3.1: Cutting Mechanisms

Hatamura and Chijiiwa (1975), (1976A), (1976B), (1977A) and (1977B) distinguished three failure mechanisms in soil cutting. The Shear Type, the Flow Type and the Tear Type. The Flow Type and the Tear Type occur in materials without an angle of internal friction. The Shear Type occurs in materials with an angle of internal friction like sand.

A fourth failure mechanism can be distinguished (Miedema (1992)), the Curling Type, as is known in metal cutting. Although it seems that the curling of the chip cut is part of the flow of the material, whether the Curling Type or the Flow Type occurs depends on several conditions. The Curling Type in general will occur if the adhesive force on the blade is large with respect to the normal force on the shear plane. Whether the Curling Type results in pure curling or buckling of the layer cut giving obstruction of the flow depends on different parameters. In rock or stone two additional cutting mechanisms may occur, the Crushed Type and the Chip Type. The 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:

$\ \mathrm{P}_{\mathrm{c}}=\mathrm{F}_{\mathrm{h}} \cdot \mathrm{v}_{\mathrm{c}}\tag{3-1}$

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.