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 Forms : OE4626 - Dredging Processes - Exam 2008/2009 E

Faculty Mechanical, Marine & Materials Engineering
Department Marine & Transport Technology
Section Offshore & Dredging Engineering

Exam OE4626 Dredging Processes

January 2009

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   Exam 2008/2009 E
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Exam date:

1. Hopper Load Parameter:
(10 Points)

Which of the following statements is true?

  1. The hopper load parameter gives the maximum load in tons a hopper can carry.
  2. The hopper load parameter gives the position of the overflow when the loading starts.
  3. The hopper load parameter is the ratio between de deadweight of a hopper dredge and the weight the hopper can carry.
  4. The hopper load parameter is the maximum mass flow that can enter the hopper.
  5. The hopper load parameter is the settling velocity of grains that will settle for 100%.
  6. The hopper load parameter is the ersion velocity of grains that will erode for 100%.

1      2      3      4      5      6
2. Soil Parameters 1:
(10 Points)

Which of the following soil mechanical parameters play a dominant role in the cutting of sand?

  1. The density of water.
  2. The angle of internal friction.
  3. The permeability of the sand.
  4. The tensile strength of the sand.
  5. The porosity of the sand.
  6. The adhesion of the sand.
  7. The angle of external friction of the sand.
  8. The shear strength of the sand.

1      2      3      4      5      6      7      8
3. Dilatation:
(10 Points)

What is the definition of dilatation?

  1. Dilatation is the increase  of the pore volume of sand caused by gravitation.
  2. Dilatation is the decrease of the pore volume of sand caused by shear stress.
  3. Dilatation is the decrease of the pore volume of sand caused by dredging.
  4. Dilatation is the increase  of the pore volume of sand caused by shear stress.
  5. Dilatation is the increase  of the pore volume of sand caused by dredging.
  6. Dilatation is the decrease of the pore volume of sand caused by gravitation

1       2       3       4       5       6
4. Soil Parameters 2:
(10 Points)

Which soil mechanical parameters dominate the cutting forces in clay?

  1. The gravitational constant.
  2. The density of the cutting blade.
  3. The internal shear strength or cohesion of the clay.
  4. The density of the clay.
  5. The permeability of the clay.
  6. The external shear strength or adhesion of the clay.
  7. The porosity of the clay.
  8. The angle of internal friction of the clay.

1      2      3      4      5      6      7      8
5. Mohr Circle:
(10 Points)

Which of the following statements are true?

  1. The Mohr circle gives the relation between normal stress and tensile stress.
  2. In the τ-σ diagram for soil the positive horizontal axis gives tensile stress.
  3. In the τ-σ diagram for soil the positive horizontal axis gives compressive stress.
  4. The Mohr circle gives the relation between normal stress and shear stress.
  5. In the τ-σ diagram for steel the positive horizontal axis gives compressive stress.
  6. In the τ-σ diagram for steel the positive horizontal axis gives tensile stress.
  7. In the Mohr circle real angles are shown by a factor 2.
  8. In the Mohr circle real angles are shown by a factor 1/2.

1      2      3      4      5      6      7      8
6. Soil Parameters 3:
(10 Points)

Which material properties play a dominant role in the cutting of rock/stone?

  1. The external friction coefficient of the rock.
  2. The external shear strength or adhesion of the rock.
  3. The external friction angle of the rock.
  4. The density of the rock.
  5. The permeability of the rock.
  6. The tensile strength of the rock.
  7. The shear strength of the rock.
  8. The internal friction angle of the rock.

One      Two      Three      Four      Five      Six      Seven      Eight
7. Cavitation:
(10 Points)

Which statements are true?

  1. Cavitation is in fact the boiling of water.
  2. Cavitation at 10 degrees centigrade occurs at about 0.1 bar absolute pressure.
  3. At 100 degrees centigrade cavitation will occur at about 100 kPa.
  4. Cavitation is the evaporation of water.
  5. Cavitation at 10 degrees centigrade occurs at about 0.01 bar absolute pressure.
  6. High in the mountains cavitation will occur at a temperature lower than 100 degrees centigrade.
  7. At an atmospheric pressure of 100 kPa cavitation occurs at 10 degrees centigrade.
  8. High in the mountains cavitation will occur at a temperature higher than 100 degrees centigrade.

1      2      3      4      5      6      7      8
8. Soil Failure:
(10 Points)

Which of the following statements are true?

