Dredging Processes - TU Delft OCW · The Sundborg-Hjulstrom diagram Faculty of 3mE – Chair of Dredging Engineering 10-2 10-1 100 101 102 103 104 10-2 10-1 100 101 Modified Sundborg-Hjulstrom

Dredging Processes

Dr.ir. Sape A. Miedema

7. Erosion

Delft University of Technology – Offshore & Dredging Engineering

Dredging A Way Of Life

© S.A.M

[1]


Offshore A Way Of Life

© S.A.M

[2]

[3]

Offshore & Dredging

Engineering

Faculty of 3mE – Faculty CiTG – Offshore & Dredging Engineering

Dr.ir. Sape A. MiedemaEducational Director

© S.A.M

The Settling Velocity

© S.A.M

Delft University of Technology – Offshore & Dredging E ngineering

Forces on a settling particle

Av21

CF 2swDup ⋅⋅⋅⋅⋅⋅⋅⋅ρρρρ⋅⋅⋅⋅⋅⋅⋅⋅====

ψψψψ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ρρρρ−−−−ρρρρ==== Vg)(F wqdownC3

d)(g4v

dw

wqs ⋅⋅⋅⋅ρρρρ⋅⋅⋅⋅

ψψψψ⋅⋅⋅⋅⋅⋅⋅⋅ρρρρ−−−−ρρρρ⋅⋅⋅⋅⋅⋅⋅⋅====

© S.A.M


Standard drag coefficient curve for

spheres

pp Re

24Cd 1Re ====⇒⇒⇒⇒

The drag coefficient as a function of the

particle Reynolds number

0.1 1 10 100 1000 10000 1000000.1

1

10

100

1000

Cd as a function of the Re number

Re number

Cd

Iteration 1 Huisman Observed Iteration 2 Turton

© S.A.M


The drag coefficient as a function of the

particle Reynolds number

© S.A.M


100 101 102 103 104 105 10610-1

100

101

102The drag coefficient for different shape factors

Re

CD

Sf=1.0 Sf=0.80-0.99 Sf=0.6-0.79 Sf=0.4-0.59 Sf=0.20-0.39

Sf=1.0 Sf=0.9 Sf=0.7 Sf=0.5 Sf=0.3

Stokes

dR424v 2ds ⋅⋅⋅⋅⋅⋅⋅⋅====

(((( ))))d

1)dR951(925.8v

3d

s

−−−−⋅⋅⋅⋅⋅⋅⋅⋅++++⋅⋅⋅⋅====

dR87v ds ⋅⋅⋅⋅⋅⋅⋅⋅====

Laminar flow, d0.1 mm and d1 mm, according to Rittinger.

The settling velocity of individual

particles

With the relative density Rd defined as:

w

wqdR ρρρρ

ρρρρ−−−−ρρρρ====

© S.A.M



particles

0.01 0.1 1 100.1

1

10

100

1000

Settling velocity of real sand particles

Grainsize in mm

Se

ttlin

g v

elo

city in

mm

/se

c

Stokes Budryck Rittinger Zanke

© S.A.M



particles using the shape factor

0.01 0.1 1 100.1

1

10

100

1000

Settling velocity of particles using the shape factor

Grainsize in mm

Se

ttlin

g v

elo

city in

mm

/se

c

Iteration (0.7) Huisman (0.7) Grace (0.7) Iteration (0.5) Huisman (0.5) Grace (0.5)

© S.A.M


The Reynolds number as a function of

the particle diameter

0.01 0.1 1 10 1000.01

0.1

1

10

100

1000

10000

100000

Reynolds number as a function of the particle diameter

Particle diameter (mm)

Re

yn

old

s n

um

be

r

© S.A.M


The hindered settling power according to

several researchers

0.001 0.01 0.1 1 10 100 1000 100002.00

3.00

4.00

5.00

6.00

7.00

Hindered settling power

Rep (-)

Be

ta (

-)

Rowe Wallis Garside Di Felici Richardson

(((( ))))C1vv

vs

c −−−−====ββββ

75.0p

75.0p

Re175.01

Re41.07.4

⋅⋅⋅⋅++++⋅⋅⋅⋅++++

====ββββ

© S.A.M


Erosion/Scour

© S.A.M


The Amsterdam

Faculty of 3mE – Chair of Dredging Engineering

© S.A.M

[4]

The loading cycle of a TSHD


-300 -275 -250 -225 -200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 1000

500

1000

1500

2000

2500

3000

3500

4000

4500

5000The hopper dredge cycle.

