Investigation of Asphalt Mixture Creep Compliance at Low Temperatures

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Investigation of Asphalt Mixture Creep Compliance atLow TemperaturesAdam Zofka a , Mihai Marasteanu b & Mugurel Turos ba University of Connecticut , 261 Glenbrook Road Unit 2037, Storrs, CT, 06269-2037, USAE-mail:b University of Minnesota , 500 Pillsbury Drive S.E., Minneapolis, MN, 55414, USA E-mail:Published online: 19 Sep 2011.

To cite this article: Adam Zofka , Mihai Marasteanu & Mugurel Turos (2008) Investigation of Asphalt MixtureCreep Compliance at Low Temperatures, Road Materials and Pavement Design, 9:sup1, 269-285, DOI:10.1080/14680629.2008.9690169

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Road Materials and Pavement Design. EATA 2008, pages 269 to 285

Investigation of Asphalt Mixture CreepCompliance at Low Temperatures

Adam Zofka* — Mihai Marasteanu** — Mugurel Turos**

* University of Connecticut261 Glenbrook Road Unit 2037Storrs, CT 06269-2037, [email protected]

** University of Minnesota500 Pillsbury Drive S.E.Minneapolis, MN, 55414, USA{maras002; [email protected]

ABSTRACT. The creep compliance is one of the main material characteristics used to describelow temperature behavior of the asphalt mixtures. It also serves as a primary input to thecurrent thermal cracking model in the US that is used to predict thermally induced crackingin asphalt pavements over their service life. The current standard method in the US todetermine creep compliance of asphalt mixtures is the Indirect Tensile (IDT) test. This paperinvestigates the feasibility of using the Bending Beam Rheometer (BBR) device to determinethe low-temperature creep compliance of thin asphalt mixture beams (127x12.7x6.35mm).The BBR was used to evaluate 20 different asphalt mixtures and the results were comparedwith the standard IDT results. Direct comparison of the BBR and the IDT results indicate thatboth methods produce slightly different creep compliance curves and the relative ratiobetween the BBR and the IDT results varies with time and temperature. A simplephenomenological relation was proposed that gives good predictions of the IDT results basedon the BBR creep compliance. Furthermore, short-term aged asphalt binders used in themixtures were also tested in the BBR. Modified Hirsch model was applied to the BBR resultson both mixtures and binders and it was shown that this model is capable of producing quiteaccurate results in forward and inverse predictions using considered dataset. It wasconcluded that the BBR can be used in practical and surrogate estimation of the mixturecreep compliance but proposed scheme requires validation on other mixture types.KEYWORDS: Creep Compliance, Thermal Cracking, Hirsch Model, Asphalt Mixture.

DOI:10.3166/RMPD.9HS.269-285 © 2008 Lavoisier, Paris

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270 Road Materials and Pavement Design. EATA 2008

1. Introduction

Thermal-cracking is a major distress of asphalt pavements in cold climateregions. In order to minimize the pavement damage and limit user-delay costs,asphalt mixtures should be designed and prepared with materials that are resistant tothe stresses induced by the cold temperatures during the winter months. To predictthe performance of asphalt mixtures in pavements subjected to real environmentalconditions, an appropriate performance model should be used. Depending upon themodel output, the material input parameters vary and are usually determined inlaboratory conditions using laboratory prepared mixtures.

The Thermal Cracking (TC) model included in the mechanistic-empiricalpavement design guide (MEPDG) requires the creep compliance of asphalt mixturesas primary input (Hallin et al., 2004). The TC model predicts the depth and theamount of thermally induced cracking in asphalt pavements over service life. Thecurrent standard test to determine the creep compliance of asphalt mixtures is theIndirect Tensile (IDT) test (AAHTO T 322-03). The main advantage of this test isthe ability to simulate a state of stress similar to the state induced under the wheel inthe asphalt mixture layer of the pavement (Roque et al., 1992). During the IDT test,the cylindrical specimen is loaded vertically along its length and displacements aremeasured on both faces of the specimen (Figure 1).

