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

Saturated Sand Cutting.
The dimensionless measured water sub-pressures of the non-cavitating cutting process are presented in Appendix
M, in which the solid line represents the theoretical distribution. The dimensionless measured water sub-pressures
in the transition region are also presented in Appendix M. The figures in Appendix M show the measured
horizontal forces Fh, in which the solid line represents the theoretical distribution. Other figures show the measured
vertical forces Fv, in which the solid line represents the theoretical distribution. Also shown in is the distribution
of the forces, for several water depths, during a fully cavitating cutting process (the almost horizontal lines). From
this research the following conclusions can be drawn:
1. The tests with the 30 blade give a good correlation with the theory, both for the forces as for the water subpressures.
For the 45 blade both the forces and the water sub-pressures are lower than the theoretical
calculated values with even larger deviations for the 60 blade. For the 60 blade the forces and the water subpressures
values are approximately 60% of the calculated values.
2. The direction of the cutting forces agrees reasonably well with the theory for all blade angles, after correction
for the gravity and the inertia forces.
3. The figures in Appendix M show that the profile of the water sub-pressures on the blade, clearly changes
shape when the peak stress close to the blade tip (sub-pressure) has a value of approximately 65% of the
absolute pressure. An increase of the cutting velocity results in a more flattening profile, with a translation of
the peak to the middle of the blade. No cavitation is observed but rather an asymptotic approach of the
cavitation pressure with an increasing cutting velocity. For the 60 blade the flattening only appears near the
blade tip. This can be explained with the large blade-height / layer-thickness ratio. This also explains the low
cutting forces in the range where cavitation is expected. There is some cavitation but only locally in the shear
zone; the process is not yet fully cavitated.
4. Since, according to the theory, the highest sub-pressures will appear in the shear zone, cavitation will appear
there first. The theoretical ratio between the highest sub-pressure in the shear zone and the highest sub-pressure
on the blade is approximately 1.6, which is in accordance with conclusion 3. Obviously there is cavitation in
the shear zone in these tests, during which the cavitation spot expands to above the blade and higher above
the blade with higher cutting velocities.
In Appendix M the pore pressure graphs show this relation between the cavitation spot and the water pressures
profile on the blade. The water sub-pressures will become smaller where the cavitation spot ends. This also implies
that the measurements give an impression of the size of the cavitation spot.
As soon as cavitation occurs locally in the sand package, it becomes difficult to determine the dimensionless
coefficients c1 and c2 or d1 and d2. This is difficult because the cutting process in the transition region varies
between a cavitating and a non-cavitating cutting process. The ratio between the average water pressure in the
shear zone and the average water pressure on the blade surface changes continuously with an increasing cutting
velocity. On top of that the shape and the size of the area where cavitation occurs are unknown. However, to get
an impression of the cutting process in the transition region, a number of simplifications regarding the water flow
through the pores are carried out.
1. The flow from the free sand surface to the shear zone takes place along circular flow lines (see equations
(6-37) and (6-38)), both through the packed sand as through the cut sand. With this assumption the distance
from the free sand surface to the cavitation area can be determined, according:
z 10 kmax
ki
0
sin
vc
sin
(6-107)
2. The flow in the cut sand is perpendicular to the free sand surface, from the breakpoint where the shear plane
reaches the free sand surface. This flow fills the water vapor bubbles with water. The distance from the free
sand surface to the cavitating area can now be determined, under the assumption that the volume flow rate of
the vapor bubbles equals the volume flow rate of the dilatancy, according:
c
sin
kmax
z 10 sin
d v d
(6-108)
3. In which the right term represents the volume flow rate of the vapor bubbles from the dilatancy zone, while
the left term represents the supply of water from the free sand surface. This is shown in Appendix M the pore
pressure graphs. With the initial value from equation (6-107) the following solution can be found:
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