Comprehensive Risk Assessment for Natural Hazards - Planat

Comprehensive risk assessment for natural hazards
guaranteed only if the probability of failure of the system is
less than or equal to 10 –7 per year.
The joint distribution of storm-surge level, basin level and
wave energy was developed for The Netherlands as follows.
Frequency analysis was applied to available storm-surge-level
data. Knowledge of the physical laws governing the stormsurge
phenomenon was used to determine whether extreme
water levels obtained by extrapolation were physically realistic.A
conditional distribution between storm-surge levels and
basin levels was derived from a simple mathematical model of
wind set-up and astronomical tide applied to simulation of
different strategies for closing the barrier gates. The basin level
was found to be statistically independent of the wave energy.A
conditional distribution between storm-surge levels and wave
energy could not be derived because of lack of data. Therefore,
a mathematical model was developed considering the two
sources of wave energy: deep-water waves originating from the
North Sea and local waves generated by local wind fields.
The advanced first-order second-moment reliability
analysis method (Ang and Tang, 1984, p. 333-433; Yen et al.,
1986) was applied to determine the failure probability of
each major system component of the storm-surge barrier.
An advantage of this method is that the contribution of each
basic variable (model parameters, input data, model correction
or safety factors, etc.) to the probability of failure of a
given component can be determined. Thus, problematic
aspects of the design can be identified and research effort
can be directed to the variables that have the greatest effect
on the probability of failure.
Application of the failure criterion of 10 –7 to the design
of each major component of the storm-surge barrier was a
substantial step in achieving a societally acceptable safety
level. However, the appropriate approach is to determine the
safety of the entire barrier as a sea-defence system. Thus, the
probability of system failure was determined as a function
of the probability of component failure, and the probability
of failure resulting from mismanagement, fire and ship collision
through application of fault-tree analysis (Ang and
Tang, 1984, p. 486-498). The fault tree for determining the
probability that parts of Zeeland are flooded because of failure
of components of the barrier, mismanagement, and/or
malfunction of the gates is shown in Figure 8.1. By using the
fault tree, the design of the barrier was refined in every
aspect and the specified safety criterion of 10 –7 per year was
achieved in the most economical manner.
Through application of sophisticated probabilistic
techniques, Dutch engineers were able to reduce the design
load for the storm-surge barrier by 40 per cent relative to
traditional design methods and still achieve a societally
acceptable failure probability or hazard level. In this case,
the societally acceptable hazard was defined by setting the
fatality rate equal to levels resulting from accidents in The
Netherlands. Thus, the completed structure reduced the risk
resulting from storm surges to fatality rates accepted by the
people of The Netherlands in their daily lives.
It could be considered that the application of the new
design procedures resulted in an increase in the hazard level
resulting from storm surges faced by society relative to the
application of the previous design standards. However, the
previous design standards were implicitly set without any
consideration of the consequences of a storm surge and
societally acceptable hazard levels. The population in the
southwestern region of The Netherlands to be protected by
the storm-surge barrier was already facing a substantial hazard.
Thus, the question was to what level should the hazard
be reduced? The Dutch Government decided that people in
The Netherlands would be willing to accept a possibility of
dying because of a failure of the sea defences that was equal
to the probability of dying because of an accident. This
resulted in substantial savings relative to the use of the
implicit societally acceptable hazard level. The key point of
this example is that when faced with the construction of a
large, complex and expensive structure for the protection of
the public, the Dutch Government abandoned implicit societally
acceptable hazard levels and tried to determine real,
consequence-based societally acceptable hazard levels.
8.3 MINIMUM LIFE-CYCLE COST EARTHQUAKE
DESIGN
Earthquake-resistant design and seismic-safety
assessment should explicitly consider the underlying
randomness and uncertainties in the earthquake load and
structural capacity and should be formulated in the
context of reliability (Pires et al., 1996). Because it is not
possible to avoid damage under all likely earthquake loads,
the development of earthquake-resistant design criteria
must include the possibility of damage and an evaluation
of the consequences of damage over the life of the
structure. To achieve this risk assessment for structures in
earthquake-prone regions, Professor A. H-S. Ang and his
colleagues at the University of California at Irvine have
proposed the design of earthquake-resistant structures on
the basis of the minimum expected total life-cycle cost of
the structure including initial (or upgrading) cost and
damage-related costs (Ang and De Leon, 1996, 1997; Pires
et al., 1996) and a constraint on the probability of loss of
life (Lee et al., 1997).
The minimum life-cycle cost approach consists of five
steps as follows (Pires et al., 1996; Lee et al., 1997).
(1) A set of model buildings is designed for different levels
of reliability (equal to one minus the probability of
damage, p f ) or performance following the procedure of
an existing design code. For reinforced concrete buildings,
this is done by following the design code except
that the base-shear coefficient is varied from code
values to yield a set of model buildings having different
strengths, initial costs (construction or upgrading), and
probabilities of damage.
(2) A relation between the initial cost of the structure and
the corresponding probability of damage under all possible
earthquake loads is established from the designs
made in step 1.
(3) For each design, the expected total cost of structural
damage is estimated as a function of the probability of
damage under all possible earthquake loads and is
expressed on a common basis with the initial cost. The
damage cost includes the repair and replacement cost,
C r , loss of contents, C c , economic impact of structural
79