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

8.2.5. Hoek & Brown (1988).
Rock Cutting: Atmospheric Conditions.
Over the years Hoek & Brown (1988) developed a failure criterion for rock, based on the UCS and BTS values of
the specific rock. The generalised criterion is empirical and yields:
min
a=0.5
max
min
UCS m s with for intact rock
UCS
s=1.0
a
(8-16)
The parameters m and s are material properties. The parameter m is related to the ratio of the UCS value to the
BTS value according to:
2 2
UCS BTS BTS UCS
m
for 1 m= (8-17)
UCS BTS UCS BTS
The parameter s is a measure for the amount of fractures in the rock and equals 1 for intact rock. The stresses σmin
and σmax are the minimum and maximum principal stresses of the Mohr circle considered. The BTS value can also
be represented as a function of m and s according to:
UCS
2
BTS m m 4 s
(8-18)
2
Based on:
max min max min
center
and max
(8-19)
2 2
An equation can be derived relating the maximum shear stress τmax (the top of the Mohr circle) to the normal stress
at the center of the Mohr circle σcenter.
1
max
m UCS m UCS 16 m UCS UCS
8
2 2
center
(8-20)
This equation results in a curve through the tops of the Mohr circles and is not yet a failure criterion. For the failure
criterion Hoek & Brown (1988) give the following method; First determine a variable h according to:
16
m s UCS
h 1
2
3
m UCS
(8-21)
Now an angle θ can be determined:
1 1
atan
3 2 3
h 1
(8-22)
Based on the angle θ the instantaneous internal friction angle can be determined, which is also the tangent to the
failure criterion:
atan
1
2
4hcos
1
(8-23)
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