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high standard deviation (0.5) also has the greatest probability of failure (shown by the area
under the curve less than 1). The case with the lower factor of safety has a lower probability
of failure. This is due to the standard deviation being much smaller for the lower factor of
safety which could demonstrate less variability in the embankment. This shows that it is
important to adopt a reliability index or probability of failure design standard rather than
achieving a certain factor of safety alone.
Figure 8.6: Comparison of two situations with different means and distributions of factor of safety (Christian, Ladd,
Baecher, 1994)
Acceptable probabilities of failure
One of the factors attributing to the reluctance in probabilistic methods of analysis is the lack
of published acceptable probabilities of failure. Whitman (2000) describes the use of
probabilistic methods and quantifying risks in decision making is limited by standards for
acceptable risks. Similarly to setting a standard factor of safety, there are many factors
affecting the stability which are not included in either a probabilistic or deterministic analysis
(for example, severe weather conditions, mining company financial issues, etc.) which make
it difficult to set standard design values. Davies (2002) states that there are “…no two sites
that have identical foundation, tectonic, hydrogeological, tailings characteristics, operating
criteria, etc.”. He refers to the following axiom: “…tailings impoundments are not
automobiles and cannot be mass produced…”. Each embankment is ultimately different, they
vary in location, construction techniques, soil properties, type of tailings, governing