Geoscience Reference
In-Depth Information
by transforming the network component PDFs of loss,
f
L
, into the frequency domain,
multiplying them in the same domain, and then apply the inverse transformations to
obtain the probability density in the time domain. In order to reduce the error in trans-
formation, two PDFs are transformed successively until the variables are exhausted and
the total loss PDF is estimated. It is recalled that eqs. (19.14) and (19.15) are for a given
event and the distributions areconditional on that event.
2.6. EVALUATION OF THE NETWORK FUNCTIONALITY LOSS
Undoubtedly, the network performance drops after an earthquake event because of its
decrease capacity or components closure. In order to quantify this reduction in function-
ality we first estimate the expected value of the operational loss of the network rela-
tive to a baseline performance, which is the performance prior the earthquake. Then the
uncertaintyonthatlosscanbecomputedconsideringvarioussourcesofvariabilityinthe
system.
2.6.1. Expected value of network functionality loss
Damage to network components defines the reduction in flow capacity. For example, a
bridge with 20% damage will have to reduce its traffic by the same percentage in order
to meet itsdemand. When the damage exceeds 40%, we assume that the bridge isclosed
and passengers have tomake adetour.
Traveltimedelaysareestimatedbysubtractingbaselinetraveltimesfromthetraveltimes
inthenetworkwithreducedcapacity.Itispossibletoconvertthisdelaytomonetaryunits,
if we know thevalue of timeand thenumber of passengers.
Bridge repair duration will depend on the damage level of the bridge and will vary for
each bridge type. In order to have a realistic assessment of the total operational loss,
we have to account for its evolution over time. To this effort, we are using the HAZUS
estimates for restoration times for the different damage states. Network performance
analyses are conducted immediately after the event and again after 1, 3, 7, 14, 30, 180
and 365 days. The results of these analyses are a mapping of the decrease in operational
loss over time as bridges in the system are successively brought to back to full function-
ality. The total indirect loss is then the integral of this curve and must be added to the
structurallossinordertoestimatethetotallossofthescenario.Thisoperationrepresents
the expected value of functionality lossfor thetransportation network.
2.6.2. Uncertainties in network functionality loss
There are numerous sources of uncertainty in the network functionality. These include
thetrafficassignmentmodel,thepost-eventbridgeclosuredecisions,therestorationtime
for individual bridges given their damage state, the value of trips taken and the number
and value of trips lost. Treatment of these uncertainties requires that the transportation
system be modeled as a stochastic network. Such a development is beyond the scope of
the current paper and will be addressed insubsequent research.
