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variable. This assumption significantly simplifies the analysis. Nevertheless, eq. (19.1)
can be computationally challenging especially if many structures need tobe evaluated.
IM
in eq. (19.1) can either be a single variable or a vector of variables. It can repre-
sent ground motion at the site of a network component or ground deformation measure.
The most commonly used ground motion
IM
s are peak ground acceleration and spec-
tral acceleration. Ground deformation
IM
s represent amount of lateral spreading and/or
settlement at a site.
IM
s are obtained through conventional probabilistic seismic haz-
ard analysis expressed as the annual probability of exceedence of the
IM
at a location.
To account for ground motion and ground deformation, the following formulation is
developed (Kiremidjian et al.,2006):
P
[
DV
≥
d
v
]=
I
A
dF
DV
|
DM
dF
DM
|
EDP
dF
EDP
|
IM
dF
IM
+
I
L
dF
DV
|
DM
dF
DM
|
EDP
dF
EDP
|
IM
=
S
H
dF
IM
=
S
H
+
I
L
dF
DV
|
DM
dF
DM
|
EDP
dF
EDP
|
IM
=
S
V
dF
IM
=
S
V
(19.2)
where
1 if there is no liquefaction, or landslide, or fault rupture at asite
0 if there is liquefaction orlandslide or fault rupture ata site
I
A
=
(19.3)
1 if there is liquefaction or landslides orfault rupture at a site
0 if there is no liquefaction or landslide or fault rupture at asite
(19.4)
I
L
=
A
=ground motion severity
S
H
= horizontal ground displacement due to either liquefaction or landslides or to dif-
ferential fault displacement
S
V
=verticalgrounddisplacementduetoeitherliquefactionorlandslidesordifferential
fault displacement.
Itisassumedinthisformulationthateitherliquefaction,orlandslides,ordifferentialfault
displacementfromfaultruptureoccuratasitebutnonesimultaneously.Similarly,ifthere
is either liquefaction or landslide or fault displacement, they govern the damage and any
damage due to ground shaking alone is considered to be already included in the ground
deformation analysis.
Giventhe
IM
,theengineeringdemandparameter(
EDP
)isevaluatedintermsofstructural
response measures such as deformations, accelerations, induced forces, or other appro-
priatequantities.Relationships between
EDP
and
IM
areobtainedthroughinelasticsim-
ulations, implementing structural, geotechnical, and non-structural damage models. The
EDP
s are then related to Damage Measures (
DM
), which describe the physical damage.
The
DM
sincludedescriptionsofdamagetostructuralelements,non-structuralelements,
andcontents,inordertoquantifythenecessaryrepairsalongwithfunctionalorlifesafety
