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

8.2.8. Linear Failure Criterion.
The Delft Sand, Clay & Rock Cutting Model.
The best way to determine the angle of internal friction is to execute at least two tests with different confining
pressures in the range of normal stresses the cutting process is expected to operate. Figure 8-16 shows this for a
φ=20º internal friction angle. The Mohr circles for UTS, BTS and UCS are determined for UCS=100 MPa,
UTS=BTS=15 MPa. The transition brittle-ductile according to Mogi (1966) is at a normal stress of 95 MPa.
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
Tensile Failure
Criterion
Shear Failure
Criterion
Mogi Criterion
Brittle Ductile
Mohr Circle
UCS Test
-80
-100
-120
-140
-100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
Normal Stress σ (MPa)
© S.A.M.
Figure 8-16: The linear failure criterion.
Mohr Circle
UTS Test
Mohr Circle
BTS Test
8.2.9. The Griffith (Fairhurst, 1964) Criterion.
Griffith (Fairhurst, 1964) has derived a criterion for brittle failure. His hypothesis aasumes that fracture occurs by
rapid extension of sub-microscopic. Pre-existing flaws, randomly distributed throughout the material. He defined
two criteria. The first criterion is:
3 0
min
max
3 UTS 0 or 3
UTS
max
max
(8-34)
3 BTS 0 or 3
BTS
max
max
Failure will occur when σmin=-UTS or σmin=-BTS, which is satisfied in the Brazilian split test. However when:
3 0
min
max
(8-35)
Failure will occur when:
2
8UTS 0
(8-36)
With:
max min max min
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