vo

An Experimental Study of 

Heavy-Mineral Segregation 

Under Alluvial-Flow Conditions

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-K
An Experimental Study of 

Heavy-Mineral Segregation 

Under Alluvial-Flow Conditions

By LAWRENCE L. BRADY and HARVEY E. JOBSON

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562-K

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1973
UNITED STATES DEPARTMENT OF THE INTERIOR 

ROGERS C. B. MORTON, Secretary

GEOLOGICAL SURVEY 

V. E. McKelvey, Director

Library of Congress catalog-card No. 73-600017

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402 - Price 85c domestic postpaid or 60c GPO Bookstore

Stock Number 2401-00294
CONTENTS

Abstract _____-__-_-_-_ 

Introduction __ ________________________________

Theoretical considerations ____--_ __ _-

Relative velocities of water-transported 

particles with differing densities ________

Shear stress as a density-segregation 

parameter ____ ___ ________ ____ __

Bed forms produced by flow in an

alluvial channel ___ _ _ ___ __ 

Relation of grain entrainment to turbulence __ 

Summary ________________ ________ _

Experimental runs and results of sediment analysis-- 

Hydraulic measurements _____________________

Sediment analysis __ _ _______ __

Sediment characteristics ________ __

Size analyses total bed material _________

Size analyses suspended sediment ____

Size analyses core samples ___________

Experimental results ____________________ 

Summary of bed form and opaque-heavymineral segregating characteristics _________

Dune bed forms (run 1) _________________

Dune bed forms (run 2) _________________

Transition bed forms (run 3) _____________

Pace 

Kl

1

2

8

9

10

10

10

12

12

12

13

13

14

14

14

15

17

Experimental results Continued

Summary of bed form and opaque-heavymineral segregating characteristics Con. 

Bed forms of moving flat-bed

conditions (run 4) _ _ . 

Relation of fall velocities of dark opaque

and light-density grains _ _ _.

Relation of grain entrainment to critical

shear stress and grain size ___ . 

Heavy-mineral transport and deposition 

in a flat-bed flow ______ __ .

Discussion of data _ _ .

Relations among sediment samples _ .

Bed forms and hydraulic variables _ _ .

Conclusions .

References ___ __ .

Appendix:

A. Symbols and nomenclature __ _ _ _. 

B. Grain-mount preparation and relationship of direct grain measurements 

to sieve-size equivalents _____________

C. Analyses of opaque-heavy-mineral 

grains and light-mineral grains 

from core samples (runs 2-4) ________

D. Sediment concentration and size .,

analyses of suspended-sediment samples

Page

KIT 

19 

22

25

25

25

27

29

29

32

33

34

38

ILLUSTRATIONS

. FIGURE 1. Graph showing resistance of a particle to motion as a function of the ratio of its size to the size of 

the bed material ___ ___ _ ______________________ _ ___ _ _ ___ ____ _ 

2. Schematic diagram of forces acting on a discrete moving particle in a fluid _ __ _ ___ _ _ _ 

3-4. Graph showing 

3. Velocity ratios for spheres of equal size but of different densities _ _ ______ _ __ _ __ _ __

4. Velocity ratios of spheres that have equal submerged weight but different densities _ ___

5. Shields diagram showing sediment entrainment as a function of the particle Reynolds number __

6. Idealized diagram of bed forms in an alluvial channel _____________________________

7. Dune profile showing dune terminology _____ _ _ _ _ _ _ __ _ _ _ _ __ _ _ _ ______ __ __ _ _ _

8. Schematic diagram of the flume used in the four experimental runs _________________ __

9. Size distribution curves for sand used in the flume _______________________ ______ 

10-12. Photographs:

10. Dune bed configuration and opaque-heavy-mineral accumulations at the bed surface following run 1 ___ __________ __ ___________________________________

11. Dune bed configuration of run 2 __ ___________________________________

12. Accumulations of dark opaque heavy minerals on the upstream sides of dunes (run 2) _

K3

4

5

6

7

8

10

11

13

15

16

16

ill
IV CONTENTS

Page

FIGURE 13. Sketch of a dune showing structures and locations of different types of opaque-heavy-mineral accumulations __________________ _ __ _ _ _ - K17

14-19. Photographs:

14. Opaque-heavy-mineral accumulations in foreset and topset beds of dunes formed in run 2 18

15. Bed configuration and opaque-heavy-mineral accumulation at the bed surface formed during

run 3 ___________________-___--___________ _ 19

16. Accumulations of opaque heavy minerals formed along the crestal region of a dune (run 3)_ 20

17. Opaque-heavy-mineral accumulations formed in topset and foreset beds during run 3 21

18. Flat-bed surface formed by run 4___ _ - _ - _ __ 22

19. Profile of flat-bed flow deposits showing opaque-heavy-mineral layers within the flat-lying

beds ____________________________________________________ 23 

20-23. Graph showing 

20. Fall-velocity relationship of light-mineral grains to opaque-heavy-mineral grains obtained

from the bed-material sample and core samples of runs 2, 3, and 4 __ _____ 25

21. Plot of median fall velocities of opaque-heavy-mineral grains and light-mineral grains __ 25

22. Critical shear relationship of light minerals to opaque heavy minerals for the bed material

and core samples _________ - ___ __ __ _____ 26

23. Relation of magnetite in transport to time in 20-cm flume and under flat-bed conditions __ 27 

24. Photograph of sections of core samples showing opaque-heavy-mineral beds _ __ ______ 34

TABLES

TABLE 1.

2.

3.

4.

5.

6.

7.

Page

Classification of flow regimes _____ K9

__ 11 

__ 15 

	24

 35

. 36

.____ 38

Hydraulic variables and parameters of runs. _ _ __ _ __ _ 

Mean dune size (with standard deviations) measured by sonic sounder _ ___ ____ __ 

Results of a resistance-to-motion experiment using a poorly sorted quartz bed material 

Size analyses of opaque heavy minerals from core samples _ .___ __ ___ 

Size analyses of light minerals associated with opaque heavy minerals in the core samples 

Size analyses and concentration of suspended-sediment samples _____________.
SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

AN EXPERIMENTAL STUDY OF HEAVY-MINERAL SEGREGATION 

UNDER ALLUVIAL-FLOW CONDITIONS

By LAWRENCE L. BRADY and HARVEY E. JOBSON

ABSTRACT

Segregation of opaque minerals (mainly ilmenite and magnetite) from the light minerals in a natural sand was observed in a large (61x2.44x1-22 meters) recirculating watersediment flume. Bed material (median size 0.286 millimeter) 

used in the study was taken from the Rio Grande near 

Bernardo, N. Mex. Opaque heavy minerals (median size 0.144 

millimeter) amounted to 0.38 percent of the bed-material 

volume. Significant hydraulic variables and the sorting and 

bedding patterns of the bed material were observed for four 

different bed configurations: a flat bed (upper flow regime), 

a transition bed, and two different dune beds (lower flow 

regime).

Accumulations of opaque heavy minerals were formed as 

three basic types:

1. Thin accumulations of small extent that were associated 

with the upstream or stoss slopes of dunes;

2. Accumulations associated with the topset deposits of large 

dunes and with dunes formed in the transition flow;

3. Accumulations associated with the flat-bed condition.

The most important factors influencing the type and 

amount of accumulation of opaque heavy minerals are bed 

configuration and grain density. The most widespread deposits were the segregations of heavy minerals associated 

with the base of the flat beds. The thickest deposits of 

opaque-heavy-mineral grains were associated with topset 

deposits of dune beds, but local conditions must be optimum 

for thick accumulations to occur. The importance of a mineral's density to segregation is shown by considering theoretically the forces necessary to move grains of two different 

densities and by analyzing the size distribution of light and 

heavy minerals in the bed-material and core samples of the 

laboratory experiments using a Shields' type criteria for 

initiation of motion.

Sediment size, sorting, and shape were determined for each 

mineral group from core samples taken from the bed. The 

sorting of the opaque heavy minerals for the flat-bed run 

was significantly different from the sorting of these minerals 

for the other runs.

Median sizes of the light minerals which were obtained 

from laminae adjacent to or within the heavy-mineral 

laminae also showed a significant variation among runs. 

Fall velocities of the grains of the two different mineral 

groups were found to have little importance as local segregating mechanisms.

INTRODUCTION

In an alluvial channel, bedding patterns produced 

in sediment are responses to the hydraulic variables 

of flow. Variations in sorting as well as the segregation of materials according to shape and density 

are important elements in the production of bedding structures and in recognition of the structures 

in sediments and sedimentary rocks.

Relatively little is understood about the local 

hydraulic conditions or the sediment responses to 

these conditions that are responsible for sorting of 

sediments. The relative densities of particles and 

the streamflow characteristics have long been assumed to be important factors in sorting, but their 

relative contributions to the sorting process have 

not been well understood.

The relationship of heavy minerals to the more 

common low-density minerals was first described 

in relation to given hydraulic conditions by Rubey 

(1933). Fall velocity was considered by Rubey to 

be the most important segregating mechanism 

accounting for the close association of small highdensity grains with low-density but larger mineral 

grains in a sediment. Other factors considered important by Rubey (1933, p. 3) were density and 

hardness of the minerals, differences in original 

sizes of the grains in the source rock, amount of 

abrasion during transport, and degree of sorting at 

the site of deposition.

Rittenhouse (1943) used the concept of hydraulic 

equivalence to explain mineral relations in sands 

of the Rio Grande in New Mexico. He described 

hydraulic equivalence (p. 1749) as "whatever the 

hydraulic conditions may be that permit the deposition of a grain of particular physical properties, 

these conditions will also permit deposition of other 

grains of equivalent value." The distribution of 

heavy minerals in the streambed was considered by

Kl
K2 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Rittenhouse (1943, p. 1742-1743) to be caused by 

varying hydraulic conditions at the time and place 

of deposition, equivalent hydraulic size of each of 

the heavy minerals, availability of the minerals, and 

unknown factors.

Studies on sorting of minerals with different 

densities were conducted simultaneously with studies 

of turbulence, bed resistance, and sediment transport at the Engineering Research Center at Colorado State University. Experiments were conducted 

in a large recirculating sediment flume using natural 

sand from the Rio Grande south of Albuquerque, 

N. Mex. This research was undertaken in an effort 

to find what sediment properties and hydraulic variables are responsible for the rapid segregation of 

certain heavy minerals during movement and deposition of a sediment load.

Four flow conditions were studied at near equilibrium conditions. Observations were made of the 

significant hydraulic variables, sediment transport 

rate, sediment segregation, and the physical characteristics of the sediments entrained by each flow 

to obtain information necessary to explain the sorting process.

This study contributes to the understanding of 

local segregation processes that affect grains of 

different densities. Techniques used and results obtained can be applied to studies of bedding in modern sediments and to the interpretation of bedding 

in ancient deposits. Further, observations made in 

these flume studies of modes of segregation, transport, and accumulation of heavy minerals should 

help in future research on and exploration for economically valuable placer deposits.

This program was completed under a cooperative 

arrangement between the U.S. Geological Survey, 

University of Kansas, and Colorado State University. The data contained herein are essentially 

the same as those contained in a dissertation by 

Brady (1971). The data were collected under the 

general supervision of the second author.

Special thanks are due the dissertation committee 

members, W. M. Merrill, E. C. Pogge, M. E. Bickford, A. J. Powell, and J. D. Winslow, of the University of Kansas, for advice and counsel during 

the research.

THEORETICAL CONSIDERATIONS

RELATIVE VELOCITIES OF WATER-TRANSPORTED 

PARTICLES WITH DIFFERING DENSITIES

An analysis of the forces acting on discrete particles in a few idealized situations can provide the

basis for estimates of their effects in the natural 

environment. Actual values for the velocities and 

forces involved in the grain movement would be 

very difficult to determine experimentally. By making certain assumptions to allow for direct comparisons between grains with different densities, 

however, approximations of the relative velocities 

of grains can be developed.

For immersed particles moving along a bed, the 

five principal forces important in determining the 

movement of the particle are the (1) gravity forces 

related to the immersed weight of the particle, the 

(2) drag and (3) lift forces that result from pressure and frictional effects of the fluid on the particle, 

(4) f rictional forces that result from contact between the grain and bed, and (5) forces resulting 

from interaction of moving grains.

If one assumes an individual sphere moves without interference from adjacent moving grains, four 

principal forces can be defined. The gravity force, 

F0, is the resultant force acting on the particle that 

is dependent on the immersed weight of the particle 

and the gravitational constant, g. The gravity force 

is defined as

O = (ps p) 9 

6

(1)

where d = diameter of the particle, ps = mass 

density of the particle, and p = mass density of the 

fluid. (All symbols used in the text are listed in 

appendix A.)

The hydrodynamic forces acting on a body are 

discussed in any standard fluid mechanics text, as 

for example that of Daily and Harleman (1966, p. 

376-394). The hydrodynamic drag force, FD, that 

acts on a particle is dependent on the frictional 

drag resulting from surface shear between the grain 

and the fluid and on the form resistance that is 

related to shape of the grain and results from pressure drag on the particle. It is customary to define 

a total drag coefficient, CD, to include both frictional 

and form drag. Some researchers have directly 

measured the drag and lift forces acting on regular 

shaped objects such as spheres (Watters and Rao, 

1971; Coleman, 1967; and Ippen and Verma, 1955) 

and hemispheres (El-Sammi, 1949) in laboratory 

flumes.

The drag force is defined as

FD -CD A, P = CD p(Vf Vs) 2 (2) 

2 8

where As = projected area of the sphere, V0 =
HEAVY-MINERAL SEGREGATION K3

relative velocity of the flow past the sphere, Vf = 

velocity of the flow at some representative distance 

above the bed, and Vs = velocity of translation of 

the particle.

Lift forces on the body are due to a difference in 

pressure between the upper and lower sides of the 

particle. The increased velocity resulting from fluid 

acceleration around the upper side of a particle 

causes a local reduction in pressure, while the pressure on the lower side of the grain surface at or 

near the bed approaches the static pressure of the 

fluid. The lift force, FL, is defined as

TV

 

2 8

(3)

where CL = coefficient of lift.

The frictional force acting on a moving particle 

is difficult to determine. The frictional force is discussed in most basic physics or mechanics texts, 

such as that of Sears and Zemansky (1963, p. 35). 

Ippen and Verma (1955, p. 921-937) have also discussed the frictional force. Bagnold (1966, p. 5) 

states that the friction coefficient for grains is of 

the same order as the static coefficient, not only 

when the grains are at rest but also when they are 

in motion. For the purposes of this study, the frictional force was assumed to be equal to the coefficient of kinetic friction, CF, times the normal force 

between the particle and the bed, FN. The frictional 

force, Fp , is defined as

(F0 cos 0 (4)

where 6 = angle between the bed surface and horizontal. A positive value of 6 indicates that the bed 

surface is rising in a downstream direction, as the 

surface does on the stoss slope of a ripple or dune.

Although the coefficient of kinetic friction for 

sediment particles is very difficult to determine, one 

would suspect that it is closely related to the coefficient of static resistance, CR, of a particular particle resting on a given bed configuration. For a 

rigid spherical particle of diameter dm resting on 

a bed of rigid spherical particles of diameter dB 

arranged in a prescribed manner, it is a simple 

matter to determine the coefficient of static resistance, CR.

For example, if the bed spheres are arranged in 

a close packed rectangular pattern and are resting 

on a horizontal plane, it can be easily shown that 

the centrally applied horizontal force required to 

move a sphere of diameter d m in the direction of

least resistance is CR FN, where CR is given by the 

relation

CR = (5)

and k is defined as the ratio of d to dB. Likewise, 

if the bed spheres are arranged in a rhombic pattern, the value of CR corresponding to movement in 

the direction of least resistance is given by

(6)

 (1/3)

It is seen that the resistance of a particle to motion 

is a function of both the size of the moving particle 

and the size of the bed particles.

