Practical risk assessment for embankments, dams, and slopes - Risk and Reliability in Geotechnical Engineering - page 450

Maximum water level (20 m)

Minimum water level (12 m)

16 m
7 m 36.8 m 29.8 m

Circular failure surfaces

Figure 11.14 Dam geometry.

The process shown in Section 11.4.3 has been followed as described below for every of
the eight steps:

• Step 1. The calculation method selected for the stability of the embankment is the sim-
plified Bishop method, thus making use of a Mohr-Coulomb type of failure criteria.
This 2D method has been introduced in a spreadsheet to facilitate fast computations.
In each computation, stability is checked for 108 different failure circles, considering
that the embankment fails when the FS is lower than 1 at least for one of these circles.
• Step 2. Water pressure is the driving force of failure though its impact has been con-
sidered in a very simplified manner. In particular, the top flow line inside the embank-
ment varies linearly from the water pool level in the upstream face to a fixed point in
the downstream face located at 3.3 m above the downstream toe. The selected range
of pool levels comprises from 12 to 20 m over the embankment base. In total, 17 water
pool levels were analyzed (equally distributed every 0.5 m within the range). Beyond
such levels, an existing parapet will likely fail and lead to an overtopping failure mode.
• Step 3. Two random variables have been considered: friction angle and cohesion.
• Step 4. To evaluate the natural uncertainty, the friction angle follows a truncated
normal distribution with average 25°, standard deviation 2°, maximum 30°, and mini-
mum 20°. The cohesion follows a log-normal distribution with average 10 kPa and
standard deviation 3 kPa. For the epistemic uncertainty analysis, the friction angle
follows a truncated normal distribution with average 25°, standard deviation 3°, maxi-
mum 30°, and minimum 20° while the cohesion follows a log-normal distribution with
average 10 kPa, and standard deviation 5 kPa.
• Step 5. The Monte Carlo method has been chosen to sample variables in both the
natural and epistemic uncertainty distributions. This method has been chosen because
its results are more accurate and the state function and calculation model selected in
Step 1 are simple enough to allow many stability computations to be rapidly made.
• Step 6. 100 pairs of values are sampled within the natural uncertainty distributions for
friction angle and cohesion following the Monte Carlo method. For each water level,
stability is checked for each pair of values (corresponding to the two random vari-
ables, friction angle and cohesion). Failure probability of each water level is obtained
dividing the number of failure cases by the total number of cases analyzed (100). The
fragility curve obtained with this process is shown in Figure 11.15 (it is important to
mention that 100% probability has not been reached since for higher pool levels, over-
topping is much more likely to control the failure and it does not make physical sense
to increase the loading range of the stability failure mode).