  1. Passive soil failure is the failure where the soil is passive, the outside world is active.
  2. Active soil failure is the failure where the outside world is active, the soil is passive.
  3. Passive soil failure is the failure where the soil is active, the outside world is passive.
  4. Active soil failure is the failure where the outside world is passive, the soil is active.
  5. The stresses with passive failure are larger than with active failure.
  6. The stresses with active failure are larger than with passive failure.
  7. Excavating soil in dredging is a typical example of active failure.
  8. Excavating soil in dredging is a typical example of passive failure.

1      2      3      4      5      6      7      8
9. Dilatation:
(10 Points)

If the porosity of a sand is 40% before cutting (in situ) and 50% after cutting,
what is the volume increase of the sand (grains + pores) as a fraction.


    (-)



10. Density:
(10 Points)

Assume a water density of 1.000 ton/m3 and a quarts density of 2.650 ton/m3.
What is the density of a mixture with a volumetric concentration of 40% quarts (sand)?


    (ton/m3)



11. Shear Angle:
(20 Points)

Which of the following statements are true in the case only the weight of the soil is considered for example if dry sand is excavated?

  1. If the blade angle α increases, the shear angle β also increases.
  2. If the angle of internal friction φ increases, the shear β angle also increases.
  3. If the external friction angle δ increases, the shear β angle also increases.
  4. If the blade angle α increases, the shear angle β decreases.
  5. If the angle of internal friction φ increases, the shear angle β decreases.
  6. If the external friction angle δ increases, the shear angle β decreases.

1      2      3      4      5      6
12. Sand Cutting:
(5 Points)

What is the value of the mean permeability km as used in the cutting equations for water saturated sand.


``Consider a sand with the following properties:

``
``Initial permeability: `k_i=0.000075 m/sec`
``Maximum permeability: `k_max=0.000125 m/sec`
``

    (m/sec)



13. Dilatancy:
(5 Points)

What is the value of the dilatancy e?


``Consider a sand with the following properties:

``
``initial porosity: `n_i=45 %`
``Maximum porosity: `n_max=50 %`
``

    (-)



14. Cutting forces:
(10 Points)

What are the horizontal cutting forces at 0 m, 10m and 20m waterdepth for the non-cavitational cutting process at a cutting velocity of 1 m/s.


``Consider a sand with the following properties:

``
``Angle of internal friction: `phi=37 dgr`
``Angle of external friction: `delta=24 dgr`
``Initial permeability: `k_i=0.000075 m/sec`
``Maximum permeability: `k_max=0.000125 m/sec`
``initial porosity: `n_i=45 %`
``Maximum porosity: `n_max=50 %`
``

The cutting blade has the following properties:

``
``The cutting angle: `alpha=60 dgr`
``The shear angle: `beta=20 dgr`
``The blade height: `h_b=0.2 m`
``The thickness of the layer to be cut: `h_i=0.1 m`
``The width of the blade: `b=1 m`
``

Coefficients for the cutting equations:

``
``The coefficient for non-cavitating cutting: `c_1=0.25`
``The coefficient for cavitating cutting: `d_1=2.5`
``

General constants:

``
``The density of water: `rho_w=1.025 tns/m^3`
``The gravitational constant: `g=9.81 m/sec^2`
``

0 m      10 m      20 m    (kN)



15. Cutting forces:
(10 Points)

What are the horizontal cutting forces at 0 m, 10 m and 20 m water depth for the cavitational cutting process.


``Consider a sand with the following properties:

``
``Angle of internal friction: `phi=37 dgr`
``Angle of external friction: `delta=24 dgr`
``Initial permeability: `k_i=0.000075 m/sec`
``Maximum permeability: `k_max=0.000125 m/sec`
``initial porosity: `n_i=45 %`
``Maximum porosity: `n_max=50 %`
``

The cutting blade has the following properties:

``
``The cutting angle: `alpha=60 dgr`
``The shear angle: `beta=20 dgr`
``The blade height: `h_b=0.2 m`
``The thickness of the layer to be cut: `h_i=0.1 m`
``The width of the blade: `b=1 m`
``

Coefficients for the cutting equations:

``
``The coefficient for non-cavitating cutting: `c_1=0.25`
``The coefficient for cavitating cutting: `d_1=2.5`
``

General constants:

``
``The density of water: `rho_w=1.025 tns/m^3`
``The gravitational constant: `g=9.81 m/sec^2`
``

0 m      10 m      20 m    (kN)



16. Transition velocity:
(10 Points)

Give the equation for the transition velocity from non-cavitating cutting to cavitating cutting.

