CHAPTER 8 
STRATEGIES FOR RISK ASSESSMENT - CASE STUDIES 
(L’NDHA. 
Airording to the Lnited Nations Department of 
Iurnmitarian Affairs 1992), assessment involves 
sursey ofa real or pomtial disaster to estimate the actual 
1 
;1 
or rxpected damages and to make recommendations for 
prevention, preparedness and rcsponse. The survey of the 
expected damages for a potential disaster essentially con- 
sists of a risk evaluation. Risk is defined as the expected 
losses (of lives, persons injured, property damaged and eco- 
nomic activity disrupted) due to a particular hazard for a 
givcn area and reference period (UNDHA, 1992). Based on 
niathematical calculations, risk is the product of hazard and 
vulnerability (UNDHA, 1992). 
Risk evaluations should be the basis of the design and 
establishment of methods to prevent, reduce and mitigate 
damages from natural disasters. Methods to evaluate mete- 
orological, hydrological, volcanic and seismic hazards are 
available and have been presented in Chapters 2 to 5, 
respectively. Methods also are available to develop a com- 
mensurate rating system €or the possible occurrence of 
multiple potentially damaging natural phenomena (e.g., 
landslides and floods) and to present equivalent hazard 
levels to land-use planners in a single map, as illustrated by 
the example given in Chapter 6. Methods also have been 
proposed to evaluate the economic damages resulting from 
natural disasters some of which are presented in Chapter 7. 
I lowever, despite the availability of the methods to evaluate 
the damages resulting from natural disasters, most societies 
have preferred to set somewhat arbitrary standards on the 
acceptable hazard level as the basis for mitigation of risks 
from natural disasters. Without a detailed evaluation of the 
damages resulting from natural disasters and the direct 
consideration of societally acceptabte damage levels 
(including loss of life), society is sure to inadequately allo- 
cate natural-disaster risk-mitigation funds and, as a result, 
is guaranteed to encounter damage that IS deemed 
ti nacceptable by society. 
In recent years, several countries have started to apply 
risk evaluations in the design and establishment of methods 
to prevent, reduce and mitigate damages from natural disas- 
ters. This chapter includes reviews of examples of these 
mcthods applied to: ( I ) the design of coastal protection 
works in The Netherlands, earthquake resistant structures 
in Mexico and japan, and flood-protection works in the 
USA; and (2) the establishment of flood mitigation via 
land-use planning in France. This chapter does not include 
an exhaustive review of risk evaluations, but rather presents 
examples to illustrate that the methods are available and 
have been successfully applied. This review provides a 
framework for the development and application of similar 
methods for mitigation of other natural disasters, as appro- 
priate, to conditions in other countries. Thus, in this 
chapter, assessment is defined as a survey and cvaluation to 
estimate the expected damages from a potential disaster and 
to recommend designs or measures to reduce damages to 
societally acceptable levels, if possible. 
S 
8.1 
In 
IMPLICIT SOCIETALLY ACCEPTABLE 
HA Z A K D 
It 15 vahable to review the history of the determination oi 
societally acceptable hazards in order to understand the 
need for risk assessment in the design and establishment of 
mitigation programmes for risks from natural disasters. In 
rhe design of structures and thc establishment of land-use 
management practices to prevent and/or reduce damages 
resulting from natural disasters, the risk or damage assess- 
ment typically has been implicit. An example can be taken 
from the area of flood protection where the earliest struc- 
tures or land-use management practices were designed or 
established on the basis of the ability to withstand previous 
disastrous floods. Chow (1962) notes that the Dun water- 
way table used to design railroad bridges in the early 1900s 
was primarily determined from channel areas correspond- 
ing to high-water marks studied during and after floods. 
Using this approach, previous large floods of unknown fre- 
quency would safely pass through the designed bridges. 
Also, after a devastating flood on the Mississippi River in 
1790, a homeowner in Saint Genieve, Missouri, rebuilt his 
house outside the boundary of that flood. Similar rules were 
applied in the design of coastal-protection works in The 
Netherlands at the time the Zuiderzee was closed (L927-32) 
(Vrijling, 1993). 
