WIND EROSION:
THRESHOLD VELOCITY FOR
INITIAL PARTICLE MOVEMENT
by
Y0N6LIAN6 TIAN, B. Engr.
A THESIS
IN
A6RICULTURAL EN6INEERIN6
Submitted to the Graduate Faculty
of Texas Tech University in
Partial Fulfillment of
the Requirements for
the Degree of
MASTER OF SCIENCE
IN
AGRICULTURAL ENGINEERIN6
Approved
Accepted
May, 1988
2 'i
ACKNOWLEDGEMENTS
I wish to express my sincere gratitude to Dr. John Borrelli for
the opportunity to study under his scholarly ^idance, and for serving
as chairmam of my committee. My special appreciation is due to Dr.
James M. Gregory and Dr. R. Heyward Ramsey for serving as merabers of my
committee, and for their infinite patience, guidance, and assistance
during my studies.
I also thank Mr. James Snyder, Jr. for his expert technical advice
and assistance in my wind tunnel tests.
11
TABLE OF CONTENTS
ACNKNOWLEDGEMENTS
ii
LIST OF TABLES
v
LIST OF FIGURES
vii
LIST OF SYMBOLS
ix
CHAPTER
I.
II.
III.
INTRODUCTION
1
Objectives
2
Organization of Study
3
LITERATURE REVIEW
4
Saltation—Threshold Particle Movement
5
Wind Profile Equation
7
Forces at Threshold of Soil Movement
8
Threshold Shear Volocity
13
Interparticle Force
16
Threshold Reynolds Number and Parameter A
17
Threshold Shear Velocity in Water
20
MATERIALS AND METHODS
24
Wind Tunnel
24
Granular Materials
25
Determining Threshold Wind Velocity
27
Wind Profile Verification
28
111
IV.
V.
RESULTS AND DISCUSSION
30
Data Results in the Test
31
Sensitivity Analysis
35
Demensionless Shear Stress Analysis
38
Discussion of Interparticle Forces
40
CONCLUSIONS AND RECOMMENDATIONS
44
REFERENCES
46
APPENDICES
A.
B.
COMPARISON OF MEASURED AND CALCULATED VELOCITY
PROFILES AT DIFFERENT HEIGHTS
48
GRAPHIC REGRESSION OF CALCULATED WIND VELOCITY
ON MEASURED WIND VELOCITY
59
IV
LIST OF TABLES
1.
Experiraental and Theoretial Values of Small
Particle Shear Flow Force Coefficients
1
2.
Diameters of Test Materials
27
3.
The Density of Test Materials
28
4.
Coefficient of Determination of Calculated and
Observed Velocities of the Particles
29
5.
Threshold Shear Velocity of Particles
31
6.
Threshold Shear Velocity and Threshold Parameter. . . .
32
7.
Standard Data Set of Soil Particles
35
Test Data in Shields' Equation
Coraparison of Measured and Calculated Velocity
Profiles at Different Heights for Soil Particle
Diameter of 0.011 cra
40
8.
A.1
A.2
A.3
A.4
A.5
A.6
49
Coraparison of Measured and Calculated Velocity
Profiles at Different Heights for Soil Particle
Diameter of 0.02 cra
50
Comparison of Measured and Calculated Velocity
Profiles at Different Heights for Soil Particle
Diameter of 0.055 cm
51
Comparison of Measured and Calculated Velocity
Profiles at Different Heights for Coal Particle
Diaraeter of 0.011 cm
52
Comparison of Measured and Calculated Velocity
Profiles at Different Heights for Coal Particle
Diameter of 0.02 cm
53
Coraparison of Measured and Calculated Velocity
Profiles at Different Heights for Coal Particle
Diaraeter of 0.055 cra
54
A.7
Comparison of Measured and Calculated Velocity
Profiles at Different Heights for Coal Particle
Diameter of 0.1 cra
55
Coraparison of Measured and Calculated Velocity
Profiles at Different Heights for Salt Particle
Diaraeter of 0.011 cm
56
Comparison of Measured and Calculated Velocity
Profiles at Different Heights for Salt Particle
Piameter of 0.02 cm
57
A.IO Comparison of Measured and Calculated Velocity
Profiles at Different Heights for Salt Particle
Diameter of 0.055 cra
58
A.8
A.9
VI
LIST OF FIGURES
1. Comparison of the Threshold Shear Velocity versus
Particle Diameter for Mars, Earth, and Venus
2.
3.
Forces of Lift, Drag, and Gravity Acting on a Soil
Grain at the Threshold of Movement
6
9
Schematic of an Erodible Spherical Particle
Resting on Other Like Particles
11
4.
Threshold Friction Speed at One Atmosphere
15
5.
Threshold Friction Speed Pararaeter versus
Friction Reynolds Number
Shields' Diagram: Condition for Incipient Motion
19
22
Graphic Regression of Threshold Velocity on Threshold
Parameter with Soil, Coal, and Salt Particles in Wind
Tunnel Tests
33
Graphic Regression of Threshold Velocity on Threshold
Parameter, Comparison between Test Data Points and
Iversen's Data Points
34
Sensitive of Threshold Shear Velocity as a Function
of Particle Diameter and Air Density in Step Sizes of
0.0082 g/cra^ for a Standard Air Density of 0.001226
g/cm-^ and Particle Density of 2.65 g/cm^
36
Sensitive of Threshold Shear Velocity as a Function of
Particle Diameter and Particle Density in Step Size of
1.5 g/cm-2 for a Standard Particle Density of 2.65 g/cmand Air Density of 0.001226 g/cm-^
37
11.
Test Data Sets in Shields' Diagram
39
B.l
Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.011 cm Diameter Soil Particles. . . .
60
Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.02 cm Diameter Soil Particles . . . .
61
Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.055 cra Diameter Soil Particles. . . .
62
6.
7.
8.
9.
10.
B.2
B.3
vii
B.4 Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.011 cra Diameter Coal Particles. . . .
63
B.5 Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.02 cm Diameter Coal Particles . . . .
64
B.6 Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.055 cm Diameter Coal Particles. . . .
65
B.7 Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.1 cm Diameter Coal Particles
66
B.8 Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.011 cm Diameter Salt Particles. . . .
67
B.9 Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.02 cm Diameter Salt Particles . . . .
68
B.IO Graphic Regression of Calculated Wind Velocity on Measured
Wind Velocity for 0.055 cm Diameter Salt Particles. . . .
69
Vlll
LIST OF SYMBOLS'^
A
an experiraental coefficient (dimensionless)
a
moment arm (1); cm
b
moraent arm (1); cm
c
raoment
arra (1); cra
D
displacement height (1); cm
D'
drag force on particle (f); dynes
ds
particle diameter (1); cm
d*
particle diameter completely submerged in the laminar
sublayer (1); cm
Fc
the threshold drag force acting on the top grain (f);
dynes
Fe
the electrostatic force between particles (f); dynes
Fm
the acceleration due to gravity of the particle (f);
dynes
Fr
relative resistance to soil erosion (l'^); cc.
Ft
the total force holding the particle in place (f);
dynes
g
acceleration due to gravity (f); dynes
H
height of velocity measurement (1); cm
Ip
the interparticle force (f); dynes
IX
K
Von Karman's constant
KD
drag coefficient (diraensionless)
KL
lift coefficient (dimensionless)
KM
moraent coefficient (dimensionless)
k
surface roughness constant (f); cm
L
lift force (f); dynes
1
the distance between the particle charges (1); cm
M raoraent on particle (fl); dynes cra
n
the ratio of drag and lift on the whole bed to drag and
lift on the topraost grain moved by the fluid
(dimensionless)
P
air density (f/l^); g./cc.
P5
particle density (f/l^); g./cc.
p
atmospheric density (f/l^); g./cc.
p'
difference in density between the grain and the fluid
(f/13); g./cc.
qi
electrical charge of the particle (f°-5/l);
dynes*^ • ^/cra
q2
electrical charge of the particle (fQ-/l);
dynes°•^/cm
r
raean
size of the surface roughness (1); cm
ri
specific weight of fluid (f/l^); dynes/cc.
rs
specific weight of sediment (f/l^); dynes/cc.
R*
Reynolds number
X
T
turbulence factor expressed as ratio ofraaxiraumto
mean lift and drag on the grain (dimensionless)
U
average wind velocity measured at height H (1/t);
cm/sec.
Ut
threshold wind velocity at geight H (1/t); cm/sec.
U*
shear velocity (1/t); cm/sec.
U*t
threshold shear velocity, also called threshold
friction speed (1/t); cm/sec.
V
kinematic viscosity of fluid (l^/t); sq. cm/sec.
