the length of flexible pipe connecting the suction side of the pump to the sump tank by a specially fabricated length of mild steel pipe. o

To avoid the entrainment of air at the pump intake a 90

bend had to

be fitted insido the tank leaving a 6 in gap between the intake and the bottom of the sump tank. The water was pumped through four 10 ft straight lenlths of 10 in diameter mild steel pipe, and thence through a 10 in diameter butterfly valve by means of which the water discharge could be controlled.

Since the whole channel, including the header tank,

was designed to move both horizontally and vertically during tilting it was necessary that some flexible connection be provided between the butterfly valve and the header tank.

However, the 4 ft length

of bellows-type tubing supplied by the manufacturers extended and pulsated violently at high discharges and had to be contained in a specially oonstructed cradle of

i

in diameter steel rods.

Water entered the base of the header tank which was 6 ft deep, 3 ft long and 18 in wide and contained a mesh screen located immediately above the inlet.

Since the header tank and the channel

were of the same width and since no curved vertical tranSition wag provided, the state of the flow entering the channel was extremely turbulent with superimposed waves and surges.

Some improvement was

obtained by placing a wire basket containing n bank of 12 in long, 3 in internal diameter fire4 clay field drains just inside the channel. The flume itself was rectangular in cross-section with glass sides and a steel base, having approximate dimensions of:length, 40 ft;

width, 18 in;

height, 21 in.

It was supported by

a frame of 5/16 in steel plate, 21 in deep, with several stiffening 126

cross-members.

Five pairs of 4 in diameter wheels, attached to the

side of the channel support frame, rested on five equally spaced fabricated steel pedestals.

The centre pedestal was bolted to the

floor and by means of a large diameter turn-buckle screw between the pedestal and the underside of the channel it was possible to move the whole channel over the length of a pedestal.

The parts of the

pedestals on which the wheels rested were sloped such that movement of the channel could produce forward (positive) or adverse (negative) slopes of up to 1 in 240. At the downstream end of the channel a 2 ft long by 4 in deep depression of the bed fitted with three 2 in diameter gns connections on ench side was provided by the manufacturers as a sediment trap.

For measurement of the rates of gravel movement

obtainable in the flume it was necessary to modify the arrangement as described in section 6.2.6. The

i

in thick aluminium adjustable outlet weir wns held in

position by a number of Allen cap head screws whose location .lose to the outlet chute made manipulation of the Allen key difficult. A further inconvenience was that the weir height could not be adjusted without the flow of water being shut off. 6.2.2.

Measurement of water Discharge

Although the measurement of water discharge was not required for the intended experiments, it was considered, however, to be an essential part of the setting up of the sediment channel. The general layout of the channel was unsatisfactory for the accurate measurement of flow rate for the following reasons. Arrangements for volumetric measurement the most direct and acourate method, were precluded by lack of space 1n the laboratory.

It would

also have been impossible to use the outlet weir as a sharp-edged 127

rectangular weir since during experiments flow conditions immediately upstream would have been disturbed by the sediment trap.

An

alternative method would have been the inatallation of an electromagnetic

flown~ter

in the 10 in diameter return pipe, but the cost

of the meter and recorder was considered dIsproportionately high. According to the BRITISH

ST~u~S

INSTITUTION (1964a)

publication doaling with pipe flow measurement there was insufficient length of pipe downstream of the double bend and axial flow pump to reduce vorticial flow disturbances to a level at which an orifice plate meter could be used.

It was deCided, however, to insert an

orifice place at n distance 30 ft downstream of the pump outlet and to attempt to reduce swirl by the installation of flow straighteners in the pipe

(fig. 6.2.c.).

Using the approximate formulae given by

the BRITISH STANDAIIDS INSTITUTION (1964a) a sharp-edged orifice pl(\te meter with D and D/2 prosllure tappings was designed for a DlOzimum discharge of 4.50 cusec and a pressure difference of 60 in of water. The required orifice size was calculated to be head loss of about 2 ft),

7i

in (irrecoverable

A suitably sized orifice plate was

machined in the Civil Engineering Department workshop and installed with pressure tappings leading to a differential pressure water manometer constructed to measure head differences of up to 5 tt of water (fig. 6.2.d.).

Large pressure fluctuations were greatly

reduced by the insertion of a cross-shaped flow straightener made of

!

in steel plate (fig. 6.2.e.) 20 ft upstream of the orifice plate. The acourate formulae of the BRITISH STANDARDS INSTITUTION (1964a)

were used to calculate the calibration curve shown in fig. 6.2.f.

As

a check on this calibration a sharp edge was machined on the crest of the channel outlet weir, the sediment trap was covered and the channel set horizontal.

(The sediment bed was not then in place). . 128

A point

h flow

orifice

straightener

plate

il

1

ZQ U

Fig.6.2.c

Location of on flc

platt!

o~o

1Ql

ond

_ ..1 01.1

flow

~

stralQhtener

O(ln.)

70

adjustable 60,n.

scale

L..

I

gl SS tu be

40 flo

50

C

II\,

c: ~

0

60 c --

hi

,.

~

S3urc>

1/2/n

Fig.6.2.d.

7Flin

Orifice

plate

m

t

r

arrangemtnt

I

flow

,,\

c: o

w

,,\\

1 3~ i,., . flo,., SJ C

Fig 62. c

Flow

~1I 1. mil e/ Sf plate

straf(;;htener.

./

ld

1011'1.

~

aeler tank

60

50

40 Pressure difference (in. water)

Calibration according to B.S. formula.

30

20

• Calibration

check

sharp-edged

with

outlet

we ir

10

o~~~

________ ____________ ______ ____- L____________ ~

~

~

DI.charge (cusec)

Flg . 6.2 . f.

Calibration

of Orifice

plate

____________

~

5

3

C'

~

meter

gauge located upstream was zeroed

OIl

the wir crest using a preoi8e

level and the head on the weir measured at several water discharges. Discharges were calculated according to the BRITISH STANDARDS INSTITUTION (1964b) publication on flow menaurement in open ohannels and found to agree well with the orifice plate meter calibration curve (fig. 6.2.'.).

At discharges above 2.15 cusec the ratio of

head to weir height exceeded the limit stipulated by the British Standard. 6.2.3.

Measurement of Channel Slope

The slope of the channel was measured by means of a form of U-tube fixed to the side of the Channel.

Two

6 in lengths of

i

in internal

diameter perapex tube were attached in a vertical position to the channel aides at a distance apart of 400 in.

The U-tube was

completed by a length of green plastic hose bracketed to the channel and filled with water lightly coloured by was

~et

fluoresc~in.

The channel

horizontal USing a precise level and two 6 in scales, graduatod

in 1/20 in., were located beside the perspex tubes and fixed with the 3 in graduat10ns at the same level as the meniaci in the tubel.

For

any inclination of the channel the rise or fall of the channel bed over a length of 400 in. was thus equal to the difference of the two scale readings. Time was not available for the provision of rails for a sliding instrument carriage or piezometer tappings to enable measurements of depth and water-surface slope to be made.

For sediment 8tudie8

involving the assessment of bed shear stre8s 8uitable equipment of this kind would be essential. Sediment One ton of rounded, uniform-sized river gray.l (£la. 6.a.S.) was obtained from Hoveringham Gravel Co., Hovertngham, Nottingham for use 129

Scale:

full size

Median diameter

0.197 in. (5.00 mm)

Geometric mean diameter

0.198 in. (5.03 mm)

Geometric standard deviation

1.30

Specific gravity

2.62

Specific weight

163.5 Ib/ft

Bulk density

92.5 Ib/ft

Fig. 6.2.g.

3

3

Gravel used in laboratory investigations

1n the experiments.

Sieve analysis produoed the particle 8ime

distribudon ourve of fig. 6.2.h. from whioh the following properties obtained:-

wer~

Median diameter, d SO

= 5.00

Geometrio mean diaceter, d g

mm

= 0.197

= 5.03

rom

in.

= 0.198

in.

Specific grrwity, specific weight and loose bulk density were determined according to the

STANDARDS INSTITUTION (1960) as

BRI~ISH

tollows:Specific gravity, Ss Specific weight,

= 2.62

Ys = 163.5 lb/tt3

Loosa buJ.k density

= 92.5

lb/ft

3

The gravel was composed of a mixturo ot partioles ot limestone, sandstone, quartz etc. About 3 in. deop

1

ton of sediment was placod in the channel to provide a

be~ ov~r

cheat brass.

n length of 35 ft and

contain~d

by end piece.

ot

The remainder of tho sediment was stored either in tho

hopr'3 :t' of tha feed dav:lce or in bins in the ground floor Hydraulics Laboratory. 6.2.5.

S~din~nt

In an

attem~t

Foad Device to determine the best method of feeding gravel at

a tixed rate into the channel several universities and research establishmen-::;a were approached.

The literature of previous laboratory

workers in sediment research and the It

fir:£lS were also consulted. be

W~:1

catalo~ue8

of several eb.mical

tound thnt most teed dtrricos

cou~.d

classified in the to110winr mrulller:1) Material contained

~_n

a hopper 1s fed axially to a rotating

disc beneath the hoppar and oxtracted by means of an adjustable deflector blade.

The hopper itself

OQll

be vibra.ted or the

drive shaft of the rotating disc can pass through thG material in the hopper. 130

... 0

.

'"

..

..

...

.

..

;.

0



0

"'"

..... !O

C>

...!=' Q

U.

N

" ...

<)

..

o

'"'"

.,

.

I

.. ..... '"IP

...

io

... ::

a rnrn.

~

3rnm.

5rnrn.

'"

'"

..

2) Material is fed from a hopper, sometimes vibrated, into oue end of a horizontal shaft in which a motor driven screw rotates. The

mat~rial

is discharged from the other cnd of tho shaft at

rate dependent upon the speed of rotation of the screw.

The

Vibra Screw Feeder manufactured by Simon Handling Engineers, Stockport, Cheshire is of this type and has been found by the Hydraulics Research Statton, Wallingford to be ideal for the feeding of sand and ground anthracite into hydraulic models

(OEDOW, 1965). 3}

Mater.ial is fed from a hopper on to a moving belt passing beneath the hopper.

The foed rnte can be controlled by tho

speed of the belt and the height of an adjustable gate on the hopper. 4) Material ia held in a tray or shallow box which is inclined

The truy is tapped or vibrated causing

at a small angle.

the material to pass under an adjustable gnte at the lower end of the tray. All types except 3 are usually unsuitable for material coarser than 2 or 3mm and the princIpal disadvantage of commerCially available machines is the difficulty of obtaining suffioiently low feed rates. Enquiries were first made to Simon Handling Engineers who claimed that their Live Bin Belt Feeder would be able to feed S mm gravel at rates between 10 and 600 lb/hour. was lenrn-I: soon after thnt

t\

The price quoted was £573.

.It

local firm, United Analyots, East Boldon,

Co. Durham used a form of belt feeder for taking and dividing snmplep> of crushed coal and other solid materials in a flowable cond-Ition. Arrangements were made to borrow one of their feeders so that could be carried out using the 5 mm gravel. a smnll hopper

<1

ft

3

cap~clty)

tOBt~

The feeder conSisted of

located above a 6 in. wide plastic 131

n

compos:=_tion belt and fitted with a 3 in. wide gate of ndjustnble height.

A spring-loaded metal plate beneath the belt mointoinAd

contact between the hopper bose and the belt.

'rhe belt was driven

by a smnll elect.dc motor through a worm reduction gear; the size of the pulley

011

either the gear or the motor it was possiblo

to determine the feed rates 0p\3ninga. in the

by changing

p~oduced

by different belt speeds and gate

It was also found that at Dmall eate openings the gravel

hop~1'

tellded to depress the spring-loaded plate and become

jammed between the belt and hopper base. On

with

the basis of the rasult3 of these tests flnd in consultation

Un~.ted

Analysts a larger, continuously variable

~elt

feeder

designed and constructed in the Uni',ed Analysts workshops. price

o:~

Wf\S

The final

the device was £203, an obvious improvomem; on the price of

commercially available machines.

The feeder is detailed in fig.

~.2.i.

it

aad can be seen in the general view of the channel, fig. 6.2.b. consisted of a S ft

3

capacity hopper located above a 4 ft long,

{3

:In.

wide contir.uous plastic composition belt which passed round two 3 in. diameter aluminium pulleys.

Although tha alignment of the rear pulley

could be finely adjusted to prevent lateral movement of the belt over the pulley sides it was found necessary to provide guide runners on each side of the belt immediately before it ran on to both pulleys. In the original design it was intended that a series of 2 in.

dirul~ter

rollers placed beneath the belt could be adjusted in he1ght to mnintnin the

bel~

in close contact with the hopper buse.

However, it was

found that small particles still tended to become jammed between hopper and the belt;

th~

this problem was overcome by providing a short,

rubber skirt around the inside of thG hopper base and by placing n smooth, thin, steel sheet between the belt and tho rollers.

The

hopper was constructed with a 2 in. wide opening and an adjustable 132

-------------

6 ft 3 ca pa c i ty hopper

12 in. long. 2 in. vvide rubber- sk i rted hopper base

4 rt Ion g. 6in . wide plast ic composition be lt ~ 3 1n

_ 60 :1

pulley

..\" orm

reduction gea r 51n. pulley -

vv.· t l:

./ 2 in . vvide ....-./'; ;;'ate opening

-,/

belt t enSIon a dfustrnen t

/

/,,/

gate h~ight ad i ustment

/'

rollers. adjus t able height. replaced by thin steel sh eet to rnaintain cOntact betw een belt and hopper t .ase

2 1r; .

varia bl e

4

4/n

rubber-lined deflector

.....-pulleJ

8in . pu l:ey

61n

~

~

freely rotat ing shaft

pulle/

3~

pu[[e, _

a . c. motor h.p .• 1420 r p.m. _______

2 1n pull -r

,.

;>

~~,

S I de e/evatJo n

supportC0 by

F'r;} . 6·2 . 1.

slotted

Sed/men t

angle

eed

fr":::uT'evvork.

deVice

Front elevation

9ft. total heIght .

vertical gate.

Experience with the small belt feed had shown that

the feed rate was particularly sensitive to the height of the gate opening;

it was decided, therefore, to arrange the gate to have

only two fixed openings of nominally was provided by a

t

!

in. and lin.

The belt drive

h.p., 3 phnlle, n.c. motor, running nt 1420 r.p.m.

Two pulleys, 2 in. and 4 in. in diameter were fixed to the drive shaft

of the motor.

A further two pulleys, 8 in. and 6 in. in diameter, on

one enc of a freely rotating shaft above the motor enabled speed reductions of 3:2 and 6:4 to be selected.

The other

eu~ of

the

freely rotating shaft WrlS connected to a continuously variable V-pulley

~nd

belt pulley.

thence through a SO:1 worm reduction gear to the front nle whole arrangement was supported by n frame of

slotted l-..ngle and located such tho";; gravel falling off the belt wae deflected by a rubber-lined chute into the centre of the

upstre~m

end of the channel. Lack of clearance between the top of the hopper and the coiling nocessitate
Since the feed device wouid probably not

give consistent feed rates with damp gravel it was necessary to dry the matorial trapped in ths sediment weighing device at the end of the channel.

Wet gravel was placed in tho top comprlrtment of n

wooden box with a horizontal division of wire and sacking

a~d

warm

air from a 2 kilowatt fan henter blown into the lower compartment. By this menns about 4ft 6 hours.

3

of gravel could be surface-dricd in about

The dry gravel was then transported upstairs and stored-in

bins above the hopper of the gravel feed device. 'I'he device was calibrated using dry gravel for severnl pulley combinations and gate openings as shown in fig. 6.2.j; 133

belt speeda

~-----------------------------------------------------------------------------------

Q ::l

~ Ii)

,~-------------------------------------=~--------------------------------------------------

were measured at the same time nnd are also shown in fig. 6.2.j. th~t

It can be seen

feed rates could be varied from 30 lb/hr to

more than 700 lb/hr. feed rates could

b~

In experiments using finer materiRls, lower obtained easily by using a smaller gate opening

or by reducing the belt speed with

n

change of pulleys or gear

reduction. 6.2.6.

Meaaurement of Sediment Discharge

The sediment trap provided by the manufacturers at the downstream end of the channel had a capacity of only I ft

3

and

could be filled by largu sediment discharges in less than ten minutes.

Several attempts were made to construct devices by manns

of which sediment could be trapped and extracted from the channel without t!-,:) necessity of making c0 11siderable alteratit1lls to the It was eventually decided, however, to construct

channel itself. ~he

continuous woighing device shown in fig. 6.2.k. A. 12 in. diameter hole was cut in the base of the depression in

the channel and the remainder of the depression :tilled v'ith a cement morta:: and moulded in auch a way that all gravel dropping over tho brass end piece rolled through the hole.

