38
4 Historic Failures “Statistics”
Fig. 4.2 A priori probabilities of failure for different tailings systems (slurry and dewatered) with
their basic level of uncertainties. The vertical axis displays the global failure probability, whereas
the horizontal axis shows the failure probabilities from individual failure modes
causality analysis in relation to design, construction, inspections, and maintenance.
These papers have shown it is possible to establish a priori a range for a portfolio
with very little actual specific data. By applying this type of procedure perceived
lack of precision is compensated for with efficiency and preliminary understanding
of ranges. Values of the probability of failure of specific failure modes for slurry
and dewatered tailings dams have been derived and compared (Taguchi 2014) to the
initial estimates (Oboni and Oboni 2013), as depicted in Fig. 4.2.
We can expect that the “world portfolio” of reasonably designed, built, maintained
and managed dams lies within the rectangle bound by model uncertainty and historic
uncertainty as already cited in the prior section. That means that we can expect that
the world portfolio of reasonably designed, built, maintained and managed dams has
a annual probability of failure between 2 × 10
−4 and 10
−3 , although the individual
failure modes may have probabilities in the range of 10
−4 –10
−6 . We also see that the
purely theoretical approach by Taguchi shows that dewatered tailings would tend to
bring the probability of failure towards the bottom of the historical range, provided,
of course the dewatering is effective and does not generate excessive risk taking
based on its promises.
External symptoms such as beach width, wet spots, good or bad maintenance
and deformations will modify the a priori p f determined above. The same occurs if
poor foundation conditions are known or suspected. A poorly designed or built or
maintained/managed dam would lie outside of the rectangle, and reach failure by a
ascending trajectory towards the left.
Please note that Fig. 4.2 shows the limit value of 10
−6 for some dewatered tailings
individual failure modes, which coincides with a value commonly considered the
credibility threshold in evaluations.
4 Historic Failures “Statistics”
Fig. 4.2 A priori probabilities of failure for different tailings systems (slurry and dewatered) with
their basic level of uncertainties. The vertical axis displays the global failure probability, whereas
the horizontal axis shows the failure probabilities from individual failure modes
causality analysis in relation to design, construction, inspections, and maintenance.
These papers have shown it is possible to establish a priori a range for a portfolio
with very little actual specific data. By applying this type of procedure perceived
lack of precision is compensated for with efficiency and preliminary understanding
of ranges. Values of the probability of failure of specific failure modes for slurry
and dewatered tailings dams have been derived and compared (Taguchi 2014) to the
initial estimates (Oboni and Oboni 2013), as depicted in Fig. 4.2.
We can expect that the “world portfolio” of reasonably designed, built, maintained
and managed dams lies within the rectangle bound by model uncertainty and historic
uncertainty as already cited in the prior section. That means that we can expect that
the world portfolio of reasonably designed, built, maintained and managed dams has
a annual probability of failure between 2 × 10
−4 and 10
−3 , although the individual
failure modes may have probabilities in the range of 10
−4 –10
−6 . We also see that the
purely theoretical approach by Taguchi shows that dewatered tailings would tend to
bring the probability of failure towards the bottom of the historical range, provided,
of course the dewatering is effective and does not generate excessive risk taking
based on its promises.
External symptoms such as beach width, wet spots, good or bad maintenance
and deformations will modify the a priori p f determined above. The same occurs if
poor foundation conditions are known or suspected. A poorly designed or built or
maintained/managed dam would lie outside of the rectangle, and reach failure by a
ascending trajectory towards the left.
Please note that Fig. 4.2 shows the limit value of 10
−6 for some dewatered tailings
individual failure modes, which coincides with a value commonly considered the
credibility threshold in evaluations.