Assessing seismic risks for new and existing buildings using performance-based earthquake engineering (PBEE) methodology - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 303

motions that can be used in the response analysis. Details of the ground
motion selection and scaling procedures can be identifi ed in many
leading research articles for additional discussion; see Abrahamson
(2006) and Haselton et al. (2009).

• Response analysis: Once the seismic hazard is quantifi ed, the response

of structural and nonstructural components under seismic excitations,
sometimes referred to as engineering demand parameters ( EDP ), is
obtained through the use of analytical, physical, or hybrid models. The
outcomes of response analysis are statistical functions that relate engi-
neering demand parameters (such as drift or stress) to the hazard expe-
rienced by the structure.

• Damage analysis: Based on test data, post-earthquake reconnaissance

reports, or analytical simulation, the damage states of structural and
nonstructural component damage can be characterized in terms of fra-
gility curves. The fragility curves are cumulative distribution functions
(CDFs) representing the probability that a damage state has been
reached or exceeded given a quantitative measure of the EDP . The
outcome of the analysis are quantitative description of the damage state
when the EDP has reached a certain threshold values.

• Loss analysis: Loss analysis translates the results of the damage analysis

to decision variables that can be used by building owners and stakehold-
ers to make a risk management decision. The outputs of the loss analysis
can be, for example, the probability of exceeding a certain threshold for
the repair cost during a period of time, the expected monetary loss for
repairs of the structure, and the total monetary loss for the structure
with a particular probability of exceedance.

Random variables are used to quantify performance and to preserve the
statistical uncertainties inherent to the problem. The seismic hazard analysis
uses a probabilistic analysis of the seismic environment, ground shaking
attenuation relations, and site conditions to derive a model for the seismic
shaking intensity at a site. The output of the seismic hazard analysis is a
statistical function that represents the annual rate of exceedance of certain
intensity measures im ). Response analysis uses the EDP as the

random variable and produces the conditional probability function,
G ( edp | im ), to represent the statistical relationship between EDP and IM .
Damage analysis uses the damage measure ( DM ) as the random variable
and the results of the analysis is a conditional probability function,
G ( dm | edp ), that relates DM and EDP . Lastly, the loss analysis uses decision
variable ( DV ) as the random variable and produces the conditional prob-
ability function, G ( dv | dm ), that relates DV and DM .
The decomposition of the PBEE process outlined above is made possible
using the following statistical independence assumptions:

λ ( IM >