Impact of Packing Density, Particle Angularity and Uniformity

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

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