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Pavement Repair Marginal Costs: Accounting for
Heterogeneity Using Random-Parameters Regression
Anwaar Ahmed, A.M.ASCE1; Tariq Usman Saeed, A.M.ASCE2; Jackeline Murillo-Hoyos3;
and Samuel Labi, M.ASCE4
Abstract: Highway agencies seek to establish road user cost responsibilities, in the form of marginal costs associated with the maintenance
and rehabilitation (M&R) of their existing infrastructure, on the basis of lifecycle data on the infrastructure usage levels and repair costs. Due
to the differences in physical characteristics and operational conditions across individual pavement segments, it can be hypothesized that the
current practice, which imposes a uniform average user fee to cover repair damage of all pavements systemwide or within specific families, is
not equitable. To address this issue, this paper assesses the marginal costs of pavement damage by accounting for segment-specific hetero-
geneity. To do this, the paper uses a random-parameters (RP) regression model. Through application of the developed model, the paper shows
that the M&R marginal cost differs significantly across pavement segments. The results suggest that it is feasible for agencies to develop fee
structures that charge different highway user fees for individual highway segments on the basis of the damage the users inflict to the pave-
ment. This outcome can help agencies introduce more equitable charging for the use of their highways. DOI: 10.1061/(ASCE)IS.1943-
555X.0000367.© 2017 American Society of Civil Engineers.
Author keywords: Cost allocation; Tolling; Weight-distance charging; Overweight fees; Direct user charging; Marginal cost; Random
parameters; Pavement cost.
Introduction
Infrastructure agencies routinely face the challenge of raising funds
for the upkeep of their physical facilities. These funds may be gen-
erated through governmental subventions of budgetary allocations
or through direct or indirect user charges. In the context of highway
infrastructure, agencies seek knowledge of the infrastructure dam-
age caused by each user class so that they can more effectively
carry out their management functions of cost allocation, tolling,
weight-distance charging, overweight (OW) fee design, and pro-
spective direct user charging. For their business processes in this
area of highway administration, highway agencies have established
aggregate values of the marginal cost of highway pavement repair
for the various pavement families (highway functional classes) in
their jurisdictions. In this regard, studies of marginal pavement
maintenance and rehabilitation (M&R) cost seek to estimate the
expenditures associated with the repair of pavement damage caused
by the different road user groups (vehicle classes). That way, the
road users can be charged on the basis of the additional repair cost
for which they are responsible. The term additional is suggestive of
extra M&R costs for the upkeep of existing infrastructure. Thus it is
useful to point out the dichotomy between the terms average cost
and marginal cost. The average cost is the total M&R cost divided
by the total usage (e.g., number of vehicles), whereas marginal cost
is the incremental pavement M&R cost due to an additional vehicle
on a given highway; the latter is more relevant in the context of
charging for the use of existing infrastructure.
Reliable determination of the marginal costs can help a high-
way agency to establish the appropriate cost responsibilities of
each vehicle class with regard to the maintenance and rehabilita-
tion of their existing pavement infrastructure. One way to do this
is to use, from in-service pavement sections, empirical data on the
life-cycle usage levels and repair costs. However, the issue of
equity also needs to be addressed: there exist significant differen-
ces in the physical characteristics and operational conditions
across pavement segments even within a given pavement family.
Using a simple average for each user family does not account for
the wide variability in the repair costs within the class and could
result in most users overpaying or underpaying their fair share of
pavement damage. As such, it can be hypothesized that the current
practice, which generally imposes a uniform average user fee to
cover repair damage of all assets within a family, may not be equi-
table as desired.
To address this issue, this paper assesses the marginal costs of
pavement damage by accounting for the segment-specific hetero-
geneity using a random-parameter (RP) regression model. The
paper first presents and discusses past work in this area, identifies
its scope and objectives, and then describes the nature of the data
collection. This is followed by an explanation of the study meth-
odology, presentation and discussion of the results, and a statement
on its conclusions and possible future research.
Outline of Past Research
The financial sustainability of civil infrastructure systems and
equity among users continues to be a matter of great concern
1Associate Professor, National Univ. of Sciences and Technology,
NUST Main Campus, H-12, Islamabad, Pakistan (corresponding author).
