154
11 Dam Stability Failures
The analyses can be performed in drained conditions (effective stress analyses,
or ESA) or undrained conditions (undrained stress analyses, or USA) based on a
number of considerations.
As neither C S nor D S are perfectly known due to the numerous uncertainties
surrounding the geomechanical properties, hydrological conditions, etc., both values
should be assumed to be stochastic variables. Thus it is spontaneous to express the
probability of failure p f of a structure (a slope) (Eq. 11.2) as
p f = p(FoS ≤ 1) or alternatively p f = p(C S ≤ D S )
(11.2)
The limit conditions FoS = 1 or C S = D S denote meta-stable equilibrium (like
the toss of a coin), with a theoretical p f value at 50%.
At this point we have a benchmark range (2 × 10
−4 to 10
−3 ) (Oboni and Oboni
2013), the credibility threshold at, say 10
−6 (see Sect. 7.3) and the meta-stable p f
value at 50% as described above. The goal of the approach will be to see where each
structure in the portfolio lies with respect to these framing values.
11.1.2 Linking FoS to P f : Three Simplified Methods
We start with Method 1, transforming a “simplified” deterministic slope stability
analysis into a “probabilistic one” using the p f = p(FoS ≤ 1) simplification (Eq. 11.2).
This is like considering the FoS a stochastic variable, for which the members of the
assessing team define the expected value, min, max (either subjectively or from
various analyses, or both) and then p f (stability) is calculated as p(FoS ≤ 1). Note
that values of p f (stability) can be estimated using other modelling procedures:
Method 2: Use point estimates methods (like that of Rosenblueth 1975) and
various later extensions) to define the variability of the FoS and then pf (stability) is
calculated again as p(FoS ≤ 1)
Method 3: Use probabilistic stability analysis methods as in (Oboni and Bourdeau
1983).
After defining the p f (stability), which should include uncertainties of the material,
construction care and design, either ETAs or FTAs can be constructed to account for
monitoring and maintenance, leading to “the complete” p f (see Taguchi 2014 for
examples).
The p f (stability) is the starting point of the ETA. Monitoring, repairs, etc. come
in as branches leading to a possible reduction of the initial probability following
procedure Methods 1, 2 or 3. It can be concluded that:
• Methods 1 and 2 plus ETA/FTA provide a good estimate of the p f .
• Method 3 plus ETA/FTA is even better, but is generally reserved for very critical
cases because it requires re-doing commonly available slope stability analyses
performed by the project’s engineers.
11 Dam Stability Failures
The analyses can be performed in drained conditions (effective stress analyses,
or ESA) or undrained conditions (undrained stress analyses, or USA) based on a
number of considerations.
As neither C S nor D S are perfectly known due to the numerous uncertainties
surrounding the geomechanical properties, hydrological conditions, etc., both values
should be assumed to be stochastic variables. Thus it is spontaneous to express the
probability of failure p f of a structure (a slope) (Eq. 11.2) as
p f = p(FoS ≤ 1) or alternatively p f = p(C S ≤ D S )
(11.2)
The limit conditions FoS = 1 or C S = D S denote meta-stable equilibrium (like
the toss of a coin), with a theoretical p f value at 50%.
At this point we have a benchmark range (2 × 10
−4 to 10
−3 ) (Oboni and Oboni
2013), the credibility threshold at, say 10
−6 (see Sect. 7.3) and the meta-stable p f
value at 50% as described above. The goal of the approach will be to see where each
structure in the portfolio lies with respect to these framing values.
11.1.2 Linking FoS to P f : Three Simplified Methods
We start with Method 1, transforming a “simplified” deterministic slope stability
analysis into a “probabilistic one” using the p f = p(FoS ≤ 1) simplification (Eq. 11.2).
This is like considering the FoS a stochastic variable, for which the members of the
assessing team define the expected value, min, max (either subjectively or from
various analyses, or both) and then p f (stability) is calculated as p(FoS ≤ 1). Note
that values of p f (stability) can be estimated using other modelling procedures:
Method 2: Use point estimates methods (like that of Rosenblueth 1975) and
various later extensions) to define the variability of the FoS and then pf (stability) is
calculated again as p(FoS ≤ 1)
Method 3: Use probabilistic stability analysis methods as in (Oboni and Bourdeau
1983).
After defining the p f (stability), which should include uncertainties of the material,
construction care and design, either ETAs or FTAs can be constructed to account for
monitoring and maintenance, leading to “the complete” p f (see Taguchi 2014 for
examples).
The p f (stability) is the starting point of the ETA. Monitoring, repairs, etc. come
in as branches leading to a possible reduction of the initial probability following
procedure Methods 1, 2 or 3. It can be concluded that:
• Methods 1 and 2 plus ETA/FTA provide a good estimate of the p f .
• Method 3 plus ETA/FTA is even better, but is generally reserved for very critical
cases because it requires re-doing commonly available slope stability analyses
performed by the project’s engineers.