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

The Delft Sand, Clay & Rock Cutting Model.
14. Fh: The horizontal force, the arrow gives the positive direction.
15. Fv: The vertical force, the arrow gives the positive direction.
10.2. The Force Equilibrium.
Figure 10-2 illustrates the forces on the layer of soil cut. The forces shown are valid in general for each type of
soil.
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 force W1 as a result of water under pressure in the shear zone.
4. A shear force C1 as a result of pure cohesion c or shear strength. This force can be calculated by multiplying
the cohesive shear strength c with the area of the shear plane.
5. A gravity force G1 as a result of the weight of the layer cut.
6. An inertial force I, resulting from acceleration of the soil.
7. A force normal to the pseudo 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.
9. A shear force C2 as a result of the mobilized cohesion between the soil and the wedge c. This force can be
calculated by multiplying the cohesive shear strength c of the soil with the contact area between the soil and
the wedge.
10. A force W2 as a result of water under pressure on the wedge.
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
(10-1)
The forces acting on the wedge front or pseudo blade A-C when cutting soil, can be distinguished as:
11. A force normal to the blade N2, resulting from the effective grain stresses.
12. 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.
13. A shear force C2 as a result of the cohesion between the layer cut and the pseudo blade c. This force can be
calculated by multiplying the cohesive shear strength c of the soil with the contact area between the soil and
the pseudo blade.
14. A force W2 as a result of water under pressure on the pseudo blade A-C.
These forces are shown in Figure 10-3. 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
(10-2)
The forces acting on the wedge bottom A-D when cutting soil, can be distinguished as:
15. A force N3, resulting from the effective grain stresses, between the wedge bottom and the undisturbed soil.
16. A shear force S3 as a result of the soil/soil friction N3·tan(φ between the wedge bottom and the undisturbed
soil.
17. A shear force C3 as a result of the cohesion between the wedge bottom and the undisturbed soil c. This force
can be calculated by multiplying the cohesive shear strength c of the soil with the contact area between the
wedge bottom and the undisturbed soil.
18. A force W3 as a result of water under pressure on the wedge bottom A-D.
The normal force N3 and the shear force S3 can be combined to a resulting grain force K3.
2 2
3 3 3
K N S
(10-3)
The forces acting on a straight blade C-D when cutting soil (see Figure 10-4), can be distinguished as:
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