332 Design and analysis of surface excavations
In the example in Fig. 18.15, we show the sensitivity of the factor of safety
for plane sliding of a rock slope to the aperture of a discontinuity. The inset
sketch shows the geometry of the slope under consideration, together with
the material properties. All of the discontinuities are assumed to be full of
water, a drainage gallery is provided at E, and the block BCD is unstable
and may slide along BC. Using the techniques described in Sections 9.4
and 17.1.2, the hydraulic pressures in the discontinuity network can be
determined and thence the factor of safety against plane sliding found, in
this case, as a function of the aperture of BD. Note that in Fig. 18.15,
this aperture has been normalized, as described above, and it is the
sensitivity that has been plotted on the vertical axis and not the factor
of safety.
This illustrates that, for factors of safety around unity, the system is
sensitive to changes in aperture of discontinuity BD. For this illustration
we have taken a normalizing aperture related to a factor of safety of 1; any
other factor of safety could equally well have been taken and produced
similar curves to establish the different sensitivities under these other
conditions.
Sensitivity analysis is useful (not least, in the significance for site
investigation), but is not the most convenient method for either analysing
or communicating the effects of variation in, what could be, a large number
of relevant parameters. For this, one must turn to other techniques, as
described next.
78.4.2 Probabilistic methods
A traditional method of describing the many values a parameter may take
is through the use of probability theory. The key difference between the
deterministic and probabilistic approaches is that in the latter we do not
actually know, or even assume, a specific value for the parameter in8’
40 501 liil p:::b I 1~:, /I
30 0.6(^20) 0.4
N
10 0.2 /x
4x /x
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
tan 0 tan 0
Figure 18.16 Direct probabilistic approach, illustrated by sliding of a block on a
plane.