In order to determine the effect of particle size 

on the resistance to motion, the resistance ratio is 

defined as the ratio of CR at any value of k to the 

value of CR with fc=l. The relation of the resistance 

ratio to k is shown in figure 1. The curves approach 

infinity at a value of k for which a small moving 

particle could fall between the interstices of the 

larger bed particles. Figure 1 illustrates that the 

resistance to motion of a small particle resting on

10.0

10.0

FIGURE 1. Resistance of a particle to motion as a function 

of the ratio of its size to the size of the bed material.
K4 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

a bed of large particles can be quite large. It is not 

presumed that the values given in figure 1 can be 

applied directly to field situations; however it is 

suggested that the trend is qualitatively correct.

The four forces as they are applied to a spherical 

particle are shown schematically in figure 2. The 

gravitational force can either oppose or supplement 

the drag force depending on the sine of 6.

By use of the four fundamental equations 1-4, a 

general equation of motion for particles can be 

derived. Direct comparisons between grains of 

different densities can then be made by establishing 

ratios of the translating motion of the grain of 

greater density to that of the grain of lesser density 

and reducing the equations to a form that expresses 

the relative difference in the velocities of the two 

grain types for the same flow conditions.

For a particle moving at a uniform velocity, the 

general translation-motion equation for the particle 

can be expressed as

FF = FD Fa sin 6 (7)

By dividing the frictional force on one particle 

by the frictional force on a particle of different 

density, the following ratio can be established using 

equations 4 and 7:

FF FD FG Sin 6 CF (FG COS 6

i Fo1 sin 6 t (Fo1 cos 6 -

-. (8)

The subscript 1 is used to denote the forces and

coefficients affecting the sphere of the lower density.

By substituting equations 1, 2, and 3 into equaFIGURE 2. Schematic diagram of forces acting on a discrete i 

moving particle in a fluid.

tion 8, and simplifying terms, the following equation can be developed :

3pCz> (Vf Vs) p sin 6

' 1 p) sin 6 

CF [4dg(Ps p) cos 0 3CLp(Vf

si p) cos

(9)

By considering 6 = 0, equation 9 can be simplified to

 VO 2 ]

(10)

Equation 10 can be used to determine the relative 

velocities of rolling spheres with different densities.

Assuming the two spheres have equal diameters 

and therefore equal drag coefficients and equal lift 

coefficients and assuming equal coefficients of friction, equation 10 reduces to

s P)

(p'l p) (11)

By applying densities of materials of interest in this 

study: 5.0 g/cm3 (gram per cubic centimeter) for p.,, 

2.65 g/cm3 for p* lf and 1.0 g/cm3 for p, equation 11 

can be expressed in dimensionless form as

Vs

= 1.56 0.56 (12)

A graph of equation 12 is shown in figure 3.

The relative velocities of spheres of the two different densities are clearly shown in figure 3. The 

velocity of the denser sphere, Vs, is always less than 

that of the lighter sphere, V^, unless both are equal 

to the fluid velocity, Vf, a condition where there is 

no frictional force. This condition could occur when 

both particles are suspended. As the velocity of the 

lighter particle becomes progressively smaller, the 

relation VJV^ also becomes progressively smaller 

until a point is reached where movement of the 

denser sphere ceases. At this point the point of
HEAVY-MINERAL SEGREGATION K5

V = Velocity of sphere with pg = 5.0 g/cm3

V = Velocity of sphere with p = 2.65 g/cm 

s i i

Vf = Velocity of fluid

FIGURE 3. Velocity ratios for spheres of equal size but of 

different densities.

incipient motion of the denser particle the velocity 

of the low-density particle is 0.36 times the fluid 

velocity.

A second situation for which the relative velocity 

can be approximated is that of two spherical particles that have equal submerged weight but different 

densities. Substituting values for the densities of 

the spherical particles of 5.0 g/cm3 and 2.65 g/cm3 , 

the ratio of diameters required to obtain equal submerged weights is 1:1.34. However, in order to 

derive a general velocity formula such as equation 

12 the following additional conditions must be assumed :

1. For the drag force equation, a drag coefficient 

ratio (CD/CDI) of 1.2:1 is stipulated. Drag 

coefficients of the two spheres will differ because the spheres are of different size. The 

value of 1.2:1 was approximated from the Cn 

versus Re diagram in the U.S. Inter-Agency 

Committee on Water Resources Report 12 

(1957, p. 20) by using grain sizes similar to 

the experimental runs (0.12 mm (millimeter) 

for the heavy grain and 0.163 mm for the light 

grains).

2. The lift forces for this situation are ignored.

3. Two relationships for friction will be considered. 

First, the coefficient of static friction is considered to be the same for both spherical particles (C*! = CF). Second, the ratio of the 

two coefficients of friction is assumed to be 

equal to the resistance ratio given in figure 1. 

It will be assumed that the bed is composed 

of particles of a size equal to that of the larger 

particles and that these particles are arranged in a rhombic pattern. From figure 1 

the value of C^/C^ is found to be 1.25.

4. An assumption is made for this analysis that 

the increase in fluid velocity with distance 

from the bed is linear, at least up to a point 

where the characteristic velocity is determined, as it is in the sublayer of laminar flow. 

The fluid velocity is assumed to be zero at the 

bed surface. The fluid velocity then at the 

point of drag force application of the small 

sphere would be 0.746 of the value of the fluid 

velocity at the corresponding point on the 

larger sphere. 

Accepting these assumptions, the basic equation

10 can be reduced to

v. / y.x y

 = 1.23 0.65 I

V-! \ Vr /

(13)

for equal friction coefficients and

 = 1.54 1.06 ( ) 

V., \ V, I

(14)

for a resistance ratio determined from figure 1. 

Equations 13 and 14 are plotted in figure 4.

For the development of equations 10-14, the bed 

surface was considered horizontal; but the relations shown in figures 3 and 4 should be qualitatively 

similar for any given bed-form slope. The basic 

difference in forces affecting the grains when a 

slope factor is introduced is related to the effect of 

grain weight on the grain movement. A gravity 

force component parallel to the bed will act against 

the drag force if the local bed surface is inclined 

in a direction opposite to the energy slope or the 

stream gradient. Such restraining pull is present in 

grain movement up the stoss side of a dune or ripple (fig. 2). When the local bed surface is inclined 

in the direction of the energy slope or stream gradient, as it is on a flat bed or the lee slope of a dune, 

the particle weight then becomes additive to the
K6 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

1.0

0.5

V = Velocity of sphere with p - 5.0 g/cm 3 

V = Velocity of sphere with p f = 2.65 g/cm 3 

V,= Velocity of fluid

0.65-

Equal friction 

coefficients

Friction 

coefficient 

ratio from

figure 1

0.5 

V.

1.0

FIGURE 4. Velocity ratios of spheres that have equal submerged weight but different densities.

drag force in influencing grain movement downstream.

In addition to the effect of gravity, frictional 

forces resulting from differences between size of 

moving particle and size of particles at the bed surface will have marked effect on the grain velocity. 

A coarser sand bed will provide a higher coefficient 

of friction than a finer sand bed for a given size of 

grain in movement.

The above analysis of grain movement assumes 

that the grains of interest are not so large or heavy 

that they tend to displace the underlying grains and 

sink into the bed during the flow. For grains that 

do, and they occasionally occur in the field, different 

methods of analysis would be required.

Grains moving along the surface of a sediment 

bed are continually being deposited and reentrained 

at a rate dependent on the local conditions of the 

flow. Light and heavy grains are most likely to be 

segregated when their velocities differ greatly. As 

grains of different densities slow to velocities that 

are much less than the fluid velocity, high-density 

grains will be deposited first. Before high-density 

grains are yet in motion, low-density grains will be 

entrained and moved much more readily. This type 

of selective deposition provides for efficient segregation by causing the accumulation of high-density 

grains in areas where the flow is not readily capable of transporting all the material supplied to the

area. In other words, if a mixture of particles is 

supplied to an area where the flow is incapable 

of transporting the total load, the heavy particles 

will be selectively deposited first.

These mathematical relationships establish in a 

semiquantitative but simplified manner what has 

long been observed, that small dense grains are more 

resistant to surface movement than are larger lowdensity grains. Graphs similar to figures 3 and 4 

can be constructed for natural materials of any 

density. Then, the graphs can be used to help explain why some of the bedding features observed in 

sediments in the natural alluvial environment are 

formed of materials of a particular density.

SHEAR STRESS AS A DENSITY-SEGREGATION 

PARAMETER

Consideration of critical shear stress, TC , which 

is the stress exerted by the flow on the bed that is 

just capable of initiating grain movement, adds insight into the segregation of grains of varying densities. Shields (1936) plotted experimental results of 

the beginning of particle motion based on a dimensionless shear stress, T , and a particle Reynolds

number, R, where

(15a)

« y) ds

and

Uds

R = (15b)

with yg equal to the specific weight of the sediment 

grains, y the specific weight of the fluid, ds the 

grain diameter, E7» is the shear velocity or JTO /P 

with p the fluid density, v is the kinematic viscosity 

of the fluid, and TO is the average shear stress at 

the bed.

Additional data and refinement of this plot by 

later workers has resulted in the generally accepted 

Shields diagram shown in figure 5 (A.S.C.E. Task 

Committee on Preparation of Sedimentation Manual, 1966, p. 297). From Shields curve (fig. 5), one 

can develop the relation of critical shear to grain 

size for grains of different densities. Grigg and
HEAVY-MINERAL SEGREGATION K7

^

lw

ii 10

K* 

/)

n

11

r

/J 0.5

r

<

11

0

n 

n

11j 

2 

D 

/> 

2 

u

I"

0.05

0.02

0

1 1 1 1 II 1 1 1 1 1 i 1 1 1 1 1 1

7, ing/cm3 

O Amber .. | ............. 1 .06

f-(Shields)

- X Sand (U.S. WES). ......... .2.65

\ 

\

i \

*X* ,, J£~~~^~^iT~~^

- ^^ & * _^£~^^~~'^*> > ^^p^ijc -1-2 T"""""""®

II II II

.2 0.5 1.0 5 10 50 100

Mill

_

_

 D I

I I

500 1000

BOUNDARY REYNOLDS NUMBER, R^= ~^-

PIGURE 5. Shields diagram showing sediment entrainment as a function of the particle Reynolds number (adapted from 

A.S.C.E. Task Committee on preparation of Sedimentation Manual, 1966, p. 297).

Rathbun (1969) have developed such a series of 

curves that show on a theoretical basis that grains 

of different density but equal fall velocity require 

different shear stress for initiation of movement. 

For a grain diameter below 0.1 mm, Grigg and 

Rathbun (1969, p. 79) show that critical shear is 

a function only of grain density, but for a grain 

diameter above 0.1 mm, they show that the critical 

shear becomes a function of size as well.

The experimental conditions under which the 

Shields diagram was developed were quite different 

from the natural conditions that exist in an alluvial channel. Data used to develop the Shields cufve 

were obtained from artificially flattened surfaces 

of sand beds that consisted of uniformly sized 

grains, and they were collected under fully developed turbulent flows in which shear at the bed 

was just large enough to initiate movement of a 

few grains. In contrast, large amounts of sediment 

are in transport at relatively high velocities on

streambeds when segregation occurs, and the size 

distribution of the bed material is seldom uniform.

Even though Shields' (1936) work was developed 

to explain very small amounts of sediment motion, it gives insight into relations among moving 

grains. During a given flow, grains are continually 

being deposited and then reentrained into the flow; 

that is, there are always some grains at the interface that are continually subject to conditions near 

incipient motion. One can see, at least qualitatively, 

from Shields' work that the denser grains will 

require a much larger shear stress for movement 

than lighter grains of the same size.

A part of the threshold of motion problem is to 

determine how much sediment is in transport along 

the bed surface. Best known among the bed-load 

equations is the Einstein bed-load function (Einstein, 1950). Einstein's bed-load equations express 

a relation between the intensity of shear on a 

tide, $, and intensity of transport, *, where
K8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

.l'|Y_JLV_

ys [\ ys 7

_

/ \ gds

(16a)

and

1 V / J

y* y\/ &s

y )\R'S

(16b)

where qB is the rate of transport of the bed load, in 

weight of total bed load per unit time and width, 

g is the gravitational constant, ds is the grain diameter, S is the energy slope, and E' is the hydraulic 

radius with respect to the particles. (Rr is based 

on the resistance to flow due to particle resistance 

as opposed to that due to the bed or streambank 

configuration.) The shear intensity parameter, ^, 

of Einstein is essentially the reciprocal of Shields'

dimensionless shear stress, T , and is important in

determining the total transport rate of the bed load, 

qB. The fact that the transport rate is a function 

of $ lends credence to the importance of Shields' 

parameter in situations other than the initiation of 

motion of uniformly sized grains on flattened beds.

BED FORMS PRODUCED BY FLOW IN AN 

ALLUVIAL CHANNEL

Shortly following initiation of movement of the 

bed material, bed forms start to develop. These 

initial forms are described by Kennedy (1963, p. 

522) as "the result of scour and deposition due to 

the perturbation velocities induced by any protuberance on the bed." Flows in alluvial channels are 

classified into two flow regimes, upper and lower,

/Water surface Water surface.

E Plane bed

A Typical ripple pattern

F Antidune standing waves

6 Dunes and superposed ripples

,Boil

C Dunes

G Antidune breaking wave

0 Washed-out dunes or transition ' H Chute and pool

FIGURE 6. Idealized diagram of bed forms in an alluvial channel (from Simons and Richardson, 1966, p. J5),
HEAVY-MINERAL SEGREGATION 

TABLE 1. Classification of fltiw regimes

[Adapted from Simons, Richardson, and Nordin (1965a, p. 36). PPm, parts per million]

K9

Flow regime

Lower regime _

Upper regime _

Bed form

Dunes _ _ 

Washed-out dunes _

Plane beds _ _

Antidunes _ _ _ 

Chutes and pools ,-

Bed material 

concentrations 

(ppm)

10-200

100-1,200

200-2,000

1,000-3,000

2,000-6,000

^2,000

^2,000

Mode of sediment transport

_ _do __ ___

._ do ______

Continuous _ _ _

- do ___ __

_ do ______

Type of

_ do _ ___ .

-do ____ .

Grain roughness

_do ______ .

__ do ______ .

roughness

predominates 

predominates ___

Phase relation 

between bed and 

water surface

Out of phase.

Do.

Do.

In phase.

Do.

Do.

with a transition zone between. These regimes are 

based on the bed configuration, mode of sediment 

transport, process of energy dissipation, and phase 

relation between the bed and water surfaces (Simons and Richardson, 1963). Relations of bed forms 

within these two regimes are shown in table 1, and 

the bed forms are shown in figure 6.

The A.S.C.E. Task Force on Bed Forms in Alluvial Channels (1966, p. 53) defines ripples as bed 

forms with wave lengths less than approximately 

1 foot and heights less than 0.1 foot. Dunes are bed 

forms larger than ripples and out of phase with 

any water-surface gravity waves that accompany 

them. A flat bed is a surface devoid of form. Antidunes and chutes-and-pools develop within the upper 

portion of the upper flow regime but were not studied in this series of experiments. These features are 

described by Simons, Richardson, and Nordin 

(1965a, p. 40-42).

Bed forms within the lower flow regime include 

ripples, ripples superimposed on dunes, and dunes. 

In the lower regime the water-surface waves and 

undulations are out of phase with the bed undulations. In general, resistance to flow is high, and 

sediment transport is small. In natural streams, 

dunes, or dunes with superimposed ripples are the 

most common bed forms (Simons and Richardson, 

1966, p. Jll).

