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

A Wedge in Dry Sand Cutting.
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
(11-4)
The forces acting on a straight blade C-D when cutting soil (see Figure 11-6), can be distinguished as:
11. A force normal to the blade N4, resulting from the effective grain stresses.
12. 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
(11-5)
The horizontal equilibrium of forces on the layer cut:
F h K 1 sin( ) I cos( ) K 2 sin( ) 0
(11-6)
The vertical equilibrium of forces on the layer cut:
F v K 1 cos( ) I sin( ) G 1 K 2 cos( ) 0
(11-7)
The force K1 on the shear plane is now:
K
1
G1
sin( ) Icos( )
sin( )
(11-8)
The force K2 on the pseudo blade is now:
K
2
G1
sin( ) Icos( )
sin( )
(11-9)
From equation (11-9) 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 K2sin( )
(11-10)
F K2
cos( )
(11-11)
The normal force on the shear plane is now:
G1
sin( ) Icos( )
N1
cos( )
sin( )
(11-12)
The normal force on the pseudo blade is now:
G1
sin( ) Icos( )
N2
cos( )
sin( )
(11-13)
Now knowing the forces on the pseudo blade A-C, the equilibrium of forces on the wedge A-C-D can be derived.
The horizontal equilibrium of forces on the wedge is:
F h K 4 sin K 3 sin K 2 sin
0
(11-14)
The vertical equilibrium of forces on the wedge is:
F v K 4 cos K 3 cos K 2 cos
G 2 0
(11-15)
Copyright © Dr.ir. S.A. Miedema TOC Page 335 of 454