31 0 Design and analysis of surface excavations
/-. .. * **-. .\
/. ... .*._.. \
k': /
-9.. .. -*
... .. -.
. .b:. .. -.
. : f. .:.
..
.'. .. .. * *,:\. .. ..
*..
.L*: : .a/
Figure 18.1 Pole plot of discontinuities in the rock mass under consideration (case
example data from Matheson, 1983).They do not provide a numerical measure of the degree of safety of the slope,
but whether or not instability is feasible in the first instance. If the system is
kinematically infeasible, a great deal has been established rapidly.
The kinematic analysis of plane, wedge and toppling instabilities for rock
slopes is explained next-in which the instability is governed by the geom-
etry of the slope and discontinuities. The method follows that presented
by Hoek and Bray (1977), and refined by Matheson (1983) and Goodman
(1989). The examples presented in the text use a data set based on field
records, recorded by Matheson.
In Fig. 18.1, the lower-hemispherical projection of the poles to the
discontinuities in the rock mass is shown. The second Appendix covers the
basics of hemispherical projection. The initial impression is that there are
two main sets of sub-vertical discontinuities, one (set A) striking approxi-
mately E-W, another (set B) striking approximately N-S. There are four
minor sets, some (sets C, D and F) being sub-horizontal, one (set E) being
sub-vertical striking NW-SE.
If necessary, we can return to these data to consider the dispersion of
the poles within each set and the different strength parameters associated
with each set. Firstly, however, consider the kinematic feasibility associated
with constructing a proposed slope of dip direction 295" and dip angle 75",
assuming that all discontinuity sets follow a Mohr-Coulomb strength
criterion with $ = 30" and c = 0 Wa.7 8.7.7 Plane instability
To consider the kinematic feasibility of plane instability, four necessary but
simple criteria are introduced, as listed below.