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

The Delft Sand, Clay & Rock Cutting Model.
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
(3-2)
The forces acting on a straight blade 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 external friction angle N2·tan(.
13. A shear force A as a result of pure adhesion between the soil and the blade a. This force can be calculated by
multiplying the adhesive shear strength a of the soil with the contact area between the soil and the blade.
14. A force W2 as a result of water under pressure on the blade.
These forces are shown in Figure 3-7. If the forces N2 and S2 are combined to a resulting force K2 and the adhesive
force A and the water under pressures forces W1 and W2 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
(3-3)
Figure 3-6: The forces on the layer cut.
Figure 3-7: The forces on the blade.
The horizontal equilibrium of forces:
F K sin( ) W sin( ) C cos( ) I cos( )
h 1 1
A cos( ) W sin( ) K sin( ) 0
2 2
(3-4)
The vertical equilibrium of forces:
F K cos( ) W cos( ) Csin( ) I sin( )
v 1 1
G A sin( ) W cos( ) K cos( ) 0
2 2
(3-5)
The force K1 on the shear plane is now:
K
1
W2 sin( ) W1 sin( ) G sin( )
sin( )
I cos( ) C cos( ) A cos( )
sin( )
(3-6)
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