E-mail: dranwaar@scee.nust.edu.pk
2Graduate Research Assistant, Dept. of Civil and Environmental Engi-
neering, Massachusetts Institute of Technology, 77 Massachusetts Ave.,
Cambridge, MA 02142; Lyles School of Civil Engineering, Purdue Univ.,
550 Stadium Mall Dr., West Lafayette, IN 47907. E-mail: tusaeed@mit.edu
3Assistant Professor, School of Civil Engineering and Geomatics,
Universidad del Valle, Cali 760013, Colombia. E-mail: jmurill@purdue.edu
4Professor, Lyles School of Civil Engineering, Purdue Univ.,
550 Stadium Mall Dr., West Lafayette, IN 47907. E-mail: labi@purdue.edu
Note. This manuscript was submitted on February 12, 2016; approved
on January 6, 2017; published online on March 25, 2017. Discussion per-
iod open until August 25, 2017; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Infrastructure
Systems, © ASCE, ISSN 1076-0342.
© ASCE 04017012-1 J. Infrastruct. Syst.
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in the development and management of these systems (Jeon and
Amekudzi 2005). In light of this, infrastructure agencies adopt a
variety of policies to ensure the adequacy of funds for the renewal
and upkeep of their physical assets (TRB 2011). Sources of infrastruc-
ture funding include government subvention, indirect user charging
(such as a fuel tax), or direct user charging [such as tolls, vehicle miles
traveled (VMT) fees, weight-distance taxes, and OW vehicle permit
fees] (Cambridge Systematics et al. 2006;Agbelie et al. 2016). With
regard to most mechanisms for user charging—particularly, direct user
charging—agencies seek to develop efficient and equitable levels of
fees for each user group. It is therefore important to establish the ap-
propriate amount to charge each user group (vehicle class) on the basis
of their shares of not only the consumption of the physical infrastruc-
ture (pavements and bridges) but also the impairment of the opera-
tional quality in terms of safety and mobility.
With regard to pavement damage in particular, which is the fo-
cus of this paper, such user fees can be established on the basis of
the marginal cost of pavement damage. The marginal cost can be
defined as the increase in pavement M&R expenditure due to the
addition of one usage unit [vehicle, weight in tons, equivalent sin-
gle axle loads (ESALs), and so on] in the traffic stream (Bruzelius
2004). Using the actual marginal cost estimated from data on high-
way traffic loading and repair expenditures at in-service pavement
sections, appropriate fees for vehicles can be established and
existing fees updated so that vehicles pay their fair share of high-
way consumption. To facilitate this, a number of studies have been
carried out worldwide, and the overarching scheme has been to sum
all the repair costs (rehabilitation, maintenance, or both) over the
infrastructure life and to attribute such costs to the different user
groups (vehicle classes) in a manner that is commensurate with
their respective incremental damage contributions to the pavement.
In the existing literature, at least two alternative approaches have
been used to estimate the marginal damage cost of highway pave-
ment consumption: the so-called econometric approach and the
so-called engineering approach (also referred to as the indirect ap-
proach, and which often involves perpetual overlays of the pavement)
(Bossche et al. 2001;Bruzelius 2004). A key aspect of each approach
is the establishment of a functional relationship between the pave-
ment repair cost (the dependent variable) and the independent var-
iables (some usage variable such as traffic volume or ESALs, climate,
and so on) and differentiating the established function withrespect to
the usage-related variable to yield the marginal M&R cost.
In certain cases of marginal pavement damage cost (MPDC)
estimation, the modeling of pavement deterioration can provide
some input. Recent pavement modeling that is useful for this
purpose includes the work of Kobayashi et al. (2010) and Nam
and Adey (2013). In cases where the deterioration model provides
a distinction between the damaging effects of load and nonload con-
tributions to deterioration (Martin 1994;Li et al. 2002), the models
can provide further useful information for estimating the pavement
damage cost responsibilities across load and nonload factors, and,
across the load factors, for estimating the responsibilities across the
road users on the basis of their loads (Volovski et al. 2015).
