Civil Engineering Reference
In-Depth Information
The fi nal balance of cost and income over the life-cycle period (Porter
et al.
, 2004) should be the key factor in evaluating the feasibility of a water
pipeline-maintenance project. This balance, which is referred to as the value
index
V
0
, is the resulting value that can be produced by the project opera-
tion, and can be expressed as (Imai
et al.
, 2010):
(
)
VBIECC
0
=+−− +
[23.41]
0
M
in which
B
,
I
,
E
,
C
0
, and
C
M
are the accumulated total amounts of social
benefi t, income gain, operational expense, initial cost, and maintenance cost,
respectively, during the life of the project. If a seismic investment,
C
S
, is
taken into account, the value index
V
1
can be represented by
(
)
=−
S
[23.42]
VBIECC C VC
1
=+−− + +
0
MS
0
It should be noted that the seismic vulnerability of the lifeline system
causes not only structural damage to the network links but also functional
damage to the demand nodes in terms of serviceability loss. This loss results,
in turn, in the loss of social benefi t,
Δ
B
, and income gain,
Δ
I
. The value index
V
2
in this situation is given by
(
)
−++
(
)
⋅
( )
VBIECC C C
=+−− + +
ΔΔ
BI
1
t
[23.43]
2
0
MS
R
EQEQ
[[
( )
]
=− + ⋅
VCC
1
t
0
S
EQEQEQ
where
C
R
is the restoration cost and
C
EQ
is the seismic damage cost, which
is defi ned as
CC BI
EQ
=+ΔΔ
[23.44]
R
and
1
:
an earthquake occurs over some time duration
t
⎩
Q
an earthquake does not occur over some time duration
E
( )
=
1
t
EQ
EQ
0:
t
EQ
[23.45]
In particular, for the major damage mode, Equation (23.43) can be
expressed as
{
}
major
(
)
−
major
major
major
major
VBI
=+−− + +
ECCCC
⋅
1
=
VCC
−
+
⋅⋅
1
D
EQ
0
MS
0
S
2
EQ
D
EQ
EQ
[23.46]
in which
C
EQ
jor
is the seismic damage cost in the major damage mode. It is
noted that in the formulation of the value index of Equations (23.41) to
(23.46), a discount rate is not taken into account because the public budget
accounting system for water supply projects cannot manage free cash fl ow
for its own fi nancial investment.
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