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132

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SYNTHESES OF THE SEDIMENT
TRANSPORI‘ENG CHARACTERESTICS OF
ALLUVEAL. CHANNELS

Them: for the Degree of M. S.
I’flCE‘ZIGM STATE ET‘EEE‘EKSKY

Geraid‘ Allen Zernial

1961

TWEQSE

This is to certify that the

thesis entitled

Synthesis of the Sediment
Transporting Characteristics of
Alluvial Channels

presented by

Gerald Allen Zernial

has been accepted towards fulfillment I
of the requirements for . ‘

M S. degree in Civil Engineering

   

Major professor

Date April 21; 1961

0-169

 

LIBRARY

Michigan State
University

 

 

 

_-—u—F-- -

SYNTHESIS OF THE SEDIMENT TRANSPORTING CHARACTERISTICS

OF ALLUVIAL CHANNELS

By

GERALD ALLEN ZERNIAL

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Civil Engineering

1961

ii

ACKNOWLEDGMENTS

The author wishes to express his most sincere thanks and appre-
ciation to Dr. E. M. Laursen whose expert guidance and encouragement
helped to make this study possible; to Mr. H. A. Elleby who so diligently
programmed the relationship for the digital computer; and to the Division
of Engineering Research of Michigan State University that partially

supported the study.

TABLE OF CONTENTS

Section
ACKNOWLEDGMENTS .....................................
I. INTRODUCTION ................................
II. DESCRIPTION OF SECTIONS .....................
Middle Loup River
Fivemile Creek
Rio Grande
III. METHOD OF ANALYSIS .........................
IV. RESULTS OF ANALYSIS .........................
V. DISCUSSION OF RESULTS ........................
VI. CONCLUSION ....................................

BIBLIOGRAPHY ...........................................

iii

10

20

26

45

dm

LIST OF SYMBOLS

mean concentration, percent by weight

diameter of sediment particle (mean diameter of fraction p
of bed material), ft.

mean diameter of bed material, it.

Manning roughness coefficient

fraction of bed material of diameter d

energy gradient, ft. /ft.

mean velocity, q/yo, fps

fall velocity of sediment particle, fps

depth of flow, ft.

critical tractive force for beginning of sediment movement
boundary shear, or tractive force, at stream bed, vyOS

boundary shear associated with sediment particles

iv

Page

ABSTRACT

SYNTHESIS OF THE SEDIMENT TRANSPORTING CHARACTERISTICS

OF ALLUVIAL CHANNE LS

by Gerald Allen Zernial

Using field data obtained by the U. 5. Geological Survey in some of
their special studies the variability of the relationship between sediment
load and stream discharge has been investigated.

A relationship proposed earlier by Dr. E. M. Laursen, which was
programmed for a digital computer, was used for computing the sediment
load curves. The sediment load as computed for a given discharge was
affected by the velocity and depth of flow, by the water temperature, and
by the size distribution of the bed material.

It was found that for a given discharge the spread normally obtained
in the sediment load can more than adequately be explained by the meas-
ured variations that occur in (1) water temperature, (2) flow characteris-

tics of unstable sections, and (3) size distribution of the bed material.

I. INTRODUCTION

Sediment loads transported by alluvial streams are determined by
many factors. In a sense the stream is formed by the hydrologic and
physical characteristics of the basin--present and past. On the other
hand, the physiography of the basin has been formed in large measure
by the activity of the stream. Thus, rainfall in its variation from day
to day and year to year, soil and rock characteristics, culture, basin
size, shape and slope, and stream characteristics are all interrelated
in their effect on the sediment load carried by the stream. The complex-
ity of the problem is reduced, however, if it is realized that at a stable
cross section, for every discharge there exists a velocity, slope, depth,
and, providing the bed material is unchanged, a sediment-transporting
capacity. This permits the separation of the runoff characteristics of
the stream from the sediment-transporting characteristics. At a stable
section, in which the bed material and temperature are the same at all
discharges, the sediment load should be a single-valued function of the
discharge. For most streams this is not true-~measured sediment
loads when plotted against discharge form a band, not a single curve.
Possible explanations of this variability of sediment load lie in temper-
ature which affects particularly the fall velocity of the particles, and in
the surface runoff from the various storms. Not only does the surface
runoff deliver water to the stream, but also a sediment load of fine

material picked up from the soil mantle. This added fine material entering

2
from surface runoff is mixed with the natural bed material, thus changing
the bed material characteristics. It is not unreasonable that for a given
flow condition, a change in bed material could change the sediment-
transporting capacity of the stream markedly.

If the probable yearly sediment load carried by an alluvial stream
is to be predicted with a dependable and a reasonable degree of accuracy,
three relatively independent factors must be taken into consideration:

1. The sediment-transporting characteristics of the stream for its
natural bed material as determined by velocity, depth, width, slope
and temperature at various discharges.

2. The changes occurring in bed material due to sediment delivered to
the stream by surface runoff.

3. The hydrologic characteristics of the basin, which determine the

probable yearly discharge variations.