In some cases, rules based on previous experience work 
well. For example, the house in Missouri was nor flooded 
until the 1993 flood on the Mississippi River and the 
Zuiderzee protection works survived the 1953 storm that 
devastated the southwestern part of The Netherlands 
However, in most cases these methods are inadequate 
because human experience with floods and other natural 
hazards do not include a broad enough range of events nor 
can they take into account changing conditions that could 
exacerbate natural disasters. As noted by Vrijling (1993) 
“‘one is always one step behind when a policy is only based 
on historical facts.” 
In the early part of the twentieth century, the concept ol 
trequency analysis began to emerge as a method to extend 
limited data on extreme events. These probabilistically 
based approaches allow estimates of the magnitude of rarely 
occurring events. Frequency analysis is a key aspect of mete- 
orological, hydrological and seismic hazard analyses as 
described in Chapters 2, 3 and 5, respectively. Thus, using 
frequency-analysis methods, it is possible to estimate events 
with magnitudes beyond those that have been observed. 
’Chis necessitates the selection of a societally acceptable haz- 
ard frequency. 
In the USA. the societally acceptable frequency of occur- 
rence of flood damage was formally set to once on average in 
100 years (the so-called 100-year flood) in the Flood Disaster 
and Protection Act of 1973. However, the 100-year flood had 
been used in engineering design for many years before 1973. 
h s Act, the US Congress specified the IOO-year flood as the . - 
78 
limit of the flood plain for insurance purposes. and this has 
become widely accepted as the standard of hazard (Linsley 
and Franzini, 1979, p. 634). This acceptable hazard frequency 
was to be applied uniformly throughout the USA, without 
regard to the vulnerability of the surrounding land or people. 
The selection was not based on a benefit-cost analysis or an 
evaluation of prcjbabk loss of life. Linsley (1986) indicated that 
the logic for one fixed level of flood hazard (implicit vulner- 
ability) was that everyone should have the same I ~ v c l of 
protection. Linsley fwthcr pointed out that many hydrologists 
readily accepted the implicit vulnerability assumption because 
a relatively uncommon flood was used to defint the hazard 
level, and, thus. 
"Thc probability t h a ~ xiyone will ever point a finger and 
'you rv.ere SLY IS eqcally rcrnote. wrong' IS 
is obvioiri L$dt new 
If the klood 
flond 13 i j r g e r than 
the 10-year or 100-year flood, as the case may bc. If the 
estimate is not exceeded, there is no reason to think 
about it." 
exceeded, I: 
ard and 5ociety's 
the 
Cornprehensivc mitigation of risks resulting from 
potentially damaging natural phenomena requires a more 
rigorous consideration of the losses resulting from the haz- 
willingness to accept these losses. 
For other types of disaster, societally acceptable hazard 
levels also ha\-e bscn selected without formal eTialuation of 
benefits arid costs. For example, in the L'SAA, clam-failure 
storm surge) is assurnt.d to coincidr with 
rriitigated by designing darns to pass the probable 
maximum flood whew Iailure may result in the loss of life. 
Also, in The Nethcrlands, coastal-protection works are nor- 
mally designed by application of a semi-deterministic 
worst-case approach wherein the maximum storm-surge 
h e ! 000-year 
Ivdrer !evel. Comparison of the :vorst- 
soiic:ally 
( 
prcscnted 
Tokyo 
lossidamage anaiyals 
risks are 
(10 
the minimum interior 
case approach to the acceptabk probabilistic-load 
approach (described in section 8.2) resulted in a 40 per cent 
reduction in the design load xvhen the actual probability of 
failure was considercd L'rijling, This exarriple illus- 
trates that when a risk messmerit is performed, a societally 
oE 
the 
ioss/damage among flood- 
1993). 
acceptahlc level of safety can be maintained and in some 
cases improved, while at the same time effectively using 
in the iollowing sections ilius- 
scarce financial resources. 