Within the transition flow the bed configuration 

is very erratic and may include forms common to 

both the upper and lower regimes. Dunes present 

in the transition zone will often decrease in amplitude and increase in length before the bed becomes 

flat (washed-out dunes) (Simons and Richardson, 

1966, p. Jll).

In the upper flow regime the usual bed forms are 

flat beds (plane beds) or antidunes. Resistance to 

flow is small, and sediment transport is large. Watersurface waves in this regime are in phase with the 

bed surface except during the breaking of an antidune (Simons and Richardson, 1966, p. Jll).

Bed forms produced by the four different experimental runs in this study were dunes in the lower 

flow regime, long profile dunes in the transition 

zone, and a flat bed in the upper flow regime. Terminology used in this report for the different surface features of dunes and the bedding structures 

associated with the dunes is shown in figure 7.

RELATION OF GEAIN ENTEAINMENT TO 

TURBULENCE

The effect of turbulence in a given flow is an 

important flow characteristic in grain entrainment. 

Local boundary shear stress must be determined 

from the velocity gradient at the bed and cannot be 

determined from the slope-depth relationship alone. 

The apparent shear stress, r, in turbulent flow is 

expressed by Streeter (1966, p. 226) as

dU

 

dY

(17)

in which ^ is the dynamic viscosity, ?/ is the eddy 

viscosity that depends on the state of the turbulent 

motion, and dU/dY is the velocity gradient normal 

to the bed. Intensity of turbulence is important, because high turbulence is indicative of large velocity 

fluctuations and usually indicates large velocity 

gradients.

McQuivey and Keefer (1969) studied the segregation of magnetite grains from quartz grains on 

the stoss side of ripples in a small flume and found 

much larger turbulent intensities over the trough 

area than over the crestal region of a ripple. Turbulent intensity also decreased with distance from 

the bed. Measurements were made with a hot-film 

anemometer. Differences in turbulent shear stress 

from ripple trough to crest and differences in shear 

stress required for movement of grains of different 

densities were considered by McQuivey and Keefer
K10 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Brink point 

Brinkline in plan view

FLOW

Trough point 

Troughline in plan view

Slipface'

FIGURE 7. Dune profile showing dune terminology used in report (X 4 vertical exaggeration). Location terminology

adapted from Alien (1968, p. 62).

as important factors in heavy-mineral segregation. 

Similar results of turbulence measurements are 

described by Raudkivi (1967, p. 206-207) for experiments conducted by Sheen (1964). Raudkivi states 

that turbulent intensities are greatest just downstream from the point of separation (brinkline) on 

a ripple, that turbulence is intense in the trough 

area, and that its intensity rapidly decreases downstream. Velocity and turbulence profiles were determined by McQuivey at selected locations for each 

of the runs of this study. These data are contained 

in a dissertation by Brady (1971).

SUMMARY

Theoretical conisderations of transport of grains 

with different densities lead to the conclusions that 

small dense grains are more resistant to tractive 

movement than larger low-density grains and that 

boundary shear is an important parameter in determining the rate of sediment transport.

Different bed forms are produced under different 

flow conditions with such common bed forms as 

ripples and dunes formed in the lower flow regime, 

flat beds formed in an upper flow regime, and 

washed-out dunes formed in the transition phase.

The turbulent intensity of the flow is large near 

the bed and decreases with distance from the bed. 

Much larger turbulent intensities occur in the trough 

regions of dune beds than on the crestal areas, and 

the intensity decreases rapidly downstream from 

the trough area toward the brinkline of a dune.

Intensity of turbulence is important because high 

turbulent intensities are indicative of large velocity 

fluctuations and usually indicate large velocity gradients. The amount of local boundary shear stress is 

dependent on the local velocity gradient.

EXPERIMENTAL RUNS AND RESULTS OF 

SEDIMENT ANALYSIS

A large recirculating.water-sediment flume of rectangular cross section and dimensions of 61 meters 

in length, 2.44 meters in width, and 1.22 meters in 

depth (fig. 8) was used for the series of four experiments. The large size of the flume permits the establishment of flow conditions that approximate those 

in a natural channel and eliminates many of the 

boundary effects that are associated with smaller 

flumes. The slope of the flume can be changed by 

use of adjustable screwjacks, and water-sediment 

discharge can be increased to a maximum of approximately 2.5 cubic meters per second. The interior of the flume is surfaced with aluminum having 

an epoxy coating. A transparent plexiglass section 

21.95 meters long is located midway along the left 

wall of the flume to allow observations to be made 

of sediment movement.

HYDRAULIC MEASUREMENTS

Near equilibrium conditions were established for 

each of the flows before sediment and hydraulic
HEAVY-MINERAL SEGREGATION Kll

data were taken. Equilibrium flow is defined as flow 

that has established a bed configuration and slope 

consistent with the fluid, flow, and bed-material 

characteristics over the working reach of the bed 

(Simons and Richardson, 1966, p. 3). After equilibrium flow was established for a given experiment, 

measurements were made of sediment discharge, 

water-sediment discharge, slope of the water surface and energy grade line, depth, and water temperature. Additional hydraulic parameters were calculated from these basic data. Mean values of significant hydraulic variables are shown in table 2.

Water-surface elevations were measured every 

1.52 m (meters) along the centerline of the flume 

for several profiles. For each profile a line was fitted 

to the water-surface-elevation measurements and 

their corresponding flume stations by the method 

of least squares and its slope determined. The mean 

value of the calculated slopes was taken to be the 

water-surface slope for the run. By adding the 

local velocity head, Q2 /2g(WD) 2 , where Q is discharge, W is channel width, D is water depth, and 

g is the gravitational constant, to the water-surface 

elevation at a given measurement point, the elevation of the energy grade line was obtained. The slope

TABLE 2. Hydraulic variables and parameters of runs

Run

1 ___

2 ___

3 ___

4 __

Bed form

Dunes _ ___ _

Flat bed -

Energy 

slope 

(X 10-3 )

1.02

1.06

1.22

1.79

Mean 

depth 

(cm)

32.9

58.5

33.7

52.8

Water 

discharge 

(cu m 

per sec-)

0.48

1.38

.73

2.08

Run Bed form

Shear

Tempera- Mean stress 

ture velocity (dynes

1 _

2

3 __

4

Transition __ 

Flat bed _ 

CO

20.8

20.9

20.7 

21.0

(cm pel 

sec)

60

97

89 

161

per 

cm 2 )

33

61

40 

93

Froude

No.

0.34

.40

.49 

.71

of the energy line was determined in much the same 

way as the slope of the water surface.

Profiles of the bed and water surfaces along the 

flume centerline were recorded on chart paper by 

use of a sonic sounder; and from these sounder profiles, the depth of flow was determined. The mean 

depth of flow (table 2) for the run was determined 

by averaging the depth values obtained every 1.52 

m along each profile.

Adjustable tailgate.

Tail 

box

"

]__

|| || y0.457mlDpipe II ' JH

I 1 1 I . 1.L-. t '

\ ^\ /j 0.660m ID pipe

| ^-^ Adjustable screwjacks "" \ \ I 0.838m ID pipe K i J //

Head box

V-i

Side contracted orifices

LONGITUDINAL SECTION

Note: Not to scale

L j

/Motor ', 

"i 1 ^l '

FT1.22r

I

/Adjus

#^7/y

^^^

CROSS SECTION

FIGURE 8. Schematic diagram of the flume used in the four experimental runs.
K12 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Water discharge was determined by use of waterair manometers that were connected to calibrated 

orifice meters located in the three return-flow pipes. 

Mean discharge for each run was determined from 

an average of four to 20 individual readings. Water 

temperature was held as constant as possible by use 

of steam and cold water. The temperature for each 

run had a fluctuation of less than ± 1°C (Celsius).

Mean velocity (u) was calculated by use of the 

continuity equation

Q Q

DXW

(18)

Any error in the mean velocity reported would be 

primarily due to an error in mean depth readings.

The shear stress at the bed, TO , and Froude number, F, are both calculated from the above measured 

variables. The shear stress is defined for a large 

area as

TO - yDS (19)

where y is specific weight of water and S is the 

energy slope. The Froude number value is a measure of the effect of gravity on the flow pattern and 

is defined as

u

F = (20)

For a Froude number less than one, a flow is defined as tranquil, because the average velocity of the 

flow is less than the velocity of propagation of small 

surface waves on the fluid. For a Froude number 

greater than one, the flow is defined as rapid, for 

the fluid velocity exceeds the velocity of movement 

of the small surface waves.

SEDIMENT ANALYSIS 

SEDIMENT CHARACTERISTICS

Sand used in the experiments was obtained from 

a conveyance channel of the Rio Grande near Bernardo, N. Mex. An arkosic sand, it contains approximately 60 percent quartz, 36 percent feldspars, 3 

percent rock fragments, and 1 percent accessory 

minerals. Heavy minerals (specific gravity >2.95)

constitute 1.13 percent of the weight and 0.72 percent of the volume of the total bed-material sample. 

Dark opaque grains, mainly ilmenite and magnetite, 

amount to 0.38 percent of the bed-material sample 

by volume. Other heavy minerals included amphiboles, pyroxenes, garnet, zircon, tourmaline, limonite, and hematite.

Within this report, sediments referred to as 

opaque heavy minerals consist of ilmenite and 

magnetite, and those referred to as light minerals 

consist of the remainder of the mineral grains. These 

two groupings provided for maximum efficiency in 

recognition and description of the segregation characteristics and conditions.

SIZE ANALYSES TOTAL BED MATERIAL

Samples for the bed-material analyses (fig. 9) 

were obtained from a composite sample of 10 vertical cores of the bed. Samples were taken at random locations in the flume after the water had been 

drained. Median size, as determined by fall diameter using visual accumulation tube (U.S. InterAgency Committee on Water Resources, 1958), was 

0.286 mm with a geometric standard deviation, 

a, (A.S.C.E. Task Committee, 1962, p, 98) of 1.59, 

where

(21)

A geometric standard deviation, hereafter referred 

to as sorting, with a value of 1.0 refers to a perfectly size-sorted sand, while a value of 3.5 or larger 

refers to a poorly size sorted sand. Sieve analysis 

of the bed material showed a median size of 0.285 

mm and a sorting, a, of 1.58, while direct measurement of grains with conversion to the weighted sieve 

size (see appendix B for a discussion of techniques) 

showed a median size of 0.287 and a sorting of 1.56.

Weighted median size of the opaque heavy minerals as determined by microscope measurement in 

the bed material was 0.144 mm with a sorting of 

1.49 (appendix C, table 5).

The total sediment discharge was determined 

from a width-depth integrated sample of the watersediment mixture collected at the lower end of the 

flume. Size and gradation of the collected sediment 

was determined by use of the visual accumulation 

tube after each sample was dried and split to a 

workable size.
HEAVY-MINERAL SEGREGATION K13

99.9

LU 99 

N

95

50

25

,.

IT 1 I

Weighted direct / xx / 

measurement ^^ / x ,'

V ' //Sieve analysis

accumulation 

tube analysis

I I I I I I

0.1 0.5 1.0 

GRAIN SIZE, IN MILLIMETERS

FIGURE 9. Size-distribution curves for sand used in the 

flume. Curves plotted from analyses by visual-accumulation (VA) tube, sieves, and weighted direct measurement 

are shown.

SIZE ANALYSES SUSPENDED SEDIMENT

Suspended-load samples were collected by a siphon 

with an inside diameter of 0.95 cm (centimeter). 

Inlet velocity at the siphon nozzle was adjusted to 

equal the local fluid velocity by changing the total 

head on the siphon. Local velocities were determined 

by a modified Ott velocity meter. For dune runs 1 

and 2, sediment concentration (in milligram per 

liter) profiles were determined at the trough, brink 

point, and high on the dune stoss side. Two sediment concentration profiles were measured for the 

transition run one in the plane-bed reach and one 

high on the stoss side of one dune. One concentration 

profile was taken during the flat-bed run. Appendix D contains the concentration and size 

analyses for all suspended sediments analyzed.

Opaque-heavy-mineral grains were present in the 

suspended-sediment samples from each vertical profile in each of the four runs. Only run 2 had a 

volume percentage of dark opaque grains approaching that of the bed material. Each of the suspendedsediment samples from the runs show the opaque

heavy minerals to be distinctly smaller than those 

of the bed-material samples.

Median size of the suspended opaque-heavymineral grains in each run falls below the 20th 

percentile size determined for the corresponding 

bed-material sample of opaque heavy minerals.

A more complete analysis of the suspendedsediment samples has been given by Brady (1971).

SIZE ANALYSES CORE SAMPLES

Opaque heavy minerals and light minerals obtained from cores were studied to determine whether 

differences in size and sorting existed among sediments in the different runs. Studies of the opaqueheavy-mineral grains were concentrated on the darkmineral laminations of runs 2-4. Only minor accumulations of opaque heavy minerals were present in 

run 1, and those were insignificant in thickness and 

areal distribution compared with heavy-mineral 

accumulations of runs 2-4.

In addition to vertical cores mentioned previously, 

horizontal core samples were taken from at least 

two networks across and along the bed following 

each run. For each network, samples were obtained 

from the flume center line and from 0.61 meter from 

each wall at 1.22 meter intervals along the flume. 

Total length of each sample network was selected 

to include the entire length of at least one bed form 

(average length of the networks was 6.1 meters). 

Small pits were dug to obtain the samples. Along the 

wall of each pit a can 6.5 cm in diameter and 12.7 

cm in length was inserted horizontally to obtain 

the horizontal cores. Similar core samples were obtained from large areas of heavy-mineral segregation that were missed in the network samples.

Inasmuch as heavy-mineral accumulations developed only near the upper surfaces of the bed, it 

was necessary that the surface sediments be included in the sampling. Therefore, most of these 

samples were taken in such a way that a small space 

remained above the sediment surface in the can. 

Plaster of Paris was poured into this open area, and 

moisture was allowed to evaporate. A chemical soil 

grout (AM-9, American Cyanamid Co.) was poured 

into the sample and allowed to harden. Adhesive 

strength of the grout was controlled to permit easy 

removal of sand grains from selected areas. The 

grouted samples were sawed to remove disturbed 

portions of the core, and the sedimentary structures 

and segregation of minerals were studied in the 

position that they were deposited.
K14 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Selection of cores for analysis was based on the 

presence of and the location in them of segregated 

beds of opaque heavy minerals. The method of 

preparation and a description of the mounting of 

grains from a lamina within a core sample is described in appendix B. Complete analyses of size, 

shape, and sorting are shown in appendix C, table 5.

In run 2, opaque-heavy-mineral samples were obtained from topset and foreset beds and from the 

brinklines of dunes. Samples from run 3 were obtained from topset and foreset beds, and one sample 

was taken from the flat-bed region. Samples from 

run 4 were obtained from dark-opaque laminae located at the base of and within the flatbed region. 

Grain size and sorting for samples shown in table 5 

(appendix C) were obtained from direct measurement of 200 individual grains per sample mount.

Size and sorting analyses were determined from 

grain mounts of light minerals obtained either from 

light-mineral laminae adjacent to or from light 

minerals present within opaque-heavy-mineral 

laminae.

Analysis of variance tests were conducted for the 

median size, sorting, and shape factor of opaqueheavy-mineral grains obtained from core samples 

from runs 2, 3, and 4. These statistical tests are 

used to determine whether two or more sample 

means could have been obtained from populations 

with the same parametric mean with respect to a 

given variable, or whether the sample means were 

drawn from different populations (Sokal and Rohlf, 

1969, p. 175). In this study the analysis of variance 

tests were conducted to determine if size and sorting of the opaque heavy minerals in the segregated 

layers of each run were significantly different in 

each run. Since the same sediment was used for 

each run, any significant differences in the data 

must be due to the effect of the different flows on 

the grains.

