15.5 Probability of Failure of the Portfolio’s Dams
245
Table 15.10 External interdependencies
Dam 1 Dam 2
Dam 3 Dam 4 Alters the probability (and
consequences) of a failure of
0
n/a
n/a
n/a
Dam 1
n/a
0
n/a
Dam 2
n/a
Could trigger liquefaction or
instability of Dam 3
0
n/a
Dam 3
n/a
n/a
n/a
0
Dam 4
independent from the others, Sect. 4.2.3 and in particular Eq. 4.2 yield the
probability of failure as
p f(a,b,c) = 1 −
1 − p a
∗
1 − p b
∗
1 − p c
.
• If the pipeline breach goes undetected (for this dam for more than 12 h) and the
crest design is such that a spill towards the downstream face of the dam is not
hindered, for example by a berm, then the spill may start scouring the face and the
tailings will start filling the next berm surface.
• If more time goes by and still no detection occurs (for example by a patroller),
then scouring may start …
• which may then evolve into sloughing and erosional instabilities …
• which may then lead to a dam global instability.
Event Trees Analyses (ETAs) or Failure Tree Analyses (FTAs) may be prepared to
model this development. As stated in Sect. 8.3.1 these analyses require the evaluation
of elemental probabilities which can be based on Appendix A.
It is therefore evident that this type of approach becomes convergent, insofar
as risks from multiple hazard types (natural, man-made, technological, etc.) can
be evaluated simultaneously and yet be extracted by queries to study their specific
impacts on the risks of the portfolio, provided the hazard and risk register is designed
with this purpose in mind.
External interdependencies
Dams 1 and 4 have no significant internal or external interdependencies.
Dam 3 has internal interdependencies (progressive failure). The probability of
failure of Dam 3 would be altered by the failure of Dam 2 and the consequences of
a compound failure would be worse than the consequences of the failure of either
Dam 2 or Dam 3 alone.
Table 15.10 explains the interdependencies between different dams. For this case
study, where only one interdependency exists, it might seem overly complicated to
prepare such a table, however it is the only way to ensure completeness and concision.
The internal interdependencies can be noted in Table 15.10. As an example, the
internal interdependencies of Dam 3 are noted by inserting -1- in the cell on the
diagonal for Dam3-Dam3.
245
Table 15.10 External interdependencies
Dam 1 Dam 2
Dam 3 Dam 4 Alters the probability (and
consequences) of a failure of
0
n/a
n/a
n/a
Dam 1
n/a
0
n/a
Dam 2
n/a
Could trigger liquefaction or
instability of Dam 3
0
n/a
Dam 3
n/a
n/a
n/a
0
Dam 4
independent from the others, Sect. 4.2.3 and in particular Eq. 4.2 yield the
probability of failure as
p f(a,b,c) = 1 −
1 − p a
∗
1 − p b
∗
1 − p c
.
• If the pipeline breach goes undetected (for this dam for more than 12 h) and the
crest design is such that a spill towards the downstream face of the dam is not
hindered, for example by a berm, then the spill may start scouring the face and the
tailings will start filling the next berm surface.
• If more time goes by and still no detection occurs (for example by a patroller),
then scouring may start …
• which may then evolve into sloughing and erosional instabilities …
• which may then lead to a dam global instability.
Event Trees Analyses (ETAs) or Failure Tree Analyses (FTAs) may be prepared to
model this development. As stated in Sect. 8.3.1 these analyses require the evaluation
of elemental probabilities which can be based on Appendix A.
It is therefore evident that this type of approach becomes convergent, insofar
as risks from multiple hazard types (natural, man-made, technological, etc.) can
be evaluated simultaneously and yet be extracted by queries to study their specific
impacts on the risks of the portfolio, provided the hazard and risk register is designed
with this purpose in mind.
External interdependencies
Dams 1 and 4 have no significant internal or external interdependencies.
Dam 3 has internal interdependencies (progressive failure). The probability of
failure of Dam 3 would be altered by the failure of Dam 2 and the consequences of
a compound failure would be worse than the consequences of the failure of either
Dam 2 or Dam 3 alone.
Table 15.10 explains the interdependencies between different dams. For this case
study, where only one interdependency exists, it might seem overly complicated to
prepare such a table, however it is the only way to ensure completeness and concision.
The internal interdependencies can be noted in Table 15.10. As an example, the
internal interdependencies of Dam 3 are noted by inserting -1- in the cell on the
diagonal for Dam3-Dam3.