A short length of 12 in.

internal diameter flexible, bellows-type tubing connected the hole ~o

the top of a 16 in. x 16 in. x 30 in. deep watertight box mode of

16 s.w.g. sheet steel.

Gravel could be removed from the container

through a watertight panel clamped by wing nuts to the downstream side of the box.

A

i

in. diameter valve was 1.nserted near the baSe

of the container to permit drainage of the box before removal of the gravel. When full of water alone the total weight of container and wator was about 300 lb; about 600 lb.

when full of gravel and water the total weight was

Lack of space in the laboratory and jnsufficiont 134

-=-

~ <4

cha nn el

. low

outlet we i rubber

l i n i ng

rr

b ross

.. ~

-

~

en do i ece - depre!5s ion r f chon n e ! ong. 4 ", dee

cernenr

rn

0

rt

0

he

~

~

I

I~

r

.--. -

II~

~ --- --

flex ibl e b e llovv s cc nnec Lon , ____ '2 i n . i nternal d I a me te r .

i_

'>

M

~

\\

!Ii ( i

I

kn i fe-edge supports. notched 2 i n.x V21 ( , ' I ''It bearing on l In SQuare t .},

ts

\

"" \

'II

+ ,I'./'"

scalc - - dr o/ n /n9

"

+'

-+

~2 in . x l~ in . 70 S "".9. R. H.S.~ ....

__- --4'4

in . ba t. in . )(

in.

, rcr-f ,.'le Facl ng ups.tream.

Se'i . men

Igr'ln~

\

~

b e o r l n g __ bloc k ~voc d ---- __

r: :Jnome:er

F I g .
II! 'J

~ +

I'1 '~

bor e :~ ope n-ended III ~ rn a no m e te r,-" .

Va in.

8 ft . long .

2 ,n. )( Flo ' r '-JOL r f e r re mo vol of sed / men ~

\~ S IX

16/nx 1 6 / n.x3 0irJ. II\. :J terr I 9 h t box. 16s.w.o. s heet ste el

I C~.

..

Inne r

' -7

tube.

to

accuracy precluded the use of most commercially available weighing machines for continuous weighing of the box as it filled with gravel. This problem was overcome by resting the box on a knife-edge on one side of n lever made of two lengths of 111n. rectnngu1ar-hollowsection bar.

The weight of the water plus container was counte;.·-

balanced by p1aciftt six 56 lb weights on the other side of the knifeedged fulcrum.

Any increase in load due to ffravol falling into the

contatner was transferred by a ball-bearing contact to a wOodc:m board resting ou a motor scooter tyre inner tube.

Tho tube was filled with

water and con.nected to a verticnl 8 ft length of

~

in. bore glass

tubing attached to n graduated scolo. Calibration of the woiffhing device was carried out by placing incrementa of weight in the container and notil1ff the height of thl3 maniscus in the open-ended manometer. that a direct

calibr~l";;ion

The loads were convertod so

of oonometer reading against dry weight of

gravel in the container was obtained (fiS. 6.2.1.).

(During

experiments an expanded graph of fig. 6.2.1. was usod for greater :;,ccuracy) •

Due to the turbulont condition of the flow immedtfltel)

downstreOlil of tha end of the gravel bed the manometer reading tended to fluctuate slightly with the fluctuating load on the inner tube. It was pOSSible, however, to read the manometer to tho nearest 1/16 1n. i.e. approximately to the nearest

1

lb dry weight of gravol in the

container. 6.3.

Microphone and Recording Equipment

In section 6.1 i t was mantioi.lad that the movement of .::oarse bed load particles can be detected by recorning the sound emitted by

eith~~

collision of the moving particles with an object placed on the sedimont The tormer technique sutfers from the

bed or inter-particle collision. same disadvantago as the use of

Q

bed load trop, viz. it causos n

135

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""

I

j:'

I

~l I.. I

I "-

11

"t-



! ..... ! · 1· '. 1--1':-- -- j-,f-;--- -'

,i' .-~ - ~ 'f-:- "-~1

.,

.1;

'1,. '

'T-'t-- -- - .• '''.. 1 r.. ',':', I

".'

.. 1

I

~-'~~I--4-L-t-L - ~!"_I--J_ .-.f--:I ~_~Ni .. !; tj, I' I I. '1.' . : ".1,., ," "." , :'

., . I.

I"~.:· ,... :.t·~· r-.....: .. ,. ; : 1:-. ' ., :. ,:.. ' I r·, l _. .:'. ,.J-." i'--.

,;

+

!

. '. _ ,

r

:1:

~

'

-1--- 1: -'~ '

i.

:!



:.

.'.

I . :. 1""

M '.1' . ".

.. ·1·:...

I

'1

j'

- I- I

~ . t-

'.

I'·

r" '

1

! i .. ;....... ! , ' I---j

,

disturb~nce

of the sediment and flow regime in the immediate vicinity

of the object placed on the bed. construct a small, streamlined

It was decided, therefore, to

micropho~\e

which could be fixed

rigidly above the gravel bed of the laboratory flume to detect the sound of uncistrubed inter-particle col11son.

This section describes

the microphone constructed for the experiments and the means by which the electrical signal picked up by the microphone was amplifiod, fllt~~ed

(when necessary), rectified and continuously recorded.

6.3.1.

Microphone

Descriptions of the various types of microphones in

existence~

e.g. cryetal, hot-wire, condenser, :zoibbon, moving-coil, carbon IdtC. can be found in most standard text books on sound and 1953b, STEPHENS and BATE, 1950). oth~r

(RICt~SON,

1953a

After referen<.\e to tho:'!le and

text books and after consultation with members of the staff of

the Physics Department of the University of Newcastle upon Tyne it was

de~ided

that a crystal microphone was the type most suited for the

intended laboratory experiments. The crystal type of micropho!le utilises the phenomenon piezoelectricity.

klOwn ftS

Certain crystalline materials (and some recently

developed ceramic materials) undergo eleotrio polarization when subjected to a mechanical streoa, the polarization being directly proportional to the stress, and depending for its Sign upon the direction of the stress. The

pheno~~non

This is known as the piezoelectric effect.

1s reversible and, in the converse pie"-oelectric effect,

when a piezoelectric material is electrically polarised it becomes strained by an amount directly proportional to the strength of the polarising field (a ICHARDSON, 1957).

The latter effect is used in

the production of sonic and ultrasonic transducers;

the former effect

is utilised in the detection of sound pressure waver. by recoldlng tho 136

electric polarization, or potential difference, produced in the material by the pressure waves. The most important

natural piezoelectric materials are quartz,

Rochelle salt and ammonium dihydrogen phosphate (KELLY I 1954).

In

recent years, however, many ceramic substances which exhibit the phenomenon have been manufactu!.'ed (CRAWFOEID, 1961). On the advice of the Physics Department of the University of Newcastle upon Tyne it was considered that a tubular ceramic element m~de

up as shown in fi •• 6.3.a. would be suitable for the detection

of underwater sound in the audio-frequency range (15-20,000 Hz). consistee of a modified lead zirconnte titanate

It

polycrystallina

ceramic (PZT4, plated and polarised) manufactured by Brush Clev1te Co. Ltd., Hythe, Southampton, moulded in the shape of the

followin~

thickness

i

d1mensions:-

in.

length, 1 in.;

Q

tube with

outs1de diameter, lin.;

Perspex endcaps were fitted (ensuring water-

tirhtness but not mechanically stressing the tube) such that incident sound pressure waves flexurally stressed the tube and cnused an electrical potential difference to be set up between outer walls.

One endcap was

therefore

th~

inner and

provided with a amnII hole

through which the centre core of a length of microphone coble could be connected to the inside of th3 tube by flexible copper foil.

The

outer insulated braiding of the cable was spread around the outside of the tube, tied by thread and soldered.

To ensure adequate

connection the whole tube was painted with conductive silver paint and then covered by a coat of waterproofing polyurethane.

Two

further coats ot each paint were also added. The prinCipal advantages ot this type of microphone are:1)

The more important physical

charact~ristics

a wide xoange of temperature and do not 137

are stable over

cha~ge

with time.

Modified l'tad Brush ClevlfQ

zircon ot~ part

titanotQ

nO. 1612

I

CQr arnlc

plc:t~d

and

PZT-4

polari~e d.

in.

durolix

~\lIt h

1/8 I". dia, hoi

for rrr (crophontt cobl

c"ntr~

ci

c

or~

o tt c

'-lJ

d

(>

to

cO(.Jp~r

II

-'" J

o

Insulation

£ out~r

broiding

or o un d

soldered

conn~ct lO rtS

p i r z o e/ectr i c tube Cooted w i l h 'conducrive

pa l nf ( ilver

wa ter proo f ing

p OIn t

pamt)

( po/y ..r e th o ne)

Fi g.6.3.a. Piezoelectric crystal.

spr~ ocJ

tub e and Sold er d

2)

It has a high mechano-electrical coupling factor, i.e. a large electrical output from a small mechanical force.

3)

In a tubular form the crystal ls non-directional, thus having littla frequency discrimination.

4)

It is possible to soft solder electrical connections without destruction of the piezoelectric properties.

5)

It is robust and reliable.

Since th3 microphone was to be suspended in flowing water it wr-s n:;!cessary to house the detecting element in a streamlined borty ac shown in fig. 6.3.b.

The solid hemispherical nose and conical

tail Eectlons were machined from glued

Hin.

sheets of perspBX.

It had be0n intended to make the centre portion aleo of porspex but it was

fo~nd

difficult to prevent the development of hairline cracks

at the connaction between the tubular brass suspension rod and tho perspex; br~3S

it was decided eventually to use a length of thin-wallod

tube for the centre portion.

Obviously, it was desirable

that minimum sound energy would be lost by reflection in the passage of

th~

sound pressure waves from the water to the detecting ei0ment.

The quantity of sound energy transmitted through the boundary of on{' medium with another is a function of the characteristic acoustic imr.~d,:tncf>s

of the two media i.e. a function of the product of density

and velocity of sound in each medium.

Since greater 30unrl energy

transmission occurs through the boundary of media with more equal acoustic impedance i t was decided that the cavity in the streamlined body should be filled with n liquid such as castor Oil.

(Table 6.3.a.

gives the velocity of sound in, and the density and acoustic impedanco of, various materials).

It would have been possible to ::i1l the

with water but since castor oil is electr1cally non-conductivo the possibility of short-circuiting due to leakage was thus prevented. 138

(~cv1ty

3~ in

brass

tube

7Bin. length .

4f::::::::

II

brass hydrofoil

I I ...II

shape #

~6in. microphone cable hemispher i cal machined from 3/ in. sheet

a

II

J.....

II

noSe

rub b er sealing r i n gs

glued

perspex .

conical

ta i l

mach i ned

3/8 ;n. shee t

from

glued

persp e x •

.r flow

c

f

crysta l

_"C'i C'i I

!a in. hole

I

;--- -.- ---- -1

for

fitl i ng cav i ty with

oil

o f I - I It t e d

ca v it y

18,n.

3

3 i n.

,

2~",in.

.

Scale:

7/,., t n.

2~

F i g . 6 .3 _b .

, crophone

i n. D .O ••

for detec ti o n

t6 of

i n . thi ck,

full

brass

sedi me n t

tube

m o v eme n t

in

l ab o ratory

c h annel.

size.

Table 6.3.a.

Acoustic properties of various materials Characteristic

Material

-

Density 3 (glcm )

1

Velocity of sound (cm/sec)

a~oustic

impedan§e (glaec cm ) I

2.62

5 4.22 x 10

Water (l5 C)

1.00

1.44 x 105

6 0.14 x 10

BraflS

8.40

5 3.40 x 10

6 2.90 x 10

Polythene

0.92

0.43 x 105

6 0.04 x 10

Perspex

1.19

1.62 x 105

0.19 x 10

Mild steel

7.70

5.05 x 105

6 3.90 x 10

CruJtor oil

0.96





Sediment particle 0

Ai5 (0 C, 760

I

1.29x10

-3

I I

5

0.33 x 10

nun) I

6 1.11 x 10

6

i

4.3~

*properties not available, but according to RICHARDSON (1957) castor oil has approximately same characteristics as water. At a distance of 2 ft from the downstream end of the sediment bed the streamlined microphone was suspended such that it could be moved horizontally and vertically inside the channel from a heavy angle-iron

fraa~

(fig. 6.3.d.). moto~

secured to the ceiling and a concrete column The transmission of vibrations from the pump and

through the channel waS thereby prevented.

Later in the

investigations, when the microphone had been connected to the amplifior and recorder, tests were carried out without the gravel bed to determine whether any sound would be detected by the microphone in the water.

At low discharges when the pump and motor were

generating most noise no signal could be detected.

At high flows,

however, it was found that air entrainment on the downstroam side of 139

the

circ~lar

brass suspension tube produced a small signalr

this

noise was eliminated by placing a length of thin, brass, hydrofoilshaped tube

al~und

the circular tube.

It was concluded that any

sound detected by the microphone with the gravel bed in place would be

caused

6.3.2.

by

the movement of the sediment particles.

Amplifier

In order to obtain an estimate of the probable strength of the output signal of the microphone and the required amplification it waa necessary to carry out some preliminary experiments.

At this stage

in the research programme the laboratory sediment channel was not completely operative and the sound emitted by moving sediment had to be

produced by allowing sediment particles to move under gravity

down an inclined trough immersed in a tonk

of water.

In the

channel the ssdiment particles would be moved along an almost level bed under the action of fluid shear forces).

The apparatus

consisted of a wooden hopper containing tin. ooncrete

ag~regate

located above a I ft wide wooden trough on which a layer of aggregate had been glued.

The microphone was suspended above the

trough and by opening a sliding gate on the hopper and allowing gravel to roll down the slope it was possible to decide upon the amplification required to give a measurable Signal. The circuit diagram of the amplifier and output oircuit used in the laboratory experiments is given in fig. 6.3.c.; itself is

~hown

in fig. 6.3.d.

the equipment

A power pack unit was constructed

which converted normal 240 volts, 50 Hz, a.c. mains supply to n 14 volt d.c. supply.

This voltage was applied across a resistance

and Zener diode to provide a ripple-free 10 volt d.c. supply, independent of mains variatiOns, to the three-stage transistorised

140

NKT

f

,

eA



m i crophon

e

204

---

680

80 2000

~

u.v.

power pock



r ecord

e r

ampl I f i er

main:!> supply

560

·2 •

A I Ire A ll

S I S t an c

CO p (lC l r.:J n

c S

es

n

0

in

4



.s

h m s. micro':tra1 s . F i g. 6 .3.c. Elect Tl c o/

c i rcu i t

labora tory

S·6K

dlogra

m c ro phon e

47K

33 0

A

8K fre quen c y iI te r

OAZ

1000

228 10

.-

'O C

~

FeINer

pac

o

00 830hrn

B

- -- ~~

S10 1

u.v: r e corde ~rnp l' f l e r

Fig. 6. 3. d.

Laboratory microphone and recording

equipn~nt .

ampl1f ieJ.~.

An emitter-follower was inserted to match the high

impedance amplifier output to the low impedance output circuit. An Audio-Frequency Signal Generator (Type H, Model IB) manufactured by Advance Electronics Ltd., lIainault, Essex was ufJed to investigate the frequency response of the amplifier.

USing this

instrument it was possible to replace the microphone by nn a.c. sino wave input signal of 1 mv. r.m.s. value at any frequency over the range 15 to 50,000 HZ, and to observe the output current on the r~corder

(fig. 6.3.e.).

It can be seen that the ampl1fer gain 19

constnnt ovel' nlmost the whole audio-frequency range (3 docibel range of 140 to 20,000 s::).

The plateau current of 0.263 ma

throu~h

the recordel' required an a.c. output from the emitted-follower of 3

1.21 volta r.m.s., i.e. the voltage gain was 1.21 x 10 •

Linearity

of gain at 1500 Hz for a range of input of 0 to 1.5 mv is shown in fig. 6.3.f. 6.3.3.

Frequency Filter

It was intended to investigate the frequency spectrum of tho sound emitted by the moving sediment particles in the chnnnel. Provision was made, therefore, for the inclusion, when necessary, of n

frequency filter between the emitter-follower and bridge rectifier.

For this purpose, two variable cut-off high and low pass filters (Mullard types GFF 001/02 and GFF 001/01) could be connected in Bel';'en enabling variOU3 frequency band widths to be selected. 6.3.4.

Output Circuit and Recorder

The n.c. output signal from the amplifior and emltter-followor was passed through a bridge rectifier nnd n smoothing circuit containin~

a direct recording Ultra-Violet

m~nufactured

O~cillograph

(Serio3 M.l300)

by Southern Instruments Ltd., Camberley, Surrey.

