Conditional Equilibrium Analysis System of Service Level and Budget
Allocation for Road Pavement by Deterioration Model of MCI
Masato Miyata1, Takashi Nishioka1, Masanobu Nishiura1,Takahiro Hayashi1, Tadashi Okutani2, Ryoma Hiraoka1, Seigo Nasu3
Kochi University of Technology(space)
ABSTRACT: Asset management is the main stream for road structures, yet the management system todetermine service standard and maintenance/repair level is not established. For example of road pavement
these are set by traffic volume, by road grade, or just by the road condition.
This study is to establish methodology to determine appropriate service level and budget allocation forinfrastructure management, in this case for road pavement, with a new evaluation system of infrastructure
value by applying depreciation model which can evaluate correctly asset conditions corresponding tomaintenance/repair pattern. Management system also assures accountability of budget allocation by thisnumerical method. Service standard and maintenance/repair level was derived from equilibrium point at theservice market of driver’s demand function (satisfaction function) and service providing cost function.
Driver’s demand function was set up as an outcome (=satisfaction level to road condition) index. Service
providing cost function was derived by evaluating the optimized maintenance/repair pattern based on thelowest life cycle cost for the required asset value necessary to provide certain service level.
If we treat roads as service markets, this equilibrium analysis is able to determine the service level andbudget allocation in various roads in accordance to the equilibrium point of satisfaction level and service
level. It is also possible to determine the satisfaction level of drivers among roads under budget restriction byconditional equilibrium analysis, such as setting equal satisfaction standard for every road.
KEYWORDS: Appraisal method of public, Finance and institution theory, Maintenance/repair for civilengineering facilities

1.

depreciation model which can evaluate correctly

INTRODUCTION

asset conditions corresponding to maintenance/repair
Asset management is the main stream for roadpattern.

structures, yet the management system to determine

accountability of budget allocation by this numericalservice standard and maintenance/repair level is notmethod.

established. For example of road pavement these are2.

set by traffic volume, by road grade, or just by thePOLICY EVALUATION

roadcondition.

This

study

istoManagement

systemalsoassures

SERVICE LEVEL, ASSET VALUE AND

establish

methodology to determine appropriate service level

Ifand budget allocation for infrastructure management,

Depreciation Model for pavement can be set, andin this case for road pavement, with a new evaluation

asset value can be measured by taking the service

systemlevel which is traveling speed, environment andofinfrastructure

valuebyapplying

thepracticaldegradation

modelofNewsafety, it is possible to obtain maintenance pattern
and maintenance cost. Use of demand function withmarketing activity can take how mach does driver
could pay money for policy. And create supply
functionfromcostofservice

level

by

maintenance/repair and calculate equilibrium pointof demand /supply, it can be decided service level ofpavement or policy strategy.
Figure 2. Example of equilibrium analysis

Figure3. Equilibrium analysis below budget restriction

Figure 1. Service Level, Asset Value and Policy

However, the budget restriction is occurring in aEvaluation

general way. Two or more roads must remain inequilibrium simultaneously and there are required
TARGET

service levels lower than point of reach equilibrium

THEas dissatisfaction level and marginal cost. For

EQUILIBRIUM POINT OF A DEMAND

example, if administration can provide each roads

FUNCTION AND A SUPPLY FUNCTION

service level of traveling speed for driver’s

3. DETERMINATIONSERVICE

LEVEL

OFA
WITH

dissatisfaction level, it is possible for equilibrium
The service level of user dissatisfaction level cananalysis that keep define dissatisfaction level of allchange demand. In fact, to set service level asroads. The condition of dissatisfaction level forsatisfaction level, this is possible to get benefit thatdriver can be changed. Do set dissatisfaction level ofdissolve dissatisfaction as upraise service level. In

each road as total of roads dissatisfaction level ataddition, supply is the repair cost of service level tominimum and incorporate various constrained

maintenance. If demand function and supplyrestriction. Administration must set equilibrium

function were made, the best budget allocation inrestriction adequately through researching driver’s

each road could be decided by the equilibrium point

concept of values or demand.

when there is no budget restriction. Two or moreroads with their dissatisfaction level, each road can4.

decide service level.