Newbery (1988), a pioneer of the indirect or perpetual overlay
indirect approach, established pavement repair marginal costs in
the range $0.0013–$0.0258=ESAL-km (in 1983 dollars). Small
et al. (1989) expanded Newbery’s approach and estimated M&R
marginal cost for different road classes under two separate scenar-
ios of optimal practice and actual practice. Vitaliano and Held
(1990) used data from New York and estimated an average M&R
marginal cost of $0.076 per ESAL-mi, or $0.0472 per ESAL-km
(in 1990 dollars). Gibby et al. (1990), using California data, esti-
mated separately the average annual maintenance cost per heavy
truck and per passenger car. Using simulated data from both new
and in-service pavements in Ontario, Hajek et al. (1998) estimated
the pavement damage cost occasioned by the various truck classes
under different load scenarios. Using maintenance cost and traffic
data from Austria, Herry and Sedlacek (2002) estimated that the
M&R marginal cost for trucks with different gross vehicle weights
(GVW) varies from $0.0007 to $0.023 per vehicle-km (in 2002
dollars). Lindberg (2002) used the Newbery approach to estimate
marginal rehabilitation cost separately for trucks and passenger cars
for different road classes. Schreyer et al. (2002) estimated M&R
marginal cost separately for passenger cars and trucks for the Swiss
highway network (Schreyer et al. 2002;Link 2002). Link (2002)
estimated marginal rehabilitation cost for different truck classes;
the average value of maintenance marginal cost was found to be
$1.486 per vehicle-km (in 2002 dollars). Using data from the
Swedish road network, Haraldsson (2007) estimated the marginal
maintenance cost for heavy vehicles on paved or gravel roads;
the estimated marginal maintenance cost ranged from $0.0007
to $0.0176 per ESAL-km (in 2007 dollars). Anani and Madanat
(2010) presented a methodology to estimate marginal M&R cost
for interrelated rehabilitation and periodic maintenance treatments;
they accommodated the interaction effect of periodic maintenance
and rehabilitation and argued that the estimation of marginal main-
tenance cost should include not only maintenance or rehabilitation
but both treatment categories; this position was subsequently ech-
oed by Ahmed et al. (2014). These studies implicitly assumed that
all pavement damage was due to load.
Other studies have assumed (mostly implicitly, a few explicitly)
that the shares of load damage and nonload damage are equal. The
very few researchers who explicitly recognized, measured, and
accounted for nonload effects include Martin (1994), who used data
from Australia and determined that the load and nonload shares of
pavement damage expenditure are approximately 55 and 45%,
respectively. Li et al. (2002) used data from the state of Indiana
to estimate the load and nonload share of highway rehabilitation
expenditure for flexible, rigid, and composite pavement and esti-
mated the marginal cost of pavement rehabilitation expenditure
as $0.023–$0.038=ESAL-mi, or $0.0143–$0.0236=ESAL-km (in
2000 dollars), depending on the pavement type. Fig. 1presents
a summary of the results of past research.
The past research established aggregate values of damage cost
either systemwide (for all pavements in a region) or for each family
of pavements. Recognizing, however, that the physical character-
istics and operational conditions across the constituent pavement
assets of each family differ widely, it can be argued that the current
practice, which imposes a uniform average user fee for all assets in
that family to cover repair damage of the assets in the family, is not
an equitable situation. This is because such a fee will be lower than
0
10
20
30
40
50
60
70
80
Newbery
(1998)
Vitaliano &
Held (1990)
Li & Sinha
(2000)
Herry &
Sedleck
(2002)*
Haraldsson
(2007)
tso
CR&MtnemevaPlani
graM
($/ESAL-km x 103)
* Marginal Pavement M&R Cost per vehicle-km
Fig. 1. Summarized results of past research
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the actual damage cost for certain assets and higher for other assets;
thus, in assessing the marginal costs of asset damage and establish-
ing updated fees, the segment-specific heterogeneity that leads to
such deviations needs to be taken into consideration so that more
equitable user charges can be realized.
Scope and Objectives of Analysis
The paper estimates the pavement M&R marginal cost using in-
service data on pavement repair costs and traffic loads experienced
at hundreds of individual pavement segments. To account for
unobserved heterogeneity (unobserved factors that vary across
the individual observations, i.e., pavement segments), the paper’s
methodology includes random-parameter modeling. The intent is
also to investigate the hypothesis that the marginal cost varies sig-
nificantly for the different pavement sections and therefore each
segment needs to be considered separately for user charging pur-
poses. The paper’s methodology is demonstrated using data from
state highway sections but can be replicated using local road data to
establish the marginal costs of pavement damage at local roads or
other jurisdictions.
Data Collection and Collation
Historical data on pavement repair cost and traffic at in-service high-
ways were collected from the contracts and construction division
and the traffic statistics division of a highway agency. Climate
data (annual average freeze index, mean annual temperature, aver-
age annual precipitation, and average number of wet days) were ob-
tained from the National Oceanic and Atmospheric Administration
(NOAA) database and the INDIPAVE-2000 Indiana pavement
research database (NOAA 2015;Labi 2001). Pavement condition
data for different pavement segments were obtained from the
Pavement Management Division of the Indiana Department of
Transportation (INDOT 2011) and INDIPAVE-2000. The treatment
application intervals of standard maintenance and rehabilitation
treatments were obtained from past studies (Irfan et al. 2009;Irfan
2010;Khurshid et al. 2011).
