Engineering Rock Mechanics

Techniques for incorporating variations in rock and site 331

We believe that this probabilistic approach is fundamentally flawed:
the basic mechanics must be understood first and then any variations in any
properties, or any lack in our knowledge, dealt with via appropriate mathematical
techniques. Such techniques are still being developed and are extensive.
They range from the simple application of probability theory through to
the development of new systems utilizing cognitive processes and neural
networks.

18.4.1 Sensitivity unulysis

In Figs 17.6 and 17.8, the variation in the factor of safety is shown for plane
instability and wedge instability with the depth of water in a tension crack,
the angle of friction and the included wedge angle. In all of the examples,
as the factor of safety varied, it passed through unity-the interface
between stability and instability. Qualitative examination of the graphs in
these figures shows that, for certain ranges of the independent variables,
the factor of safety is more sensitive to these variations than for other ranges
(eg in Fig. 17.8 the range 10-20" for the included wedge angle). This
behaviour can be expressed quantitatively through a formal definition of
sensitivity, as follows:

sensitivity = ~ dF = slope of the factor of safety

p is any parameter involved in the analysis, and
p1 is the value of this parameter which produces a factor of safety
of unity (all other parameters remaining constant for this
analysis).
The use of a normalized parameter is a simple device whereby the curve
is scaled around the region of interest.

d(p/p,) vs normalized parameter curve

where

Normalised aperture, e/e(F=,)

0 I 2 3 4 5 6 7 8

0 I

-0.2

-0.4

-0.6

region are extremely sensitive to the aperture values

-1.2

-1.4

-1.6

y = 22kN/m3

\afety IS equal to I and factors of safety in this

.- region are extremely sensitive to the aperture values

.t: -0.8

I;m

Figure 18.15 Illustration of sensitivity analysis applied to plane sliding.