3 1 4 Design and analysis of surface excavations
a variation of plane instability, in that the sliding takes place on two
discontinuity surfaces, as shown in Figs 17.2(c) and 17.3(c). The resultant
sliding direction is assumed to be in a direction common to both surfaces,
i.e. along their line of intersection.
To consider the kinematic feasibility of wedge instability, we therefore
need to consider only three criteria relating to the line of intersection, as
listed below. The plane instability criterion relating to the 220" variation
in sliding direction is no longer required, as the sliding direction is uniquely
defined by the line of intersection.
(a) The dip of the slope must exceed the dip of the line of intersection of
the two discontinuity planes associated with the potentially unstable
wedge in order that the appropriate conditions for the formation of
discrete rock wedges exist, in a similar fashion to criterion (a) of plane
instability.
(b) The line of intersection of the two discontinuity planes associated with
the potentially unstable wedge must daylight on the slope plane. This
is necessary for a discrete rock wedge formed by the first criterion to be
capable of movement.
(c) The dip of the line of intersection of the two discontinuity planes
associated with the potentially unstable wedge must be such that the
strengths of the two planes are reached. In the case of friction-only
planes, each possessing the same angle of friction, the dip of the line of
intersection must exceed the angle of friction.In an analogous fashion to the analysis of plane instability, in Figs 18.4(a)
and (b), the generation of the hemispherical projection instability overlays
based on the criteria above is shown.
The radial solid line at the right but pointing to the left is taken to be the
slope direction. (Note that, as before, if the perimeter of the projection
represented the plan of a circular projection, then the location of the crest of a slope
dipping in this direction would be on the right-hand side of the perimeter.)
Ilowever, because we are analysing lines of intersection, this overlay is to
be used with intersection plots and consequently the construction to locate
the region of instability will be on the same side of the projection as the
slope dip.
Thus, criterion (a) is implemented using the series of great circles
(because the slope is a plane, and planes are plotted as great circles) and
criterion (c) is implemented by the series of concentric circles (because lines
of equal dip form a concentric circle). Because this is a direct plot of dips
and dip directions, the dips of the slope and the line of intersection are
numbered towards the centre of the overlay. Because intersection plots are being
used, the region of instability on the overlay is on the same side as the
considered dip direction of the slope.
Note the large size of the region of instability developed on the projec-
tion-often covering a range of dip directions as large as 150". This
means that attempting to vary the slope orientation as a means of
reducing instability is not likely to be as effective as in the case of plane
instability.