Data used for the analysis of variance tests were 

obtained from laminae of dark opaque minerals in 

the core samples (appendix C, table 5). A more complete presentation of these results has been given by 

Brady, (1971, p. 44).

The results of the tests on the median grain 

diameter and the grain-shape factor of opaqueheavy-mineral grains showed no differences among 

runs at the 5 percent level of significance. A significant difference, however, did exist in the sorting 

among runs at the 1 percent level. An a posteriori 

SNK test (Sokal and Rohlf, 1969, p. 239-246) of 

the sorting means of the three runs was conducted 

to determine which run was significantly different 

from the others. Results of the SNK show that the

mean sorting value of the opaque-heavy-mineral 

samples in run 4 is significantly larger than the 

sorting values are for the other two runs at the 1 

percent significance level.

The median diameter and sorting for light-mineral 

samples that were obtained adjacent to and within 

the opaque-heavy-mineral laminae also were tested 

by analysis of variance tests (sorting and median 

diameter values of the samples are listed in appendix C, table 6). The tests show that no difference in 

sorting of light minerals existed between runs 2-4; 

but, a significant difference did exist at the 5 percent level between the median diameter of the samples. Results of these tests should indicate whether 

a given flow had an effect on the properties of lightmineral grains that were closely associated with 

opaque-heavy-mineral grains that differed significantly from the effects that other flows had.

A SNK test of the mean of the sample median 

grain sizes for each of the three runs showed that 

no significant difference existed between the three 

runs. However, a SNK test for uneven sample sizes, 

such as was used for runs 2-4, does not provide 

sufficient sensitivity to determine which run differed 

significantly from the other two in its effect on 

sample median size.

EXPERIMENTAL RESULTS

SUMMARY OF BED FORM AND 

OPAQUE-HEAVY-MINERAL SEGREGATING 

CHARACTERISTICS

Four different flow runs were observed in this 

study (table 2) ; based on the terminology of Simons 

and Richardson (1966), two runs were made in the 

lower flow regime, one run was made in the upper 

flow regime, and one run in the transition regime. 

The bed configuration consisted of dunes (lower 

flow regime) in runs 1 and 2. Transition bed forms 

were long profile dunes and a near flat-bed condition in run 3. Run 4 consisted entirely of a flat bed 

formed in the upper flow regime. Average lengths 

(L) and heights (H), measured from sonic sounder 

charts, and length/height ratios for the dunes of 

different runs are given in table 3.

DUNE BED FORMS (RUN 1)

Dunes in run 1 were formed by flow that produced a low shear stress at the bed surface (table 

2). In profile the dunes were generally triangular 

in shape, with the crestline coinciding with the dune 

brinkline. Topset beds occurred on only a few dunes.
HEAVY-MINERAL SEGREGATION K15

FIGURE 10. Dune bed configuration and opaque-heavy-mineral accumulations at the bed surface following run 1. A, Dunebed configuration B, Stoss slopes of dunes showing small areas of accumulated opaque heavy minerals (length of rule 

is 30.5 cm).

TABLE 3. Mean dune size (with standard deviations) measured by sonic sounder

Run

1 ___.

2

3

Number 

of dunes 

measured

115

28

46

Height i 

(cm)

10.2 + 4.9

30.0 + 13.2

12.3 + 6.8

Length 2 

(meters)

1.63 + 0.66

7.24 + 4.67

5.66 + 2.48

Length /height 

ratio

18.2 + 8.7

26.3 + 15.0

46.6 + 29.6

1 Dune height, H, determined by maximum vertical distance between 

the trough point and the summit point of the dune as measured along 

center line of the flume.

2 Dune length, L, was determined from the low trough point between 

dunes to the next trough point downstream as measured along the centerline of the flume.

The average angle of inclination of the foreset beds 

in run 1 was 32.4°, with a standard deviation of 

2.3°. Configuration of the dunes forming the bed 

surface (fig. 10A) can best be described as linguoid. 

Rates of movement of the dunes ranged from 0.6 to 

1.0 meter per hour.

Opaque heavy minerals associated with the dunes 

were limited to small very thin ripple-form accumulations on the stoss slopes of the dunes (fig. 10B). 

The small thin accumulations of opaque heavy minerals appear to develop just downstream from the 

reattachment point (the location where the flow impedes on the back of the downstream dune after 

it has passed over the upstream dune front) and 

migrate up the dune stoss slope. No accumulations 

of opaque heavy minerals were observed in the 

foreset beds.

DUNE BED FORMS (RUN 2)

Dunes formed by flow conditions in run 2 (table 

2) were longer and higher than dunes produced by
K16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

the other runs. Distance between brinkline and crestline commonly ranged from 25 to 110 cm and averaged 60 cm. Topset beds, which are generally composed of rather fine material, were present on most 

dunes; they reached a total thickness of as much as 

3 cm. Foreset beds in run 2 showed an average dip 

of 29.2° and a standard deviation of 3.1°. Generally 

the inclination angles of the foreset beds ranged 

from 28° to 32°, but some low bed angles of 21° to 

23° indicate unstable hydraulic flow during dune 

development. Dune fronts in run 2 were sinuous 

across the width of the flume (figs. 11, 12), and 

rates of movement of the dunes down the flume 

(based on successive brinkline locations) ranged 

from 1.5 to 3.4 meters per hour.

Accumulations of opaque heavy minerals associated with the dunes (fig. 13) were present commonly as:

1. Opaque heavy minerals on the dune stoss slopes 

in the form of thin ripple accumulations or 

very thin almost sheetlike accumulations. The 

thin ripple accumulations, which resembled 

those shown in figure WB, were very common. 

They appear to have originated on the lower 

part of the dune stoss slope and to have migrated up the dune slope. Thin sheetlike accumulations of the opaque heavy minerals like

FIGURE 11. Dune bed configuration (view upstream) of run 

2. Figure 12 is a close view of the large dune (center of the 

photograph) on which the white square is located.

FIGURE 12. Accumulations of dark opaque heavy minerals 

on the upstream sides of dunes (run 2). Location of cutaway view of dune (fig. 14) is shown by the line near the 

flume wall on left side of photograph. The ripple surface 

that is shown on the dune is due to abrupt changes in 

hydraulic flow that occurred when the flume was shut down 

at the end of the run. Segregation of the heavy minerals 

was not formed by shutdown of the flume.

those shown in figure 12 were present on 

many dune stoss slopes.

2. Thick accumulations of opaque heavy minerals 

associated with the dune crest area. These 

accumulations formed the thickest beds of 

opaque heavy minerals observed, and the beds 

were nearly 100 percent opaque heavy minerals. Observations made through the plexiglass wall of the flume during the flow showed 

that the opaque-heavy-mineral accumulations 

formed on the highest portion of the dune (in 

dune profile). The accumulation as a whole 

moved downstream at a rate approximately 

equal to the rate of movement of the dune. 

Scour occurred periodically both upstream and 

downstream from the heavy-mineral area. If 

degradation immediately downstream reached 

approximately 1-2 cm below the high point 

of the accumulation, large amounts of the 

heavy minerals were transported from the 

accumulation by suspended and tractive movement and redeposited as a heavy-mineral 

lamina along the lee slope.

3. Accumulations of opaque heavy minerals that 

were deposited between the dune crestline and 

the brinkline. These deposits, derived from the 

thick crest area accumulation of opaque heavy 

minerals, formed part of the topset beds of 

the dune. An example of numerous opaqueheavy-mineral laminae in the topset beds is 

shown in figure 145.
HEAVY-MINERAL SEGREGATION KIT

FIGURE 13. Generalized view and cut-away of a dune showing structures and locations of different types of opaqueheavy-mineral accumulations: a, thin ripple-form accumulations on stoss slope; b, crestal region accumulation; 

c, region between the crestline and brinkline where accumulations occur; d, accumulations in f oreset beds.(X 3 vertical exaggeration).

4. Accumulations of opaque heavy minerals deposited at the brink point and on the slipface 

of the dune. These deposits formed dark laminae in the foreset beds like those shown in 

figure HA. The concentrated opaque-heavymineral layers did not extend down the foreset 

beds more than 8 cm (total slipface length on 

the dunes commonly was 20-30 cm), and concentration of heavy minerals decreased with 

increased distance down the bedding plane 

from the brinkline. Opaque heavy minerals 

were lost from the topset beds by tractive and 

suspended transport over the brink point.

TRANSITION BED FORMS (RUN 3)

During the run the bed forms alternated between 

large dunes (fig. 15A and B) and a near flat-bed 

condition (very long profile dune). The near flatbed condition of the run differed from a true flat 

bed in that it did not at any time extend over the 

entire length of the flume. In addition, the near 

flat-bed condition differed from the flat bed of run 

4 by having a slipface on its downstream edge as 

well as slight form irregularities on its surface. 

Dunes associated with run 3 had a much larger 

length-to-height ratio than the dunes of runs 1 and 

2.

The distance from the crestline to the brinkline 

for the dunes of run 3 commonly ranged from 15 to 

85 cm, but for some dunes the distance was as much 

as 2.5 meters; the mean distance was 53 cm. Topset 

beds of fine material were present on virtually all 

the dunes. Dune fronts were sinuous across the 

flume as shown in figure 15A and B. Angles of 

inclination of foreset beds averaged 28.6° with a

standard deviation of 3.2°. Several foreset dip 

values of 21° to 23° indicated locally unstable deposition. Rates of movement of the dune fronts ranged 

from 2.7 to 4 meters per hour.

Opaque-heavy-mineral accumulations commonly 

associated with the transition bed forms can be 

classified as follows:

1. Thin but widespread accumulations near the base 

of flat beds, just above foresets formed with 

or as part of dunes deposited earlier.

2. Thin laminae of concentrated opaque heavy minerals within the flat beds. These laminae were 

usually thinner than the opaque-heavy-mineral 

beds at the base of the flat-bedded sediments.

3. Accumulations associated with the dune phase 

of the transition bed forms. They were basically the same as those associated with the 

dunes of run 2, namely:

a. Thin accumulations in ripple-form and 

sheetlike accumulations that advance up 

the stoss side of dunes.

b. Thick accumulations that were commonly 

present along the crestal region of the 

dune (fig. 16A and B).

c. Accumulations that extended downstream 

from the crestline to the brinkline (fig. 

17A and B). In several dunes opaqueheavy-mineral segregation was observed 

in the foreset beds (fig. 17A). 

d. Thick accumulations were often present in 

the topset beds. These deposits resulted 

from burial of surface accumulations.

BED FORMS OF MOVING FLAT-BED CONDITIONS (RUN 4)

The flow that produced the flat beds of run 4 had
K18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

T

i

i

FIGURE 14. Opaque-heavy-mineral accumulations in foreset and topset beds of dunes formed in run 2. A, Cut-away part 

of dune shown in figure 12 showing accumulation of opaque heavy minerals (dark beds) in the foreset beds (can diameter is 6.5 cm); B, Segregation of opaque-heavy-mineral grains in topset laminations.
HEAVY-MINERAL SEGREGATION K19

A B

FIGURE 15. Bed configuration and opaque-heavy-mineral accumulation at the bed surface formed during run 3. A, Dune 

region of transition flow; B, Close-up view of dunes showing opaque-heavy-mineral segregation on the dune stoss slopes. 

Ripples present on the dunes were not present during the run but were formed as the result of abrupt changes in flow 

conditions during flume shutdown.

the highest shear stress and Froude number of any 

flow during the four runs. Under equilibrium flow 

the sediment bed had an essentially featureless surface (fig. 18), the bed elevation at any point departing only a few centimeters from the mean elevation. A study of bed-surface-elevation fluctuations 

at one location during the equilibrium flow showed 

a maximum fluctuation of only 1.8 cm during a 12 

hour period. Studies by Guy, Simons, and Richardson (1966, p. 24, 29) show vertical fluctuations with 

time of flat-bed surfaces during several runs as 

ranging from 1 to 3 cm. Bedding structures were all 

flat lying and covered preexisting bed forms. Generally the material in the flat lying deposits was 

finer than the material in the preexisting foreset 

beds. Total thickness of the flat beds in the run was 

usually less than 3 cm.

Of the four runs studied in detail, total sediment

concentrations in the total-load and suspended-load 

samples were by far the largest in run 4.

Opaque-heavy-mineral accumulations were common in the flat-bed run, and accumulations of the 

heavy minerals were present at the base of and 

within the flat beds over virtually the entire flume 

area (fig. 19). The individual beds, however, tended 

to lense out within a few meters. Accumulations 

were often the thickest and most widespread at or 

near the base of the flat beds. In run 4 no opaqueheavy-mineral accumulations were present at bed 

surface.

RELATION OF FALL VELOCITIES OF DARK OPAQUE 

AND LIGHT-DENSITY GRAINS

Samples of light minerals obtained from laminae 

adjacent to or within laminae having a high con-
K20 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 16. Accumulations of opaque heavy minerals formed along the crestal region of a dune (run 3). A, Accumulation 

on the crestal region of a long dune in the transition flow; B, Exposed topset beds (located at the right side of the 

71-cm rule in top photograph) showing the thick accumulation.
HEAVY-MINERAL SEGREGATION K21

FIGURE 17. Opaque-heavy-mineral accumulations formed in topset and foreset beds during run 3. A, Opaque heavy minerals 

in dark laminae of topset beds near the brinkline and in the foreset beds in laminae composed of the grains that have 

passed over the brink point; B, Foreset beds have very few opaque heavy minerals present, but a large amount of opaque 

heavy minerals are present in the thin topset beds.
K22 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGURE 18. Flat-bed surface formed by run 4. Ripples at the 

surface were due to shutdown of the flume.

centration of opaque heavy minerals were studied 

to examine the role fall velocities play in the association of light- and heavy-mineral grains.

To do so, a graph (fig. 20) relating sieve size to 

fall velocity for grains with a shape factor of 0.7 

and with specific gravities of 2.65 and 5.0 was 

plotted from data reported by the U.S. Inter-Agency 

Committee on Water Resources (1957). Values of 

fall velocities for the d16, dso, and d84 grain sizes 

were determined from figure 20 by using the samples 

described in tables 5 and 6 (appendix C). These 

fall-velocity values have been tabulated by Brady 

(1971, p. 112). Fall-velocity relations between 

opaque-heavy-mineral grains and light-mineral 

grains of the bed-material sample and the average 

of all the core samples are shown in figure 20. If 

one averages the range between the 16th and 84th 

percentiles of the opaque-heavy-mineral grains and 

the light-mineral grains for the sampled laminae in 

the core samples, 78 percent of the light mineral 

grains have fall velocities within the same range as 

80 percent of the opaque-heavy-mineral grains. For 

the bed-material samples, 74 percent of the lightmineral grains had fall velocities equal to 78 percent of the opaque-heavy-mineral grains.

Median fall-velocity values of the opaque heavy 

minerals and the median fall velocities of light 

minerals sampled adjacent to (18 samples) or

within (five samples) the opaque-heavy-mineral 

laminae have a correlation coefficient of 0.369 (fig. 

21), a value that suggests no correlation exists. The 

lack of correlation for medians of fall velocities 

between the two mineral groups shows that the 

median fall velocity of one group is not a predictor 

of the median fall velocity of the other group despite 

the fact that a large number of grains have equivalent fall velocities in adjacent laminae. The lack of 

correlation for mean fall velocities of the opaque 

heavy minerals and light minerals, therefore, suggests that other grain properties were much more 

important for local sorting.

