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

7.5.4. The Resulting Cutting Forces.
Clay Cutting.
Substituting the mobilized shear strength cm and the mobilized ac ratio rm gives the horizontal and vertical forces
in the case of brittle failure, the Tear Type cutting mechanism:
F h w
h s T i
sin
sin
r
m
sin
sin
sin
rm
cos( ) sin( )
sin
(7-75)
s T hi w rT
r
HT
T
F h w
v s T i
cos
sin
r
m
cos
sin
sin
rm
cos( ) sin( )
sin
(7-76)
s T hi w rT
r
VT
T
The cutting forces are not dependent on the shear strength anymore, but completely dependent on the tensile
strength and the adhesion.
Figure 7-29, Figure 7-30, Figure 7-31 and Figure 7-32 show the shear angle β, the horizontal cutting force
coefficient λHT/rT, the vertical cutting force coefficient λVT/rT and the last one zoomed for the Tear Type of cutting
mechanism. The figures show that for large values of rT, the shear angle and the cutting force coefficients hardly
depend on the factor rT. It should be mentioned that the graphs show λHT/rT and λVT/rT and not λHT and λVT. A
large or very large value of rT means a very small tensile strength compared to the adhesion. Equations (8-112)
and (8-113) can be rewritten for the case of a very small relative tensile strength according to:
HT
a
hb
HT
h s T i T s T i
rT T
hi rT
HT
s a hb w r T
F h w r h w
VT b VT
v s T i T a h
s T i
r
T T
h
i rT
VT
s
a hb
w r T
F h w r h w
(7-77)
(7-78)
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