Kinematic analysis of slope instabiliiy mechanisms 3 1 7From the pole plot of the discontinuities shown in Fig. 18.1, a basically
orthogonally fractured rock mass was indicated, with the result that the
intersections would be expected to be sub-vertical and sub-horizontal.
Thus, wedge instability problems are only likely to arise for steep slopes
or low angles of friction-as indicated in Fig. 18.5. Note, though, that an
essentially orthogonally fractured rock mass which has undergone a tilting
of only 30” or so will give rise to problems of wedge instability.
What are the implications of having a different friction angle on the two
discontinuity planes forming the wedge? Utilizing a ‘generalized friction
circle’, Goodman (1989) presents a method of analysing wedge instability
with different friction angles. He notes that “in view of the uncertainty
with which friction angles are assigned in practice, it is more useful to
express the degree of stability in terms of such a sensitivity study [referring
to his stereographic method] than to force it to respect the factor of
safety concept”. So, although using a different method, Goodman is also
of the opinion that an appreciation of the problem is more important
than a rigid adherence to the factor of safety concept, as stated at the end
of Section 18.1.1.7 8.7.3 Toppling instability
For the third mode of instability, toppling, both direct toppling and flexural
toppling as illustrated in Fig. 17.9, will be studied. The same overlay
technique that was presented for plane and wedge instability can be
used, except that there is the need to analyse intersections (defining the
edges of toppling blocks) and poles (defining the basal plane about which
toppling takes place). An overlay is required which makes use of both
pole and intersection plots, as a result of the feasibility criteria associated
with toppling. It is also important to note (with reference to Fig. 17.10)
that toppling instability is being considered in isolation. Plane and wedge
instability, which may or may not be occurring contemporaneously, can be
established from the instability analyses already presented.
Direct toppling instubdity. In the case of direct toppling instability, the
kinematic feasibility criteria will only relate to the geometry of the rock
mass, rather than the geometry plus the strength parameters-although
the latter can be used to establish the cut-off between toppling only and
sliding plus toppling illustrated in Fig. 17.10. Therefore, the only two criteria
required are as follows (see Fig. 17.2(d)).
(a) There are two sets of discontinuity planes whose intersections dip into
the slope, in order to provide the appropriate conditions for the forma-
tion of the faces of rock blocks.
(b) There is a set of discontinuity planes to form the bases of the toppling
blocks, so that, in association with criterion (a), complete rock blocks
may be formed.
Naturally, toppling is more likely if the basal planes dip out of the slope, but
such a condition is not necessary. If the dip of the basal planes is less than
the friction angle, then sliding will not occur in association with toppling.