Wt
weight force of the particle (f); dynes
y
the thickness of laminar sublayer (1); cm
Zo
aerod^Tiaraic rouglmess (1); cm
Zt
threshold shear stress (f/l^); dynes/sq. cm
z
the angle of repose of the grain with respect to
direction gravitation forces acting through center
of gravity of the grain (degrees)
* Basic dimensions of terms used are indicated in parenthesis by
dimensional symbol m, 1, t, and f, denoting mass, lenj^th, time, and
weight or force, respectively.
Units of English or raetric system are
given after the dimensional symbols.
XI
CHAPTER I
INTRODUCTION
Wind erosion is a serious problera in raany areas of the world.
It
is one of the great destructive agents of soils and other raaterials.
The top layer of fertile soil in farm lands is, unfortunately, the
first soil to be lost from a field.
In the United States, wind erosion
daraages frora 0.4 to 6 million hectares annually and about 2 million
hectares are moderately to severely daraaged each year (Gregory and
Borrelli, 1986).
Becaues of the serious wind erosion and huge econoraic
losses in the Great Plains during the decade between 1930 and 1940,
people began to pay attention to wind erosion, especially to its cause
and effect.
Federal agencies and sorae of the States set up some
emergency wind control programs.
Beginning in 1947, USDA obtained
funds to perform sorae research on wind erosion.
A Wind Erosion
Laboratory was ,set up at Manhattan, Kansas, and has operated
continuously since that time.
Wind erosion is one of several geological processes that occur at
a partical site.
It is active in almost all locations with some
locations experiencing severe probleras due to the interaction of man.
The raain factors that contribute to wind erosion at a site include the
particle size distribution of the soil, mechanical stability of the
surface, wind velocity, soil raoisture, orientation of eroding site, and
vegetative cover.
The wind speed required to initiate movement of a
soil particle is one of the most important interaction of the wind
erosion process and is the research focus of this thesis.
This research is one part of an overall study to develop the Texas
Tech University Wind Erosion Model (Gregory and Borrelli, 1986).
The
model has several submodels including submodels for soil detachment
(Gregory and Borrelli, 1986), soil detachment with length (Gregory,
1986), and determination of the wind velocity profiles (Abtew et al.,
1986).
Additional refinements have been made to mathematical
relationships for ridges and soil clods (Arika et al., 1986) as they
interact with the wind and soil in the wind erosion process.
This
thesis will add to the Texas Tech University Wind Erosion Model by the
development of a subraodel for deterraining the threshold wind velocities
forraoveraentof individual soil particles.
Qb.jectives
The priraary objective of this thesis was to develop a relationship
to determine the threshold wind velocity needed to initiate moveraent of
a single soil particle.
To better understand the process, threshold
wind velocities were deterrained for particles of different densities
and different diaraeter.
Data frora the literature were collected to
expand the range of information available on threshold wind velocities.
Subobjectives of the study were:
1. To measure, in the wind tunnel, the threshold wind velocities
for salt, coal, and soil:
2. To develop a matheraatical relationship for the threshold wind
velocities with particle density, particle diameter, and the
properties of air; and
3. To perform a sensitivity analysis of the various factors
affecting the initiation of particle raoveraent.
Organization of Study
Chapter I contains the introduction to the wind erosion study,
the concept of the threshold friction velocity, and objectives of this
study.
Presented in Chapter II are related research on threshold wind
velocity and a review of literature of related topics.
Chapter III
concerns the materials and methods which were used in the wind tunnel
test.
Chapter IV provides the discussion and statistical analyses of
the data which was obtained and its coraparison to published data.
Finally, the conclusions and recommendations are presented in Chapter
V.
CHAPTER II
LITERATURE REVIEW
Wind erosion is a major social and economic problera.
Wind erosion
not only removes soil but also damages crops, buildings, fences, and
highways.
The areas most subject to damage are the sandy soils along
streams and lakes, and the sandy soils of coastal plains and many of
our most fertile soils.
In all these areas, control of wind erosion would be improved if
more information was available on the wind erosion process, especially
the threshold shear velocity.
Depending on the erodibility of a
specific soil, the threshold velocity is a certain critical wind
velocity required to cause initial disturbances of soil particles so
that continuous moveraent occurs (Bagnold, 1941).
By definition, the
threshold shear velocity is the value of the surface shear velocity at
initiation of particle motion.
The threshold wind velocity is the
value of wind velocity at a given reference height, at initiation of
grain motion (Greeley and Iversen, 1985).
Movement is initiated when
the pressure of the wind against the surface soil grains overcoraes the
force of gravity on the grains.
The grains are raoved along the surface
of the ground in a series of jumps known as saltation.
grains jump, the more energy they derive from the wind.
The higher the
Bagnold (1941)
discribled the basic mechanics of saltation and suspension; and
presented a coraprehensive framework of theoretical, experimental, and
field work.
W. S. Chepil researched the physics of soil movement by
wind beginning from 1940.
He reported his finding in a large number of
papers, especially emphasing agricultural applications,
Based on wind
tunnel studies, Chepil presented an analysis of the nature and
magnitude of forces on soil grains at the threshold of moveraent in
wind; and
analyzed the forces of drag, lift, and gravity and their
relationship to each other (Chepil and Woodruff, 1963).
Another person who researched extensively.in this field is J. D.
Iversen.
Iversen and White (1982) stated that observations of dust
storms in the atraosphere of Mars led to speculation about the raagnitude
of wind velocities necessary to initiate raovement of surface particles.
Subsequent experiraental deterraination of particle threshold speeds for
a variety of particles and fluid densities has led to new understanding
of threshold phenoraena.
Saltation—Threshoid Particle Movement
The three types of soil raovement that occur during wind erosion
erosion are: suspension, saltation, and surface creep.
These usually
occur simultsmeously.
Saltation is the raost iraportant of the three types of raovement
since more soil is raoved by saltation than what occurs in the other two
types.
Neither creep nor suspension can occur without saltation.
The
size range of particle diaraeters which may move in saltation is from
0.05 to 0.5 mra. Most raovement occurs araong particles 0.1 to 0.15 mm
diameter
(Hudson, 1981; Chepil and Woodruff, 1963).
From Figure 1,
the threshoid shear velocity curve, it can be seen that the nram size
lOOOro
(U
CJ
Q
LU
100
uu
Q.
EARTH
co
O
I(J
£r
u.
û
10
_j
VENUS
O
X
co
LU
cr
X
IL
10
Fig. 1.
100
1000
PARTICLE DIAMETER.Mm
10 000
Coinparison oí' thc Threshold Shear
Velocity versus Particle Diametejfor Mai~s, Earth, and Venus (Greeley
& Iversen, 19S5).
most easily moved by the wind is about 0.1 mm in diameter (fine sand).
Information from this curve was to help select the size range for
particles utilized in this study.
Wind Profile Eguation
The wind profile equation is an equation that estimates the wind
velocity distribution with height.
be used.
There are several raodels that could
However, for the purposes of this study the logrithraic raodel
appears most appropriate.
The equation is given as follows:
U = (U*/K)ln((H-D)/Zo)
(1)
where
U = average wind velocity measured at height H (cm/sec),
U*= shear velocity (cm/sec),
H = height of velocityraeasureraent(cra),
D = displaceraent height (cm),
Zo = areodynamic roughness (cm), and
K = Von Karman's constant which is 0.4 under neutrai condition.
Abtew, Gregory and Borrelli (1986) physically defined the displaceraent
height and developed a prediction equations for displaceraent and
aerodynaraic roughness for indivial soil grains , which showed
D = TIX of the particle diameter
Zo = 9.36?^ of the particle diameter
So Equation 1 can be written as
U = (U*/0.4)ln((H-0.72ds)/0.0936d5)
where
ds = t h e p a r t i c l e diaraeter (cm).
(2)
8
Forces at Threshold of Soil Moveraent
Chepil and Woodruff (1963) state that there are three types of
pressure being exerted on a soil particle by a raoving fluid such as air
or water.
The first type of pressure is a positive pressure (velocity
pressure) against that part of the grain facing into the direction of
fluid raotion, The second type is a negative pressure on the lee side
of the grain (it is called viscosity pressure), and the third type is a
negative pressure on the top of the particle caused by the Bernoulli
effect.
The drag on a soil particle is the sura of velocity pressure and
viscosity pressure.
The drag force, Fc, on the top grain at the
threshold of itsraoveraentis due to the pressure difference against its
windward said leeward side.
The arrow raarked by Fc in Figure 2
indicates the general direction and the average levei at which it acts.
Therainimumraeandrag and lift force, required to move the top soil
grains by the wind, are the threshold drag and lift.
There forces are
influenced by the diameter, shape, and the immersed density of the
grain.
They are also influenced by the angle of repose of the grains
with respect to the mean drag level of the wind and the impulse of wind
turbulence, "T," associated with drag and lift.