The portion of the problem considered in this study is to determine
whether the multiple-valued function of sediment load and discharge found
in field data can be explained by the effects of the variations that can be
expected in the flow, fluid, and sediment characteristics. Field data used
in this study were obtained from USGS Water Supply Papers and personal

correspondence.

II. DESCRIPTION OF SECTIONS

Middle Loup Rive r

 

The major portion of the Middle Loup River, upstream from
Dunning, Nebraska, which was investigated by the USGS from 1948 to
1952 (1), traverses the sandhill region of north-central Nebraska. The
drainage area of the reach considered is approximately 1760 square miles,
only 80 square miles of which contribute directly to surface runoff. Be-
cause of the sandy mantle flow is derived from groundwater accretion,
varying from about 200 to 600 cubic feet per second. For approximately
1500 feet upstream from the turbulence flume, located at Dunning, Nebraska,
the channel is straight with a uniform or nearly constant cross section.
Although meanders were not well developed, bank erosion was prevalent
and the source of most of the sediment load. The topography of the basin
was formed by sand dunes and stabilized by sparse trees, brush and grass
cover, with the valley floor composed of sand deposited by the stream and
topped in some places with a thin layer of soil. The banks of the Middle
Loup River through Dunning, Nebraska have been artificially stabilized
with trees, brush, and grass.

Investigation of the Middle Loup River by the USGS included six
selected river sections and the turbulence flume. However, due to the
extreme non-uniformity of some sections, only sections C and C2 were
considered and included herein.

At section C, the upstream side of the turbulence flume which was

located at section D, suspended sediment and flow measurements were

4

made in order to define the sediment load and discharge entering the flume.
It was anticipated that the difference in suspended and total load at section
C and D would be representative of the unmeasured sediment of an average
reach. This, however, proved invalid since section C was not representa-
tive of normal sections. A permanent water stage recorder and a contin-
uous water- and air-temperature recorder were housed about 15 feet up-
stream. Three staff gages, one outside the recorder and one at section C
and one at section D, were used to establish the slope through the flume.
Measurements at section C were made from a walkway which spanned the
stream.

Section C2, about 600 feet upstream from the entrance of the turbu-
lence flume, produced a greater depth and sediment concentration in the
left one-half of the channel, with stream velocity remaining fairly uniform
across the section. The slope was determined by staff gages located 300

feet up and downstream from the section.

Fivemile Creek

 

Fivemile Creek (2, 3), a tributary in the Wind River drainage basin
in west-central Wyoming, rises in the vicinity of Circle Ridge anticline
northwest of Pavillion, Wyoming and joins the Wind River near Riverton,
Wyoming. Numerous tributaries join the Wind River, which discharges
through Thermopolis, Wyoming, where the name is changed to the Bighorn
River. Quantitative analysis of the sediment transported by the Bighorn
River at Thermopolis, prior to the construction of Boyson Reservoir,

showed that Fivemile Creek contributed approximately 7 percent of the

total average water discharge and approximately 57 percent of the total
average sediment discharge.

The drainage basin of Fivemile Creek is long and narrow with the
floor of the basin characterized by sparse semi-arid vegetation and soils
composed of water-deposited silts, clay, and gravel. The headwaters of
Fivemile Creek do not reach the Owl Creek mountains, and thus flow
resulting from snow-melt is usually small. During the summer, storms
occasionally produce stream flow at the gaging station near Pavillion,
where much of the year there is no flow. Tributary inflow downstream
from the gaging station at Pavillion would be very low were it not for the
waste water resulting from irrigation. Not only does the returning waste
water contribute to the stream flow, but it also carries sediment. However,
even without irrigation, the sediment discharge near the mouth of Five-
mile Creek probably would be greater than at the station near Pavillion
since stream characteristics are such that a larger load can be carried--
thus picking up material from the bed and banks of the channel.

Fivemile Creek flows with an average slope of 32 feet per mile with
severe bank erosion prevalent in the lower 25 miles of its course where
the gradient is 23 feet per mile. During the years 1949 to 1950, it was
estimated by the USGS that 87 percent of the total sediment discharge came
from the bed and banks of the stream.

Three sediment and streamflow stations were maintained on Fivemile
Creek for 3 or 4 years before October 1, 1952. During the 1949 water year,

the station near Pavillion was downstream from the Bureau of Reclamation's

6

Wyoming Canal. However, in the latter part of 1949, it was moved a short
distance upstream from the canal. Another sediment station is near River-
ton and is about 3 miles downstream from the mouth of Ocean drain. Much
of the sediment at this section was forced into suspension by the flow in a
natural contracted section. The third sediment station is near Shoshoni and
is about two and one-half miles upstream from the mouth of Fivemile Creek.
The sediment at the Shoshoni station was forced into suspension by an arti-
ficial contraction. Sediment measurements made at Riverton and Shoshoni
sections were considered by the USGS to be nearly total loads. On four days
during 1951, sediment concentration measurements were made at the same
time at a normal section about three-eighths of a mile upstream from the
gaging station and at the daily sampling section, which is also the contracted
section. Ratios of total load as indicated at the contracted section to
measured suspended-sediment discharge at the upstream normal section
ranged from 1. O7 to l. 44, or an average of l. 31 for the four days. Similar
measurements for the contracted section near Shoshoni for 2 days of
August of 1953 yielded ratios of l. 43 to 1. 56 when compared with a normal
section 400 to 500 feet upstream.

