Research Topic

Updated on Oct. 9, 2014

• Flocculation

• Deposition

• Erosion

• Transport

• Consolidation

*: It has been recognized that when the

fraction of fine-grained sediments is larger

than about 10%, a mixture consisting of

cohesive and non-cohesive sediments may

exhibit cohesive properties.

Sedimentation

in Estuary:

Mixed Cohesive/Non-cohesive Sediments

2

1-D fractional sediment transport equation

Qtk total-load transport rate of size class k

Ebk erosion rate

Dbk deposition rate

βtk correction factor

U flow velocity

qtlk side inflow of sediment per unit channel length

tk tkbk bk tlk

tk

Q QE D q

t U x

(k=1, 2, …, N)

Mixed Cohesive/Non-cohesive Sediments

• Deposition Rate:

,bk k sf k kD B C B channel width

ak deposition probability or adaptation coef.

wsf,k settling velocity

Ck section-averaged sediment concentration

3

Coefficient αk

For non-cohesive sediment, k is the adaptation

coefficient, calculated by

1/6

,

*

11 exp 1.5

sf k

k

a a a

h h h u

(Armanini and

di Silvio, 1988)

For cohesive sediment, k is the deposition probability

coefficient, which is related to the bed shear stress as

,min ,max ,min

1

1 /

0

b bd bd bd

,min

,min ,max

,max

b bd

bd b bd

b bd

4

Settling Velocity wsf,k

• For cohesive sediment, sf,k is calculated by Wu and Wang’s (2004)

formula, through which the effect of flocculation is considered

50/ dn

d rK d dd50 medium diameter

dr reference diameter, about 0.0215 mm

nd coefficient, approximated to 1.8

sf

d s sa t

sd

K K K K

sf median settling velocity of flocs

d50 median settling velocity of dispersed particles

1

2

1

1

n

s r

k CK

k k C

0 p

p

C C

C C

C concentration, in kg/m3

Cp sediment concentration at the maximum settling

n, r, k1, k2 coefficient, ranging from 1 to 2

k coefficient, equal to 1 21 / 1r

n

p pk C k C

1

2

1

1

1 /

1 /

t

t

n

t b p

t n

t b p

kK

k

0 p

p

kt1, nt1, nt2 empirical coefficient

p threshold bed shear stress at maximum Kt

1.0saK

5

Erosion Rate

*

bk bk bkE p E

pbk fraction of the kth size class in the surface layer of bed material

Ebk* potential erosion rate of the kth size class

For non-cohesive sediment

,* *k sf k

bk tk

tk

E B QAU

For cohesive sediment

* 1

n

bbk

ce

E BM

ce critical bed shear stress for surface erosion

M erodibility coef., related to bed material properties

n coefficient, equal to 2.5

6

Critical Bed Shear Stress

• The incipient motion of non-cohesive sediment is affected by the cohesion if

non-cohesive and cohesive sediments coexist in the bed material.

,

, , min max min/

ck n

ck ck n ce ck n c c c c

ce

p p p p

min

min max

max

c c

c c c

c c

p p

p p p

p p

ck,n critical bed shear stress of the size class in the

situation where only non-cohesive sediment exists

ce critical bed shear stress for cohesive sediment

pc fraction of cohesive sediment

pcmin minimum fraction of cohesive sediment, below

which the critical bed shear stress for non-cohesive

sediment is the same as that when no cohesive

sediment exists

pcmax maximum fraction of cohesive sediment, above

which the critical bed shear stress of non-cohesive

sediment is equal to that of cohesive sediment

0 0

n

ce ce d dk

(Nicholson and O’Connor, 1986)

ce0 initial critical bed shear stress

d0 initial critical dry bed density

d dry bed density

k, n empirical coefficients

7

Bed Deformation

• The fractional bed mass deformation rate is determined by

• Then the total rate of change in bed mass is

• which can be converted to the change in bed cross-sectional area:

bks bk bk

MD E

t

1

Nb bk

k

M M

t t

1

1

b b

s m

A M

t p t

mp bed material porosity

*( )m bk bk m bbk

M p M M Mp

t t t t

Bed Material Sorting

8

Consolidation

• Dry bed density in the first year (Hayter, 1983):

• Dry bed density after 1 year (Lane and Koelzer,1953):

• Bed Change due to Consolidation:

1

1 ptd

d

a e

d dry bed density

d1 at one-year consolidation time

a ,p empirical coefficients

t consolidation time, in hour

1 logd d t empirical coefficient

t consolidation time, in year

0j djt

j thickness of the jth layer of bed material

dj dry bed density of the jth layer of bed material

1

, 11 1

1

nJ Jdjn n n

b c j j j nj j dj

z

9

• Mainstream:

from a dam at De Pere to

Green Bay (11 km)