This

instrument wns capable of simultaneous recording of up to tf.'n channels

111

0 '25

0·20

0-15

Output U. V. re cor d e r

~

( mAl

3dB

range. 140 - 20,000

Hz .

0 ' 10

1 mV si n e

wave

input .

0 '05

o~

__________

~

____

~

50

10

(HZ) __________Frequency ____ __________

100

F ig .6.3 . e .

~

~

500

Frequency

~

____

~

__________

~

sqoOO

1.000

response

of

laboratory

amplif;

0 ·4

0·3 Output Uv. recorde r Sine wave

(m A)

frequency,

0-2

i nput . 7.500 Hz.

Input (mV)

o~----------~------------~------------~------------~---

o

0'5

7· 5

1·0

F i g.6.3.f. Linear

gain

of

__

laboratory

2'0

amplif ie r .

r.

~

at d.c. information, with reference traces, timing marks and event marks, at paper speeds ranging :from 0.15 to 100 in/sec.

Rocording

of each channel was effected by means of a zero mass beam of ultraviolet light reflected from a plane mirror mounted above the coil of a small galvanometer on to S in. wide photo-sensitive paper.

For

recording ot the microphone signal galvanometer SMI/R (sensitivity of 0.01 mA(cm

d~flection),

saunted by a 100 ohm resistance, was in•• rted

in the oscillograph. Since the microphone signal was composed of a series of dist tnct impulses it was necessary to decide upon the extent to which the rectifier output should be damped in order to provide a convenient measure of the average sound level in the channel.

This cou ld be

effected by altering the value of the tima constant, i.e. the product of capacitance and total resistance in the final output circuit.

Some

preliminary experiments were therefore carried out with the miorophone fixed in the sediment channel over a high discharg9 of gravel. aecorder trances were obtained with time constants 0.5 to 7 seconds (fig. 6.3.g.) in the circuit.

vary~ng

from

by chanling the value of the capacitance

After examination of these traces a time oonstant

of 5.63 seconds was selected. A trace was also obtained during these experiments on a chart speed of 50 in/sec with no smoothing capacitance, i.e. zero time constant (fig. 6.3.h.).

Distinct impulses at the rate of about

500 per s0cond are evident.

Al though ref lect ion f rom the water-

surface and from the channel sides must be taken into consideration, the alternative possibility is indicated of acoustically measuring gravel mO'vements by recording the rate at which impulses are received by the microphone.

An impulse rate meter, possibly with an adjustable

threshold setting, could be used for this purpose. 142

80r-------------------------------------------------------~

Time

constant:0'56 aec.

60

Time(sec)

.....

0

'{

0

~

'"

30

20

10

80

"

11

'"

0

Time

0

"'"

con fa ant

=

3 ' 37 Se c .

6

~

:J c: 0 0

C 01

., :J

....Q :J

0

0

T II'M. (s ec ) 0

70

0

20

80

Time

constant

=

6 ' 79aec .

60

20

TIme (sec) OL-________________L-~~~~~~----~----------------L-------~ 30 20 70

o

Fig . 6.3.g . Effect

of time

constant on laboratory

microphone Signa/.

Paper

Timer

speed

marks

at

==-

50 in/sec

0 ' 07 second

intervals

100~i----~~----~----'-----~~--~------~----'-----~~--~------~----~----~----~-------r----,------r----,-----~--_,----~

80

60

Out pur V.V. recorder ~A )

40

Number

of

impulses

approximately

Fig.6.3.h.

Labc:!ratory

in

0'2 sec

=

91 .

500 im pulses/sec.

m i crophon

s I 9n al

with

zero

time

constant.

6.4. The experience gained in

Conclusions development of apparatus for tll3

th~

laboratory inve0tigation of sediment traOlsport indicated that the following aspects should receive particular attention in the design of a laboratory sediment channel:1)

Measurement of water discharee. either for the installation of mcns~r0ment

Provision should be made equipm~nt

for the volumotric

of discharge, which is possibly the most &ccuratc

method of measurem3nt, or for a suitable looation Rt which a pr~AGUre

ba used.

difference device such as an orifice plate motAr may With the layout of the sediment chnnnel used in

the present laboratory investigations an electromagnetic flow meter would have been dtloirable (but disproportionntoly expensive, since measurement of water discharge was not cssc!ltial for the intended experiments) dua to the flow conditions

existi~g

in the return

pi~e.

verticll~.

Tho acourncy

of t.he orifice plate meter which was installed to measura discharge could possibly be increased by the insertion of a second cross-shaped flow straightener upstreAm of 2)

Hea.der tank.

th~

meter.

Provision should be made tor a smooth and

grndual transition from header tank to Channel.

A cona Idet'nble

length of channel can be wasted due to the turbulence ganerated by a sudden transition and th3 consequent waves and surges superimposed upon the flow in the channel. 3)

Measurement of slope.

Not only should channel slope be

lOOAsured but also, especially in experiments invol..-:i.llg thC3 estimation of bed shear stress, the water-surfaco slopo. This would involve the provision of n series of piezometric tappings or an instrument carriage slIding on rails fixed above the complete channel length. ),43

4)

Sediment foed.

A number of methOds exist for the injection

of sediment into the upstream ond of the channel.

For the

present investigations a sediment feed device was doveloped which was capable of feeding 5mm gravel at rates from 30 Ib/hr to more than 700 lb/hr.

It operated on a hopper and continuollS

moving belt principal, tae feed rate being

controll~d

by nn

adjustable gate on the hopper and a continuously variable V-pulley system. 5)

Measurement of sediment discharge. suitable device

fo~

the

The installation of n of sediment discharge

measure~nt

involved considerable modification of the original channol design.

lI.

41

ft

3

capacity watertight container was connected

by flexible tubing to the base of the down£troam end of the cba!lnel such that 1:<.:.1 load was discharged continuously into The l\oight of the container was transforred

the container.

through a counter-balanced lever to a water-filled motor scooter tyre inner tube connected to a vertical open-ended manometer.

The manometer was calibrated to give diroctly

the dry weight of gravel in the container, and by this means a continuous record of sediment discharge could be obtained. The weight of dry gravel in the container could be determined to the nearest

i

lb.

For the detection of the sound emitted by

int~r-part:l.(~h

of moving sediment a piezoelectric ceramic microphone filled streamlined body suspe:'lced above the and constructeG.

sed~.ment

hou~ed

001l1r1.')'1 in au 'J11-

bed was design"ld

After some preliminary exper.'.l.lents it was concl<.lried

that a three-stage tr&JU:listorised amplif ier and emttter-followo:.' 3

(voltage gain of 1.21 x 10 , 3 dB frequency range of 140-20,000 Hz) was sufficient to obtain a measurable signal. 144

The amp11fer output

was conn.Jcted to a bridge rectifier and a smoothing circuit (time constant 5.63 sec) containing a direct recording ultra-violet oscillograph. Some experiments with zero time constant 1n the output circuit showed that impulses were receivee by the

micro~hone

when suspended

over moving sediment at the rate ot about 500 impulses per second. This suggested an alternative possibility ot acoustic measurement of bed load

dis~hargo

using an impulse rate meter.

Further experiments with tho microphone suspended 1n the chRnnel from a rigid angle-iron frame attached to the ceiling indicated that any sound detected by the microphone would be due movement ot sediment particles in the channel.

115

~olely

to the

Section 7 7.

~boratory

Investigation at the Acoustic Detection

of Bed Load Movement

Th3 principal aim of the laboratory investigations was to

detormine experimentally the relationship between averaee bed load discharge and the average signal recorded by the microphone. It was considered, however, that certain aspects of the acoustic detection of bed load movement in the laborator.y channel should be

investigated before carrying out the main series of experiments.

Section 7.1., therefore, briefly discusses a number of preliminary experiments

concernin~

the location of the microphone above the

bed, the area of sensitivtty of the microphone, the influence of the channel sides and the frequency spectrum of inter-partiole collison sound emitted by the channel sediment.

The main series

of calibration experiments is then described in sention 7.2., followod by a theoretical derivation of the relationship betwoen bed load discharge and microphone signal in section 7.3.

Section 7.4.

includes a discussion of the experimental and theoretical relationships, and section 7.5. summarises the conclusions reached during the laboratory investigations. 7.1. ~JCation

Preliminary Experiments

of Microphone above the Sediment Bed

The height of the microphone above the sediment bed could be expected to 1)

i~luence

the results of the main experiments in two ways:-

Location of tho microphone close to the sediment bed would produce an increase in the velocity of flow near the surfBce of the bed.

The resulting local disturbance of tho sediment

rogime immediately below the microphone would not be representative of the general conditions of sediment transport in the remainder of the channel bed.

Since

the microphone was most sensitive to inter-particle co1lis10n sound emitted by this part of the bed it was

140

considered necessary to avoid such disturbance of the flow velocity near the bed.

Experiments were carried

out" before the sediment bed was placed in the channel, with the microphone fixed at various heightD above the motal base of the channol.

Flow velocities near the

bed were measured using a miniature velocity probe, the axis of the propeller of the probe being located at n heIght of 0.33 in. above the bad.

It WRS found that

maximum disturbance of the flow velocity occurred at n point 3 In. downstream of the hemispherical perspex noso of the microphone.

Measurements of bed velocity were

made at this point for several water

dls~harie ••

Fig. 7.1.a. shows the increase in flow voloclty as the mi,~rophone

discharges.

was lowerod towards the bed at two water A1th~ugh

turbulent velocity fluotuations

made the detection of small increases in bottom velooity difficult it was conaluded that, with the microphone located at least 3 in. :t:rom the bed, veloci t~.es nea!' the bed s\lrfllCe would be unaffected. 2)

The height of the microphone above the bed could possibly affect the magnitude of the signal detected by the microphone.

However, if the moving sediment bod is

assumed to act as a large source of olosely-spaoed spherical wavefronts, each produced by an inter-particle collision, then it can be ooncluded that the avernge distance of the microphone from a wavefront source would not be changed Significantly by a relatively large chnnge in the vertical distance of the microphone from the bed. Alternatively" since the impulse sources 147

~~e

not only

DIscharge

4

Discha rge

, , 95 cusec

3 · 0 5 cus ec

p.

3 microphone ~ flow

microphone height

heigh t .

I I

( in)

I

I

2

I

I I I

I

I

I ~I

I~ ________ und is t ur be d .-mean

OIL-______________L-____________

o

0 ·5

~L_

____________

·0

~L_

_ _ _ _ _ _ _ _ _ _ _ _ _ _L __ _ _ _ _ _ _ _ _ _ _ _ _ _

2- 0

' 5

e an F i g . 7 . 1 a ."" Effect

of

v e lo c i t

ve l 0

m i cr o phone

C I t

Y

~

______________

25

a t

h e i ght

po i n t

on

A .

flow

( f

~

______________

3 ·0

t/ Sec J

v eloc i t y

near

bed .

~

3·5

________________

~

4'0

closely-spaced but also frequently occurring (section 6.3.4), the

l~d

could be considered to act

as a source of plane waves such that, with negligible attenuation by turbUlence and viscous damping, the magnitude of the microphone signal would be independent of the height of the microphone.

A controlled series

of tests to confirm these conclUSions, with the microphone fixed at soveral positions above the moving bed, could not be carried out, however, since it was im?ossible to ensure exact reproduction of interparticle collision sound for each position of the microphone. In the li&ht of the above considerations it was decided to rn~tntain th~

miorophone at a height of 3 in. above the plane

sediment bed throughout

~ho

main sories of experiments.

It was

n6sumcd that small variations in the distance between tho microphone and the bed due to changes in bed configuration would have negligible effect upon the magn5.tude of the micro?hone signal. 7.1.2.

Area of Sensitivity of Microphone

The length of channel over which the microphone was able to detect the sound emitted by inter-particle colliSion was by the following approximate, but direct, method.

esti~~ted

The outlet

weir was raised and th"3 channel filled with wa':':er to nuanerge the micr.ophone.

At various distances from the microphone a wooden

rule was drawn lightly but firmly across the width of the channel, disturbing the bed particles in a manner similar to that in which they are disturbed when moving as bad load.

The rosulting

tr~ceo

produced by the ultra-violet recorder are shown in fig. 7.l.b.

It

was concluded that the microphone was sensitive to the movement of 148

JA-A,~

2:[

~

to

-------I~.

I

Ti m e

I

10

I

30 sec .

20

Paper

]

' -Oft

L----=

I

o

speed

Q'15 ,. n / sec .

A

t

f<

0 -5ft

70

O,-.e-=

,-5 ft

C

Recorder

traces

Fig . 7.1 , b .

produced

-=

2 -0 ft

by

movement

Determ i nation of area

of

of

2- 5 ft

bed

se nsit i v i ty

particles

of

3 ' 5 ft

3 - 0 It

at

v ar i ous

laboratory

d i stances

m i crophone.

from

microphone .

gravel nt distances of up to 2~ to 3 ft.

Since the microphone

was located 2 ft. upstream of the end of the sediment bed the length of chnll.lel to which the microphone responded was thus estimated to be approximately 5 ft.

The microphone signal was

therefore dependent upon the condltioCls of sediment movement over 2

an area of about 7! ft , inter-particle collisions nearer the m1crophon€ having greater influence on the magnitude of the Signal. 7.1.3.

Influence of Channel Sides

If the microphone was suspended above an infinitely wide movement of gravel it would be most probablQ, on the basis of the experiments of section 7.1.2., that inter-particle collisions at distanoes of up to 2! to 3 ft. on each side of the microphone would Since the width of the laboratory channel was only

be detected. I! ft.

cond~tions

of sound propagation within the channel were thu3

different from those over a bed of infinite width.

In the

laboratory, impulses generated by inter-particle collision within the

cha~~el

probably reach the microphono both directly nnd by

reflection from the glass-air intarface of the channel sides (dUG to the dissimilarity of the characteristic acoustic glass and air).

~mpednnces

of

Attempts were made to distinguish experimentally

between the direct and reflected impulses.

The streamHned

microphone body and the glass channel side were in turn given sharp taps with a metal rod. fig. 7.l.c.

The resulting traces are shown in

It was hoped that the seoond trace would roveal a

slower decay rate due to the reception by the microphone of reflected impulses.

However, as can be seen from fig. 7.1.c., a

logarithmic plot of the decay parts of both traces revealed no significant difference in slope.

It was thus not possible with

the apparatus nvailable at the time to demonstrate the existence 149

'p- A

t

.3

.20

Channel

Microphone

side

oLlo ____~--~~==~==~~~--~--~----~==~~== 5 10 0 10 1S

5

----t~~

Tim e

1S

(se c)

Semi-logarithmic

plot

of

decay

signals

by

sharp

Impacts

microphone

and

produced on

channel

side,

70

3

Channel

side

2

'0L---------------~5~--------------~1~0----------------,~5~--------------~20 - - --tl .....

Pi g. 71 . c.

Time (sec)

Comparison

o f

decay

signals,

at reflection from the channel sides, but it was concluded upon

theoretical considerations that reflection most probably takes place. It was decided that, inatcnd of

lini~g

the gla.ss sides of the channel

with a sound absorbing material, reflection should be allowed to ,occur, since the reflected impulsa could be considered to have originated at a point outside the channel which would have been an impulse source in an infinite width of movement.

That is, by

permitting reflection to take place at the channel sides conditions remained more like those in an infinitely wide chunnel. Observation of sediment movement in the channel showed that sediment particles only rarely impinged upon the glass sides of the Nevertheless, tests were carried out in which several

channel,

particles were projected underwater directly agai!lst the glass Side, It was considered

but no signal could be obtained on the recorder. unnecossary,

therefor~,

that tho sides of the channel nenr to tho

sediment bed should be lined with a sound absorbing material such as rubber.

In this way observation of particle movewmt and bod

configuration was still possible during the 7.1.4.

~~in

experiments.

Frequency Spectrum

Since the sediment usod in the laboratory experiments was essentially single-sized it waS considered possible that the sound emitted by the particles might be characterised by a smnll range of frequency.

It was decided to set a high discharge of sediment in

the channel and to investigate the frequency spectrum of the resulting sound.

Using the high and low pass filters (described in

section 6.3.3.) in series i t was possible to select frequency bandwidths with centre frequencies at t:'.pproximotely

i

octave

intervals (ratio at bandwidth to centre frequency, 1:3.25). main difficulty in these experiments was the maintenance of 0

150

The

sedimeltt discharge which produced a signal sufficiently large and steady to enable the various bandwidths to be accurately sampled. Fig. 7.l.d. shows a plot of filtered signal per Hz bandwidth against centre frequency.

It can be seen that the frequency

spectrum extends ovor a wide range, almost the whole audio-frequency range, and that there is no particular characteristic peak It was deCided, ther8forc, not to filter any selected

frequency. rang~s

of frequency during the main experiments but to sample the

total Signal within the frequency cut-off.range of the amplifier (3dB range, 140 - 20,000 7.2.