Time in min

Lo

ad

in

to

ns

phase 1

phase 2 phase 3

phase 4

phase 5 phase 6

phase 7 phase 8

Total load Effective (situ) load Tonnes Dry Solids Overflow losses Maximum production

© S.A.M

The loading part of the cycle of a TSHD


0.0 4.2 8.4 12.6 16.8 21.0 25.2 29.4 33.6 37.8 42.00

500

1000

1500

2000

2500

3000

3500

4000

4500

5000The loading curves for an 0.3 mm d50 sand.

Time in min

Lo

ad

in

to

ns

phase 5

phase 6

phase 7 phase 8

Total load Effective (situ) load Tonnes Dry Solids Overflow losses Maximum production

© S.A.M

Phase 8 of the loading cycle


Erosion/scour starts to occur.

© S.A.M

The equilibrium of forces on a particle

Camp approach


w

swqs 3

dg) - (40 = s

ρρρρ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ρρρρρρρρ⋅⋅⋅⋅

w

swqs

dg) - ()n1(8 = s

ρρρρ⋅⋅⋅⋅λλλλ⋅⋅⋅⋅⋅⋅⋅⋅ρρρρρρρρ⋅⋅⋅⋅−−−−⋅⋅⋅⋅µµµµ⋅⋅⋅⋅

2s

wq

ws sg) - (40

3 = d ⋅⋅⋅⋅

⋅⋅⋅⋅ρρρρρρρρ⋅⋅⋅⋅ρρρρ⋅⋅⋅⋅

© S.A.M

History


ShieldsExperimentsHjulstromSundborg

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The original Shields curve


© S.A.M

A modified Shields diagram


© S.A.M

The original Shields diagram


0.1 1 10 100 10000.010.01

0.10.1

11

Original Shields Diagram vs Theory

Re*

Shi

elds

Par

amet

er

Theory E=0.5 Original Shields Data

© S.A.M

Data points


0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11

Data from Shields, Zanke, Julien, Yalin & Karahan & Soulsby

Re*

Shi

elds

Par

amet

er

Soulsby Zanke Julien Yalin & Karahan Shields

© S.A.M

The Hjulstrom curve


© S.A.M

The Hjulstrom diagram


10-2 10-1 100 101 102 103 10410-3

10-2

10-1

100

101Modified Hjulstrom Diagram

Dimensionless grain diameter D*

Mea

n ve

loci

ty (

m/s

ec)

Deposition Hjulstrom max Hjulstrom min Hjulstrom mean

0.0005 0.005 0.05 0.5 5 50 500

Grain diameter d (mm), for quarts in water of 0 degrees centigrade

Erosion

Transportation

Deposition

A

B

© S.A.M

The Sundborg-Hjulstrom diagram


10-2 10-1 100 101 102 103 10410-2

10-1

100

101Modified Sundborg-Hjulstrom Diagram


Vel

oci

ty (

m/s

ec)

Soulsby H=0.01 m Soulsby H=0.1 m Soulsby H=1 m Soulsby H=10 m

Brownlie H=0.01 m Brownlie H=0.1 m Brownlie H=1 m Brownlie H=10 m

Miedema H=0.01 m Miedema H=0.1 m Miedema H=1 m Miedema H=10 m

0.0005 0.005 0.05 0.5 5 50 500

Grain diameter d (mm), for quarts in water of 0 degrees centigrade

10-2 10-1 100 101 102 103 10410-2

10-1

100

101Modified Sundborg-Hjulstrom Diagram


Vel

oci

ty (

m/s

ec)

