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

8.3. Cutting Models.
Rock Cutting: Atmospheric Conditions.
Figure 8-18: The Crushed Type.
Figure 8-19: The Chip Type.
When cutting rock with a pick point, usually a crushed zone will occur in front of and under the tip of the pick
point. If the cutting depth is small, this crushed zone may reach the surface and a sand like cutting process may
occur. If the cutting depth is larger, the crushed material cannot escape and the stresses in the crushed zone increase
strongly. According to Fairhurst (1964) the cutting forces are transmitted through particle-particle contacts. The
stresses are transmitted to the intact rock as discrete point loads this way, causing micro shear cracks and finally a
tensile crack. Figure 8-18 and Figure 8-19 sho this cutting mechanism.
As mentioned the type of failure depends on the UCS/BTS ratio. Geking (1987) stated that below a ratio of 9
ductile failure will occur, while above a ratio of 15 brittle failure will occur. In between these limits there is a
transition between ductile and brittle failure, which is also in accordance with the findings of Fairhurst (1964).
The mechanism as described above is difficult to model. Still a method is desired to predict the cutting forces in
rock cutting in order to estimate forces, power and production. In literature some models exist, like the Evans
(1964) model based on tensile failure and the Nishimatsu (1972) model based on shear failure. From steel cutting
also the Merchant (1944) model is known, based on plastic shear failure. The Evans (1964) model assumes a
maximum tensile stress on the entire failure plane, which could match the peak forces, but overestimates the
average forces. Nishimatsu (1972) build in a factor for the shear stress distribution on the failure plane, enabling
the model to take into account that failure may start when the shear stress is not at a maximum everywhere in the
shear plane. Both models are discussed in this chapter.
Based on the Merchant (1944) model for steel cutting and the Miedema (1987 September) model for sand cutting,
a new model is developed, both for ductile cutting, ductile cataclastic cutting, brittle shear cutting and brittle tensile
cutting. First a model is derived for the Flow Type, which is either ductile shear failure or brittle shear failure. In
the case of brittle shear failure, the maximum cutting forces are calculated. For the average cutting forces the
maximum cutting forces have to be reduced by 30% to 50%. Based on the Flow Type and the Mohr circle, the
shear stress in the shear plane is determined where, on another plane (direction), tensile stresses occur equal to the
tensile strength. An equivalent or mobilized shear strength is determined giving this tensile stress, leading to the
Tear Type of failure. This approach does not require the tensile stress to be equal to the tensile strength on the
whole failure plane, instead it predicts the cutting forces at the start of tensile failure.
This method can also be used for predicting the cutting forces in frozen clay, permafrost.
Roxborough (1987) derived a simple expression for the specific energy based on many experiments in different
types of rock. The dimension of this equation is MPa. The two constants in the equation may vary a bit depending
on the type of rock. The 0.11 is important at small UCS values, the 0.25 at large values.
Esp
0.25 U.C.S. 0.11
(8-40)
The fact that cutting rock is irreversible, compared to the cutting of sand and clay, also means that the 4 standard
cutting mechanisms cannot be applied on cutting rock. In fact the Flow Type looks like cataclastic ductile failure
from a macroscopic point of view, but the Flow Type (also the Curling Type) are supposed to be real plastic
deformation after which the material (clay) is still in tact, while cataclastic ductile failure is much more the crushing
of the rock with shear falure in the crushed rock. We will name this the Crushed Type. When the layer cut is
thicker, a crushed zone exists but not to the free surface. From the crushed zone first a shear plane is formed from
which a tensile crack goes to the free surface. We will name this the Chip Type.
Copyright © Dr.ir. S.A. Miedema TOC Page 261 of 454