A number of maintenance and rehabilitation treatments
typically used for flexible and rigid pavement were considered.
For the flexible pavement, maintenance treatments included micro-
surfacing, thin hot mix asphalt (HMA) overlay, functional HMA
overlay, structural HMA overlay, and resurfacing (partial 3R
standards); maintenance treatments for rigid pavement include rubb-
lization of portland cement concrete (PCC) pavement and overlay,
HMA overlay, and crack-and-seat PCC and HMA overlay. The treat-
ments were applied in different years, therefore the cost data were
converted into base-year dollars (of year 2010) using Federal High-
way Administration (FHWA) highway construction price indices.
The summary statistics of key variables are presented in Table 1.
Study Methodology
As evidenced in past research in statistical methodology, RP
models can identify the existence of unobserved heterogeneity
in data. This is because, unlike their traditional fixed-parameter
(FP) counterparts, RP models allow the parameter values to vary
across the observations (Hensher and Greene 2003). In the past,
RPs have been applied in different modeling techniques to account
for unseen heterogeneity in the data (Brownstone and Train 1998;
McFadden and Train 2000;Eluru et al. 2008;Anastasopoulos and
Mannering 2012). In cases where the parameter values are con-
strained to be constant despite a priori intuition that they seem to
actually differ across observations, the resulting FP model may
yield estimates that are biased, inefficient, and inconsistent
(Washington et al. 2011).
In estimating the pavement M&R marginal cost, the general
procedure is to first establish a statistical relationship between
pavement M&R expenditures and the different factors responsible
for or associated with such cost: road use such as traffic volume or
loading, climate severity, geographic location, and so on. Differen-
tiating the statistical function with respect to some road-use vari-
able, such as ESALs, yields the marginal M&R cost. For this, the
ordinary least square (OLS) FP regression is a widely used tech-
nique (Hajek et al. 1998;Herry and Sedlacek 2002;Schreyer et al.
2002;Link 2002). In the present study, both FP and RP models
were developed.
Different functional forms were investigated. The selected
form is
lnCðiÞ¼β0þβiðln XiðtÞÞþβiðln XiðntÞÞþεið1Þ
where CðiÞ= pavement repair cost ($/lane-km) over the lifecycle;
i= observation; β0= constant term; βi= vector of the estimated
coefficients; XiðtÞ= road-use-related explanatory variable; XiðntÞ=
non road-use explanatory variables such as climate, pavement
features, and geographic location; and εi= normally distributed
disturbance term.
It is assumed that each pavement segment has unique character-
istics in terms of geographic location, traffic and climatic loading,
surface and structural deterioration, quality of initial pavement
construction and rehabilitation/periodic maintenance treatment
application, weather condition at time of treatment application,
and contractor skill and workmanship. Data on some of these attrib-
utes are unavailable in the agency databases. Therefore it was con-
sidered appropriate to explore for segment-specific heterogeneity,
whereby each segment is considered as having some unique,
unobserved properties including pavement construction quality,
subsoil type (subgrade quality) and moisture conditions, and main-
tenance history. It was assumed that the model parameters are
randomly distributed. Thus, under such circumstances, βican be
defined as a function of a vector of estimable parameters and a
Table 1. Descriptive Statistics of Key Variables
Variable Mean SD Minimum Maximum
Dependent variable: cost per lane-kilometer of M&R treatment (2010 constant $) 73,950 47,832 6,210 338,876
Total ESALs sustained by the pavement segment 2,375,610 2,819,633 8,095 18,883,667
Annual average daily traffic (AADT) 10,819 10,660 58 70,880
Annual average daily truck traffic (AADTT) 1,659 2,219 5 14,817
Annual average freeze index (degree-days) 514 238 0 889
Average annual precipitation (mm) 1,117.6 76.2 889 1,219.2
Average annual number of wet days (average days with precipitation) 117 12 95 134
Total (lifecycle) freeze index (degree-days) 5,857 3,031 0 12,852
Total (lifecycle) precipitation (mm) 11,709 2,591 4,775 18,745
Total (lifecycle) number of wet days 1,336 300 580 2,304
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randomly distributed term ui(with zero mean and standard
deviation σ)asfollows(Greene 2010;Washington et al. 2011):
βi¼βþuið2Þ
The random term is statistically significant if its standard
deviation is significantly different from zero; otherwise, it reduces
to zero. Halton (1960), Bhat (2003), and Train (2003) showed that
simulated maximum likelihood estimation with a Halton sequence
approach can be used to estimate the RP model. The method of
maximum simulated likelihood has been found effective in over-
coming the higher dimensional numerical integration issues arising
from efforts to maximize the log-likelihood function containing
an unobserved heterogeneity term (Craig et al. 2003). The use of
Halton draws has been found effective in such situations, which
speeds up the convergence and assumes that intelligent draws
are more effective compared to a random sample of draws (K. Train,
“Halton sequences for mixed logit,”working paper, Univ. of
California, Dept. of Economics, Berkeley, CA; Bhat 2003;
Anastasopoulos and Mannering 2009;Greene 2010). Random
parameters are assumed to be normally distributed, and 200 Halton
draws were found to be sufficient for model parameter estimation.
