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of tolerability used for new dams or major augmentations.* The computed life-loss risk after
the rehabilitation approaches this more severe limit.
ANCOLD also has an individual tolerable risk guideline of a probability of life loss of
1 × 10 −4 per year for the individual at most risk for existing dams (and 1 × 10 −5 for new dams
and major augmentations). The existing earth dam does not meet this guideline, but is esti-
mated to do so after the implementation of remedial measures.
The comparisons with the ANCOLD societal (F-N chart in Figure 11.8 ) and individual
tolerable risk guidelines should take into account additional considerations of satisfying
the ALARP (as low as reasonably practicable) principle, as explained by Bowles (2007).
Nevertheless, both the ANCOLD societal and individual tolerable risk guidelines support
proceeding with the proposed remedial measures at the earth dam presented in the example.
11.3 role oF FragIlItY CurVeS to eValuate the
unCertaIntY In ProbabIlItY eStIMateS
11.3.1 Concept of uncertainty
When failures of complex structures are analyzed, evaluation of uncertainty should play
an important role in the analysis of the behavior of a constructed facility. In general, two
sources of uncertainty should be considered (Hartford and Baecher, 2004; Hoffman and
Hammonds, 1994):
1. Natural uncertainty or randomness: Produced by the inherent variability in the natu-
ral processes. An example of this kind of uncertainty is the variability of the loads that
the structure has to withstand, for instance, the variability in the earthquake intensity
that can occur. Another example is the resistance's variability of the terrain where the
structure is settled. This type of uncertainty, sometimes also called aleatoric uncer-
tainty, cannot be reduced, though it can be estimated.
2. Epistemic uncertainty: Resulting from not having enough knowledge or information
about the analyzed system. This lack of information can be produced by deficiency of
data or because the structure's behavior is not correctly represented. The more knowl-
edge is available about a structure, the more this type of uncertainty can be reduced.
On the other hand, it is usually very difficult to estimate or quantify this uncertainty.
An example of this type of uncertainty can also be found in the resistance of the ter-
rain. The information about the foundations may be limited so the parameters used
to characterize its resistance are estimated from probing and exploration. With more
resources, the terrain can be better characterized and the epistemic uncertainty is
reduced, although the natural variability of the terrain may still be very significant.
The distinction between natural and epistemic uncertainty takes added importance for
a quantitative risk analysis in complex structures (Baraldi and Zio, 2008). In this context,
* From Bowles et al. (2003): According to the glossary in the draft ANCOLD (2001) guidelines, “major augmen-
tations of existing dams … refers to modification of an existing dam involving a relatively large expenditure and
creating a significant new benefit (typically, but not always, a major increase in volume of stored water), such that
the economic case for marginal risk reduction would be approaching that for a new dam.” McDonald (personal
communication, November 17, 2002), chair of the Working Group that prepared the ANCOLD (2003) draft
guidelines, states, “It is (a) subjective (guideline), since there are no clear boundaries that can be defined. Indeed,
the distinction we have made can be seen to low from the ALARP principle. If there is low marginal cost to build
in additional safety, then do it if significant risk remains.”
 
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