Post on 18-Jan-2021
Dredging Processes
Dr.ir. Sape A. Miedema
7. Erosion
Delft University of Technology – Offshore & Dredging Engineering
Dredging A Way Of Life
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[1]
Delft University of Technology – Offshore & Dredging Engineering
Offshore A Way Of Life
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[2]
[3]
Offshore & Dredging
Engineering
Faculty of 3mE – Faculty CiTG – Offshore & Dredging Engineering
Dr.ir. Sape A. MiedemaEducational Director
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The Settling Velocity
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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⋅⋅⋅⋅⋅⋅⋅⋅====
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Delft University of Technology – Offshore & Dredging E ngineering
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
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Delft University of Technology – Offshore & Dredging E ngineering
The drag coefficient as a function of the
particle Reynolds number
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Delft University of Technology – Offshore & Dredging E ngineering
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====
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Delft University of Technology – Offshore & Dredging E ngineering
The settling velocity of individual
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
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Delft University of Technology – Offshore & Dredging E ngineering
The settling velocity of individual
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)
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Delft University of Technology – Offshore & Dredging E ngineering
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
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Delft University of Technology – Offshore & Dredging E ngineering
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
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Delft University of Technology – Offshore & Dredging E ngineering
Erosion/Scour
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Delft University of Technology – Offshore & Dredging E ngineering
The Amsterdam
Faculty of 3mE – Chair of Dredging Engineering
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[4]
The loading cycle of a TSHD
Faculty of 3mE – Chair of Dredging Engineering
-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
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The loading part of the cycle of a TSHD
Faculty of 3mE – Chair of Dredging Engineering
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
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Phase 8 of the loading cycle
Faculty of 3mE – Chair of Dredging Engineering
Erosion/scour starts to occur.
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The equilibrium of forces on a particle
Camp approach
Faculty of 3mE – Chair of Dredging Engineering
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⋅⋅⋅⋅
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History
Faculty of 3mE – Chair of Dredging Engineering
ShieldsExperimentsHjulstromSundborg
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The original Shields curve
Faculty of 3mE – Chair of Dredging Engineering
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A modified Shields diagram
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The original Shields diagram
Faculty of 3mE – Chair of Dredging Engineering
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
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Data points
Faculty of 3mE – Chair of Dredging Engineering
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
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The Hjulstrom curve
Faculty of 3mE – Chair of Dredging Engineering
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The Hjulstrom diagram
Faculty of 3mE – Chair of Dredging Engineering
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
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The Sundborg-Hjulstrom diagram
Faculty of 3mE – Chair of Dredging Engineering
10-2 10-1 100 101 102 103 10410-2
10-1
100
101Modified Sundborg-Hjulstrom Diagram
Dimensionless grain diameter D*
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
Dimensionless grain diameter D*
Vel
oci
ty (
m/s
ec)
Smooth flow
Transitional flow
Rough flow
Unconsol
idated cla
y and sil
t
Consolidated clay and silt
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Shields Diagram with Criterion for
Ripples (Chabert and Chauvin (1963))
Faculty of 3mE – Chair of Dredging Engineering
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
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Classification of flow layers
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Classification of flow layers
Faculty of 3mE – Chair of Dredging Engineering
•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.
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Friction velocity
Faculty of 3mE – Chair of Dredging Engineering
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
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Engineering classification
Faculty of 3mE – Chair of Dredging Engineering
κκκκ==== ∗∗∗∗
0zz
lnu
)z(u
Velocity distribution:
zuz
)z(u2*b ⋅⋅⋅⋅
νννν====
νννν⋅⋅⋅⋅
ρρρρττττ====
Viscous sublayer Turbulent layer
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Engineering classification
Faculty of 3mE – Chair of Dredging Engineering
•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
≤≤≤≤ ∗∗∗∗
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The velocity distribution
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The velocity distribution
Faculty of 3mE – Chair of Dredging Engineering
*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:
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Literature
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Delft University of Technology – Offshore & Dredging E ngineering
Wiberg & Smith (1987)
Faculty of 3mE – Chair of Dredging Engineering
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Wiberg & Smith (1987)
Faculty of 3mE – Chair of Dredging Engineering
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Wiberg & Smith (1987)
Faculty of 3mE – Chair of Dredging Engineering
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The Physics
Faculty of 3mE – Chair of Dredging Engineering
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
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The velocity profile near the wall
Faculty of 3mE – Chair of Dredging Engineering
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
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The transition smooth-rough
Faculty of 3mE – Chair of Dredging Engineering
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