The variable names you have to use are:

c_1 for `c_1` , the non-cavitating coefficient

rho_w for `rho_w` , the density of water in ton/m3

g for `g` , the gravitation constant in m/sec2

h_i for `h_i` , the thickness of the layer cut in m/sec

b for `b` , the width of the blade in m

v_c for `v_c` , the cutting velocity (transition velocity)

e for `e` , the dilatation

k_m for `k_m` , the permeability of the sand in m/sec

d_1 for `d_1` , the cavitating coefficient

z for `z` , the waterdepth in m






Example

17. Transition velocity:
(10 Points)

At which velocities are the transitions between the cavitational and the non-cavitational cutting process at 0 m, 10 m and 20 m waterdepth?


``Consider a sand with the following properties:

``
``Angle of internal friction: `phi=37 dgr`
``Angle of external friction: `delta=24 dgr`
``Initial permeability: `k_i=0.000075 m/sec`
``Maximum permeability: `k_max=0.000125 m/sec`
``initial porosity: `n_i=45 %`
``Maximum porosity: `n_max=50 %`
``

The cutting blade has the following properties:

``
``The cutting angle: `alpha=60 dgr`
``The shear angle: `beta=20 dgr`
``The blade height: `h_b=0.2 m`
``The thickness of the layer to be cut: `h_i=0.1 m`
``The width of the blade: `b=1 m`
``

Coefficients for the cutting equations:

``
``The coefficient for non-cavitating cutting: `c_1=0.25`
``The coefficient for cavitating cutting: `d_1=2.5`
``

General constants:

``
``The density of water: `rho_w=1.025 tns/m^3`
``The gravitational constant: `g=9.81 m/sec^2`
``

0 m      10 m      20 m    (m/sec)



18. Specific energy:
(10 Points)

What is the specific energy at 0 m, 10 m and 20 m waterdepth at a cutting velocity of 1 m/s.


``Consider a sand with the following properties:

``
``Angle of internal friction: `phi=37 dgr`
``Angle of external friction: `delta=24 dgr`
``Initial permeability: `k_i=0.000075 m/sec`
``Maximum permeability: `k_max=0.000125 m/sec`
``initial porosity: `n_i=45 %`
``Maximum porosity: `n_max=50 %`
``

The cutting blade has the following properties:

``
``The cutting angle: `alpha=60 dgr`
``The shear angle: `beta=20 dgr`
``The blade height: `h_b=0.2 m`
``The thickness of the layer to be cut: `h_i=0.1 m`
``The width of the blade: `b=1 m`
``

Coefficients for the cutting equations:

``
``The coefficient for non-cavitating cutting: `c_1=0.25`
``The coefficient for cavitating cutting: `d_1=2.5`
``

General constants:

``
``The density of water: `rho_w=1.025 tns/m^3`
``The gravitational constant: `g=9.81 m/sec^2`
``

0 m      10 m      20 m    (kPa)



19. Specific energy:
(10 Points)

What is the specific energy at a waterdepth of 0 m, 10 m and 20 m at a cutting velocity of 3 m/s?


``Consider a sand with the following properties:

``
``Angle of internal friction: `phi=37 dgr`
``Angle of external friction: `delta=24 dgr`
``Initial permeability: `k_i=0.000075 m/sec`
``Maximum permeability: `k_max=0.000125 m/sec`
``initial porosity: `n_i=45 %`
``Maximum porosity: `n_max=50 %`
``

The cutting blade has the following properties:

``
``The cutting angle: `alpha=60 dgr`
``The shear angle: `beta=20 dgr`
``The blade height: `h_b=0.2 m`
``The thickness of the layer to be cut: `h_i=0.1 m`
``The width of the blade: `b=1 m`
``

Coefficients for the cutting equations:

``
``The coefficient for non-cavitating cutting: `c_1=0.25`
``The coefficient for cavitating cutting: `d_1=2.5`
``

General constants:

``
``The density of water: `rho_w=1.025 tns/m^3`
``The gravitational constant: `g=9.81 m/sec^2`
``

0 m      10 m      20 m    (kPa)



20. Hopper sedimentation:
(10 Points)

What is the value of the so called Hopper Load Parameter in m/sec.

Use the Stokes equation for settling velocities (the Stokes equation is in mm and mm/sec).


``Consider a TSHD with a hopper with the following properties:

``
``Length: `L=100 m`
``Width: `W=15 m`
``Height: `H=10 m`
``Flow: `Q=10 m^3/sec`
``Design density: `rho_d=1.5 tns/m^3`
``Mixture density: `rho_m=1.5 tns/m^3`
``

    (m/sec)



21. Grain diameter:
(10 Points)

What is the diameter in mm of a grain with the Hopper Load Parameter as settling velocity?


