Civil Engineering Reference
In-Depth Information
=15
°
=25
°
=35
°
=45
°
Convex slopes
Concave slopes
-10
-8
-6
-4
-2
0
2
4
6
8
10
Slope height/radius of curvature
Figure 10.1
Results of FLAC axisymmetric analyses showing effect on factor of safety of slope curvature.
the axis of revolution and the toe of the slope.
For the convex slopes, the radius of curvature is
defined as the distance between the axis of revolu-
tion and the crest of the slope—not the toe. Under
both definitions, cones have a radius of curvature
of zero.
Figure 10.1 shows the results with
FS
/
FS
plane strain
versus height/radius of curvature
(H/R
c
)
, which is positive for concave and negat-
ive for convex slopes. The figure shows that the
factor of safety always increases as the radius of
curvature decreases, but the increase is faster for
concave slopes. One unexpected result is that as
the friction angle increases, the effect of curvature
decreases. One possible explanation is that as
Janbu's lambda coefficient
(λ
beneficial effects of slope curvature should not be
ignored—particularly in open pit mines, where
the economic benefits of steepening slopes can be
significant. The same is true for convex slopes,
which are also more stable than plane strain
slopes. This goes against observed experience
in rock slopes. If the slide surface is defined
in terms of active (top) and passive (bottom)
wedges, the ratio of the surface (and weight)
of the passive wedge to the active wedge in a
convex slope is greater than the plane strain
condition. However, this only applies to a homo-
geneous Mohr-Coulomb material that might
be found, for example, in waste dumps. The
reason why “noses” in rock slopes are usu-
ally less stable may be related to the fact that
they are more exposed to structurally controlled
failures.
γH
tan
φ/c)
increases, the slide surface is shallower with only
a skin for purely frictional material. This, makes
the slope less sensitive to the confining effect in
concave slopes, and to the ratio of active/passive
wedges for the convex ones.
One reason that designers are reluctant to
take advantage of the beneficial effects of con-
cave slope curvature is that the presence of
discontinuities can often negate the effects.
However, for massive rock slopes, or slopes
with relatively short joint trace lengths,
=
10.3.2 Continuum versus discontinuum
models
The next step is to decide whether to use a
continuum code or a discontinuum code. This
decision is seldom straightforward. There appear
to be no ready-made rules for determining which
type of analysis to perform. All slope stability
the