The exampies 
trate how risk assessment can be done to keep Ivsses! 
damages resulting from potentialty damaging natural phe- 
nomena within societally acceptable bounds. In the case of 
storm surges in The Netherlands, the loss/darnage analysis 
fatalities (section considered only the rat< of 8.7'). I n the case 
earthquakes in and Mexico City, the loss/damage 
analysis considered the cost, including the cost of fatalities, 
with possible additional constraints on the rate of fatalities 
(section 8.3). In the cast' of flood management in the USA, 
was approached in tzrrns of eco- 
nomic benefits and costs, with other consequences of 
flooding and the flood-management projects considered in 
the decision-making (wction Fillally, in the case of 
flood managemcnt in France, soc.ietalfy acceptable 
8.4.1). 
\\'as dctcrmined by negotiation 
plain land owners and local or national government 
- 
representatives. These lossesldamagcs were transformed 
into hazard units for comparison with the flood hazard at a 
given localion (section 8.4.2). 
DESIGN OF COASTAL PROTECTION WORKS 
I N THE XETHERLANDS 
1949. After a locg 
Chapter 8 - Strntegies for risk as.wsrrzent - case studies 
10 
lation of the country (Agema, 1982). Therefore, protection 
of coastal areas from storm surge and coastal waves is of 
paramount importance to the survival of The Netherlands. 
These concerns are especially importnnt in the southwest- 
ern coastal Province of Zeeland where the funnelling effect 
Eriglish Channel on m r r n surges in the Sorth Sea 
greatly magnifies the height and intensity of the surges. The 
following discussion of design of coastal-protection works 
in The Netherlands is based on Vrijling (1993) and readers 
are referred to this payer for further inlormation. 
Application of frequency analysis to storm-surge levels 
was first proposed in The Setherlands in 
debate in thc committee to provide coastal protection in the 
Maas-Rhine delta in a:id near Zeeland (Delta Committee), 
the acceptable return period €or storm surges was sct a t once 
on average in 000 years. This resulted in a storm-surge 
level of 5 IE above mean 5ea level t o which a freeboard for 
wave run-up would bc added in design. This Delta Standard 
design rulc has been applied in the analysis of all Dutch sea 
dikes since 1953. 
A new design method and evaluation of societally 
acceptable hazard levcls were needed for the design of the 
storm-surge barrier for :he Eastern Schrldt Estuary because 
of thc strui!ural and operational complexity of the barrier 
f h ~ a simple dikc.. .I'hrrefore, the design 
10 
t o those 
rules for dikes established by the Delta Committee in the 
1930s had tcl bc transhrmed into a ser of rules suitable for a 
complicatcd srructure. A consistent approach to the struc- 
tural safrty o f the harrier was unlikdy if the components 
thc foundation, concrete piers, sill and gatcs were 
designed according t o the rules and principles prevailing in 
the various fields. Thus, the Delta Commission developed a 
procedure for probabiiistii design that rould be consisten:ly 
applied for each strucrurzl component of the barrier. 
The totd design load on the 13clta Conmiittee set the 
storm -surgc barrier at the load with an exceedance proba- 
bility 2.5 x !()-.' per !rear (that is, the 4 OOO-year water level) 
determined integration of the joint probability distribu- 
tion amoiig storm-surge levels, basin levels and the 
wavc-energy spectrum. A single iailure criterion then was 
developed for the functioning of all major components of 
the storm-surge barrier (concrete piers, steel gates, founda- 
load. The farlurr 
criterion was tentativcly established at 10-7 per year on the 
basis or 
8.2 
Lhari one half ofthe land surlaie in The Netherlands 
Iies below the 000-year storm-surge level. clcvatioiis 
These arcas include approximately 60 per cent of the p o p - 
More 
at 
of the 
cornpi ed 
such as 
result in 
bf 
tion, sill, t t c . ' , under the stlrcted &sign 
Netherlands 
from 
thc followirig reasoning. Fatality statistics for The 
indicatc Lhat the averagc probability of death 
resulting an accident is 10-4 per year. Previous experi- 
ence has shoi1.n that the failure of a st.,t-defense system ma); 
casualtics. Thus, a normal safety level can be Compreherrsive risk assessmenifor natiird hazards 
guaranteed oniy il the probability of failure of the system is 
less than or equal to 10-7 per year. 