Smooth flow

Transitional flow

Rough flow

Unconsol

idated cla

y and sil

t

Consolidated clay and silt

© S.A.M

Shields Diagram with Criterion for

Ripples (Chabert and Chauvin (1963))


0.01

0.1

1

10

1 10 100 1000 10000 100000Rep

ττ ττ*motion mod Brownlieripplessuspensiondunes C&Cripples C&Cextrap C&C dunes

2

pv

6.11orD

=τδ= ∗

Re

[ ]2pfs )(orvu ReR=τ= ∗∗

modified Brownlie

C&C ripples/no ripples

C&C no dunes/dunes

extrapolated C&C no dunes/duneslower regime plane bed

dunes

ripples

no motion

suspension

© S.A.M

Classification of flow layers


© S.A.M

Classification of flow layers


•Viscous sublayer: a thin layer just above the bottom. In thislayer there is almost no turbulence. Measurement shows thatthe viscous shear stress in this layer is constant. The flow islaminar. Above this layer the flow is turbulent.•Transition layer: also called buffer layer. viscosity andturbulence are equally important.•Turbulent logarithmic layer: viscous shear stress can beneglected in this layer. Based on measurement, it is assumedthat the turbulent shear stress is constant and equal to bottomshear stress. It is in this layer where Prandtl introduced themixing length concept and derived the logarithmic velocityprofile.•Turbulent outer layer: velocities are almost constant becauseof the presence of large eddies which produce strong mixing ofthe flow.

© S.A.M

Friction velocity


The bottom shear stress is often represented by friction velocity, defined by

ρρρρττττ====∗∗∗∗

bu

The term friction velocity comes from the fact that

has the same unit as velocity and it has something to do with friction force.

ρρρρττττ /b

2cr

2* U8

u ⋅⋅⋅⋅λλλλ====

2

9.0

2

9.0 Re

75.5D7.3

dlog

25.0

Re

75.5D7.3

dln

325.1

++++⋅⋅⋅⋅

====

++++⋅⋅⋅⋅

====λλλλ

© S.A.M

Engineering classification


κκκκ==== ∗∗∗∗

0zz

lnu

)z(u

Velocity distribution:

zuz

)z(u2*b ⋅⋅⋅⋅

νννν====

νννν⋅⋅⋅⋅

ρρρρττττ====

Viscous sublayer Turbulent layer

© S.A.M

Engineering classification


•Hydraulically smooth flow for

Bed roughness is much smaller than the thickness of viscoussublayer. Therefore, the bed roughness will not affect the velocitydistribution

5ku s ≤≤≤≤νννν∗∗∗∗

•Hydraulically rough flow for

Bed roughness is so large that it produces eddies close to the bottom. A viscous sublayer does not exist and the flow velocity is not dependent on viscosity.

70ku s ≥≥≥≥νννν∗∗∗∗

•Hydraulically transitional flow for

The velocity distribution is affected by bed roughness and viscosity.

70ku

5 s ≤≤≤≤νννν

≤≤≤≤ ∗∗∗∗

© S.A.M

The velocity distribution


© S.A.M

The velocity distribution


*0 u

11.0zνννν⋅⋅⋅⋅====

s0 k033.0z ⋅⋅⋅⋅====

s*

0 k033.0u11.0z ⋅⋅⋅⋅++++

νννν⋅⋅⋅⋅====

Hydraulically smooth flow 5ku s ≤≤≤≤νννν∗∗∗∗

70ku s ≥≥≥≥νννν∗∗∗∗

70ku

5 s ≤≤≤≤νννν

≤≤≤≤ ∗∗∗∗

Hydraulically rough flow

Hydraulically transitional flow

*u6.11

νννν⋅⋅⋅⋅====δδδδννννTheoretical viscous sub layer thickness:

© S.A.M

Literature

© S.A.M


Wiberg & Smith (1987)


© S.A.M

The Physics


The equilibrium equations for sliding and rollingThe velocity distribution

The transition smooth-roughThe drag coefficient CDThe lift coefficient CL

The friction coefficient/angle of internal friction

© S.A.M

The velocity profile near the wall


0.1 1 10 100 10000

3

6

9

12

15

18

21

24

27

30

The transition laminar - turbulent smooth

Non-dimensional distance to the wall y+

Non

-dim

ensi

onal

ve

loci

ty u

+

Laminar Law of the wall Reichardt

Reichardt

Laminar

Turbulent - Smooth

© S.A.M

The transition smooth-rough


1 10 100 1000 100000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

The offset of the logaritmic velocity profile

k+

y0/k

s

Data of Nikuradse (1933) Theoretical bed Smooth Asymptote Rough Asymptote

Rough

Smooth

Transition

© S.A.M

The transition rough-smooth


0.1 1 10 100 1000 100005

6

7

8

9

10

11

The Transition Smooth - Rough

Roughness Reynolds Number ks+=Re*

Vel

ocity

at y

=ks

Garcia (2008) Garcia (2008) Asymptote Asymptote

Empirical y=ks Empirical y=0.9ks Empirical y=0.8ks Empirical y=0.7ks

Empirical y=0.6ks Empirical y=0.5ks Empirical y=0.4ks

RoughSmooth Transition

© S.A.M

The angle of repose for granular material


10-1 100 101 102 10325

30

35

40

45

Angle of repose vs particle diameter

d (mm)

Phi

(de

gree

s)

Rounded Rounded & Angular Angular

Rounded Rounded & Angular Angular

© S.A.M

Drag induced sliding & rolling


Sliding

Rolling

2*

2 2d Drag D D

u 4 1R g d 3 f C

µµµµθ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅ α ⋅ ⋅α ⋅ ⋅α ⋅ ⋅α ⋅ ⋅ℓℓℓℓ

2Roll*

2 2Drag D D Lever Roll

sin( )u 4 1R g d 3 f C ( cos( ))

ψ + φψ + φψ + φψ + φθ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅

⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅ α ⋅ ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φℓ ℓℓ ℓℓ ℓℓ ℓ

© S.A.M

Thye Drag Coefficient of Spheres


© S.A.M

1 10 100 1000 10000 1000000.1

1

10

100

Drag coefficient of spheres

Re

CD

Turton & Levenspiel Turton & Levenspiel Stokes

The drag coefficient CD


100 101 102 103 104 105 10610-1

100

101

102The drag coefficient for different shape factors

Re

CD

Sf=1.0 Sf=0.80-0.99 Sf=0.6-0.79 Sf=0.4-0.59 Sf=0.20-0.39

Sf=1.0 Sf=0.9 Sf=0.7 Sf=0.5 Sf=0.3

Stokes

© S.A.M

The Drag Coefficient for Natural

Sediments


© S.A.M

10-3 10-2 10-1 100 101 102 10310-1

100

101

102

103

104The drag coefficient of natural sands

Re

CD

Wu & Wang Wu & Wang Stokes Julien

Drag induced sliding & rolling


0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11

Only Drag & Gravity

Re*

Shi

elds

Par

amet

er


Theory Sliding Theory Rolling

© S.A.M

Drag & Lift induced sliding & rolling


2*

2 2d Drag D D L L

u 4 1R g d 3 f C f C

µµµµθ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅ α ⋅ ⋅ + µ ⋅ ⋅α ⋅ ⋅ + µ ⋅ ⋅α ⋅ ⋅ + µ ⋅ ⋅α ⋅ ⋅ + µ ⋅ ⋅ℓℓℓℓ

