Seismic risk and possible maximum loss (PML) analysis of reinforced concrete structures - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 735

conducted through probabilistic seismic risk analysis (PSRA) (e.g. Chang
et al. 2000; Porter et al. 2001; Cornell et al. 2002; FEMA 2003; Goulet et al.
2007; Yoshikawa et al. 2007, 2009).
The PSRA quantitatively evaluates, through probabilistic calculus, the
potential damage and loss that a certain group of structures in a region is
likely to experience due to various seismic events. Although details of the
existing methods are different, the fundamental framework is broadly
similar for these methods, and is based on the total probability theorem. It
combines seismic hazard (e.g. chance of experiencing strong ground motion
excitation) with structural vulnerability (e.g. chance of reaching a specifi c
damage/loss level for a given seismic intensity level). For instance, Chang
et al. (2000) and Yoshikawa et al. (2007, 2009) considered scenario-based
representation of seismic hazard, while Cornell et al. (2002) took advantage
of the seismic hazard curve that is often available from a reliable third body,
such as US Geological Survey (USGS). For vulnerability analysis, simpler
nonlinear static methods via pushover analysis can be used (Yoshikawa
et al. 2007, 2009). Alternatively, more rigorous methods, such as incremental
dynamic analysis (Vamvatsikos and Cornell 2004), can be adopted in the
assessment.
Mathematically, seismic risk due to a scenario earthquake can be defi ned
as the product of the seismic hazard function and the vulnerability or fragil-
ity of structures. By taking into account possible scenarios with occurrence
probabilities, overall seismic risk can be expressed as a seismic risk curve,
which is a plot of seismic risk measure (e.g. structural drift response or
specifi c damage level) as a function of occurrence probability. Moreover,
from a seismic risk curve, various risk indices, such as normal expected loss
(NEL) and probable maximum loss (PML), can be derived. These indices
are useful to summarize succinctly the important features of the seismic
risk, expressed in monetary terms, and facilitate the risk-based decision
making by various stakeholders (e.g. owner, investor, and risk consultant).
The adoption of such seismic risk indices has been greatly promoted in
Japan (e.g. Kanda and Okamura 2006); for instance, PML values are included
in fi nancial reports of building/property assets, providing valuable informa-
tion for investors and asset managers who are not familiar with engineering-
based indices (e.g. design base shear coeffi cient).
This chapter presents seismic risk analysis and risk quantifi cation, which
are essential in the decision-making process of catastrophe risk manage-
ment. The seismic risk obtained from both earthquake hazard curve and
vulnerability characteristics of structures is discussed. In particular, focus is
given to an analytical procedure for developing seismic risk curve, seismic
event risk curve, and scalar risk measures in monetary terms, such as PML
and NEL. Then, the proposed method is demonstrated through four case
studies for reinforced concrete structures in Japan, such as railway viaducts