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

The General Cutting Process.
2 2
N1
cos sin sin 1 sin
min
c cos
cos cos
N1
1
sin
c
cos
cos
(3-42)
Figure 3-13: The Mohr circles of the Tear Type.
Now ductile failure will occur if the minimum principal stress σmin is bigger than then tensile strength σT, thus:
(3-43)
min
T
If equation (3-43) is true, ductile failure will occur. Keep in mind however, that the tensile strength σT is a negative
number. Of course if the minimum normal stress min is positive, brittle tensile failure can never occur.
Substituting equation (3-39) for the normal stress on the shear plane gives the following condition for the Tear
Type:
sin cos
r cos sin
sin 1 sin
c
sin
cos
T
(3-44)
In clay it is assumed that the internal and external friction angles are zero, while in rock it is assumed that the
adhesion is zero. This will be explained in detail in the chapters on clay and rock cutting.
The ratios between the pore pressures and the cohesive shear strength, in the case of hyperbaric rock cutting, can
be found according to:
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