Due to insufficient data for some of the sections, only the Riverton

and Shoshoni sections were considered in this study.

Rio Grande

 

The Rio Grande watershed is located in the southwest United States
and northeast Mexico (4, 5). The total area within the outer limits is

335, 000 square miles. A large part of this is in closed basins with only

171, 900 square miles contributing runoff to the Rio Grande. Meanders of
the wide, shallow, silt-laden river are well-defined on the flat valley floor.
While flow of the stream is often nil, the river, with its main source in
barren, rocky mountain slopes, has the potential to flood the valley in a
matter of hours. Frequently referred to as "The Dirtiest River in the
World, " the river is raising its own bed at a rate of approximately four
inches per year.

The mantle of the region consists of sand, rock, and wind-blown
deposits. These arid conditions result in sparse vegetation on the basin
floor and upper valley slopes. Small tributaries flowing in an east-west
direction frequent the basin floor, many having no natural course.

Stream measurements used in this investigation were taken at
Bernalillo, New Mexico (6). The station is located two miles northwest
of Sandia Pueblo, three miles southwest of Bernalillo, three and a half
miles from State Highway 44, and eight and a half miles downstream from
the Jemez River. Bed material characteristics were obtained from a
study, which included the Bernalillo station, conducted by Vanoni and
Brooks (7).

The drainage area contributing to Bernalillo station is approximately
17, 300 square miles. This includes 2, 940 miles of closed basin in the

San Luis Valley in Colorado.

III. METHOD OF ANALYSIS

Field sites from which data were obtained included the Middle Loup
River in Nebraska, the Wind River basin in Wyoming, and the Rio Grande
in New Mexico. Data for the Middle Loup and a portion of the data for
Fivemile Creek were obtained from the pertinent USGS Water Supply Papers.
Supplementary material for Fivemile Creek as well as all data for the Rio
Grande were obtained from offices of the USGS (2, 3). Even though the
USGS and the Bureau of Reclamation have been making special studies in
the Rio Grande basin, published data are not presently available. Additional
data for the Rio Grande were obtained from a study carried on at the Cali-
fornia Institute of Technology (7).

For computing the sediment load, a relationship proposed by Laursen

(8) was used:

/6 VTO/p

(T ,/T - 1) f(
O C

 

E = 2p<d/y0)7 )

W

where E is the mean sediment concentration by weight, yO the depth of flow,

Via—p
W

 

p the fraction of bed material of size d, and the function f( ) is pre-

sented in Fig. 1. Due to the difficulty in expressing the function as a poly-
nomial, the relationship was programmed for the MISTIC, a digital computer,

T /P
using straight line segments for the functional value. Since values of-V o” ,

 

 

the shear-velocity/fall-velocity ratio, encountered in this study were less
than 100, error resulting from the major deviation of the last line segment
for the original functional value was not encountered. The program for the
relationship was designed for suspended load only by subtracting the bed-

load from the total-load function.

9
Temperature effects on the fall velocity of a particle in suspension
are known and can be predicted within reasonable limits. However, the
effects of temperature--if there are any--on the critical tractive force TC
and the particle shear T0! are unknown and were not considered. The
critical tractive force can be written as TC = Cd where C is a coefficient,

assumed to be 4. O in this study, depending on flow conditions near the

for the

boundary and the sediment characteristics. The expression To',
fraction of the total shear, which contributes to the actual movement, was
obtained by the use of the Manning equation and Strickler's evaluation of n
as a function of the sediment diameter.

2 1/3

vdm

709—173

30 yo

These evaluations of TC and T0! are in accord with the development of the
original relationship.

To determine the relative effect of the variations in water tempera-
ture, depth of flow (since the sections were unstable), and bed material on
the sediment-transportation rate, computations were performed using
these as principle variables for each section. Approximate maximum,
minimum, and mean values for the depth of flow, for the water tempera-
ture, and for the size distribution of bed material were determined from
measured values. To determine the effect of variation of one of these
factors, mean values of the remaining two factors were used. A mean

measured value of slope was used throughout because so few measurements

of slope were available.

10

IV. RESULTS OF ANALYSIS

The characteristics of the Middle Loup basin are such that almost
no fine material is added. However, the data from this stream have been
used to test the relationship and to assess the effects of instability as
shown in Figs. 2 and 3, where the mean velocity is plotted against dis-
charge. The numbers are actual measured depths with the decimal point
the plotted point, and the lines are theoretical depths based on a mean
width of 82 feet. As shown in Fig. 2, for a discharge of 380 cubic feet
per second at section C, the velocity varies from 2. 4 to 2. 8 feet per
second with corresponding depth of flow values of 1. 84 and 1. 72 feet.
Similarly in Fig. 3, section C2, for a discharge of 410 cubic feet per
second the velocity varies from 2. 4 to 3. 2 feet per second with corre-
sponding depth values of 1. 96 and 1. 55 feet. The instability resulting
from depth and velocity variations at the sections is readily apparent,
since for a measured discharge various depth and velocity combinations
existed.

