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

Which Cutting Mechanism for Which Kind of Soil?
The horizontal and vertical forces on the blade, chisel or pick point are:
F h W2
sin( ) K2
sin(
) Acos( )
(4-22)
F W cos( ) K cos(
) Asin( )
(4-23)
v 2
2
The equilibrium of moments around the blade tip is:
N
W
R G R N
W
1 1 1 3 2 2 2
R
(4-24)
Analyzing these equations results in the following conclusions:
Since the argument in the cosine of the cohesive term in the force K1 is always greater than 90 degrees, the
cosine is negative and the term as a whole is positive. This results in positive forces on the blade, chisel or
pick point and also positive normal forces. The minimum normal stress however equals the normal stress on
the shear plane, minus about the radius of the Mohr circle. The result may be a negative minimum normal
stress. If this negative minimum normal stress is smaller than the negative tensile strength, brittle tensile failure
will occur. Otherwise brittle shear failure will occur. In both cases the forces calculated are peak forces. The
average forces are somewhere between 50% and 100% of the peak forces.
On the blade the normal stresses are always high enough to avoid the occurrence of the Curling Type. In fact
the forces on the blade do not depend on the length of the blade. The cohesive force on the shear plane however
depends on the (mobilized) cohesion or shear strength, so the Tear Type, here named the Chip Type may
occur.
When the argument of the sine in the denominator gets close to 180 degrees, the forces become very large. If
the argument is greater than 180 degrees, the forces would become negative. Since both conditions will not
happen in nature, nature will find another cutting mechanism, the wedge mechanism.
4.5. Cutting Rock Hyperbaric.
In the case of hyperbaric rock cutting, the pore pressures cannot be neglected anymore. Gravity and inertial forces
can still be neglected. Usually rock has no adhesion. When the hydrostatic pressure is larger than or approaching
the UCS value of the rock, the rock tends to fail in a semi-ductile manner, named cataclastic failure. It is almost
like the hydrostatic pressure can be added to the tensile strength of the rock.
Rock cutting under hyperbaric conditions (deep sea mining) is dominated by the internal shear strength, the pore
vacuum pressure forces and by the internal and external friction angles. The main cutting mechanism is the
Crushed Type, cataclastic semi-ductile cutting. This is covered in Chapter 9: Rock Cutting: Hyperbaric
Conditions.
Figure 4-8: The Crushed Type in hyperbaric rock cutting.
Copyright © Dr.ir. S.A. Miedema TOC Page 101 of 454