Figure 1. IDT experimental setup

In the IDT test, a creep displacement curve is obtained under constant load andthe creep compliance can be calculated using appropriate data interpretationprocedures (Buttlar et al., 1994; Zhang et al., 1997; Christensen, 1998). Accordingto AASHTO T 322-03, the IDT creep test is performed at three temperatures 0°C, -10°C and -20°C, regardless of the PG grade of the asphalt binder in the mixture.

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Investigation of AC Creep Compliance 271

The Bending Beam Rheometer (BBR) is used to determine the creep complianceof asphalt binders as part of the PG specification in the US (Bahia et al., 1992,AAHTO T313-05). The BBR concept is based on 3-point bending setup commonlyused in mechanics. A constant force is applied in the middle of the beam anddeflections of the beam are measured throughout the duration of the test (Figure 2).BBR testing has several advantages compared to IDT: testing procedure is very easyand repeatable, the sample size allows for almost nondestructive evaluation of theasphalt mixtures in existent pavements, and the small beam thickness allowsanalyzing the effect of aging at very small pavement depths. Furthermore, by usingappropriate composite materials models, such as Hirsch model (Hirsch, 1962;Christensen et al., 2003) asphalt binder creep compliance can be used to predictasphalt mixture creep compliance (forward analysis) or binder compliance can beback-calculated from the asphalt mixture results (inverse analysis). Thus, chemicalextraction of the binder, typically performed for pavement cores, can be eliminated(Zofka et al., 2005).

Figure 2. BBR testing concept on asphalt mixtures

One of the drawbacks of testing thin mixture beams is the fact that the thicknessof the beam is smaller than the maximum aggregate size for most mixtures andviolates the representative volume element (RVE) concept that defines the minimumspecimen dimensions that are required to obtain reliable and repeatable test results.At higher temperatures, at which asphalt mixture components have drasticallydifferent mechanical properties, the scale effect plays a significant role. However, atlow temperatures (in the vicinity of asphalt binders’ glass transition temperature) themismatch between the aggregates and the binder diminishes considerably as asphaltbinders start to behave as brittle linear viscoelastic materials (for which the responsecan be easily obtained from elastic behavior using the elastic-viscoelasticcorrespondence principle). Since both constituent materials, at any time point, havesimilar responses, the bulk properties of the composite asphalt mixture become lessdependent on the size and spatial distribution of aggregate particles. Several authorsreported this phenomenon in their research publications (Weissman et al., 1999;Romero et al., 2001) and suggested that RVE can be significantly reduced at lowertemperatures.

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2. Objectives

The objectives of the study presented in this article are as follows:– Compare mixture creep compliance data obtained from the IDT and from the

BBR and investigate the relation between these two datasets for 20 different asphaltmixtures;

– Investigate the capabilities of Hirsch model in forward and inverse predictionson asphalt binders and mixtures.

3. Materials

10 different asphalt binders and two aggregate sources were considered in thisstudy which resulted in 20 different asphalt mixtures. The binders representedtypical grades used in the cold climates including both modified and unmodifiedmaterial. Two aggregate types were limestone and granite. Mixture specimens wereprepared using gyratory compactor and after volumetric properties were measured,every gyratory specimen was cut into IDT specimens. After IDT testing wasfinalized, part of IDT specimens were further cut into small beams that were nexttested in the BBR at the same temperature as the IDT. The nominal maximumaggregate size (NMAS) of the aggregate blends was 12.5 mm. The optimum asphaltcontent in the mix design was determined at 4% air voids and VMA (Voids in theMineral Aggregate) and VFA (Voids Filled with Asphalt) values were evaluatedaccording to Superpave specifications (SP-2) for design traffic level of 3-30 millionsequivalent single axle loads (ESALs). The final mix design parameters are presentedin Table 1. Table 2 shows the PG grades of the binders and the mixtureidentification system used throughout this study. It should be mentioned that prior toBBR testing, binders were short-term aged using AASHTO procedure T240-03(RTFOT) to simulate aging level in the corresponding asphalt mixtures.

