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

Rock Cutting: Atmospheric Conditions.
Figure 8-3: The Chip Type.
So in time it starts with a crushed zone, then a shear plane with possibly shear failure and than possibly tensile
failure. If the tensile strength is large, it is possible that only shear failure occurs. If the tensile strength is small, it
is possible that only tensile failure occurs. Crushing will start if locally a certain criterion is exceeded. Often the
Mogi (1966) criterion is applied, giving a certain ratio between the maximum principal stress and the minimum
principal stress. Ratio’s used are 3.4 for sandstone and 4.2 for limestone, while Verhoef (1997) found 6 for
limestone. Of course crushing does not start instantly, but gradually, based on the structure of the rock, especially
the distribution of the microcracks and the skeleton. With the hypothesis that crushing starts where the rock is the
weakest, one may assume that crushing starts at the scale of the microcracks, giving relatively large particles still
consisting of many grains. With increasing normal stress these particles will also be fragmented into smaller
particles. This process will go on until the smallest possible particles, the rock grains, result. Up to the Mogi (1966)
criterion intact rock is assumed, however some fracturing or crushing may already have taken place.
140
120
100
80
Shear Stress τ vs. Normal Stress σ
Sigma Axis
Tau Axis
Shear Stress τ (MPa)
60
40
20
0
-20
-40
-60
-80
Mohr Circle UCS
Test
Mohr Circle UTS
Test
Mohr Circle BTS
Test
Ellipse
-100
-120
-140
-50 -30 -10 10 30 50 70 90 110 130 150 170 190 210 230 250 270 290 310 330 350
© S.A.M.
Normal Stress σ (MPa)
Figure 8-4: Failure envelopre according to Verhoef (1997) (Figure 9.4) of intact rock.
Mogi Criterion
Brittle Ductile
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