Seismic risk and possible maximum loss (PML) analysis of reinforced concrete structures - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 737

level. Typically, it can be the peak ground acceleration (PGA) or peak
ground velocity (PGV) at bedrock. The seismic hazard curves at specifi c
locations are derived from probabilistic seismic hazard analysis (Cornell
1968; McGuire 2004; see Chapter 1), and may be available from the respon-
sible governmental body/institution, such as the Japan Meteorological
Agency and the USGS. By introducing the seismic loss function f C ( c | )

(precisely, this is the conditional probability density function of earthquake
loss c for given ground motion level

α

), the seismic risk curve G C ( c ) can be
formulated by the convolution of the two random variables (Cornell et al.
2002):

α

∞ c

⎡

max

⎤

() =

∫

()

∫

( )

Gc p α f ς α dd ς α [27.1]

⎢ ⎥

C A C

⎣ ⎦

0 c

The G C ( c ) represents the probability of exceedance of seismic loss c ,
noting that the seismic intensity parameter

is integrated out. This means
that, in the assessment, uncertainty of various possible ground motion levels
is taken into account. For risk-based earthquake risk management, it is
useful to express the seismic risk measure c in monetary values, such as
structural loss (direct loss), operating loss (indirect loss), or outage days
(suspension period), facilitating the informed decision making and risk
communication by different stakeholders. The analysis procedure of Equa-
tion 27.1 is illustrated in Fig. 27.1. It is noted that other scalar risk measures,
such as expected seismic loss, standard deviation of seismic loss, and frac-
tiles of seismic loss (corresponding to specifi c selected probability levels),
can be calculated based on G C ( c ).

α

27.2.2 Seismic event risk curve based
on multi-event model

There are alternative formulations/methods to derive seismic event risk
curves. In this subsection, a method that adopts the so-called multi-event
model is introduced (Chang et al. 2000; Yoshikawa et al. 2009). The advan-
tage of this method, in comparison with the above analytical method based
on the seismic hazard curve, is the explicit consideration of earthquake
scenarios that contribute to seismic hazard at a site. The main idea is to
retain earthquake scenario information during the seismic risk assessment;
this approach is particularly useful clearly when dominant earthquake
sources are identifi ed (e.g. major faults and subduction zones in Japan and
California), and facilitates the transformation between multi-event-based
results and specifi c-scenario-based results.
The fi rst step in the multi-event model is to develop an inventory of pos-
sible seismic events at the proximity of a building site. This can entail, for