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

The Delft Sand, Clay & Rock Cutting Model.
13.2. The Equilibrium of Forces.
Figure 13-2 illustrates the forces on the layer of soil cut. The forces shown are valid for clay.
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 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.
3. A force normal to the pseudo blade N2, resulting from the effective grain stresses.
4. 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 forces acting on the wedge front or pseudo blade A-C when cutting clay, can be distinguished as (see Figure
13-3):
5. A force normal to the blade N2, resulting from the effective grain stresses.
6. 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.
The forces acting on the wedge bottom A-D when cutting clay, can be distinguished as:
7. A force N3, resulting from the effective grain stresses, between the wedge bottom and the undisturbed soil.
8. 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 forces acting on a straight blade C-D when cutting soil (see Figure 13-4), can be distinguished as:
9. A force normal to the blade N4, resulting from the effective grain stresses.
10. 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.
The horizontal equilibrium of forces on the layer cut:
F h N 1 sin( ) C 1 cos( ) C 2 cos( ) N 2 sin( ) 0
(13-1)
The vertical equilibrium of forces on the layer cut:
F v N 1 cos( ) C 1 sin( ) C 2 sin( ) N 2 cos( ) 0
(13-2)
The force N1 on the shear plane is now:
C1 cos( ) C2
N1
sin( )
(13-3)
The force N2 on the pseudo blade is now:
N
2
C1 C2cos( )
sin( )
(13-4)
From equation (13-4) the forces on the pseudo blade can be derived. On the pseudo blade a force component in
the direction of cutting velocity Fh and a force perpendicular to this direction Fv can be distinguished.
Fh N2sin( ) C2 cos( )
(13-5)
F N2 cos( ) C2
sin( )
(13-6)
Now knowing the forces on the pseudo blade A-C, the equilibrium of forces on the wedge A-C-D can be derived.
The adhesive force does not have to be mobilized 100%, while this force could have both directions, depending
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