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

Rock Cutting: Atmospheric Conditions.
The force K1 on the shear plane is now:
K
1
Ccos( )
sin( )
(8-100)
The force K2 on the blade is now:
K
2
Ccos( )
sin( )
(8-101)
Figure 8-28: The forces on the layer cut in rock
(atmospheric).
Figure 8-29: The forces on the blade in rock
(atmospheric).
The force C due to the cohesive shear strength c is equal to:
s ch
C
sin
i
w
(8-102)
The factor λs in equation (8-102) is the velocity strengthening factor, which causes an increase of the cohesive
shear strength. In clay (Miedema (1992) and (2010)) this factor has a value of about 2 under normal cutting
conditions. In rock the strengthening effect is not reported, so a value of 1 should be used. From equation (8-101)
the forces on the blade can be derived. On the blade a force component in the direction of cutting velocity Fh and
a force perpendicular to this direction Fv can be distinguished.
Fh K2sin( )
(8-103)
F K2
cos( )
(8-104)
Substituting equations (8-102) and (8-101) gives the following equations for the horizontal Fh and vertical Fv
cutting forces. It should be remarked that the strengthening factor λs in rock is usually 1.
s c hi
w cos( ) sin( )
Fh
sin sin( )
F
s c hi
w cos( ) cos( )
sin sin( )
(8-105)
(8-106)
Copyright © Dr.ir. S.A. Miedema TOC Page 275 of 454