Geology Reference
In-Depth Information
Table 10.3
Key equations for calculating important rock mass geotechnical
properties. RMR is a variable in both Hoek-Brown parameters
m
and
s
and
can be calculated easily to obtain an estimate of the compressive and tensile
strength of a rock mass.
Property
Symbol
Expression
a
m
σ
3
σ
c
Hoek-Brown criterion
(biaxial strength)
σ
1
=
σ
3
+
σ
c
+
s
Hoek-Brown parameter
m
m
=
m
i
exp[
(
RMR
−
100
)/
28]
Hoek-Brown parameter
s
s
=
exp[
(
RMR
−
100
)/
9]
2
c
)
1
/
2
Rock mass compressive
strength
σ
cm
σ
cm
=
(sσ
σ
2
[
m
−
(m
2
1
/
2
]
Rock mass tensile
strength
σ
tm
σ
tm
=
+
4
s)
tan
−
1
4
cos
2
30
◦
+
2
1
−
1
2
1
3
h
−
sin
−
1
Instantaneous friction
angle
φ
i
φ
i
=
h
−
16
(mσ
n
+
s)
3
m
h
h
=
1
+
2
Mohr-Coulomb equation
τ
=
c
+
µσ
n
,µ
=
tan
φ
Instantaneous cohesion
(
σ
n
>
0)
c
i
c
i
=
τ
−
σ
n
tan
φ
c
c
=
τ
Cohesive strength
(
σ
n
=
0)
values can then be averaged to give one RMR value for that segment. Alterna-
tively, just the horizontal RMR might be sufficient. You make the call. RMR
values calculated using the steps outlined above and based on an averaged ver-
tical and horizontal RMR for a range of igneous rock types are summarised in
Table 10.4. Although the ages and tectonic settings of volcanic activity (Snow-
donia, UK and Tenerife, Canary Islands) differ markedly, it is clear that the
compressive strength (MPa) of each rock mass is considerably weaker than the
intact rock itself. The implication is that a volcanic edifice will be a much
weaker structure than the material comprising it, regardless of composition.
10.4.2 The geological strength index (GSI)
The GSI is a descriptive system similar to the RMR but regarded by many as
providing better strength estimates where the quality of the rock mass is poor
(for example, RMR
<
25). The GSI differs from the RMR in that it relies much