The joint distribution of storm-surge leve1,basin level and 
wave energy was developed for The Netherlands a5 foliows. 
Frequency analysis was applied to available storm-surge-level 
data. Knowledge of the physical laws governing the storm- 
surge phenomenon was used to determine whether extreme 
water levels obtained by extrapolation were physically reahs- 
tic. ,4 Conditional distribution between storm-surge levels and 
basin levels was derived from a simple mathematical model of 
wind set-Ep and astronomical tide applied LO simulation of 
different strategies for closing the barrier gatcs. The basin level 
was found to be statistically independent of the wave energy.A 
conditional distribution between storm-surge levels and wave 
energy couId not be derived because of lack of data. Therefore, 
a maLhematica1 model m.5 developed considering the huo 
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 methud (Ang and Tang, 1984, p 333-433;Yen ef nl., 
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 mntribution of each 
basic variable (model parameters, input data, model correc- 
tion or safety factors, etc.) to the probabllity of failure of a 
given iomponer:: 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. 
Apphcatiun of the failure criterion uf 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-defencc system.Thus, the 
probability of system failure was 
of the probability of component failure, and the probability 
10-7 
determined as a function 
of failure resulting from mismanagement, lire and ship col- 
lision through application of fault-tree analysis {Ang and 
Tang, 1984, p. 496-498). The fault treu for determining the 
probability that parts of Zeeland are flooded because of fail- 
ure of components of the barrier, mismanagement, andlor 
malfunction of the gates is shown in Figure 8 1. By using the 
fault tree, thr design of the barrier was refined in evsry 
aspect and the specified safety criterion of lo-’ per year ivas 
achieved in the n o s t economical manner. 
Through application of sophisticated probabilistic 
techniques, Dutch engineers were able to reduce the design 
load for the storm-surge barrier by 40 pcr 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 ol the previous design standards. However. the 
previous design standards were implicitly set without any 
_ _ 
79 
coilsideration of the consequcnccs 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 haz- 
ard. 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 ot 
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 soci- 
etaIIy acceptabIe hazard levels and tried to determine real, 
consequence-based societally acceptable hazard levels. 
MINIMUM LIFE-CYCLE COST EARTHQUAKE 8.3 
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 i n the 
context of reliability (Pires rt d, 1996). Because it is not 
possible to avoid damage under all likely earthquake loads, 
thc 
must 
development of earthquake-resistant design criteria 
include the possibility of damage and an evaluation 
of the consequences of darnagc over the life of thc 
structure. To achieve this risk assessment for structures in 
earthquake-prone regions, Professor A. H-S. Ang and his 
colledgues at the University of California at Irvine haire 
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 
darnage-related costs (Ang and De Leon, 1996, 1997; Pires 
, 1996) and a constraint on the probability of loss of 
life (1.e~‘ eta!., 1997). 
The minimum life-cycle cost approach consists of five 
steps as follows (Pires et d., 1996; Lee et al., 1997). 
( 1 ) A set of model buildings is designed for different levels 
(3) 
et af 
of rellabihty (equal to one minus the probability of 
damage, pi) or performance following the procedure oi 
an existing design code. For reinforced concrete build- 
ings, this is done by following the design code except 
that the base-shear coefficient is varied from code 
values to yield a set of rnodcl buildings having different 
strengths, initial costs (construction or upgrading), and 
probabilities of damage. 
relation between the initial cost of the structure and 
the corresponding probability ofdamage under all pos- 
sible earthquake loads is established from the designs 
in step 1. 
