15.5 Probability of Failure of the Portfolio’s Dams
239
Table 15.7 (continued)
III
Average
Maintenance
limited to
emergency
repairs
0.6
0.6
0.6
0.6
0.6
IV
Poor
No field
investigation
No
laboratory
tests on
samples
obtained at
the site
Approximate
analyses
using
assumed
parameters
No
construction
supervision
by
qualified
engineer
Occasional
inspection
No
construction
on control
tests
No field
measurements
0
0
0
0
0
15.5.5 Categories, FoS and Probabilities of Failure
of the Dams
Using the Categories from both the SLM method and ORE2_Tailings together with
the results (Table 15.4) of the engineers’ stability analyses for the various dams of
the portfolio, Table 15.9 can be built, using the curves of Fig. 11.1. Values are cut at
credibility threshold of one in a million or 10
−6 (see Sect. 7.3).
As can be seen from Table 15.9, short boreholes (Dams 1A and 1B) deliver
higher probabilities of failure to a dam that is overall well-designed, built, maintained
and managed under constant FoS. Needless to point out that this corresponds to
observations in various recent catastrophic failures. The same occurs (Dam 3) if
liquefaction is suspected, again in compliance with recent observations.
Also, from Table 15.9 it is easy to see that the difference between “optimistic”
and “pessimistic” category classifications delivers probabilities of failure which lie
within one order of magnitude or less. That variation is compatible with extant
uncertainty about the performance of the world-wide portfolio over the last hundred
years, leading to the conclusion that the portfolio prioritization does not require
systematic optimistic/pessimistic range evaluation but, more importantly, requires
consistency in the evaluation for each single item.
For Dam 4, Sect. 11.1.2 reported a probability of failure between 6 and 13%
based on the sole analysis of Eq. 11.4 and some simple considerations related to the
empirical distribution of the FoS. The p f evaluations in Table 15.9 yield higher values
(19–38%) because they take into account all the uncertainties, lack of monitoring,
repairs and maintenance surrounding this dam, and in particular the uncertainties on
the geotechnical investigations that are not at all included in the FoS determination.
A careful reader will see from Table 15.9 that, generally speaking, the SLM
method and ORE2_Tailings deliver similar values of the categories for the portfolio’s
239
Table 15.7 (continued)
III
Average
Maintenance
limited to
emergency
repairs
0.6
0.6
0.6
0.6
0.6
IV
Poor
No field
investigation
No
laboratory
tests on
samples
obtained at
the site
Approximate
analyses
using
assumed
parameters
No
construction
supervision
by
qualified
engineer
Occasional
inspection
No
construction
on control
tests
No field
measurements
0
0
0
0
0
15.5.5 Categories, FoS and Probabilities of Failure
of the Dams
Using the Categories from both the SLM method and ORE2_Tailings together with
the results (Table 15.4) of the engineers’ stability analyses for the various dams of
the portfolio, Table 15.9 can be built, using the curves of Fig. 11.1. Values are cut at
credibility threshold of one in a million or 10
−6 (see Sect. 7.3).
As can be seen from Table 15.9, short boreholes (Dams 1A and 1B) deliver
higher probabilities of failure to a dam that is overall well-designed, built, maintained
and managed under constant FoS. Needless to point out that this corresponds to
observations in various recent catastrophic failures. The same occurs (Dam 3) if
liquefaction is suspected, again in compliance with recent observations.
Also, from Table 15.9 it is easy to see that the difference between “optimistic”
and “pessimistic” category classifications delivers probabilities of failure which lie
within one order of magnitude or less. That variation is compatible with extant
uncertainty about the performance of the world-wide portfolio over the last hundred
years, leading to the conclusion that the portfolio prioritization does not require
systematic optimistic/pessimistic range evaluation but, more importantly, requires
consistency in the evaluation for each single item.
For Dam 4, Sect. 11.1.2 reported a probability of failure between 6 and 13%
based on the sole analysis of Eq. 11.4 and some simple considerations related to the
empirical distribution of the FoS. The p f evaluations in Table 15.9 yield higher values
(19–38%) because they take into account all the uncertainties, lack of monitoring,
repairs and maintenance surrounding this dam, and in particular the uncertainties on
the geotechnical investigations that are not at all included in the FoS determination.
A careful reader will see from Table 15.9 that, generally speaking, the SLM
method and ORE2_Tailings deliver similar values of the categories for the portfolio’s