Probabilistic seismic hazard analysis of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 19

knowing the annual occurrence probability of the factor of safety being less
than 1.0, which can be readily obtained from the fi gure.

1.3.2 PSRA

PSRA evaluates the seismic performance of a structure quantitatively and
is one of the key building blocks in the PBEE methodology (Cornell et al. ,
2002; McGuire, 2004; Ruiz-Garcia and Miranda, 2007). The output renders
the statistical distribution of an engineering seismic demand/damage quan-
tity, such as the maximum inter-story drift over building height, and can be
further utilised to estimate seismic loss, and eventually to make decisions
regarding seismic risk mitigation (Goda and Hong, 2006; Goulet et al. , 2007).
The essential component for extending PSHA to PSRA is the seismic
vulnerability/fragility function, which describes the statistical characteristics
of an engineering demand/damage parameter (EDP) for a given ground
motion intensity level (e.g. PGA and SAs). Then, the occurrence rate of
EDP ν EDP exceeding a specifi ed damage level (e.g. maximum inter-story

drift ratio of 0.03 for moderate damage) is given by:

( ) =

∫

( ) ( )

ν EDP ≥ edp P EDP ≥ edp gm f gm d gm , [1.8]

GM

Ω

GM

where P ( EDP Ω GM are

the probability density function of a ground motion measure and its domain
for integration (note: it is common to defi ne f GM based on the annual
maximum quantity so that

≥ edp | gm ) is the vulnerability function; and f GM and

ν EDP is interpreted as the annual exceedance

rate), respectively. A plot of ν EDP as a function of edp is a seismic risk curve.

Using a simulation-based PSHA approach, it is straightforward to carry
out numerical evaluation of Equation [1.8]. For instance, various ground
motion parameters for each scenario event in a synthetic catalogue are
readily available from PSHA to assess seismic vulnerability of a structural
system. Consider that the seismic performance of a conventional wood-
frame house in Vancouver needs to be assessed for the 16th scenario event
in Fig. 1.4 ( M w

44.9 km). For such purposes, an existing
structural model for typical wooden houses with unblocked plywood shear-
walls and gypsum wall board (GWB) interior fi nish (Ventura et al. , 2002;
White and Ventura, 2006) can be adopted. For characterising the seismic
performance of a house model subjected to various ground motion levels,
incremental dynamic analysis can be conducted by taking into account
regional features of seismic activities (consistent with PSHA) and by select-
ing and scaling adequate sets of ground motion records based on condi-
tional mean spectra (Baker, 2011). Such a model has been developed by
Goda and Atkinson (2011) by considering the maximum inter-storey drift
ratio as EDP and SA at 0.3 s as GM . Figure 1.8a shows the incremental

= 7.04 and r jb =