(2) -4 
made 
For each design, the expected total cost of structura! 
damage is estimated as a function of the probability ot 
damage under all possible earthquake loads and is 
the initial cost. ‘The expressed on a common basis with 
damage cost includes the repair and replacement cost, 
C,, loss of contents, C,, economic impact of structural 80 
, 
Chapter 8 - Strategies for risk assessment - case studies 
- CLOSAlLE PART 
DAM SECTON 
SLIDING SYSTEM 
I (pyKp=+] 
MORE FlLUS SLlOlNG SYSTEM 
>BEARING CAP 
FOUNOATKJN 
for computation 
o l 
of the failure probability of the Eastern SchedIt storm-surge barrier in the Netherlands 
in 
(after 
and cost fatalities resulting from " " 
C] (8.1) 
Figure 8 1 - Fauh . tree 
,,I- " . 
damage, 
damage, 
tural damage, Cf 
C,.., 
(4) The expected risk of death for all designs under all 
likely earthquake intensities also is expressed as a func- 
of the probability of damage. rion 
(5) A trade-off between initial cost of the structure and the 
damage cost is then done to determine the target relia- 
bility (probability of damage) that minimizes the total 
expected life-cycle cost subject to the constraint of the 
socially acceptable risk of death resulting from struc- 
Vrrilinfi 1993) - - 
C,,, COST of injuries resulting from suucrural 
struc- the 
Dererrnination of rhe relarion between damage cost and 
Drobabilitv of damage 3 is the key cornmnent of steD 
the minimum life-cycle-cost earthquake-design method. 
The estimate of the damage cost is described rnathemat- 
icaliy as given by Ang and De Leon ( 1997) and summarized 
in the following. Each of the damage-cost components wrll 
depend on the global damage level, x , as. 
where j 
If 
= C,td 
= r, c, ec, in andfare as previously described in item 3 
the damage level x resdting from a given earthquake with tural damage. Comprthensivr risk msesmenf for natiird hazards 
a specified intensity A=LI, is defined with a conditional 
probability density function (pdf), IXxa(x), each of the 
expected damage cost items would be 
(8.2) E [ Cj"] 
8,3.1 
= Cj(~),fy~a(~) dx 
The intensity of an earthquake also may be defined as a pdf, 
,fA(u), and the total expected damage cost under all likely 
earthquake intensities may be computed by integration as 
where the bounds of integration are urnin and ama, which 
are the minimum and maximum values of the likelysange 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 earthquake- 
design method. These aspects of the method are described 
in the following sections. 
was developed for 
0.5; and C, = C,, D, 
Damage costs 
The global damage of a structure resulting from an earth- 
quake 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 rein- 
forced-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) structural- 
member damage index. Each of the damage costs then is 
related to the median damage index, D,, for the structure. 
The repair cost is related to D, on the basis of available 
structural repair-cost data for the geographic region. For 
example, the ratio of repair cost, C,, to the initial construc- 
tion cost, Ci, 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 retarion 
Mexico City by De Leon and Ang (1994) as: 
0 D, C, > 0.5 C, = 1.64 
C, 
D, 
where 
which is equal to 
Mexico City. 
(8.4) 
is the replacement cost of the original structure, 
1.15 times the initial construction cost for 
The loss of contents cost, C, is typically assumed to reach 
a maximum of a futed percentage of the replacement cost, C,, 
and to vary linearly from 0 to this maximum with D, for 
intermediate levels of damage to the structure (D, < i ) . For 
reinforced-concrete structures, the loss of contents was 
assumed to be 50 per cent for Mexico City (Ang and De Leon. 
0 Building B 
Building C 
Building D 
-7 
Building E 
X Building F 
1 0.25 0.50 0 
+ 
0.75 
Median Global Damage Index, d, 
Figure 8.2 - Damage repair cost function derived from datu 
for reinforced-concrete structures damaged by earthquakes 
C,,, 
in Tokyo {after Lee, 1996) 
1996,1997) and 40 per cent for Tokyo (Fires et al., 1996). Lee 
et al (1997) applied a piecewise-linear relation €or the range of 
D,,, for intermediate levels of damage. 
