Empirical Modeling of Pavement Overlay Crack Progression with Field Data

Empirical Modeling of Pavement Overlay Crack Progressionwith Field Data

Samer Madanat, M.ASCE1; Ziad Nakat2; and Eui-Jae Jin3

Abstract: We present the development of an empirical pavement overlay crack progression model using condition survey data for thehighway system in the state of Washington. The crack progression model uses random-effect panel data regression techniques, withcorrection for incidental truncation, endogeneity bias, and unobserved heterogeneity. The parameter estimation results show that existingcracking prior to the overlay, traffic loading, overlay thickness and materials, and some environmental factors play important roles inexplaining crack progression. The model developed in this paper is used jointly with a probabilistic model of overlay crack initiation asinputs to a Monte Carlo simulation of overlay cracking trends over time. These trends are realistic for overlays in the estimation database,but caution should be used when applying the model to other states. Specifically, it should only be used in situations where themaintenance policy used is similar to that used by the Washington DOT.

DOI: 10.1061/�ASCE�IS.1943-555X.0000034

CE Database subject headings: Pavement overlays; Cracking; Maintenance; Regression models; Washington.

Author keywords: Pavement overlays; Cracking; Maintenance; Regression models.

Introduction

The progression of alligator cracking in pavement overlays is acontinuous process and represents the change in the percentage ofcracking in time under certain structural, traffic, and climate con-ditions. Overlay crack progression occurs due to the combinationof the following conditions: The widening and propagation ofthose cracks that have already initiated, the initiation of newcracks, and the propagation of cracks from past layers up to thesurface of the new overlay known as reflection cracking. Theprediction of crack progression is important for pavement man-agement because the extent of crack progression reflects the struc-tural condition of a pavement section and triggers maintenanceand rehabilitation activities.

In the following sections of this paper we present the devel-opment of empirical crack progression models using field data.We start by describing the methodology used to develop our em-pirical progression model. We then present the model that wasdeveloped using data from the Washington State DOT conditionsurveys. This model, combined with a crack initiation model de-veloped in previous research, is used to predict the progression ofalligator cracking for representative sections in our sample. We

1Professor, Dept. of Civil and Environmental Engineering, Univ. ofCalifornia, 110 McLaughlin Hall, Berkeley, CA 94720-1720 �correspond-ing author�. E-mail: [email protected]

2Transport Economist, The World Bank, 1818 H St. NW, Washington,DC 20433. E-mail: [email protected]

3Graduate Student Researcher, Dept. of Civil and Environmental En-gineering, Univ. of California, 110 McLaughlin Hall, Berkeley, CA94720-1720. E-mail: [email protected]

Note. This manuscript was submitted on October 15, 2008; approvedon May 4, 2010; published online on May 11, 2010. Discussion periodopen until May 1, 2011; separate discussions must be submitted for indi-vidual papers. This paper is part of the Journal of Infrastructure Sys-tems, Vol. 16, No. 4, December 1, 2010. ©ASCE, ISSN 1076-0342/2010/
4-292–298/$25.00.
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conclude by discussing the limitations of the model and outliningthe limits of its applicability.

Methodology

When using field data for the development of empirical models,or observations of in-service pavements, a number of statisticalissues must be addressed. In the context of progression models,the three salient issues are unobserved heterogeneity, selectionbias, and endogeneity of the design variables.

Unobserved Heterogeneity

When modeling crack progression, we are interested in thechange in the percentage of alligator cracking over the years forevery section where cracking has already initiated. Thus, we areobserving the yearly change in alligator cracking percentage overtime. The data for the progression model therefore have a panelstructure.

A panel, or longitudinal, data set is one that follows a sampleof pavement sections over time and thus provides multiple obser-vations on each section in the sample. Panel data usually give theresearcher a large number of data points, increasing the degrees offreedom and reducing the collinearity among explanatory vari-ables, hence improving the efficiency of the parameter estimates.More importantly, longitudinal data allow a researcher to analyzea number of important questions, such as the progression ofcracking over time for different pavement sections, that cannot beaddressed properly using cross-sectional or time-series data sets.On the other hand, panel data raise an important issue that mustbe considered during the analysis: unobserved heterogeneity,which refers to the differences across sections that may not beappropriately reflected in the available explanatory variables. If itis not accounted for in the model, the estimated parameters will
be inefficient. A panel data regression can be written as
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tion subject to ASCE license or copyright. Visithttp://www.ascelibrary.org

yit = ��xit + uit, i = 1, . . . ,n; t = 1, . . . ,T �1�

where i refers to the pavement sections; t refers to the time peri-ods; �=vector of parameters to be estimated; xit=vector of ex-planatory variables; and uit=disturbance term.