E~).

Calibration

~xperiments

and Analysis

This section desoribes the main series of calibration and the analysis of results.

experim~nts

The principal aim of the experiments

was to determine the relationship butween average bed load di8chargo and the average signal recorded by the microphone in the laboratory fluDle. 7.2.1.

Experimontal Procedure

The main laboratory investigations comprised a number of expe~imental

runs, each conducted at a constant water discharge;

during each run a continuous record was k&pt of sediment discharge, sediment feod rote and microphone signal. Throughout the whole series of experiments the at the maximum slope of 1 in 240.

ch~nel

was se:

Beforo each run the surface of

the sediment bed was mGulded to a parallel slope by a wooden template, and the microphone fixed at a height of 3 in. above the plane sediment bed.

At the start of each run a steady water discharge

was set and measured, and approximate depths of flow noted at upstream and downstream sections of the channel; 151

the height of the

0-01

Plot of fit tered



per

o·oos

...............

Hz

Filtered

stren wtll

bandwidth against

~.



sign a I

frequency

of

~

octave

centre sample .



microphone sign at

()'- AI Hz • 0-001

0-0005 ...

3dS

frequency

response

of

amplifier.

....

0-0007'~--------------------------L---------~~------------------------~----------~----------

100

1.000

500

5.000

______________- J 50.000

10.000

Frequency (Hz)

Fig 77 d.

Frequency

spectrum

of

inter-porticle

col/ision

r;;.ound

in

laboratory

channel.

outlet weir was then adjusted until the bed-surface and watersurface profiles were approximately parallel. The establishment of equilibrium water-sediment conditions was not required for the experiments.

Reading of the manometer of the

sediment weighing device and recording of the microphone signal were therefore commenced simultaneously within several minutes of the setting of a steady water discharge. The sediment discharge weighing manometer was read at intervals of one minute to the nearest 1/16 in., i.e. to dry gravel in the container.

t~o

nearest

i

lb of

This enabled the average bed lond

discharge over a two minute period to be plotted against time during the experimental run.

An example vf the continuous record kept in

this way is shown in fig. 7.2.a. Examirv.tion of the continuous plot of sediment diacharge witi.\ t~.100

dur:l.ng the experimer.t indicated the rate at which sediment

shoulrl be injected :.nto the upstream end of the channel to lr.aintain a constant volume of sediment in the channel bed.

The sediment feed

device was then set and adjusted to the appropriate fead

rat~,

ns

shown in fig. 7.2.a. The paper speed on the ultra-violet recorder was set at the slOWGst

sp~ed

of approximately 0.15 in/Sec and the timing device

adjusted to mark the paper at intervals of 10 sec.

An example of

the type of trace recorded during a run is shown in fig. 7.2.b. At the

e~~

of each run the average microphone signal

du~ing

interva13

of one minute, calculated by averaging the instantaneous signal magnitudes at 6 sacond intervals, was plotted against time for comparison with the sediment discharge during the run (fig.7.2.a.) water temperature in the sump tank was measured at the start and o finish of each run, and was generally found to riso about 1 C during

152

Fig. 7.2.a.

'lrt

fFi



~

tit ..

,t

:! ~ .... ~

q.,

~,..,..

,. Itt 't'

i±t:t:H

c~~I 1i I'iii:: ~

ft1j ~Ht

·t··

~rm

,."

Ft·

.. ~. ~?~ ~ti

i']

..;

[ti

ft

..f

tff ftt

Paper

Timer

07S,n!c;;ec

speed

morx. s

ot

'0

~ec

,ntervals

700r-----------------~----------------_,r_----------------,_----------------~------------------~-----------------r-

Microphone

----------------~700

9

90

80

80

70

70

60

60 MIcrophone

signal

;!LA)

50

50

(j)- A J

----------.t----:.:. 40

signal

40

~---~

30

20

20

70

10 o~----------------------------------------------

________________________________________________________ ______________________________________________________________________________________________________-JO ~

35

36 Time

after

overage

Sample

trace

of rnicrophone

sIgnal

produced

by

inter-particle

start

!5ional

37 of

Run

during

_ o lllf~ i on

of

no , S

one

(min)

minute

sed ' ment

{:le

rio d

fTlOV,ng

In

{oboro!or f

channel.

a run.

Over the whole series of experiments water temperature

remained in

th~

range 16.0-19.5

o

c.

Each experimental rJD was continued until the sediment weighing device was filled; sir..gle run varied from 40

m:I.nut~s

average sediment discharge.

co~tainer

of tho

the total time required for a

to 4 hours cioP.pending upon the

A total of 24 runs was conducted

covering the full range of sediment discharges poGsible in the lnbor~·,tory

7.2.2.

cbmnel.

Time Lag between Microphone and Weighing Device

Since the microphone was located a distance 2 ft upstrepm of the end o! the sediment bed it was evident thnt a certain time lag in thG recording of sediment discharge should exist between tho microphone and the sediment weighing device.

In order to

oc~pare,

or develop a relationship between the nverage microphone signnl nnd the the

av~rage

theroforo

bed load discharge over a short per10d of time it was

necessar~T

to deterlDine the magnitude of;;his time lag.

The magnitude of the lag would be expected to be some function of the average bed load

discharg~.

ripnce, if a curve of

secti~~nt

discharge against t1me lag CQuid be established it would be possible to obtain the correct average mlcrophone Signal corresponding to an average oed load discharge by lagging the microphone record hy the appropriate time interval.

Consideration of fig. 7.2.0., which

shows the variation with time of microphone signal and bed load discharge during run 19, suggested a possible means of obtaining the required relationship.

It can be seen that both tha

mic~ophone

signal and the bed load discharge exhibit a cyclic pattern of variation, with the peaks and troughs of the latter lagging behind the former.

(Similar unexplained periodic fluctuations of sediment

discharge in laboratory channels were noted by and RATHBUN and GUY (1967». 153

Eins~eln

(JOHNSON, 1938)

If QB(i) is the average bed load discharge in the ith minute and M (i-I) is the average microphone signal in ths (i-l)th minute, s where 1 minutes is the lag of the weighing device behind the microphone, then it is possible to calculate a cross-correlation, or product moment

correlntio~coefficient

for n lag of 1 min, r(l),

defined as the ratio of the covariance of QB(i) and Me(i-l) to the geometric mean of their variances. Putting:QB(i) = x and M (i-I) = y s then the cross-correlation coefficient can be calculated from:-

r(l)

~ JF ~X

2

-

(!:x)21['". 2 --~yn

-

where 1: signifies summation over a selected range of i, and n is the number of one minute intervals in that range.

(Since the

cross-correlation coefficient is in fact identical to the correlation coefficient between two variables this technique implies a linear relationship between microphone signal and bed load discharge over the range of variation of each within their cyclic fluctuations). In run 19 (fig. 7.2.a.), for example, a range of 100 min, compriBing three complete cycles, from i

= 21

to i

= l?O

was

select~d.

The value of r(l) was calculated for 1 min increments of 1 from 0 to 12 min and plotted against 1 as shown in fig. 7.2.c.

From this

graph a maximum cross-correlation coefficient was taken to occur nt a lag time of 6 min, corresponding to an average bed load discharge,

Q , of 1.45 1b/min, during the selected time range. B

154

-2-( .~~"-:.:I .{. if .r'-m -++f/.l·t_1.1"::.( T'7 .( {l ft:.:. . .(J. .{ '( :t /I""T/;':';/,·J'I·~'_I I . ... ··/ .'n-7.. .l.I 'f-l-··f ( .I:::1.·...

../

/ / '-' , (:/ I/' . .,_ L. .' .... '«'+i'~ .. ·1 : - Lf.! .... .....1 ,I·

~

'1

!

r71_.+::\ :=+ ; -r~"~l f++-+-! -\·.\·llt~f+·i=t i '"

'

f

I

I·,

-

:-f



I

~ -I :-- J - l t 1-'I t ~rL l m l r:~~u_L_!_ ~~' r1 -\"':- l0h: -I·J UT I ~: r ·=t - ..:~:!

-Y=r lj-I

-I'

~ . 1,\

-7;7" .;-.- -:.... /~.

-- 1- / .)' ,..:- ' \ ---.\,'-_. j _. ~ -t·_~ -" r. - t 1

t

J....

I T--_

;\

1I

"



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\

oe

f,!2 t

r (I

)

~

i -'

1

\

I' r

I

Ij

\ : - -r! .-j ,

,

,

' I

f~un 1=

I

----~

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-

,.:,:

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.'; •• ,

i!

•••

!--j-

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i

- ~ ... -1

t-.

-

.~-. :i• I

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.f..

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l

cn-~T' \KLl·



I

;;j;:l .. ,....

f"

1

1 +--t ~-~~t~ 2f~~rdf!!l~;:t-:.-I~~tJq --L.~:I ·\·· 1·- ~ L;_ ~ 1~ -I J~J~;~! ' } . )'J f-J t--Lr~L-~_J~ + r , , I _, _.,, __."1 l/t:) ~-~.n~lJwJ,.., J.\]· .l!frJLT-r-r lfi r-rl I I , t !

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r--' , -

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.:'.

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Qt.::: $~1:fOI ~/rl1;r: . ,\\ -l - - ' I I



1

~'1

-

. , l //l L't- - .. 1 . ' . '! :-~r W R-J·+· ~ -Yr~hF.+- +-l~~f:;'+'-F+ +~'1 -~"N\J -'\ \- \. {~-fP1±f~ '['j 'lr: i

1

I"

- -: ~ I . :! .. , 1 ~"l- "'b i ' ::

,. -~-

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-T"-

-: - If'--f-- 1-. -- 1-\-\11--I - .- - +- - - 1-- . !-- . -I --- 1:-- S..:1\"" ' I \.

!

.-~' - I -~'

\'K

1-1 \ -\- \. L~ ~ \

-_. , .::':'1--

I\j1---, -·1-- .~--+-r' "-B::\ -i--' ~t' . .i-I - -;-.. t. j; -. - +,I. 'f . .,!-_..--lI . --.L , ~_ . , !. ..-'--l" . .\ 1--+-

,~--

' ; I

/

l1 -t ~!

·t··i\ '\ \ - -,''j--:- :..J''- \' !1' ,,\

"

, j

~--.'.;

1 '., ~

I

I .,

IV I--- L-

..

,

\1r-· --/ -jf. ·T----' ;

,-

:~

. IT

~ ~tl,.-

-,_.1-

f

1

i:

-~

l

,

j

orr ~

'

f..--

.,

1"\ I

i"

1-.....-

-8 fB£f .1.I:Qj,· I-•. l>k·I. I:·~·I--f~t -1 -=~I~dT:T I

1 1 ~"1 tfFFFE~ -~hH~F t-XVl ftN-~·~T·l-.- l ~r r-' -'+ -'-\-~ '1-+-T F+' -F~J \.:.\ " r

:

"

/ .

trn H+ t

U \ \ ; \ L H~\-\ \H ~HE

ro S

I

"

la 9

t I me

an d

cross c.o rrelat l o n

o f microphone

s i gno/

_..... 0

an d

-

.

'

bed loa d

1

..... . . - +-

d ; scharge.

The analysis was repeated using five other experimental runs, covering a range of average bed load discharge, and the resulting curves of r(l) against 1 plotted in fig. 7.2.c.

At the higher

sediment discharges smaller time ranges had to be selected with less evident cyclic patterns;

maximum cross-correlation coefficients

were thus found to be somewhat lower.

The time lags corresponding

to the six maximum cross-correlation coefficients of fig. 7.2.c. were plotted against the appropriate average bed load discharge as shown in fig. 7.2 .d. In an attempt to confirm the results of the above

techni~ue

an

approximate theoretical relationship between the time lag and average bed load discharge was derivod as follows. The time lag, 1 min, was ascumed to be made up of the time taken for a sediment particle to move from the microphone section to the end of the sediment bed, t min, plus the time taken for the particle to fall over the edge, down the slope into the container of the weighing device; and on to the sediment already in the container. This was estimated to be about 1

=t

+ 0.2

:.t

=1

- 0.2

0~2

min i.e.

The distance of the microphone section from the end of the sediment bed was 2 ft.

U~ = 2/(1

Hence the mean particle velocity,

- 0.2) ft/min

The bed load discharge in dry weight per unit time (lb/min) was given by:-

~here

,

Y is the specific weight of the sediment particles s Ais the porosity of the sediment bed, i.e. the fraction of tile volume not occupied by particles. 155

~--------------------------------------------------

. i

...

.

J

i

.

1 r"\

.

. I

[)

-

- J

y

s

(1 - t..) is therefore the bulk density which was found to

be 92.5 Ib/ft

3

(section 6.2.4.)

w is the width of the channel (1.5 ft) z is the average depth of particle movemsnt. z may only be 2 or 3 grain diameters

(~

discharges when a noticeable dune bed

-

At low dischargen

i

in.);

at high

configu~ation WQS

observed to occur z could be as high as 3 in. Assuming an average value of z of 0.15 ft (nearly Ii in.) then:4.16 (1 -

0.2)

which has been plotted in fig. 7.2.d. After consideration of both the theoretical curve and the points obtained USing the cross-correlatlon t0chnique a curve giving the estimated relationship between average sediment diecharge and the time leg was assumed, enabling the following tablo to be drawn up:Teblo 7.2.a.

Time lag corresponding to an avera.ge bod load dlschcrp;e :lange of bod 10:..(1. disch~lrgo (lb/m1n)

Time lag (m:1.r.)

$

0

4 - 6

1

3 - 4

2

2.5 - 3.0

3

2.0 - 2.5

4

1.5 - 2.0

5

1.25 - 1.50

6

1.00 - 1.25

7

0.75 - 1.00

8

0.50 - 0.75

9

0.25 - 0.50

10

0 - 0.25

11

156

Abstraction of Data from Experimental Results

7.2.3.

Having established the time lag between the weighing device and tho microphone for any given range of sediment discharge it was than poss1ble to abstrnct from the continuous records obtained during the experimental runs the average bed load discharge over nny selected length of time together with the corresponrting average microphon~

signal over the same length of time lngged by the

appropriate amount.

At high sediment discharges the

~ediment

weighing device could be filled in leso than 40 minutes so that averages over periods of time greater than this could not be obtained.

It was decided

therefo~e

to take average values of

bed load discharge and microphone Signal over lengths of time of 10, 20, 30 and 40 minutes. The db.;;a obtained in this manner are plott:Jd in flga. 7.2.0., 7.2.f., 7.2.g. and 7.2.h.

7.3.

Theoretical Relationship bctwt:!6n Microphone Signnl and:3ed Load Discharge

In figD,

o~er

7.~.e.

to fit a curve to the experimental data plotted in

to 7.2.h. a tentntive theoretical relationchip was

derived between the microphone' output slg!'"Aal, M , and tho bed load s dischnrg3 in dxy weight per unit time per unit Width,

of a

~I

sedtment of Single size, d, on a plane bod of infinit(, width. TWo basic assumptions concorning the mode of movement of th3 c~diment

1)

particles as bod load were made:Ench particle

mOV03

in a series of jumps or stepo, the

probab:Uity of its being moved from the bed being dependent upon the shape, size and weight of the particle and upon the flow conditions near the bed. distance travelled by the particle is a 157

The average

const~nt

for any

--.-----,-._. I

;

t ----6~\/'.era.g.£.

micro phone

_

I

A li gn.

f(

2

I

4'3

' -r- .

1t2

--~ 43=[:l·~2 +Q r3~ ,L-:M2J

,

~1---"-

.5.

d

of

percen ta~JJitSli1u..a1 s -

2

M~ ,

!t.

. ..

I .



. : . ':

' ,' I

!

-I

a 6 'ji

• :--t ..

r.--;-T1 --- ~

-t--

," . ~

• •

1



I

;01·' .- ;

-1-



,---.+.

. •



--+

---+--~--



.j :":·~·-·Ll: ·.~l·:J ~··i--"----~

'It--~~-:--,::,-,,;,.--+I-::-.:- _ .

-1--- -

__ . ! - -

.-

-=..------

..- ...... --;--~----

F i g7.2.~ -

discharge T

I

l~-

-L_

___L

R§!-9ress Aon l i ne

..-

i

AVe. ro.g e

I

~B -= [( 3~.2+ Q~~ M ~3 ]12 -3'.2 5]3-2 i

L __.

i microphon~

S;

_ --.Sj gn.a.L...

:5, d~

I

01 p~CCl

tage residuals

= 34.' Jy'

-

-.-.--



I

-~T--

I

I :--. :-~-

---,'---.- ~--=- +---_._--:.--

-'-~-

'

-

1

r



-

.