Chepil (1959) derived
the following equation:
Fc = (0.52gds-p'-L)tan z
(3)
in which
Fc = the threshold drag force acting on the top grain (dyTies);
g = acceleration due to gravity (cm/sec/sec.);
ds = diameter of particle (cra);
WIND
DIRECTION
HEIGHT
MEAN BED LEVEL. 2 Û
Fig. 2.
Forces of Lift, Drag, and Gravity
Acting on a Soil Grain at the
Threshold of Movement (Chepil, 1959).
10
p'= the difference in density between the grain and the fluid
(g./cc);
Lc = lift force on top of grain (dynes); and
z = the angle of repose of the grain with respect to direction
of gravitation forces acting through center of gravity
of the grain (degrees).
Chepil determined from wind tunnel tests that Lc was equal to
approximately 0.75Fc
For uniform velocity, the equation used to
calculate the threshold shear stress and mean threshold stres is:
Zt = (0.66gdsp'ntan z)/(l + 0.75tan z),
(4)
For turbulent flow, it is:
Zt (ave.) = (0.66gdsp'ntan z)/[(l + 0.75tan z)T]
(5)
where
Zt = threshold shear stress (dynes/sq, cm);
Zt (ave.) =raesinthreshold stress (dynes/sq. cm);
n = the ratio of drag and lift on the whole bed to drag and
lift on the topmost grain moved by the fluid
(diraensionless);
T = The turbulence factor expressed as ratio of the maximum
to the mean lift and drag on the grain (diraensionless).
Chepil also found z = 24 degrees, n = 0.24, T = 2.5 approximately.
Greeley and Iversen (1985) predicted a loose gram at rest on top
of a bed of small particles.
As shown in Figure 3, the forces on the
particle are drag force, D', lift force, L, moment, M, weight, Wt, and
interparticle force (cohesion), Ip. They derived an equation:
D'a r Lb + M = Wtb ^ Ipc
(6)
11
FLOW
0
Fig. 3.
Scheraatic of an Erodible Spherical
Particle Resting on Other Like
Particles (Greeley & Iversen, 1985)
12
where
a , b, c, are theraomentarms (cm) described in Figure 3.
Table 1 contains the different values of KD (drag coefficient), KL
(lift coefficient), KM (moment coefficient), and Reynolds number (R*)
by the various researchers.
Table 1.
Experiraental and Theoretical Values of Sraall
Particle Shear Flow Force Coefficients^
Investigator
KD
KL
KM
R*
Fluid raedium
<0.45
Theoretical
Goldman et al (1967)
and O'Neill (1968)
0.74
8.01
0.808R*
Saffman (1965, 1968)
<0.45 Theoretical
Hydroxyethyl-
ColeraEin & E l l i s
(1976)
0.95
5.44
cellulose
solution
Coleman (1972) and
Coleman & Ellis
(1976)
130-13200 Water
15.42
E i n s t e i n & El-Sarani
(1949)
Chepil (1958)
2.42
3-4.7
2.2-5
3600
Water
1000-1400 Air
a From Greeley & Iversen (1985)
Greeley and Iversen (1985) also stated that Coleman and Ellis
(1976) measured the drag force on a sphere resting on a bed of similar
13
s p h e r e s c o n d u c t e d t h r o u g h a l a r g e r a n g e of Reynolds numbers.
So D ' , L,
M i n e q u a t i o n (6) can b e e x p r e s s e d a s f o l l o w s :
D* =
KD
X p X U*2 X ds2
(7a)
L =
KL
X p X U*2 X ds2
(7b)
M=
KM
x p X U*2 X ds3
(7c)
where
p = the atmospheric density (g./cc).
Threshold Shear Velocity
Bagnold (1941) defined two levels of threshold shear velocity, one
for static conditions and one for actively saltating grains.
If
particles are introduced from upstream, continuous movement of
particles from the initially quiescent surface begins at a lower wind
speed.
This is called the irapact threshold, which is about 80% of the
static value.
The static threshold, is defined as the wind speed at
which continous motion starts without impact from upwind (Greeley and
Iversen, 1985).
The threshold curve in Figure 1 shows the minimum wind speeds
needed to set particles of various sizes into motion.
The threshold shear velocity (U*t) of a particle is the shear
velocity (U*) needed to initiate grain moveraent.
U* = (Z/pf)^^^ where
Z is the surface shear stress and pf is the fluid density.
U* is
directly proportional to the wind velocity for a neutral adiabatic
atraosphere (negligible heat exchange between the atmosphere and the
surroundings); at an ambient pressure of 5 milli bar, the free stream
velocity is about 17 times the shear velocity in the wind tunnel
(White, et al. 1976).
14
Bagnold (1941) used an experimental coefficient in a dimensionless
formula to describle a threshold velocity.
From equilbrium of forces
acting on the grain under threshold conditions, he derived the
following equation:
U*t = A[(Ps-P)gds/P]o-s
(8)
in which
U*t = threshold shear velocity (cm/sec);
Ps = the particle density (g./cc);
P = the air density (g./cc); and
A = an experimental coefficient (dimensionless).
From Equation 8, the threshold wind velocity Ut at any height H
above the surface is given by
Ut = 5.75A[(Ps-P)gds/P]o-51og(H/k)
(9)
in which k is the surface roughness constant (cm).
For nearly uniform sand grain of diameters larger than 0.2 mm in
air, the coefficient A is equal to 0.1.
The most readily eroded particles ranged from 0.1 to 0.15 mm in
diameter.
From this range, the threshold velocity increases with both
for £in increase or decrease in particle size. The impact threshold
velocity for particles smaller than 0.05 mm could not be determined
because of great difficulty in obtaining sufficient material, but the
threshold velocity, requiring a much smaller sample, was determined.
The data in Figure 4 (Greelye and Iversen, 1985) show the
relationship between the threshold shear velocity, U*t, and the product
of specific gravity and the diameter of the grains. The product is
drawn on a square root scale to show the relationship of U*t aind
15
THRESHOLD FRICTION SPEEO
vs
/pp<;Op
o
E
3
í
o
DENSITY-
UJ
LLI
o.
MûTERlAL
«1
gm/cm^
DlAMETER-um
INSTANT TEA
0.21
719
SILICû GEL
0.89
17; 169
l.l
NUT SHELL
4 0 TO 359
1.3
CLOVER SEED
1290
1.59
393
SUGAR
2.42
31 TO 4 8
GLASS
2.5
38 TO 586
6LASS
2.65
526
SANO
2.7
36 TO 2 0 4
ALUMINUM
3.99
55 TO 5 I 9
GLASS
6.0
10
COPPER OXIDE
7.8
616
BR0N2E
8.94
12; 37
COPPER
11.35
8:720
LEAO
0.001226 qim/cm^
AIR DENSITY ~ ^ «
u ' 0.1464
cm^/ sec
KINEMATIC VISC. ~
2
g
»o
cr
o
I
m
u
CE
I
100
200
300
400
THRESHOLD PARAMETER
Fig. 4.
500
600
/ppqO^
700
800
900
cm/sec
Threshold Friction Speed at One
Atmosphere (Greeley & Iversen, 1985
16
(Psgd/P)0-5.
it illustrates the existence of an optimum diaraeter for
miniraum threshold.
When the diameter is large, the threshold
parameter, A, is essentially constant (if it were exactly constant,
however, all data points would lie on a straight line through the
origin).
Interparticle Forces
An important factor in particle threshold is the effect of
cohesion.
In the case of fine dust, cohesive forces may well be of a
different order larger than those of gravity.
The cohesion may arise
from diffeirent causes, physical, chemical, and biological.
Iversen and
White (1982) state:
For grains below 0.1rarain diameter the values of A
(Figure 1) rise with the decrease in grain diameter,
indicating that the threshold equation does not apply
to such fine material. The existence of the
interparticle forces for sraall particles is due to
the effects of moisture, van der Waal's forces,
electrostatic charges and forces between adsorbed
films. These forces are not well understood, and
the particles of any solid, if small enough, cohere
on contact even when thoroughly dry and particlarly
well in a vacuum. Electrostatic forces appear to
be particularly important in the saltation phenomenon
(Greeley and Leach, 1978). The Eingle of repose for a
group of particles is one indicator of the effect of
cohesive forces. For ordinary dune sand, the emgle
of repose is 34 degrees frora the horizontal. For
small particles it can be much higher, and can even
approach the vertical (Bagnold, 1960). The angle of
repose for 0.02 ram particles at reduced pressures is
temporarily less than that at one atmosphere but out
gassing will return that angle to the one atmosphere
value. (Greeley 1980)
The raain interparticle force bonding between sraall particles
occurs priraarily due to the force between electrical charges.
The
force Fe between two electrical charges qi and q^ can be predicted by
17
the following equation (Hodgman, 1946):
Fe = qiqz/P
(10)
where
1 = the distance between the charges (cm).
The average distance between the two particles is approximately
twice the radius of each particle.