Fig. 4 shows a comparison between stream discharge and suspended
sediment discharge for section C, with plotted points as actual measured
values and theoretical lines for maximum, minimum and mean values of
water temperature in the upper graph and of depth of flow in the lower
graph. For a discharge of 400 cubic feet per second, the sediment load
is increased fivefold by decreasing the depth of flow from 2. 0 to 1. 5 feet

and tenfold by decreasing the depth of flow from 2. O to 1. 0 feet. Theoretical

11
lines obtained from the various depths of flow encountered are approxi-
mately parallel and equally spaced with the majority of the measured
values lying between the curves for assumed constant depths of 1. 5 and
2. 0 feet. It is interesting to note that in Fig. 2, where the velocity at
section C is plotted against discharge, the majority of the measured
values fall between the l. 5 and 2. O depth lines, and that the actual meas-
ured depths of flow also lie between 1. 5 and 2. 0 feet.

The effect of variations in water temperature on the sediment load
was not as large as it was for the variations in depth, and did not produce
a set of curves sufficient to enclose the measured values. For the maxi-
mum range of water temperatures considered-~70 to 32 degrees--the
sediment load was increased about 3. 5 times for a decrease in temperature
from 70 to 32 degrees. The theoretical lines for temperature variations
are approximately parallel, but are not equally spaced. The effects
resulting from a decrease in the temperature from 70 to 50 degrees are
approximately one-third as large as those for a temperature decrease from
70 to 32 degrees.

In Fig. 5 the same analysis was made as in Fig. 4, only this time
the factors were taken into consideration at section C2 rather than section
C. At section C2 the variations in depth of flow were sufficient to band the
measured values, and for a discharge of 600 cubic feet per second, the
decrease in depth of flow from 2. O to l. 0 feet produced a sixfold increase
in the sediment load. All of the measured values fall between a discharge

of 350 and 600 cubic feet per second with the majority of the plotted points

12
lying between the 1. 5 and 2. 0 depth lines. Again the theoretical lines for
various depths of flow were approximately parallel and equally spaced.

Temperature effects at section C were such that for a discharge of 600

2
cubic feet per second, a decrease in the water temperature from 70 to 32
degrees resulted in a 3. 5 fold increase in the sediment load, with a 1. 5

fold increase being attributed to the decrease in water temperature from

70 to 50 degrees. The bands resulting from water temperature variations
are adequate to enclose approximately 90 percent of the measured values
with the remaining 10 percent being located in the immediate vicinity of

the lines.

Similarly, in Fig. 6 a comparison is shown between stream discharge
and suspended sediment discharge for section C and C2 to determine the
effect the characteristics of the bed material have on the transporting rate
of the stream. At section C the computed sediment load was increased two-
fold by decreasing the maximum size distribution of bed material (mean
particle diameter of O. 45 mm) to the minimum size distribution of the bed
material (mean particle diameter of O. 28 mm). Thus, with approximately
50 percent of the measured values falling between the bands, the spread of
the band was insufficient. At section C2 the increased sediment load,
resulting from decreasing the size distribution of the bed material from
its maximum size (mean particle diameter of O. 73 mm), to its minimum
size (mean particle diameter of O. 33 mm) resulted in a band sufficient to

enclose the measured values. For a discharge of 400 cubic feet per second,

the computed sediment load was increased by a multiple of 10 by decreasing

13
the size distribution of the bed material from its maximum value to its
minimum value. Variations in the increased sediment load resulting
from size distribution of the bed material of section C and C2 are not
unreasonable, since for section C, the variation in maximum and minimum
size distribution of bed material, especially the finer material, is not as
well pronounced as is the case in section C2 (see Fig. 7). The greater
deviations experienced in the larger particle range for section C contribute
little to increasing the spread of the theoretical lines.

At the stations on Fivemile Creek, the same three factors--section
instability and temperature, and bed material variability--contribute to
the spread of the sediment load-discharge relation. However, the data
were handled in a slightly different manner than for the Middle Loup
River. Due to the instability of the section, as shown in Fig. 8, where
stream discharge is plotted against depth of flow, an arbitrary mean line
was drawn for the depth and two other lines were drawn to band the
measured values. The measured values were such that for a discharge
of 100 cubic feet per second the gaging station near Shoshoni showed depth
values from O. 65 to 1. 0 feet while at the Riverton station values of O. 8 to
1. 0 feet were obtained.

In the same figure, where stream discharge is plotted against width
for the stations near Riverton and Shoshoni, an arbitrary mean width line
was drawn through the approximate center of the measured values. For a
discharge range from 20 to 400 cubic feet per second, the width varied

from approximately 35 to 60 feet for Shoshoni and from 38 to 55 feet for

14
Riverton. The Riverton section appears to be more stable than the Shoe
shoni section since the measured values of depth and width at Riverton have
less scatter than the Shoshoni section. The maximum and minimum
velocities used in the computations were obtained by dividing the discharge
by the area, which was taken equal to the mean width times the maximum
or minimum depth of flow.