RELATION OF GRAIN ENTRAINMENT TO CRITICAL 

SHEAR STRESS AND GRAIN SIZE

By using Shields diagram (fig. 5), one can develop 

the relation of critical shear to grain size for grains 

of different densities.

Such a series of curves was developed by Grigg 

and Rathbun (1969, p. B79). Two curves similar to 

those constructed by Grigg and Rathbun are plotted 

in figure 22 for grains of 5.0 and 2.65 specific gravities. The range between the 16th and 84th percentiles of the opaque-heavy-mineral grains and the 

light-mineral grains of the bed material and the 

average values for the sampled laminae in the core 

samples from runs 2, 3, and 4 are plotted in figure 

22 to show the relation between the critical shear 

stress of the two mineral groups. The large difference in critical shear indicates that quartz and feldspar grains would be entrained from sands in this 

study much more readily than magnetite and ilmenite grains.

Figure 22 is based directly on Shields diagram. 

The data on which the Shields diagram was based 

were obtained by laboratory experiments in which 

particles moved over a bed that consists of particles 

of the same size. How differences in size affect the 

moving and stationary particles has been discussed 

on pages 3 and 4. By use of figure 1, one can 

qualitatively adjust figure 22 so that it is more 

applicable to the flume situation. For example, figure 1 indicates that the resistance of a 0.1 mm 

particle resting on a bed of 0.2 mm particles is 

underestimated in figure 22 by as much as a factor 

of 3. Once a small magnetite or ilmenite grain is 

deposited on a bed of large quartz and feldspar 

grains, it is extremely difficult for the flow to move 

it again.

The resistance of a 0.4 mm particle resting on a 

bed composed of 0.2 mm particles is overestimated
HEAVY-MINERAL SEGREGATION K23

FIGURE 19. Flat-bed flow deposits showing opaque-heavy-mineral layers (dark beds) within the flat-lying beds. Lower 

dark-mineral bed directly overlies foreset beds of an earlier run. Wavy appearance of the dark laminae in the photograph is due to an irregular cross-section cut. The rule is 71 cm in length.

in figure 22 by perhaps a factor of 2. The flow will 

quickly remove a large quartz or feldspar particle 

from a bed which is composed of small dense grains.

In addition, distinct differences in physical size 

between grains also leads to a "hiding factor," or 

a shielding of the smaller grains from the flow by 

the larger grains. Einstein and Chien (1953) discussed the "hiding factor."

To test whether the slope of the lines in figure 22 

may actually be negative when the bed is composed 

of a poorly sorted material in the size range of 

interest here, an experiment was conducted to determine what effect the sorting of the bed material 

might have on a particle's resistance to motion. A 

flat bed of quartz sand (d50 = 0.280 mm, a = 1.50) 

was placed over a 94-cm section of a flume 20 cm 

deep, 20 cm wide, and 10 meters long. The bed 

roughness for a section 6 meters long upstream 

from the sand bed was similar to that of the sand 

bed. The flow was started at a velocity insufficient 

to move any of the bed material, and the velocity 

was gradually increased. During the velocity increase the water depth was held constant at 3.5 cm, 

while the slope of the water surface remained 

parallel to that of the bed. The velocity was increased slightly each 24 hours for 6 days. The total 

material transported from the test section during 

each day (run) was collected and sieved.

Results of this experiment (table 4) show that 

little sediment was eroded during the first five runs. 

During the last run, ripples developed, and a considerable amount of sediment was eroded, mainly 

producing a few isolated scour holes several millimeters deep.

The selectivity with which the flow transported a 

particular size fraction of the bed material can be 

determined by computing the ratio of the percent of 

that size fraction in the material transported out of 

the test section to the percent of the size fraction 

which was available for transport. This ratio will 

be called the transport ratio. Transport ratios which 

are greater !:han one indicate size fractions which 

are readily transported or which have a low resistance to motion. If a particle's resistance to motion 

were correctly represented by figure 22, one would 

expect the transport ratio to decrease continuously 

with increasing particle size.

By assuming that a representative sample of the 

bed material was available for transport on the bed 

surface at the beginning of run A, the transport 

ratios for each size class and run were computed 

from the data given in table 4. Except for run A, 

which did not transport any sediment larger than 

0.707 mm, the transport ratios were larger than 

one for all grain sizes greater than 0.35 mm. The 

increase in the value of the transport ratio indicates 

a decrease in resistance to motion with increase in 

grain size in the range 0.25 to 1.0 mm, a relationship opposite to that indicated in figure 22.

It is suspected that some sorting of the bed material occurred at the bed surface as a result of the 

placement of the bed and that this sorting affected 

the resulting transport ratios of the smaller grain 

sizes during the first five runs. Therefore, no significance is attached to the transport ratios of the finer 

sizes for the first five runs.

Ripples were developing during run F, and a few 

scour holes were eroded several millimeters deep.
K24 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 4. Results of a resistance-to-motion experiment using a poorly sorted quartz bed material

Run

A _ _

B _ _ _ _

C ___ 

D _ _

E

F __ _

Total

0- 

0.062

0.0006

.0007

.0016

.0013

.0016

.000

.006

0.02

0,2

0.1

Size, in millimeters

0.062- 0.125- 0.177- 0.250- 0.350- 

0.125 0.177 0.250 0.350 0.500

Weight (in grams) of material eroded during the

0.0089 0.0126 0.0132 0.0157 0.0285

.0067 .0100 .0089 .0098 .0180

.0110 .0147 .0109 .0075 .0136

.0104 .0235 .0387 .0528 .0784

.0111 .0133 .0236 .0827 .2505

.019 .594 3.221 8.106 11.106

.067 .668 3.316 8.275 11.495

Percent of total eroded material

0.24 2.37 11.7 29.3 40.6

Percent of bed material

4.9 11.0 22.8 33.2 22.2

Ratio (percent eroded/percent in bed)

0.05 0.22 0.52 0.88 1.8

0.500- 

0.707

run

0.0010

.0109

.0146

.0554

.2033

4.085

4.370

15.5

5.6

2.8

0.707-

00

0

.0010

.0017

.0012

.0051

.057

.066

0.23

0.05

5

Total

0.0805

.0660

.0756

.2617

.5912

27.188

28.263

Because of this erosion pattern, it is believed that 

the size distribution of the material which was available for transport was nearly the same as the size 

distribution of the total bed material and that the 

computed transport ratios for run F accurately represent the resistance to motion of the particles.

The transport ratios for run F increased consistently with particle size throughout the entire 

range of ^article sizes. Therefore, it is concluded 

that the resistance to motion of sand grains decreases with increasing grain size when the transport is occurring over a poorly sorted bed. There 

obviously must be some maximum size above which 

this relation is no longer true. The data presented 

in table 4 indicate that this maximum size is larger 

than 0.1 mm.

These results indicate, as the plot of figure 1 suggests, that figure 22 does not correctly depict the 

resistance to motion for particles for material being 

transported over a poorly sorted bed material. The 

resistance to motion should decrease, rather than 

increase, with increasing particle size for particle 

sizes within the range of 0.05 to 1.0 mm.

The median size of the total load transported in 

these small flume experimental runs made at the 

point of initiation of grain movement was larger 

than the median size of the bed material, whereas 

the median size of the total-transport-load samples 

from the large flume runs was smaller than that of 

the bed material. In natural streams, total-load samples almost always have smaller median sizes than 

does the bed material of the stream (Carl F. Nordin, 

oral commun., April, 1971).

Smaller particles are, of course, more easily entrained and carried in suspension by the flow, and 

the suspended load always has a smaller median 

size than does the total load. It is usually impossible 

to determine the size distribution of the entire suspended load so that the true size distribution of the 

bed load is seldom known either in the field or in 

the laboratory.

In addition, the median size of the bed material 

tends to increase with distance below the mean bed 

elevation for fully developed bed forms. As a consequence the coarser particles tend not to be exposed to the flow and are not available for transport 

as frequently as the finer particles deposited at 

higher elevations in the bed. Their availability would 

tend to account for a higher transport rate of small 

particles even though their resistance to motion 

along the bed is greater than that of larger particles.

The small flume experiment shows that a marked 

"hiding effect" does exist for a poorly sorted bed 

material, and this result is consistent with flume 

and field data. When small grains form only a small 

part of the surface material as the small opaquemineral grains did in this study prior to their concentration, the selective removal by the flow of 

larger less dense grains can play an important part 

in their segregation.
HEAVY-MINERAL SEGREGATION K25

HEAVY-MINERAL TRANSPORT AND DEPOSITION 

IN A FLAT-BED FLOW

Accumulations of dark opaque minerals were 

widespread in the flatbed runs (run 4). The accumulations of opaque heavy minerals at the base of 

the flat-bedded sands suggested that the heavy minerals were concentrated at the base of the tractive 

load during degradation and were the first deposited 

during aggradation. To test this hypothesis, a study 

was made of the transport of heavy minerals relative to time under equilibrium hydraulic conditions. 

The small recirculating water-sediment flume (20 

cm deep, 20 cm wide, and 10 m long) was used in 

the experiment with a sand bed of the same Rio 

Grande sand that was used in the large flume runs. 

The sand bed was thoroughly mixed after the flow 

was started. Mixing of the sand provided maximum 

possible exposure of heavy minerals to the flow. The 

run, which lasted for 47 hours, was started just 

after the mixing of the sand.

Hydraulic conditions necessary to form the flat 

bed were held as constant as possible throughout 

the run. Average discharge for the run was 10.98 

liters per second with an average water depth of 

7.36 cm. Water-surface slope was 0.0045, and the 

average temperature was 16.9°C. Total-load samples 

containing 80-135 grams of sediment were collected 

at close time intervals (15 min) early in the study 

and at increasingly longer time intervals (up to

1.0

0.5

0.1

0.05

Bed-material sample

-B 

Core sample average

Shape factor = 0.7 

Temperature = 20.8° C

1.0 5.0 10.0, 30.0 

FALL VELOCITY, IN CENTIMETERS PER SECOND

FIGURE 20. Fall-velocity relationship of light-mineral grains 

to opaque-heavy-mineral grains obtained from the bed-material sample and core samples of runs 2, 3, and 4.

5.0

2 Q

D O

O DC 3.0 -

u- Q.

° CO

>- DC

t U

O t

3 I 2'°

LU I 

1.0

Run 2

A 

Run 3

Run 4

1.0 2.0 3.0 4.0 

MEDIAN FALL VELOCITY OF LIGHT MINERALS, 

IN CENTIMETERS PER SECOND

5.0

FIGURE 21. Plot of median fall velocities of opaque-heavymineral grains and light-mineral grains.

7 hr) as the study progressed. Total-load concentrations for the study averaged 2,699 mg/1.

Sediment from the total-load sample that passed 

the 60 mesh (0.25 mm) sieve was retained for magnetite separation. Magnetite less than 0.25 mm was 

used in this study as the marker mineral because 

of the ease of separation of magnetite and because 

88 percent of the dark-opaque-minerals of the bedmaterial sample were finer than 0.25 mm. A strong 

hand magnet was used to separate the magnetite 

grains from the sample. The percentage of magnetite in the sand that passed the 60 mesh sieve was 

calculated, and the results of these percentage plots 

relative to time (fig. 23) confirm the hypothesis that 

in a flat-bed flow under equilibrium conditions there 

is a decreasing volume of transport of heavy minerals with increasing time of transport.

DISCUSSION OF DATA

RELATIONS AMONG SEDIMENT SAMPLES

Analysis of variance tests of median sizes and 

shape factors of opaque-heavy-mineral grains obtained from laminae having high concentrations of 

opaque heavy minerals show no significant variance 

at the 5 percent level among sediment samples taken 

from each of runs 2-4. There was, however, a significant difference at the 1 percent level in sorting
K26 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

10.0

CO O 

LU LU

DC UJ 

O 0-

 & Bed-material sample

-B Core sample average

1.0 

0.05 0.10 0.50 

GRAIN SIZE, IN MILLIMETERS

1.0

FIGURE 22. Critical shear relationship of light minerals to 

opaque heavy minerals for the bed-material and core samples.

among the three runs. Among the light minerals 

from runs 2-4 sampled from laminae adjacent to the 

opaque-mineral laminae, a significant difference 

existed in the median size at the 5 percent level, and 

no significant difference (5-percent level) existed 

for the sorting values.

Sorting values determined for opaque-heavymineral samples from run 4 were much larger than 

for those from other runs. Sorting values for opaqueheavy-mineral samples of run 4 were close to those 

for dark opaque grains in the bed-material samples. This correlation indicates that all sizes of the 

high-density material in run 4 were being moved 

by the flow, whereas sorting of opaque heavy minerals towards finer sizes was occurring in runs 2 

and 3.

Sorting is the grain distribution parameter most 

affected by the different hydraulic conditions. In the 

flat-bed flow (run 4), segregation apparently occurred first at the base of the bed load and formed 

a widespread layer of opaque-heavy-mineral grains. 

As local erosion of the bed occurred, the opaque 

minerals became concentrated at the base of the 

flow, and subsequent deposition allowed preservation of the dark laminae. For such a concentrating 

mechanism, the sorting would have a wide range of 

values and would depend on the ability of the local 

flow to sort the sample as to size. The smaller sorting values obtained for the dune flows shows that 

sorting as to size is accomplished more efficiently in 

the lower flow regimen.

Analysis of the critical shear stress for grain 

movement indicates that the larger low-density 

grains of the bed material require a much smaller

shear for movement than the smaller, more dense 

grains. Relations of velocities of heavy minerals 

and light-density minerals (figs. 3, 4) and the critical shear relationship of opaque heavy minerals in 

the bed-material (figs. 1, 22) all seem to support the 

idea that the less dense grains are much more readily 

entrained and moved. In addition, the difference in 

size between the low-density grains and the highdensity grains leads to a "hiding effect" that can 

effectively shield the smaller grains from the flow.

A large percentage of the light-mineral grains 

and opaque-heavy-mineral grains in adjacent laminae had fall velocities in the same range. However, 

comparison of fall velocities of median sizes of the 

dark-opaque-mineral samples and light-mineral samples from the core samples showed that no correlation exists (correlation coefficient of 0.369) for the 

median values of these two groups. The light-mineral 

samples were obtained from within (five samples) 

and adjacent to (18 samples) the opaque-heavymineral laminae. All the light-mineral samples examined were taken from positions within 2 mm of 

the sampled heavy-mineral laminae. The lack of 

correlation and the presence of distinct segregated 

laminae, even though an adequate supply of both 

mineral groups having equal fall velocities was 

available, suggest that factors other than grain fall 

velocity were important to ths occurrence of local 

sorting.

Gross transfer of the sediment load, however, may 

be related to the fall velocities, for the fall velocities 

of 78 percent of the opaque-heavy-mineral grains 

in the bed-material samples overlap those of 74 

percent of the light-mineral grains in the size distribution range between the 16th and 84th percentiles.

Turbulence is more intense in the trough region 

than on the higher portions of the stoss side or near 

the brink point of the dune; and, in general, turbulence is more intense near the bed. A large shear 

stress at the bed, caused by the turbulent eddies, is 

probably important in the initiating movement of 

the opaque heavy minerals, especially in the region 

of the reattachment point.

Intermittency of turbulence was not studied quantitatively, but strong turbulent eddies passing over 

the crestal region were observed in the flow and 

strong intermittent turbulence is suggested by the 

presence of opaque-heavy-mineral laminae in the 

topset beds. Strong turbulence which increases the 

local shear could cause a rapid movement of the 

opaque-heavy-mineral grains from the crestline 

toward the brinkline and the low-density material 

could then move rapidly over the dense grains or be
HEAVY-MINERAL SEGREGATION K27

carried temporarily in suspension. With a decrease 

in turbulence, the heavy minerals would be deposited before the light minerals.