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The transition rough-smooth
Faculty of 3mE – Chair of Dredging Engineering
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
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The angle of repose for granular material
Faculty of 3mE – Chair of Dredging Engineering
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
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Drag induced sliding & rolling
Faculty of 3mE – Chair of Dredging Engineering
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
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Thye Drag Coefficient of Spheres
Delft University of Technology – Offshore & Dredging Engineering
© 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
Faculty of 3mE – Chair of Dredging Engineering
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
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The Drag Coefficient for Natural
Sediments
Delft University of Technology – Offshore & Dredging Engineering
© 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
Faculty of 3mE – Chair of Dredging Engineering
0.01 0.1 1 10 100 1000 100000.010.01
0.10.1
11
Only Drag & Gravity
Re*
Shi
elds
Par
amet
er
Soulsby Zanke Julien Yalin & Karahan Shields
Theory Sliding Theory Rolling
© S.A.M
Drag & Lift induced sliding & rolling
Faculty of 3mE – Chair of Dredging Engineering
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
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The lift coefficient CL
Faculty of 3mE – Chair of Dredging Engineering
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
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Drag & Lift induced sliding & rolling
Faculty of 3mE – Chair of Dredging Engineering
0.01 0.1 1 10 100 1000 100000.010.01
0.10.1
11
Drag, Lift & Gravity
Re*
Shi
elds
Par
amet
er
Soulsby Zanke Julien Yalin & Karahan Shields
Theory Sliding Theory Rolling
© S.A.M
Drag & Lift induced sliding & rolling
Faculty of 3mE – Chair of Dredging Engineering
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
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Turbulence
Faculty of 3mE – Chair of Dredging Engineering
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
Faculty of 3mE – Chair of Dredging Engineering
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
Soulsby Zanke Julien Yalin & Karahan Shields
Theory Sliding Theory Rolling
© S.A.M
Initiation of motion for sliding & rolling
Faculty of 3mE – Chair of Dredging Engineering
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
Soulsby Zanke Julien Yalin & Karahan Shields
Theory Sliding Theory Rolling
© S.A.M
Sensitivity Analysis Shields
Curve
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Delft University of Technology – Offshore & Dredging E ngineering
Different Angles of Internal Friction
Delft University of Technology – Offshore & Dredging Engineering
© S.A.M
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
Soulsby Zanke Julien Yalin & Karahan Shields
Phi=25 Degrees Phi=30 Degrees Phi=35 Degrees
Different Levels of Turbulence
Delft University of Technology – Offshore & Dredging Engineering
© S.A.M
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
Soulsby Zanke Julien Yalin & Karahan Shields
n=0 n=1 n=2 n=3 n=4
Sand Standard & Spheres with 2 CL’s
Delft University of Technology – Offshore & Dredging Engineering
© S.A.M
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
Soulsby Zanke Julien Yalin & Karahan Shields
Spheres - Full Lift Sand Grains Spheres - Reduced Lift
Resulting Curves
Delft University of Technology – Offshore & Dredging Engineering
© S.A.M
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
Soulsby Zanke Julien Yalin & Karahan Shields
Upper - Spheres Medium - Spheres Lower - Spheres Lower Sand
Sensitivities
Delft University of Technology – Offshore & Dredging Engineering
© 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
Faculty of 3mE – Chair of Dredging Engineering
Sliding versus rolling for spheresDifferent protrusion levels for spheres
Different protrusion levels for sandThe Shields-Parker diagram
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Exposure Levels - Protrusion Levels
Delft University of Technology – Offshore & Dredging Engineering
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Exposure Levels Sliding
Delft University of Technology – Offshore & Dredging Engineering
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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
Soulsby Zanke Julien Yalin & Karahan Shields
Exposure Levels Rolling
Delft University of Technology – Offshore & Dredging Engineering
© 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
Soulsby Zanke Julien Yalin & Karahan Shields
Exposure Levels Both (Spheres)
Faculty of 3mE – Chair of Dredging Engineering
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
Soulsby Zanke Julien Yalin & Karahan Shields
© S.A.M
Exposure Levels Both, Bonneville
Parameter
Delft University of Technology – Offshore & Dredging Engineering
© 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)
Faculty of 3mE – Chair of Dredging Engineering
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
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Exposure Levels Experiments
Delft University of Technology – Offshore & Dredging Engineering
© 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
Delft University of Technology – Offshore & Dredging Engineering
© 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
Delft University of Technology – Offshore & Dredging Engineering
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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
Delft University of Technology – Offshore & Dredging Engineering
© 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
Faculty of 3mE – Chair of Dredging Engineering
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
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Application of the model
Faculty of 3mE – Chair of Dredging Engineering
The governing equationsThe friction coefficient
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Application to scour in a TSHD
Faculty of 3mE – Chair of Dredging Engineering
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:
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The friction coefficient
Faculty of 3mE – Chair of Dredging Engineering
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
Faculty of 3mE – Chair of Dredging Engineering
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
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Hopper Sedimentation, verification
Faculty of 3mE – Chair of Dredging Engineering
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
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Questions?
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Delft University of Technology – Offshore & Dredging Engineering
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.