Investment planning for sewer pipes rehabilitation based on
social cost
Aguru TANAKA
Candidate for the Degree of Master of Engineering
Supervisor: Naoyuki FUNAMIZU
Division of Built Environment
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INTRODUCTION
plans was developed. The model was verified, using
sewer network of Sapporo city.
Sewer pipe breakage has increased in Japan recently
TIME BASED MAINTEMANCE SCHEME
[1]. This is due to huge amount of hard assets and
aging of infrastructures. This sort of accidents
increases cost for repair and indirect social cost.
Time based maintenance (TBM) was applied as a
Social loss constitutes impacts on traffic and
basic planning scheme. The framework of TBM is
interruption of sewer collection service etc. Among
portrayed in Fig1. Investment for replacing old pipes
the social loss, effect on traffic is particularly huge
is conducted with 1 year interval and distributed to
because disruption of traffic spreads to surrounding
sewer pipelines. Pipe spans to be replaced are
area of accident point through affecting traffic flow.
selected based a priority standard which will be
Therefore, social loss is a critical factor of failure
discussed later. As the whole planning horizon is set
cost. Rising failure cost imposed by pipe failure
to 100 years, investment is assumed to be done 100
merits attention of public sectors and public
times.
authorities are concerned with asset management to
The developed model calculates failure cost with
prevent accident and reduce failure cost [2].
different budget level during the single investment,
Replacing old pipes is considered a measure for
as shown in Fig1. Let us call the model as ‘SI (single
avoiding accidents, though planning method for
investment) model’. Integrated failure cost during
replacement program has not been produced. Sewer
100 years is computed by replicating SI model 100
pipelines are generally gigantic, so planning of
times. Invested money for replacing old pipes is
replacement
important
certainly a part of cost. Hence, we define total cost
procedure. Setting the budget level and prioritizing
which is composed of failure cost and investment.
pipe sections affect the effectiveness of replacement
The optimal budget level is determined by finding
work. The research produces a procedure to come up
out the budget amount which achieves the minimum
with optimal replacement scheme from the view of
total cost.
program
is
critically
reducing failure cost. A model which describe the
Fig2 is GIS image of sewer pipelines of Sapporo
degree of failure cost under various maintenance
city which consists of approximately 200,000 pipe
1
portions. The budget selected for simulation is
pipe portions which do not have corresponding road
presented in Table1.
spans on the road network, social cost was
considered to be 0 yen.
Fig1 Framework of TBM
Fig3 GIS image of road network of Sapporo
MODELING FRAMEWORK
As stated, the model describes failure cost under
various budget levels. Failure process of sewer pipes
is modeled according to Weibull distribution. Effect
Fig2 GIS image of sewer pipelines of Sapporo [3]
of investment and repair is expressed as updating
failure probability. Determining if the failure occurs
Table1 Budget level [10million yen]
or not is done, using Monte Carlo method.
0
0.001
0.01
0.1
1
4
Weibull distribution is often used to describe
7
10
40
70
100
-
failure probability of materials and machinery [4].
As Weibull distribution has pipe age as independent
variable, it is suitable to model mechanical
SOCIAL LOSS
deterioration of materials.
Social loss is defined as negative impacts on traffic
μ
as the degree of traffic interruption is considered to
be huge. Increase of travel time due to road closure
where fi is failure probability, ti is pipe age, μ,m:
is estimated and integrated over all vehicles in the
parameters.
city. Therefore, intergrated travel time increase is
Flow of SI model is shown in Fig4. Annual budget is
taken
set as input parameter. Budget is distributed to sewer
as
social
loss.
Conversion
factor
40[yen/vehicle/min] is used to convert time increase
network
to
define
specific
pipe
spans
for
into monetary value. Road network of Sapporo
replacement. Selecting pipe segments is modeled as
(Fig3) was adopted for estimating traffic disruption
prioritization process. Expected failure cost is used
to reflect spreading nature of traffic impacts. In each
as criteria for prioritization,
estimation, one road span is assumed to be closed to
where si is social loss[yen], ri is repair cost[yen],
see the effect of breakage of one pipe section. For
2
pi(ti) is failure probability.
Ｍ
Repair cost is estimated using the following equation
[1].
M: number of failed pipes.
where x is diameter of sewer pipes.
The total cost during the planning horizon is written
After prioritization process, selected pipes are
as,
replaced and the effect of replacement is expressed
by updating pipe age to 0.
T: Planning horizon, I: investment during the
planning period.
Investment cost which is cost to replace old pipes is
computed using [1]
where mi is replacement cost [yen]
The total cost is calculated with various budget
levels to see the optimal budget amount which
achieves the minimum budget level.
RESULT AND DISCUSSION
Evaluated failure cost is shown in Fig5. We can
observe that failure cost reduces with increasing
budget level. The degree of reduction diminishes as
invested money increases. Then, the next question is
Fig4 Flow of SI model
which investment level is optimum?
Deterioration of sewer pipes is modeled as
update of pipe age. To determine whether pipe
sections fail or not, Monte Carlo method was applied.
Uniform random number is generated for each pipe
portion and compare with failure probability. if the
random number is larger than the probability, the
corresponding pipe section is considered to be failed.
Pipe age of failed pipe is updated to 0. The same
Fig5 Cost profile of TBM scheme. y axis is
procedure is performed for all pipe portions
cost[100million yen]
considered in the research. After failure judgment of
all spans, integrated failure cost over pipe network is
To answer this question, reduction of failure cost is
derived,
plotted along with investment in Fig6. When the
3
annual investment is 10 million yen, reduction of
to be an influential factor. This means that
total cost is maximized. Reduction of total cost is
misevaluation of social loss could cause huge
expressed as the following equation,
divergence of optimal investment from the real value.
Reduction of failure cost – investment
As
we
increase investment,
investment
The result of the sensitivity analysis shows that
cost
estimation of social cost should be conducted
increases which tradeoff reduction of failure cost.
carefully to avoid miss estimation of the optimal
Hence, the effect of investment should be evaluated
value.
by net cost reduction considering increase of
investment cost.
Fig8 Sensitivity analysis
REFERENCES
Fig6 y axis is monetary value [million yen]
[1] Ministry of Land, Infrastructure, Transportation
If we compare the optimal investment case and no
and Tourism. http://www.mlit.go.jp/
investment case in terms of cost structure, the
[2] S.J.Rubin, A call for water utility reliability
benefit of replacement program is clearly seen
standards: Regulating water utilities’ infrastructure
(Fig7). By investing 10 million yen per year for
programs to achieve a balance of safety, risk, and
replacing old pipes, the total cost declines.
cost, National regulatory research institute, 2010.
[3] Sapporo city government, Department of sewer,
http://www.city.sapporo.jp/gesui/
[4] K.Fujiu, C.Miyauchi, Statistical life data analysis
of sewers and prediction of future rehabilitation
needs, Journal of construction management and
engineering, Vol14, 65-72, 2007.
Fig7 Cost structure of the optimal investment case
Moreover, sensitivity analysis was conducted to see
which cost factor affects the optimal value of
investment (Fig8). As a result, social loss was found
4