15.7 Portfolio Risk Assessment and Benchmarking
249
C min = (PL + (HS ∗ 2.5) + ED)
(15.1)
C max = (PL + (HS ∗ 2.5) + ED) ∗ RD
(15.2)
Table 15.12 displays, for each dam and for the scenario of Dam 2 interdependent
on Dam 3, the risk evaluation for various cases of p f (ESA) and C min and C max . The
italic rows correspond to the lower estimates of the p f (ESA). In other words, the
italic rows correspond to the optimistic category classification of Table 15.9, whereas
the rows in roman correspond to the pessimistic category classification. Thus, for
each dam four risk estimates are generated.
If the failure criteria (see Sect. 7.7) has been carefully selected, bench-marking
becomes a powerful tool of comparison. Whereas risk comparison amounts to showing different activities of comparable risks, benchmarking corresponds to rating a
given activity’s risk related to other similar activities. Benchmarking of a tailings dam
portfolio’s probability of failure can assume the aspect shown in Fig. 15.7 (Oboni
and MDA 2018).
The extremes of the bars represent the minimum and maximum estimates of
the probability of failure for each dam. Hence the length of the bars measures the
uncertainty on the evaluation of the probability at the time of the assessment and
with the data available at that time. The vertical axis shows four benchmark values
(green), namely:
• Mount Polley and Samarco annual p f evaluated with data available to us BEFORE
the respective failures;
Table 15.12 Risk evaluation for various cases of p f (ESA) and C min , C max
Dam
p f (ESA)
Consequences
Risk
min
max
min
max
min
max
1A
1.00 * 10 −6 1.20 * 10 −6 235
1175
2.35 * 10 −4 1.41 * 10 −3
1A
2.61 * 10 −5 7.80 * 10 −5 235
1175
6.13 * 10 −3 9.17 * 10 −2
1B
1.00 * 10 −6 1.79 * 10 −6 540
5400
5.40 * 10 −4 9.67 * 10 −3
1B
4.71 * 10 −5 1.74 * 10 −4 540
5400
2.54 * 10 −2 9.40 * 10 −1
2
1.95 * 10 −5 8.30 * 10 −5 45
90
8.78 * 10 −4 7.47 * 10 −3
2
5.92 * 10 −5 2.16 * 10 −4 45
90
2.66 * 10 −3 1.94 * 10 −2
3
1.16 * 10 −3 3.52 * 10 −3 125
625
1.45 * 10 −1 2.20 * 10 0
3
7.00 * 10 −3 1.65 * 10 −2 125
625
8.75 * 10 −1 1.03 * 10 1
4
2.50 * 10 −1 2.50 * 10 −1 153
459
3.83 * 10 1
1.15 * 10 2
4
3.80 * 10 −1 3.80 * 10 −1 153
459
5.81 * 10 1
1.74 * 10 2
Dam 2 on 3 7.80 * 10 −6 3.32 * 10 −5 325
3250
2.54 * 10 −3 1.08 * 10 −1
Dam 2 on 3 2.37 * 10 −5 8.64 * 10 −5 325
3250
7.70 * 10 −3 2.81 * 10 −1
249
C min = (PL + (HS ∗ 2.5) + ED)
(15.1)
C max = (PL + (HS ∗ 2.5) + ED) ∗ RD
(15.2)
Table 15.12 displays, for each dam and for the scenario of Dam 2 interdependent
on Dam 3, the risk evaluation for various cases of p f (ESA) and C min and C max . The
italic rows correspond to the lower estimates of the p f (ESA). In other words, the
italic rows correspond to the optimistic category classification of Table 15.9, whereas
the rows in roman correspond to the pessimistic category classification. Thus, for
each dam four risk estimates are generated.
If the failure criteria (see Sect. 7.7) has been carefully selected, bench-marking
becomes a powerful tool of comparison. Whereas risk comparison amounts to showing different activities of comparable risks, benchmarking corresponds to rating a
given activity’s risk related to other similar activities. Benchmarking of a tailings dam
portfolio’s probability of failure can assume the aspect shown in Fig. 15.7 (Oboni
and MDA 2018).
The extremes of the bars represent the minimum and maximum estimates of
the probability of failure for each dam. Hence the length of the bars measures the
uncertainty on the evaluation of the probability at the time of the assessment and
with the data available at that time. The vertical axis shows four benchmark values
(green), namely:
• Mount Polley and Samarco annual p f evaluated with data available to us BEFORE
the respective failures;
Table 15.12 Risk evaluation for various cases of p f (ESA) and C min , C max
Dam
p f (ESA)
Consequences
Risk
min
max
min
max
min
max
1A
1.00 * 10 −6 1.20 * 10 −6 235
1175
2.35 * 10 −4 1.41 * 10 −3
1A
2.61 * 10 −5 7.80 * 10 −5 235
1175
6.13 * 10 −3 9.17 * 10 −2
1B
1.00 * 10 −6 1.79 * 10 −6 540
5400
5.40 * 10 −4 9.67 * 10 −3
1B
4.71 * 10 −5 1.74 * 10 −4 540
5400
2.54 * 10 −2 9.40 * 10 −1
2
1.95 * 10 −5 8.30 * 10 −5 45
90
8.78 * 10 −4 7.47 * 10 −3
2
5.92 * 10 −5 2.16 * 10 −4 45
90
2.66 * 10 −3 1.94 * 10 −2
3
1.16 * 10 −3 3.52 * 10 −3 125
625
1.45 * 10 −1 2.20 * 10 0
3
7.00 * 10 −3 1.65 * 10 −2 125
625
8.75 * 10 −1 1.03 * 10 1
4
2.50 * 10 −1 2.50 * 10 −1 153
459
3.83 * 10 1
1.15 * 10 2
4
3.80 * 10 −1 3.80 * 10 −1 153
459
5.81 * 10 1
1.74 * 10 2
Dam 2 on 3 7.80 * 10 −6 3.32 * 10 −5 325
3250
2.54 * 10 −3 1.08 * 10 −1
Dam 2 on 3 2.37 * 10 −5 8.64 * 10 −5 325
3250
7.70 * 10 −3 2.81 * 10 −1