``Consider a TSHD with a hopper with the following properties:

``
``Length: `L=100 m`
``Width: `W=15 m`
``Height: `H=10 m`
``Flow: `Q=10 m^3/sec`
``Design density: `rho_d=1.5 tns/m^3`
``Mixture density: `rho_m=1.5 tns/m^3`
``

    (mm)



Settling Velocity

22. Settling efficiency:
(10 Points)

Determine the setting efficiencies of grains with a diameter of 0.06 mm, 0.10 mm and 0.15 mm.


``Consider a TSHD with a hopper with the following properties:

``
``Length: `L=100 m`
``Width: `W=15 m`
``Height: `H=10 m`
``Flow: `Q=10 m^3/sec`
``Design density: `rho_d=1.5 tns/m^3`
``Mixture density: `rho_m=1.5 tns/m^3`
``

0.06 mm      0.10 mm      0.15 mm    (-)



Turbulence efficiency

23. Settling efficiency:
(10 Points)

What is the total settling efficiency if a sand consists of 40% grains of 0.06 mm, 40% grains of 0.1 mm and 20% grains of 0.15 mm?


``Consider a TSHD with a hopper with the following properties:

``
``Length: `L=100 m`
``Width: `W=15 m`
``Height: `H=10 m`
``Flow: `Q=10 m^3/sec`
``Design density: `rho_d=1.5 tns/m^3`
``Mixture density: `rho_m=1.5 tns/m^3`
``

    (-)



24. Maximum load:
(10 Points)

What is the maximum load of the hopper in tons?


``Consider a TSHD with a hopper with the following properties:

``
``Length: `L=100 m`
``Width: `W=15 m`
``Height: `H=10 m`
``Flow: `Q=10 m^3/sec`
``Design density: `rho_d=1.5 tns/m^3`
``Mixture density: `rho_m=1.5 tns/m^3`
``

    (tons)



25. Filling time:
(10 Points)

How long does it take to fill the hopper to overflow level in minutes?


``Consider a TSHD with a hopper with the following properties:

``
``Length: `L=100 m`
``Width: `W=15 m`
``Height: `H=10 m`
``Flow: `Q=10 m^3/sec`
``Design density: `rho_d=1.5 tns/m^3`
``Mixture density: `rho_m=1.5 tns/m^3`
``

    (min)



26. Volumetric concentration:
(10 Points)

Give the equation for the volumetric concentration `c_v` of a sand/water mixture with a mixture density of `rho_m` by using the following variable names:

c_v for `c_v` , the volumetric concentration

rho_w for `rho_w` , the water density

rho_q for `rho_q` , the quarts (sand grain) density

rho_m for `rho_m` , the mixture density

all densities are in tons/m3






Example

27. Ratio Ws/TDS:
(10 Points)

Give the equation for the ratio between the situ weight in the hopper `W_s` and the Tonnes Dry Solids `TDS` by using the following variable names:

c_v for `c_v` , the volumetric concentration

rho_w for `rho_w` , the water density

rho_q for `rho_q` , the quarts (sand grain) density

rho_m for `rho_m` , the mixture density

rho_s for `rho_s` , the situ sediment density

all densities are in tons/m3






Example

28. Shields parameter:
(10 Points)

What are the values of the Shields parameter with a water layer of 2 m, 1.0 m and 0.5 m above the sediment for the 0.15 mm grain.


``Consider a TSHD with a hopper with the following properties:

``
``Length: `L=100 m`
``Width: `W=15 m`
``Height: `H=10 m`
``Flow: `Q=10 m^3/sec`
``Design density: `rho_d=1.5 tns/m^3`
``Mixture density: `rho_m=1.5 tns/m^3`
``

2.0 m      1.0 m      0.5 m    (-)



Moody Diagram

29. Reynolds Numbers:
(10 Points)

What are the matching Reynolds numbers based on the friction velocity u* for water depths of 2.0 m, 1.0 m and 0.5 m.


``Consider a TSHD with a hopper with the following properties:

``
``Length: `L=100 m`
``Width: `W=15 m`
``Height: `H=10 m`
``Flow: `Q=10 m^3/sec`
``Design density: `rho_d=1.5 tns/m^3`
``Mixture density: `rho_m=1.5 tns/m^3`
``

2.0 m      1.0 m      0.5 m     (-)



Shields Diagram

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