Comprehensive Risk Assessment for Natural Hazards - Planat

Comprehensive risk assessment for natural hazards
81
a specified intensity A=a, is defined with a conditional
probability density function (pdf), f Xa (x), each of the
expected damage cost items would be
E[C j a] = C j (x) f Xa (x) dx (8.2)
The intensity of an earthquake also may be defined as a pdf,
f A (a), and the total expected damage cost under all likely
earthquake intensities may be computed by integration as
E[C j ] = E[C j a] f A (a) da (8.3)
Repair cost ratio, CR/C1
1.0
0.8
0.6
0.4
Building A
Building B
Building C
Building D
Building E
Building F
where the bounds of integration are a min and a max ,which
are the minimum and maximum values of the likely range of
earthquake intensities, respectively.
The evaluation of equations 8.1 to 8.3 requires: (a)
development of relations between the level of physical,
structural damage and the associated damage cost and loss
of life; and (b) application of a structural model to relate
earthquake intensity to structural damage. Further, the time
of earthquake occurrence and the transformation of this
future cost to an equivalent present cost are not considered
in equation 8.3. Thus, the establishment of a probabilistic
model to describe earthquake occurrence and an economic
model to convert future damage cost to present cost also are
key features of the minimum life-cycle-cost earthquakedesign
method. These aspects of the method are described
in the following sections.
8.3.1 Damage costs
The global damage of a structure resulting from an earthquake
is a function of the damages of its constituent
components, particularly of the critical components. In
order to establish a consistent rating of the damage to reinforced-concrete
structures, Prof. Ang and his colleagues
(Ang and De Leon, 1996, 1997; Pires et al., 1996; Lee et al.,
1997) suggested applying the Park and Ang (1985) structuralmember
damage index. Each of the damage costs then is
related to the median damage index, D m , for the structure.
The repair cost is related to D m on the basis of available
structural repair-cost data for the geographic region. For
example, the ratio of repair cost, C r , to the initial construction
cost, C i , for reinforced-concrete buildings in Tokyo is
shown in Figure 8.2 as determined by Pires et al. (1996) and
Lee et al. (1997). A similar relation was developed for
Mexico City by De Leon and Ang (1994) as:
C r = 1.64 C R D m ,0 D m 0.5; and C r = C R , D m > 0.5 (8.4)
where C R is the replacement cost of the original structure,
which is equal to 1.15 times the initial construction cost for
Mexico City.
The loss of contents cost, C c , is typically assumed to reach
a maximum of a fixed percentage of the replacement cost, C R ,
and to vary linearly from 0 to this maximum with D m for
intermediate levels of damage to the structure (D m < 1). For
reinforced-concrete structures, the loss of contents was
assumed to be 50 per cent for Mexico City (Ang and De Leon,
0.2
0
0
0.25
0.50
0.75
Median Global Damage Index, d m
Figure 8.2 — Damage repair cost function derived from data
for reinforced-concrete structures damaged by earthquakes
in Tokyo (after Lee, 1996)
1996, 1997) and 40 per cent for Tokyo (Pires et al., 1996). Lee
et al. (1997) applied a piecewise-linear relation for the range of
D m for intermediate levels of damage.
The economic loss resulting from structural damage,
C ec , may be estimated in several ways. Ideally, this loss
should be evaluated by comparing the post-earthquake economic
scenario with an estimate of what the economy
would be if the earthquake had not occurred. A complete
evaluation of all economic factors is difficult, and simplified
estimates have been applied. For example, Pires et al. (1996)
assumed that the loss of rental revenue, if the building collapses
or exceeds the limit of repairable damage, is equal to
23 per cent of the replacement cost of the building, and
varies nonlinearly with D m up to the limit of repairable
damage (D m = 0.5). They developed this function on the
basis of the average rental fees per square metre per month
for office buildings at the site, and assuming that 1.5 years
will be needed to reconstruct the building. Lee (1996) used
an economic input-output (I-O) model to compute C ec .The
I-O model (see Chapter 7) is a static general-equilibrium
model that describes the transactions between various production
sectors of an economy and the various final
demand sectors. Lee aggregated I-O model data for 46 economic
sectors from the Kanto region of Japan, which
includes the city of Tokyo, into 13 sectors for the estimation
of the economic loss resulting from structural damage. Lee
also used time-to-restore functionality curves for professional,
technical and business-service buildings reported by
the Applied Technology Council (1985) to relate D m to economic
losses as a piecewise-linear function.
The cost of injuries, C in , also may be estimated in several
ways. Pires et al. (1996) and Lee et al. (1997) assumed
that 10 per cent of all injuries are disabling for D m 1, and
that the loss due to a disabling injury was equal to the loss
due to fatality (as described in the following paragraph).
Pires et al. (1996) estimated the cost for non-disabling
injuries to be 5 million Yen (approximately US $50 000). A
nonlinear function was used to estimate the cost of injuries
1