STRUCTURE AND INFRASTRUCTURE ENGINEERING 1525
seismic retrot of existing bridges considering the eciency of
the post-disaster evacuation and relief. e other aspect is related
to the post-earthquake trac-carrying capacity and trac cost
according to the vulnerability and trac analysis results. e
assessment results can be used to estimate the trac status of
the damaged HBN in emergency conditions.
3. Topological analysis of the HBNs
e post-earthquake emergency responses of an urban city,
including the evacuation of residents and rescues of injured per-
sons, are dependent on the connectivity of the transportation
network system and the damage level of the individual bridges.
Aer an earthquake event, the connectivity of a transportation
network system is an important measure for assessing the traf-
c-carrying capacity of an HBN. erefore, the topological anal-
ysis of the network is essential to understanding the structural
properties of the network and identifying which bridges are the
important components of a city in terms of connectivity. An
HBN is assumed to comprise several nodes and edges. A node of
the bridge network is dened as the location where the highway
segments intersect, and an edge is dened as a highway segment
connecting two neighbouring nodes. erefore, from a mathe-
matic point of view, the HBN of an urban city can be represented
as a graph model, G(V,E), which consists of a nite set of vertices
(or nodes) V and a nite set of links (or edges) E.
For a graph model of the transportation network system,
the connectivity can be measured by the topological properties,
named betweenness, path length and clustering coecient, to
interpret the involvement of bridge nodes and links in the whole
network (Brandes, 2001). However, although betweenness, which
is related to the number of shortest paths through a vertex or link,
can measure the importance of each component of the network at
some aspect, it is still not enough to fully interpret the connectiv-
ity of an HBN without considering the path length characteristics
of a transportation network system. erefore, the average path
length of a network, which is dened as the average length of all
of the shortest paths, is used to consider this inuence (Watts &
Strogatz, 1998). If some bridges failed in a seismic event, resulting
in the disappearance of the corresponding edges in the graph
model, the vehicles would search for other paths to reach the
target destinations due to the substitutability of the bridge link.
e average path length of the new network,
L
�
0
(e
ij
)
, including
the failure of edge e
ij
is then calculated by
where
L
�
min
(v
i
, v
j
)
is the shortest distance between vertices v
i
and
v
j
considering the failure of edge e
ij
. us, a new parameter can
be dened to measure the change of the average path length of
the network due to the failure of the edge as follows
e above parameter can eectively represent the passing e-
ciency of the network. A larger value of this parameter means
that the corresponding link more signicantly impairs the traf-
c-carrying capacity of the HBN due to the failure of this link.
e betweenness and average path length mainly represent
the inuences of a node or link failure on the connectivity of
the global network. For a local region, the clustering coecient
(1)
L
�
0
(e
ij
)=
1
N(N − 1)
∑
v
i
≠v
j
∈V
L
�
min
(v
i
, v
j
)
(2)
R
(e
ij
)=L
�
0
(e
ij
)−L
0
Figure 1.Flowchart of the seismic performance assessment methodology.
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