Practical risk assessment for embankments, dams, and slopes - Risk and Reliability in Geotechnical Engineering - page 442

11.3.3 role of fragility curves in risk analysis
Event trees are a mathematical tool widely used to compute risk in dam engineering. They
are sometimes referred to as the “risk model,” as they are in fact a logical and analytical
structure for risk calculation. An event tree is a graphical representation of a logical model
that includes all the conceivable chains of events resulting from an initiating event that
can produce the structural failure (SPANCOLD, 2012). Defining each of the probabilities
along these chains of events, the overall failure probability and risk of the structure can be
obtained. Figure 11.10 shows an example of an event tree.
Each node of the tree represents an event. The root node is called an initiating event.
Branches that grow from an event represent the possible outcomes of their event of origin.
Branches must represent mutually exclusive and collectively exhaustive events, so an event
will always be reflected in a single fashion in only one branch. In this way, if a probability
is assigned to each possible outcome (for every event), the addition of all probabilities of
the outcomes arising from any node should be 1. Probabilities in event trees, except for the
initiating event, are always conditional, that is, for any intermediate node it is assumed that
all preceding events (parent nodes) have already happened.
When a structural failure is analyzed with an event tree, the initial node is usually used
to introduce the full range of probability of the loads that could produce the failure of the
structure. In the other nodes, the conditional probabilities of the different failure mecha-
nisms in which the failure mode is decomposed are then introduced. These conditional
probabilities are generally introduced using fragility curves, as explained in the previous
section. A single value of failure probability along each branch of the tree can be obtained
combining the conditional probabilities of all the failure mechanisms in the branch.
In general, when failure probability is computed using an event tree, the probabilities
introduced in each node (in terms or not of fragility curves) capture the existing natural
uncertainty. This uncertainty includes the probability of occurrence of different loading
states (in general introduced in the first node) and the conditional probability of the differ-
ent failure mechanisms for these loading states. In some event trees, epistemic and natural
uncertainties are mixed (SPANCOLD, 2012), for instance, with a higher variability in the
fragility curves introduced in the event tree. In general, it is advisable to analyze indepen-
dently the two sources of uncertainty (Ferson and Ginzburg, 1996), to allow a better inter-
pretation of the results.
Furthermore, event trees can be used to combine different failure modes with techniques
such as common cause adjustment (SPANCOLD, 2012), which combines the conditional
probabilities of different failure modes produced by the same loads.
Root
Branch
Node
Figure 11.10 An example of an event tree. (From SPANCOLD. 2012. Risk analysis applied to management of
dam safety—Technical Guide 8 (Vol. 1), Spanish National Committee on Large Dams.)