When differences across sections can be captured in differ-ences in the constant, a section-specific constant term may beintroduced to allow for the effects of omitted variables that arespecific to sections but do not change over time. This type ofmodels is known as fixed-effect models. The parameters can beestimated using ordinary least-squares techniques. A fixed-effectmodel may be written as

yit = �i + ��xit + uit; i = 1, . . . ,n; t = 1, . . . ,T �2�

where �i=scalar constant representing unobserved effects pecu-liar to the ith section and constant in time.

The fixed-effect specification suffers from an obvious short-coming in that it requires the estimation of many parameters �theconstant terms� with the associated loss of the degrees of free-dom. This can be avoided by using the random-effect models.Unlike the fixed-effect model where inference is conditional onthe particular sections sampled, the random-effect model is anappropriate specification if n sections are randomly drawn from alarge population. This is reflected in the formulation of the dis-turbance term

uit = ui + vit, i = 1, . . . ,n; t = 1, . . . ,T �3�

where ui=random disturbance characterizing the ith section and isconstant in time and vit=uncorrelated random disturbances. Byrewriting Eq. �1� using Eq. �3�, the random-effect model is givenby

yit = ��xit + ui + vit �4�

The parameters � of the random effects are estimated by usinggeneralized least squares.

Selection Bias due to Incidental Truncation

Selection bias due to incidental truncation arises in the estimationof empirical crack progression models because crack progressionis observed only after crack initiation has occurred. Crack pro-gression is therefore only observed in sections that have alreadyfailed. The sample selection problem results in an overrepresen-tation of weaker sections in the sample, and the estimated param-eters may have been biased �Greene 1997�. This requires theintroduction of a correction term in the panel regression model tocorrect for this bias, as suggested by Heckman �1976�.

The incidental truncation problem can be explained as follows.Suppose that y and z have a bivariate distribution with correlation�. We are interested in the distribution of y given than z exceedsa particular value. In our case, y is observed and represents theyearly change in the percentage of alligator cracking and z is anobserved variable that represents the difference between loadingand resistance.

Let the equation that describes the unobserved variable z be

zi = ��wi + �i �5�

Furthermore let the equation that describes the annual change incracking be

yit = ��xit + uit �6�

where yit=dependent variable of interest �change in the per-
centage of alligator cracking�; zi=unobserved variable; � and �
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=vectors of parameters to be estimated; wi and xit=vectors ofexplanatory variables; and uit and �i=error terms. The dependentvariables in Eqs. �5� and �6� are likely correlated because unob-served factors that cause a pavement section overlay to crackearlier �such as poor construction quality� are also likely to in-crease the annual change in cracking. Note that yit is only ob-served for those sections that have cracked. Since zi represents thedifference between loading and resistance, then a section i hascracked only if zi�0.

Define �u and �� as the standard deviations of uit and �i,respectively. If uit and �i are assumed to have a bivariate normaldistribution with zero means and correlation �, then, as shown inGreene �1997�

E�yit�yit is observed� = E�yit�zi � 0� = ��xit + ��i�� 7�

where

�� =− ��wi

��

�8�

and

�� =��wi/��wi/��

�9�

where �� · �=standard normal probability density and � · �=standard normal cumulative distribution.

Therefore

yit�zi � 0 = ��xit + ��i�� + it �10�

where it=random error term.Thus, our panel data model with incidental truncation is given

by Eq. �10�. The parameters �, ��, �, and �i of the sample selec-tion model are estimated using two-step Heckman’s procedure:

In the first step, we estimate the parameters of the sampleselection equation, i.e., the equation that predicts the probabilitythat pavement section i has cracked. This is a binary Probitmodel, with the right-hand side given by the denominator of Eq.�9�, with normalization �u=0. Maximum likelihood is used toobtain estimates of �. Then for each observation in the selectedsample compute

�i =

��wi��wi�

�11�

where �i and �=estimated values of �i and �, respectively. In the

second step of Heckman’s procedure, we estimate the parameters� and �� of Eq. �10� by regressing the dependent variable yit on

�i and the vector of explanatory variables xit.

