Practical risk assessment for embankments, dams, and slopes - Risk and Reliability in Geotechnical Engineering - page 447

1.E+00
1.E-01
1.E-02
1.E-03
1.E-04

1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10

0 20 40 60 80 100

Water level (m)

F i g u r e 11.11 Fragility curve for the sliding failure mode of a concrete gravity dam. (From Altarejos-García,
L. et al., 2012. Structural Safety , 36-37, 1-13.)

This is another reason why the failure probability approach is sometimes preferred, as it
provides a unique estimation of the structure safety. In both cases, it should be explicated
how the values of R or φ have been derived. It is important to specify if they are best esti-
mate values, prudent estimates, minimum values, or other. The numerical value of the FS
changes dramatically depending on how the resistance and strength parameters are chosen.
If failure probabilities are to be calculated, there is no doubt on what values are used, as
the engineer is somehow forced to assess the whole probability distribution function of the
variables if they are random, or to declare a unique value if the variable is considered deter-
ministic, thus eliminating much confusion in the analysis.
In any case, for a specific problem, and for a certain failure mode (i.e., slope stability), it
is possible to derive a relationship between FS and conditional failure probability once the
fragility curve has been obtained by simply mapping the factors of safety along the loading
interval. The curve thus obtained represents the equivalence between FS and probability of
failure for the given problem.
Figure 11.11 shows the fragility curve derived by the authors for the problem of sliding
of a concrete gravity dam along a dam foundation contact. The curve was derived with the
following assumptions. The calculation model for sliding was a 2D numerical model imple-
mented in the finite difference code FLAC (ITASCA, 2014). A cracked base analysis was
performed, allowing a crack to open and progress along the dam foundation contact, with
uplift updating as the crack propagates. Elastic constitutive models were used for both dam
and foundation. Random variables were friction angle and cohesion at the dam-foundation
contact. The reliability technique used was Monte Carlo analysis.
The FS was evaluated by a coupled progressive reduction of strength parameters, friction
angle, and cohesion, from their estimated mean values to the values where sliding starts,
using Equation 11.13 for the calculation for each loading level. The FS versus probability of
failure curve obtained is shown in Figure 11.12 .

11.4.3 building fragility curves
Having already introduced all the substantial issues that concern fragility analysis in the
previous points, a general flowchart to build fragility curves in the context of risk analysis
is presented ( Figure 11.13 ) .