Shown in Fig. 9 is a comparison between stream discharge and
suspended sediment load for the station near Shoshoni, with points of
actual measured values. The theoretical lines for maximum and minimum
bed material were obtained by combining the respective bed material, Fig.
11, with the mean water temperature, 58 degrees, and the mean velocity
of flow, and are shown by the dark, solid continuous lines. For each
grain size distribution--that is, the maximum and minimum--the range
of water temperature, 32 to 78 degrees, was combined with a mean velocity,
resulting in two pairs of curves, and the velocity range was combined with
the mean temperature, also producing two pairs of curves. The effects of
the water temperature and velocity range for each size bed material are
shown by the cross-hatched bands between the dashed lines. Effects of the.
variations in the grain size distribution of the bed material alone were
nearly adequate to band the measured values. By decreasing the size
distribution of the bed material from the maximum size (mean particle
diameter of 0. 50 mm) to the minimum size (mean particle diameter of 0.28
mm) the computed sediment load was increased approximately tenfold--

that is, from 300 to 3000 tons per day for a discharge of 100 cubic feet per

15
second. For the minimum size bed material, the effects of variation in
the water temperature changed the sediment load by a factor of 2. 5, where
a change in the sediment load by a factor of 3. 5 was obtained by varying
the velocity of flow. Similarly, for the maximum size bed material, the
variation in water temperature changed the sediment load by a factor of
3, with variations in the velocity resulting in a factor of 4.

In Fig. 10 is shown the same comparison as is shown in Fig. 9, but
with consideration being given to the gaging station near Riverton. For a
discharge of 100 cubic feet per second, a decrease in the size distribution
of the bed material--from its maximum size (mean particle diameter of
0. 38 mm) to its minimum size (mean particle diameter of 0. 22 mm)--
resulted in a 7. 5 fold increase in the sediment load. Variations in the
water temperature and velocity of flow encountered at this section were
such that the respective sediment load was changed by factors of 4 and 2
for the maximum size bed material, and of 3 and 2 for the minimum size
material. Maximum, mean and minimum temperature values of 77, 61,
and 32 degrees were used to assess the effects of temperature at this
section.

From the results obtained in Figs. 9 and 10, it is apparent that if
conditions resulting in maximum and minimum sediment-transport were
assumed, by combining the appropriate depth, temperature, and grain
size distribution of bed material, there would be no question as to the
computed bands enclosing the measured values. In actual stream flow,

any combination of velocity, temperature of water, and size distribution

16
of bed material is possible; however, the probability of occurrence of
these maximum or minimum transporting conditions is unknown.

In Fig. 11 is shown the grain size frequency distribution curves for
Fivemile Creek near Shoshoni and Riverton, Wyoming. Distributions of
the particle size as well as deviations for both sections are very nearly
the same, since the mean particle diameters for maximum and minimum
bed material were 0. 5 mm and 0. 28 mm near Shoshoni, and 0. 38 mm and
0. 22 mm for the station near Riverton.

Data from the Rio Grande were included in this study to determine
the value of the relationship for computing sediment loads for a stream
carrying an exceptionally large sediment load. Characteristics of the
basin are such that a large quantity of sediment is brought into the stream
from the mantle by waste water from irrigation projects and by surface
runoff.

Fig. 12 shows a comparison between stream discharge and depth of
flow, with plotted points the actual measured values. The parallel lines
which band the measured values were computed using maximum and
minimum n values of 0. 033 and 0. 015 in the Manning formula. The center
or lazy S curve was arbitrarily drawn through the measured values.

It is interesting to note that the majority of the measured values fell
between the parallel lines. The lines are so spaced that for a discharge of
500 cubic feet per second, a maximum and a minimum depth of flow of 4. 7
and 3. 0 are possible. Since the width for the section was nearly constant,

the velocity of flow could easily be obtained by considering the variation in

l7
depth with stream discharges, which is represented by the lazy S curve.
Shown also in Fig. 12 is the size frequency distribution of the bed

material for the section. The only values obtainable (7) were for (1 nd

35a

d65; therefore a straight line relation on log probability paper was assumed.
Mean particle diameters resulting from the straight line approximation

for the maximum and minimum bed material were 0. 40 mm and 0. 23 mm
respectively.

Fig. 13 shows a comparison between stream discharge and suspended
sediment load, with plotted points the actual measured values. The dark,
solid continuous lines were computed from the straight line approximation
of maximum and minimum size bed material with water temperature and
depth of flow bands similar to those used in the Riverton and Shoshoni
sections of Fivemile Creek. Maximum, mean and minimum temperature
values of 75, 65, and 57 degrees were used at this section. For a discharge
of 10, 000 cubic feet per second, the sediment load was increased sixfold
by considering the decrease in the size distribution of the bed material.

