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!