Data Description

The sample used for the estimation of the progression model wasselected from the Washington PMS database. The following is adescription of the relevant explanatory variables:• Yit: Percentage of alligator cracking in pavement section i at

time t, where t=number of years since the last overlay wasbuilt.

• Yi�t−1�: Percentage of alligator cracking in pavement section iat time �t−1�.

• �it: Represents the yearly change in the percentage of alligatorcracking for pavement section i between time t and �t−1� and
is given by
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https://www.researchgate.net/publication/285705454_Econometric_Analysis?el=1_x_8&enrichId=rgreq-207b11dc2e9e4012f506591d6522fbb3-XXX&enrichSource=Y292ZXJQYWdlOzI0NTI4OTA0MztBUzoxMDIzNzQxMzU4Mjg0OTJAMTQwMTQxOTMwNTAxMA==

�it = Yit − Yi�t−1� �12�

• E_Long, and E_Alli: Existing longitudinal and alligator crackbefore rehabilitation, respectively.

• Trafficit: Traffic in equivalent single axle loads �ESALs� forpavement section i at time t.

• Y_ESAL: Traffic in ESALs in year 1999.• SURFTHK: Layer thickness of the last overlay �in feet�.• ULT: Sum of the thickness of the underlying asphalt concrete

pavement layers �in feet�.• Untrthick: The thickness of the nontreated base �in feet�.• Actbthick: The thickness of asphalt concrete treated base �in

feet�.• Pctbthick: The thickness of portland cement treated base �in

feet�.• BA, AA: Dummy variables that take the value of 1 if the ma-

terial type of the overlay is “BA” or “AA,” respectively, and 0otherwise. The Material Types BA and AA are defined in theWashington State PMS �1999� as asphalt concrete cements thathave the same binder type �AR4000W�, but with different mixclasses: BA is a Class B mix and has a maximum aggregatesize of 5/8 in. and is described as a standard mix, while AA isa Type A mix which also has a maximum aggregate size of 5/8in., but that is a higher grade mix with more fractured rocks.

• Tmin: Average monthly minimum temperature of the coldestmonth in °C.

• FTprep: Product of annual precipitation and freeze-thawcycles.

• Mintempcit: Average monthly minimum temperature of thecoldest month �December� in °C.

• Precipit: annual precipitation �in millimeters�.

Model Development

Endogeneity Bias Correction

When dealing with crack progression of in-service pavementoverlays, two explanatory variables are likely to be endogenous:the overlay thickness and the pavement material type becausethey are design variables, which are selected by pavement engi-neers. Therefore, these explanatory variables are predeterminedand cannot be assumed random �Madanat et al. 1995; Madanatand Mishalani 1998�. In order to correct for the endogeneity inthe observed thickness of the overlay, we predicted the overlaythickness, and named this predicted value Newoverlay1. Thisvariable will be used as an instrumental variable for the measuredvalue of the overlay thickness in the crack progression model

ln�SURFTHK� = �0 + �1 ln�E_Alli� + �2 ln�Actbthick�

+ �3 ln�Pctbthick� + �4 ln�Untrthick�

+ �5 ln�Y_ESAL� + �6 ln�ULT� + �7 ln�Tmin�

+ �8 ln�FTprep� + �13�

where ln�x�=natural logarithm of x; �0–�8=parameters to be es-timated; and =error term.