BED FORMS AND HYDRAULIC VARIABLES

Observations of the four runs in this study and 

other experimental runs made in the large flume, as 

well as field observations, indicate that the bed configuration is the most important single factor affecting the opaque-heavy-mineral segregation. Bed configuration, however, is not an independent variable 

but is dependent on a large number of hydraulic 

variables as shown by Simons and Richardson (1966, 

p. J13-J16). The most important variables affecting 

the bed forms are the energy slope, depth of flow, 

physical properties of the bed material, and velocity 

of flow. In flume studies, flow velocity is considered 

to be dependent on the energy slope and depth of 

flow; however, in field relations, velocity is the independent variable, and depth of flow is probably the 

dependent variable.

Under the flow conditions of this study there 

appears to have been three fundamental types of 

heavy-mineral segregation.

1. Thin accumulations of opaque heavy minerals 

covering small areas, associated with dunes 

without topset beds and the stoss slope of 

large dunes with topset beds.

2. Accumulations of opaque heavy minerals associated with topset deposits of large dunes.

3. Accumulations of opaque heavy minerals that 

were associated with flat-bed movement of the 

sediment.

The small areas of thin accumulations of opaque 

heavy minerals were found in association with ripples and small dunes. On larger dunes small areas 

of heavy-mineral accumulations formed on the dune 

stoss slope, commonly in the areas just downstream 

from the reattachment point of the flow (the location where the flow impedes on the bed after it 

passes over the upstream dune front). The accumulations of opaque heavy minerals moved up the stoss 

side of the dune as units, and additional grains were 

added to the migrating areas during their movement. Dark opaque-heavy-mineral accumulations 

generally moved as very thin ripples having very 

large length to height ratios (fig. 105).

The buildup and movement of these accumulations 

may be described somewhat as follows. The intense 

turbulence associated with the reattachment point 

supplies both heavy and light material to the section 

just downstream from the reattachment point. Before segregation occurs, the bed at this section consists primarily of rather coarse foreset material. 

This coarse bed material serves as an effective trap 

for the small dense particles supplied to the area 

(figs. 1, 22). As more and more of the dense particles are trapped and segregated at this location, a 

small area of the bed will become covered. Once covered, the area becomes more resistant to erosion (fig. 

22), and the erosion of the light particles around 

the heavy-mineral area tends to expose the accumulation to increasingly stronger flow conditions. 

Finally the segregated accumulation starts to move 

up the stoss slope of the dune as the dense particles 

are eroded from the upstream edge of the accumulation, move across the relatively smooth surface 

of the heavy mineral area, and are deposited at the 

downstream edge of accumulation. All during this 

process large quantities of the larger less dense particles are transported over the smooth surface of 

the accumulation.

Large areas of opaque-heavy-mineral accumulations often were associated with topset deposits that 

occurred on large dunes and transition bed forms. 

The greatest thicknesses of accumulations of dark 

opaque-mineral grains were associated with this 

type of deposit. Three different situations associated 

with the topset accumulations of opaque-heavymineral grains were as follows: (1) Accumulations 

that occurred along the crestal region of the dunes. 

These opaque-heavy-mineral accumulations moved 

downstream with the dune if the dune maintained 

approximately the same shape and height. Losses 

from the crestal region were offset by additions of 

heavy minerals from upstream areas. (2) Laminae 

of opaque heavy minerals that occurred downstream 

from the crestline were found both upon and within

0.16

0.12

UJ

t 0.08

I I

* Sample

0.04

16 32 40 48

TIME, IN HOURS

FIGURE 23. Relation of magnetite in transport to time in 

20-cm flume and under flat-bed conditions.
K28 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

the topset beds. These heavy-mineral deposits were 

derived from a crestal accumulation. (3) Foreset 

laminae of opaque-heavy-mineral grains. The segregated opaque-heavy-mineral laminae in the foreset 

could be traced up slope in many cases into the topset beds. The foreset accumulations were caused by 

conditions similar to those that deposited the opaqueheavy-mineral laminae in the topset beds except that 

the heavy-mineral grains were transported in sufficient quantities past the brink point to allow some 

to slide down the lee slope and form the concentrated laminae in the foreset beds. A decrease in 

degree of concentration of opaque-heavy-mineral 

grains within laminae with distance down the foreset indicates a diluting of the opaque heavy minerals with low density grains or a decrease in the 

proportions of opaque heavy minerals transported 

to that point.

When accumulations of opaque heavy minerals 

are deposited just past the brinkline in the foreset 

beds, a periodicity of transport is indicated by the 

alternate layers of light and heavy minerals in the 

foreset sequence (fig. 14A). The most plausible 

explanation of this alternation is that strong intermittent turbulent eddies increased motion of the 

high-density grains and moved them past the brink 

point of the dune and that most of the lower density 

material was either carried into suspension by the 

increased turbulence or moved rapidly over the 

small, high-density grains.

The bed-surface elevation of flat-bed flow under 

equilibrium conditions varied randomly with time 

but by only a few centimeters from a mean elevation at any location. Therefore, for thick laminae 

of opaque heavy minerals to form in a flat-bed flow 

it is important that a flow condition produce a deep 

scour (in this study, a transition flow) prior to the 

flat-bed flow. Such erosion is necessary in order to 

expose the heavy minerals in a thick section of bed 

material to the flat-bed flow.

During the flat-bed run, accumulations of opaque 

heavy minerals occurred near the base of the tractive load. Other accumulations of opaque heavy minerals that were present within the flat beds probably 

also represent heavy minerals deposited in the same 

way as those at the base of the flat beds but subsequent to deposition of the basal accumulations. Results of the 20-cm flume experiment show a decrease 

with time in the-volume of heavy-mineral grains 

transported in a flat-bed flow at near equilibrium 

conditions. This decrease in heavy-mineral transport 

indicates that a large percentage of the heavy minerals were deposited early during the flow and that 

the heavy minerals either remained at rest or were

reentrained at a rate that was less than the rate 

of deposition.

On dunes, the thickest accumulations of opaque 

heavy minerals occurred in the topset bed area near 

the crest of the dune. Runs 2 and 3 had large dunes 

that had a fairly large crest-to-brink distance and 

topset beds that had large areas of thick heavymineral accumulation associated with them, while 

dunes of run 1 had a crestline corresponding to the 

brinkline, and no topset beds or large areas of concentrated heavy minerals.

In order to determine why the opaque heavy minerals form large accumulations near the crest of 

dunes, consider the expression for the rate of sediment transport as given by Simons, Richardson, and 

Nordin (1965b)

0 (22)

where y = elevation of the bed surface, t = time, 

A = porosity of the sand bed, q* = bed-load transport rate in volume per unit time per unit width, 

and x = distance along the bed surface in the direction of the flow. This equation states that the rate 

of change of bed elevation with time (that is, the 

rate of deposition or erosion) is proportional to the 

rate of change of bed-load transport with respect to 

distance. From the negative ratio obtained by applying this equation to the area upstream from the crest 

of a dune, it is apparent that this is a region of 

erosion. Erosion is needed in order to keep the thin 

accumulations on the stoss slope of the dunes exposed to the flow so that they continue to move. However, downstream from the crest of the dune 

d y/ d t is positive, indicating that this is generally 

a region of deposition. Because of their large resistance to motion, dark opaque minerals are selectively 

deposited from the moving bed load after it passes 

over the crest. The net result is that the thin accumulations move up the stoss slope of the dune and 

are deposited just downstream from the crest. At 

this point the heavy minerals accumulate to rather 

large thicknesses, for the material is transported 

out of the region only by occasional bursts of extreme turbulence. Thick accumulations probably 

could not build up in run 1 because the crestline and 

brinkline were coincident; the brink point is a place 

where the grains can be lost to suspension and to 

the foreset material.

Topset beds were deposited with a small dip angle 

in the downstream direction (generally 4°-6°) between the crestline and the brinkline. In general
HEAVY-MINERAL SEGREGATION K29

appearance the topset beds resembled planar beds 

of a flat-bed run.

The topset beds are generally composed of material which is finer than the bed material. At first, 

this appears to be paradoxical since, as can be seen 

from equation 22, the crestal region represents the 

region of the flow where the transport capacity of 

the flow is greatest. The topset material must be 

selectively deposited from the moving load that 

passes the crest. The particles with the greatest 

resistance to motion should be deposited first. Thus, 

the segregation by the flow, that is deposit of the 

finer material in the topset beds and transport of 

the coarse material on to the brink point, indicates 

that the trend of the resistance to motion with increasing sieve size is opposite to that indicated in 

figure 22. This reverse trend can be predicted by 

qualitatively adjusting figure 22 using the information provided in figure 1 and the experimental results presented in table 4. Results of field experiments by Rathbun, Kennedy, and Culbertson (1971, 

p. 143-145) show that up to a limiting size, the 

coarser material in a flat-bed flow has greater 

velocities than the central sizes of the grain distribution.

CONCLUSIONS

1. The type of bed configuration appears to be the 

most important factor affecting local segregation of heavy minerals in an open channel 

flow. Bed configuration, however, is not an 

independent variable but is dependent on a 

large number of hydraulic variables, the most 

important being energy slope, depth of flow, 

velocity of flow, and the physical properties 

of the bed material.

2. Three fundamental types of heavy-mineral accumulations were observed in this study.

a. Small areas of thin accumulations of opaque 

heavy minerals that were associated with 

the stoss side of dunes. They move as thin 

ripples and commonly originate in the 

area just downstream from the reattachment point.

b. Accumulations of opaque-heavy-mineral 

grains that were associated with the topset deposits of large dunes. These accumulations often formed thick deposits 

along and adjacent to the crestal area of 

the dune. Opaque-heavy-mineral segregations were also present within the topset 

beds, at the surface between the crestline

and brinkline, and some formed deposits 

in the foreset beds. The segregated layers 

in the foreset beds were probably due to 

mass transport of heavy minerals from 

the topset area past the brinkline by 

strong turbulent motion.

c. Accumulations of opaque heavy minerals 

that were associated with the flat-bed 

flows. The thickest and most widespread 

of the flat-bed segregations of heavy minerals generally occurred at the base of the 

flat beds, but additional laminations of 

heavy minerals were present in the flat 

beds.

3. Among the sediment properties of size, sorting, 

and shape obtained for opaque heavy minerals 

from core samples taken from the bed, the 

only significant variance that occurred between runs 2, 3, and 4 was a difference in the 

sorting of the opaque-heavy-mineral grains.

4. Theoretical considerations indicate a distinct 

difference exists in the transport rates of 

spheres of different densities moving as bed 

load. The initiation of motion of grains is 

illustrated by the Shields diagram (fig. 5). 

Based on the Shields criteria, curves can be 

developed to show the relationship between 

critical shear and grain size for materials of 

different densities. The curves constructed 

clearly show that the opaque heavy minerals 

are much more resistant to motion than the 

light minerals.

5. Theoretical analysis and experimental results 

illustrate that the size of the particle in transport as well as the size of the bed material 

affects the resistance of a particle to tractive 

motion. For the particle sizes of interest in 

this study, it is found that a particle's resistance to tractive motion over a poorly sorted 

bed material decreases with increasing particle size at least in the size range studied.

6. Fall velocity values for median sizes of opaqueheavy-mineral grains and associated light 

minerals from laminae adjacent to or within 

the opaque-mineral laminae are not correlated. 

This lack of correlation and the presence of 

distinct segregated laminae, suggests that fall 

velocity alone has little or no effect on the 

local sorting of heavy minerals.

REFERENCES

Alien, J. R. L., 1968, Current ripples their relation to patterns of water and sediment motion: Amsterdam, NorthHolland Publishing Co., 433 p.
K30 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

American Society of Civil Engineers, Task Committee on 

Preparation of Sedimentation Manual, 1962, Introduction and properties of sediment; Am. Soc. Civil Engineers Proc., v. 88, no. HY4, p. 77-107.

 1966, Sedimentation transportation mechanics: Initiation of motion: Am. Soc. Civil Engineers Jour., v. 92, no. 

HY2, p. 291-314.

American Society of Civil Engineers, Task Force on Bed 

Forms in Alluvial Channels, 1966, Nomenclature for 

bed forms in alluvial channels: Am. Soc. Civil Engineers 

Proc., v. 92, no. HY3, p. 51-64.

Bagnold, R. A., 1966, An approach to the transport problem 

from general physics: U. S. Geol. Survey Prof. Paper 

422-1, 37 p.

Brady, L. L., 1971, An experimental study in a large flume 

of heavy mineral segregation under alluvial flow conditions: Ph.D. dissert., Lawrence, Kans., Univ. Kansas, 

115 p.

Coleman, N. L., 1967, A theoretical and experimental study 

of drag and lift forces acting on a sphere resting on a 

hypothetical streambed: Internat. Assoc. Hydraulic Research Gong., 12th, Proc., Fort Collins, Colo. U.S.A., v. 

3, p. 185-192.

Corey, A. T., 1949, Influence of shape on the fall velocity of 

sand grains: M.S. thesis, Fort Collins, Colo., Colorado 

State Univ., 102 p.

Daily, J. W., and Harleman, D. R. F., 1966, Fluid dynamics: 

Reading, Mass., Addison-Wesley Publishing Co., 454 p.

Einstein, H. A., 1950, The bed load function for sediment 

transportation in open channel flows: U.S. Dept. Agriculture Tech. Bull. 1026, 70 p.

Einstein, H. A., and Chien, N., 1953, Transport of sediment 

mixtures with large ranges of grain sizes: Berkeley, 

Calif., Univ. California Inst. Engineering Research, 

49 p.

El-Sammi, E. A., 1949, Hydrodynamic forces on particles in 

the surface of a stream bed: Ph.D. dissert., Berkeley, 

Calif. Univ. California.

Grigg, N. S., and Rathbun, R. E., 1969, Hydraulic equivalence of minerals with consideration of the reentrainment process, in Geological Survey research 1969; U.S. 

Geol. Survey Prof. Paper 650-B, p. B77-B80.

Guy, H. P., Simons, D. B., and Richardson, E. V., 1966, Summary of alluvial channel data from flume experiments: 

U.S. Geol. Survey Prof. Paper 462-1, 96 p.

Henderson, F. M., 1966, Open channel flow: New York, The 

MacMillan Co., 522 p.

Ippen, A. T., and Verma, R. P., 1955, Motion of particles on 

bed of a turbulent stream: Am. Soc. Civil Engineers 

Trans., v. 120, p. 921-939.

Kennedy, J. F., 1963, The mechanics of dunes and antidunes 

in erodible-bed channels: Fluid Mechanics Jour., v. 16, 

p. 521-544.

Lane, E. W., 1947, Report of the Subcommittee on Sediment 

Terminology: American Geophysical Union Trans., v. 

28, p. 936-938.

McQuivey, R. S., and Keefer, T. N., 1969, The relation of 

magnetite over ripples in Geological Survey research 

1969: U.S. Geol. Survey Prof. Paper 650-D, p. D244- 

D247.

Rathbun, R. E., Kennedy, V. C., and Culbertson, J. K., 1971, 

Transport and dispersion of fluorescent tracer particles

for the flat-bed condition, Rio Grande Conveyance Channel, near Bernardo, New Mexico: U.S. Geol. Survey 

Prof. Paper 562-1, 56 p.

Raudkivi, A. J., 1967, Loose boundary hydraulics: Oxford, 

Pergamon Press, 331 p.

Richardson, E. V., and McQuivey, R. S., 1968, Measurement 

of turbulence in water: Am. Soc. Civil Engineers Proc., 

v. 94, no. HY2, p. 411-430.

Rittenhouse, G., 1943, Transportation and deposition of heavy 

minerals: Geol. Soc. American Bull., v. 54, p. 1725-1780.

