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

Rock Cutting: Atmospheric Conditions.
140
120
100
Shear Stress τ vs. Normal Stress σ
Sigma Axis
Tau Axis
Shear Stress τ (MPa)
80
60
40
20
0
-20
-40
-60
-80
-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.
For a given radius a this gives:
Normal Stress σ (MPa)
Figure 8-15 The Parabolic and Ellipsoid failure envelopes, with a=100·UCS.
Mohr Circle
UCS Test
Mohr Circle
UTS Test
Mohr Circle
BTS Test
Parabole
Mogi Criterion
Brittle Ductile
Failure Criterion
Pseudo-Ductile
Ellipse
Mogi Criterion
Brittle Ductile
Failure Criterion
Pseudo-Ductile
b
2
1
p
2
p
a
UTS
a
2
2
(8-33)
Figure 8-14 shows both the parabolic and the ellipsoid failure envelopes. The ellipsoid failure envelope is
determined for a=1.75·UCS. The Mohr circles for UTS, BTS and UCS are determined for UCS=100 MPa,
UTS=BTS=15 MPa. At low normal stresses the parabolic and ellipsoid failure envelopes behave almost identical.
Also the Mogi brittle-ductile transition points are very close. Chosing a>10·UCS gives about identical envelopes
in the normal stress range considered.
Copyright © Dr.ir. S.A. Miedema TOC Page 257 of 454