Table 1. Mix design results

Granite mixtures Limestone mixtures

Optimum asphalt content [%] 6.0 6.9

VMA [%] 16.3 16.2

VFA [%] 75.9 75.0

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Table 2. Designation system for asphalt mixtures

AggregateBinder*

Granite (GR) Limestone (LM)

A PG 58-40:M1 58-40:M1:GR 58-40:M1:LMB PG 58-34:M1 58-34:M1:GR 58-34:M1:LMC PG 58-34:M2 58-34:M2:GR 58-34:M2:LMD PG 58-28:U1 58-28:U1:GR 58-28:U1:LME PG 58-28:U2 58-28:U2:GR 58-28:U2:LMF PG 64-34:M1 64-34:M1:GR 64-34:M1:LMG PG 64-34:M2 64-34:M2:GR 64-34:M2:LMH PG 64-28:U1 64-28:U1:GR 64-28:U1:LMI PG 64-28:M1 64-28:M1:GR 64-28:M1:LMJ PG 64-22:U1 64-22:U1:GR 64-22:U1:LM

Note: * M – modified binder, U – unmodified binder.

4. Experimental testing

10 RTFOT binders were tested in BBR and 20 mixtures were tested in IDT andBBR. Creep tests in IDT and BBR were performed for 1000sec at three temperaturesthat were related to the lower PG grade of the binder used in a given mixture. Due todifferent temperature susceptibility, the temperature step between testingtemperatures was different for the mixtures and the binders: shorter step, 6°C wasused for the binders and larger step, 12°C was used for the mixtures (see Table 3).For example, binder PG 64-28 was tested at -18°C, -24°C, and -30°C whereasmixture 64-28:U1:GR was tested at -6°C, -18°C and -30°C. This testing systemallowed for a direct comparison of laboratory results for the binders and themixtures at two matching temperatures as presented in Table 3.

The BBR testing on asphalt binders was performed according to AASHTOT313-05 using 2 specimens for each test temperature.

The IDT testing was performed according to AASHTO standard T322-03. Eachspecimen was treated separately and the creep compliance was calculated as thearithmetic mean from at least two specimens.

The BBR testing on asphalt mixtures followed the binder standard except that ahigher load of 500g was used during the creep test and the duration of the test wasextended to 1000s. According to the BBR manufacturer (Cannon Industries) nomodification of the instrument was required to accommodate these changes in thetesting procedure. The number of BBR replicates varied from 5 to 11 with majority

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of mixtures having at least 9 replicates. This variation was caused by the preparationprocess where some specimens were damaged. More details on the experimentaleffort can be found in (Zofka, 2007).

Table 3. Test temperatures for binders and mixtures

Temperature level Binders Mixtures

H (High) PG+10 (PG+10)+12

I (Intermediate) PG+10-6 (PG+10)

L (Low) PG+10-12 (PG+10)-12

* PG is the lower PG limit of the binder

5. Hirsch model

Hirsch model was originally proposed by Hirsch 1962 and recently was adoptedto asphalt mixtures by Christensen et al. (2003). The authors proposed a three phasesemi-empirical mechanical model for extensional |E*|mix and shear |G*|mix dynamicmodulus of the asphalt mixture. The model is shown in Figure 3 and the generalequation is given by the following expression

( ) ( )12

11 aggagg

mix agg agg binder binderagg binder binder

VVE Pc E V E V Pc

E E V

− − = + + − +

[1]

The authors introduced contact volume parameter, Pc that controls the relativeproportions of the series and parallel phases and proposed the following expressionfor Pc:

1

0

1

2

Pbinder

Pbinder

VFA EPVMAPc

VFA EPVMA

⋅ + =

⋅ +

[2]

VFA – percent of the VMA filled with binder [%],VMA – voids in mineral aggregate [%], VMA=100-Vagg,VFA – voids filled with binder [%], Vbinder=VFA*VMA,P0, P1, P2 – fitting parameters.