• Tributary:

East River (joins the Fox

River approximately 2 km

upstream from the river

mouth)

• Size Classes:

Fine ~ 0.00316 mm

Medium ~ 0.0316 mm

Coarse ~ 0.447 mm

10

Lower Fox River

Flow Discharge at the Dam Sediment Concentration at the Dam

Sediment Concentration at the River Mouth

11

1-D Simulation in Lower Fox River

(Lin and Wu, 2013)

Gironde Estuary, France

12

2-D simulation using

FASTER2D (Wu and Wang,

2004)

Mesh: 157×69

Δt=30 min

Period: May 19-22, 1974

Gironde Estuary, France

13

Tidal Flow in Gironde Estuary, France

Ebb Tide

-1.80 -1.60 -1.40 -1.20 -1.00 -0.80 -0.60 -0.40 -0.20 -0.00 0.20 0.40 0.60

Flood Tide

ws

14

Tidal Level in Gironde Estuary

Time (hour)

Wat

erE

levat

ion

(m)

60 70 80 90

-2

-1

0

1

2

(b). Lamena

Time (hour)

Wat

erE

levat

ion

(m)

60 65 70 75 80 85 90 95

-2

-1

0

1

2

(c). PK47

Time (hour)

Wat

erE

levat

ion

(m)

0 10 20 30 40 50 60 70 80 90

-2

-1

0

1

2

Simulated

Measured

(a). PK82

15

Velocity in Gironde Estuary

Time (hour)

Vel

oci

ty(m

/s)

60 70 80 90

-2

-1

0

1

(b). Lamena

Time (hour)

Vel

oci

ty(m

/s)

60 65 70 75 80 85 90 95

-1

0

1

2

(c). PK47

Time (hour)

Vel

oci

ty(m

/s)

0 10 20 30 40 50 60 70 80 90

-2

-1

0

1

Measured, 1m below SurfaceMeasured, 1m above BedSimulated

(a). PK82

16

Salinity in Gironde Estuary

Time (hour)

Sal

init

y(k

g/m

3)

60 70 80 902

3

4

5

6

7

8

9

10

11(b). Lamena

Time (hour)

Sal

init

y(k

g/m

3)

60 65 70 75 80 85 90 95

1

2

3

4

5(c). PK47

Time (hour)

Sal

init

y(k

g/m

3)

0 10 20 30 40 50 60 70 80 90

10

15

20

25

30SimulatedMeasured, 1m below SurfaceMeasured, 1m above Bed

(a). PK82

17

Sediment Discharge in Gironde

Time (hour)

US

(kg

/m2s)

75 80 85 90 95

-1

0

1

2

3

(b). PK54

Time (hour)

US

(kg

/m2s)

75 80 85 90 95

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

(c). PK47

Time (hour)

US

(kg/m

2s)

0 25 50 75-1.5

-1

-0.5

0

0.5

1(a). PK82

18

San Francisco Bay

19

San Francisco Bay –Mesh

20

3-D

Simulation

using

CRESTS3D

(Wu and

Lin, 2011)

Flow near Golden Gate Bridge

26000 28000 30000 32000

41000

42000

43000

44000

45000

46000

47000

1 m/s

(m)

(a)

Gold

enG

ate

Brid

ge

26000 28000 30000 32000

41000

42000

43000

44000

45000

46000

47000

1 m/s

(m)

(b)

Gold

enG

ate

Brid

ge

21

Flow near Port Chicago

68000 70000 72000

70000

71000

72000

73000

74000

75000

76000

1 m/s

(m)

(a)

Port Chicago

68000 70000 72000

70000

71000

72000

73000

74000

75000

76000

1 m/s

(m)

(b)

Port Chicago

22

Water Level

23

Currents

24

W. Wu and S. S.Y. Wang (2004). “Depth-averaged 2-D calculation of tidal flow, salinity and cohesive

sediment transport in estuaries,” Int. J. Sediment Research, 19(3), 172–190.

W. Wu and Q. Lin (2011). “An implicit 3-D finite-volume coastal hydrodynamic model.” Proc., 7th

Int. Symposium on River, Coastal and Estuarine Morphodynamics, September 6-8, Beijing, China.

Q. Lin and W. Wu (2013). “A one-dimensional model of mixed cohesive and non-cohesive sediment

transport in open channels.” Journal of Hydraulic Research, IAHR, 51(5), 506–517, DOI:

10.1080/00221686.2013.812046.

25

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