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

Rock Cutting: Atmospheric Conditions.
8.4. The Flow Type (Based on the Merchant Model).
Rock is the collection of materials where the grains are bonded chemically from very stiff clay, sandstone to very
hard basalt. It is difficult to give one definition of rock or stone and also the composition of the material can differ
strongly. Still it is interesting to see if the model used for sand and clay, which is based on the Coulomb model,
can be used for rock as well. Typical parameters for rock are the compressive strength UCS and the tensile strength
BTS and specifically the ratio between those two, which is a measure for how fractured the rock is. Rock also has
shear strength and because it consists of bonded grains it will have an internal friction angle and an external friction
angle. It can be assumed that the permeability of the rock is very low, so initially the pore pressures do no play a
role or cavitation will always occur under atmospheric conditions. But since the absolute hydrostatic pressure,
which would result in a cavitation under pressure of the same magnitude can be neglected with respect to the
compressive strength of the rock; the pore pressures are usually neglected. This results in a material where gravity,
inertia, pore pressures and adhesion can be neglected.
Merchant (1944), (1945A) and (1945B) derived a model for determining the cutting forces when machining steel.
The model was based on plastic deformation and a continuous chip formation (ductile cutting). The model included
internal and external friction and shear strength, but no adhesion, gravity, inertia and pore pressures. Later
Miedema (1987 September) extended this model with adhesion, gravity, inertial forces and pore water pressures.
Definitions:
1. A: The blade tip.
2. B: End of the shear plane.
3. C: The blade top.
4. A-B: The shear plane.
5. A-C: The blade surface.
6. hb: The height of the blade.
7. hi: The thickness of the layer cut.
8. vc: The cutting velocity.
9. α: The blade angle.
10. β: The shear angle.
11. Fh: The horizontal force, the arrow gives the positive direction.
12. Fv: The vertical force, the arrow gives the positive direction.
Figure 8-26 gives some definitions regarding the cutting process. The line A-B is considered to be the shear plane,
while the line A-C is the contact area between the blade and the soil. The blade angle is named α and the shear
angle β. The blade is moving from left to right with a cutting velocity vc. The thickness of the layer cut is hi and
the vertical height of the blade hb. The horizontal force on the blade Fh is positive from right to left always opposite
to the direction of the cutting velocity vc. The vertical force on the blade Fv is positive downwards. Since the
vertical force is perpendicular to the cutting velocity, the vertical force does not contribute to the cutting power Pc,
which is equal to:
Pc Fh vc
(8-96)
Figure 8-26: The definitions of the cutting process.
Copyright © Dr.ir. S.A. Miedema TOC Page 273 of 454