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Figure 3. Semi-empirical model proposed by Christensen et al. (2003)

All mixtures used in this study were produced using the same mix designpresented in Table 1 which resulted in a very narrow range of VMA and VFAvalues. Using only narrow set of volumetric properties for calibration of the originalPc expression could lead to the unreliable fitting parameters P0, P1, and P2. Due tothese limitations, it was decided to drop the volumetric information from Pcexpression but keep its time and temperature dependence through Ebinder as discussedby Christensen et al., 2003. As the results, the following expression was proposed

( )ln binderPc a E b= + [3]

It should be also mentioned that the model proposed by Christensen et al. (2003)was developed for the different modes of loading than the BBR and it was expectedthat fitting parameters in the original expression for Pc (Equation [2]) may notnecessarily predict relaxation modulus E calculated from the BBR measurements.

6. Results

The results are presented in two parts. First part shows the direct comparison ofthe mixture creep compliances obtained from the IDT and the BBR together with aproposed phenomenological equation to predict IDT results from the BBR results.Second part shows forward and inverse predictions of Hirsch model based on theproposed simplified expressions for contact volume parameter, Pc.

6.1. Comparison of BBR and IDT results on asphalt mixtures

The experimental data allows the direct comparison of the 1000sec creepcompliance curves obtained from both tests at three temperature levels. Figure 4shows such comparisons for two mixtures: 58-28:U2: GR and 58-34:M2:LM using

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average results from each test. Visual inspection of the curves indicates that thecreep compliance curves do not perfectly match. The difference between the curvesvaries primarily with test temperature and to lesser degree with time. The trends aresimilar for both mixtures, which were prepared with unmodified and modified bindersand with granite and limestone aggregate, respectively. At the higher temperature theIDT creep compliance is larger, at the intermediate temperature both curves are almostsimilar, and at the lower temperature the BBR compliance is larger.

0.0

0.1

1.0

10.0

10 100 1000Time [sec]

Cre

ep c

ompl

ianc

e [1

/GPa

]

58-28:U2:GRIDTBBR

L

I

H

0.0

0.1

1.0

10.0

10 100 1000Time [sec]

Cre

ep c

ompl

ianc

e [1

/GPa

]

58-34:M2:LMIDTBBR

L

I

H

Figure 4. Measured IDT and BBR creep compliance curves for two mixtures

The creep compliance at 60sec was further selected to perform simple statisticalanalyses since this time is used in the binder specification. It should be mentionedthat compliance values at any other times could be chosen as well. In order toquantitatively assess the influence of the individual parameters, such as aggregate,

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temperature level or presence of modification, on the relation between IDT and BBRresults, it was decided to perform Analysis of Variance Analysis (ANOVA) on thedifference between the natural logarithm of the IDT and natural logarithm of theBBR results. The aforementioned parameters were considered as factors withappropriate levels.

Table 4. ANOVA for ln(IDT)-ln(BBR) at 60sec

Source DF Seq. SS Adj. SS Adj. MS F P-value

Temp 2 4.95 4.69 2.34 54.85 0.000Aggregate 1 0.00 0.00 0.00 0 0.965Modyfication 1 0.10 0.10 0.10 2.24 0.141Temp.*Agg. 2 0.11 0.11 0.05 1.29 0.285Temp.*Modyf. 2 0.14 0.14 0.07 1.61 0.211Agg.*Modyf. 1 0.05 0.05 0.05 1.23 0.273Error 50 2.14 2.14 0.04Total 59 7.49

Figure 5 shows the variation of the difference between IDT and BBR as a functionof the considered factors and the real temperature values for all 20 mixtures.

Visual inspection reveals that the difference in natural logarithms of creepcompliance at 60sec varies almost linearly with the temperature but no consistentconclusion can be made in terms of the influence of aggregate type and presence ofmodification. ANOVA results (Table 4) confirmed that observation and showed thatonly temperature level factor is significant which was also confirmed by theBonferroni comparisons between levels within each factor.

