Using a performance-based earthquake engineering (PBEE) approach to estimate structural performance targets for bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 530

(3) distribution of damage measures (DMs; e.g. physical condition of a
damaged element) given EDPs, and (4) evaluation of the probability of
exceeding decision variables (DVs; e.g. human or collateral loss, post-earth-
quake repair time, and other parameters of interest to an owner) given
appropriate DMs. These four steps in the performance-based design meth-
odology are linked through the theorem of total probability. The relations
between key variables in the PEER-PBEE framework are illustrated in Fig.
20.1 and the PBEE integral is presented in Equation 20.1:

( ) =

∫∫∫

( ) × ( ) × ( ) × ( )

ν DV G DV DM d G DM EDP d G EDP IM ν IM

[20.1]

where (DV) is the annual rate of exceeding the decision variable;

G ( DV | DM ) is the probability of exceeding the decision variable given
the damage measure; d G ( DM | EDP ) is the probability of exceeding the
damage measure given the engineering demand parameter; d G ( EDP | IM )
is the probability of exceeding the engineering demand parameter given
the intensity measure; and

ν

( IM ) is the annual rate of exceeding the ground
motion intensity measure (Cornell and Krawinkler, 2000; Krawinkler, 2002).
Integrals in Equation 20.1 represent the variability in each key item,
conditioned on the previous variable in the chain. In order to simplify
the problem, the distributions of the variables are assumed to be indepen-
dent of each other. For example, DM is a function of EDP only and knowl-
edge of IM provides no additional information (Baker and Cornell, 2003).
This assumption permits the user to treat each part of the integral
separately.

ν

PSDM

Damage
measure

Ground motion
intensity

Definition of
seismic sources

•

Definition of suitable
ground motion
intensity measures

•

• Performance

assessment

Seismic source
characterization

• Selection of proper

ground motion
prediction
equations

•

• Nonlinear structural

analysis

Earthquake
scenarios

Engineering
demand parameter

PSHA

Fragility

20.1 PEER performance-based earthquake engineering framework
(PSDM = probabilistic seismic demand model, PSHA = probabilistic
seismic hazard analysis).