Civil Engineering Reference
In-Depth Information
150
2.0
Fully drained slope
Range of strength values
for slope failure
1.8
1.6
100
1.4
1.2
50
1.0
0.8
0.6
0
10
20
30
Saturated slope
Friction angle,
°
0.4
0.2
Figure 4.19
Shear strength mobilized on bedding
plane for slope failure shown in Figure 4.18.
20
30
40
50
60
70
80
90
Face angle,
f
(degrees)
the limestone was fine-grained and the bedding
planes smooth, it was estimated that the friction
angle was in the range of 15-25
◦
. The next step
was to carry out a number of stability analyses
with a range of cohesion values and a factor of
safety of 1.0. The results of this analysis show
that, at a friction angle of 20
◦
the correspond-
ing cohesion value is about 110 kPa, and that
for higher friction angles the required cohesion
is reduced (Figure 4.19).
The shear strength values calculated in this
manner can be used to design slopes excavated
in this limestone, provided that careful blasting
is used to maintain the cohesion on the bed-
ding planes. Figure 4.20 shows the relationship
between the factor of safety and the face angle
for a 64 m high cut, assuming plane failure on a
bedding plane dipping at 20
◦
out of the face. If
the slope is drained, the shear strength is sufficient
for the face to stand vertically, but if the slope is
saturated, the steepest stable slope is about 50
◦
.
In many cases it may not be feasible to carry
out a back analysis of a slope in similar geolo-
gical conditions to that in which the new slope
is to be excavated. In these circumstances, pub-
lished results of rock mass shear strength can be
used in design. Figure 4.21 shows the results of
back analyses of slope failures in a variety of geo-
logical conditions (as described in Table 4.2), and
the shear strength parameters (
φ/c
values) calcu-
lated at failure. By adding additional points to
Figure 4.20
Relationship between factor of safety and
face angle of dry and saturated slope for slope shown
in Figure 4.18.
Figure 4.21 for local geological conditions, it is
possible to draw up a readily applicable rock mass
strength chart for shear failures. Point 6 is for the
slope shown in Figure 4.18.
4.5 Hoek-Brown strength criterion for
fractured rock masses
As an alternative to back analysis to determine the
strength of fractured rock masses, an empirical
method has been developed by Hoek and Brown
(1980a,b) in which the shear strength is repres-
ented as a curved Mohr envelope. This strength
criterion was derived from the Griffith crack the-
ory of fracture in brittle rock (Hoek, 1968), as
well as from observations of the behavior of rock
masses in the laboratory and the field (Marsal,
1967, 1973; Brown, 1970; Jaeger, 1970).
Hoek and Brown introduced their failure cri-
terion to provide input data for the analyses
required for the design of underground excav-
ations in hard rock. The criterion started from
the properties of intact rock, and then intro-
duced factors to reduce these properties based on
the characteristics of joints in a rock mass. The