-





----

_~-_-

-;------r-

~



4-.:....-_1

l

_J_~---'

-r--.-'

---- - -

--_

..,.-

-1

r

._---

-+---rl---

I

-'---~1 -_l-

I

-. -l--~ -',·~r --

-r--.-,- - - --~

,-

:-- .----+-I

.~ Average

.2 F i n . 7, .2 .~-. Rdat i onshi p v

"

befwectn

.;.:....._-r-_ _

:..._:..-:..-~+......::::.......:c

1_'·_ _

r ~ I'~ --"----r-~i

I

bed ,load l d i SCharg 3

-----" . j.



• ••

\--i

301

.



,--1-

-- -

t-- ~- .







per unit

w f1 th . 9

,--

-..-1 8

Clblrn i n . fL )

1

4

average irnic rcpnone '

&ignat~n

t

over 2 0 m i nutet period

r

.

- 7-6 1-

-_ I

"--t-- _ . -

:S.d. of r--- - ,

,

-1. ,-

~

.



J

I

------

-o phonc Signal aoq' -aver-

---

<-

--~-.-

•• 1

-,.- ---1' ----r.. - .:::.....---

ICX1CI

.-:.::::---

-

-~

-'

t

---::

.it

,~

~--~---

-

.I

--f -7

i--~-~~--

-t !..--- .-

--6Gr

~v~§l.e

~ ' -

;

- f-I-~,

,

microphone - S i.Q.ru:z1..

, ~-

,

,-- -I

_~~~j dJ..Lal.:s ~ ~

--'- - -- ! - --4- --

I'

•• -._---,



L



_-...___- ~t---....::.~- -

l-.4Gt-I-- - ' -

~o ~

-I • I'



• ,I

t

--;---,-1

_ I __ j

\.~-__-j -'~~_L __,_: ____ \___ -_-to-! 1 ,-:

t ·

--l

L

-t-'---..... -=-- ----.-- --I

,

I

:.

~ ~

-_

.:

-

,

~

t-

I

.

- - - l--- -

f

_I

~- - - 1 " - '

I I

!

+

t~'---1-. ! t~i' '

-r--'. -

.. I

.

I~

~

,...•

-

:.

.

----+-- -

.

J' - - -

~1 .

-_~

J.

~-'---"------r---;j

t

-I ",

---t-- -- ...

1

d> -;

1

II . ..

+

F'ig. 7.2.h. R-eiatiOJ1lShip betWe-f!:Tl ave-rage f[Ji crophone

--- -r-

signal

and

average bed

OV~ ,J

r

40 minute

'f .t

- __ - -t j I

-

.

::. !

-..,.....-~

particle and is independent of the flow conditions, the rate of transport and the bad composition, i.e. the average length ofa particle step is equal to kId, where kl 10 a dimensionless constant. 2)

average velocity of a particle during n step,

The

equal to the mean flow velocity near the bed,

Us ,

is

U.

After observation of the movement of sediment particles in a numbor of lnborotory flumes EINSTEIN (1950) used both the above ussumptions in the development of his bed load theory (section 4.1.9.). At any

pal~icular

cross-section, of unit width, in a bed load

discharge of qn all particles are psrforming a step length of kId and will therefore be deposited at some distance from zero to kId The area of deposition is thus equal

downstream of the section. to kId. weight is

~le

Ys'

volume of each particle is n d 3 /6 and its specific The number of particles deposited in unit area

per unit time is therefore given by:-

According to the Hertz law of impact (GOLDSMITH, 1960), which is applicable to elastic bodies moving at low velOCities, the ratio of the vibrational energy emitted by the collision of a moving sphore, velocity

Us ,

witha~ianary sphere to the initial kinstic energy

of the moving sphere is equal to of sound in the sphere.

Ut¥150c s ,

where c

s

is the velocity

Assuming that this law can be applied to

the impact, or deposition, of a particle on the bed, the vibrational enarcy emitted by a single deposition is given by:-

-U 2 s

158

The average vibrational energy emitted per unit time per unit aroa by inter-particle collision of the bed particles is given by:-

It has been assumed that the average velocity of a particle

-

during a step, U , is equal to the mean velocity of flow near the s bed, U.

-

Boundary layer theory indicates tho U is proportional

to the shear velocity,

(o.g. the Prandtl-VOll Kartnlln velocity

~,

distribution equation given in section 3.4.5.) an assumption made by KALINSlm (1947) in the development of his bed load theory (section 4.1.8.).

where

Hence:-

is the fluid shear stress on the bed particlea o P f is tho mass density of the transporting fluid 'T"

~

is a dimensionless constant

The vibrational energy omitted by the bod particles per unit area per unit time can then be expressed as:-



• •



• 7.3.a •

METI::t-PETER and MULLER (1948) produced a bed load formula, borne out by experiment to be applicable principally to coarse material (section 4.l.7.), i.e. to sediment sizes which emit substantial inter-particle

colli~

sound.

infinite width the formula can be written:-

159

For a plane bed of

T 0

_ y \2/3

y \1/3/y

~

O.047(V.- Vf)d + 0.25 (

!) \. Vi

j

%/3

where Y f is the specific weight of the trlUlsporting fluid. substituting for

r

E =

k 3

2

I lOOk g P c L If S

Since the

o

in equation 7.3.a.:- 3/2

1' B rI q

3/2

'T

-

f ,, 10.047(Y - Yf)d+0.25 ~-

d ~

n~r

/y \1/3 (y

L

s

g





sourc~

given by

th~

2/3

f 1 -s - Yf /

J

q 2/3

, I •







B

7.3.b.

and rate of impacts on unit area of the bod

is high the moving sediment particles can be assumed to to a

-y \

approxim~te

of continuous, plane, sound waves with an energy flux above equation 7.3.b.

Before reaching the piezoelectric crystal the enorgy of these sound waves must be transmitted from the sediment particles to tho fluid and then through the fluid, a thin brQSs partition and the oilfilled microphone cavity.

It can be shown (STEPHENS and BA'rE, 1950)

that the ratio of transmitted acoustiO energy to incident enorgy at the junction of two materials is 4Z Zz!(Zl + Z2)2, where Zl and Z2 1 arc the characteristic acoustic impedances of the

m.~8rials,

i.e. the product of density and velocity ot sound in each material. The

~nergy

flux of tho sound pressure waves received by the

piezoelectric crystal is therefore equal to k3E where the dimensionless constant k3 is a function of the characteristio acoustic impedallces of the sediment particles, fluid nnd materials

ot the microphone housing. The

ener~1

flux of the sound pressure waves can be shown to be

proportional to the square of the amplitude of the pressure fluctuations

(a. ICHARDSON,

1953a).

In the piezoelectrio

c~ystal

the amplitude of the induced electrical potential difference is proportional to this pressure amplitude. 160

The induced voltage or

curren~

is amplified linearly (fig. 6.3.f.) and the output

measured as a current,

M ,

s

by a continuous recorder.

The

acoustic energy flux received by the piezoelectric crystal i8 therefore proportional to the square of the amplified recorder output, 1.e. 2 lis

= k4 k 3 E

where the constant k4 is a function of the mechano-electrical characteristics of the piezoelectric crystal, amplifier and recorder output circuit Substituting for E from equation 7.3.b. gives:-

M 2

s

1~ r

k_ 3 = k4 k 3-~

q

[ lOOk1 gp f 3/2 C

s._

~2/3q

y } 1/3/ y - y ' ~ S f

O.047( Y _ Y )d+O.2S/--.! d f s f \ g i..

Y f

1

3/2

2/3 B

" .

For a given microphone suspended over a bed of most natural sediment particles the above equation can be reduced to:-

Expressing

CIa

explicitly as a fUnction of Me and d:-

• 7.3.c •



For a glven sediment size the relationship between qB

~nd

Me

can be written:-

13/ 2

- aJ in which the constants a and b 1.

• ~re











functions of:-

The ratio of average particle step length to particle diamoter

2.

The ratio of mean flow velocity near the bed to shear velocity 161

• 7.3.d •

3,

The velocity of sound in, and the size and specific weight of, the sediment particles

4.

The velocity of sound in, and the specific weight of, the transporting fluid

5.

The characteristic acoustic impedances of the materials of the microphone hOUSing

The machano-electrical characteristics at the piezoelectric

6.

crystal, amplifier and recorder output circuit. 7.4.

Discussion of Observed and Theoretical Relationships

Determination of the theoretical values of the constants a and b 1n the microphone equation 7.3.d. would have required a number of hydraulic and acoustic experiments for which neithor suitable It was possible, however, to

apparatus nor time was available.

calculate the best values of a and b in the equation such that curveo could be drawn through the points plotted in figs. 7.2.e. to 7.2.h. for the prediction of average bed load discharge, qB' from a knowledge of the averago microphone Signal, M • a Evaluation of the constants a and b was effected by a least squ~res

curvilinear regression of

M , the independent variable. S

~,

the dopendent variable, on

Partial differentiation with reepect

to a and b of the weighted residuals given by equation 7.3.d. yielded simultaneous normal equations which were not directly soluble for a and b.

The regreSSion had to be carried out by iterative

procedure for which a computer proeramma was developed for use on the KDF 9 computer of tho University of Newcastle upon Tyno.

A

description of the method of regression analysis, a copy of the computer programme and samples of thG input and output data given in the Appendix.

nr~

The analysis was carried out on the data

from each of the graphs of the 10, 20, 30 and 40 minute averages. 162

From the computer output data it was possible to obtain the values of a and b giving the least sum of squares of percentage residuals and the value of the standard deviation of the percentage residuals. These ar3 givsn in table 7.4.8. Table 7.4.a.

Results of curvilinear regression analysis

Period of averages (min)

_.

I

Number of points

s.d a

b

of

percentage residuals

I

10

141

3.42

0.173

36.6 %

20

63

3.24

0.165

34.1 %

30

42

3.47

0.173

32.2 %

29

3.09

0.156

33.2 %

40

I

The curves obtained using the regressed values ot a and b in equation 7.3.d. are given in the appropriate graphs of figs. 7.2.e. to 7.2.h.

A measure of the accuracy of the prediction of bed

load discharge from the microphone signal using these curves can be given by the 65% confidence lines, approximately equal to + 1 S.d. of the parcentage residuals. It can be seen that the regreSSion ourves, while giving the least sum of squares of percentage residuals (and hence the least s.d. of the percentage errors of prediction) do not appear to be a good fit of the plotted pOints, consistently overestimating bed load discharge in one other.

pa~t

of the graph and underestimating in the

It was possible to select values of a and b in equation

7.3.d. giving curves which appeared to fit the data better.

For

example, with the 30 minute averages of fig. 7.2.g. putting a

= aO

and b

= 1.85

yielded curve 2, which gives a s.d. of

percentng~

rasiduals of 33.7%, slightly greater than thnt of the curve.

regression

Curve 3 of fig. 7.2.g. was drawn through the plotted points 163

by eye to no particular mathematical function and, although sec"ling to be an even better fit tha.n curves I and 2, gives a greater s.d. of parcontngo residuals of 35.4%. Attempts were made to determine whether the plotted data fitted more closely to a power rolationship of the type:q

B

= e. M s

b

or a polynomial such as:qB = a Me + b Ms

2

Both regressions were carried out using a modificatj.I.>n of the iterative regression programme (see Appendix) and produced curves similar to the regressed theoretical equation, but with larger s.ds of the percentage residuals. p~67

The value of the exponent b in the

relationship was calculated to bo 1.72;

a. plot of qB again"t

Ms on 10ga.:.:1thmically scaled graph paper appeared to ff t well to a straight line with a slope of 2. tho

b~d

the

microph~ne

Suc~

This would seem to suggest that

load discharge might be correlated well with the square of output signal, i.e. with power output of the amplifier.

a technique, involving continuous recording of

t.h~

ampi!fiod

a.c. output on a milliwatt-metar, would dispense with the need for a rectifier and arbitrarily selected time constant in the output smoothing circuit.

It might also result in an increase in the

possible accuracy of prediction. COD.Bideration of the curves of fig. 7.2 .g. indicated ti.lat the actual relationship between bed load discharge and microphone signal appeared to deviate from the theoretical in section 7.3.

relatlonshi~

derived

This could be due to the neglect in the theory of

certain physical conditions in the laboratory channel and also the assumption of some "constants" which in reality vary with bed load dischB,rge.

The major difference batwaen the 164

cond~.tions

of the

theory and those in the laboratory is the constricted width of tho channel bed.

In the discussion on the influence of the channel

sides in section 7.1.3., however, it was concluded that, due to reflection from the sides, the channel might still approximate to an infinitely wide bed.

Nevertheless, this Ride effect and

reflection from the water surface must be expected to cause some The ratio of particle step length to particle

discrepancy. diamater,

... was assumed in the derivation of the theory not to

k~,

vary with bed load discharge.

In fact, it is possible thnt at

eodiment discharges the average particle step length

h~.gher

becomes

~omewhat

greater:

since the microphone signal, i.e. Inter-

particle colliSion sound, dQpends upon the actual deposition or impact of particles on the bed then an increase in bed load discharge would

resul~

signal.

in a proportionately smaller incrense in microphone

A further result of high sediment discharges was observen

to bs the formation of a noticeable bed configuration,

consistin~

of

intermittently appearing dunes of approximate wavelength 4 ft and crest to trough amplitude of up to nearly 5 in. of the

~lane

The

~.estruction

b:3d (together with the existence of sitio friotion)

wouln require the inclusion on the left hand side of the MeyerPeter and Uijller formula of a fnctor of less than unity .. /itiving :l.n equation 7.3. b. a smaller energy output from the bed, i.e. a sms.ller microphone signal for a given be:1 load discharge.

The pr.ohablo

increase in kl nnd the production of a bed configuration both provide possible

explanat~.on

for the lower microphono Signals

observed at high level bed load discharges. Due to the above effects at high sediment discharges the microphone signal becomes relatively insensitive to large increasas in bed load discharge above approximataly 3 lb/min"ft ,width. 165

This

demons~rates

one of the major disadvantages of the present

acoustic technique since it then becomes difficult to make accurate predictions of bed load discharge from a knowledge of the microphone signal. Some of the scatter evident in the experimental observations plotted in figs. 7.2.e. to 7.2.h. can probably be attributed to the fact that the two methods of measurement, the microphone and the weighing device, did not refer to identical physical phenomena. While the microphone signal was dependent upon the general conditions of movement, or, more precisely, deposition within a length of channel of about 5 ft (section 7.1.2.), the weighing device

reco~od

the variation with time of the bed load discharge at one particular cross-section

i~

The mode of movement of the bed

that length.

particles within that length was by no means uniform.

At low flows,

areas of the bed surf ace were oboerved to move in "gus ts " in a random manner;

at high flows a distinct intermittent dune movement

of the bed became evident.

Since such spatial distr4bution of

movement occurs within a length of channel then it would be possibl€ that a bed load discharge at one particular cross-scctton could be associated with different microphone Signals from that length. However, since the passage of a dune past a cross-section was rarely observed to take more than 4 to 5 minutes,

ocatt~r

due to

this effect should be minimised by taking average values OV3r longer p3riods. Scatter can also be attributed to the fact that the plotted pOints are the averages of instantaneous valuas which have varied over a considerably wide range.

This refers not to the long term

periodic fluctuations obtained in some experimental runs e.g. run 19, fig. 7.2.a (table 7.4.a. shows that an increase in the time over 166

which

t~e

averages are taken does not reduce scatter to a

significant extent), but to the irregular variations superimposed upon these fluctuations.

The average microphone signal and the

average bed load discharge over a period of time can therefore lie within a relatively wide range of each variable, resulting in a statistical scatter of the observations, especially in the less sensitive range of the curve. Since the microphone signal is dependent upon the rate of deposition of particles on the bed it was considered possible thnt accretion, essentially a process of particle deposition, might produce n greater microphone Signal than scour, a process of entrainment, for the same instantaneous bad load dischargo.

That

is, lass oound would be emitted during a rising (or scouring) bed load discharge thnn during a falling (accreting) discharge. Possibly also, experimental points lying above the mean curve might represent predominantly accreting periods of time (B greater M for a given q ) and similarly those below might represent S B predominantly scouring periods.

An attempt was made to confirm

this hypothesis by describing each point as scour or accretion depending upon whether, for more than half the t1me, the instantaneous bed load discharge was greater or less, respectively, than the average bed load discharge over that period.

No

cO:lclusive evidence, however, could be found 1n the distrib\1!;ion of the scour and accretion pOints.

On a smnllor time scnle

attempts were made to determine whether, during the movement of well-formed dunes past the microphone, the occurrence of doposition on the downstream face of a dune immediately below the mic:;:'opho'ls resulted in an increase in the recorded signnl.

No ev idence of

this effect Vias observed either, probably becauso t:1e signnl was

167

influellced to a large extent by particle movement in other parts of the channel. It is still possible, however, th:!t whilo some I)f the ncntter of the experimental observations may be statistical in nature a further parameter, perhaps invt)lving scour

OJ:

nccrotion, may be

required to completely describe each observation. 7.5.