Rubey, W. W., 1933, The size distribution of heavy minerals 

within a waterlaid sandstone: Jour. Sed. Petrology, v. 

3, p. 3-29.

Schultz, E. F., Wilde, R. H., and Albertson, M. L., 1954, Influence of shape on the fall velocity of sedimentary particles: U.S. Army Corps of Engineers, Missouri River 

Div., Sediment Ser., no. 5, 161 p.

Sears, F. W., and Zemansky, M. W., 1963, University physics, 

[3d ed.], pt. 1: Reading, Mass., Addison-Wesley Publishing Co., 548 p.

Sheen, S. J., 1964, Turbulence over a sand ripple: M.S. 

thesis, New Zealand, Univ. Auckland.

Shields, A., 1936, Anwendung der Ahnlichkeitsmechanik und 

der Turbulenzforschung auf die Geschiebebewegung: 

Mitteilungen der Press. Versuch anst. f. Wasserbau u. 

Schiffbau., Berlin, no. 26, 26 p.; Application of similarity 

principles and turbulence research to bed load movement translated to English by W. P. Ott and J. C. 

van Uchelen, U.S. Dept. Agriculture, Soil Conservation 

Service Coop Lab., Calif. Inst. Technology, Pasadena, 

21 p.

Simons, D. B., and Richardson, E. V., 1963, Forms of bed 

roughness in alluvial channels: Am. Soc. Civil Engineers Trans., v. 128, p. 284-302.

 1966, Resistance to flow in alluvial channels: U.S.

Geol. Survey Prof. Paper 422-J, 61 p. 

Simons, D. B., Richardson, E. V., and Nordin, C. F., Jr.,

1965a, Forms generated by flow in alluvial channels:

Soc. Econ. Paleontologists and Mineralogists Spec. Pub.

12, p. 34-52.

 1965b, Bed load equations for ripples and dunes: 

U.S. Geol. Survey Prof. Paper 462-H, 9 p.

Sokal, R. R., and Rohlf, F. J., 1969, Biometry: San Francisco, W. H. Freeman and Co., 776 p.

Streeter, V. L., 1966, Fluid Mechanics, 4th ed.: New York, 

McGraw-Hill Book Co., 705 p.

Tourtelot, H. A., 1968, Hydraulic equivalence of grains of 

quartz and heavier minerals, and implications for the 

study of placers: U.S. Geol. Survey Prof. Paper 594-F, 

13 p.

U.S. Inter-Agency Committee on Water Resources, 1957, 

Some fundamentals of particle size analysis, Report 12 

of A study of methods used in measurement and analysis 

of sediment loads in streams: Washington, U.S. Govt. 

Printing Office, 55 p.

 1958, Operator's manual on the visual-accumulation-tube method for sedimentation analysis of sands, 

Report K of A study of methods used in measurement and 

analysis of sediment loads in streams: 30 p.

Watters, G. Z., and Rao, M. V. P., 1971, Hydrodynamic effects 

of seepage on bed particles: Am. Soc. Civil Engineers 

Proc., v. 97, no. HY3, p. 421-439.
APPENDIX
K32 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

A. SYMBOLS AND NOMENCLATURE

Symbol Definition

A Area, such as the cross-sectional area of the flume.

A, Projected area of a sphere.

a Longest diameter of a grain -with three mutually 

perpendicular axes.

b Intermediate diameter of a grain with three mutually perpendicular axes.

CD Coefficient of drag for a sediment particle. The coefficient of drag varies with the particle geometry, 

relation of particle shape to flow, and the Reynolds 

number of the flow.

CF Coefficient of friction for a sediment particle. The 

coefficient of friction depends primarily on the 

nature of the particle surface and the surface of 

the material with which it is in contact.

CL Coefficient of lift for a sediment particle. The coefficient of lift depends on the shape of the particle, 

relation of particle shape to flow, and the Reynolds 

number of the flow.

CR Coefficient of static resistance of a sediment particle. 

The coefficient of static resistance depends on the 

shape and size of the particle and the arrangement, size, and shape of the bed particles.

c Shortest diameter of a grain with three mutually 

perpendicular axes.

D Flow depth.

d Diameter of a spherical particle.

dn Diameter of spheres making up bed material.

dm Diameter of a sphere resting on the bed.

d, Diameter of a grain equal to sieve diameter or 

approximately equal to b diameter of a particle.

FD Hydrodynamic drag force force exerted by the flow 

on the particle parallel to the relative motion of 

the flow.

FF Frictional force resistance to motion between two 

bodies in contact.

Fo Gravity force.

FL Hydrodynamic lift force the force component produced by the flow on a particle that is perpendicular to the direction of the flow and opposite to 

the gravity force.

Fir Resultant force normal to the bed surface.

F Froude number = L7/V gD a ratio of inertial forces 

to gravitational forces.

g Gravitational constant (980 cm per sec2 ).

H Dune height vertical distance from trough point to 

crest point.

k Ratio dm to da .

L Dune length measured from trough of a given dune 

to trough point of the next dune upstream.

n Number count of a given size in grain-size analysis.

Q Fluid discharge (cubic meter per sec).

qn Bed-load discharge weight of sediment carried in 

bed load per unit width per unit of time.

qt, Bed-load discharge volume per unit width per unit 

time.

CD

Re Reynolds number = a ratio of inertial forces

V

to viscous forces for the mean flow. 

R* Particle Reynolds number = U d/v a ratio of inSymbol

R'

S

t

U

U

U

Vf

Vo

V,

W

x

Y

y

 y

Definition

ertial forces to viscous forces relative to a particle.

Hydraulic radius a channel would have if the resistance to flow were limited to grain roughness 

(no resistance due to bed-form or streambank 

roughness). This term can be stated in terms of 

the average flow depth, Z>, with corrections for 

bed-form roughness.

Energy slope of the fluid.

Time.

Fluid velocity.

Mean fluid velocity.

Shear velocity = VTO/P. The shear velocity is not a 

real velocity but is related to the real velocity 

which would give rise to shear stress TO (Henderson, 1966, p. 412).

Velocity of flow at a representative distance from 

the bed.

Relative velocity of flow past a body.

Velocity of translation of a particle.

Channel width.

Distance along bed surface.

Elevation of the bed surface.

Height above the bed surface.

Specific weight of water.

Specific weight of a sediment grain.

Eddy viscosity that depends on the state of turbulent motion.

Angle between the bed and horizontal line.

Porosity of the bed.

Dynamic viscosity of the fluid.

Kinematic viscosity of the fluid

viscosity to mass density. 

Mass density of water. 

Mass density of a particle. 

Geometric standard deviation

distribution.

= a ratio of 

P

of a sediment size

1 / dy, dsi \ 

= { + }

2 \ di« dso /

Shear stress in the fluid. For turbulent flow

dU

T = (fL + 1}) 

dY 

and for laminar flow

dU

T II 

dY 

Average shear stress at the bed = yDS force per

unit area acting on the bed in the direction of

flow. 

Critical shear stress for sediment particles the

minimum amount of shear stress necessary to

start movement of particles at the bed. 

Dimensionless shear stress (Shields entrainment

function) =

Einstein's intensity of bed-load transport. 

Einstein's intensity of shear on a particle.
HEAVY-MINERAL SEGREGATION K33

B. GRAIN-MOUNT PREPARATION AND

RELATIONSHIP OF DIRECT GRAIN

MEASUREMENTS TO SIEVE-SIZE

EQUIVALENTS

Preparation of grain mounts Grain mounts for 

size analyses were prepared for the bed-material 

sample, core samples and many of the suspendedsediment samples studied. Where loose sample grains 

were used, as they were from the bed-material sample, the sample was reduced by a microsplitter to 

the desired size. For samples of opaque-heavymineral grains and light-mineral grains that were 

obtained from selected laminations or areas of a 

grouted core, the material was removed by use of 

a blunted dissecting needle. Both types of samples 

were prepared by distributing the grains as evenly 

as possible onto a petrographic slide that had previously been covered with alcohol. The grains, in 

settling through the alcohol, oriented themselves 

with their shortest axis (c axis) perpendicular to 

the slide. Measurement of 500 grains for shape 

factor analysis showed that this orientation occurred for 88 percent of the grains. Those grains 

with the c axis lying parallel to the slide usually had 

a c axis length very similar to the intermediate axis 

(b axis) length.

When the alcohol evaporated, a residue remained 

that caused the grains to adhere to the slide. After 

grain shape studies were made, Lakeside 70 and a 

cover glass were applied for permanent mounting 

and grain-size measurement.

Sieve-analysis equivalent of direct measurement 

Mounted mineral grains were measured directly by 

use of a petrographic microscope with a calibrated 

eyepiece that was divided into units of 12.1 microns. 

For most samples, intermediate axes (b axis) were 

measured in units of 200 grains per slide. Where 

more than 200 measurements were used for a given 

sample, additional slides were made.

If an abundance of material was available, as it 

was for the bed-material sample, grains were selected by an equal-interval point-count method. A 

pattern of evenly spaced intervals was made by use 

of a modified stage micrometer mounted on the 

microscope. If a grain was present under the stage 

stop, that grain was measured. A stage interval was 

selected that was large enough to prevent repetition 

of individual grain measurements.

Slides made from samples with limited amounts 

of material (samples from grouted cores) were 

analyzed by a line-measurement technique. In the 

line method, horizontal traverses were made over

the slide at equal intervals and the b axis was 

measured for each grain of the particular mineral 

being studied that the line crossed.

The probability that a grain will be measured by 

the point method is in direct proportion to its projected area on the slide, and the probability that a 

grain will be "hit" by the line method is in direct 

proportion to its diameter as measured perpendicular to the traverse line. Neither of these methods, 

however, allows for differences in the thickness of 

the grains perpendicular to the slide.

Opaque heavy minerals and light minerals were 

studied separately, and both groups had mean shape 

factors (appendix C) of near equant shape (0.68- 

0.75 shape factor) ; therefore, a relation between 

measured size and sieve equivalence was determined.

In order to make the direct measurements equivalent to the size equivalents determined by sieving, 

a common measuring factor was used. The best 

common standard for such a relation was the nominal grain diameter defined as the diameter of a 

sphere that has the same volume as the particle 

(Lane, 1947, p. 937). The U.S. Inter-Agency Committee on Water Resources (1957, p. 31, 33-35) 

developed graphs from extensive studies that show 

the relation of the intermediate axes of grains to 

their nominal diameters and the sieve-size equivalents of grains to their nominal diameters for various shape factors. Based on the graphs of the U.S. 

Inter-Agency Committee on Water Resources (1957, 

figs. 4, 5), the sieve diameter equivalent of the 

grains is 0.85 times the value of the direct intermediate axis measurement (using a shape factor of 

0.7) for the grain sizes in this study.

Besides adjustments to convert b axis to sievesize measurement, other factors had to be considered in conversion of direct measurement to the 

weight frequencies of a sieve analysis; these factors 

include adjusting for different grain thicknesses 

and assuring that a certain size grain occurred in 

the measurement in its correct proportion relative 

to the total grain-size population. Differences in 

grain thicknesses were corrected by multiplying the 

b size frequency count by the 6-axis diameter. To 

compute a weight frequency distribution from direct measurement, the following manipulations of 

the direct 6-axis measurements were made.

1. For the line method, the size frequency was determined by taking the percentage of each 

size from the sum of the sizes determined by 

%nb2 , where n is the 6-axis frequency and b 

is the 6-axis size.

2. For the point-count method, the size frequency
K34 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

was determined by taking the percentage of 

each size from the sum of the sizes determined 

by

Cumulative curves were plotted with the weighted 

percentages as the ordinate and with the &-axis 

values multiplied by 0.85, the correction factor, on 

the abscissa.

A check of the 0.85 conversion factor was made 

by using the bed-material sample. The results 

showed close agreement to a sieve analysis of the 

same material except on the large-grain-size end 

(fig. 9). Direct measurement of the b axis of 1,000 

grains showed a weighted median value of 0.338 

mm and a sorting (a) of 1.56. A sieved sample of 

the same bed material gave a median value of 

0.285 mm and a sorting of 1.58. The sorting values 

of the sieved sample and of the weighted direct 

measurements were similar. Applying the correction factor of 0.85 to the median diameter of 0.338 

mm determined by direct measurement gives a corrected value of 0.289 mm, which is in good agreement with the median diameter of 0.285 mm determined from sieve data.

Values stated in the text of this study for a given 

grain-size measurement are the sieve-size equivalent 

values determined by the method just described and 

by the use of 0.85 as the size conversion factor.

C. ANALYSES OF OPAQUE-HEAVY-MINERAL

GRAINS AND LIGHT-MINERAL GRAINS FROM

CORE SAMPLES (RUNS 2-4)

Data on size and sorting shown for each of the 

samples in tables 5 and 6 were determined from 

direct measurement of 200 individual grains using 

techniques described in appendix B. The bedmaterial size analyses, however, were based on 

1,000 measurements.

Twenty grain measurements per sample were 

made for determination of mean shape factor. The 

shape factor used in this report was originally defined by Corey (1949) as

S.F. =

Jab

for three mutually perpendicular axes of the grains, 

where

a = maximum diameter of the grain, 

b = intermediate diameter of the grain, and 

c = smallest diameter of the grain. 

One advantage in the use of the Corey shape 

factor over other shape factors is the extensive 

experimental data available on sediment analysis by 

Schultz, Wilde, and Albertson (1954) and a summarization by the U.S. Inter-Agency Committee on 

Water Resources (1957) of the work in which the 

Corey shape factor was used. Discussion of the

(Text continues on p. 37.)

F

FIGURE 24. Sections of core samples showing opaque-heavymineral beds. A, Run 2 topset beds (sample B-47-Xwas 

obtained from a crestal accumulation) ; B, Run 2 foreset 

beds; C, Run 3 topset beds; D, Run 3 foreset beds (sample B-48-B) and flat bed area (samples B-48-3, 10, and 

12); E, Run 4 within the flat bed deposits; F, Run 4 at 

the base of the flat beds.
HEAVY-MINERAL SEGREGATION 

TABLE 5. Size analyses of opaque heavy minerals from core samples

K35

Sample dso 

(mm)

Median

die 

(mm)

(fel

(mm)

Sorting 

(<r)

Representative

Bed Material 0.144 0.099 0.220 1.49

Shape 

factor

sample

0.684

Description of location in bed 1

of bed material

Run 2

B-47-B-1 _ _ _

B-47-X-1 __

B-47-36-1 ___ 

B-47-37-1 _ __

B-47-46-1 ________

B-47-46-2 _

B-47-47-1 ________

Average _ _

0.140 

.133 

.105 

.115 

.132 

.140

.112

.125

0.098 

.104 

.083 

.081 

.103 

.107

.087

.095

0.180 

.158 

.150 

.155 

.162 

.176

.138

.160

1.36

1.23 

1.34 

1.39 

1.25 

1.28

1.26

1.30

0.735 

.747 

.715 

.711 

.711 

.718

.698

.719

Foreset, 2-mm dark-mineral streak with interspersed lightdensity minerals (sta. 86, 1.06 m right of centerline). 

Topset, 7-mm dark-mineral zone near surface (sta. 176, 

1.00 m left of centerline) . 

Topset, dark-mineral zone (0.5 mm), 3 mm below the surface (sta. 100, 0.61 m right of centerline). 

Topset, dark-mineral zone (1 mm), 1.5 mm below the surface (sta. 96, 0.61 m left of centerline). 

Brink point, dark-mineral zone (1 mm), 4.5 mm below the 

surface (sta. 85, 0.61 m left of centerline) . 

Foreset, downstream from B-47-46-1, same dark-mineral 

streak but with light-density minerals interspersed (sta. 