The effects of water temperature and velocity on the sediment load for
minimum and maximum bed material were not as large as they were at

the Riverton and Shoshoni sections of Fivemile Creek. Variations in the
water temperature and velocity changed the sediment load by a factor of

1. 8 for both the minimum and maximum size bed material. The spread
obtained in the sediment load curves computed from maximum and minimum

size bed material would enclose the measured values if shifted. The

apparent shift that exists for the set of curves can be partially explained

18
by the straight line approximation that was made for the size distribution
of the bed material. If finer material than was accounted for in the
straight line approximation was present, the resulting computed sediment
load curves would be shifted.

Figs. 14 and 15 show a comparison between the composition of the
predicted suspended sediment and measured suspended sediment for sec-
tions C and C2 of the Middle Loup River, and the Riverton and Shoshoni
sections of Fivemile Creek. The predicted suspended sediment is a mean
value which was obtained by averaging the suspended sediment values
calculated from concentrations for a specific size bed material.

The predicted suspended sediment for section C2 resulted in a set
of curves that formed a band about the measured values. The measured
suspended composition curve is approximately equally spaced between
the set of predicted composition curves. Mean particle diameters of
0. 24 mm and 0. 08 mm for the maximum and minimum size bed material
were obtained for the predicted composition, and 0. 15 mm for the meas-
ured composition.

The predicted suspended sediment and the measured suspended
sediment for section C are nearly the same with a mean particle diameter
of approximately 0. 18 mm for the measured.

Measured suspended sediment values for the Shoshoni section agreed
quite well with the predicted suspended sediment. For the predicted sus—
pended sediment a mean particle diameter of approximately 0. 06 mm was

obtained for both the maximum and minimum size bed material as compared

19
with 0. 07 mm for the measured suspended sediment. It was noted that
the measured sediment tended to deviate from the predicted in the smaller
particle range. However, for the range that could be predicted the agree-
ment is good.

For the larger particle sizes at the Riverton section the predicted
composition curves are nearly the same for the two assumed bed compo-
sition, but tend to deviate for the smaller particle sizes. It is interesting
to note that the measured composition curve is representative of a well-
graded material, which is not normally the case for river sediment loads.
The Shoshoni measured suspended load appears to be less uniformly dis-

tributed and the Middle Loup sections are even more as would be expected.

20

V. DISCUSSION OF RESULTS

For a given discharge the spread that normally exists for the sedi-
ment load can be explained by the variation in depth of flow which exists
at an unstable section, changes that occur in the temperature of the water,
and variations in the size distribution of the bed material. From the
results of this study, the combined effects resulting from variations in
these factors would be more than adequate to explain the spread. In table
A is shown the approximate effects that a change in the depth of flow,
temperature of the water and size distribution of the bed material have
on the parameters contained within the relationship along with the total
change in the sediment load obtained from the curves. The approximate
change for the individual parameters was obtained from key values.

In part 1 of table A is shown the effect that a variation in the depth
of flow has on the parameters, and thus the total change in the sediment
load. The percent change in depth of flow shown for each section is an
approximate value that was obtained from the velocity, depth of flow, and
discharge curves. For section C of the Middle Loup River a 10% increase
in the depth of flow resulted in a 35% decrease in the sediment load,whereas
for section C2 of the Middle Loup River and for the Shoshoni and Riverton
stations on Fivemile Creek, and the Bernalillo station on the Rio Grande
24%, 55%, 27%, and 20% increases in the depth of flow resulted in decreases
of 50%, 66%, 50%, and 30% in the sediment load. Thus, the ratios of the
change in sediment to the change in depth of flow of 3. 5 and 1. 2 were

obtained. Such variations at first seem strange, but can be explained by

21
considering the effects that a change in the depth of flow has on the various
parameters of the relationship. For example, at section C of the Middle

Loup River, if a 10% increase in the depth of flow is introduced in the

/6

7
parameter (d/yo) , the numerical value of the parameter is decreased

by 12%. Thus, the change in the parameter resulting from a change in the
depth of flow would simply be the inverse of the change raised to a power

of 7/6. For sections C and C2 of the Middle Loup River, the Shoshoni and

Riverton stations of Fivemile Creek and the Bernalillo station on the Rio

Grande, numerical values of 12%, 22%, 40%, 24%, and 19% were obtained
7

from the (d/yo) /6 parameter.

The effect of a change in the depth of flow on the parameter cannot
'r
I
be as easily obtained. Rewriting the parameter (--0— - 1), one obtains
2dm1/3 Tc
3 773 - 1 where the depth of flow enters to the 7/3 power. To fully
d

 

120 yO

assess the effects of the entire parameter, numerical values have to be
T 1
introduced for the ratio 79-, with consideration being given to the change
c 'r
in depth of flow. It is apparent that the closer the ratio

 

approaches
c

unity, the greater will be the influence of a change in the depth of flow.
1'

The ratio 0
1.

c
rial from which the minimum change of the parameter can be expected.

T l

I
will have its maximum value for the smallest 5% of the mate-

 

 

For the larger particles, the ratio of is smaller, giving the max-
c

imum change in the parameter--a1though this may not be fully reflected

in the sediment load.
T I

 

In computing the approximate change in the parameter ( f - 1)
c

an average mean particle diameter was used. Approximate numerical

22

values of 25%, 55%, 70%, 25%, and 34% were obtained for changes in the
parameter for sections C and C2 of the Middle Loup River, the Shoshoni
and Riverton station on Fivemile Creek, and the Bernalillo station on the
Rio Grande.

