Sediment Transport
Outline
1. Incipient motion criteria for unisize and
mixed-size sediments
2. Modes of sediment transport
3. Bedload transport
4. Suspended load
5. Bedforms
Incipient Motion
Forces Acting on Stationary Grain
(Middleton and Southard, 1984)
Threshold of Motion
(Shields,1936; Julien, 1998)
(Middleton and Southard, 1984)
FD
FG
 

 0D
2
   gD
3


0
   gD
c 

c
   gD
Smooth
 c  0 . 045
Transitional
Rough
Motion
No Motion
(Miller et al., 1977)
Sample Calculation
What is c for D = 0.005 mm quartz-density
particle?
c 

c
   gD
 c   c     gD
 0 . 045  2650  1000 9 . 81  0 . 005  3 . 6 Pa
Entrainment of mixed-size sediment
Due to:
1. Relative Protrusion
2. Pivoting angle
Relative Protrusion
Pivoting Angle
Threshold of Motion for a Stationary
Grain (Unisize or Graded Sediment)
Mixtures
FD
FG

l G
l D  tan  cos   sin 
1  l G l D  tan   F L F D 
: yD ,
Wiberg and Smith (1987), Bridge and
Bennett (1992), + many others
Entrainment of mixedsize sediment
 ci  0 . 045     g  D 50 
0 .6
 D i 0 .4
Sample Calculation
What is c for 0.001 and 0.010 m quartz-density
particles in a mixture with D50 = 0.005 m?
 ci  0 . 045     g  D 50 
0 .6
 D i 0 .4
For 0.001 m
 0 . 045  2650  1000 9 . 81  0 . 005
0 .6 0 . 001 0 .4
 1 . 9 Pa
Using Shields
for unisize
sediment
0.7 Pa
For 0.01 m
 0 . 045  2650  1000 9 . 81  0 . 005
0 .6 0 . 01 0 .4
 4 . 8 Pa
7.3 Pa
Sediment Transport
Modes of sediment transport
(Leeder, 1999)
Criteria for Sediment Transport
Modes
• Bedload:  0   c
• Suspended bed material:
• Washload: D  0.063 mm
au *  u s
Modes of sediment transport
au *  u s
0 c
Washload:
D  0.063 mm
(Bridge, 2003)
Bedload Transport Equations
Meyer-Peter and Muller (1948)
q b  8    c 
3 2
 g

3

 1  gD
 g

Bagnold (1966)
qb 
a
tan 
u *  u *c  0
c
Measuring bedload transport
Bedload traps (K. Bunte)
Helley-Smith sampler
Bedload Transport Observations
HS
ib  f 

ib  f Q 
trap
Gravel-bed streams
(Bunte et al., 2004)
Gravel-bed stream
(Cudden & Hoey, 2003)
HS
Bedload Transport Equations
Wilcock & Crowe (2003)
Reference threshold condition
Hiding function
Reference dimensionless shear stress for
median size base don fraction of sand
Transport rate based on /ri
Bedload Transport Equations
Barry et al. (2004)
Meyer-Peter and Muller (1948)
q b  8    c 
3 2
 g

3

 1  gD
 g

qb 
tan 
u *  u *c  0
 3 . 41

Q
 2 . 45 q *  3 . 56
q *  f  Q 2 ,  d 5 0 s ,  d 5 0 ss

Abrahams and Gao (2006;
following Bagnold, 1966, 1973)
Bagnold (1966)
a
q b  257 A
c
ib   G
3 .4
  U
G
2
 Tg T
Predicting
bedload transport
Abrahams and Gao (2006)
following Bagnold (1966, 1973)
Barry et al. (2004)
(a) Meyer-Peter
and Müller [1948]
equation by d50ss
(c) Ackers and White
[1973] equation by di
(e) Bagnold
equation by dmqb
(g) Parker et al. [1982]
equation by di (Parker et
al. hiding function)
Predicting
bedload transport
(b) Meyer-Peter and
Müller equation by di
(d) Bagnold
equation by dmss
(e) Bagnold equation
by dmqb
(h) Parker et al. [1982]
equation by di (Andrews
[1983] hiding function)
(Barry et al., 2004)
Suspended Sediment
• Simple criterion for suspension: au *  u s
(van Rijn, 1993)
Measuring suspended
load transport
DH59 – Hand line Sampler
DH48 – Wading Sampler
D74 – Hand line Sampler
Others: Super-critical flumes, ISCO, OBS, Acoustics
Suspended Sediment
• Sediment-diffusion balance (equilibrium):
u s C 1  C    s
C
y
0
qs 
downward settling + upward diffusion

h
uC d y
a
Total suspended load
• Rouse equation:
C
Ca
d  y
a 
 


d a
 y
z
z
us
 u *
Suspended sediment profiles and Rouse equation
Z
(van Rijn, 1993)
Ripples
Dunes
Upper-stage plane beds
Bedload sheet
Bedform
Stability
Suspended Load Observations
Mobile orbital ripples with
acoustic probes, P. Thorne
Mobile river dunes with acoustic
probe, Wren et al. (2007)
Stochastic simulation,
Man (2007)
Sediment Transport and Stream
Restoration
• Deficient or excessive sediment transport based
on design discharge will result in erosion or
deposition, which can redirect flow and threaten
infrastructure and ecologic indices
• Sediment transport prediction depends on grain
size, gradation, and bed topography
• Uncertainty can be large
• Excludes bank erosion and wash load
• Use multiple relationships
Sediment Transport
Conclusions
• Threshold conditions defined by Shields
criterion
• Modes of sediment transport depend on
Shields criterion and grain size
• Bedload and suspended load transport
treated separately
• Load is modulated by bedforms