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

The Delft Sand, Clay & Rock Cutting Model.
Crushed Type will occur if a thin layer of rock is scraped or cut like in oil and gas drilling. The mechanism of the
Crushed Type is similar to the Shear Type, only first the rock material has to be crushed. The Chip Type will
occur when cutting thicker layers of rock or stone. This type is similar to the Tear Type.
Figure 3-1 illustrates the Curling Type, the Flow Type and the Tear Type mechanisms as they might occur when
cutting clay, the Shear Type mechanism as it might occur when cutting sand and the Crushed Type and Chip
Type as they might occur when cutting rock or stone. Of course also mixed types may occur.
To predict which type of failure mechanism will occur under given conditions with specific soil, a formulation for
the cutting forces has to be derived. The derivation is made under the assumption that the stresses on the shear
plane and the blade are constant and equal to the average stresses acting on the surfaces. Figure 3-2 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.
The shear angle β is determined based on the minimum energy principle. It is assumed that failure will occur at a
shear angle where the cutting energy is at a minimum. The cutting power is the cutting energy per unit of time, so
the cutting power also has to be at the minimum level.
Since the vertical force is perpendicular to the cutting velocity, the vertical force does not contribute to the cutting
power, which is equal to the horizontal cutting force times the cutting velocity:
Pc Fh vc
(3-1)
Whether the minimum energy principle is true and whether the approach of using straight failure planes is right
has been validated with experiments. The experimental data, usually measurements of the horizontal and vertical
cutting forces and pore pressures, shows that the approach in this book gives a good prediction of the cutting
forces.
3.2. Definitions.
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.
Figure 3-2: The cutting process, definitions.
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