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

A Wedge in Atmospheric Rock Cutting.
The force K2 on the pseudo blade is now:
K
2
C1 cos( ) C2cos( )
sin( )
(14-8)
From equation (14-8) 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 K2sin( ) C2 cos( )
(14-9)
F K2 cos( ) C2
sin( )
(14-10)
The normal force on the shear plane is now:
C1 cos( ) C2 cos( )
N1
cos( )
sin( )
(14-11)
The normal force on the pseudo blade is now:
C1 cos( ) C2cos( )
N2
cos( )
sin( )
(14-12)
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 K sin K sin C
h 4 3 3
C cos K sin 0
2 2
(14-13)
The vertical equilibrium of forces on the wedge is:
F K cos K cos
v 4 3
C sin K cos 0
2 2
(14-14)
The unknowns in this equation are K3 and K4, since K2 has already been solved. Two other unknowns are, the
external friction angle δ, since the external friction does not have to be fully mobilized, and the wedge angle θ.
These 2 additional unknowns require 2 additional conditions in order to solve the problem. One additional
condition is the equilibrium of moments of the wedge, a second condition the principle of minimum required
cutting energy. Depending on whether the soil pushes upwards or downwards against the blade, the mobilization
factor is between -1 and +1.
The force K3 on the bottom of the wedge is now:
K
3
sin
K2sin C3 cos C2 cos
(14-15)
The force K4 on the blade is now:
K
4
sin
K2sin C3 cos C2 cos
(14-16)
This results in a horizontal force on the blade of:
Copyright © Dr.ir. S.A. Miedema TOC Page 387 of 454