FUNCTION ON PAVEMENTDERIVATIONOFTHE

DEMAND

4.1 SECTIONALIZE DEMAND FUNCTION

Table 1. Criterion of dissatisfaction

Decide the area from traffic volume and speed limit,

Dissatisfaction

and actually drove there. After that, define 0level

dissatisfaction level of road condition as a favorable

100%0km/h, Don't want to drive

speed and decide the favorable speed in each80%

Can't stand with this speed

classified area. In addition, this dissatisfaction level20%

Not to feel uneasy

has evaluated as a driver’s well-rounded and plotted0%

Comfortable speed, Not worrisome at all

Evaluation

favorable speed on graph. This graph showsfavorable speed is related to traffic volume and4.3 PREPARE DEMAND FUNCTIONS

speed limit. From this analysis, There exist a relationthat when traffic volume density increases, theFrom all of these data, demand function consistingfavorable speed allows down in each speed. Then15of 3 linear and 4 points (0%, 20%, 80% and 100%)

areas can be established corresponding to traffic

can be drawn by evaluated dissatisfaction level. In

volume 10000 car/day with speed limit asaddition, traffic volumes are 0-9999 car/day,40km/h, 50km/h and 60km/h.

10000-19999

car/day,

20000-29999

car/day,30000-39999 car/day and 40000-49999 car/day.

Figure 4. Traffic volume, speed limit and favorable

Figure 5. Demand function -Legal speed 40 km/h-speed

54.2 CRITERION OF DISSATISFACTION LEVELDERIVATIONOFTHE

SUPPLYFUNCTION ON PAVEMENT

It is necessary to fix dissatisfaction level of driver’s

5.1 MAINTENANCE/REPAIR METHOD FORspeed

GENERATE MINIMUM LCC

tomakedemand

function.

Then,

dissatisfaction level was evaluated as 0%, 20%, 80%
and 100%. Dissatisfaction level’s grades are writtenLife Cycle Cost (LCC) is the most importanton Table 1.

consideration when generating supply functions.
LCC may shift when service level or repair method
is changed in service period. Therefore, on pavement
asset management, it is necessary to constructminimum LCC and chose best choice of repair
method for service level. However, now CR (cut andoverlay) deterioration Model is only used. In fact,
this research use CR deterioration model only as

The figure below shows relative frequency of therepair method.

valuation (amount of the change) in each state ofdeterioration.

Thedeterioration

curve

which

becomes the mainstream of maintenance and repair

5.2 MAKING OF DETERIORATION CURVE

is analyzed in C(%) in construction method CR.
By evenly dividing a lot of analysis data, a curve

5.2.1 About MCI

corresponding to a physical characteristic can be
In order to make the deterioration function of themade.

road, the investigated data base about MCI is

0 % of initial value. Deterioration characteristics

analyzed.

vary in the state of no crack or some cracks. WhenThe road pavement is comprehensively

More than half of data used in analysis have

The evaluation equation

there is no crack (0 %), a different treatment is used.

consists of crack, C(%), rut, D(mm), and flatness,

When there is no amount of change (0%), a different

σ(mm).

treatment is also used.

evaluated by MCI.

C, D and σ substitute for four evaluation

expression to MCI.

By calculation result, MCI is

The more deterioration

occurs, the more dispersion occurs.

This could be

MCI is evaluated by

due to repairing frequency and kinds of pavement.

ten levels, and the tenth level has the best condition.

The use of the amount of the change with the highest

decided as minimum value.

relative frequency leads to extraction of the points
with the highest probability of deterioration.

5.2.2 About analytical data

Bigger the initial value, the bigger will be ⊿ C(%)
Adispersion. The amount of the change with the mostsmall point on the time axis is set to be an initialfrequency is extracted to be the amount of thevalue.

change in each deterioration state.

The following figure explains analytical data.

Date is obtained every three years. TheThe order of andifference in the measurement value in three years is

initial value is assumed to show deterioration. The

defined as ⊿ C.

mode value is considered to be the amount of theRut and flatness are similarly

defined as ⊿D and ⊿σ.

change with the highest likeliness of deterioration.
Similarly D and σ are analyzed, and a deteriorated
amount of the change is obtained.