85, 0.61 m left of centerline) . 

Topset, dark-mineral zone (3 mm), 5 mm below the surface (sta. 85, on centerline).

Run 3

B-48-A-1 _ _ _

B-48-B-1 ___ _

B-48-B-2 _ __ _

B-48-10-1 _ _

B-48-37-1 _

B-48-40-1 __ ____

B-48-52-1

Average ____

.126 

.154

.150 

.087 

.124 

.122

.110

.125

.101 

.102

.115 

.063 

.099 

.088

.082

.093

.154 

.198

.192 

.111 

.161 

.154

.145

.159

1.23 

1.40

1.29 

1.33 

1.28 

1.32

1.33

1.31

.754 

.744

.769 

.724 

.721 

.723

.751

.741

Topset, thickest laminae in zone, 1.5 mm thick of several 

thin dark-mineral laminations; 5 mm from surface (sta. 

98, 1.07 m right of centerline) . 

Topset (near brink point), dark-mineral zone (1 mm) at 

base of topset 3 mm from surface (sta. 114, 0.79 m left 

of centerline). 

Foreset, 2-mm dark-mineral zone with interspersed lightdensity minerals (sta. 114.2, 0.79 m left of centerline). 

Flat Bed, dark-mineral zone (0.5 mm) 35 mm from the 

surface (sta. 18, 0.61 m left of centerline). 

Topset, thick dark-mineral zone (4 mm) at the surface 

(sta. 94, 0.61 m left of centerline) . 

Topset, uppermost dark-mineral laminae (0.5 mm) in 

dark-mineral zone 17 mm from surface (sta. 90, 0.61 m 

left of centerline). 

Topset, dark-mineral zone (0.5-1 mm) 4 mm below the 

surface (sta. 74, 0.61 m left of centerline).

Run 4

B-46-5-1 ______

B-46-12-1 _ _

B-46-20-1

B-46-20-2

B-46-26-1

B-46-52-1 __ _ __

.144 

.100 

.135

.103 

.147 

.150

.102 

.076 

.095

.070 

.095 

.082

.218 

.120 

.173

.150 

.201 

.205

1.46 

1.26 

1.35

1.47 

1.46 

1.59

.744 

.715 

.693

.748 

.758 

.781

Dark-mineral zone (1.5 mm) at base of flat-bed sands, 6 

mm from surface (sta. 176, on centerline). 

Dark-mineral zone (1 mm) at base of flat-lying sand, 8 

mm from surface (sta. 168, 0.61 m right of centerline). 

Dark-mineral zone (0.5 mm) interbedded with light-density, flat-lying sand, 11 mm from surface (sta. 110, on 

centerline). 

Mixed dark-mineral and light-density minerals zone (1.5 

mm) just below sample B-46-20-1. Taken 20 mm above 

base of flat-bed sand (sta. 110, on centerline). 

Dark-mineral zone (1 mm) 6.5 mm from surface, overlain 

and underlain by light-density sand, 22 mm above base 

of flat-bedded material (sta. 102, on centerline). 

Zone of dark minerals with interspersed light-density 

minerals (1 mm), 16 mm below surface, 35 mm above 

base of flat-bedded sands (sta. 130, on centerline).
K36 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

TABLE 5. Size analyses of opaque heavy minerals from core samples Continued

Sample

B-46-55-1 _ __ _

Average _ 

dso 

(mm)

.135

.131

Median

die 

(mm)

.086

.087

(fe* Sorting 

(mm) (a)

Run

.173 1.43

.177 1.43

Shape 

factor

Description of location in bed 1

4 Continued

.757

.742

Dark-mineral 

(zone is 2.5 

15 mm from

zone with interbedded light-density grains 

mm thick) at base of flat-bedded material, 

surface (sta. 155, on centerline).

Runs 2-4

Average __ .127 .091 .165 1.35 .735

1 Stations along the flume are designated in feet (1 ft = 0.3048 m) downstream from the headbox. (Example: the distance between sta. 100 and 

sta. 110 is 10 ft (3.05 m).)

TABLE 6. Size analyses of light minerals associated with opaque heavy minerals in the core sample

Sample

dr,o 

(mm)

Median

die 

(mm)

dsi 

(mm)

Sorting

<<T)

Description of location in bed 1

Representative sample of bed material

Bed material _ _ 0.287 0.190 0.462 1.56

Run 2

B-47-B-2 _ _

B-47-X-2 __ _ _

B-47-36-2

B-47-36-3 _ _ _

B-47-37-2 _ _ _

B-47-46-2 __

B 47 46 3 _ 

B-47-47-2 _ _ _ _

B 47 47 3 _ _ __

Average ____

0.201 

.219 

.176 

.167 

.180 

.222

.236 

.188 

.207

.200

0.150 

.155 

.131 

.121 

.136 

.150

.168 

.138 

.150

.144

0.247 

.276 

.244 

.229 

.248 

.315

.349 

.268 

.266

.271

1.29 

1.33 

1.37 

1.38 

1.35 

1.45

1.44 

1.39 

1.33

1.37

Foreset, light-mineral zone (2 mm) underlying dark-mineral zone 

sample in B-47-B-1 (sta. 86, 1.06 m right of centerline). 

Topset, light-mineral zone (1.5 mm) underlying dark-mineral zone 

sampled in B-47-X-1 (sta. 176, 1.00 m left of centerline). 

Topset, light-mineral zone (2 mm) overlying dark-mineral zone 

sampled in B-47-36-1 (sta. 100, 0.61 m right of centerline). 

Topset, light-mineral zone (2 mm) underlying the dark-mineral 

zone sampled in B-47-36-1 (sta. 100, 0.61 m right of centerline). 

Topset, light-mineral zone (1.5 mm) underlying dark zone sampled 

in B-47-37-1 (sta. 96, 0.61 m left of centerline). 

Foreset below brink point, light-density grains within the darkmineral zone sampled in B-47-46-2 (sta. 85, 0.61 m left of centerline). 

Brink point, light-mineral zone (2 mm) overlying the dark-mineral 

zone sampled in B-47-46-2 (sta. 85, 0.61 m left of centerline). 

Topset, light-mineral zone (2 mm) overlying dark-mineral zone 

sampled in B-47-47-1 (sta. 85, on centerline). 

Topset (low angle), light-mineral zone (2 mm) underlying darkmineral zone sampled in B-47-47-1 (sta. 85, on centerline).

Run 3

B-48-A-2 __ _ _

B-48-B-2 _ _ _ -

B-48-B-3 _ _ _

B-48-B-4 _ _ 

0.236 

.254

.290 

.212

0.170 

.183

.196 

.151

0.309 

.343

.388 

.280

1.35 

1.37

1.41 

1.36

Topset, light-mineral zone (2 mm) underlying the dark-mineral 

zone sampled in B-48-A-1 (sta. 98, 1.07 m right of centerline). 

Foreset, light-density minerals from within the zone where dark 

minerals were sampled in B-48-B-2 (sta. 114, 0.79 m left of 

centerline). 

Foreset, light-mineral zone (2 mm) overlying the dark mineral 

foreset in B-48-B-2 (sta. 114, 0.79 m left of centerline). 

Topset (near brink point), light-mineral zone (1.5 mm) overlying 

the dark-mineral zone sampled in B-48-B-1 (sta. 114, 0.79 m 

left of centerline) .
HEAVY-MINERAL SEGREGATION K37

TABLE 6. Size analyses of light minerals associated with opaque heavy minerals in the core sample Continued

Median

Sample

dso 

(mm)

die 

(mm)

dst 

(mm)

Sorting 

(a)

Description of location in bed 1

Run 3 Continued

B-48-10-2 _____

B-48-37-2 _____

B-48-40-2

B-48-52-2 _____

B-48-52-3 _____

_ _ .243

_ .199

_ .232

_ .200

__ .220

.173

.155

.159

.141

.169

.305

.260

.299

.332

.285

1.33

1.30

1.37

1.54

1.30

Flat Bed, light-mineral zone (2 mm) overlying dark-mineral zone

sampled in B-48-10-1 (sta. 18, 0.61 m left of centerline). 

Topset, light-mineral zone (2 mm) underlying dark-mineral zone

sampled in B-48-37-1 (sta. 94, 0.61 m left of centerline). 

Topset, light-mineral zone (2 mm) overlying the dark-mineral

zone sampled in B-48-40-1 (sta. 90, 0.61 m left of centerline). 

Topset, light-mineral zone (2 mm) overlying the dark-mineral zone

sampled in B-48-52-1 (sta. 74, 0.61 m left of centerline). 

Topset, light-mineral zone (2 mm) underlying the dark-mineral

zone sampled in B-48-52-1 (sta. 74, 0.61 m left of centerline).

Average __ .232 .166 .311 1.37

Run 4

B-46-5-2 _ .

B-46-12-2 _ .

B-46-20-2 __ .

B-46-52-1 _ .

B-46-55-1 __ _

._. 0.258

. _ .218

. _ .201

. __ .218

.227

0.167

.162

.134

.152

.136

0.360

.285

.286

.301

QCO

1.47

1.33

1.46

1.40

1

/;Q

Light-mineral zone (2 mm) overlying the dark-mineral zone sampled in B-46-5-1 (sta. 176, on centerline). 

Light-mineral zone (2 mm) overlying the dark-mineral zone sampled in B-46-12-1 (sta. 168, 0.61 m right of centerline). 

Light-density minerals within dark-mineral zone sampled in B-46-

20-2 (sta. 110, on centerline). 

Light-minerals directly overlying and within the dark-mineral zone

sampled in B-46-52-1 (sta. 130, on centerline).

pled (B-46-55-1). Light minerals separating the very thin darkmineral laminations (sta. 155, on centerline).

Average __ .224 .150 .319 1.46

Runs 2-4

Average ____ 0.218 0.154 0.297 1.40

1 Stations along the flume are expressed in feet (0.3048 m) in a downstream direction.

Corey shape factor's relation to other shape factors 

is presented by Tourtelot (1968, p. F4-F7).

Measurements of the shape factor determined for 

the bed-material sample of opaque heavy minerals 

and of light minerals were each based on 60 shape 

factor measurements, 20 measurements on each of 

three grain mount slides.

For identifying the numbers in tables 5 and 6, the 

following criteria should be used:

B - 47 - B - 1 

(1) (2) (3) (4)

1. The "B" refers to a "bed" sample as opposed to 

a "S" for suspended sample (appendix D).

2. The "47" refers to a continuous flume experiment 

series run number. The following numbers are 

the designated run numbers for this study:

45 = Run 1

47 = Run 2

48 = Run 3 

46 = Run 4

3. The "B" used in the example is a selected core 

sample. All letters in the third position designate selected samples, while numbers indicate core samples obtained in the established 

sample network. Numbers and letters used are 

usually consecutive except for "X" used in 

run 2.

4. The "1" in the fourth position designates the 

grain mount number made from the particular core sample.

Examples of horizontal core samples obtained 

from the bed including the cores from which the bed 

sample of light mineral and opaque heavy mineral 

grains were obtained are shown in figure 24. (See 

p. 34.)
K38 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

D. SEDIMENT CONCENTRATION AND SIZE ANALYSES OF 

SUSPENDED-SEDIMENT SAMPLES

TABLE 7. Size analyses and concentration of suspended-sediment samples

Run Location

1 ___ Trough __ __

Brink point _ .

2 _ _ Trough _ _ .

Brink point _ _

Stoss side __ _.

3____ Stoss side _ _.

Flat bed __ _ .

4 _ __ Flat bed _ ___ .

above bed 

(cm)

33.6

18.3 

9.2 

3.1

24.4

18.3 

9.2 

3.1 

18.3

9.2 

3.1

. _ 42.7

30.5 

24.4 

9.2 

36.6

18.3 

12.2 

3.1 

. _ 33.6

21.4 

9.2 

3.1 

33.6

18.3 

9.2 

3.1 

27.5

21.4 

12.2 

7.6 

33.6

21.4 

9.2 

3.1

(mg/l)

122

236 

475 

501 

66

130 

117 

290 

291

234 

343 

458

2304 

1554 

2022 

176

256 

345 

551 

391

513 

569 

763 

59

328 

279 

618 

25

39 

218 

974 

512

940 

2103

6477

dso 

(mm)

0.146

.186 

.172 

.172 

.158

.143 

.148 

.165 

.174

.174 

.177 

.138

.187 

.173 

.186 

.127

.138 

.140 

.145 

.140

.157 

.146 

.150 

.130

.155 

.144 

.146 

.116

.119 

.134 

.172 

.123

.136 

.151 

.183

Size 1

die 

(mm)

0.116

.154 

.132 

.134 

.127

.108 

.116 

.128 

.140

.140 

.146 

.104

.146 

.123 

.128 

.092

.101 

.103 

.110 

.107

.116 

.107 

.120 

.102

.117 

.112 

.115 

.090

.096 

.105 

.133 

.088

.099 

.110 

.133

<fe*

(mm)

0.184

.225 

.215 

.217 

.200

.179 

.187 

.212 

.207

.216 

.224 

.172

.230 

.209 

.244 

.157

.184 

.183 

.184 

.176

.205 

.190 

.188 

.165

.212 

.184 

.184 

.159

.150 

.160 

.220 

.156

.168 

.195 

.226

(<F)

1.26

1.21 

1.28 

1.28 

1.25

1.25 

1.27 

1.29 

1.22

1.24 

1.24 

1.29

1.26 

1.31 

1.38 

1.31

1.35 

1.33 

1.29 

1.28

1.33 

1.33 

1.25 

1.27

1.35 

1.28 

1.26 

1.33

1.25 

1.24 

1.29 

1.33

1.30 

1.33 

1.31

1 Size determined by VA-tube sedimentation analysis.
Sediment Transport in 

Alluvial Channels, 

1966-1972

GEOLOGICAL SURVEY PROFESSIONAL PAPER 562

This volume was published 

as separate chapters A-K
UNITED STATES DEPARTMENT OF THE INTERIOR

ROGERS C. B. MORTON, Secretary

GEOLOGICAL SURVEY

V. E. McKelvey, Director
CONTENTS

[Letters designate the separately published chapters]

(A) Sediment transport in Cache Creek drainage basin in the Coast Ranges west of 

Sacramento, California, by Lawrence K. Lustig and Robert D. Busch.

(B) Flume experiments on the transport of a coarse sand, by Garnett P. Williams.

(C) The behavior of large particles falling in quiescent liquids, by G. E. Stringham, 

D. B. Simons, and H. P. Guy.

(D) Response of a laboratory alluvial channel to changes of hydraulic and sedimenttransport variables, by R. E. Rathbun, H. P. Guy, and E. V. Richardson.

(E) Fluorescent sand as a tracer of fluvial sediment, by Vance C. Kennedy and 

Dorothy L. Kouba.

(F) Statistical properties of dune profiles, by Carl F. Nordin, Jr.

(G) Field measurement of the initiation of large bed particle motion in Blue Creek 

near Klamath, California, by E. J. Helley.

(H) Flume width and water depth effects in sediment-transport experiments, by 

Garnett P. Williams.

(I) Transport and dispersion of fluorescent tracer particles for the flat-bed condition, 

Rio Grande conveyance channel near Bernardo, N. Mex., by R. E. Rathbun, 

V. C. Kennedy, and J. K. Culbertson.

(J) Summary of alluvial-channel data from Rio Grande conveyance channel, New 

Mexico, 1965-69, by J. K. Culbertson, C. H. Scott, and and J. P. Bennett.

(K) An experimental study of heavy mineral segregation under alluvial-flow condiditions, by Lawrence L. Brady and Harvey E. Jobson.

U.S. GOVERNMENT PRINTING OFFICE: 1973 S1S 658/14