Sediment transportPart 1: initial motion

GEOL/CE/EEB 8601 Intro to Stream Restoration

Why does it matter?

1. A common requirement in channel design is that the bed be stable under some specified discharge, i.e. the sediment will not move

2. Total transport of bed-material sediment plays a major though incompletely understood role in setting channel width

Why does it matter?

3. Changes in the transport capacity of the reach may cause erosion or deposition

4. In-stream organisms are often sensitive to bed texture, especially fines content of gravel bed streams

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. Estimate bed-material transport rate if desired – note that existing formulas are highly imprecise/inaccurate

4. Consider the watershed, boundary conditions and natural history:

Watershed and historya) What is being supplied from upstream? Does

it/will it/could it include material not represented in the bed (e.g. fines from upland land management)?

b) Is there morphologic evidence (e.g. air photos) for changes in stream type related to sediment supply (e.g. braided vs meandering)?

c) What is the long-term trend (depositing, degrading, bypass)? Why?

d) Are there downstream changes (e.g. reduction in base level) that could lead to aggradation or degradation?

Step 1. Sediment characterization

• Gravel beds: usually bimodal– Gravel mode: Wolman

count+gravelometer, image-based measurement

– Distinguish surface vs subsurface

Step 1. Sediment characterization

• Gravel beds: usually bimodal– Greater intrinsic mobility of

sand often leads to higher gravel fraction in surface layer: “armor” or “pavement”

– You can measure GSD of either depending on your purpose. Usually do surface Note higher sand content

– subsurface GSD is usually closer to the GSD of material in transport

Frey & Church Science 2009

Step 1. Sediment characterization

• Sand beds: usually unimodal– sieve– automated size counter

Either way you end up with something like this:

Unimodal sand

or this:Bimodal gravel-sand

Summary: grain-size distributions

• Logarithmic size scales: ln2 [], -ln2 [], or log10

• Standard form: percentages in size range; cumulative

• Common percentiles: 90, 84, 65, 50, 16

• Unimodel or bimodal (e.g. gravel-sand)

• No standard form at present for single modes (e.g. log-normal)

Summary: size and mineralogy

• Gravel, cobble, etc: > 2 mm; all common rock lithologies

• Sand: 62 m – 2 mm; quartz, feldspar, other

• Silt: 4 m – 62 m; quartz, feldspar, other• Clay: < 4 m; clay minerals• Cohesive effects important for D <~ 10 m

and/or clay minerals and/or biological effects

Settling velocity, ws

• Two regimes, distinguished by Reynolds number: Stokes (laminar, R<~1) vs impact (turbulent, R>~100)

• General formula, Ferguson & Church 2004

5.0321

2

)75.0( RgDCC

RgDws

C1 = 18

C2 = 0.4 1

R = s/f – 1

= kinematic viscosity

Settling velocity

• Rule of thumb, qtz density in water:

for D < 100 m, ws in diam/s D in m

for 100 < D < 1000, ws in diam/s 100 diam/s

D > 1000, ws increases as D1/2

5.0321 )75.0( RgDCC

RgDws

R < 1

R > 104

C2 1

C2 0.4

2. Will it move? Shields initial motion

From Buffington (1999)

Duu

Dsg

u

Re

)1(0

2

Shields stress:

2. Will it move? Shields initial motion

2. Will it move? Shields initial motion

DgDs-

p)( 1

Re

)7.7(6.06.0

1006.022.0 p

pcRe

Re

Initial motion: standard conditions

stolen from Peter Wilcock, JHU

Motion

No motion

What not to use Less objectionable if this is interpreted as initial motion, but still better to use shear stress

Hjulstrom diagram

What to do about size mixtures?

When grain sizes are clearly segregated into patches like this, you have to apply Shields to each patch separately.

Within a mixture, all sizes tend to move together up to very large clasts

0.1

1

10

0.1 1 10x

x

50c

ci

Di / D50

Parker; Wilcock; Proffitt & Sutherland

mixture effects diminish for extremely large grain sizes

Modifying Shields for slope effects

ccoc

tan1cos

tan slope streamwise xS

2/1

2

2tan1cos

ccoc

tan slope lateral yS7.0c

Streamwise slope

Lateral slope

Transport ofBiota

Hondzo & Wang 02

Initial motion -- summary• Brownlie formula for Shields curve:

• Correction for streamwise slope:

• Correction for side slope:

• Correction for mixtures:

)7.7(6.06.0

1006.022.0 p

pcRe

Re

NB Parker et al. (2003) have suggested reducing this by a factor of 2

ccoc

tan1cos tan slope streamwise xS

2/1

2

2tan1cos

ccoc

tan slope lateral yS

DgD

p

RRe

5050 D

Dic

ci 85.0

7.0c