The values of qi and qz will be
constant for the material concerned, so the bonding force becomes large
when the particle size is small. The threshold wind velocity needed to
make the small particle move becomes larger. So there exists an
optimum diameter (minimum threshold shear velocity) due to the
interparticle forces of cohesion and not to the Reynolds number effect
(viscous forces).
This can explain why there is a sharp upturn in
threshold shear velocity for small particles in Figure 4.
Threshold Reynolds Number and Parameter A
There are two types of fluid flow, laminar and turbulent. The
Reynolds number defines the transition of fluid behavoir from laminar
to turbulent flow. Bagnold (1941) states that if the wind exceeds 1
meter per second the air moveraent must be turbulent.
The Threshold Reynolds number is:
U*r/v = 3.5
(11)
where
U* = shear velocity cm/sec);
r =
the mean size of the surface roughness, which is of
the same order as the grain diameter (cm); and
V = the kinematic viscosity of the fluid (sq. cm/sec).
18
The kinematic viscosity value varies somewhat with the temperature
and pressure of the fluid.
value of 0.14
value for air,
For air at sea level it may be taken as a
and for water it is 0.01, only about one-tenth of the
both under atmospheric condition, and in centimeter-
gram-second units.
If U*r/v > 3.5, the surface is rough.
In Equations 8 and 9
presented above, for air, the coefficient A is equal to 0.1; whereas
for water, A is nearly equal to 0.2.
The discrepancy is probably due
to the difference in the surface texture; for in air the surface is
pitted with little impact craters.
The particles on the crater lips
are more exposed, whereas in water the surface is much smoother since
particle impacts do not appreciably disturb the surface.
If U*r/v = 3.5, it is the Threshold Reynolds Number, it
distinguishes the surface condition as either rough or sraooth.
When the grains are very small, U*r/v <3.5, and the surface
becomes smooth.
laws.
The flow close to the bed begins to obey different
A is not a constant but now increases as the grains become
smaller and smaller.
At first the threshold value of U* reaches a
minimum, then grows larger, till for very fine grains the initial
moveraent of individual grains is not easily raoved by the fluid.
For
the bed of raixed grain sizes, the grains first moved are those for
which U*t is a minimum (Bagnold, 1941).
Figure 5 (Greely and Iversen, 1985) shows the relationship among
the threshold paramrter A and the particle friction Reynolds number.
It contains the data from studies of Bagnold (1941), Chepil (1945,
1959) and Zing (1953).
The data are plotted in dimensionless form, as
19
MATERIAL
A
A
c
Q.
o
a
•
C71
Q.
V
>
"^
V
4->
3
o
o
o
—
* 1.0
U
\
.7
«*
< •
~
O
\
a
.5
\
3
^
\a\
UJ
rj
X\\
^ \
t—
LU
s:
«*
O
O
OIAHETER-Mim
719
17;169
40 TO 359
1290
393
31 TO 48
38 TC 586
526
36 TO 204
55 TO 519
10
616
12,37
8.720
0.21
0.89
1.1
1.3
1.59
2.42
2.5
2.65
2.7
3.99
6.0
7.8
8.94
n.35
\ ^ ^
.2
o
>l^
_l
o
1/1
LiJ
CC
\
INSTANT TEA
SILICA GEL
NUT SHELL
CLOVER SEED
SUGAR
GLASS
aASS
SANO
ALUMINUM
GLASS
COPPER OXIDE
BRONZE
COPPER
LEAO
OENSITY
gin/cm^
\
.1
f^
1 1
fl'
>^^i-^w^
_.
:;':i:i':Ct: S2r5CJ^".'=Q J ^ J Q ^ ^
BAGNOLO (1941)
. _.—— CHEPIL (1945, 1959)
ZINGG (1953)j
1
I
\
t
^
**-
1
2
5
7 10
2
5
1
.5 .7
PARTICLE: FRICTION REYNOLDS NUMBER -^ R * ^ = u , ^ D p / v
.2
Fig
- ^
5.
Threshold Friction Speed Parameter
versus Friction Revnolds Number
(Greeley & Iversen, 1985)
20
the Shear Reynolds number is greater than 3, the data of Bagnold,
Chepil and Zing were agreed because the threshold parameter A is almost
constant.
For smaller Reynolds numbers which are less than 3, the
threshold parameter A varies because of the force of cohesion (causing
A not to be a function only of the friction Reynolds number), the
differences in particle-size distribution, and the difficulty in
measuring threshold naturally.
Threshold Shear Velocity in Water
In water erosion, water flowing over a bed of sediment exerts
forces on the particles at the surface.
The forces that resist the
entraining action of the water flow, like air flow, differ according to
the particle size of the sediment.
For coarse sediments, like sands and gravels, the forces resisting
motion are caused mainly by the weight of the particles. Finer
sediment, due to the cohesive force, like silt or clay, resists
entrainment mainly by cohesion rather than by the weights of the
particles.
Shields (1936) determined the threshold shear stress as the value
of the stress for zero sediment discharge obtained by extrapolating a
graph of observed sediment discharge versus shear stress. This value
does not depend on a qualitative criterion.
Shields obtained a formula
to predict the initiation of motion in water as follows:
Zt/[(rs-rf )ds] = f(U*tds/v)
(12)
in which
U*t = threshold shear velocity (cm/sec), U*t = uw'pf)°-^;
Zt = threshold shear stress (dynes/sq. cra);
21
rs = specific weight of sediment (dynes/cc);
rf = specific weight of fluid (dynes/cc);
ds = average diameter of the particle (cm);
Pf = density of fluid (g./cc); and
V = kinematic viscosity of fluid (sq. cm/sec).
Figure 6 shows the variation of Equation 12 as obtained by Shields
based on his experimental data, these data were collected in a flume
with fully developed turbulent flow, using sediment ranging in size
from 0.04 cm to 0.34 cm (R. J. Garde and K. G. Ranga Raja, 1985).
The
incipient condition was obtained as that corresponding to the case when
the bed load transport tends to zero.
On Shields' curve, the straight line portion on the left
represents the case when y (the thickness of laminar sublayer) is
greater than d* ( the diameter the particle completely submerged in the
laminar sublayer).
If y = d*, turbulent eddies occur, disturbing the
laminar sublayer and affecting the flow around the particle. The dip
in the curve for 2.5 < R*t < 40 represents this case. When y < d* , the
right portion
of the curve shows that
the laminar sublayer is
destroyed amd the dimensionless shear stress Zt/[(rs-rf)ds] for initial
motion becomes independent of y/d*.
For very coarse materials at
initial motion, in such case, the dimensionless shear stress is 0.06.
The difference between wind erosion and water erosion is that the
value of dimensionless shear stress is smaller in air than in water at
the same boundary Reynolds Number.
It shows the particle of same size
in air starts to move easily because the cohesive force among the
particles in water is large.
90
tO
I
aio
aoi
tooo
:Í£.
Fig.
S h i e l d s ' Diagrara: C o n d i t i o n for I n c i p i e n t
Motion ( R . J . Grade 8. K.G. Ranga Ra.ia; 1985)
23
From this literature review, one can conclude that the size of
soil grains is the greatest single factor influencing the threshold
velocity.
The existence of an optimum diameter (minimum threshold
shear velocity) might be due to the variation of particle cohesion
forces instead of, or in addition to, viscous forces.
For small
particles, the interparticle forces due to moisture, electrostatic
force and other forces of cohesion small particles less capable of
accurate prediction of threshold shear velocity than for particles
greater than 0.1 mm.
Since the forces of cohesion are not linearly
proportional to fluid density, the threshold coefficient, A, could not
be expressed as an explicit function of density ratio Ps/P. The
texture of soil and the roughness of the surface also influence the
threshold velocity.
Soils containing high organic matter or high clay
content are more resistant to soil erosion than soils containing silt
and fine sand.
The higher the roughness of field, the greater the
value of the threshold shear velocity.
The analysis and data in
Chapter III provides a verification of the above statement.
CHAPTER III
MATERIALS AND METHODS
The grcinular materials selected to make the threshold velocity
test in the wind
tunnel were soil, salt (NaCl), and coal particles.
Several different sizes of each material are selected for each test.
Particle diameters varied from 0.011 cra to 0.1 cm.
and for each size, three repetitions were used.
For each material
Wind velocity profiles
were measured in the wind tunnel and set to simulate wind profiles as
found in nature.
To ensure that the wind profile was correct, it was
precalculated according to Equation 2 (Wind Profile Equation) developed
by Abtew, Gregory, and Borrelli (1986).
The wind tunnel that was used
was constructed and calibrated to insure that the results were
reproducible and typical of other wind tunnels (Arika, 1986).
Presented in the following sections are the details of materials and
methods used in this study.
Wind Tunnel
The wind tunnel is 4.87 meters in length, 0.5 meters wide and 0.75
raeters high.
