298 Surface excavation instability mechanisms
and the limiting lines at an angle of qbj on either side of this normal, is
shown. By analysis of the geometry of this figure, the basic criterion for
inter-layer slip potential can be established.
Fig. 17.11@) shows that for inter-layer slip to take place, the geometry of
the system must be such that the triangle ABC will be formed: if the
orientation of the discontinuities relative to the slope surface is such that
AC and AB are parallel or diverging downwards, the conditions for inter-
layer slip will not be met. The inset diagram of Fig. 17.11(b) shows the
geometry of triangle ACD, from which it can be seen that a - 4 > 0. The
basic geometry of the system shows that a = y + - 90, with the result
by inspection that, for inter-layer slip to take place,
Using these angles, we can utilize a 'geometrical factor of safety' to provide
some indication of how close the slope conditions are to this criterion. If
the factor of safety is defined as that factor by which tan @must be divided
to bring the slope to limiting equilibrium,tan 4
tan(y + p - 90).F=As an example, if we require F = 1.3 when 4 = 30" and p = 70", then the
limiting angle for yis 44". For steeper slopes the factor of safety is reduced;
for shallower slopes it is increased.
This concludes the descriptions of the basic mechanics of rock slope insta-
bilities. In Section 17.2, foundation instability is discussed, this being the
other manifestation of surface excavation instability. The application of
these basic analyses to the design of surface excavations, with additional
techniques, is described in Chapter 18.17.2 Foundation instability
Instabilities in slopes are caused by alteration of the rock mass geometry,
whereas foundation instabilities are caused by the direct application of
load. In Fig. 17.12, this fundamental difference between the two
mechanisms is illustrated, with the distinction being reduced to one of
gravitational versus applied load instability. Also shown in Fig. 17.12 is the
fact that the foundation instability may result from the creation of new slip
surfaces or from movement on a pre-exisiting discontinuity. Since the load
is being applied by a structure, the rock-structure interaction has to be
considered. This is summarized in the flow chart in Fig. 17.13.17.2. I Equlibrium analysis of foundations
As an illustration of the equilibrium analysis approach to foundation insta-
bility, consider the plane two-dimensional case of a uniformly distributed
line load inducing instability. Two different approaches exist to the solution
of this problem: