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

9.7. Example.
The Delft Sand, Clay & Rock Cutting Model.
In this chapter many graphs are given for an α=60º blade and different internal friction angles. Chosing φ=20º,
like in chapter 8, gives the possibility to compare atmospheric and hyperbaric cutting of rock. The external friction
angle is assumed to be δ=2/3·φ. Assume a blade width w=0.1 m and a layer thickness hi=0.1 m, similar to chapter
8.
Also choosing UCS=100 MPa gives a specific energy to UCS ratio 0f 0.669 for very small hydrostatic pressure to
UCS ratios, which is equal to the peak values found for atmospheric cutting. The atmospheric cutting process
however is brittle shear failure in this case, resulting in lower average forces, while the hyperbaric process is
supposed to be cataclastic or pseudo ductile. At very small hydrostatic pressures the behavior will still be brittle
shear, but at larger water depths pseudo ductile.
Now suppose a rock with a UCS value of 10 MPa and water depths of 100 m, 1000 m and 3000 m. This results in
the following forces and specific energies.
Water
Depth z
(m)
Table 9-1: Forces and specific energy example.
Hydrostatic
Pressure/UCS
Ratio
β (º)
hb,m/hi
(-)
λHC
(-)
λVC
(-)
Esp/UCS
(-)
0 0 43.23 0.584 1.94 0.58 0.68
100 0.1 42.33 0.602 2.20 0.60 0.77
1000 1.0 38.51 0.707 4.62 0.81 1.62
3000 3.0 36.50 0.800 10.17 1.12 3.56
The mobilized blade height h b,m is smaller than 1, which means that under normal circumstances the mobilized
blade height is smaller than the actual blade height, resulting in the Curling Type. If the mobilized blade height
is larger than the actual blade height, the Flow Type or Crushed Type will occur and the numbers in the above
table will be different. Figure 9-17, Figure 9-18, Figure 9-19, Figure 9-20 and Figure 9-21 are used to determine
the values in the above table.
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