Figure 6. Explanation of analytical data

Figure 7. Initial value C ⊿ C distribution

5.2.4 MAKING THE DETERIORATION CURVES
5.2.3 Extraction method by mode value

FOR C, D, AND σ

The number of data which extracted by the mode
value assumed to be a number of samples.
Variation (the amount of the change) in three years
which is shown in article 4.2 was calculated in oneyear.

The relation between an initial value andvariation (the amount of the change) was distributed

Figure 10. Deriving process 3 of deteriorationin ascending order in the number of samples usingcurve

the absolute value in an initial value. Next, thenumber of samples was calculated in 10 years.

The

5.2.5 DETERIORATION FORECAST OF MCI

approximation curve was made from a physicalcharacteristic of asphalt and it was made intoThefunction.

The approximation curve was integrated

deterioration model type of C, D, and each σ. The

in year of passage and the state of C (%), D (mm)calculated value was substituted for the model typeand σ (mm) are shown.

C shows suddenof MCI.

deterioration as time passes.

This is due to the fact

From the interview, it is said that repairing by CR

that cracks increase geometrically from one to two,

method reaches the recovery state of (C, D, σ)=(0%,from two to four.

0mm, 2.4mm) and MCI=9.4.

However the lowest

value of D was 2mm in data.

Assuming that thepassage

year

wassubstitutedfortheMCI in the passing year is forecasted.

recovery rate was (C, D, σ)=(0%, 2mm, 2.4mm) andMCI=9.0, deterioration of MCI was forecasted.

Figure 8. Deriving process 1 of deterioration curve

Figure 11. MCI deterioration forecast

5.3 CONVERSION CURVE
Supply function is a service level (as Maintenancecontrol index (MCI).) corresponding to repair cost ofFigure 9. Deriving process 2 of deterioration curve

maintain it. Demand function is a service level (astravel speed) corresponding to dissatisfaction level.
Therefore, to make equilibrium of supply anddemand, it clearly requires the relationship of MCI

and travel speed as service level. Then constructlinear model with hypothecated MCI and travelnspeed of driver’s needs. For example this model,

Cost =

when MCI is 2, pavement condition is not good andcan’t drive high speed. While on the other hand,when MCI is 10, pavement condition looks like flat

∑ ( Ni × Di ) × C

(2)

in

∑ Di × Yi

Cost = maintenance/repair unit cost of pavement area for the year (Yen/Year ⋅ m 2 )or such a not deteriorated pavement and driver cann = Number of area Y = Service period (30 years)
Ni = Number of maintenance/repair at area i

comfortably drive. In addition, experience was also

Di = Pavement area at area i ( m 2 )C = maintenance/repair cost（Yen / m 2 ）incorporated. After that, conversion curve function
was constructed (1). For the future, conversion curve

MCI of maintenance levels are 0.1 sectioning. Aftershould approximate like a driver’s feeling.

that, supply function is decided. In addition, supply
function’s X axis; MCI was changed travel speed by

MCI = S / 10 + 2,

But if S >= 80, MCI = 10.0

S = Travel speed(1)*conversion curve and maintenance/repair cost wasinstalled 2000 Yen/m2 irrespectively thickness ofasphalt and assortment.

5.4 SUPPLY FUNCTION
To construct supply function, the 2003 fiscal year
pavement conditions data were used. Pavement
conditions data can sectionalize about 100m andtotal section in Kochi prefecture are 3361. Then,
intended for 30 year service period, repair cost ofunit area for the year not dip from service level thatis set in period was calculated. First, set up MCI
level of maintenance, calculate term of next repair

Figure 12. Degradation of MCI by passing year and recovery byby MCI deterioration function. Next, divide MCI

repairsuch a more than maintenance level or less thanmaintenance level. The area under maintenance levelshould repair as quickly and start service afterrepaired. Furthermore, calculate period of not under
maintenance level area and decide number ofmaintenance/repair in each area for 30 years. Further,
decide maintenance/repair area with multiplication
number of maintenance/repair and pavement area,
because pavement area is different from all area.
After that, multiply maintenance/repair unit cost

Figure 13. Supply function

times area equals LCC of pavement area for 30 years.
Maintenance/repair unit cost of pavement area for

6

EQUILIBRIUM ANALYSIS

the year can be calculated with the division ofLCC and all pavement area with service period (2).