The fan is powered by a 40 watt electric raotor, and the
wind velocity can be changed and controlled by changing the area to the
inlet of the tunnel.
The air is moved frora the fan into a pressurizing
charaber, which is a 1 raeter long, 1 meter wide by 1.2 meter high box
24
25
with one side open for connection to the tunnel.
Both the chamber and
the tunnel were made from plywood.
To obtain the wind profile in the wind tunnel, wind velocity
raeasurements were taken at difforent heights above the bottom of the
tunnel.
The distribution of air was controUed with a double layer of
masonite, which has 2.54 cra holes punched in it.
The control was
obtamed by offsetting holes in the two pieces of masonite that could
be moved independently.
To control the overall volume of air into the
tunnel, air flow was controlled on the suction side of the fan by a
simple gate.
A 0.45 m long test section is located about 1.32 m downstream in
the tunnel.
A glass observation window by the test section enables one
to observe the particle threshold raotion process occurring in the
tunnel without disturbances to the wind flow in the test.
To raake the
upstream portion of the wind tunnel the same roughness as the test
section, boards with the same sample material glued on to the board
were placed at the bottora of the wind tunnel.
A Weather Measure raodel NO. W241M velocity meter was used to
measure the wind velocity in the wind tunnel.
The velocity meter works
on the sarae principle as the hot wire anonometer, except it is more
durable.
Wind velocities were measured at 17 points starting 1 cra from
the bottom of the tunnel to a height of 49.8 cm.
The wind polfile test
section was 0.355 ra frora the upstream edge of the test section.
Granular Materials
The granular raaterials selected were soil, salt, and coal
particles.
These various niaterials are of different density, but are
26
materials of concern in this region.
In preparing the sample, the
soil, salt, and coal were crushed into small particles and sieved the
materials to obtain a uniform size.
The sieve numbers used were No.l4
(opening diameter: 0.141 cm), No.30 (opening diameter: 0.06 cra), No.35
(opening diameter: 0.05 cm;, No.60 (opening diameter: 0.025 cm), No.lOO
(opening diameter: 0.0149 cra), and No.200 (opening diameter: 0.0074
cm).
The average value of sieves trapping the material was used to
estimate the average material size.
The average diameter of these
samples are shown in Table 2.
Table 2.
Material
Diameters of Test Materials
Average Diameter of Samples
(cm)
soil
0.011
0.020
0.055
salt
0.011
0.020
0.055
coal
0.011
0.020
0.055
0.100
27
Before conducting a test, each sample was placed in an electrical
oven to dry at 65 ^C for 24 hours.
pycnometer method.
The density was measured using the
The results are shown in Table 3.
Table 3.
The Density of Test Materials
Material
Density
(g/cm2)
Soil
2.14
Salt
2.00
Coal
1.189
Determining Threshold Wind Velocity
To measure the threshold velocity for each test particle size, the
wind velocity was increased little by little until the sample on the
test section started to move.
To help determine when movement was
initiated, a sampler 13 mm wide by 0.6 ra high was set in the tunnel.
The particles moved by the wind went through the slot and collected in
a small box under the tunnel. The tirae of each test was 1 minute.
If
the nuraber of the particles collected in the box was raore than 10, it
was assuraed that particleraoveraenthad been initiated and the measured
velocity was approximately the threshold wind velocity.
Three replications were raade for each size particle.
The results
of the three replications were averaged as the final estimation of the
threshold wind velocity for the particular partii ie size.
28
Wind Profile Verification
For each test, the measured wind velocity profile was compared to
the calculated wind velocity profile as calculated using Equation 2.
The calculation procedure is as follows:
1. Suppose the value of U* is 1 at all conditions, and use
Equation 2 to obtain the wind velocity profile for different
particle diameters.
2. Using linear regression, select a simple linear function
(Y = AX) to functionally analysis our measured wind velocity
profile, in which Y is the calculated wind velocity values from
step 1 when U* = 1, and X is our measured wind velocity
profile at the same particle size. The value of A for
different size particles can be obtained.
3. The threshold shear velocity (U*t) of different kinds and sizes
(reciprocal of A) can be obtained from U*t = 1/A.
4. Using Equation 2 again, put the different values of U*t
obtained in step 3 and input different diameters of the
particles to get the calculated wind velocity profile for the
test particles.
Tables A. 1 - A. 10 show the comparison between the measured wind
velocity profile and the calculated wind velocity profile at different
heights in the wind tunnel tests (the value of U*t of test data sets
are in Table 5, page 31).
In comparing the calculated wind velocity profile data with the
raeasured wind velocity profile data, it can be verified that the
precision of our wind tunnel test is very good.
Figures B. I - B. 10
29
show the fit of these data. Through linear regression analysis, the
values of R2 of each size and kind of particles are shown in Table 4.
Table 4. Coefficient of Determination of Calculated
and Observed Velocities of the Particles
Material
Diameter
R2
(cm)
Soil
0.011
0.850
Soil
0.020
0.946
Soil
0.055
0.886
Coal
0.011
0.959
Coal
0.020
0.976
Coal
0.055
0.895
Coal
0.100
0.969
Salt
0.011
0.972
Salt
0.020
0.951
Salt
0.055
0.961
CHAPTER IV
RESULTS AND DISCUSSION
There are two main methods to prevent wind erosion of soil.
The
first is reduction of wind velocity near the ground surface, and the
second is to improve soil texture.
The threshold velocity is smallest
for a grain diameter of 0.1 to 0.15 mra.
threshold velocity increases.
Above this size range the
This was verified from wind tunnel tests
conducting as part of this study.
The high resistance of the fine dust
particles to be raoved by the wind is both due to the cohesion of the
particles and to their small size which does not permit them to
protrude above the laminar boundary layer.
The threshold shear
velocity of particles with diameter less than 0.05 mm is difficult to
predict because the cohesive forces and their effects can not be
estimated.
In this study, the range of particle diameters tested was
frora 0.11 to 1 mm, and therefore the sraall cohesive force could be
neglected.
Presented below is a discussion of the results obtained
frora this study.
Also, a comparison of test results with published
data, discussions of general trends, and a sensitivity analysis.
30
31
Data Results in the Test
From the wind tunnel tests, data sets were obtained on the
threshold shear velocities of the different particle sizes of soil,
salt, and coal.
Average results are presented in Table 5.
Table 5.
Material
Diameter
Threshold Shear Velocity of Particles
Threshold shear velocity
Temp.
R.H.
(percent)
(cm)
(cm/s)
(°C)
Soil
0.011
18.2429
27
68
Soil
0.020
23.0528
31
64
Soil
0.055
34.1981
30
66
Coal
0.011
13.4664
27
50
Coal
0.020
18.2900
21
86
Coal
0.055
21.3691
22
82
Coal
0.100
36.2870
25
74
Salt
0.011
15.9715
29
52
Salt
0.020
19.9253
21
61
Salt
0.055
27.5262
23
60
From Table 5, it can be observed that the threshold shear velocity
increases as the particle diameter increases. This is because the
smallest particle diameter used in the test is above 0.1 mm (Greeley
and Iversen,1985).
These tost data were used to calculatc the
threshold parameter (Psgd^/P)'^^ associated with the threshold shear
vclocity.
The results aro shown in Table 6.
32
Table 6.
Material
Threshold Shear Velocity and Threshold Parameter
Diameter
Threshold shear velocity
Threshold parameter
(cm)
(cm/s)
(cra/s)
Soil
0.011
18.2429
137.174
Soil
0.020
23.0258
184.965
Soil
0.055
34.1981
306.730
Coal
0.011
13.4664
102.248
Coal
0.020
18.2900
137.871
Coal
0.055
21.3691
228.634
Coal
0.100
36.2870
308.289
Salt
0.011
15.9715
132.611
Salt
0.020
19.9253
178.812
Salt
0.055
27.5262
296.527
A graph of measured threshold shear velocity as function of the
threshold pararaeter is shown in Figure 7. Measured threshold shear
velocities were observed to be a linar function of the threshold
pararaeter. given an R^ of 0.84.
In Figure 8, the ten small circle
points and the straight line is a portion of the curve from Iversen's
graph (Figure 4, Greeley and Iversen, 1976), m which the particle
diaraeter is above 0.01 cra. The ten star points which are shown are
frora Table 6.
The R^ is 0.84 forraeasureddata, and is 0.997 for
Iversen's data.
This comparison shows that the measured data fit
Tvefsen's strai>;lit line and data ciosely.
33
CO
O
I
3 >-
o
_J
LU
>
2 -
o
co
LiJ
a:
h- 1 1
2
3
4
THRESHOLD PARAMETER ( 1 0 ^ 2 cm/s)
Fig. 7.
Graphic Regression of Threshold Velocity
on Threshold Pararaeter with Soil, Coal.
and Salt Particles m Wind Tunnei Tesls.