In order to correct for the endogeneity in the asphalt overlaymaterial type, the probability of the agency choosing a certainmaterial type given certain structural conditions, climate vari-ables, and yearly traffic was computed using a multinomial logit�MNL� model. In the Washington State PMS �1999� data, therewere two dominant material types: BA and AA. The other mate-
rial types seem to have been used less often and thus formed


smaller fractions of the data. Thus, they were all grouped togetherin the “others” group, which was used as the reference group forthe MNL model. Under this specification, the parameters of thegroup others were set to zero. The MNL model is given by

Pr�i� =exp�Vi�

�j=1

J

exp�Vj�

�14�

where Pr�i�=probability of selecting material type i; exp�x�=exponential of x; and i and j=indices for the material types,where the material types are BA, AA, and others. V is defined as

Vi = �0 + �1Newoverlay · 1 + �2Y_ESAL + �3FTprep for i = BA

�15�

Vi = �0 + �1Newoverlay · 1 + �2Y_ESAL + �3FTprep for i = AA

�16�

Vi = 0 for i = other �17�

where �0–�3 and �0–�3=parameters to be estimated andNewoverlay1, Y_ESAL, and Ftprerp were all defined earlier.Table 1 shows the estimated values of the parameters of Eq. �13�.Table 2 shows the estimation results of the parameters of Eq. �14�.

Table 1. Parameter Estimates of the Overlay Thickness Regression andGoodness-of-Fit Measure of Overlay Thickness Regression

Variable Coefficient t-statistics

Constant 4.24�10−2 3.19

ln�E_Alli� 3.28�10−3 6.71

ln�Actbthick� −2.86�10−2 �3.24

ln�Pctbthick� −7.64�10−3 �1.74

ln�Untrthick� −1.16�10−2 �5.00

ln�Y_ESAL� 7.12�10−3 10.5

ln�ULT� −1.66�10−2 �4.55

ln�Tmin� −1.46�10−2 �6.63

ln�FTprep� 5.66�10−3 9.63

Number ofobservations

R-squared AdjustedR-squared

7,162 0.66 0.65

Table 2. Parameter Estimates of the MNL Model and Goodness-of-FitMeasures of MNL Model

Category Variable Coefficient t-statistics

Material Type BA Constant 3.35 7.62

Newoverlay1 −1.03�101 �3.14

Y_ESAL −1.09�10−6 �6.25

FTprep −3.03�10−5 �17

Material Type BA Constant 4.04 7.93

Newoverlay1 −2.77�101 �7.34

Y_ESAL 1.11�10−6 6.98

FTprep −1.21�10−5 �6.16


Pseudo-R-squared Likelihoodratio

7,162 0.07 945

010


Estimation of the Incidental Truncation BiasCorrection Term

Heckman’s procedure is used to correct for incidental truncation.Define the unobserved variable zi of Eq. �5� as

zi = �0 + �1Actbthick + �2Pctbthick + �3Untrthick + �4ULT

+ �5Pr_aa + �6Pr_ba + �7Cum_ESAL+�8FTprep

+ �9Newoverlay1 + �i �18�

Then the Probit model representing the probability that a sectioncracks �z�0� is specified as

P�z � 0� = ��0 + �1Actbthick + �2Pctbthick + �3Untrthick

+ �4ULT + �5Pr _ aa + �6Pr _ ba + �7Cum_ESAL

+ �8FTprep + �9Newoverlay1� �19�

The parameter estimates of the Probit model are shown in Table3.

Development of the Progression Model

In order to estimate the progression model, a sample consisting of5,441 pavement sections observed over 1–12 years for each dif-ferent section was used. It constitutes a panel with 36,194 obser-vations. A panel data model was used, and the dependent variable,�it, was regressed on explanatory variables, using the followingmodel specification:

�it = �0 + �1Yi�t−1� + �2E _ Allii + �3Actbthicki + �4Pctbthicki

+ �5Untrthicki + �6ULTi + �7Overlayaai + �8Overlaybai

+ �9Trafficit + �10Precipit + �11Mintempcit + ��i + ui + vit

�20�

where Overlayaai=product of Newoverlay1 and Prob_aa andOverlaybai=product of Newoverlay1 and Prob_ba.

