Impact of Packing Density, Particle Angularity and Uniformity

Coefficient on the Erodibility of Coarse-grained Particles

Hyunwook Choo1, Ph.D., Qian Zhao2, Ph.D., Terry Sturm1, Ph.D., P.E., and Susan Burns1, Ph.D., P.E.

30

Combined Rolling Model: Eq (27)

Critical Shear Stress, c (Pa)

z

z

b

d/2

20

in (27)=

25

15

10

10

(a) Sliding

where, E = erosion rate; Kc = erodibility factor;

n = empirical constant; b = applied bottom

stress; c = critical shear stress.

(28) Lower Limit

25

30

2400

10

1800

(29) Mean Threshold

0.04

(28) Lower Limit

0.02

15

20

25

5

30

10

15

20

Angle of (degrees)

25

FL

b

x

d/2

a

539

P

x

Critical Shear Stress (Pa)

FD

0

0

ASTM 20/30

ASTM graded

F80mix

1.25 sand

2.0

FD

0

0

GS22 20/30

F80

F110

2.64 sand

1.5

0.6

0.8

Shear Stress (Pa)

W

1.17

1.17

1.67

1.56

1.44

1.56

2.68

2.22

Cc

1.006

1.006

0.938

0.966

0.864

1.092

0.663

1.233

Roundness

0.90

0.23

0.75

0.70

0.42

0.32

0.78

0.80

*c

2 tan

c

3

'd (1 f (Re) tan ) TF

*c

2 sin

c

3

'd (0.5 cos f (Re) sin ) TF

0.8

0.12

(b) Two Rolling Models

0.6

0.12

0.4

0.2

This Study

Shields (1936)

2

0.09

0.06

*c 0.045

(Shields, 1936)

1.5

1

0.03

0.00

10

0.0

0.4

*c 0.045 (Shields 1936)

23

27

31

35

0.6

0.8

1

*c 0.062 (Briaud et al. 1999)

Angle of Repose (degrees)

10

17

24

31

38

Angle of (degrees)

50

Bed-load transport by

rolling is the more

likely mechanism for

the initiation of

particle motion in

fluid flow.

:Region of Combined Sliding (Eq. 18, 25<<37)
:Region of Combined Rolling (Eq. 27, 15<<40)
40
30
20
10
0
0
5
10
15
Diameter, d (mm)
20
25
45
38
45
0
0
0.5
1
1.5
Measured c (Pa)
2
Reasonable agreement between the theoretical
prediction (combined rolling model) and the test
results
Regression
0.analysis:
016 (2.2 e) C
*c
2
*c 0.045 (Shields 1936)
31
However, characteristics of different materials cannot
be fully captured via the theoretical model.
Void Ratio, e: 0.63~0.67
0.00
39
24
1.15
c
0.08
*c 0.062 (Briaud et al. 1999)
0
17
Angle of (degrees)
2.5
0.04
1.1
2.5
1.0
Decreasing void ratio will result in a higher
coordination number and a higher rotational
frustration.
Effect of Particle Size
0.16
(a) Two Sliding Models
0.9
Angularity
(or Cu)
Void Ratio, e
Comparison w/ Experimental Results
0.7
Shear Stress (Pa)
0.5
Critical Shear Stress (Pa)
2.65
2.65
2.65
2.65
2.65
2.65
2.65
2.65
Cu
0.5
GS22 20/30
Comparison b/w Theory and
Experiments / Regression Analysis
0.5
(b) Combined Rolling
Shields Parameter, *c
0.72
0.72
0.184
0.121
2.64
1.25
0.192
0.365
Gs
Shields Parameter, *c
ASTM 20/30
GS22 20/30
F-80 sand
F-110 sand
Coarse 1
Coarse 2
F80 mix
ASTM graded
D50 (mm)
Critical Shear Stress, c (Pa)
Soil type
(a) Combined Sliding
ASTM 20/30
0.3
1
Materials and Method
You can change the color scheme etc., just keep the margins, size, general style consistent.
W
GS22 20/30 (e: 0.6751)
2000
As the coefficient of uniformity or particle angularity is
increased, the coordination number, or number of
interparticle contacts, increased, which results in a
higher friction angle and soil stiffness.
Effect of Void Ratio
2.5
0
0
GS22 20/30 (e: 0.7546)
1000
Results and Discussion
FL
d/2
GS22 20/30 (e: 0.8967)
600
0.4
c 0.425 d 1.139
Mean
Upper limit - c 0.724 d 1.139
c
2
sin
'd 3 (1 cos )
V
ASTM 20/30 (e: 0.5112)
30
Place Poster Content Here
V
F80mix (e:0.6953)
1200
1.139
Combined (Drag + Lift forces) Sliding and
Rolling Mechanism z
ASTM 20/30 (e: 0.5368)
3000
F80mix (e:0.4613)
c
(b) Rolling
*c
ASTM 20/30 (e: 0.6246)
F80 (e:0.5404)
Envelopes of Paphitis (2001): compiled
existing data;Lower limit 0.253 d
x
ASTM 20/30 (e: 0.6436)
F80 (e:0.7972)
0.06
Diameter, d (mm)
a
4000
(30) Upper Limit
Shields Parameter,
z
20
0.00
5
W=N
: E K c ( b c ) n
(29) Mean Threshold
15
0
P
c
2
tan
'd 3
15
Normalized Paphitis (2001):
0
cA
x
10
5
N=W
d/2
0.08
Paphitis (2001)
25
Simple Sliding and Rolling Mechanism
(30) Upper Limit
5
Estimated c (Pa)
3 1/ 3
( / 1) g D50
*c c f d* solid water 2
'D50
T
Diameter, d (mm)
0
Erosion Rate (mm/hr)
Shields Parameter
Transport of coarse-grained sediments :
f(hydrodynamic conditions, geotechnical
properties of sediments)
Among various geotechnical properties of
soils, the effect of mean grain size on the
erodibility of coarse grains : well quantified.
However, studies on the impact of other
geotechnical properties (e.g., void ratio,
uniformity coefficient, and particle shape)
on the erosion potential of coarse grains :
very limited.
Common erodibility model for coarse grains
Effects of Uniformity Coefficient and
Particle Shape
Combined Rolling vs. Paphitis Envelopes
Erosion Rate (mm/hr)
Theoretical Analysis
*c
Introduction
School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia
2
Department of Civil & Environmental Engineering, University of Louisville, Louisville, Kentucky
Shields Parameter, *c
1
'D50
u
R 0.28
where, c is in Pa; D50(mean grain size) is in mm; Cu =
uniformity coefficient; R = roundness.
1.5
c = 0.788D50
R = 0.918
Acknowledgments
1
0.5
0
0
0.5
1
1.5
2
Median Grain Size, D50 (mm)
2.5
3
As D50 increased, individual grains had more weight
and more resistance to buoyancy and shearing forces
Partial funding for this investigation was provided by the
Georgia Department of Transportation, and the authors
are grateful for their support. The authors especially
appreciate the thoughts and insights of Mr. Jon D.
Griffith, P.G., P.E.
2.5