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 302

( ) =

∫

( ) ( ) =

∫

() ()

PA a > PA aE > = dd d e P e Gae Ge d [12.3]

E E

where d e represents a small range of the continuous random variable E and
the integration bound is set over the entire range of E .

12.2.1 Derivation of the PBEE framework
Equation [12.4] and Fig. 12.1 show the PBEE framework established by the
Pacifi c Earthquake Engineering Research (PEER) Center (Moehle and
Deierlein 2004, Goulet et al. 2007, Solberg et al. 2008, Yang et al. 2009,
ATC-58 2010, Bradley and Lee 2010).

( ) =

∫ ∫ ∫

( ) ( ) ( ) ( )

λ DV > dv G dv dm d G dm edp d G edp im d λ im [12.4]

im dm edp

As implemented in Eq. [12.4], the PEER PBEE framework decomposes
the performance assessment into four analysis steps: (1) seismic hazard
analysis, (2) response analysis, (3) damage analysis, and (4) loss analysis. The
outcome of the analysis is then then combined using the total probability
theorem as described in Eq. [12.4]. The decomposition of the framework
into the individual analysis phases allows the experts from different disci-
plines to work independently towards the PBEE assessment. The following
paragraphs summarize the PBEE assessment in each of the analysis phases.

• Seismic hazard analysis: Probabilistic seismic hazard analysis is usually

used to describe the seismic hazard at a site. The outcome of the proba-
bilistic seismic hazard analysis is a seismic hazard curve, ( IM ), that

quantifi es the annual rate of exceeding a given value of seismic intensity
measure ( IM) . For example,

λ

( IM ) may represent the rate at which peak
ground acceleration will exceed 0.2 g for a particular site in a given year.
In addition, seismic hazard analysis is used to characterize the ground

λ

Seismic hazard
analysis
l

Response
analysis
G ( edp

Damage
analysis
G ( dm

Loss
analysis
G ( dv

( im ) | im ) | edp ) | dm )

12.1 Performance-based earthquake engineering framework (Yang
et al. 2009) dv represents the decision variable (such as repair cost);
dm represents damage measure (such as amount of crack in the
concrete shear wall); edp represents engineering demand parameter
(such as inter-story drift ratio); im represents intensity measure (such
as the peak grand acceleration).