Post on 07-Jun-2020
1
Erosion and Sedimentation
Dr. Pierre Y. JulienDept. of Civil and Environmental Engineering
Colorado State University, Fort Collins
Short CourseGadjah Mada UniversityYogyakarta, Indonesia
July 21, 2009
ObjectivesErosion and Sedimentation:
1. Sediment Properties and Fall Velocity; 2. Flow Properties;3. Incipient Motion;4. Riprap Design;5. Bed Load and Suspended Load;6. Flow in Bends.
1. Sediment Properties and Fall Velocity
2
Los Corales
Sand Gravel Cobblesv.f. fine med. c. v.f. fine med. c.v.c. v.c. small large
100
90
80
70
60
50
40
30
20
10
0
% b
y w
eigh
t fin
er th
an
25612864321684210.50.250.1250.0625
d d d10 50 90Diameter (mm)
Vs
d d d16 50 84
Vv
φ
3
Fall Velocity( )
( )
( ) 31
2*
5.03*
2
1
172
18
&,134
&18
1
⎥⎦
⎤⎢⎣
⎡ −=
⎥⎥⎦
⎤
⎢⎢⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛+=
−=
→−
=
ms
s
m
D
s
s
vgGdd
diameterparticlesmensionlesdi
ddv
bouldescobblesgravelsforvalidC
dGg
clayssiltsforvalidLawStokesv
dGg
ω
ω
ω
2. Flow Properties
Logarithmic Velocity Profile
o
x
zz
uv ln1
* κ=
4
Open Channel Flow• Pressure Distribution
• Shear Stress
• Shear Velocity
( )zhgp
gdzdph
zp
−=
−= ∫∫ρ
ρ0
( )fo
fzx
ghSSzhg
ρτ
ρτ
=
−=
fo ghSu ==
ρτ
*
Sw
So
Datum
zo
h
SfV2/2g
g
g sin at o
t zxp
Q
x
z
Example - Shear Velocity
smu
msmghSu f
113.0
0001312.0*9.9*81.9
*
2*
=
==
Resistance to Flow
5
3. Incipient Motion
Incipient Motion
Angle of Repose Effects of Angularity
Motion occurs when the center of gravity (G), is inline with the point of contact (C). o60== φθ
6
Angle of ReposeGranular Material
Shields Parameter• Ratio of
Hydrodynamic Forces to Submerged Weight
( ) ( ) ss
m
ss
o
du
d γγρ
γγττ
−=
−=
2*
*
Beginning of Motion• Critical Shields Parameter(τ*c)
– beginning of motion (τo = τc) ( ) ss
cc dγγ
ττ−
=*
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Critical Shear Stress
4. Riprap Design
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CHANNEL PROTECTION - RIPRAP
Θβ
δλ
A
Au
F
F sin
F sinF a
FBed
Top of bank
Sideslope gradient
Streamline
View normal to sideslope
Horizontal
s θ1
s
D
s 1
s 0
F sins 1
F
F cos
F 1 - a cos
O'
OF a
1
2 3
4
2
s θ D δ
s βθ
LParticle P
Section A - A
1
3
F sinD δParticle P
OF 1 - a sin2
s βθ
Section normal to section A - A
Θ
ΘΘΘ
ΘDownstream
1Θ0Θ
δ βλ ΘDownstre
am
Streamline drag component
Particle pathline
Weight component
Q
l
l
l
l l
l
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Velocity Method
( )
φtan4log
12
⎟⎟⎠
⎞⎜⎜⎝
⎛=
−=
sc
scc
dhK
gdGKV
Riprap Design
Gradation of Riprap• Well graded riprap
scours less than uniform size riprap due to the process of armoring
• Suggested Riprap gradation from USACE is shown to the right
• Riprap with poor gradation may be used, but a “filter” layer is required
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Gravel Filters• Gravel filters should
not be less than 15 to 23 cm
• ½ thickness of Riprap layer is a good guideline
• Suggested gravel filter gradation equations are shown to the right
5)()(
40)()(5
40)()(
85
15
15
15
50
50
<
<<
<
bankdfilterd
bankdfilterd
bankdfilterd
CHANNEL PROTECTION - RIPRAP
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5. Bedload and Suspended Load
Incipient Motion
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Medición Transporte Sedimento 36 Prof. Em. Ing. J.J. Peters | ConsultorProf. Em. Ing. J.J. Peters | Consultor
Muestreador US BL-84
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1.5
*
*
*
*
τ
*q = 40 τ 3
– 0.391τ
1/τ
q
10 10 1 102 -1
2
-1
-2
-3
-4
10
10
1
10
10
10
10
310
10 10 1 10-1-2
bv*
bv*
*
bvq
=w
d os
q = 15 τ
q = 2.15 e
bv*
bv*
IsokineticIsokinetic DepthDepth--integrating Samplerintegrating Sampler
isokineticnozzle
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Collapsible-bagsampler array
As used in:AmazonOrinocoMississippi
15
10
10
1
1010 10 1 10 10 10
1
11
R = 0.63
oR = 0.49
o
Run 19 Vanoni, 1946 h = 0.236 ft d = 0.10mm κ = 0.33
Run 55 h = 0.590 ft d = 0.10mm κ = 0.34
Run S-16 Einstein & Chien, 1955 h = 0.390 ft d = 0.274mm κ = 0.18
R = 1.86
o
Hyper-conc.Suspension
2
-1-2 -1 2 3
Concentration C (g/ )
(h -
z)/z
50
5050
l
SEDIMENTRATINGCURVES
1.0
0.8
0.6
0.4
0.2
01 10
Bedload Suspended load
d = 190 µm d = 270 µm d = 280 µm d = 450 µm d = 930 µm
5050
50
50
50
Data Guy et al., 1966h = 0.1 - 0.3 m
Ratio shear velocity - fall velocity, u /ω*
st
Rat
io su
spen
ded
- tot
al lo
ad, q
/q
Mixed load
10 -1
Lowest incipient motion (gravel)
100010 000
100 000
100
h/d = 100s100010 000100 000
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AGU Hydrology days 2005 Flood Damages
6. Flow in Bends
τ tan λ τ
λoo
τ tan λ o
Thalweg
Sedimentation Erosion
λ = 10°SF
1
Thalweg
Lateral migration
Sedimentation Erosion
(a)
(b)
(c)
(d)
Fine Coarse
Equilibrium
Point bar
Fine sediment in suspension
Coarse sediment bedload
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Mississip
pi River
< - 20 ft below LWRP
> - 20 ft below LWRP
> - 30 ft below LWRP
Fine sand concentration
0 100 200 300 400 500 mg/L
250
750
30004000
Right bank Left bankWater surface12
10
8
6
4
2
00 100 200 300 400 500 600 700 800 900
Stationing across section (ft)
Dis
tanc
e ab
ove
stre
am b
ed (f
t)
= 31 600 ft /s = 4.9 ft/s = 838 ppm - sand = 0.20 mm - bed sediment = 1.5 x 10
Q V S
C d
m50 -4
3
3500
500
1000
15002000
2500
5000
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Old River Control Complex
Mississippi RiverMississippi River
Outflow ChannelOutflow Channel
Example 3-D Model Mississippi
Erosion and River Mechanics Textbooks
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pierre@engr.colostate.edu
THANK YOU for your Attention!