Civil Engineering Reference
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the presented model, the adopted meshing solution has several advantages
and it is also convergent to the individual building modelling upon mesh
refi nement. However, attributing the sampled physical damage state to
all
the buildings of a given type within a cell can lead for coarse meshes, as in
this simple example, to an overestimation of the likelihood of extreme
damage states. Similarly, plot (b) shows how the long pipelines connecting
the three urban areas are automatically discretised into smaller segments,
in a relatively rough manner. Large values for maximum pipe segment
length employed in the discretisation will result in biased estimates of
extreme damage states. Caution should therefore be used in selecting these
meshing parameters when looking for a good compromise between com-
putational effort and accuracy of the results.
The functional and, ultimately, the social consequences of the above state
of physical damage are illustrated in Fig. 18.13. The reduced service level
in the EPN and WSS can be measured with different metrics. Plots (a) and
(b) provide maps of the voltage and water head ratios VR and HR. These
quantities, computed in the demand nodes of the two networks, are repre-
sented on the tributary cells, which are hatched with a shade of increasingly
darker grey corresponding to lower values of either VR or HR. Given the
relatively strict tolerance on the voltage of supplied electric power, the
darker grey areas in both cities B and A, where VR < 0.9, can easily be
associated with a likely failure in dependent systems. This indeed is what
happens in the WSS, where cities B and A have no water at all (black cells),
since in both cases the pumping stations had EPN reference nodes located
in the VR < 0.9 areas. This loss of functionality affects the number of dis-
placed people, shown in Fig. 18.13(d). The pattern of plot (b) is repeated,
with the populations of cities B and A almost entirely displaced as a result
of a severe utility loss. Fatalities instead, being just a function of direct
physical damage to buildings, are mostly located in city B, where damage is
non negligible, as already shown in Fig. 18.12(c). More details on these
aspects can be found in Cavalieri
et
al.
(2012).
18.8.3 Results for the whole simulation
This section presents consolidated results obtained from the entire simula-
tion. Figure 18.14 illustrates the seismic hazard. In particular, plot (a) com-
pares the histogram of relative frequency of the sampled magnitude values,
with the original probability density obtained as a weighted average of the
truncated exponential distributions relative to each source:
3
∑
(
)
λ
fM m
=
0
ii
()
=
fm
i
=
1
[18.17]
M
3
∑
λ
0
i
i
=
1
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