158
11 Dam Stability Failures
Fig. 11.1 pf-FoS empirical relationships per structure category as per (Altarejos et al. 2015)
Table 11.3 Variation of the
probability of failure for
constant FoS, but varying
Category of structure
Category
FoS
Annual p f
I
1.3
9.31 × 10 −5 or appx 10 −4
II
5.93 × 10 −3 or appx 6 × 10 −3
III
6.4 × 10 −2 or 6.5%
IV
2.36 × 10 −1 or 23.6%
world-wide portfolio of active dams is probably constituted by structures between
Category I and II, and that those which have failed having likely belonged to Category
II to IV.
It is interesting to look at the values of p f for FoS = 1 in Fig. 11.1. The metastable condition leads to p f = 0.5 for Category II, and slightly higher values for
Cat. III and IV. We wonder what the reasoning of Silva-Lambe-Marr was, but notice
some “observation points” that leave us quite surprised. In any case, once a structure
has reached p f = 0.5, all discussions become useless, as the structure has virtually
failed. The other interesting point is Category I, with p f = 0.05 for FoS = 1. In
order to understand this apparently odd value, let’s use an example from aerospace:
if design, control, construction and monitoring are developed to the highest standards, as in aerospace, then a FoS near 1 can be accepted because the very narrow
uncertainties lead to a lower probability of failure than in “normal” applications.
Many rockets/missiles are built that way to maximize payload, and the media report
corresponding failures at a rate that leaves the public baffled, but is not, after all, very
significant considering the low-margin design.
Finally, if we look at the other end of the spectrum, we are not keen on using
empirical relationship that go below credibility. The nuclear industry has shown, for
example, that extremely low theoretical probabilities result in significantly larger
actual real-life probabilities and rates of failure (Oboni and Oboni 2013). Likewise,
we “do not trust” very large factors of safety (above 2), because the models used are
generally incomplete and approximate.
11 Dam Stability Failures
Fig. 11.1 pf-FoS empirical relationships per structure category as per (Altarejos et al. 2015)
Table 11.3 Variation of the
probability of failure for
constant FoS, but varying
Category of structure
Category
FoS
Annual p f
I
1.3
9.31 × 10 −5 or appx 10 −4
II
5.93 × 10 −3 or appx 6 × 10 −3
III
6.4 × 10 −2 or 6.5%
IV
2.36 × 10 −1 or 23.6%
world-wide portfolio of active dams is probably constituted by structures between
Category I and II, and that those which have failed having likely belonged to Category
II to IV.
It is interesting to look at the values of p f for FoS = 1 in Fig. 11.1. The metastable condition leads to p f = 0.5 for Category II, and slightly higher values for
Cat. III and IV. We wonder what the reasoning of Silva-Lambe-Marr was, but notice
some “observation points” that leave us quite surprised. In any case, once a structure
has reached p f = 0.5, all discussions become useless, as the structure has virtually
failed. The other interesting point is Category I, with p f = 0.05 for FoS = 1. In
order to understand this apparently odd value, let’s use an example from aerospace:
if design, control, construction and monitoring are developed to the highest standards, as in aerospace, then a FoS near 1 can be accepted because the very narrow
uncertainties lead to a lower probability of failure than in “normal” applications.
Many rockets/missiles are built that way to maximize payload, and the media report
corresponding failures at a rate that leaves the public baffled, but is not, after all, very
significant considering the low-margin design.
Finally, if we look at the other end of the spectrum, we are not keen on using
empirical relationship that go below credibility. The nuclear industry has shown, for
example, that extremely low theoretical probabilities result in significantly larger
actual real-life probabilities and rates of failure (Oboni and Oboni 2013). Likewise,
we “do not trust” very large factors of safety (above 2), because the models used are
generally incomplete and approximate.