Results and Discussion
Using data from 508 pavement segments that received some repair
action between 1994 and 2006, fixed and random parameter regres-
sion models were estimated with the help of statistical software
LIMDEP (Greene 2010). A number of alternative functional forms
were investigated, and best model was identified as follows:
lnðM&RCPLKmÞ
¼9.911 þ0.0623ðlnTESALsÞþ0.0005ðAAFZÞ
þ0.006ðAWETDÞþ0.0004ðTPPTÞ−1.232ðPTYPEÞ
þ0.160ðFHMAOÞ−0.851ðMSTMTÞþ0.239ðDISTINDÞ
ð3Þ
The details of response and explanatory variables are provided
in Table 2.
Of the seven significant variables, three had statistically signifi-
cant RPs. The standard deviations of the parameter density for
total ESALs, total precipitation, and the microsurfacing indicator
variable were found to be statistically significant. These RPs had
standard deviations that were statistically different from zero. For
all the RPs in this study, it was found that the normal distribution
provided the best statistical fit. To test the overall significance
of the RP model over the FP model, a likelihood ratio test was
used. Knowing the log-likelihood for FP and RP models at con-
vergence, the likelihood ratio test statistic is given as (Washington
et al. 2011)
χ2¼−2½LLðβFPÞ−LLðβRP Þ ð4Þ
where LLðβFPÞ= log-likelihood at convergence of the FP model;
and LLðβRPÞ= log-likelihood of the corresponding RP model.
The resulting χ2value is 10.14 with 3 degrees of freedom. The
critical value of χ2ðχ2
ð0.05;3ÞÞis 7.815. Thus it is seen that there
is at least 95% confidence that the RP model provides statistically
superior results compared with its FP counterpart.
The forecasting accuracy of the developed model was evaluated
using the mean absolute percent error (MAPE). This concept,
widely used in validating statistical models by measuring the
deviation between actual and predicted responses (Washington et al.
2011), is given as follows:
MAPE ¼1
nX
n
i¼1100 ×ðAi−PiÞ
Ai ð5Þ
where Aiand Pi= actual and predicted damage costs, respectively
($/lane-km). MAPE values closer to zero indicate greater accuracy
of the estimated model. A calculated MAPE value of 0.41 for
the estimated model indicates that model has reasonable goodness
of fit.
Table 2. Estimation Results of RP and FP Linear Regression Models
Response variable = ln(M&RCPLKm)
[ln(pavement repair cost, $/lane-km) variable description]
Fixed parameter Random parameter
Parameter
estimated t-stat
Parameter
estimate t-stat
Constant 10.465 19.529 9.911 38.735
Traffic variable
lnTESALs [natural logarithm of total traffic (total ESALs)] 0.0548 2.538 0.0623 (0.0243) 6.013 (33.445)
Nontraffic variables
AAFZ [annual average freeze index (degree-days)] 0.0005 4.666 0.0005 9.183
AWETD [average number of wet days
(average number of days with precipitation)]
0.006 2.295 0.006 4.948
TPPT [total precipitation (mm)] 0.0004 3.434 0.0010 (0.0002) 7.170 (22.591)
PTYPE [pavement type indicator variable
(1 if pavement is flexible, 0 otherwise)]
−1.222 −8.482 −1.232 −17.111
FHMAO [functional HMA overlay indicator variable
(1 if treatment is functional HMA overlay, 0 otherwise)]
0.157 3.075 0.160 6.588
MSTMT [microsurfacing indicator variable
(1 if treatment is microsurfacing, 0 otherwise)]
−0.883 −7.579 −0.851 (0.474) −15.299 (9.673)
DISTIND [district indicator variable
(1 if district is Seymour, 0 otherwise)]
0.239 2.871 0.239 6.147
Log-likelihood at convergence −354.558 −349.486
Number of observations 508
Note: Standard deviation for random parameters presented in parentheses.