2Roll*

2 2d Drag D D Lever D Roll L L Lever L Roll

sin( )u 4 1R g d 3 f C ( cos( )) f C ( sin( ))− −− −− −− −

ψ + φψ + φψ + φψ + φθ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅

⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅ α ⋅ ⋅ ⋅ + ψ + φ + ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φ + ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φ + ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φ + ⋅ ⋅ + ψ + φℓ ℓ ℓℓ ℓ ℓℓ ℓ ℓℓ ℓ ℓ

Sliding

Rolling

© S.A.M

The lift coefficient CL


100 101 102 103 104 105-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Lift coefficient vs the boundary Reynolds number

Re*

Lift

Co

effic

ient

CL

Coleman (1967) Bagnold (1974) Davies & Samad (1978) Walters (1971)

Cheng & Clyde (1972) Apperley & Raudkivi (1989) Chepil (1958) Einstein & B-Samni

© S.A.M



0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11

Drag, Lift & Gravity

Re*

Shi

elds

Par

amet

er



© S.A.M



2*

2 2d Drag D D L L

u 4 1R g d 3 f C f C

µµµµθ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅ α ⋅ ⋅ + µ ⋅ ⋅α ⋅ ⋅ + µ ⋅ ⋅α ⋅ ⋅ + µ ⋅ ⋅α ⋅ ⋅ + µ ⋅ ⋅ℓℓℓℓ

2Roll*

2 2d Drag D D Lever D Roll L L Lever L Roll

sin( )u 4 1R g d 3 f C ( cos( )) f C ( sin( ))− −− −− −− −

ψ + φψ + φψ + φψ + φθ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅θ = = ⋅ ⋅

⋅ ⋅⋅ ⋅⋅ ⋅⋅ ⋅ α ⋅ ⋅ ⋅ + ψ + φ + ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φ + ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φ + ⋅ ⋅ + ψ + φα ⋅ ⋅ ⋅ + ψ + φ + ⋅ ⋅ + ψ + φℓ ℓ ℓℓ ℓ ℓℓ ℓ ℓℓ ℓ ℓ

Sliding

Rolling

© S.A.M

Turbulence


0 1 2 3 4 5 6 7 8 9 100.00.00.50.51.01.01.51.52.02.02.52.53.03.03.53.54.04.04.54.55.05.0

A: Turbulence

y+

u'/u

*

Effective turbulence velocity Turbulence r.m.s. value

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 300.00.0

0.10.1

0.20.2

0.30.3

0.40.4

0.50.5

0.60.6

0.70.7

0.80.8

0.90.9

1.01.0

D: Simultaneous Occurence Distribution

y+si

mul

tane

ous

Occ

uren

ce F

acto

r

0 10 20 30 40 50 60 70 80 90 1000.00.00.50.51.01.01.51.52.02.02.52.53.03.03.53.54.04.04.54.55.05.0

C: Turbulence

y+

u'/u

*

Effective turbulence velocity Turbulence r.m.s. value

0 2 4 6 8 10 12 14 16 18 200.00.00.30.30.60.60.90.91.21.21.51.51.81.82.12.12.42.42.72.73.03.0