The economic loss resulting from structural damage, 
may be estimated in several ways. Ideally, this Ioss 
should be evaluated by comparing the post-earthquake eco- 
nomic 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 col- 
lapses 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, up to the limit of repairable 
damage (D, = 0.5). They developed this function on the 
basis of the average rental fees per square metre per month 
fur 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 (1-0) model to compute Cec The 
1-0 model (see Chapter 7 ) is a static general-equilibrium 
model that describes the transactions between various pro- 
duction sectors of an economy and the various final 
demand sectors. Lee aggregated 1-0 model data €or 46 eco- 
nomic 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 profes- 
sional, technical and business-service buildings reported by 
the Applied Technology Council (1985) to relate D, to eco- 
nomic losses as a piecewise-linear function. 
The cost of injuries, C,, also may be estimated in sev- 
(1996) and Lee er al. (1997) assumed 
that 10 per cent of all injuries are disabIing for D, 1, and 
that the loss due to a disabling injury was equal to the loss 
due to fatality (as described in the following paragraph). 
cost for non-disabling 
eral ways. Fires et al. 
el Pires af, [1996) estimated the 
injuries to be 5 million Yen (approximately US $50 000). A 
nonlinear function was used to estimate the cosr of injuries (D, < 1). Lee et a1 
et 
D,. 
f The cost of fatalities, C also may be estlmated 
ways as discussed in detai in Chapter 7. Ang and De Leon 
(1996, 1997) and Pires et a1 (1996) estimated the cost of 
fatalities on the basis of the expected loss to the national 
gross domestic product determined through the human- 
capital approach. Pires et al. (1996) estimated the number of 
fatalities per unit floor area of a collapsed building on the 
basis of data from the earthquake in Kobe, Japan. in 1995 
For intermediate values of D,n, Ang and De Leon (1996, 
made the cost of fatalities pro- 1997) and Pires el a!. [ 19%) 
portional to the 4th power of D,. Lee et d. (1997) estimated 
the cost of fatalities on the basis of the willingness-to-pay 
approach for saving a life through the revealed preferences 
method as given in Viscusi (1993). The difference in 
methodology between Pires et af. (1996) and Lee 
(1997) results in an increase in the cost of fatalities from 
approximately US $1 million for the human-capital 
approach, to US $8 million in the willingness-to-pay 
al. 
approach. Lee et al. (1997) used relations between collapse 
rate and fatality rate proposed by Shiono et al. (1991). 
Despite the differences in the economic-evaluation 
approaches taken by Pires er al. (1996) and Lee et al. (1997). 
the optrmal base-shear coefficients for the design of five- 
story reinforced-concrete buildings in Tokyo were 
essentially identical. 
8, 
for the intermediate damage range 
(1997) estimated the cost of nonfatal accidents using labour 
market data compiled by Viscusi ( 1993). Lee et al related the 
injury rate to the fatality rate with the ratio of the injury rate 
to the fatality rate expressed in terms of 
in several 
8.3.2 Determination of structural damage resulting 
from earthquakes 
Because the structural response under moderate and severe 
earthquake loads is nonlinear and hysteretic, the computa- 
tion of response statistics (e.g., the damage index) under 
random earthquake loads using appropriate random struc- 
tural models and capacities is an extremely complex task. 
Pires et al. (1 996) recommended that Monte Carlo slmula- 
tion be applied to determine the desired response statistics. 
The approach involves the selection of an appropriate struc- 
tural computer code capable of computing key structural 
responses, such as maximum displacement and hysteretic- 
energy dissipated. The earthquake ground motions used as 
input can be either actual earthquake records or samples of 
nonstarionary filtered Gaussian processes with both fre- 
quency and amplitude modulation (Yeh and Wen, 1990). In 
Monte Carto simulation, (1) a random earthquake load is 
selected, ( 2 ) the structural damage index is computed using 
the selected structural model considering uncertainties in 
the structural properties and capacities, and (3) the damage 
cost is computed as per section 8.3.1. This is essentially a 
numerical integration of equations 8.1 to 8.3. The prob- 
ability of damage and the probability of death resulting 
from earthquake damage also are computed in Monte Carlo 
simulation. An empirical ioint pdf amang the response sta- 
tistics is obtained by performing a large number of 
simulations. 