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To facilitate discussion of the results, the final model’s signifi-
cant explanatory variables were categorized as follows: traffic,
climate, and treatment history.
Traffic Variable
The positive sign of traffic loading (total ESALs) suggests that
pavement segments with higher traffic loadings are associated
with higher levels of pavement repair expenditure. The parameter
estimate for the natural logarithm of this variable was found to b
e normally distributed with a mean of 0.0623 and a standard
deviation of 0.0243. The mean and standard deviation are statisti-
cally significant, indicating that the influence of the variable is dif-
ferent for different pavement segments. Approximately 99.47% of
the distribution is greater than zero [Fig. 2(a)]. This indicates that
for almost all road segments, an increase in total ESALs over the
analysis period resulted in increased M&R expenditure, albeit with
varying magnitude across the roadway segments. Because M&R
marginal cost is obtained by differentiating the estimated model
with respect to the traffic variable (ESAL), the differences in
the parameter estimates for traffic load from segment to segment
therefore means that the marginal damage cost is different across
the pavement segments. This is an important finding: because mar-
ginal damage cost varies from segment to segment, it seems ap-
propriate to charge highway users different fees on different
highway functional classes and on different road segments (same
functional class).
Climate Variables
The model results indicate that a higher annual average freeze index
resulted in higher levels of repair expenditures over the analysis
period, which is generally consistent with previous studies (Irfan
et al. 2009;Khurshid et al. 2011;Ahmed et al. 2013). Pavement
segments located in freeze-prone climate regions are expected to
experience more severe damage and thus higher maintenance
expenditures compared with those in low-freeze regions. For exam-
ple, the model suggests that Interstate pavements in freeze regions
of the state have as much as 56% higher damage costs compared
with those in relatively non-freeze regions of the state.
The parameter estimate for the precipitation variable was found
to be normally distributed with a mean of 0.0004 and a standard
deviation of 0.0002 (Table 2). For given distributional parameters,
98.14% of the distribution is greater than zero and 1.86% is less
than zero [Fig. 2(b)], indicating that for a majority of the road seg-
ments, the precipitation had an intuitive impact on M&R marginal
cost. The total number of wet days in the year was found to
have significant influence on pavement damage costs. Pavement
segments located in high-precipitation regions are expected to
have higher M&R marginal cost and thus higher maintenance
0
2
4
6
8
10
12
14
16
18
-0.05 0 0.05 0.1 0.15 0.2
0
100
200
300
400
500
600
700
800
900
-0.002 -0.001 0 0.001 0.002 0.003 0.004
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-3 -2 -1 0 1 2
(a) (b)
(c)
Fig. 2. Random parameter distributions for the three RP variables: (a) natural logarithm of total traffic (total ESALs); (b) precipitation; (c) micro-
surfacing treatment
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expenditures compared with those in low-precipitation regions.
For example, the model suggests that Interstate pavements in
regions of the state having relatively high precipitation have as
much as 26% higher damage costs compared with those regions
with relatively low precipitation.
Treatment History
The indicator variable for a functional HMA overlay treatment
indicates that the pavement segments that had received this treat-
ment were associated with higher repair costs compared with those
that had received other treatments. This indicates a treatment-
specific characteristic pointing toward lower performance of func-
tional HMA overlay treatment compared with other treatments.
This finding could prompt highway agencies to revisit the current
specifications for HMA overlay as a functional treatment. The
model parameter for the variable representing historical microsur-
facing treatment application was found to be associated with lower
M&R cost per lane-mile. This finding is intuitive. Microsurfacing is
a preventive maintenance treatment used to retard the pavement
deterioration, thus those pavement segments that received this treat-
ment had overall lower damage cost ($ per lane-mile). The param-
eter estimate for the microsurfacing indicator variable was found to
be normally distributed with a mean of −0.851 and a standard
deviation of 0.474 (Table 2). For given distributional parameters,
almost 96.38% of the distribution was less than zero [Fig. 2(c)],
indicating that for majority of the road segments, microsurfacing
treatment resulted in decreased M&R expenditure, albeit at varying
rates.