B: Turbulence

y+

u'/u

*

Turbulence r.m.s. value Original

© S.A.M

Drag, Lift & Turbulence induced sliding &

rolling


0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11

Drag, Lift, Turbulence & Gravity

Re*

Shi

elds

Par

amet

er



© S.A.M

Initiation of motion for sliding & rolling


0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11

Drag, Lift, Turbulence, Gravity & Transition Zone

Re*

Shi

elds

Par

amet

er



© S.A.M

Different Angles of Internal Friction


© S.A.M

0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11


Re*

Shi

elds

Par

amet

er


Phi=25 Degrees Phi=30 Degrees Phi=35 Degrees

Different Levels of Turbulence


© S.A.M

0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11


Re*

Shi

elds

Par

amet

er


n=0 n=1 n=2 n=3 n=4

Sand Standard & Spheres with 2 CL’s


© S.A.M

0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11


Re*

Shi

elds

Par

amet

er


Spheres - Full Lift Sand Grains Spheres - Reduced Lift

Resulting Curves


© S.A.M

0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11


Re*

Shi

elds

Par

amet

er


Upper - Spheres Medium - Spheres Lower - Spheres Lower Sand

Sensitivities


© S.A.M

0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11

Drag, Lift, Turbulence & Gravity

Re*

Sh

ield

sP

ara

me

ter

Theory Sliding

Lift

Drag

Turbulence

Friction

Friction

The resulting curves


Sliding versus rolling for spheresDifferent protrusion levels for spheres

Different protrusion levels for sandThe Shields-Parker diagram

© S.A.M

Exposure Levels Sliding


© S.A.M

0.01 0.1 1 10 100 1000 100000.001

0.01

0.1

1

Exposure Levels, Sliding

Re*

Shi

elds

Par

amet

er

E=0.2 E=0.3 E=0.4 E=0.5 E=0.6 E=0.7

E=0.8 E=0.9 E=1.0 E=1.1 E=1.2


Exposure Levels Rolling


© S.A.M

0.01 0.1 1 10 100 1000 100000.001

0.01

0.1

1

Exposure Levels, Rolling

Re*

Shi

elds

Par

amet

er

E=0.2 E=0.3 E=0.4 E=0.5 E=0.6 E=0.7

E=0.8 E=0.9 E=1.0 E=1.1 E=1.2


Exposure Levels Both (Spheres)


0.01 0.1 1 10 100 1000 100000.001

0.01

0.1

1

Exposure Levels, Mixed

Re*

Shi

elds

Par

amet

er

E=0.2 E=0.3 E=0.4 E=0.5 E=0.6 E=0.7

E=0.8 E=0.9 E=1.0 E=1.1 E=1.2


© S.A.M

Exposure Levels Both, Bonneville

Parameter


© S.A.M

0.01 0.1 1 10 100 1000 100000.001

0.01

0.1

1

Exposure Levels, Mixed (Dimensionless Grain Diameter)

D*

Shi

elds

Par

amet

er

E=0.2 E=0.3 E=0.4 E=0.5 E=0.6 E=0.7

E=0.8 E=0.9 E=1.0 E=1.1 E=1.2

Soulsby Zanke Julien Yalin Shields

0.0005 0.005 0.05 0.5 5 50 500

Grain Diameter (mm)

Different protrusion levels (sand)


0.01 0.1 1 10 100 1000 100000.001

0.01

0.1

1

Exposure Levels, Mixed, Sand Grains

Re*

Shi

elds

Par

amet

er

E=0.2 E=0.3 E=0.4 E=0.5 E=0.6 E=0.7

E=0.8 E=0.9 E=1.0 E=1.1 E=1.2

© S.A.M

Exposure Levels Experiments


© S.A.M

1 10 100 1000 100000.001

0.01

0.1

1

Protrusion Levels, Fenton & Abbot, Chin & Chiew, Coleman

Re*

Shi

elds

Par

amet

er

E=0.2 E=0.3 E=0.4 E=0.5 E=0.6 E=0.7 E=0.8 E=0.9

E=1.0 E=1.1 E=1.2 FA: A FA: B FA: C FA: D FA: E

FA: F FA: G FA: H Coleman CC: A CC: B CC: C CC: D

CC: E CC: F CC: G CC: H

Stages of Entrainment


© S.A.M

0.1 1 10 100 10000.01

0.1

1

Delft Hydraulics (1972), Graf & Pazis (1977), Vanoni (1964), Dey (2007) & Ziervogel (2003)

