Geoscience Reference
In-Depth Information
Linktraveltimeadjustmentsaremadeaftersomeusershavechosenaspecificlinkwhich
becomes less attractive to the other users. The adjustments are based on empirical data
that require calibration of the parameters
a
and
β
with location, time of day and road
type.
Transportationnetworkfunctionalitylossesaredirectlyrelatedtotraveltimedelay
D
per
unit time (e.g. average daily traffic) computed over the duration of component closure.
Operational loss as functions of time, where the time is duration of repairs of damaged
bridges, isused todetermine theloss ofthe system.
2.3. ESTIMATION OF TOTAL RISK
Theriskcanbeexpressedastheexpectedlossortheprobabilityofexceedingalosslevel.
Forspatiallydistributedsystemsestimationoftheprobabilityofexceedinglosslevelcan
be particularly challenging, because components of the system are subjected to different
ground motions with each earthquake event. Most frequently a simulation approach is
usedtoestimatethelosstoasystemwherecomponentandfunctionalitylossisevaluated
for each event and then the contribution of loss from all events is combined for a total
riskformulation.Inthefollowingsubsectionswefirstaddresstheestimationofexpected
lossandtheuncertaintyofthatloss,referredtoas
point estimates of loss
andthendiscuss
the total riskcurve analysis.
2.3.1. General formulation of point estimates of loss
The total expected loss foragiven event isgiven by thefollowing equation:
E
(
L
|
Q
)
=
l
s
f
L
s
|
Q
(
l
s
|
Q
)
dl
s
+
l
n
f
L
n
|
Q
(
l
n
|
Q
)
dl
n
(19.8)
where
L
s
isthestructural lossof the components
Q
isthescenario event
L
n
is the loss due to network disruption
f
istheprobability density function of the random variable
E
(
L
|
Q
) is theexpected value of loss
L
given the event
Q
In eq. (19.8) the decision variable
DV
has been expressed in terms of monetary loss
L
.
The event
Q
is defined by its magnitude, rupture length and location, rupture depth, and
dip angle of fault. With these specifications, the
IM
are estimated for events with rate
ν
i
at all bridge sites. The structural loss is evaluated based on the PEER methodology
discussed in the previous section. The operational loss in the same equation requires a
networkanalysismodelwithtrafficassignmentsfortheregionpresentedinthepreceding
section. It implies that traffic delays
D
on various links of the system are first computed
andthenthelosses
L
n
areestimatedasfunctionoftheoperationallossesduetothattime
delay
D
.
