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

Rock Cutting: Atmospheric Conditions.
2
max min max min
4 UTS
2 2
(8-37)
This can be written as a parabole for the center of the Mohr circles:
2
max
4UTS (8-38)
center
For a UCS test this gives:
2
UCS UCS UCS
4 UTS or 8
2
2 UTS
(8-39)
If the UCS/UTS or UCS/BTS ratio is larger than 8, brittle failure will occur.
The Griffith criterion as mentioned here is not the failure curve, but the curve connecting the tops of the Mohr
circles.
In the original articles tensile is positive and compression negative, resulting in a sign change compared with the
equations mentioned here. Als the minimum and maximum principal stresses were reversed.
8.2.10. Conclusions & Discussion.
6 concepts for the angle of internal friction and the failure criteria have been discussed. Figure 8-14 and Figure
8-17 show these criteria. To find the best failure criterion curve, many tests should be carried out at different
confining pressures, resulting in shear failure and a set of Mohr circles. Since this information is not always
available, The Hoek & Brown, Parabole or Ellipse approximations can be used. The preference of the author is the
Ellipse Envelope method or the Linear Failure Criterion method, where the internal friction angle is based on the
average of the Parabole Envelope method or measured by experiments.
Above the brittle-ductile transition normal stress, the failure curve will decrease according to Verhoef (1997),
based on research of van Kesteren (1995). As mentioned before, at higher stress situations there will be fracturing
and crushing. This results in a decrease of the angle of internal friction. The higher the normal stresses, the stronger
the fracturing and crushing, the smaller the angle of internal friction. When this starts there is a decrease of the
angle of internal friction, while the failure curve is still increasing. However at a certain stress situation the failure
curve may be at a maximum, since the angle of internal friction decreases to much. This maximum is often close
to the Mogi (1966) criterion. Since intact rock and crushed rock are two different materials with different
properties, one has to be very carefull with the interpretation of the resulting failure curve. In fact the material has
continuously changing properties from the moment is starts fracturing and crushing. First larger particles are
formed, consisting of many rock grains. When the stresses increase, these particles will also be fractured or
crushed, resulting in smaller particles, until the rock grains are left.
When the angle of internal friction decreases faster than the increase of normal stresses, the failure curve decreases.
This does however not mean that there is negative internal friction, normally the tangent to the failure curve. Just
that the angle of internal friction decreases faster than the increase of normal stresses and most probably that the
shear strength of the crushed rock decreases to zero. Verhoef (1997) and Vlasblom (2003-2007) show a failure
curve reducing to zero for very high normal stresses. This seems to be unlikely to happen. It would imply that at
very high normal stresses the shear stress equals zero, so no friction at al, which sounds like liquid behavior. It is
more likely that the crushed rock, once completely crushed, will have a residual internal friction angle and possibly
a residual shear strength. The latter is possible, for example when the particles are so small that van der Waals
forces start playing a role. But this will depend completely on the type and composition of the rock.
Figure 8-14 shows a residual internal friction angle for both the ellipse and the parabole, tangent to the failure
envelopes at the Mogi brittle-criterion.
For the models derived in this chapter, a constant internal friction angle is assumed, where this constant
internal friction angle should match the stress state of the cutting process considered.
Copyright © Dr.ir. S.A. Miedema TOC Page 259 of 454