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

The Occurrence of a Wedge.
19. A force normal to the blade N4, resulting from the effective grain stresses.
20. A shear force S4 as a result of the soil/steel friction N4·tan(.
21. 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.
22. A force W4 as a result of water under pressure on the blade.
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
(10-4)
The horizontal equilibrium of forces on the layer cut:
F K sin( ) W sin( ) C cos( ) I cos( )
h 1 1 1
C cos( ) W sin( ) K sin( ) 0
2 2 2
(10-5)
The vertical equilibrium of forces on the layer cut:
F K cos( ) W cos( ) C sin( ) I sin( )
v 1 1 1
G C sin( ) W cos( ) K cos( ) 0
1 2 2 2
(10-6)
The force K1 on the shear plane is now:
K
1
W2 sin( ) W1 sin( ) G1 sin( ) I cos( )
sin( )
C1 cos( ) C2 cos( )
sin( )
(10-7)
The force K2 on the pseudo blade is now:
K
2
W2 sin( ) W1 sin( ) G1 sin( ) I cos( )
sin( )
C1 cos( ) C2 cos( )
sin( )
(10-8)
From equation (10-8) 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 W2 sin( ) K2sin( ) C2cos( )
(10-9)
F W2 cos( ) K2 cos( ) C2
sin( )
(10-10)
The normal force on the shear plane is now:
W2 sin( ) W1 sin( ) G1 sin( )
N1
cos( )
sin( )
sin( )
I cos( ) C1 cos( ) C2
cos( ) cos( )
(10-11)
Copyright © Dr.ir. S.A. Miedema TOC Page 327 of 454