Civil Engineering Reference
In-Depth Information
an upper bound value and may give optimistic
results in stability calculations. Consequently,
an average value, determined by fitting a lin-
ear Mohr-Coulomb relationship by least squares
methods, may be more appropriate. In the 1994
paper, Hoek also introduced the concept of the
Generalized Hoek-Brown criterion in which the
shape of the principal stress plot or the Mohr
envelope could be adjusted by means of a vari-
able coefficient
a
in place of the 0.5 power term
in equation (4.13).
Hoek and Brown (1997) attempted to consol-
idate all the previous enhancements into a com-
prehensive presentation of the failure criterion
and they gave a number of worked examples to
illustrate its practical application.
In addition to the changes in the equations,
it was also recognized that the Rock Mass Rat-
ing of Bieniawski was no longer adequate as a
vehicle for relating the failure criterion to geo-
logical observations in the field, particularly for
very weak rock masses. This resulted in the intro-
duction of the Geological Strength Index (GSI)
by Hoek
et al
. (1992), Hoek (1994) and Hoek,
Kaiser and Bawden (1995). This index was sub-
sequently extended for weak rock masses in a
series of papers by Hoek
et al
. (1998), Marinos
and Hoek (2000, 2001) and Hoek and Marinos
(2000).
The GSI provides a system for estimating the
reduction in rock mass strength for different geo-
logical conditions. Values of GSI are related to
both the degree of fracturing and the condi-
tion of fracture surfaces, as shown in Tables 4.3
and 4.4 respectively for blocky rock masses and
schistose metamorphic rock masses. The strength
of a jointed rock mass depends on the properties
of the intact rock pieces, as well as the free-
dom of the rock pieces to slide and rotate under
different stress conditions. This freedom is con-
trolled by the geometrical shape of the intact rock
pieces and the condition of the surfaces separat-
ing the pieces. Angular rock pieces with clean,
rough surfaces will result in a much stronger
rock mass than one that contains rounded
particles surrounded by weathered and altered
material.
The description of the Hoek-Brown strength
criterion in this section includes all the data in
this work up to 2002.
4.5.1 Generalized Hoek-Brown strength
criterion
The generalized Hoek-Brown strength criterion
is expressed in terms of the major and
minor principal stresses, and is modified from
equation (4.13) as follows (Figure 4.22)
σ
ci
m
b
s
a
σ
3
σ
1
=
σ
3
+
σ
ci
+
(4.14)
where
m
b
is a reduced value of the material
constant
m
i
for intact rock and is given by
m
i
exp
GSI
−
100
m
b
=
(4.15)
28
−
14
D
Table 4.5 gives values of
m
i
for a wide variety of
rock types, and
s
and
a
are constants for the rock
mass given by
exp
GSI
−
100
s
=
(4.16)
9
−
3
D
1
2
+
1
6
(
e
−
GSI
/
15
e
−
20
/
3
)
a
=
−
(4.17)
D
is a factor that depends upon the degree of
disturbance to which the rock mass has been sub-
jected by blast damage and stress relaxation. It
varies from 0 for undisturbed
in situ
rock masses
to 1 for very disturbed rock masses; guidelines
for the selection of appropriate values for
D
are
discussed in Section 4.5.6.
The uniaxial compressive strength of the rock
mass is obtained by setting
σ
3
=
0 in equa-
tion (4.14), giving
s
a
σ
c
=
σ
ci
·
(4.18)
and, the tensile strength is
sσ
ci
m
b
σ
t
=−
(4.19)