Based on the previous observation that the ratio between the measured BBR andIDT values changes with temperature and also with time, and on ANOVA results, anattempt was made to develop a temperature-dependent relation between the IDT andthe BBR for all experimental results. Regression analysis was performed using alinear model and treating (ln) IDT results as the response and (ln) BBR data as theexplanatory variable. The regression analysis was then repeated for creepcompliances obtained from the IDT and the BBR at several loading times: 16, 60,120, 240, 500, and 1000sec. A final expression was obtained combining the resultsas follows

, ,ln( ( , )) ln( ( , ))t T t TIDT t T a BBR t T b= + [4]

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where coefficients at,T and bt,T vary with time t and temperature level T. The valuesof a and b found in this study are presented in Table 5.

0-10-20-30-40

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

Temp. [C]

ln(J

_ID

T) -

ln(J

_B

BR

) [1

/GP

a]

0

GraniteLimestone

Aggregate

J difference @ 60sec

0-10-20-30-40

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

Temp. [C]

ln(J

_ID

T) -

ln(J

_B

BR

) [1

/GP

a]

0

ModifiedUnmodified

Binder

J difference @ 60sec

Figure 5. Difference ln(IDT)-ln(BBR) at 60sec

The proposed relation can be next used to predict the IDT creep compliancecurves using the BBR results. The prediction, for the mixtures presented in Figure 4,is shown in Figure 6. It can be observed that measured and predicted IDTcompliance curves are matching very well for both mixtures across all threetemperature levels.

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Table 5. Regression coefficients on ln-ln scale (IDT vs. BBR)

Test Temperature Level, T

Time, t [sec] H I L

Slope, at,T

16 0.7346 0.6123 0.4040

60 0.6250 0.8207 0.4101

120 0.5949 0.9099 0.4395

240 0.5643 1.0008 0.4323

500 0.5138 1.0625 0.4374

1000 0.5142 1.1668 0.4780

Intercept, bt,T

16 -0.1863 -0.9603 -1.9873

60 -0.0216 -0.2753 -1.8303

120 0.1192 0.0080 -1.6860

240 0.2627 0.2541 -1.6369

500 0.4098 0.4010 -1.5788

1000 0.5740 0.5806 -1.4513

0.0

0.1

1.0

10.0

10 100 1000Time [sec]

Cre

ep c

ompl

ianc

e [1

/GPa

]

58-28:U2:GRIDT measuredIDT predicted

L

I

H

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0.0

0.1

1.0

10.0

10 100 1000Time [sec]

Cre

ep c

ompl

ianc

e [1

/GPa

]

58-34:M2:LMIDT measuredIDT predicted

L

I

H

Figure 6. IDT measured and predicted creep compliance curves for two mixtures

6.2. Hirsch model predictions

In order to use Hirsch model (Equation [1]), the creep compliance functions forthe binders and the mixtures obtained from the BBR measurements were firstconverted to relaxation modulus E. The conversion was done using Prony seriesrepresentation of the creep compliance function and the convolution integral,assuming a linear and non-aging behavior of both materials. It should be also notedthat Hirsch model predictions for a given mixture were made at two temperaturesthat matched binder and mixture testing temperatures in the BBR (for temperaturelevels see Table 3). Furthermore, based on the literature review, the aggregate wasassumed as isotropic linear elastic materials, with E = 25.0GPa for the limestoneand 30.0GPa for the granite.