D*

Shi

elds

Par

amet

er

E=0.2 E=0.3 E=0.4 E=0.5 E=0.6 E=0.7

E=0.8 E=0.9 E=1.0 DHL1 DHL2 DHL3

DHL4 DHL5 DHL6 DHL7 GP1 GP2

GP3 GP4 VAN1 VAN2 VAN3 VAN4

DU DM DL Ziervogel 1 Ziervogel 2

Laminar Main Flow


© S.A.M

0.01 0.1 1 10 100 10000.010.01

0.10.1

11

Laminar Main Flow - Natural Sands

Re*

Shi

eld

s P

aram

eter

n=0 n=1 n=2 n=3 n=4 n=0.5

Prager Pilotti Laminar Pilotti Turbulent

Resulting Curves


© S.A.M

0.01 0.1 1 10 100 1000 100000.010.01

0.10.1

11

Proposed Shields Curves

Re*

Shi

eld

s P

aram

eter

Spheres Turbulent Spheres Laminar Sands Turbulent Sands Laminar

The Shields-Parker diagram


10-2 10-1 100 101 102 103 10410-2

10-1

100

101Shields-Parker River Sedimentation Diagram

Re*

Shi

eld

s P

aram

ete

r

Re*=5

Re*=11.6

Re*=70

Re*=5

Re*=11.6

Re*=70

Smooth Transitional Rough

Suspension

No suspension

DunesRipples

© S.A.M

Application to scour in a TSHD


2cr

2* U8

u ⋅⋅⋅⋅λλλλ====

dgRU

8dgRu

d

2cr

d

2*

cr ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅

λλλλ====⋅⋅⋅⋅⋅⋅⋅⋅

====θθθθ

cr d scr

8 R g dU =

⋅ θ ⋅ ⋅ ⋅

λ

2 2* cr

sd d cr

u Ud

R g d 8 R g

λ= = ⋅

⋅ ⋅ ⋅ ⋅ θ

2

9.0

2

9.0 Re

75.5D7.3

dlog

25.0

Re

75.5D7.3

dln

325.1

++++⋅⋅⋅⋅

====

++++⋅⋅⋅⋅

====λλλλ

First determine the friction velocity and the friction coefficient:

Second determine the Shields parameter for the grain diameter:

Third, determine the average velocity above the bed given a grain diameter:

or, determine the grain diameter given an average velocity:

© S.A.M

The friction coefficient


100 1000 10000 100000 1000000 10000000 1000000000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Moody Diagram

Re

La

bd

a

La

bd

a

Mo

od

y d

iag

ram

for th

e d

ete

rmin

atio

n o

f the

Da

rcy W

eis

ba

ch

frictio

n c

oe

fficie

nt.

Th

e le

ge

nd

sh

ow

s th

e re

lativ

e ro

ug

hn

ess.

Laminar Smooth 0.000003 0.00001 0.0001 0.0003 0.001 0.003 0.01 0.02 0.03 0.04 0.05

2

9.0

2

9.0 Re75.5

D7.3d

log

25.0

Re75.5

D7.3d

ln

325.1

++++⋅⋅⋅⋅

====

++++⋅⋅⋅⋅

====λλλλ

© S.A.M

The Shields-Parker diagram


10-2 10-1 100 101 102 103 10410-2

10-1

100

101Shields-Parker River Sedimentation Diagram

Re*

Shi

eld

s P

aram

ete

r

Re*=5

Re*=11.6

Re*=70

Re*=5

Re*=11.6

Re*=70

Smooth Transitional Rough

Suspension

No suspension

DunesRipples

© S.A.M

Hopper Sedimentation, verification


0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.50

400

800

1200

1600

2000

2400

2800

3200

3600

4000

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000The loading curves.

Time in min

Load

in to

ns

Load in tons

Load TDS Miedema Overflow TDS Miedema Load TDS van Rhee Overflow TDS van Rhee TDS in Miedema TDS in van Rhee

© S.A.M

Sources images

82

1. A model cutter head, source: Delft University of Technology.2. Off shore platform, source: Castrol (Switzerland) AG3. Off shore platform, source: http://www.wireropetraining.com4. The Amsterdam, source: IHC Merwede.

Documents

Dredging Processes - TU Delft OCW · The Sundborg-Hjulstrom diagram Faculty of 3mE – Chair of Dredging Engineering 10-2 10-1 100 101 102 103 104 10-2 10-1 100 101 Modified Sundborg-Hjulstrom