Civil Engineering Reference
In-Depth Information
left side of this equation equals 49
◦
, which is less
than the dip of the bedding (70
◦
-80
◦
). The poten-
tial for toppling is indicated by the poles to the
bedding planes lying inside the toppling envelope.
This preliminary analysis shows that the right
(east) cut slope has potential stability problems
and that more detailed investigation of struc-
tural geology conditions would be required before
finalizing the design. The first step in this invest-
igation would be to examine the spacing of the
bedding planes and determine if the center of
gravity of the slabs will lie outside the base, in
which case toppling is likely. Note that it is rarely
possible to change the alignment sufficiently to
overcome a stability problem, so it may be neces-
sary to either reduce the slope angle on the right
side, or stabilize the 76
◦
face.
blocks. Envelopes have been drawn for slope
face angles of 60
◦
and 80
◦
, which show that the
risk of instability increases as the slope becomes
steeper as indicated by the larger envelopes for
the steeper slope. Also, the envelopes become lar-
ger as the friction angle diminishes. The envelopes
also indicate that, for the simple gravity loading
condition, instability will only occur in a limited
range of geometric conditions.
2.6.6 Applications of kinematic analysis
The techniques demonstrated on Figures 2.16-
2.19 to identify both potentially unstable blocks
of rock on the slope and the type of instability
can readily be applied to the preliminary stages
of slope design. This is illustrated in the two
examples that follow.
Open pit slopes
: During the feasibility studies on
a proposed open pit mine, an estimate of the safe
slope is required for the calculation of ore-to-
waste ratios and the preliminary pit layout. The
only structural information that may be avail-
able at this stage is that which has been obtained
from diamond drill cores drilled for mineral eval-
uation purposes, and from the mapping of surface
outcrops. Scanty as this information is, it does
provide a basis for preliminary slope design.
A contour plan of the proposed open pit mine
is presented in Figure 2.21 and contoured ste-
reo plots of available structural data are super-
imposed on this plan. Two distinct structural
regions, denoted by A and B, have been identified
and the boundary between these regions has been
marked on the plan. For the sake of simplicity,
major faults have not been shown. However, it is
essential that any information on faults should be
included on large-scale plans of this sort and that
the potential stability problems associated with
these faults should be evaluated.
Overlaid on the stereonets are great circles rep-
resenting the orientations of the east and west pit
faces, assuming an overall slope angle of 45
◦
. Also
shown on the stereonets is a friction cone of 30
◦
,
which is assumed to be the average friction angles
of the discontinuity surfaces. The stereonets show
that the western and southern portions of the pit
Highway
: A proposed highway on a north-south
alignment passes through a ridge of rock in which
a through-cut is required to keep the highway
on grade (Figure 2.20(a)). Diamond drilling and
mapping shows that the geological conditions in
the ridge are consistent so that the same structure
will be exposed in each face. The predominant
geological structure is the bedding that strikes
north-south, parallel to the highway alignment
and dips to the east at angles of between 70
◦
and
80
◦
(i.e. dip and dip direction of 70-80/090).
The stereonets in Figure 2.20(b) show poles
representing the dip and dip direction of the
bedding, and great circles representing the orient-
ations of the left and right cut faces. Also plotted
on the stereonets is a friction cone representing
a friction angle of 35
◦
on the bedding. These
stereonets show that on the left (west) face, the
bedding dips towards the excavation at a steeper
angle than the friction angle so sliding can occur
on the bedding. The cut face has been made along
the bedding to create a stable face.
On the right (east) face the bedding dips steeply
into the face and there is a possibility that the
slabs formed by these joints will fail by toppling.
According to equation (2.3), toppling is possible
if (90
◦
−
φ
j
<ψ
p
. If the face is cut at 76
◦
(0.25V:1H) and the friction angle is 35
◦
, then the
ψ
f
)
+