A Priori ExpectationsA characteristic of the Washington State PMS data is that alligatorcracking rarely exceeds 10% because WSDOT essentially followsa pavement preservation approach and a new overlay is usuallyput in place before alligator cracking exceeds 10% of the wheelpath. The overwhelming majority of the overlays are also what

Table 3. Parameter Estimates of the Probit Model for P�z�0� andGoodness-of-Fit Measures of Probit Model


Constant 6.53 9.55

Actbthick −1.60 �6.49

Pctbthick −7.95�10−1 �6.26

Untrthick −5.44�10−1 �11.28

ULT −9.00�10−1 �10.96

Prob_aa −4.25 �5.26

Prob_ba −9.99�10−1 �1.87

Cum_ESAL 2.27�10−6 29.28

Ftprep 1.22�10−5 4.64

Newoverlay1 −4.02�101 �15.95


Likelihoodratio

Pseudo-R-squared

7,162 1,150 0.15

would be defined as “maintenance overlays” with typical thick-

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nesses of about 2 in. �45 mm�. For thin overlays on crackedpavements it would be expected that reflection cracking would bea contributor to overlay cracking, with the cracks in the existingpavement reflecting up through the overlay.

It is expected that a thicker structure will have higher resis-tance to cracking and will reduce the rate of progression of alli-gator cracking. Accordingly, an increase in the thickness of theoverlay both for Material Types AA and BA, an increase in thethickness of the untreated or treated base, and an increase in thethickness of underlying asphalt concrete layers are expected todecrease the rate of alligator cracking progression. On the otherhand, an increase in existing cracking before rehabilitation is ex-pected to increase the rate of crack progression because existingcracking propagates to the overlay surface.

The effect of environmental variables can also be predicted. Itis known that as the minimum temperature increases, the stiffnessof the asphalt concrete overlay decreases, which is expected toreduce the rate of alligator cracking progression. Greater precipi-tation would also be expected to increase the cracking suscepti-bility of the overlay.

Model Parameter Estimates and Their InterpretationsTable 4 shows the results of the estimation of the parameters ofEq. �20�. The results shown in Table 4 confirm the expectations interms of the correctness of the signs. Furthermore, the t-statisticsshow that each variable is a significant explanatory variable of theprogression of alligator cracking at the 5% significance level. Thesigns of the explanatory variables indicate the following effectson the rate of crack progression.

The value for �1 indicates that the greater the amount of alli-gator cracking in the overlay is, the smaller the increase in alli-gator cracking is, which means that the cracking progressiontrend is concave in time. This trend is different from what isfound in some of the literature on empirical modeling of crackingprogression, where convex trends have been reported �Paterson

Table 4. Parameter Estimates of the Progression Model, Distribution ofthe Error Terms of the Progression Model, and Goodness-of-Fit Measuresof the Progression Model


Constant 1.18 3.39

Yi�t−1� −5.86�10−1 �39.1

E_Allii 8.07�10−2 20.01

Actbthicki −1.75�10−1 �4.89

Pctbthicki −1.71�10−1 �8.91

Untrthicki −3.57�10−2 �5.09

ULTi −1.26 �8.77

Overlayaai −3.78 �4.32

Overlaybai −1.54 �6.56

Trafficit 4.06�10−6 4.57

Precipit 4.40�10−4 10.18

Mintempcit −5.42�10−2 �5.74

�i 1.20 15.97

Error term variance Value t-statistics

sigma_u 0.84 14.7

sigma_e 4.41 230.79

Rho 0.035 N/A


Wald test

36,194 2,231

1987�. The explanation for this behavior is that the data used for



development of this model come from in-service pavements. Assuch, these overlays were subjected to �unrecorded� maintenanceactivities, possibly including crack sealing or patching. For someobservations, the value of �it was negative, and we replaced thesenegative values with zeros. �We also attempted a Tobit model toaccount for the censoring of the negative values of crack progres-sion, but were unable to obtain meaningful parameter estimates.�The effect of these zero values for �it is to force a leveling off ofalligator cracking. Therefore, this model predicts cracking pro-gression in overlays that are subject to maintenance activities.The implication of this result is that the model should only beused to predict cracking progression for agencies that follow asimilar maintenance policy.

The value for �2 indicates that the greater the existing alligatorcracking in previous layers is, the faster the progression of alli-gator cracking in the overlay is, confirming the hypothesis thatreflection cracking is an important contributor to overlay crack-ing. A thicker underlying structure �base thickness, previous as-phalt concrete �AC� layer thickness, and overlay thickness� resultsin a smaller rate of crack progression. AC- or Portland cement�PC�-treated bases do not seem to differ much in reducing the rateof crack progression; however, they are both significantly better�almost by a multiple of 5� in resisting crack progression thanuntreated bases of the same thickness. The underlying AC layer isabout 10 times more effective in resisting crack progression thaneven the strongest base of the same thickness.

