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

Saturated Sand Cutting.
Figure 6-26: The force Fh as function
of the ratio between ki and kmax.
Figure 6-27: The reciprocal of the force Fh as
function of the ratio between
ki and kmax.
6.11. Determination of the Coefficients c1, c2, d1 and d2.
If only the influence of the water under-pressures on the forces that occur with the cutting of saturated packed sand
under water is taken in to account, equations (6-14) and (6-15) can be applied. It will be assumed that the noncavitating
process switches to the cavitating process for that cutting velocity vc, for which the force in the direction
of the cutting velocity Fh is equal for both processes. In reality, however, there is a transition region between both
processes, where locally cavitation starts in the shear zone. Although this transition region starts at about 65% of
the cutting velocity at which, theoretically, full cavitation takes place, it shows from the results of the cutting tests
that for the determination of the cutting forces the existence of a transition region can be neglected. In the simplified
equations the coefficients c1 and d1 represent the dimensionless horizontal force (or the force in the direction of
the cutting velocity) in the non-cavitating and the cavitating cutting process. The coefficients c2 and d2 represent
the dimensionless vertical force or the force perpendicular to the direction of the cutting velocity in the noncavitating
and the cavitating cutting process. For the non-cavitating cutting process:
F
ci
In which:
2
i w c i
c g v h w
(6-71)
k
m
sin( ) hb
sin( )
p1m
p2m
sin( )
sin( ) hi
sin( )
sin( )
a k a k
c1
kmax
h
b sin( )
p2m
hi
sin( )
And:
c
2
1 i 2 max
sin( ) hb
sin( )
p1m
p2m
cos( )
sin( ) hi
sin( )
sin( )
a k a k
kmax
h
b cos( )
p2m
hi
sin( )
1 i 2 max
(6-72)
(6-73)
Copyright © Dr.ir. S.A. Miedema TOC Page 149 of 454