34
(n
12
\
B
O
10 -
i
2 8
>-
u
o
_J
>
o IVERSEN' DATA SET
R-SQUARE - 0.997
• TEST OATA SET
R-SQUARE - 0,84
^
o
tn
LU
Ql
X
0
0
2
4
6
8
10
12
THRESHOLD PARAMETER (10^2 cm/s)
ig. 8.
Graph Regression of Threshold Velocity on
Threshold Paraineter, Comparison between
Test Data Points and Iversen's Data Points
35
Sensitivity Analysis
From Iversen's graph (Figure 4), the relationship between
threshold friction velocity and threshold parameter shows that there
exist an optimum diameter for miniraum threshold and that for large
particles the threshold parameter, A, is essentially constant.
Using
the formula U* = A^Psgds/P^o • ^, the calculated value for A was
0.1117586.
To determine how the different variable interact, a sensitivity
was performed using a reference set of data.
The reference set of data
used for sensitivity amalysis is presented in Table 7.
Table 7.
U*t
(cm/s)
50
Standard Data Set of Soil Particles
Ps
(g/cm^)
2.65
P
ds
(g/cm^)
(mm)
0.001226
0.1
Figure 9 shows the effect of the air density change from 0.001134
to 0.001381 g/cm^ by the step size of 0.00082 g/cm^ for a constant
particle density of 2.65 g/cm^, the relationship between threshold
shear velocity and particle diameter.
It shows that as the air density
increases, the threshold shear velocity increases at very smail rate
for the same size particle diameter.
Figure 10 shows that the air density is 0.001226 g/cm-^, when the
particle density changes from 0.21 to 6.21 g/cra^ by the step size of
1.5 g/cra-^ , the relationship between threshold shear velocity ind
36
/ ^
Air Density
(g/cm^)
0.00138
0.00129
0.00122
0.00113
o
n:
co
UJ
01
n:
0
20
40
60
80
100
PARTICLE DIAMETER (10^~3 cm)
Fig. 9.
Sensitive of Threshold Shear Vt-iocity as
a Function of Particle Dianieter and Air
Density in Step Sizes of 0.00082 g/cmfo!- a Standard Air Density of 0.001226 g cn\~
and Particle Density of 2.65 ii/o:n .
3'
Particle Density
(g/cm^)
/^
6.21
4.71
a
_j
o
co
LU
X
0
20
40
60
80
100
PARTICLE DIAMETER (10-^-3 cm)
Fig. 10.
Sensiti\-e of Threshold Shear Velociiy is
a Funcrion of Particle Dianieter and Par::cle
Densi;:>- in Slep Sjzi:' of 1.5 li/cv.]-^ for .i
Standard Particle Density of 2.65 g, ( r.:^
and Air Densitv of 0.001226 H/C!II-.
38
particle diameter.
It shows that as the particle density increases,
the threshold shear velocity also increases for the same particle
diameter.
It is very sensitive.
From the Figures 9 and 10, we can observe that the range of
threshold shear velocity varied widely in different particle densities
and was dependent primarily on the range of the particle sizes.
Air
density slightly influences the threshold shear velocity.
Dimensionless Shear Stress Analysis
Shields* equation for the critical motion of sediment particles is
Equation 12 in the literature review of this paper.
Zt/[(r5-rf )ds] = f(U*tds/v) .
The left-hand side of Equation 12 is the dimensionless critical
shear stress and the variable on the right is the critical boundary
Reynolds nuraber.
Using the data collected in this study and Equation 11, the
following results in Table 8 were obtained.
Coraparing the results in Table 8 in the Shields' diagram (Figure
6) and connecting them according to material types as shown in Figure
11, the dimensionless shear stress Zt/[(Ps-P^ds] of test data are much
less thgm these values in the Shields' diagram for the same boundary
Reynolds number.
This is because the fluid density and viscosity of
the test fluids are different.
The density and viscosity of air are
rauch less them the density and viscosity of water, so wind erosion
occurs easily for the sarae particle diameter of similar raaterial. The
important fact is that the shape of three test curves and Shields'
curve are similar.
39
t'Or
AMftCK
Yi
LlOMiTC
o
o
cnAHni
V06
1.27
2.70
•AXITC
O-
-o
o
A
SANO (CASCY)
2.65
SANO (KRAMCR}
2.(5
9
I
IWAGAXI
f í • 2 . 4 3 - 2.70
2.6S
TISOM
2.€3
«
SCHO>a.lTSCH
S.60
U.S.WE.S.
2.65
U.S.W.E.S.
PANDE
CILBCRT
2.69
2.65
aoi
K300
K SOIL
• COAL
A SALT
Fig. 11.
Test Data Sets in Shields' Diagrara.
40
Table 8.
Material
Test Data in Shields' Equation
Diameter
(cm)
Zt/[(Ps-P)ds]
U*tds/v
(dimensionles) (dimensionless)
Soil
0.011
0.0169
1.27
Soil
0.020
0.01489
2.93
Soil
0.055
0.01197
11.98
Coal
0.011
0.0165
0.93
Coal
0.020
0.0169
2.46
Coal
0.055
0.0084
7.90
Coal
0.100
0.0134
23.10
Salt
0.011
0.01396
1.12
Salt
0.020
0.0119
2.67
Salt
0.055
0.00829
10.10
Discussion of Interparticle Forces
Particle size is the greatest single factor influencing the
threshold velocity.
The threshold velocity is least for grains 0.01 to
0.015 cm in diameter (Chepil, 1945).
From our wind tunnel tests, we
verified that the threshold velocity increases with the size of grains
above this size range.
But, if the particle diameter is less than 0.01
cm, the threshold velocity increases with a decrease in particle size.
We found high resistance to erosion by wind is fine dust particles that
was caused by the interpartricle forces. Small particles, even though
very dry, will cohere on contact. Bagnold (1959) stated that the
41
viscous effect increases at a relatively rapid rate as grain size is
reduced.
This is due to the dual effects of viscosity, one is to
•reduce the chances that an individual grain will be disturbed by direct
fluid action, whereas the other is to prevent the disturbance of one
grain by the impact of another.
in
interparticle cohesion.
Electrostatic force is the key force
The total force holding the particle in
place can be predicted due to the combined force of acceleration due to
gravity and the electrostatic force (J. M. Gregory, 1982).
The total
force Ft is:
Ft = Fm + Fe
(13)
in which:
Fm = the acceleration due to gravity of the particle (dynes);
Fe = the electrostatic force between the particles (dynes);
Fm = Mg = PsVg = Ps(3.14ds3/6)g (dynes); and
Fe = (qiq2)/12 = o/12 (dynes).
in which:
ds = particle diameter (cm);
1 = the distance between two particles (cra);
Ps = the density of the particle (g./cc);
qi,q2 = the electrical charges of the particles
(d^Ties'^-s/cm); and
Ko = qiq2 (dynes/cm^).
From Equation 13, Gregory obtained the equation (J. M. Gregory 1982):
Ft = (3.14Psg)(ls-/(412) + 13/6)
in which:
Ft = the total force holding the soil particle in place
(14)
42
(dynes)
The relative resistance to soil erosion Fr is
Fr = dsV(412} + 13/6
(15)
in which:
Fr = relative resistance (cc.)
From Equation 15, the relative resistance to soil erosion Fr is
function of particle diameter and the distance between two particles.
For small particles, the distance 1 can be considered the same value of
the particle diameter ds , so that the particle diameter is the key
parameter of Fr .
If the ds is equal to 0.005 cm, the value of the Fr
is the smallest, which equals to 1.
If the ds equals to 0.002 cm and 0.01 cm respectively, Fr will be
3.8 and 3.4, so that a particle diameter of 0.002 cm to 0.01 cm is the
most erosive soil, these are size ranges typical of silts and very fine
sand.
If the diameter of the particle is 0.00001 cra, Fr is equal to
1,500.
The force between electrical charges is the key bonding force
for the particles.
Soil of this type is clay which is difficult to
erode by wind.
If the diaraeter of particle of 0.1 cra, Fr is equal to 3,200.
The
force due to the acceleration of gravity becomes the key force of the
particles.
Soil of this t\'pe is coarse sand which is also difficult to
erosive.
Now we can conculde that the raost erosive soils are silts and very
fine sand.
Diameters of these niaterials are near to the 0.01 cra size.
Comparing these results with the curves in Figiire 1 and Fiv ire l, and
43
with our test data sets, all shows there exists an optiraum particle
size diameter of about 0.01 cm toraoveraosteasily by the wind.
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
From the wind tunnel tests, and the research results concerning
the threshold shear velocity for initial soil particle movement, we can
conculde:
1.
The salt smd coal threshold values followed the same patten as
these for soil, except they were a different density.
There
exists a minimum threshold shear velocity for different size
and different kinds of particles.
2.