Estimation of Marginal Pavement M&R Cost
The MPDC is the cost of an additional traffic unit (ESAL) on a
given pavement segment. This cost can be estimated by differen-
tiating the estimated model [Eq. (3)] with respect to the road-use
variable (in this case, ESAL). Following the procedures estab-
lished in Johansson and Nilsson (2004) and Anderson (2007),
the marginal cost of repairing pavement damage through main-
tenance and rehabilitation (M&R) is determined in this paper
as follows:
MðM&RÞ¼∂C
∂ESAL ¼∂ln C
∂lnESAL×C
ESALð6Þ
MðM&RÞ¼ðφÞ×C
ESAL¼ðElasticityÞ×ðAverage costÞð7Þ
where MðM&RÞ= marginal pavement damage repair cost; φ=
cost elasticity, and in log-log specification the corresponding
parameter estimate (0.0623) has the interpretation of elasticity
(Table 2).
Therefore the marginal cost is the product of cost elasticity and
average cost. On the basis of the elasticity values and average pave-
ment M&R cost, the mean MPDC was estimated as $0.0018 per
ESAL-km ($0.003 per ESAL-mi). Using segment-specific param-
eter estimates obtained from the model, the MPDCs were estimated
for individual pavement segments of the different functional classes
(Interstate, U.S. Roads, and State Roads). The results (Table 3
and Fig. 3) further confirm the hypothesis that the MPDC signifi-
cantly varies across the pavement segments even within each
pavement family. This, plausibly, is due to the segment-specific
heterogeneity associated with unobserved attributes associated with
each segment’s subgrade quality, quality of contractor responsible
Table 3. Segment-Specific Estimates of Marginal Damage Cost for
Selected Pavement Segments
Highway
functional
class
Highway
route name
Indiana
county
Marginal costs
of pavement damage
($/ESAL-km)
Interstates I-65 Jasper 0.00312
I-469 Allen 0.00028
I-70 Marion 0.00175
I-65 Lake 0.00156
I-74 Franklin 0.00096
I-64 Crawford 0.00128
U.S. Roads US-136 Fountain 0.00435
US-24 Allen 0.00079
US-136 Hendricks 0.00341
US-421 Clinton 0.00199
US-31 Bartholomew 0.00183
US-231 Dubois 0.00313
State Roads SR-59 Clay 0.00105
SR-3 Noble 0.00077
SR-26 Grant 0.00130
SR-25 Fulton 0.00392
SR-101 Ripley 0.00184
SR-68 Gibson 0.00320
Fig. 3. Segment-specific estimates of marginal damage cost for selected
pavement segments: (a) Interstates; (b) U.S. Routes; (c) State Routes
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for the pavement construction, supervision and quality assurance
of workmanship and materials at the time of construction, and
subsoil moisture content. These results support the hypothesis
that the MPDC can differ significantly across pavement segments.
As such, it seems justified to propose the charging of different
highway user fees for each individual pavement segment. For ex-
ample, as the calculated damage costs for the sample segments in
Table 3show, the highest marginal cost is 15 times greater than the
lowest cost.
Example Application
In order to facilitate replication of the paper’s methodology or to
facilitate implementation via a computer program or spreadsheet,
this section provides detailed sample calculations of damage cost
using the developed model. Consider a six-axle tractor-semitrailer
with a GVW of 97,000 lbs. Using the fourth power law and a
standard truck configuration (GVW of 97,000 lbs with 12,000
lbs on a single axle, 34,000 lbs on a tandem axle, and 51,000
lbs on a tridem axle) the truck produces 2.60 ESALs. Consider
that this truck travels 10,000 km annually on each of the following
segments: Interstate 65 in Jasper County, Interstate 469 in
Allen County, and U.S. Road 24 in Allen County. The marginal
damage cost can be estimated using study results and Table 3as
follows:
Interstate 65 M&R Cost ¼0.00312ðESALsÞðDistanceÞ
¼$0.00312ð2.6Þð10,000Þ¼$81.12
Interstate 469 M&R Cost ¼$0.00028ð2.6Þð10,000Þ¼$7.28
U:S:Road 24 M&R Cost ¼$0.00079ð2.6Þð10,000Þ¼$20.54
Clearly, if an average of these costs was used as is done in tradi-
tional practice, the truck will be overpaying its fair share of road
use for certain roads and underpaying for others. By determining
the specific costs for specific trucks and specific routes, greater
equity in both vertical (across truck types) and horizontal (across
specific routes) dimensions is achieved. This analysis is useful in
the current era as agencies mull determining appropriate weight-
distance fees, particularly when highway funding seems to be
evolving from fuel tax structures to those that involve direct user
charging.
