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

The Delft Sand, Clay & Rock Cutting Model.
2 kmax
z 10
0
2
sin
vc
sin
(6-109)
The distance from the blade to the cavitation spot is considered to be constant over the blade. The magnitude of
this distance is however unknown.
Figure 6-49: The development of cavitation over the blade.
The relation between the dimensions of the cavitation spot, and the water pressure profile on the blade.
The progressive character of the cavitation spot development results from equation (6-109). If, at a certain cutting
velocity, cavitation occurs locally in the cavitation zone, then the resulting cavitation spot will always expand
immediately over a certain distance above the blade as a result of the fact that a certain time is needed to fill the
volume flow rate of the vapor bubbles. The development of the water sub-pressures will, in general, be influenced
by the ever in the pore water present dissolved air. As soon as water sub-pressures are developing as a result of the
increase in volume in the shear zone, part of the dissolved air will form air bubbles. Since these air bubbles are
compressible, a large part of the volume strain will be taken in by the expansion of the air bubbles, which results
in a less fast increase of the water sub-pressures with an increasing cutting velocity. The maxima of the water subpressures
will also be influenced by the present air bubbles. This can be illustrated with the following example:
Assume the sand contains 3 volume percent air, which takes up the full volume strain in the dilatancy zone. With
a volume strain of 16%, this implies that after expansion, the volume percentage air is 19%. Since it is a quick
process, it may be assumed that the expansion is adiabatic, which amounts to maximum water sub-pressures of
0.925 times the present hydrostatic pressure. In an isothermal process the maximum water sub-pressures are 0.842
times the present hydrostatic pressure. From this simple example it can be concluded that the, in the pore water
present (either dissolved or not) air, has to be taken into account. In the verification of the water sub-pressures,
measured during the cutting tests in the 105 m sand, the possibility of a presence of dissolved air is recognized
but it appeared to be impossible to quantify this influence. It is however possible that the maximum water subpressures
reached (Appendix M the pore pressure graphs) are limited by the in the pore water present dissolved
air.
Page 178 of 454 TOC Copyright © Dr.ir. S.A. Miedema