Conclusions

Consideration of the results of the preliminary laboratory experiments enabled the following conclusions to be drnwn:1.

To avoid disturbance of the velocity of flow near the bed the microphone should be fixed at a height of 3 in. above the plane sediment bed.

2.

Since the moving bed particles approximated closely to a source of plane sound prassure waves small variations in the height 01 the microphone above the bed have littlo effect on the strength of the microphone signal.

3.

The microphone was ablo to detect inter-particle collision at distances of up to 2! to 3 feeti

it wus therefore

sensitive to the general conditions of sediment movement in a length of channel of about 5 ft. of the sediment channel was only

Ii

Since the width

ft the microphone

signal would moot likely be influenced by tho of the channel sides.

e~iRtence

However, by permitting re'election

of sound from the glass sides, the conditions were probably maintained more like those in an infinitely wide channel. 5.

Ths sound emitted by the inter-particle collision of the u~iform-sized sediment extended over most of the audio-

frequency range, with no characteristic peak freqwency. 160

It was decided to sample all frequencies within the amplifier cut-off rango (140-20,000 H ) throughout the z remainder of the experiments. A total of 24 experimental runs were conducted with a

constant

w~ter

discharge and continuous recording of bed lond

discharge and microphone signal.

From the results of these

experimentp it was possible to obtain graphs of nverage bed load di~nharge,

~,

against average microphone signal, Ma' over poriods

of 10, 20, 30 and 40 minutes. An approximate theoretical derivation indicated that the form of the relationship between qB and Ms should be:-

qB =

where a

i~s

an~

I

2

a

+ bMs

413' i )

3/2

- a]

b are undetermined constants depending upon the

physical, acoustic and hydraulic properties of the sodlmont, water and microphone.

Curvilinear regression analysis produced

curves of the theoretical function giving the least

s(~ul1rea

residuals (for the 30 min. perio.i, 65% confidence limits of + 32.2%), but not appearing to be a good fit to the plotted data.

An

apparently closer fit was obtained by selecting dlffct"ent vnluas of a and b in the theoretical equation, but resulted in 65% confidence limits of

~35.4%.

No improvement in

curve-fit~ing

was obtained by regression analysis according to power or polynomial relationships. Deviation of the observed relationship from the theory was probably due to:1.

The influence of the restricted channel width.

2.

An increase in particle step length with increaSing bed load discharge.

169

3.

The formntion of a distinct bed configuration at high bad load discharges.

Tho InttGr two effects cause a relatively small increase in microphone sisnal for a large increase in bed load discharge. The major disadvantage of the

pres~nt

technique is the resulting

difficulty in making accurate predictions of bed load discharge from n knowledge of the microphone Signal. Scatter of the observed data was probably dua to the 1.

followin~:-

The two measurements did not refer to identicnl physical phonomenon.

The microphone

rospon~ed

to the general

conditions of movement within a length of channel, while the sediment weighing dovico recorded the bed load dischargo at one particular cross-section in that length. 2.

Each point was the average of a number of instantaneous values which varied over a wide range.

Over a period

of time the al/erage microphone signal and average bed load dischllre'3 could therefore

110

wi thin

D

relati valy

wide range of each variable, resulting in a statistical scatter of the observations, especially in the lese sensitive range of the curve. 3.

Tho m:l.crophone signal was dopondent upon the rate of depOSition, not entrainment, of particles on the bod of the cuonnel.

It is

p~sible

that a iurther parameter,

probably involving accr(3tion (deposition) or scour (entrainment) is necesflary to

DCCOU.l"!;

for the obsorv(;Id

scntter. The results of these laboratory studies of the acoustic detection of bed load movement indicate that with the present

ric

technique measurement of bed load discharge in laborntory channels can be made with 65% confidence limits of about +35%.

Possi ble

improvement in the accuracy could bo obtained by either recording the rate of occurrence of inter-particle collisions on on imp·lllao rate

n~ter

or by continuously

the microphone amplifier.

r0~ording

the a.c. power output of

Any further laboratory studies should

be carried out in a widG channel to eliminate thG influence of the

channel sides, or the microphone should be made directional, thereby restricting the area of bed to which it is sensitive. For U3e with different sediments the microphone would havo to be calibrated for the particle size of each sediment.

It is

possible that the theoretical equation 7.3.c., which includos partic!a size in the empirical constants, could bo used to extrapolate to slightly different sizes.

171

Section 8

8.

Aoouotic Detection of Bed Load

Movemen~

1n Rivera

Sections 6 and 7 have described the experiments carried out on the acoustic detection of bed load movement in the controlled conditions of the laboratory sediment channel.

Contemporaneous

with these investigations an instrument was being designed for the detection of inter-particle collision sound when suspended above the bed of the River Tyne from the Bywell cableway.

With this

instrument it was intended to investigate the temporal and spatial distributions of sediment noise at

~he

cableway section and to

compare relative noise intensities at various river stages with the estimates of bed load discharge computed in section 4.

A

review of the aYailab1e information on previous work in this field of bed load discharge measurement is first given, followed by a description of the design and testing of the microphone used on the River Tyne.

Opportunities for testing preliminary deSigns of

the instrument were, however relatively few and little progress could be made in extending the acoustic technique from the laboratory to the river. 8.1.

Previous Investigations

Microphones for the detection of underwater sounds have been used for many years for a variety of purposesj

detailed designs

of several hydrophones, as they are called, can be found in standard text books on sound (RICHARDSON, 1953).

Their principal

applications are usually to be found in marine and coastal investigations.

General studies of ambient noise propagated

through the oceans and seas have been carried out by many countries throughout the world (WENZ, 1962), while more specific applications are common in the fields of oceanography, geophysics, navigation (STEPHENS and BATE, 1950), zoology (the Department of zoology of the University of Newcastle upon Tyne utilised a 172

specially constructed hydrophone during a study of the behaviour patterns of lobsters off the North-east coast of England), ultrasonics (RICHARDSON, 1957) and, recently, fisheries (TUCKER, 1967). The detection of sediment movement in rivers by acoustic methods is not a recent development.

According to LABAYE (1948)

Muhlhofer, as early as 1931, was able to listen to the sound of gravel movement in the River Inn in Austria by placing a box containing a microphone on the bed.

Soon after, in 1936, Reitz

used some kind of microphone placed just below the water surface to record the sound of sediment disturbed by the formation and passage of large-scale boils (HUBBELL, 1964).

In 1942 a

hydrophonic detector was constructed at Grenoble, France and later modified by BRADEAU (1951) at the Service des Etudes et Recherches Hydrauliques, d'Electricitie de France.

The instrument consisted

of a flat plate installed on the stream bed and provided with a microphone to pick up the sound of gravel and coarse sand sliding over, or colliding with, the plate.

I-HJBBELL (1964) described an

instrument developed by Juniet in 1952 called l'Arenaphone, which consisted of a fork-shaped rod attached to a transducer.

The

assembly was supported on a tripod such that the rod was inserted a short distance into the river bed.

Vibrations caused by

sediment particles impinging upon the forked rod were amplified and transmitted to headphones or tape recorder. CARLSON and MILLER (1956), and KAIlOLYI (1957), have stI8Ssed the need for a continuous method of recording bed load discharge, such as the acoustic technique, which could be used to determine the commencement and cessation of sediment movement, the effective width of movement, and the temporal and spatial distribution of 173

movement.

Such an instrument could also be used to determine the

number and location of sampling verticals to be used with trap-type bed load samples.

More recently, BEDEUS and IVICSICS (1963) in

Hungary made further progress with the acoustic technique by developing a microphone which could be suspended at some height over tho river bed.

By virtue of its pOSition the instrument did

not l therefore, influence the bed load movement and recorded only the sound emitted

~

inter-particle collision.

This sound was carried

from the large crystal microphone, housed in a weighted, streamlined body, through the suspension cable to a small boat where it was amplified and its intensity registered on an ammeter. It was learned (by personal

cow~unication)

that some research

was carried out on this topic by TUrk at the Techniuche Hochschule, Karlsruhe,

Gerw~ny,

but no published information i8 available.

The author has a1Do learned recently (December, 1967) that Plessey Electronics Ltd., Marine Systems Division, are conducting investigations into the acoustic detection of

underwat~r

sedimont.

IIowever, their work is at present concerned solely with tho d8tection of fine particles in suspension. Although it is not directly associated with the present research, it is interesting, perhaps, to note the phenomenon of. "singing" observed to occur with certain natural senshore sands. Experiments have been carried out in the University of Newcastlo upon Tyne by BROWN, CAMPBELL, ROBSON and mOMAS (1963) on the high frequency sounds emitted by these sands when subjected to the sudden impact of a large weight, e.g. the impact of the human foot when walking.

A similar phenomenon, known as "the booming sands of the

Kalnhari", was alao studied by HAGNOID (1966). 174

8.,2.

Development of an Acoustic Bed Load Detector for use at Bywell Cnbleway Gauging Station

As mentioned earlier, opportunities for testing preliminary designs of a bed load detector under conditions of sediment movement at the Bywell cableway gauging station occurred relatively int requent ly •

It cnn be seen from calculations made in section 4

of this thesis (e.g. fig. 4.I.m) that bed load movement is unlikely to occur at river stageD below 54 ft. A.O.D.

(7.75 ft. above

staff gauge zero) i.e. at discharges below about 12,000 cusec. According to the flood frequency curve given by HALL (1964) this flow is exceeded on average only six times per year.

Further

examination of discharge records over the ten year period 1956/66 shows that almost three-quarters of the flood discharges greater than 12,000 cusec occurred during the hours of darkness.

For

practical reasons, and in the interest of the safety of both equipment and pe::-sonnel, work at Bywell had to be restricted to daylight hours. ThU.:J, in the time available for this research, only limited field experience with the acoustic detector could be gained, and it prov~d

impossible to establish a final, tested design.

An account

of the various stages of development of a suitable instrument is given first, followed by a description of the latest design of the microphone and associated electrical recording equipment. 8.2.1.

Design and Development of the Bed Load Detector

Ideally, the application of the

to the river should involve a minimum of operation of the instrument.

acoustic technique

ln~oratory ch~

in the oonditions of

It would seem, thereforo, thnt

U1C

microphone should be located at a fixed height above the sediment bed at some point in the cat,lcway cross-section. 178

The installation

and maintenance of the microphone, with some form of support frame, in the river bed would have required personnel skilled in underwater operations;

such help was not at the time available.

Moreover, i t was intended to investigate not only tecporal, but spatial, variations of bed load movement in the cross-section. Basically, therefore, the acoustic detector was to consist of R

microphone which would be suspended above the river bed at any

point in the cross-saction and which would transmit the sound emi tted by inter-particle collision thr01Jgh the suspension cable to a recorder on the

b~nk.

The arrangement was similar to that

in the laboratory, but with sevaral unavoidable differonces. absonce

of

The

a rigid suspension of the detector introduced problems

of stability, especially in the considerably greater flow ft/s~c

veloci ties occurring in the rive:;.' (velocities of up to 13 have been rocorded at Bywell).

The existence of a long length of

coaxial suspension cable, the electrical resistance of whioh variod with the distance of the detector across the section, that the

n~plifier

be

~ocess1tated

located close to the microphone;

in this wny

it was possible to minimise loss of signal and acquisition of extraneous noise during the transmission of the sound to the recorder.

Since mains supply of electricity was not available

at the cableway the microphone amplifier had to be battery-powered; similarly the recording instrument had to be either mechanically or battery-operated. It wn.s decided to house a small crystal micropbono

ill

an

oil-filled cavity in the undersids of a streamlined metal b':>d,y; the

60

lb weight used by

H/:..LL

(1964) to stabilio0 a suspended

sodiment sumpler in high flows was considered SUitable. sta~e,

tra~istorised,

A throe-

battery-powered amplifier was contnined

176

inside a watertight brass cylinder attached to a vertical hanger bar above the streamlined body.

Tho cylinder was enclosed by a

sheet brass faring ro reduco resistnnc3 to flow.

To minimioe

excessive drainage of the batteries a mercury switch was installed in the cylinder such that the amplifer was powored only when the instrument was in an upright position.

The amplified signal was

transmi tted through the coaxial suspension cable either to hoadphones or to a portable Everett Edgcumbe moving-coil recorder, with mechanically operated chart drive (full scale deflection lmA, paper speed I in/min).

'Ibe instrument at this early design stage

is shown in fig. 8.2.a. 'Ibe instrument was tested in moderately high flows at tho cableway section and several improvements made to the streamlining of the instrument.

As the results of laboratory investigations

became available further the electrical equipment.

Ii1ccl:!.~ications

were also carried out

011

Later, a battery-powered, portable,

potentiometric voltmeter, an improvement on the old

moving~coil

rocorder, became available, and provision was also made tor inclusion of a frequency filter, it required. No suitably large flows for testing the instrument occurred at Bywoll for a period of over ten months, until continuous, h3avy rainfall on both the Nor"i;h Tyne and South Tyne catchments produced the highest flood in the lower reaches of the River Tyne Since 19';4. PeRk stage at Bywe11 reached just over 18 ft abovo .:ltaff gauge zoro (64.25 ft A.O.D.), corresponding to an estimated pealt discharge of about 68,000 cusec. ~t

Attempts to immerse the bed load detector

this discharge resulted in the instrument being thrown completely

clear of the wnter;

the stability problem had obviously been

greatly underestimated.

Even at a stage of 14.5 i t (44,000 ousee), 177



«I

• C\J •



btl

.~

~

when it became possible to maintain the instrument below the watersurface, the mercury switch was observed to open and close rapidly, indicating thnt correct location and orientation of the detector could still not be ensured. In the light of this experience the instrument was modified considerably and several further improvements made.

Unfortunately,

no more suitably high flows have occurred since the latest design, shown in fig. B.2.b., was completed and further testing of the detector has not been possible. microphone and

~ecording

A complete description of the

equipment at the present stage of development

is given below. 8.2.2.

Bed Load Detector

A diagram of the latest dosiGn of the acoustic bod load dotoctvr is given in fig. 8.2.c.

The detecting element is identical to thnt

used in the laboratory microphone, i.e. a modified lead zirconnto titanate polycrystalline ceramic tube (PZT 4, plated and polarised), manufactured by Brush Clevite Ltd., Hythe, Southampton.

It is made

up as shown in fig. 6.3.a. and housed in a 2! in. dir.,moter in the underside of a streamlined mild steel weight.

cr~vity

The cavity is

filled with castor oil (of charncteristic acoustic impedance similar 'i;o that of water, thereby minimising sound energy transmlssion );18ses) and sealed with a sheet of 1/16 in thick polythene secured in poSition by a thin brass ring screwod into the metal weight. of the str3amlined body io built up with araldi'::o to eliminate noiso generated by the flow of water past protuberances near the microphone cavity. The signal from the microphone is carried by a

twin-cor~

couxinl

cable to the amplifier which is housed in a 10 in. long, 2 in. internel diameter, length of pipe welded to the rear of the streamlinod body. 178

• • C\J ,0



(X)

• .....b() Ii-<

standard current meter connection armoured coaxial sus~nsion cable rubber- I In e ,: j bolt Connection

. 1 ~ J n . x '4 In. L

steel

·

1,

hanger

flo t bar

---

twin core coaxial cable, amplifier to susr enS ion cable

--------

fixing bolt

------------

I, ,II

1,1

I

.,

', \31

oli -f lile:!

--

--'.

,--

,.. ~---

/,

I, ~

rubber-lined seat fix#'!d to h,ngcr bar

standard current meter weight (100Ib)

.,./

'I II

I· I I

"

I· I

, II

" II

-- --

I twin core coaxial cable. m/ croph one to arnpl I fier

c a "IC' y

three-stage transistor , sed amplifier waterti9 r t

scre w~ r"

,

tubu( q r I - Ie z oe [ e;c t r I C cryst -l l

SIN

74 vc , t b

\

a r<'I/:1/ Ie

I

2 in. Internal dlam .

mild stee I (6C It,

~6in sheet p ol yt hene

2ft . 91n . over a I .

~ ---

\veipht

stee I

l ~ngth

-~

";COUSUc

b ed

/0

ad

dete ctcr.

~ full

rnercury

tie r y p ower supply

pipe

Scale

Fig, B, 2 ,c

r-

~

\

r>1 /c ropl en e

(c

I. d

S i ze

A watertight screw-on lid on the end of the pipe enables a switch connecting the batteries with the atilplifer to be operated when required

The amplified signal 1s then carried to the suspension

cable by a length of twin-Gore coaxial cable fitted with a standard Hilger and Watts current meter two-pin socket end-connection.

Ii

The

i

in x

in flat steel hanger bar is provided with a

rubber-lined seat and bolt-hole enabling a 100 lb current meter bomb to be rigidly fixed to the bar.