Chapter S - Strategies for risk assessment - case studies 
The uncertainties in the structural properties and 
capacities and critical earthquake load parameters may be 
modelled as lognormally distributed variables, and, thus, 
from the Central Limit Theorem, the distribution of the 
damage response statistics also can be expected to be log- 
normal. Therefore, to reduce computational costs and time, 
a relatively small number of simulations, on the order of a 
few hundred, are done, and the joint lognormal pdf of the 
response statistics is fitted from the empirical results. 
8.3.3 Earthquake occurrence model 
tions 8.3.1 
The expected damage costs computed as described in sec- 
and 8.3 2 are associated with structural damage 
or collapse resulting from future earthquakes, whereas the 
initial (or upgradrng) cost is normally a present value. Thus, 
the present worth of the respective damage costs will 
depend on the times of occurrence of these earthquakes 
(Ang and De Leon, 1996, 1997). A suitable earthquake 
occurrence model may be derived by assuming that: (1) the 
probability of occurrence of possible future damaging 
earthquakes at the building site constitutes a Poisson 
process, (2) earthquake occurrences and their intensity are 
statistically independent; and (3) the structure is repaired to 
its original condition after every damaging earthquake 
(Pires et al., 1996). These assumptions are common in 
seismic-hazard evaluation, although they may not always be 
appropriate as discussed in Chapter 5 If earthquake occur- 
rences follow a Poisson process, then the occurrence time of 
each earthquake is defined by the Gamma distribution (Ang 
and De Leon, 1996, 1997). The discount rate, q, used to 
transform future damage costs to present worth may be eas- 
ily incorporated into the gamma distribution for earthquake 
occurrences. This results in a present worth factor that is 
multiplied by the darnage cost computed as per sections 
8.3.1. and 8 3 2 to obtain the present cost of damages result- 
ing from possibIe Euture earthquakes. The present worth 
factor for a structural design life of 50 years in Mexico City 
7 
5 
CL 3 
3 
1 
0.1 0.025 0.075 0 0.05 
9 
Figitre 8.3 -Present worth factorfor Mexico City RS a function 
of the annual discount rate, 9 (after Angand De Leon, 1996) Comprehensive rrsk ussessment for natural kazurds 
is shown as a functlon of the discount rate in Figure 8.3 
(Ang and De Leon, 1946. 1997). Lee (19%) varied the dis- 
count rate between 2 and 8 per cent and found that although 
the total expected life-cycle costs decrease significantly as 
the discount rate decreases, the optrmai design levels and 
target reliabilities are much less sensitive to changes in dis- 
count rate. 
8.4 ALTERNATIVE APPROACHES FOR 
RISK-BASED FLOOD MANAGEMENT 
When considering flood-management issues, the question 
that must be answered is not if the capacity of a flood- 
reduction project will be exceeded, but what are the impacts 
when the capacity is exceeded, in terms of economics and 
threat to human life (Eiker and Davis, 1996). Therefore, risk 
must be considered in flood management. Flood risk results 
from incompatibility between hazard and acceptable risk 
levels measured in commensurate units on the same plot of 
iand (Gilard, 1996). However, in traditional flood manage- 
ment in many countries, an impiicit acceptable-risk level is 
assumed, and only the hazard level is studied in detail. 
In the USA, the implicit acceptable-risk level for flood- 
plain delineation and other flood-management activities LS 
defined by the requirement to protect the public from the 
flood exceeded once on average in 100 years (the 100-year 
flood). Linsiey (1986) indicated that the logic for this fixed 
level of flood hazard {implicit acceptable risk) is that every- 
one should have the same level of protection. However, he 
et ul , 1994) These approaches 
noted that because of the uncertainties in hydrological and 
hydraulic analyses all affected persons do not receive equal 
protection. He advocated that the design level for flood haz- 
ard should be selected on the basis of assessment of hazard 
and vulnerability In this section, two approaches for risk 
assessment for flood management are described. These are 
the risk-based approach developed by the US Army Corps 
of Engineers (USACE, 1996) and the InondabilitC method 
developed in France (Gilard 
offer contrasting views of flood-risk management. The risk- 
based approach seeks to define optimal flood protection 
through an economic evaluation of damages including con- 
sideration of the uncertainties in the hydrologic. hydraulic 
and economic analyses; whereas the Inondabilitk method 
seeks to determine optimal land use via a comparison of 
flood hazard and acceptable risks determined through 
negotiation among interested parties. 