The functional value is determined from the shear-velocity/fall-

. . To/ P . . ngos
veloc1ty ratio, —, which may be rewritten as
w

 

The change in
the shear-velocity/fall-velocity ratio, resulting from a change in the depth
of flow, can be defined by a simple relation. However, the change in
functional value resulting from a change in the depth of flow is dependent
upon the segment of the curve from which functional values are obtained.
The maximum and minimum slopes of the function curve are 2. 22 and 0.25,
so the change in the functional value resulting from a change in the depth
of flow is related approximately to the 1. 11 and 0. 125 power of the depth.
For the sections. considered in this study, approximate numerical values
of 12%, 22%, 55%, 29%, and 21% were obtained for changes in the func-
tional parameter.

It is thus clearly evident that the change in sediment load resulting
from a change in the depth of flow cannot be defined by a simple ratio.
Indeed, the variations obtained in the ratio of the sediment load to the
depth of flow are to be expected.

It is noteworthy that, for the sections considered, the changes in
the numerical values resulting from a change in the depth of flow intro-

/6 VTo/P

duced in the parameters (Til-)7 and f(-—W—-) tended to cancel each other,
0

and, thus, the resulting change in the sediment load could be attributed

23
largely to the effect that a change in the depth of flow has on the parameter
(:3:— - 1).

c

Shown in the second part of table is the effect that a variation in water

temperature has on the sediment load transported by the streams at the
various sections considered in this study. The only part of the relation-
ship where water temperature enters, is in the parameter for the shear-
velocity/fall-velocity ratio from which the functional value is obtained. For
a specific size particle, a decrease in the temperature would result in a
decrease in the fall velocity. At the Shoshoni, Riverton and Bernalillo
sections, maximum and minimum water temperature were combined with
the maximum and minimum grain size distribution of the bed material.
Therefore, at these sections for a decrease in water temperature, there
corresponds a decrease in the fall velocity for the maximum and minimum
size bed material. Since the sediment load transported by a stream is
composed mostly of the finer material, with the larger particle sizes con-
tributing little to the stream's load, the change in fall velocities resulting
from the decrease in water temperature can be approximated from the
smallest 5% of the bed material. The change in functional value resulting
from a change in the fall velocity is similar to that discussed previously--
that is, the change in the functional value is dependent on the segment of
the curve from which the change is being considered. Therefore, the
change in sediment load resulting from a change in the temperature of

the water cannot be expressed as a simple ratio. For the change in water

temperature that was considered at each section, numerical values of 236%,

24

190%, 230%, 110%, 294%, 135%, 52%, and 88% were obtained for the changes
in the parameter. I

The data from a study conducted on the Colorado River (9), where
the approximate seasonal variation in the water temperature is from 50 to
87 degrees, indicated that a much larger sediment load is carried by the
river during the winter than during the summer with approximately the same
flow. It was noted that for a given discharge the load may be as much as
2. 5 times as great in the winter as in the summer. The effect of water
temperature noted in this study is of this order of magnitude.

In the third part of table A is shown the effect that a decrease in the
size distribution of the bed material can have on the various parameters
of the relationship as well as the resulting increased sediment load. The
change in the size of the smallest 5% of the bed material was used in com-
puting the approximate numerical values for the individual parameters.
For a decrease in the particle size with constant temperature the fall
velocity of the particle is decreased. Therefore, by decreasing the parti-
cle size two factors must be considered as contributions to the change in
the sediment load. Analyses similar to those previously discussed may
be used to determine the numerical values for the individual parameters
when a change occurs in one of the variables contained in the parameter.
For the sections considered in this study a change in the bed material from
its maximum to its minimum size resulted in the sediment loads being
increased by 100%, 900%, 1100%, 510%, and 600%, with the larger por-

tion of the change being attributed to the change in the function of the shear-

25
velocity/fall-velocity ratio. It is thus apparent that the change in sediment
load resulting from a change in the size distribution of the bed material
cannot be defined by a simple ratio.

Measurements taken at the contracted sections on Fivemile Creek
near Shoshoni and Riverton were assumed by the USGS to be total loads.
However, due to the programming of the relationship, computations were
performed assuming the measured values to be the suspended load only.
Anslysis of the computations for these sections show the functional values
to be in the range of 500 to 10, 000 for approximately 80% of the finer por-
tion of bed material. Therefore, subtraction of the bed load functional
values, which lie in the range from 20 to 30, would have little effect on the
computed concentrations. Thus, the error induced in this range for func-
tional values would be no larger and perhaps less than the error that
exists in considering the width of the line representing the curve. However,
for smaller discharges and lower shear-velocity/fall-velocity ratios, the

error introduced in ignoring the bed load is considerably larger.