Summary and Conclusions
Highway agencies traditionally use aggregate values of the
marginal cost of repairing highway damage for a wide range of
applications including cost allocation, OW fee design, tolling,
and direct-user charging. Typically, for a given vehicle type or class
there is one fee for all highway segments that belong to a specific
pavement family. However, it can be argued that due to differences
in the physical characteristics and operational and environmental
conditions across pavement segments, models that account for
pavement-specific heterogeneity (instead of the traditional FP mod-
els) should be used as a basis for user fees in order to achieve
greater equity in user charging.
In a pioneering effort toward the use of the RP regression model
in marginal pavement cost studies, this paper used RP to capture the
segment-specific heterogeneity in the marginal costs of pavement
repair. Using data from 508 pavement segments that received some
repair treatment, FP and RP regression models were developed.
From these models, the factors that were found to significantly
influence the M&R marginal cost include traffic loading, freeze
index, precipitation, number of wet days, repair (treatment) history,
and geographical location (district). The following variables were
found to have statistically significant RPs: traffic loading, precipi-
tation, and the repair (treatment) history. The RPs for these varia-
bles had standard deviation values that were statistically different
from zero. For all the RPs identified, the best statistical fit was
obtained using the normal distribution.
The results also confirmed that pavement segments that are
subjected to relatively high traffic loading levels or are located
in regions with high climatic severity (higher precipitation and/or
freeze index) deteriorate significantly faster and thus incur higher
M&R expenditures, and that the magnitude of these load and non-
load (climate) effects varies significantly across the individual road
segments. It was also observed that the geographic location and
treatment type significantly influence the M&R marginal cost; such
influence may be attributed to jurisdiction-specific pavement main-
tenance and administration practices and culture, pavement con-
struction standards, and subsoil conditions.
The parameter estimate for total traffic (ESALs) was found
to be normally distributed with a statistically significant mean
and standard deviation (RP), indicating that the influence of the
traffic is significantly different across the individual pavement
segments. This is an important finding because it suggests that
it is justified to charge different fees to highway users at different
highway segments within a given highway pavement family based
on the user contribution to load-related damage. The model results
(Table 2) revealed that RP models are more promising compared
with their FP counterparts and help to identify and account for the
heterogeneity across the pavement segments. Specifically, the RP
model yielded a statistically superior fit compared with its FP
counterpart and showed that substantial unobserved heterogeneity
exists in the variables representing traffic, precipitation, and treat-
ment history, suggesting that the magnitude of their effect on the
marginal cost varies significantly across the different pavement
segments.
Equity can be viewed from either of two perspectives: temporal
equity (equity across time) and cross-sectional equity (equity
among users at any given time). The equity addressed in this paper
is the cross-sectional equity. This is what is often of great concern
in any cost allocation study. With regard to equity across time, the
issue is that the fair share for a given user group may not be the
same between two different periods, because the share distributions
across the user groups may differ from year to year due to a differ-
ent mix of project types, different compositions of the traffic stream
from year to year, different funding levels across the years, and so
on. Because these data (usage levels, factors of deterioration, and
repair costs) are generally increasing gradually with time rather
than wildly fluctuating, it is considered more appropriate to use
the recent years’data rather than a long-term average of the past
several years. Moreover, studies of this nature are meant to be
carried out frequently in order to keep ahead of trends that would
otherwise render the fee costs obsolete after a few years.
The study results can provide guidance to highway agencies
that are considering reviews or updates of their OW vehicle fee
policies or are considering the establishment of new weight-
distance fees on the basis of the responsibilities of each user group
(vehicle class) for the infrastructure rehabilitation and maintenance
expenditures.
Acknowledgments
The funding for the present study was provided by the
NEXTRANS Center, Purdue University, under U.S. Department
© ASCE 04017012-7 J. Infrastruct. Syst.
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of Transportation, Research and Innovative Technology Adminis-
tration (RITA), University Transportation Centers Program. One
of the authors was funded by the Colombian Government’s
Department of Science and Technology and the Universidad
del Valle, under the Colciencias, Generaci ´on del Bicentenario
Fellowship Program. The contents of this paper reflect the views
of the authors, who are responsible for the facts and the accuracy
of the information presented herein, and do not necessarily reflect
the official views or policies of the FHWA and INDOT, nor do the
contents constitute a standard, specification, or regulation.
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