Kinematic analysis of slope instability mechanisms 3 1 1(a) The dip of the slope must exceed the dip of the potential slip plane
in order that the appropriate conditions for the formation of discrete
rock blocks exist.
(b) The potential slip plane must daylight on the slope plane. This is
necessary for a discrete rock block formed by criterion (a) to be capable
of movement.
(c) The dip of the potential slip plane must be such that the strength of
the plane is reached. In the case of a friction-only plane, this means that
the dip of the plane must exceed the angle of friction.
(d) The dip direction of the sliding plane should lie within approximately
220" of the dip direction of the slope. This is an empirical criterion and
results from the observation that plane slides tend to occur when the
released blocks slide more-or-less directly out of the face, rather than
very obliquely.
In Figs 18.2(a) and (b), the generation of hemispherical projection insta-
bility overlays based on the criteria above is shown. These will be used over
a plot such as Fig. 18.1. There can be uncertainty about the directions on
these overlays, and so it is important to understand the location of a slope
in plan and the associated directions of the slope in these overlays, together
with the lunematic criteria.
Each family of lines or curves in the overlay of Fig. 18.2(a) represents one
of the criteria listed above. The radial solid line pointing to the left is taken
to be the slope direction. (Note that if the perimeter of the projection represented
the plan of a circular projection, then the location on the crest of a slope dipping
in this direction would be diametrically opposite, i.e. on the right-hand side of the
perimeter). The two radial dashed lines to the right represent criterion (d),
and serve to concentrate the search for instability within a region k20" of
the slope direction. Note that this overlay is to be used with pole plots.
Therefore, concentric circular arcs within the sector-which represent
criteria (a)-(c), the dips of the slope and the potential plane of sliding-are
tiumbered away from the centre uf the overlay and so provide the remaining
bounding lines of the region of instability.
Figure 18.2(b) shows the completed specific overlay for a slope dip of
75" and an angle of friction of 30". The innermost bounding arc is the
friction angle (criterion (c)) and the outermost bounding arc is the slope
angle (criterion (a)). Because pole plots are being used, the region of
instability on the overlay is on the opposite side to the dip direction of the
slope.
The final step in assessing the kinematic feasibility for plane instability
is to superimpose the specific overlay (in this case Fig. 18.2(b)) onto the
projection representirlg the rock mass discontinuity data (in this case
Fig. 18.1). The result for this example is shown in Fig. 18.3.
The advantage of the overlay technique is immediately apparent. We can
say directly that there is a severe potential for plane instability associated
with discontinuity set B. Plane instability cannot occur on any other
discontinuity set. The exact value of the innermost bound of the instability
region, i.e. the friction angle, is not critical in the analysis-any variation
between, say, 30" and 50" will not prevent instability. The dip of the slope