Figure 7 shows the results of the forward prediction of Hirsch model for all themixtures. Measured Emix from the BBR at 60sec is compared with predicted Emixat 60sec calculated using original (a) and proposed (b) expression for Pc parameterin Hirsch model. For each mixture, corresponding binder Ebinder data was used topredict Emix. It is observed that the original Hirsch model consistently overpredictsthe measured Emix values for both aggregate types. As discussed earlier, this isalmost certainly caused by different mode of loading and different mix designs usedto calibrate the original Hirsch model. Figure 7 also shows that Hirsch model with anew expression for Pc predicts measured Emix relatively well for both aggregatetypes and all points follow the line-of-equality (LOE). The coefficients for theproposed Pc expression were calculated using least-squares approach and thefollowing model was found:

( )0.100 ln 0.609binderPc E= ⋅ + [5]

where Ebinder is expressed in GPa.

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0

5

10

15

20

25

0 5 10 15 20 25

Emix measured [GPa]

Emix

pre

dict

ed [G

Pa]

E@60sec [GPa]Granite

Limestone

0

4

8

12

16

20

0 4 8 12 16 20

Emix measured [GPa]

Emix

pre

dict

ed [G

Pa]

E@60sec [GPa]Granite

Limestone

Figure 7. Hirsch model forward predictions using, a) original Pc, b) proposed Pc,at 60sec

Hirsch model predictions can be also used to plot the entire asphalt mixturerelaxation modulus curves Emix(t). Figure 8 shows Emix(t) prediction using proposedPc expression for PG 58-34:M2:GR mixture at two test temperatures. The predictedcurves match very well the experimental data. This suggests that Hirsch model,together with proposed Pc expression, can be potentially used for the back-calculation of asphalt binder relaxation modulus Ebinder from the results on theasphalt mixtures. Similar observation was reported already by the authors for theRAP mixtures (Zofka et al. 2005).

The results of the inverse calculations are plotted in Figure 9. In order to predictEbinder(t) curves, the volumetric properties and measured Emix(t) from the BBR areinput into back-calculation procedure proposed by Zofka et al. 2005 and the

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predictions are compared with measured Ebinder(t) from the BBR. The binder shownin Figure 9 corresponds to the mixture presented in Figure 8 for the forward Hirschmodel predictions. It can be noticed that a small difference in the forward methodproduces significantly larger error in the inverse scheme results. Similar observationwas pointed out by Zofka et al. 2005 that this back-calculation scheme is verysensitive to the input mixture data and a small variation in the mixture data iscausing several times greater error in the predicted binder modulus.

1

10

100

10 100 1000Time [sec]

E [G

Pa]

58-34 M2 GR -24Measured EPredicted E

1

10

100

10 100 1000Time [sec]

E [G

Pa]


Figure 8. Hirsch model forward predictions for the mixture at, a) -24°C, b) -36°C

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0.01

0.10

1.00

10 100 1000Time [sec]

E [G

Pa]


0.10

1.00

10.00

10 100 1000Time [sec]

E [G

Pa]


Figure 9. Hirsch model inverse predictions for the binder at, a) -24°C, b) -36°C

7. Summary and Conclusions

In this paper, the feasibility of using the BBR device to perform creep tests onthin asphalt mixture beams was investigated. The comparison of the experimentalresults for 20 different asphalt mixtures showed that the ratio between the creepcompliance determined with the BBR and the IDT depends on the test temperatureand loading time. Using statistical analysis, a simple relation was derived and it wasshown that this relation gives good predictions of the IDT compliance curves fromthe BBR results.

Results from the Hirsch model analysis showed that this model can besuccessfully used for the forward predictions of the asphalt mixture relaxationmodulus based only on the volumetric properties of the mix and measured relaxationmodulus of the binder. It was also shown that Hirsch model can be used to back-calculate binder compliance from the mixture data but scheme is very sensitive to

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the input mixture data and a small variation in the mixture data is causing severaltimes greater error in the predicted binder modulus.

Generally, results from this study suggest that BBR can be used for practicalestimation of mixture creep compliance. However, further research is needed tounderstand the scale effect in thin beams at low temperatures. Before furtherresearch and validation, this methodology should be used with caution since it wasverified on limited number of mixtures with identical mix design.

