164
11 Dam Stability Failures
Fig. 11.4 Comparison of
the annualized probability of
failure derived from a direct
geomechanical probabilistic
approach (blue) and the
empirical method (green) for
various return periods
(horizontal acceleration) in
cohesive materials. The
slopes are the same as those
in Fig. 11.2
Engineered materials have fewer uncertainties than natural ones, as they are
selected and carefully compacted under controlled water content. This reduces their
variability. Thus we consider that categories III, II, and I of the empirical method
reflect the reduction of uncertainties leading to lower probabilities for similar theoretical FoS. Controls and monitoring further amplify these effects.
As per the evaluation of pseudo-static conditions, our tests have also shown good
agreement between the two methodologies. As Figs. 11.4 and 11.5 show, for cohesive,
respectively granular materials, the annualized probability of failure can be higher
for low magnitude, more frequent events than for high magnitude, long-return events.
NB: the reason for this apparently odd statement is very simple. The pf is equal to
the pf under horizontal acceleration multiplied by the annual probability of the quake
generating that acceleration. Low magnitude events are more frequent, so the product
can be higher (it depends, of course on the FoS-acceleration relationship.
So, what the graphs of Figs. 11.4 and 11.5 show is that if one looks at the annualized
probability of failure, the smaller events may give a higher annual probability of
failure than the larger ones! The implications for design are simple: one must check
Fig. 11.5 Comparison of the annualized probability of failure derived from a direct geomechanical
probabilistic approach (blue) and the semi-empirical method (green) for various return periods
(horizontal acceleration) in cohesive materials. The slopes are the same as those in Fig. 11.3
11 Dam Stability Failures
Fig. 11.4 Comparison of
the annualized probability of
failure derived from a direct
geomechanical probabilistic
approach (blue) and the
empirical method (green) for
various return periods
(horizontal acceleration) in
cohesive materials. The
slopes are the same as those
in Fig. 11.2
Engineered materials have fewer uncertainties than natural ones, as they are
selected and carefully compacted under controlled water content. This reduces their
variability. Thus we consider that categories III, II, and I of the empirical method
reflect the reduction of uncertainties leading to lower probabilities for similar theoretical FoS. Controls and monitoring further amplify these effects.
As per the evaluation of pseudo-static conditions, our tests have also shown good
agreement between the two methodologies. As Figs. 11.4 and 11.5 show, for cohesive,
respectively granular materials, the annualized probability of failure can be higher
for low magnitude, more frequent events than for high magnitude, long-return events.
NB: the reason for this apparently odd statement is very simple. The pf is equal to
the pf under horizontal acceleration multiplied by the annual probability of the quake
generating that acceleration. Low magnitude events are more frequent, so the product
can be higher (it depends, of course on the FoS-acceleration relationship.
So, what the graphs of Figs. 11.4 and 11.5 show is that if one looks at the annualized
probability of failure, the smaller events may give a higher annual probability of
failure than the larger ones! The implications for design are simple: one must check
Fig. 11.5 Comparison of the annualized probability of failure derived from a direct geomechanical
probabilistic approach (blue) and the semi-empirical method (green) for various return periods
(horizontal acceleration) in cohesive materials. The slopes are the same as those in Fig. 11.3