9.7: Example

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In this chapter many graphs are given for an α=60^o blade and different internal friction angles. Chosing φ=20^o, 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 h_i=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.

**Table 9-1: Forces and specific energy example.**
Water Depth z (m)	Hydrostatic Pressure/UCS Ratio	β (^o)	h_b,m/h_i (-)	λ_HC (-)	λv_C (-)	E_sp/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 hb,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.