Sediment transportPart 2: transport rate

GEOL/CE/EEB 8601 Intro to Stream Restoration

Steps in analyzing sediment mobility

1. Determination of bed sediment characteristics: grain size distribution and texture

2. Will it move? Apply the Shields criterion (Shields diagram)

3. Estimation of bed-material transport rate4. Understanding channel change:

watershed, natural history and effects of imposed changes

Bedload: the movie!

John Gaffney movie

Measuring bedload

Helley-Smith sampler

Estimating bedload: Meyer-Peter & Müller2/3)( cskMPMs Kq

qs =

qs

(s–1)gD3 1 21 2

qs =volumetricsedimentdischarge

perunitwidth.............[L2T–1]

s=sedimentspecificgravity.............[0]

g =gravitationalacceleration.............[LT–2]

=

u 2

( s – 1 ) gD

u =frictionvelocity=

0

1212

0=boundaryshearstress.............[ML–1T–2]

=fluiddensity.............[ML–3]

c= forinitiationofsedimentmotion

KMPM = 8 in the original formulation; corrected to 4 by Wong & Parker (2005)

Form drag: Smith & McLeanIndirect estimate of skin friction component of total stress

28.00 ))/(1.0ln(105.0

skbf

sk

skT zh

0sk 50

spatially averaged skin friction stress

total stress

z skin roughness length = / 30

0.4

sk

T

D

hbf

Surface layer thickness La [1-2]Ds90

fraction of material in the surface (active) layer in the ith size range = Fi

unit bedload transport rate in the ith size range = qbi

Mixed sizes: definitions

Lasurface

subsurface

Bedload vs suspension

Fw ~ w’ (turbulence)

Fw ~ bed (collisions, contact)

suspension

bedload

Turbulent fluctuations w’ ~ u* suspension if u* ~ settling vel ws

Bedload vs suspension

Turbulent fluctuations w’ ~ u* suspension if u* ~ settling vel ws

u

ws

Ro

Low Ro: turbulence > settling, suspension > bedload; sediment column is well mixed

High Ro: turbulence < settling, bedload only; sediment transport confined to bed region

Bedforms

Bedform types: unidirectional flow

ripples

Bedform types: unidirectional flow

dunes

Bedform types: unidirectional flow

plane bed

Bedform types: unidirectional flow

antidunes

Bedform stability

Southard (1991)

0.2 0.4 0.6 1.0 2.00.2 0.4 0.6 1.0 2.0

Bedform stability

Southard (1991)

0.2 0.4 0.6 1.0 2.0 0.2 0.4 0.6 1.0 2.0

Bedform stability

Southard (1991)

Bedform stability

Southard (1991)

Bedform stability

Southard (1991)

Bedforms - summaryRipples

• D < 0.5 mm

< 0.3 m

/hbf ~15

• u ~ uc

Dunes

• D > 0.2 mm

• hbf ~ 0.3 h

/hbf >15

• ws> u >> uc

Upper plane bed

• D = any

• u > ws

Antidunes

• D = any

• Fr = U/gh ~ 1

Can you explain this?

Pigeon Roost Creek, Mississippi

Total load formulasEngelund-Hansen (1967)

05.0 2/5

f

s cq

2

2

U

uc f

Brownlie (1981)3301.0

50

6601.0978.10

r )(7115

DSFFKqq ggws

50)1( Dsg

UFg

r = hydraulic radius (Area/wetted perimeter

K = 1 for lab data

= 1.268 for field data

Bedload, suspended load, gravel and sand: adding fines to a gravel channel

• Establish steady-state slope profile with constant sediment feed Qs_coarse of a fixed coarse grain size, fixed water supply Qw

• Double Qs by adding an equal supply rate of a second finer grain size

• Measure new steady-state slope with the additive Qs_coarse + Qs_fine

John Gaffney, Sarah Baumgardner, Kimberly Hill, Peter Wilcock

Adding fines to gravel channel

John Gaffney, Sarah Baumgardner, Kimberly Hill, Peter Wilcock

D50 coarse/D50 fine

Adding fines to gravel channel

John Gaffney, Sarah Baumgardner, Kimberly Hill, Peter Wilcock

Adding fines to gravel channel

John Gaffney, Sarah Baumgardner, Kimberly Hill, Peter Wilcock

Adding fines to gravel channel