332 Design of surface excavationsand N(0 < F < 1.5) = 19, giving Pr(0 < F < 1.0) = 7/32 = 0.22 and
Pr(0 < F < 1.5) = 19/32 = 0.59. Using the probabilistic criteria given by
Priest and Brown (1983) ', the slope can be regarded as unstable, despite
the mean factor of safety being 1.86.
Finally, in order to investigate the form of the distribution of factors
of safety more precisely, we must perform many more trials. For^10000
trials, the histogram looks like that shown below, and gives a mean factor
of safety of 2.19, with probabilistic assessments of Pr(0 < F < 1.0) = 0.29
and Pr(0 < F < 1.5) = 0.54. The distribution can be seen to be lognormal
in form, the mean factor of safety has increased, but the slope remains
unstable when judged against the probabilistic criteria.
0.12.- 5 0.062 0.04r 0
Q
Q0.020.00478.9 A proposed dam will exert a vertical force of 9400 kN/m and
a horizontal force of 4400 kN/m on its horizontal foundation, as
shown in the figure below. At a depth of 6 m below the founding
surface there is a horizontal bedding plane, the strength of which is
purely frictional with 4 = 32O. The unit weight of the rock above this
plane is 22 kN/m3.
For a polar co-ordinate system,
the origin of which coincides with
the rectangular co-ordinate system
as shown in the diagram, the com-
ponents of radial stress due to a
- vertical line load P and a hori-
zontal line load 4 may be calcu-
lated from a,(p) = (2PsinO)/xr and
ur(Q) = (24 cos O)/nr, respectively.
At what value of x-ordinate is the
radial stress on the bedding plane
'Priest S. D. and Brown E. T. (1983) Probabilistic stability analysis of variable rock
slopes. Trans. Inst. Min. Metall. 92, A1-12.