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

The Delft Sand, Clay & Rock Cutting Model.
6. 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.
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
(14-1)
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.
9. 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.
These forces are shown in Figure 14-3. 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
(14-2)
The forces acting on the wedge bottom A-D when cutting soil, can be distinguished as:
10. A force N3, resulting from the effective grain stresses, between the wedge bottom and the undisturbed soil.
11. A shear force S3 as a result of the soil/soil friction N3·tan(φ between the wedge bottom and the undisturbed
soil.
12. 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.
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
(14-3)
The forces acting on a straight blade C-D when cutting soil (see Figure 14-4), can be distinguished as:
16. A force normal to the blade N4, resulting from the effective grain stresses.
17. A shear force S4 as a result of the soil/steel friction N4·tan(.
The normal force N4 and the shear force S4 can be combined to a resulting grain force K4.
2 2
4 4 4
K N S
(14-4)
The horizontal equilibrium of forces on the layer cut:
F h K 1 sin( ) C 1 cos( ) C 2 cos( ) K 2 sin( ) 0
(14-5)
The vertical equilibrium of forces on the layer cut:
F v K 1 cos( ) C 1 sin( ) C 2 sin( ) K 2 cos( ) 0
(14-6)
The force K1 on the shear plane is now:
K
1
C1 cos( ) C2 cos( )
sin( )
(14-7)
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