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

The Delft Sand, Clay & Rock Cutting Model.
W2 sin( ) W1 sin( )
N1
cos( )
sin( )
C cos( ) A cos
cos( )
sin( )
(9-10)
The normal force on the blade is now:
W2 sin( ) W1 sin( )
N2
cos( )
sin( )
C cos( )
A cos
cos( )
sin( )
(9-11)
The pore pressure forces can be determined in the case of full-cavitation or the case of no cavitation according to:
sin
sin
w g z 10 hi w p1m hi
w
W 1
or W 1
sin
w g z 10 hb w p2m hb
w
W 2
or W2
sin
(9-12)
(9-13)
The forces C and A are determined by the cohesive shear strength c and the adhesive shear strength a according
to:
c
h
C sin
i
w
a
hb
w
A sin
(9-14)
(9-15)
The ratio’s between the adhesive shear strength and the pore pressures with the cohesive shear strength can be
found according to:
a
h p h g z 10 h p h
r= , r = or r ,r =
ch ch ch ch
b 1m i
w
i 2m b
1 1
2
i i i i
w
g z 10 h
or r2
ch
i
b
(9-16)
Finally the horizontal and vertical cutting forces can be written as:
Fh HF chi w
(9-17)
F VF c hi
w
(9-18)
Figure 9-9, Figure 9-10 and Figure 9-11 show the horizontal and vertical cutting force coefficients and the shear
angle as a function of the ratio of the hydrostatic pressure to the shear strength of the rock rz for a 60 degree blade
and full cavitation. If this ratio equals 1, it means the hydrostatic pressure equals the shear strength. At small ratios
the resulting values approach atmospheric cutting of rock. Also at small ratios the shear angle approaches the
theoretical value for atmospheric cutting. Figure 9-12 shows the Esp/UCS ratio, which is very convenient for
production estimation.
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