The total weight of the bed

load detector is thus approximately 160 lb. to the upper end of tho hanger bar by connection

80

Il

A ring is attaohed

rubber-lined bolt

thllt the instrument can be suspended from a stllndard

Hilger and Watts current meter hook end-connection. 8.2.3.

41i1pl1f ier

The electrical circuit diagram for the amplifer and output circuit is shown in fig. 8.2.d. In order to conserve spllce mercury batteries are used in place of the normal dry cell type;

ten 1.4 volt batteries

(type RM1H), contained in a small perspex box, are connected by an on-off switch across a stabilising 10 volt Zener diode in series with a 220 ohm resistance.

Selection of n suitable

resistance value is important since sufficient current must be taken to drive the diode without excessive drainage of the batteries.

The three-stago, transistorised amplifcr and emitter-

follower is similllr to that used with the laboratory microphone. An audio-frequency a.c.

Si~11l1

generator was used as described

in section 6.3.2. to investigate the frequency response and gain of the amplifier. has a linear

Figs. 8.3.e. and 8.3.f. show that the amplifier

~m.s.

3

voltage gain of 1.21 x 10

range of 140-20,000 Hz. 179

over a 3dB frequency

'6K

5'6K

47K

3 '3K

220

68K

10 14'2\.1.

OAZ 228

10xRfv1TH

~11

I~ OC20050

500

t ~OC200

IT ,

~ ~A

resis t ances

in ohnl s .

All capaci t ances in

microfarads

TOV

560 100

7K

,<

7K 4

• •

cry st al





••



-s

am pi if i e r Streamlined

b od

Fig . 8 . 2 . d .

frequency , i I t£ r

Electrical

susp en s i an c '"1 ble :::: 15 ohr-· A·

ri ver

~Att1 ~~

0-

-..!<;)

r

o

e--

• heQ~phones





OJ l put

2500

ai/recorder potentlornetric voltmeter.

~

c lrcuU.

!

c i rcui t

di a gram

nJi crophone .

'·2

1·0

0 ·8

n '6

Out pu t Po/yrecorder

l~

( V )

3dS

rgng~,

140-20.000 Hz

0 ·'"

T mV

sine wave Input

0·2

Frequenc v

( Hz '

OL-----------~--~----------~----~----------~----~----------~--~ 50 10 0 soc .. OW 10 ~0<...(.., 10.000 SO,OCO

Flg . 8 . 2 e .

F requen c y

res p onse of ampll fl er of

river mlcroph one .

1·5

Output , ,0

Po/yrecorder ( V)

Si ne

wave

frequency,

i np u t

1.500 Hz .

/ 0·5

O

~--

________

o

Input (mV)

~

__________- L - -________

0 '5

Fig . 8 . 2 . f .

LIne a r

1' 0

gain of

ampl i fir of

~

____________

1' 5

river

~

___

2 '0

m ic rophone .

8.2.4.

output Circuit nnd Recorder

The n.c. output from the amplifier is

c~rried

to a

three-w~y

switch on the bonk by the nrmoure<.l coaxial suspension cable (inner insulated core 2 .. 5 ohm/lOO ft.". outer brlddtng 5 ohm/IOO ft.) insulation is provided on the

out~r

the microphone signal is earthed.

j

110

braiding so thnt one line of The signal can be passed direct

to headphones, or through a frequency filter

and

rectifier to a

smoothing circuit containing n battery-powered, high impendance, potentiomotric voltmeter (Electronic Polyrecorder, Model EPR.-2T, manuf actur6d by Toa Elec -:: ronics Ltd. 1 Toleyo, Japan).

This

instrument is capable of continuous recording of d.c. voltages from 0.1 mV to lOOV with chart speeds ranging from 20 180 mm/min.

Mn/hour to

On the basis of the results of laborntory experit:.lonts

(section 6.3.4.) capacitance and resistance values in the output smoothing circuit were selected to give a time constant of 5.5 sec. 8.3.

Use of Acoustic Bed Load Dectector at Bywell Cableway Gauging Station

Due to the difficulty of maintaining the acoustic bed load detector correctly orientated beneath the water surfecs during high flows littls information can be extracted from the results obtained to date.

However, at river stnges up to 5.80 ft above

stC£f gauge zero (54.05 ft A.O.D.), at which flow velocities of 7 ft/sec occur, no sound could be detected by the instrument (at the time in a design stage similar to that shown in fig. 8.2.0.., but with nn output circuit and rocorder similar to the latest

dosl~n).

DUring the 68,000 cusec flood mentionod previously it was eventually possible to mnintain the instrument beneath the water surface when the river stage had subsided to 14.5 ft above stnff gauge zero.

Tole microphone was highly unstable, 180

howeve~,

and it is

evident

fro~

the recorder trace shown in fig. 8.3.a. that movement

of the microphone within the wnter was causing the mercury switch to open

~Gd

close rapidly.

The sound heard in the headphones

consisted mainly of high frequency "hissing" noises with lower frequency impulse sounds.

It would appear that noise is generated

not only by the flow of water past the streamlined body but by the production cf large scale turbulence within the river.

According

to AnABADZHr (1967) the formation and collapse of large air bubbles in normal stream flow generates sound waves with a frequency spectrum extending over the range 40 to audio-frequency range;

8,000 Hz, almost the whole

the possibility of filtering out inter..

particle collision sound therefore seems doubtful since laboratory experiments have shown that this sound also extends over the audiofrsquency range (section 7.1.4.). The existence of the turbulence generated sound was shown by moving the microphone into still water close to the left bank. In this pOSition an almost steady signal of about 0.1 volts was recorded.

A possible further difficulty waS thanobserved when the

microphone was immersed in still water near the right bank at a distance of about 230 feet from the winch.

The Signal observed

at this position was about 0.5 volt, suggesting that noise was being picked up in the extended length of suspension cable. 8.4.

Concllklions

An instrument has been designed for the detection of bed load movement when
It consists of a piezoelectric

crystal microphone housed in a 60 lb streamlined, metal body to which a standard current meter 100 lb weight can be nttached.

A three-

stage, transistorised, battery-powered amplifier with a voltage 181

. Or.---------------------------------------------------------------------------------

(l

08

O·~

Microphone 51

gna /

(VC/tS)

1

06

05

04

03 R,ver

staye

fv",croph one

0

14·5 ft

above

40 ft

located

staff frorr

gauye left

zero.

bClnk.

zero peg

1

I

C

2

T'1 rr e

r=-

;;.8 3

T

_

i_

'1:.:

c~

S

:J'''-'~}!

I

...

c' .....,-

iC"O..Jst.c

-

(n-.' r)

L~·.'

. .-.

-;

--/

.;

3

~/e~~':tc

"

Ir

r~

ver

.1

rl

e

1/

P,' ...... e!!

gain of 1.21 x 10

3

over a 3dB frequency range of 140 to 20,000 Hz

is located at the rear of the strenmltned body, nnd transmits tho oound of

collision thToUgh the suspencion cable to

i~ter-particle

either headphones or n

continuo~sly

recording potentiometric

voltmete!" (tima const3.at 5.5 sec). Infrequent occurrences of sufficiently high flows in the aiver T"Jne during the time avnilable for this research did not permit a

final, tested design to be established.

However, experience has

shown that the application of the acoustic technique to rivers is complicated by a number of difficulties.

The principal difficulty

is the maintenance of the bed load detector at a fixed position above the sediment bed when suspended from the cableway in high flow velocities.

The latest

desi~n

of the microphone weighs a total of

160 Ib, but it mcy still be necessary to make use of retention cables

to ensure co:crec"i; orientation and stability.

Problems of expenso

and manpower might then arise. Ho noise could be detected at river stages up to 5.80 ft above ~·;;a:ff

occur;

gnug3 zero (6,600 cusec), when flow velocities of up to 7

ft!~oc

at higher discharges, however, a distinct "hissing" sound was

picked up by the microphone.

ThiS noise is moot likely produced by

both the flow of water past the streamlined body and lArge scalc turbulence wi"i;hin the river;

the noise spectrum most 111<:ely 3xtelldc

over a wide frequency range. Experiments also indicated that some extraneous noise may be picked up in the long length of coaxial suspension oable through which the amplified microphone signal is transmitted to the recorder. In attempts to extend the acoustic technique of bed lond measurement to rivers conditions should ideally be mnintainud aD similar as possible to those 1n ths laboratory.

Hence, even if the

above difficulties of stability and extraneouA noise cnn be oliminntod 182

(possibily by means of a rigid suspension and frequency filters, respectively) then the microphone must be calibrated in the laboratory with the appropriate size of sediment.

Further

difficulty may then arise in obtaining bed lond discharges in n laboratory flume as large as those occurring in the river.

183

Section 9 9.

Summary of Conclusions

'1'11.9 principal objectives of this research programme,

viz. a study of the estimation and measurement of bed load discharge in the section 1.3.

~iver

Tyne at Bywell, have been discussed in

The conclusions of sections 3 and 4, dealing with

estimation of bed load discharge, are summarised in section e.l., and those of sections 5, 6, 7 and C, dealing with the measurement of bed lond discharge are Recomt~ndations

s~mmari6ed

in section 9.2.

for further research, section 9.3. complete the

section. 9.1.

Estimation of Bed Load Discharge

For the estimation of bed load discharge by the rationol bed load theories the selection of a reach of river in which conditions approximate as closely as possible to uniform flow was found to he important; prese~ts

in "pool-bar" rivers, such as the River Tyne, this

some difficulty.

Measured water-surface and energy-

surface slopes at Dywell were found to vary linearly with the logarithm of river

stag~

(figs. 3.4.c.,

3.~.d.)

Bulk sampling and sieve analysis of 2/3 ton of bed m..'ltC':!'inl at Bywell yielded the particle size distribution curve of

fig. 3.5.e.

Investigations indicated that certain information can

be obtained by the quicker, more cOl1venient, method of areal sampling, as suggested by WOLMAN (1954). material at 3yWell were found to IU.VMBEIN

bC3

Areal s amr los of the bed

best described fo:.,' shape by til;)

(1941) sphericity meaSure and ZINGG (1935)

cln!'l~Hlcation

(tables 3.5.i. and 3.5.j.), and for roundness by the nUMBEIN (1941) visual chart method (table 3.5.k.) (table 3.5.1.)

s~owed

A petrographic analysis

that the majority of the bad material at

Bywell is sandstone, with on appreciable number of bed particles originating from parent rocks outside the River Tyne catchment. 184

Of the many bed load theories found in the available

literature only nine were considered to be possibly applicable to the flow and sediment conditions at BYWGllj

extrnpolntion

sometimes considerable, was necessary, nevertheless, in the application of all these methods.

The major defects of most

bed lond formulae available at present were found to be the necessity for accurate measurement of energy-surface slope, neglect of the mutual interference between particles of different Sizes, and neglect of the influence of particle shape. Fig. 4.l.m. shows the bed load rating curves computed by the nine methods applied to the

~iver

Tyne at Bywell.

Estimates of

bed load discharge at near bankfull stage (61 ft A.O.D., 14.75 ft above staff gauge zero) vary from 120 Ib/sec to 1350 lb/sec. Predictions of the critical stage at which bed load movement commences range from 54 i t to 57 ft

~.O.D.

(7.75 to 10.75 ft above

staff gauge zero). The bed load curve computed by the MEYER-PETER and MtlLLEa (1948) formula is considered to be the most reliable. natural

~aving

However, due to n

of coarse material on the bed surface and the

resistance to entrainment of the predominantly disc-shaped

l~d

particles, bed load discharge most probably commences at a slightly higher stage than that indicated by the rating f'urve, i.e. at about 56 ft A.O.D. (9.75 ft above staff gauge zero). Use of the Meyer-Peter and MUller rating curve with the flo·'1 frequency curve for the ten year period, 1956/66, indicated an average annual bed load discharge at Bywell of about 15,000 ton, approximately 10% of the average annual suspended sediment dischargo. The estimation of average annual bed load discharge by assuming n certain percentage of the average annuel suspended sediment dischrrgc, 185

as recolnmended by IANE and BORLAND (1951), is considered to be as accurate as, and more easily obtained than, that givon by the application of bed load formulae. The regimo approach to sediment transport appears to be insuffiCiently developed for the determination of bed load discharge in coarse gravel-bed rivers. sediment

One most promising solution to the

however, seems to lie in the ultimnte combination

p.:.~oblcm,

of the rcgin3 and rational approaches.

9.2.

Measurement of Bed Load Discharge

The socond part of the reseaTch programme proved unsuccesoful in achieving its

immedia~;e

objective, the confirmation by direct

measurement of tho estimated bed load discharge in the River Tyne at Dywell.

Some progress was mado, however, in the development of

a posoible mcthod of continuous meal3urement of bed load dischargr>

iT'

gravel rivers by an acoustic technique. A survey of available literature (section 5.1.) showed that tIlo

illOOt

accu~ate

slot

o!'

ccthod of measurement of bed load discharge is the

p:!.t type structure;

high construction and maintenanco costs

are usually pTohibitive. The most accurate and reliablc bod load sampler for the flow

and sediment conditions at Bywell was considered to pres~:lUre-difference

~~

sampler designed by NOVAK (1959).

thC'!

·v. U. ;; •

However, use

of the sampler at a cableway gauging station requires n complex system of retention nnd suspension cables to ensure corroct orientation and stability.

Such nn arrangement is likely to be

expensive and require at least three winches and n team of three winch operators (section 5.2.). 186

Tole accuracy of bed load traps is usually low, due to their effect on the surrounding flow and sediment regime, tho necessity for laboratory cnllbration, the variability of their efficiencies with

paramete~s

such as particle size, flow velocity etc. and tho

oscillatory, or unsteady, nature of bed load movement. In the design of a laboratory sediment channel (section 6.2.) particular attention 8hould be given to the measurement of water discharge, design of channel inlet conditions, and measurement of water-surface and energy-surface slopes.

It was found that feod

rates of 5 rom, gravel varying continuously from 30 Ib/hr to 700 lb/hr could be obtained by a hopper and belt arrangement. Measurement of sediment discharge in the channel could be made by oontinuous weighing of a watertight container, connected by flexible t'lbing to the downstream end of the channel. Preliminary experiments (section 6.3.) indicated that interparticle collis10n sound in the lnooratory sediment channel could be convenie:ltly recorded by a piezoelectriC crystal n!icrophone

J

and three-stage, transistorised amplifier (voltage gain 1.21 x 10 , 3dB frequency range 140-20,000 Hz).

The amplif ied,

re~tif ied

signal was fed to an output sl.loothing circuit (time constant 5.63 sec) containing a continuously recording Ultra-Violet oscillograph. The frequency spectrum of the inter-particle collision so\md emitted by the single-sized 5 rom gravel in the labor.ntory channol was found to extend over the whole audio-frequency rango (section 7.1.4.).

Measurement of microphona signal was therefore

made over the cut-off frequency rango of the amplifier. Theoretical consideratiolls (section 7.3.) indicate that tho relationship between bed lond discharge of a giv,-:m sediment per 187

unit wldth, qB' and microphone signal, Ma' expressed as a current or voltage, is given by:-

qB ==

ir

(a

2

+ b Ms 4/3)

~ - a

L

13/2 ~

where c and b arc constants dependent upon the physical and electrical properties of the sediment, fluid, microphone and recording

equip~~nt.

Analysts of experimental results indicated that average bed load discharge in the laboratory channel over periods of 10, 20, 30 and 40

~inutes

micropho~e si~c.l

level.

could be predicted from a knowledge of the with an accuracy of +35% at the 65% confidence

Scatter of the observational results might possibly be

reduced by the introduction of n third parameter involving f!1cotlr or accretio~.

The principal disadvuntage of the present acoustic tochniquo is tho insensitivity of the mj.crophone signal to relatively larcse changes in bod load discharge. Development of an acoustic bed load detector for usa at Bywoll cnblewny gauging station was hampered by a lack of opportunjties for the testing of preliminary designs.

The latest deDign (sel!tion 8.2.)

consists of a piezoelectric cry.stal microphone housod in

Ii\

str911rnli nod,

60 lb. weig:lt connected to a battery-powered, thrse-stagr.., transist~rised,

3

amplifier (voltnge gain 1.21 x 10 , 3ctil frequency

rnnge 140-20,000 Hz) located at the rear of the stroamlined body. The amplified signal is transmitted through the cO"l-:c1al suspension cable to headphones or a smoothing circuit (time cOllstnnt !".5

sacon~I~)

containing a battery-powered, continuously recording, potontiom.et·.;.c voltmeter.