Overlay thickness appears to have the largest effect on resist-ing crack progression as one would expect, with Type A overlaysabout more than twice as effective in reducing the rate of alligatorcrack progression than Type B overlays of the same thickness.Traffic loading �ESAL� appears to have a significant effect on therate of progression of alligator cracking; the higher the trafficloading is, the larger the rate of crack progression is. Climatevariables, particularly yearly precipitation and minimum tempera-ture, also play a significant role: the higher the yearly precipita-tion is, the higher the rate of crack progression is, while higherminimum temperatures reduce the rate of crack progression.

The coefficient �� is significant, suggesting that the correctionfor the incidental truncation is appropriate. Moreover, since ��

�0, this indicates that the rate of increase of alligator cracking isreduced when the correction term is introduced in the regression.This result is expected since the correction term corrects for theoverrepresentation of weaker pavement overlays in the sample.

sigma_u represents the standard deviation of the random dis-turbance ui, discussed in Eq. �4�, characterizing the ith overlaysection and accounting for cross-sectional heterogeneity in arandom-effect panel data model. sigma_e represents the standarddeviation of the random disturbances �it in Eq. �4� and accountsfor random error terms in time and across sections. Rho repre-sents the fraction of the total error term that is due to unobservedheterogeneity and is given by

Rho =�sigma_u�2

�sigma_u�2 + �sigma_e�2 �21�

The model of Eq. �20� is a random-effect model with a very lowvalue of Rho �0.035, which is almost zero�. However, this doesnot mean that unobserved heterogeneity is nonexistent in themodel. Rather, the incidental truncation correction terms, whichonly vary across cross-sectional observations, act as dummy vari-ables for the different pavement sections. As such, the modelbehaves as a fixed-effect model. This model differs slightly from
a fixed-effect panel data model since some, but only a few, pave-


ment sections can have the same correction term �i and thus sharethe same identifier.

Model Predictions

In previous research �Nakat and Madanat 2008�, the writers de-veloped a stochastic crack initiation model using the same data-base. The two models �crack initiation and progression� form asuite that can be used to perform predictions of the initiation andprogression of alligator cracking with time. A spreadsheet wasused for applying the models of crack initiation and progressionand microsimulation was used as a prediction method. Thespreadsheet creates a graph that shows the cracking paths result-ing from 1,000 simulated experiments. Each curve in Figs. 1–6represents a different cracking path, resulting from a differentoutcome of the simulation. To show that different cracking pathshave different probabilities, a bar is shown next to each path. Thenumbers on the bars represent the number of realizations for eachpath.

In order to perform predictions, a typical pavement sectionwas selected, and the values of its explanatory variables weredefined as “default values.” Each of the explanatory variables ofthe typical section was varied from its 25th percentile to its me-dian and then its 75th percentile. The variables that made the mostvisible difference in the alligator cracking initiation and progres-

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Fig. 1. Overlay Type AA, all explanatory variables set at their me-dian values, ACTB=0, PCTB=0, annual ESAL=250,000 over twolanes, and 3% traffic growth

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Fig. 2. Overlay Type AA, all explanatory variables set at theirmedian values, base dummy variables as in Fig. 1, but ESAL=100,000 over two lanes

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sion paths were overlay material type �AA versus BA� and ESAL.The predictions for different values of overlay material type andESAL are shown in Figs. 1–6.

The following observations can be made on the basis of Figs.1–6:• The crack progression paths are concave. The concavity and

the convergence in value are the consequences of the mannerwe treated the negative increments in crack progression. Cen-soring these negative observations �which correspond to unre-corded maintenance in later stages of overlay life� leads to apreponderance of observational zeros at larger values of age,thus the reduction in crack progression slope. There are, ofcourse, other possible reasons for the observed negative valuesof crack progression: measurement errors �it is known thatcrack extent measurement is especially prone to human errors�and crack healing, which is a frequent phenomenon at lowvalues of cracking.

