Assessing the seismic vulnerability of masonry buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 347

0.8

LS EC8 soil type B
NLS EC8 soil type B
PP Combined
PP IP
PP OOP
Mean CC Comb
Mean CC IP
Mean CC OOP

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0

5 10 15 20

Displacement (cm)

25 30 35 40

13.6 Performance points in the acceleration/displacement space and
average capacity curve for three mechanism types for the signifi cant
damage limit state.

13.4 Stochastic and epistemic uncertainty
quantifi cation
Advanced uncertainty modelling and probability of occurrence of given
phenomena are usually confi ned to the hazard component of the risk equa-
tions, but when probabilistic models are developed for vulnerability com-
ponents, they usually relate to very simplifi ed modelling of seismic response
of the structure. It is hence interesting to analyse the previous results by
taking into account the distinction between structural behaviours and loca-
tions of the buildings.
Fragility curves for different limit states are modelled as the lognormal
distribution and its parameters are obtained by calculating mean and stan-
dard deviation of the performance point displacement. Specifi cally, the
average displacement for each limit state can be calculated as:

1
n

∑

( )

Δ LS = e

μ

ith μ = ln x [13.6]

and the corresponding standard deviation as:

∑

( )

2

ln l xx

n

−

1
2

2

μσ + 2

β = e e

σ

− 1 with σ = [13.7]

LS