8.4.1 Risk-based analysis for flood-damage-reduction 
projects 
A flood-darnage-reduction plan includes measures that 
decrease damage by reducing discharge, stage and/or dam- 
age susceptibility (USACE, 1996). For Federal projects in 
the USA, the objective of the plan is to solve the problem 
under consideration in a manner that will “... contribute to 
national economic development (NED) consistent with 
protecting the Kation’s environment, pursuant to national 
environmental statutes, applicable executive orders and 
83 
other Federal planning requirements (USA Water Resources 
Council, 1983)1’ In the flood-damage-reduction planning 
traditionally done by the USACE the level of protection pro- 
vided by the project was the primary performance indicator 
(Eiker and Davis, 1996). only projects that provided a set 
level of protection (typically from the 100-year flood) 
would be evaluated to determine their contribution to XED, 
effect on the environment and other issues.The level of pro- 
tection was set withour regard to the vulnerability level of 
the land to be protected. In order to account for uncertain- 
ties in the hydrological and hydraulic analyses applied in the 
traditional method, safety factors, such as freeboard, are 
applied in project design in addition to achieving the speci- 
fied level of protection. These safety factors were selected 
from experience-based rules and not from a detailed analy- 
sis of the uncertainties for the project under consideration. 
The USACE now requires risk-based analysis in the for- 
mulation of flood-damage-reduction projects (Eiker and 
Davis, 1996). In this risk-based analysis, each of the alterna- 
tive solutions for the flooding problem is evaluated to 
determine the expected net economic benefit (benefit 
minus cost), expected level of protection on an annual basis 
and over the prolect life, and other decision criteria. These 
expected values are computed with expliat consideration of 
the uncertainties in the hydrologic, hydraulic, and economic 
analyses utilized in plan formulation. The risk-based analy- 
sis is used to formulate the type and size of the optimal plan 
that will meet the study objectives. The USACE policy 
requires that this plan be identified in every flood-damage- 
reduction study. This pian may or may not be the 
recommended plan based on “additional considerations” 
(Eiker and Davis, 1996). These “additional considerations” 
include environmental impacts, potential for fatalities and 
acceptability to the local population. 
In the traditional approach to planning flood-damage- 
reduction projects, a discharge-frequency relation for the 
prolect site can be obtained through a variety of methods 
(see Chapter 3) These include a frequency analysis of data 
at the site or from a nearby gauge through frequency trans- 
position or regional frequency relations. Rainfall-runoff 
models or other methods described by the USACE (1996) 
can be used to estimate flow for a specific ungauged site or 
site with sparse record. If a continuous hydrological simula- 
tion model is applied, the model output is then subjected to 
a frequency analysis; otherwise flood frequency is deter- 
mined on the basis of the frequency of the design storm. 
Hydraulic models are used to develop stage-discharge rela- 
tions for the project location, if such relations have not been 
derived from observations. Typically, one-dimensional, 
steady flows are analysed with a standard step-backwater 
model, but in some cases, streams with complex hydraulics 
are simulated using an unsteady-flow model or a two- 
dimensional flow model. Stage-damage relations are 
developed from detailed economic evaluations of primary 
land uses in the flood plain as described in Chapter 7. 
Through integration of the discharge-frequency, stage- 
discharge and stage-damage relations, a damage-frequency 
relation is obtained. By integration of the damage-frequency 
relations for without-project and varlous with-project con- 
ditions, the damages avoided by implementing the vartous