Seismic risk assessment of water supply systems - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 666

where Q - i is the customer demand at node i , and n i 0 and n i are number of
satisfi ed customer demands before and after imposing damage scenario,
respectively.
Plate IV ( between pages 452 and 453) shows an example of the simulated
spatial distribution of water outage areas after the Scenario 175 Verdugo
earthquake according to GIRAFFE simulation. The unsatisfi ed demand
nodes are shown by yellow dots and the pipes with no fl ow as a result of
earthquake-induced damage are shown by red lines. Note that the pipes
with no fl ow in the undamaged LADWP system to provide redundancy in
the system are shown by pink lines. As a result of high PGV values in the
upper right quarter of the fi gure and concentrated damage in those areas,
most water outage clusters in the upper right quarter. Sparse water outage
also occurs in other parts of the system and the overall system serviceability
index SSI 0.81. Similar procedures were applied for each of the 59 sce-

nario earthquakes and the simulation results from the 59 individual sce-
nario earthquakes were integrated in the form of risk curves, as described
in the next subsection.
In addition, GIRAFFE was utilized to study the effects of water loss from
storage tanks. Leaking and ruptured pipelines will draw down the water
levels in tanks and local reservoirs, thereby further reducing fl ow and pres-
sure in the pipeline network. Evaluating the effects of water losses from
tanks and reservoirs may provide a more representative model for post-
earthquake performance because it will take water utility crews some time
to isolate leaks and pipeline breaks to reduce their impact on local water
sources.
For each simulation that accounts for tank water losses, after all negative
pressure nodes were eliminated and the simulation results were obtained,
the water levels of the storage tanks in the system were updated according
to the fl ow rates determined from the hydraulic analysis to simulate the
impact of leakage from damaged pipelines for a 24-hour period after the
earthquake. The system with the updated tank water level was reanalyzed
in GIRAFFE to eliminate additional negative pressure nodes resulting
from the loss of storage water in tanks, and the second set of simulation
results with a 24-hour period of running tanks was generated.

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24.6.2 Risk curves
The simulation results for the 59 scenario earthquakes were integrated in
the form of risk curves, plotting the variation of annual exceedance fre-
quency as a function of system serviceability index SSI. Each scenario
earthquake is characterized by an optimized annual frequency of occur-
rence, as shown in Table 24.2. If n mc Monte Carlo samples were generated
for each of the 59 scenario earthquakes and the corresponding n mc set of