My test data verified that there exists an optimum particle
size diameter of about 0.01 cm is the most easiest size to
move by wind.
3.
The data from my test verified that Ivernson's threshold
parameter (Psgds/P)°-^ can be used to predict the
threshold shear velocity for any combination of diameter,
particle density, and air density for (Psgds/P)^-^ > 100 cm.
4.
The threshold value for small particles are high because of
particle cohesion and the fact that these particles are too
small to protrude above the laminar boundary layer at the soil
surface.
In order to prevent the soil and other particles being eroded
the wind, we can apply following two methods:
44
by
45
1.
Making efforts to reduce the wind velocity near the ground by
such practices as the roughening of surface, use of clod and
ridge in the path of the wind, and vegetative protection on
the ground.
2
To increase the size of the particles by various cropping and
tillage practices.
Wind erosion is a serious problem in the world.
We must make
every efforts to prevent and reduce it. This thesis is concerned only
about the wind threshold velocity for theraovementof individual
particle and its relative threshold shear velocity, and acts as one of
the submodels of the Texas Tech University Wind Erosion Model.
REFERENCES
Abtew, W., Gregory, J. M., and Borrelli, J. 1986. Wind Profile:
Estimation of Displacement Height and Aerodynaraic Roughness. American
Society of Agricultural Engineers, NO.86-2529, pp. 1-10.
Abtew, W. , Gregory, J. M., and Borrelli, J. 1987. Wind Barriers: A
Reevaluation of Height, Spacing, and Porosity. American Society of
Agricultural Engineers, NO.87-2031. pp. 1-7.
Anderson, R. S. and Hallet, B. 1986. Sediment transport by wind:
Toward a general model. Geologicai Society of America Bulletin, v.97.
pp. 523—535.
Arika, Caleb N., Gregory, J. M., Borrelli, J., and Zartman, R. E.
1986. A Ridge and Clod Wind Erosion Model. Presented at the 1986 ASAE
Annual Winter Meeting, Chicago, Illinois.
Bagnold, R. A. 1941. The Physics of Blown Sand and Desert Dunes.
Methuen & CO. LTD. London. pp. 85-106.
Bagnold, R. A. 1960. The re-entrainraenrat of settled dusts.
International Journal of Air Pollution, 2. pp. 357-36o.
Chepil, W. S. 1945a. Dynamics of Wind Erosion: II. Inititation of
Soil Movement. Soil Science, v. 60. pp. 397-411.
Chepil, W. S. 1945b.
Capacity of the Wind.
Dynamics of Wind Erosion: III. The Transport
Soil Science, v. 60. pp. 475-480.
Chepil, W. S. 1959. Equilibrium of Soil Grains at the Threshold of
Move.ment by Wind. Soil Science Society of Araerica Proceedings, 23(60).
pp.422-428.
Chepil, W. S. and Woodruff, N. P. 1963.
The Phvsics of Wind Erosion
and Its Control. Advances in Agronoinv. US Departraent of Agriculture,
15. pp. 211-302.
Coleraan, N. L. .lui Ellis, W. M. 1976. ModeJ Study of the Drag
Coefficient of a Streambed Partirle. Proceedings 3rd Federal
Tnteragenev Sedimentation Conference, Denver, Colorado. pp. o4-12.
Garde, R. J. and Ranga Raju, K. G. 1985. Mechanics of Sediment
Transportation and Alluvial Stream Problems. John Wiley & Sons, Inc.,
New York. pp. 66-70.
46
47
Greeley, R. and Iversen, J. D. 1985. Wind as a Geological Process on
Earth, Mars, Venus and Titan. Cambridge University Press. pp. 67-82.
Greeley, R. and Leach, R. 1978. A Preliminary Assessment of the
Effects of Electrostatics on Aeolian Processes. Reports Planetary
Geology Program 1977-78. NASA. TM 79729. pp. 236-237.
Greeley, R., Leach, R. , White, B. R. , Iversen, J. D. , and Pollack, J.
B. 1980. Threshold Windspeeds for Sand on Mars: Wind Tunnel
Simulations. Grephysical Research Letters, 7. pp. 121-124.
Greeley, R., White, B. R., Leach, R. N., Iversen, J. D., and Pollack,
J. B. 1976. Mars: Wind friction speeds for particle movement.
Geophysical Research Letters, 3. pp. 417-20.
Gregory, J. M.
1982. Soil Resistance to Erosion.
Gregory, J. M. and Borrelli, J. 1986. The Texas Tech Wind Erosion
Equation. American Society of Agricultural Engineers, Number 86-2528.
pp. 1-8. ^
Hudson, N.
1981. Soil Conservation.
Cornell University Press.
Iversen, J. D. , Pollack, J. B. , Greeley, R. , and White, B.R. 197G.
Saltation Threshold on Mars: The Effect of Interparticle Force, Surface
Roughness, and Low Atmospheric Density. Icarus, 29, Number 3. pp.381393.
Iversen, J. D. and White,B. R. 1982.
Saltation Threshold on Earth,
Mars and Venus. Sedimentology, 29. pp. 111-19.
Schwab, G. 0., Frevert, R. K., Edrainster, T. W., and Barnes, K. K.
1981. Soil and Water Conservation Engineering. Jolin Wiley & Sons,
Inc, New York. pp. 122-141.
Vanoni, V. A. Editor. 1975. Sediraentation Endineering. American
Society of Civil Engineering, Number 75-7751. pp. 91-114.
White, B. R. , Greeley, R., Iversen, J. D., and Pollack, J. B. 1976.
Estimated Grain Saltation in a Martian Atraosphere. Journal of
Geophysical Research, 81. pp. 5643-5650.
Zingg, A. W. 1953. Wind Tunnel Studies of the Movement of Sedimentary
Material. Proceeding 5th Hydraulic Conference Bulletin, 34. F>P-Í1I135.
APPENDIX A
COMPARISON OF MEASURED AND CALCULATED VELOCITY
PROFILES AT DIFFERENT HEIGHTS
48
49
Table A.l
Height
(cm)
Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Soil Particle Diaraeter of 0.011 cra
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
3.53
3.6
2.3
3.77
3.9
4.6
4.03
4.3
7.1
4.17
4.5
10.0
4.33
4.6
12.3
4.5
4.7
14.6 '
4.6
4.8
16.9
4.83
4.9
20.2
4.93
4.9
22.2
5.0
5.0
24.8
5.03
5.0
27.1
5.13
5.1
30.2
5.2
5.1
35.0
5.4
5.2
40.3
5.4
5.3
45.2
5.57
5.3
49.8
5.7
5.4
Air Teraperature: 27 ^0
Relative Humidity: 68?o
Test Date: July 14, 1987
50
Table A.2 Comparion of Measured and Calculated
Velocity Profiles at Different Heights
for Soil Particle Diameter of 0.02 cm
Height
(cm)
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
4.2
4.2
2.3
4.5
4.7
4.6
4.8
5.0
7.1
5.06
5.3
10.0
5.3
5.5
12.3
5.4
5.6
14.6 '
5.7
5.7
16.9
5.9
5.8
20.2
5.96
5.9
22.2
6.03
6.0
24.8
6.1
6.0
27.1
6.16
6.1
30.2
6.26
6.1
35.0
6.26
6.2
40.3
6.37
6.3
45.2
6.47
6.4
49.8
6.6
6.4
Air Temperature: 31 °C
Relative Humidity: 64%
Test Date: July 14, 1987
•
51
Table A.3
Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Soil Particle Diameter of 0.055 cm
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
6.0
5.3
2.3
6.37
6.0
4.6
6.5
6.6
7.1
6.7
7.0
10.0
7.0
7.3
12.3
7.07
7.5
14.6 '
7.17
7.6
16.9
7.37
7.7
20.2
7.53
7.9
22.2
7.8
8.0
24.8
8.0
8.1
27.1
8.2
8.1
30.2
8.3
8.2
35.0
8.43
8.4
40.3
8.6
8.5
45.2
8.8
8.6
49.8
8.97
8.7
Height
(cm)
Air Temperature: 30 °C
Relative Humidity: 66%
Test Date: July 14, 1987
52
Table A.4 Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Coal Particle Diameter of 0.011 cm
Height
(cm)
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
2.53
2.6
2.3
2.83
2.9
4.6
3.0
3.1
7.1
3.2
3.3
10.0
3.37
3.4
12.3
3.43
3.5
14.6 *
3.47
3.5
16.9
3.57
3.6
20.2
3.63
3.6
22.2
3.7
3.7
24.8
3.77
3.7
27.1
3.8.