• Overlays made of Type AA material consistently perform bet-ter than those made with Type BA material. The graphs showthat, in the median case, overlays of Type AA may crack aslate as in the 15th year, whereas the crack initiation of overlaysof Type BA occurs in the first 3 years in the median case.Moreover, for the median case, the maximum cracking per-centages around Year 14 �which is the average time intervalbetween overlays in Washington State� are around 6% forType AA and closer to 8% for Type BA materials. This behav-

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Fig. 4. Overlay Type BA, all explanatory variables set at their me-dian values, ACTB=0, PCTB=0, annual ESAL=250,000 over twolanes, and 3% traffic growth

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ior was expected given that Type AA asphalt concretes aremade with coarser aggregate gradations than Type BA mixes.

• The effect of traffic loading is clearly important. As can beseen, both cracking initiation and progression accelerate sig-nificantly as loading is increased from 100,000 ESALs overtwo lanes to 250,000, then to 500,000. In the case of Type AAoverlays, the percentage cracking at Year 14 increases from3.5 to 6 and 11%, respectively. For Type BA overlays, thepercentage cracking at Year 14 increases from 4.5 to 8 and12%, respectively.

Conclusions

This paper described the development of an alligator crackingprogression model using empirical data from WSPMS. Econo-metric methods were used to correct for empirical data problemssuch as sample selection, endogeneity bias, and unobserved het-erogeneity. The resulting model is rich in relevant explanatoryvariables and produces realistic predictions.

It must be emphasized that the model predicts well for ex-planatory variables varied within the range of its values in thedata, but it must be recalibrated for data outside this range. This isespecially true for overlay thickness �variables Overlayaa andOverlayba� since Washington State’s maintenance strategy is toperform pavement preservation mainly with overlays averaging

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Fig. 5. Overlay Type BA, all explanatory variables set at their me-dian values, base dummy variables as in Fig. 4, but annual ESAL=100,000 over two lanes

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about 2 in. �45 mm� thickness. Recalibration is also essential ifoverlays are being placed after cracking in the existing pavementhas propagated to greater extents than is the practice of WSDOT�variable E_Alli�. WSDOT almost always places overlays beforecracking has exceeded 10% of the wheel path cracked and typi-cally overlays at about 5% of the wheel path cracked.

Another caveat is that this model predicts cracking progressionin overlays that are subject to maintenance activities. The impli-cation of this result is that the model should only be used topredict cracking progression for agencies that follow a similarmaintenance policy.

Acknowledgments

The California Department of Transportation’s Division of Re-search and Innovation funded this work through a contract withthe Partnered Pavement Research Center at the University of
California at Berkeley and Davis. The writers are grateful for the


assistance provided by Dr. John Harvey of UC Davis in obtainingthe data used in this research.

References

Greene, W. H. �1997�. Econometric analysis, 3rd Ed., Prentice-Hall, NewYork.

Heckman, J. �1976�. “The common structure of statistical models of trun-cation, sample selection and limited dependent variables, and a simpleestimator for such models.” Annals of Economic Social Measure-ments, 5�4�, 475–492.

Madanat, S., and Mishalani, R. �1998�. “Selectivity bias in modelinghighway pavement maintenance effectiveness.” J. Infrastruct. Syst.,4�3�, 134–137.

Nakat, Z., and Madanat, S. �2008�. “Stochastic duration modeling ofinfrastructure distress initiation.” J. Infrastruct. Syst., 14�3�, 185–192.

Washington State Dept. of Transportation Materials Lab. �1999�. Wash-ington State pavement management system (WSPMS), pavement man-agement software guide, Washington State Dept. of Transportation,
Olympia, Wash.
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https://www.researchgate.net/publication/239387893_Selectivity_Bias_in_Modeling_Highway_Pavement_Maintenance_Effectiveness?el=1_x_8&enrichId=rgreq-207b11dc2e9e4012f506591d6522fbb3-XXX&enrichSource=Y292ZXJQYWdlOzI0NTI4OTA0MztBUzoxMDIzNzQxMzU4Mjg0OTJAMTQwMTQxOTMwNTAxMA==





Empirical Modeling of Pavement Overlay Crack Progression with Field Data

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