6.1 DETERMINATIONOFSERVICE

LEVEL

know how mach does driver could pay money for

AND BUDGET ALLOCATION

maintenance/repair cost of dissolve dissatisfaction.
Using decided demand function and supply function,

For all pavement roads, there maintenance speed

enforce equilibrium analysis. When Equilibrium

were decided, MCI and maintenance/repair cost andrestriction is “50% Dissatisfaction level in all pavement

figure 12 is a conclusion of maintenance/repair costroads”, service level and maintenance/repair cost canfor the year. When all pavement roads dissatisfaction

decide like figure 14 and 15.

level is 50%, total maintenance/repair cost of
pavement area for the year is about 540,000,000 Yen.
In addition, it can decide various maintenance/repair
patterns by changing dissatisfaction level 1%
sectioning.

Figure 14. Equilibrium analysis

Figure 17. Dissatisfaction level and cost for theyear

Figure 15. Equilibrium analysis as dissatisfaction level is 50%

6.2 TRANSFERFORCOSTOF

DISSATISFACTION LEVEL
If 50% dissatisfaction level of conspired
equilibrium can be set, it is possible to change fromdissatisfaction level to cost, because demand andsupply reached on the equilibrium point. That able toTraffic volume0-999910000-19999

20000-29999

30000-39999

40000-49999

Speed limit(km/h）

Confortablespeed (km/h)

Corresponding

405060405060405060405060405060―4353
30
3948
27
34
43
25
33
41
40
31
40

―
6.3
7.3
5.0
5.9
6.8
4.7
5.4
6.3
4.5
5.3
6.1
4.3
5.1
6.0

Total traffic area

MCI

2
Total maintenance/repair cost for the year (Million Yen)
CostArea (m )2Route 32 Route 33 Route 55 Route 56 All route (Yen/year・m ) Route 32 Route 33 Route 55 Route 56 All route―――
―
―
―
―
―
―
―
―
354,795
290,230
510,992
7,062 1,163,079
180.0
69.6
54.4
95.7
1.1
220.7
5,858
090,109
095,967
240.3
1.6
0.0
22.9
0.024.50047,235047,235
148.6
0.0
0.0
7.9
0.0
7.9
0
110,278
235,082
209,397554,756
167.7
0.0
18.7
44.1
40.2
102.9
107,03300
0
107,033
201.8
26.0
0.0
0.0
0.0
26.0
5,610
38,64843,934
134,087
222,279
143.8
0.8
5.2
7.5
21.4
34.9
0
76,706
136,555
58,337
271,597
156.0
0.0
13.2
24.9
10.7
48.8
0
0
44,914044,914
180.0
0.0
0.0
9.0
0.0
9.0
64,90066,17200131,072
140.9
9.1
8.8
0.0
0.0
17.9
0
17,556
0
46,69864,254
153.9
0.0
2.6
0.0
7.4
9.9
0092,100
092,100
173.6
0.0
0.0
18.1
0.0
18.1
12,636000
12,636
170.6
1.7
0.0
0.0
0.0
1.7
28,8310069,211
98,041
150.4
4.0
0.0
0.0
10.0
14.0
34,795032,629067,424
170.6
6.4
0.0
6.5
0.0
12.9

614,458

599,589

1,233,549

524,791

2,972,386

―

119.1

102.9

236.5

90.7

Figure 16. Maintenance/repair cost for the year of 50% dissatisfaction level

549.3

7CONCLUSION

The proposed system can determine service leveland budget allocation for road pavement. Inaddition,

it can establish accountability ofmaintenance/repair system by determining in line
maintenance/repair

cost

as

evaluation

ofdissatisfaction.
In

thisresearch,

only

driver’s

dissatisfaction was included. But it is necessary to
study about several benefits of society as noise andvibration for the future. In addition, there is anecessity to develop policy evaluation system bythis method.