26

CONC LUSION

From the results of this study, it is apparent that the relationship
used for computing the sediment load transported by a stream is adequate,
and that for a given discharge the spread normally obtained in the sediment
load can more than adequately be explained by the effects of instability of
sections, changes that occur in the water temperature, and changes in
size distribution of the bed material.

Analyses similar to those included in this study may be used to pre-
dict the sediment load transported by a stream provided sufficient infor—
mation can be obtained concerning the flow and bed characteristics along
with the water temperature. Any stable stream that has been gaged for a
reasonable period of time should have sufficient information concerning
the hydraulic factors needed for the prediction of the sediment load. For
an unstable stream, depth-discharge measurement would have to be made
for a reasonable period of time to determine the ranges in depths that can
be expected for various discharges. Information obtained from the depth-
discharge measurements can then be used to plot stability curves similar
to those presented in this study and thus obtain the hydraulic factors
needed for the prediction of the sediment load. Variations in water tem-
perature that can be expected for a stream can be reasonably approximated
if consideration is given to the geographical location of the stream along
with the season of the year and the source of the stream flow. The size

distribution of the bed material, and if the bed material is changing, the

27
variations in the size distribution can only be obtained by periodical
measurements. If the factors discussed above are at hand, can be ob—
tained, or can be reasonably approximated, the range in sediment load
that can be expected for a given discharge can easily be predicted with
fair confidence. Since the use of such a relationship is usually in pre-
dicting the behavior of the stream over a period of time, the inability
to specify the conditions--and, therefore, the load--of a particular flood

tends to be averaged out.

28
TABLE A

Effects of Channel Instability

 

 

 

 

 

 

Measured Approximate effects on Change
Stream - section increase 7/6 T -\/?/_p Total obtained
, (d/y ) o' 0 effects from
in y o —— - 1 f(
o c w curves
Middle Loup River
Section C 1070 -1270 - 25% +12% -25% - 3570
Middle Loup River
Section C2 24% -22% -55% +22% -55% -50%
Fivemile Creek
Shoshoni 55% -40°/o -7070 +55% -65% -66%
Fivemile Creek
Riverton 27% -Z4% -55% +29% -50% -50%
Rio Grande
Barnalillo 20% -19% - 34% +21% - 31% - 30%
Effects of Temperature Variations
Measured fiesulting 1' /p Chiming:
Stream - section increase in ecrease f( O O aine
in fall W from
temperature ,
veloc1ty (w) curves
Middle Loup River
Section C 54% 42% 236% 233%
Middle Loup River 38% 190% 191%
Section C2 54% max size 43% 230% 225%
Fivemile Creek min size 50% 110% 153%
Shoshoni 59% max size 46% 294% 287%
Fivemile Creek min size 55% 135% 185%
Riverton 58% max size 17% 51% 55%
Rio Grande
Bernalillo 24% min size 25% 88% 80%

 

Effects of Bed Material Variations

29

 

 

Resulting ‘r 1' /p Change
, Decrease 7/6 0' 0 Total obtained
Stream - section in d decrease (d/yo) ( "r - l) f(—v-v——) effects from
in w c
(5%) curves
Middle Loup River
Section C 1370 2470 +1370 -13a/o +84%) +8 4070 10070
Middle Loup River
Section C2 49% 68% +59% -30% +1160% +1189% 900%
Fivemile Creek
Shoshoni 49% 71% +59% - 29% +1400% +1430% 1.100%
Fivemile Creek
Riverton 33% 52% +59% - 23% +415% +431% 510%
Rio vGrande
+525% 600%

Bernalillo 49% 65% +59% - 24% +49 0%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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BIBLIOGRAPHY

Hubbell, D. W., and Matejka, D. (2., "Investigation of Sediment
Transportation Middle Loup River at Dunning, Nebraska, U. S.
Geo. Survey Water Supply Paper 1476, 1959.

Colby, B. R., Hembree, C. H., and Rainwater, F. H., ”Sedimen-
tation and Chemical Quality of Surface Waters in the Wind River
Basin, Wyoming, " U. S. Geo. Survey Water Supply Paper 1373,

19 56.

Correspondence, T. F. Hanly, District Engineer, U. S. Geo. Survey,
Worland, Wyoming, August 23, 1960.

Williams, Albert N. , Rivers of the West, Duell, Sloan and Peane,
New York, 1951.

 

Secretary of the Army, letter on "Rio Grande and Tributaries,
Albuquerque, New Mexico, and Vicinity, " Committee on Public
Works, June 6, 1954.

Correspondence, J. Culbertson, District Engineer, U. S. Geo.
Survey, Albuquerque, New Mexico.

Vanoni, V. A. , and Brooks, N. H. , "Laboratory Studies of the
Roughness and Suspended Load of Alluvial Streams, " California
Institute of Technology, Pasadena, California, Report No. E-68,

1957, page 59.

Laursen, E. M. , "The Total Sediment Load of Streams, " Journal
of the Hydraulics Division, ASCE, No. HYl, February, 1958.

 

Lane, E. W., Carlson, E. J., and Hanson, O. 5., "Low Temper-
ature Increases Sediment Transportation in Colorado River, " Civil

Engineering, September, 1949.

on?

 

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