The dotector is designed to enuble a standard current

meter 100 Ib weight to be attached.

lse

Ex~rience

indicated that the principal difficulties involved

in the use of acoustic detector from a cablewny arc the mnintannnce of corrGct orientation and stability, noise generated by flow past the microphono and in

l~r~e~calo

turbulence (probably extending

over a wide frequency spectrum) and extraneous noise picked up in the extended length of suspension cable. For

US~

cali~rated

in rivers the acoustic bod load detector must be

in a wide laboratory channel over the appropriate Dize

of sediment. :lecomlOOndationa for Further Research

g.3. Most

bed load

rivel" engi:leering problems, including the estimation of disc~arge

usually requiru somo knowledge of the material Experience at Bywell has shown that

forminc the bed of the river.

further investigations into th\3 Dampling, analys1s, and description of coarse

are r0quired.

sedi~nts

bulk and araal sampling

n~thods,

Comparison of the

r~sults

of

for instance, indicates that the

latter method might possibly bo used to obtain certain il!formntion more quickly and more conveniently.

There appoars, in fact, to be

a need for the systematic collection of river data, as described recently by

Cf~BELL

and CADDIE (1964) arA NEILL and GALAY (1ge7).

For estinmtion by formula of the bod load discharge of coaree sediment there is

a

need, not necessarily for a new formula but for

the modification of an existing method, possibly that of and MULLE1 (1948).

~mYE~-PETE~

The new development should enable atimates of

E:ffective bed shear stress to be nlade without the nece88ity for accurate measure,:lent of enorgy-surface slope, and shoUld include also the ip1luence of particle shape and the mutual interforonco of particles of different sizes. fully

iil

This possibility is discussed

section 4.5. 199

n~re

Laooratory experiments have shown that the acoustic tachn:f.que is

potenti~lly

discharea.

capable of continuOUD measurement of bed load

';'11 th tIl..::; nid of expert Imowledge and

methods, the accuracy of tho

tec~nique

mO)~e

sophisticated

could no doubt be 1r.lproved.

Possible alternatives to the technique used in the present research are the reoording of t!le power output of the microphonG a.nd the measuren~nt

of the rate at which impulses produced by inter-

p?.rticle impacts are recoived.

Future laboratory exporiments

nhot:ld be cqr:-ied out in wide channels to elininate side effacts j construction of a directional oicrophone may similarly improve the method. More field experience is required.

The most

promisill~

reGul ts

would probably be obtained by the location of a microphone, carefully

d~~such

that flow past it produces no noise, nt a

fixed height above the river bed.

In this way ildormntion could

be obtnined on the magnitude and frequency spectr11m of tl.1e sound emitted by inter-particle col11sion, and of other noisGs within the river.

190

App~ndix

1og~.'.Jss1ol1

Analysis of Laboratory Experimental jJutn

APPENDIX

In section 7.4. it was required to obtain the values of the constants a and b to give a least squares fit to the experimental I data.

Since partial differentiation with respect to a and b of

the residual given by the theoretical equation 7.3.d. resulted in normal equations not directly soluble for a and b, the following iterative procedure for the curvilinear regression analysis was cn;;"=-icd out. It was required to fit an equation of the type:-

• where



• • •











• • • .A-I

is the dependent variable

~

M is the independent variable

s

a,b, ora undetermined constants If a , b o

~,

0

are the best fit vnlues of the undetermined constants

b, and qB is the observed value corresponding to the observed Ms'

then the residual (the difference between observed ond predicted

~)

Is equal to:-

a = qB - f(Ms' a 0 , b0 ) Let a, b be first approximation of a , b

0

0

such that 6

D,

b.

b,

are small corrections required to give:-

a

=a+ lla

o

.', :'1 =

qB - f (M ' a + s

b OJ

a, b +

t.l

o

=b+llb

b)

Expanding the right hand sidl3 of the above theol~m

by Tnylor'n

for a function of several variables:-

o[f(M, a, b)] R

equat~.n!'l

=q

B

- f ( M, a, b) -

s

s

o[feM, II n

Oa

u...

_

0, b)] S ------

Ob

+ higher powers and products of

191

~

a, 0 b.

Denoting f(I.1 , s

R

=

(q

B

b) by F, then:-

Il,

-ofcb

- F) -

"b

/.:,

Sincs greater scatter was evident at higher values of qB the residuals were weighted by multiplying by the inverse i.e. by t~e

l/F.

of

qB'

The regression thereby involved the minimisation of

sum 01 squares of the percentcgs residuals.

The weighted

residual is given by:-

1

VI

=

(qB - F)

F

=Z where Z

=

of

1 F

1 F

ecLln.

-XL.a -yLob

(q

B

- F)

1

X

F

of

= F bn'

of

1

y

=F



[h'

A-2



The sum of squares of the weighted residuals is thus givcn by:) R 2 = 'L' (Z - X ila L

W

- Y u b) ~

Partially diffcrentiu';ing with respect to t.n and Ob, equating to zero and solving fort. a and ob gives:-





• A-3

• •











A-4

The procedure is then repeated using new values of a, b equal

to n + ua, b + t. b until:t. a t.b absolute values of a + Li a ' b + Ii b

< 0.005 i.e.

i%

111e theoretical microphone equation 7.3.d. which it was requh'cd to fit to the experimental data was:-

_r

n

qB - L (...

2

+

; -1/3

b~"D

)

i _ Il J3/2

192

1n the determination of 6 a,

Th~refore,

6 b by equat tonR

A-3, A-4:-

Z =

[(a 31 2 X

2

+ bMs

'Is i 4/3) n

[

(a

2

= [

(a

2

+ bM 4/3) s + bMs

_ a

2 _2(a

y =

2

rL

(20 2

+

3 2 /

- 1

-1

, -1]

I 4/3)

M 4/3

3/

1

I •

_

A-5



a]

]

8 bM. 4/

3) I

+ bM 4/3) S

i

l

- a -1

I

A computer programm<3 was developed for use on the IIDF 9

computer of the University of Newcastle upon Tyne.

The programme

used for the regression of the 10 minute averages of qB on Ms is incltided in this

appElnc1'~;

the number of observational points was

141 and the initial assumed values of a and b were 7.0 and 0.31,

respectively. Tha required input data and the computer output are also

includod. Since Z

The latter givea the final values of a, band

= (qB

- F)/F the standard deviation of the percentfl.ge

residuals, or

p~rcentage

errors, is thus given by

lovJI z2/n-l~-

The 65% confidence limits for the prediction of qB fr0m Me are appr~ximately ~l

s.d. of the percentage residuals.

The programme can be used with little modification

fOl'

regression

p.ccording to any function of tho typa given in equation A-l, e.g. q

B

= aMs b + br.I

2

s

193

The only nlterations necessary, apart from the number of points and the initial assumed values of a and b, are the lines for the calculation of Z, X and Y (equations A-2 and A-5).

194

!tera·l;ive ourvilinear regression programme for KDF9 computer.

CV09*MICROPHONE*EQN~

begin begin

library A(),A6; open(20);open(30); real a,dela,b,delb, slgXZ,slgXY,slgYZ, slgXsq,slgYsq,slgZsq; lnteger l,p; array qB,Ms,LZ,LX,LY[1:141];

S(2P0) ;1 untll d(2b );1 until

ror i :- 1 CiIITl] : = read for 1 :- , NSfl]:= rea

14, do 14, do

a:- 7.0; b: a 0.3';

p:- 0; WOP:

wrltetext(30,[[p]]); slgXY:.aslgXZ:;;SlgYl :=slgYsq :-slgXsq :-slgZsq :-0; p : ... p+1;

for 1 :- 1step 1 untll 141 do l>egln LZ[l]:a qB[1]/«ai2 + bxMs[l]t1.333)iO.5 - a)11.5 - '; LX[l):- 1.5x(a/«ai2 + bxMs[l]rl.333)tO.5)' - 1)/ «ai2 + bXMS!1]11. 333 )iO. 5 - a)o LY[1]:- 1.5x(Ms[1]t1.333/2/( a12 + bXMS[11.,.1.333)iO.5»! «a 12 + bXMs 1] .333) iO.5 - a);

t,

slgXZ:- slgXZ + LX[l]xLZ[l]; slgXY:- slgXY + LX[l]xLY[l]; slgYZ:- slgYZ + LY[l]xLZ[l]; slgXsq:= slgXsq + LX[l]xLX[l]; slgYsq:- s1gYsq + LY[l]xLY[l]; slgZsq:= slgZsq'+ LZ[1]xLZ[1]; end"

-'

dela:-

delb:-

(slgXZxslgYsq - slgYZxslgXY)/ SlgYSqXSlgXSq - slgXYXslgXY); sigYZxslgXsq - slgXZxslgXY)! slgYsqxslgXsq - slgXYXslgXY);

i

wrltetext( 30, [ [2c] 1 teratlon*coun ter*-*] ); wrlteTIO,format( [nddccl) ,p); wrl tetext( 30, [slgZsq*=* J1; wr 1 te T3 0 .. forma tTL+ndd. dddddcc1) ,s 19Zsq) ; 195

Regression programme (oont.).

wr 1 te te x t ( 3 (), [a *= *] ); ,

wrlter30,fOrmat([+ndddd.dddddc])~a);

wrl tetext (30, b*=*]); wrl teT30,format( [+ndddd. dddddcc]), b);' wrltetext(30, [delta*a*a*T); -, wrlteT3 0 ,format(T+ndddd.dddddc]),dela); wrltetext(30,[delta*b*=*T); -

wrIteT30~format(T+ndddd.dddddccl),delb);

If abs(dela/(dela + a» > 0.005 and abs(delb/(delb + b»~ 0.005 then Degln -

wrltetext(3U,[delta*a*dlvlded*by*a+delta*a~

*and*delta*b*alvlded*by*b+delta*b*[c] are*both*greater*than*1/2*percent.T2c] a*+*delta*a*=J); - , wrlteT30,format( [+ndddd.dddddc]) ,a+dela); wrltetext(3()~ b*+*delta*o*-J); ,-

wrlteT30~format(1+naddd.dddddccl)~b+delb);

a :b :a goto end

a + dela; b + delb; LOOP;

else

be~ln

wr tetext( 30, [one*or*both*of*them*wlthln*1/2*percent[ 2c] a*+*delta*a*=T); - wri teT3 0, format ( [+ndddd. dddddc]) ,a+dela); wrltetext(3 0 , b*+*delta*o*-*J); wrlteT30,format( [+ndadd.dddddc]), b+de"lb); end; \ end;

ena..

close(20) ;close(30);

196

Input data.

0.07; 0.13; 0.13; o. 20; 0.20; c. 17; 0.20; 0.27; 0.27; 0.27; 0.30; 0.40; 0.30; 0.40; o. 43; 3.24; 1.80; , .80; 2. 71; 2. 40; 1 • 17; 1 .40; 2. 0('; 1.77; 2. 0('; 2. 20; , .64; 1.33; 1•40; 1• 77 ; 2 • 07; 1 • 47; 2. 2(); 1•70; 1 • 74; 1• 60; 2. 47; 2. 78; 1•87;1 • 74; 1 .97; 1 .94; 1.40; 1• 13; 1.87; 8. 77; 7 • 03; 6. 36; 6. 66 ; 6. 76 ; 7.23; 6. 53; 6.59; 7 .33; 7.00; 7.26; 6. 16; 7 • 70; 7 • oC; 7. co; 7.20; 3.41 ; 3.88; 3.55; 1.44; 2. 17; 4. 15; 2. 81 ; 3. 11; 3.33; 5.29;4.35;3.24;3.31;3.71;3.98;4.05;6.00;5.79;4.72; 4.52; 4.67; 4. 15; 4.52; 4.40; 4. 18; 4.44; 4.27; 5. 98; 5. 07; 4.63;4.20;4.23;5. 23;S.54;S.10;5. 17;S.S4;5.57;5. 13; 4.73; 4.79; 4 .67; 0.33; o. SO; 0.97.; 0.77; 1.47; 1.23; 0.53; 1 .30; 1.03; 0.50; 0.93; 1.17; 0.77; 1. CJf; 0.77; 0.97; 1.03; 0.77; 0.67; 0.77; 0.67; 0.43; 0.36; 0.43; 0.46; 0.43; 0.40; 8.14;8.24;9. 10 ;1.23;0.73;0.87;0.60;0.SO;7.5 4;6.97; 7.47;

·10 minute average

5. 4 ; 6.6; 6.9; 6.8; 6.9; 6.8; 7.1; 6.8; 7.7; 8.4; . 8.0; 7.7; 8.0; 9.1; 8.5;39.S;35.0;32.1;34.S;29.0; 28.8;29.9;35.3;35.4~36.5:34.();30.3;30.3;29.8;35.6;

33.8;29.9;34.9;33.4;32.2;31.5;37.S;35.9;28.3;28.S; 29. 1;27.1;24.5;26.1;28.7;53.9;38.3;3 4 •6 ;39. 2;41.6; 40.1;43.2;44.4;48.8;S1.7;S4.3;41.8;45.9;5 1• 6 ;S1.3; 46.2;39.8;36.2;28.9;2S.6;3 h.9;40.5;39. 0 ;41.3;43. 2; 44.9;39.8;44.6;44.8;46.3;46.5;44.S;44.6;41.1;41.9; 40.5;38.0;44.6;42.1;42.4;40.4;39. 8 ;38.8;44.8;44.6; 40.5;37.8;3 6 • 4 ;40.S;40.5;46.1;46.9;44.5;47.7;44.3; 44.3;45.3;43.3;16.4;18.5;21.3;18.8;22.1;19. 4 ;15.9; 21.8;20.0;15. 8 ;21.3;23.9;21.8;21.6;20.4;21.0;22.0; 19.8;10.6; 9.6;1'.5;11.0;12.2;11.9;11.2;11.6;11.6; 55.3;57.7;57.1;12.6;15.1;13.6;13.2;13.2;52.6;61.3; 58.3;

..

197

1'0 minute

average ,

M

II

Regression programme output.

=

ITERATION COUNTER

=

SJGZSQ

=

A

B

+22.04616

+1.00000 +0.31000

I:

DEL.TA A DEL.TA B

=

-6.11348 -0.23276

=

CEL.TA A DIVIDED BV A+OELTA AI AND DELTA B DIVIDED BV B+OEL.TA B ARE BOTH GREATER THAN 1/2 PERCENT, A + DEL.TA A • B + DELTA B =

+0.8e652 +0.07724

=

ITERATION COUNTER SIGZSQ

+20.41553

II

=

A B

2

+0.88652 +0.07124

II

DELTA A DEL.TA B

=

=

+0.91905 +0.03495

DELTA A DIVIDED BY A+DELTA AI AND DELTA B DIVIDED BV B+DEL.TA B ARE BOTH GREATER THAN lIZ PERCENT. A + DEL.TA A • B + DELTA B • ...

,- .

+1.80557 +0.11220

\

-

ITERATION COUNTER

=

3 c-

srGZSQ

A

II

B ;:

DELTA A DELTA B

/

+17.79675

I:

+1t80557 +0.11220

= ==

+0.92587 +0.03478

DE~IA A DIVIDED BY A+OELTA A, AND DELTA B DIVIDED BV B+DELTA B ARE BOTH GREATER THAN 1/2 PERCENT'

A + DELTA A • B + DELTA B •

+2.13143 +0.146ge

198

Regression programme output (oont.).

-

ITERATION COUNTER SIGZSQ = A B

= =

4

+18.06950

+2.1314'3 +0.146ge

DELTA A = DELTA B =

+0.54111 +0.02030

DELTA A DIVIDED BY A+DELTA A. AND DELTA 8 DIVIDED 8Y 8+DELTA B ARE 80TH GREATER THAN 1/2 PERCENT. A + DEL,T A A = B + DELTA B =

+3.21315 +0.16128

ITERATION COUNTER SIGZSQ. A B

= =

=

5

+16.63421 +3.27315 +0.'1672e

DELTA A DELTA B

+0.13243 +0.00502

II: II

DELTA A DIVIDED BY A+DELTA AI AND DELTA B DIVIDED BY 8+DELTA B ARE BOTH GREATER THAN 1/2 PERCENT. A + DELTA A • B • DELTA 8 •

+3.40557 +0.17230

\

..

ITERATION COUNTER SIGZSQ

6

+18.17420

s

=

II:

A B =

+3.40557 +0.17230

DELTA A DELTA B

= =

+0.01106 +0.00046

ONE OR BOTH OF THEM WITHIN 1/2 PERCENT A + DELTA A I: B + DEL.TA B •

+3.41143 +0.17276

RAN/EL/OOIM17S/OOIM23S

199

'lei.renees

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Newcastle University, Newcastle upon Tyne, United Kingdom, NE1 7RU
Newcastle University is a modern civic university with a proud tradition, committed to world-class academic excellence -

Press Release - research.ncl.; ; Newcastle University
Ben Mesmia Hajer. Handicap International. Khlifi Adel ... Karoui Med Noureddine Tunisian Agency of Cooperation (ATCT). P