sediment transport - lth classification of sediment • cohesive (clay) electro-chemical forces;...
TRANSCRIPT
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Basic Sediment Transport and Boundary Layer Theory
Environmental Hydraulics
Sediment Transport
Interaction between fluid flow (water or air) and its loose boundaries.
Strong interaction between the flow and its boundaries.
Professor H.A. Einstein: ”my father had an early interest in sediment transport and river mechanics, but after careful thought opted for the simpler aspects of physics”
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Overview
• introduction
• properties of sediment
• current boundary layers
• threshold of motion
• bed features
• suspended load transport
• bed load transport
• total load transport
Importance of Sediment Transport
• erosion (land, rivers, coast)
Examples: soil erosion, local scour around structures, beach erosion
• accumulation (rivers, lakes, reservoirs coast)
Examples: reservoir sedimentation, infilling of harbors, navigation channels, and water intakes
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Classification of Sediment
• cohesive (clay)
electro-chemical forces; form a coherent mass
• non-cohesive (sand)
frictional forces; collection of individual particles
Classification of Sediment Transport
• bed load
along the bottom; particles in contact; bottom shear stress important
• suspended load
in the water column; particles sustained by turbulence; concentration profiles develop
• wash load
more or less evenly distributed through the water column; little relationship with (river) flow properties
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Agents for Sediment Transport
• wind
• water
uni-directional flow (rivers)
oscillatory flow (waves)
combined flow (waves + current)
Properties of Sediment
• grain size (diameter)
• density
• porosity
• concentration (by volume or mass)
• angle of repose
• permeability (fluidization)
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Grain-Size Classification
φ log d=− 2
Phi scale:
Grain-Size Fractions
dn = the grain diameter for which n% of the grains by mass is finer
Geometric standard deviation: σ /g d d= 84 16
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Sediment Sorting
/ well sorted
/ well mixed
d d
d d
<>
84 16
84 16
2
16
Grain-size distribution often follows a log-normal distribution
Density, Concentration and Porosity
Density of sand grains (quartz): 2650 kg/m3
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Bulk Density
mass of mixtureρ
volume of mixtureB =
Angle of Respose
The angle to the horizontal at which grains start to roll on a flat bed of sediment that is gradually tilted from the horizontal.
A representative value on the angle of repose is 32 deg.
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Permeability and Fluidization
ρυP
B
K dpV
dz=
Bulk velocity:
Current Boundary Layers
Velocity profile over a loose boundary (bed).
Vertical gradients are much larger than horizontal ones.
Logarithmic velocity profiles:
*
*
( ) lnκ
τρ
o
o
u zU z
z
u
=
=
Mean velocity: ( )h
U U z dzh= ∫
0
1
κ .=0 4
Von Karman’s constant
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Bed Roughness Length
*
*
*
*
νν
ν
ν
so
so
s so
u kz
u
kz
u
k u kz
= <
= +
= >
59
30 9
7030
Smooth flow
Transitional flow
Rough flow
Nikuradse roughness:
.sk d= 502 5
Current Skin Friction Shear Stress (Flat Bed)
Shear stress: τ ρo DC U= 2
Drag coefficient:( )κ
ln /Do
Cz h
⎛ ⎞⎟⎜= ⎟⎜ ⎟⎜ ⎟⎜ +⎝ ⎠
2
1
Relationship with other friction coefficients:
/D
f g gnC
C h= = =
2
2 1 38
( Darcy-Weisbach / Chezy / Manning )
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Current Total Shear Stress (Non-Flat Bed)
τ τ τo os of= +
Shear stress from skin friction and form drag:
ripples
High flow speed => sheet flow => additional roughness
o os of otz z z z= + +
Wilson (1989): τ(ρ ρ)
osot
s
zg
=−
530
Threshold of Motion
Conditions for initiation of motion.
Shields diagram
*τρ ( ) ν
cr u df
g s d
⎛ ⎞⎟⎜= ⎟⎜ ⎟⎜⎝ ⎠−50
501(Shields 1936)
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Threshold current speed (Soulsby 1997):
( )( )
( )( )
//
*
* **
/
*
( )
.( ) . exp .
.
( )ν
cr
hU g s d f D
d
f D DD
g sD d
⎛ ⎞⎟⎜= −⎟⎜ ⎟⎟⎜⎝ ⎠
= + − −+
⎛ ⎞− ⎟⎜= ⎟⎜ ⎟⎜⎝ ⎠
1 71 2
5050
1 3
502
7 1
0 300 055 1 0 020
1 1 2
1
Threshold bed shear stress (Soulsby and Whitehouse 1997):
( )( )**
.θ . exp .
.cr DD
= + − −+0 30
0 055 1 0 0201 1 2
τθ
(ρ ρ)cr
crsg d
=− 50
Threshold Shields parameter:
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Bed Features
A variety of features appears on a loose bed exposed to flowing water:
• ripples
• dunes
• antidunes
Example of Bed Features
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Characterization of Bed Forms
Current Ripples
Geometric properties (Soulsby 1997):
rλ d= 501000
Δ rr
λ=7
Ripple wavelength
Ripple height