The Delft Sand, Clay & Rock Cutting Model, 2019a

The Delft Sand, Clay & Rock Cutting Model.
16.6.10. Calc.: Cutting Forces & Specific Energy.
Consider a sand with the following properties:
Angle of internal friction: φ=36º
Angle of external friction: δ=24º
Initial permeability: k i=0.000025 m/sec
Maximum permeability: k max=0.000125 m/sec
initial porosity: n i=42%
Maximum porosity: n max=50%
The cutting blade has the following properties:
The cutting angle: α=60º
The shear angle: β=20º
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: w=1 m
Coefficients for the cutting equations:
The coefficient for non-cavitating cutting: c 1=0.45
The coefficient for cavitating cutting: d 1=5.5
General constants:
The density of water: ρ w=1.025 tons/m 3
The gravitational constant: g=9.81 m/sec 2
A: What are the horizontal cutting forces at 0 m, 10 m and 20 m water depth for the non-cavitational cutting
process at a cutting velocity of 1.5 m/s?
2 2
1 w c i
c g v h w 0.451.025 9.81 0.1 0.161
Fh
vc
k 0.000075
c
m
96.53 v 96.531.5 144.8
(kN)
The non-cavitational force does not depend on the water depth.
B: What are the horizontal cutting forces at 0 m, 10 m and 20 m water depths for the cavitational cutting
process?
h 1 w i
F d g z 10 h w 5.51.025 9.81 0.11 z 10
5.53 z 10
(kN)
This gives for 0 m water depth a force of 55.3 kN, for 10 m water depth a force of 110.6 kN and for 20 m water
depth a force of 165.9 kN.
C: At which velocities are the transitions between the cavitational and the non-cavitational cutting process
at 0 m, 10 m and 20 m water depths?
c
96.53 v 5.53 z 10 v 0.0573 z 10 (m/sec)
c
This gives for 0 m water depth a transition velocity of 0.573 m/sec, for 10 m water depth a transition velocity of
1.146 m/sec and for 20 m water depth a transition velocity of 1.719 m/sec.
D: What is the specific energy at 0 m, 10 m and 20 m water depth at a cutting velocity of 1 m/s?
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