3.7
30.2
3.87
3.8
35.0
3.9
3.8
40.3
3.93
3.9
45.2
3.97
3.9
49.8
4.03
3.9
Air Temperature: 27 °C
Relative Humidity: 50%
Test Date: June 5, 1987
53
Table A.5
Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Coal Particle Diameter of 0.02 cm
Height
(cm)
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
3.33
3.3
2.3
3.67
3.7
4.6
3.97
4.0
7.1
4.1
4.2
10.0
4.27
4.4
12.3
4.37
4.5
14.6 *
4.47
4.5
16.9
4.53
4.6
20.2
4.63
4.76
22.2
4.73
4.7
24.8
4.9
4.8
27.1
4.9.
4.8
30.2
4.97
4.9
35.0
5.0
4.9
40.3
5.0
5.0
45.2
5.0
5.0
49.8
5.13
5.1
Air Temperature: 21 °C
Relative Humidity: 86%
Test Date: June 8, 1987
54
Table A.6
Height
(cm)
Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Coal Particle Diameter of 0.055 cm
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
3.53
3.3
2.3
3.73
3.8
4.6
3.9
4.1
7.1
4.17
4.4
10.0
4.37
4.5
12.3
4.47
4.7
14.6
4.53
4.8
16.9
4.67
4.8
20.2
4.8
4.9
22.2
4.93
5.0.
24.8
5.03
5.0
27.1
5.1
5.1
30.2
5.43
5.1
35.0
5.43
5 "^
40.3
5.5
5.3
45.2
5.53
5.4
49.8
5.53
5.4
•
Air Temperature: 22 °C
Relative Humidity: 82%
Test Date: June 8, 1987
55
Table A.7
Height
(cm)
Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Coal Particle Diameter of 0.1 cm
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
5.2
5.0
2.3
5.7
5.8
4.6
6.3
6.5
7.1
6.63
6.9
10.0
6.93
7.2
12.3
7.13
7.4
14.6
7.4
7.5
16.9
7.67
7.7
20.2
7.73
7.8
22.2
8.03
7.9
24.8
8.1
8.0
27.1
8.27
8.1
30.2
8.3
8.2
35.0
8.53
8.3
40.3
8.6
8.4
45.2
8.6
8.6
49.8
8.6
8.6
•
Air Temperature: 25 ''C
Relative Humidity: 74%
Test Date: June 8, 1987
56
Table A.8 Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Salt Particle Diameter of 0.011 cm
Height
(cm)
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
3.3
3.1
2.3
3.43
3.5
4.6
3.8
3.7
7.1
3.97
3.9
10.0
4.03
4.0
12.3
4.1
4.1
14.6*
4.2
4.2
16.9
4.2
4.3
20.2
4.33
4.3
22.2
4.33
4.4
24.8
4.4
4.4.
27.1
4.5
4.4
30,2
4.5
4.5.
35.0
4.5
4.5
40.3
4.57
4.6
45.2
4.6
4.6
49.8
4.67
4.7
Air Temperature: 29^0
Relative Humidity: 52%
Test Date: June 4, 1987
57
Table A.9
Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Salt Particle Diameter of 0.02 cm
Height
(^"•^
Measured Velocity
(m/s)
Calculated Velocity
(ra/s)
1.0
3.7
3.6
2.3
4 .13
4.0
4.6
4,.3
4.4
7.1
4 .47
4.6
10.0
4..67
4.7
12.3
4,.77
4.8
14.6
4.
4.87
.87
4.9
16.9
4.97
4,.97
5.0
20.2
5.07
5.,07
5.1
22.2
5..07
5.07
5.1
24.8
5.1
5..1
5.2
27.1
5.2
5.,2
5.2
30.2
5. 33
5.33
5.3
35.0
5.
5.43
,43
5.4
40.3
5.5
5. 5
5.4
45.2
5. 63
5.63
5.5
49.8
5. 87
5.87
5.5
Air Temperature: 21°C
Relative Humidity: 61%
Test Date: June 5, 1987
58
Table A.10
Height
(cm)
Comparison of Measured and Calculated
Velocity Profiles at Different Heights
for Salt Particle Diameter of 0.055 cm
Measured Velocity
(m/s)
Calculated Velocity
(m/s)
1.0
4.3
4.2
2.3
4.7
4.8
4.6
5.03
5.3
7.1
5.4
5.6
10.0
5.77
5.9
12.3
5.9
6.0
14.6 *
6.03
6.1
16.9
6.27
6.2
20.2
6.33
6.3
22.2
6.4
6.4
24.8
6.47
6.5
27.1
6.53
6.5
30.2
6.8
6.6
35.0
6.9
6.7
40.3
6.93
6.8
45.2
7.0
6.9
49.8
7.1
7.0
Air Temperature: 23°C
)%
Relative Humidity: 60î
Test Date: June 5, 1987
APPENDIX B
GRAPHIC REGRESSION OF CALCULATED WIND
VELOCITY ON MEASURED WIND VELOCITY
59
60
(D
E
LiJ
ZD
-J
5 -
<
>
Q
LLl
4 •
ZD
R-SÛUARE - 0.85
SOILt d - 0. C n cw
u
<
CJ
4
^
5
MEASURED' V A L U E
Fig. B.l
(m/s)
Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocity for
0.011 cra Diameter Soil Particles.
61
æ
\
E
UJ
<
>
Q
LiJ
<
_J
Z)
•
u
R-SQUARE - 0 . 9 4 8
SOILt d - 0 . 0 2 ctn
<
u
5
6
MEASURED VALUE (m/s)
Fig. B.2
Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocity for
0.02 cm Diameter Soil Particles.
7
62
(D
X
E
8
LLI
7
Q
LU
•
R-SQUARE - 0 . 8 8 8
SOILt d - 0 . 0 5 5 cn
U
<
u
7
8
MEASURED VALUE (m/s)
F i g . B.3
Graphic Regression of C a l c u l a t e d Wind
V e l o c i t y on Measured Wind Velocity for
0.055 cm Diameter Soil P a r t i c l e s .
63
5. 0
E
4. 5
^
LLI
•
R-SQUARE - 0 . 9 5 9
COAU d - 0 . 0 1 1 cin
4. 0
_J
<
>
3: 5
Q
^/
LLJ
h<
_J
ZD
U
_J
^ /
3. 0
V
2. 5
^Y
2. G
2
1
-
<
u
1
1
.
1
1
2. 5 3. 0 3. 5 4. 0 4. 5 5. 0
MEASURED VALUE ( m / s )
Fig. B.4
Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocity for
0.011 cm Diaraeter Coal Particles.
64
6.0
0)
\ 5 5 E ^tt! 5.
y^
x*
<
> 4.5
Q
LLJ
4.0
«
R-SQUARE - 0.978
COALt d - 0 . 0 2 cra
^, 3 . 5
<
U
3.0
4. 5 5. 0 5. 5 6. 0
3. 0 3. 5 4.
MEASURED VALUE (m/s)
Fig. B.5
Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocity for
0.02 cm Dianieter Coal Particles.
65
u
5
UJ q
0
-J
<
*
X
5
*
Q
X
LLJ
*
4.
y
/
R-SQUARE - 0.895
COALt d - 0.055 ctn
H 3. 5
<
u
•
1
. . .1
1
1
1
.
3. n
3. 0 3. 5 4. 0 4. 5 5. G 5. 5 6. 0
MEASURED VALUE (m/s)
Fig. B.6
Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocity for
0.055 cm Diameter Coal Particles.
66
0)
\
E
8 -
LLI
Z)
<
>'7
Q
LU
R-SQUARE - 0 . 9 6 9
COALi d . 1 cni
U
<
U
7
8
MEASURED VALUE (m/s)
Fig. B.7
Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocity for
0.1 cm Diaraeter Coal Particles.
67
5.0
0)
E
^^
4.5
•
R-SQUARE - 0.972
SALTi d - 0.011 cm
LU
<
> 4.0
Q
LU
U
<
u
3. 0
3. 0
3. 5
4. 0
4. 5
5. G
MEASURED VALUE (m/s)
Fig. B.8
Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocity for
0.011 cm Diameter Salt Particles.
68
6.0
XN
0)
í 5. 5f-
R-SQUARE - 0.951
SALTI
d -
0.02
*
^
cra
LLI
5. 0
<
>
LLI
4. 5 -
u 4.0 <
u
3. 5
3. 5
4.
4. 5 5.
5. 5 6. 0
MEASURED VALUE (m/s)
Fig. B.9
Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocity for
0.02 cra Diameter Salt Particles.
69
7.5
/ ^
0)
^
E
LLI
o
-J
7. 0
6. 5
<
6.
>
•
Q
LLI
•
_
R-SQUARE - 0.981
SALTi d - 0.055 cn
5. 5
I<
-J
5.
= )
u
-J
4. 5
<
u
4.
4 0 4. 5 5. 0 5. 5 6. 0 6. 5 7. 0 7
MEASURED VALUE (m/s)
Fig. B.IO Graphic Regression of Calculated Wind
Velocity on Measured Wind Velocily for
0.055 cra Diameter Salt Particles.
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