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

8.2.4. Based on BTS and UCS.
The Delft Sand, Clay & Rock Cutting Model.
Here a linear envelope tangent to the BTS and the UCS Mohr circles is assumed, based on the assumption that the
failure curve always has to be tangent to at least two Mohr Coulomb circles. This gives for the principal stresses:
min,1
BTS
3
BTS
max,1
min,2
0
(8-15)
max,2
UCS
UCS 3 BTS UCS 3
BTS UCS
r 3 m
3
0 BTS BTS BTS
This method results in a rather high value for the internal friction angle and consequently a rather low value for
the shear strength (cohesion), although the internal friction angle will be lower than from the first method. To find
a good estimate for the internal friction angle, there should be two Mohr circles based on shear failure. In this case
one circle is based on shear failure, but the other circle is based on tensile failure. So this method is rejected.
Figure 8-10 shows the Mohr circles for UTS, BTS and UCS for UCS=100 MPa, UTS=BTS=15 MPa. The
resulting angle of internal friction φ=34.8º. The transition brittle-ductile according to Mogi (1966) is at a normal
stress of 316 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 8-10: Construction of the angle of internal friction BTS-UCS based.
Mohr Circle
UTS Test
Mohr Circle
BTS Test
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