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

The Delft Sand, Clay & Rock Cutting Model.
Definitions:
1. A: The wedge tip.
2. B: End of the shear plane.
3. C: The blade top.
4. D: The blade tip.
5. A-B: The shear plane.
6. A-C: The wedge surface.
7. A-D: The wedge bottom.
8. D-C: The blade surface.
9. hb: The height of the blade.
10. hi: The thickness of the layer cut.
11. vc: The cutting velocity.
12. α: The blade angle.
13. β: The shear angle.
14. Fh: The horizontal force, the arrow gives the positive direction.
15. Fv: The vertical force, the arrow gives the positive direction.
For the weight of the layer cut G1, see chapter 5: Dry Sand Cutting.
The weight of the wedge G2 is given by:
2
h
b 1 1
G2 s
g w
2
tan tan
(11-1)
11.2. The Force Equilibrium.
Figure 11-4 illustrates the forces on the layer of soil cut. The forces shown are valid in general for dry sand. The
forces acting on the layer A-B are:
1. A normal force acting on the shear surface N1, resulting from the effective grain stresses.
2. A shear force S1 as a result of internal friction N1·tan(φ.
3. A gravity force G1 as a result of the weight of the layer cut.
4. An inertial force I, resulting from acceleration of the soil.
5. A force normal to the pseudo blade N2, resulting from the effective grain stresses.
6. A shear force S2 as a result of the soil/soil friction N2·tan(λ between the layer cut and the wedge pseudo
blade. The friction angle λ does not have to be equal to the internal friction angle φ in the shear plane, since
the soil has already been deformed.
The normal force N1 and the shear force S1 can be combined to a resulting grain force K1.
2 2
1 1 1
K N S
(11-2)
The forces acting on the wedge front or pseudo blade A-C when cutting soil, can be distinguished as:
7. A force normal to the blade N2, resulting from the effective grain stresses.
8. A shear force S2 as a result of the soil/soil friction N2·tan(λ between the layer cut and the wedge pseudo
blade. The friction angle λ does not have to be equal to the internal friction angle φ in the shear plane, since
the soil has already been deformed.
These forces are shown in Figure 11-5. If the forces N2 and S2 are combined to a resulting force K2 and the adhesive
force and the water under pressures are known, then the resulting force K2 is the unknown force on the blade. By
taking the horizontal and vertical equilibrium of forces an expression for the force K2 on the blade can be derived.
2 2
2 2 2
K N S
(11-3)
The forces acting on the wedge bottom A-D when cutting soil, can be distinguished as:
9. A force N3, resulting from the effective grain stresses, between the wedge bottom and the undisturbed soil.
10. A shear force S3 as a result of the soil/soil friction N3·tan(φ between the wedge bottom and the undisturbed
soil.
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