Acknowledgements

The IDT experimental work in this paper was sponsored by Federal HighwayAdministration National Pooled Fund Study 776. This support is gratefullyacknowledged. The results and opinions presented are those of the authors and donot necessarily reflect those of the sponsoring agencies.

8. Bibliography

American Association of State Highway and Transportation Officials (AASHTO) Standard T322-03, “Determining the Creep Compliance and Strength of Hot-Mix Asphalt (HMA)Using the Indirect Tensile Test Device”, Standard Specifications for TransportationMaterials and Methods of Sampling and Testing, 25th Edition, 2005.

American Association of State Highway and Transportation Officials (AASHTO) StandardT313-05, “Standard method of test for determining the flexural creep stiffness of asphaltbinder using the Bending Beam Rheometer (BBR)”, Standard Specifications forTransportation Materials and Methods of Sampling and Testing, 25th Edition, 2005.

American Association of State Highway and Transportation Officials (AASHTO) StandardT240-03, “Standard method of test for effect of heat and air on a moving film of asphalt(Rolling Thin-Film Oven Test)”, Standard Specifications for Transportation Materialsand Methods of Sampling and Testing, 25th Edition, 2005.

Bahia H., Anderson D.A., Christensen D., “The Bending Beam Rheometer; a simple devicefor measuring low-temperature rheology of asphalt binders”, Journal of Association ofAsphalt Paving Technologists, Vol. 61, 1992, p. 117-153

Buttlar W.G., Roque R., “Development and evaluation of the Strategic Highway ReasearchProgram measurement and analysis system for Indirect tensile testing at lowtemperatures”, Transportation Research Record: Journal of the Transportation ResearchBoard, No. 1454, 1994, p. 163-171.

Christensen D., “Analysis of creep data from Indirect Tension test on asphalt concrete”,Journal of the Association of Asphalt Paving Technologists, Vol. 67, 1998, p. 458-477.

Christensen D., Pellinen T., Bonaquist R.F., “Hirsch model for estimating the modulus ofasphalt concrete”, Journal of Association of Asphalt Paving Technologists, Vol. 72, 2003,p. 97-121.

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Hallin J.P. et al., Development of the 2002 guide for the design of new and rehabilitatedpavement structures: Phase II, Report for National Cooperative Highway ResearchProgram, Transportation Research Board, National Research Council, 2004.

Hirsch T.J., “Modulus of elasticity of concrete affected by elastic moduli of cement pastematrix and aggregate”, Journal of the American Concrete Institute, Vol. 59, No. 3, 1962,p. 427-452.

Mechanistic Empirical pavement Design Guide (MEPDG), version 1.003, built 5/24/2007.

Romero P., Masad E., “Relationship between the representative volume element andmechanical properties of asphalt concrete”, Journal of Materials in Civil Engineering,Vol. 13, No. 1, 2001, p. 77-84.

Roque R., Buttlar W.G., “The development of a measurement and analysis system toaccurately determine asphalt concrete properties using the Indirect Tensile mode”,Journal of the Association of Asphalt Paving Technologists, Vol. 61, 1992, p. 304-328.

Weissman S.L., Sackman J.L., Harvey J., Long F., “Selection of laboratory test specimendimension for permanent deformation of asphalt concrete pavements”, TransportationResearch Board Annual Meeting, 1999.

Zhang W., Drescher A., Newcomb D.E., “Viscoelastic analysis of diametral compression ofasphalt concrete”, Journal of Engineering Mechanics, Vol. 123, No. 6, 1997, p. 596-603.

Zofka A., Marasteanu M., Li X., Clyne T., McGraw J., “Simple method to obtain asphaltbinders low temperature properties from asphalt mixtures properties”, Journal of theAssociation of Asphalt Paving Technologists, Vol. 80, 2005, p. 255-282.

Zofka A., Investigation of asphalt concrete creep behavior using 3-point bending test,Ph.D. dissertation, University of Minnesota, July 2007.

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Documents

Investigation of Asphalt Mixture Creep Compliance at Low Temperatures