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Developing Master Curves and Predicting Dynamic Modulusof Polymer-Modified Asphalt Mixtures
Haoran Zhu1; Lu Sun, M.ASCE2; Jun Yang3; Zhiwei Chen4; and Wenjun Gu5
Abstract: Four kinds of polymer modifier widely used in China are selected to modify the performance of asphalt mixture: styrenebutadiene styrene �China�, PR PLAST.S �France�, Domix �Germany�, and Rad Spunrie �China�. The main objective of this paper is toevaluate the influence of these polymer modifiers on the performance of asphalt mixture with the dynamic modulus �E�� indicator throughsimple performance test. Dynamic modulus is adopted as the primary material property of hot mix asphalt mixtures in the M-E PavementDesign Guide 2002. In this study, the influences of temperature, frequency, and confining pressure on the dynamic characteristic of asphaltmixture are analyzed, and the master curves of dynamic modulus are developed and interpreted. The Witczak �E�� predictive model, whichis used in the M-E Pavement Design Guide, is also applied to predict the dynamic modulus, and the predicted values are compared withthe examined results. Results show that all these polymer modifiers, especially Domix, can strengthen the mixture stiffness, and that highfrequency, low temperature, and high confining pressure increase the dynamic modulus of asphalt mixtures. Additionally, the Witczak �E��model can soundly predict the dynamic modulus of polymer-modified asphalt mixtures.
DOI: 10.1061/�ASCE�MT.1943-5533.0000145
CE Database subject headings: Polymer; Asphalts; Mixtures; China.
Author keywords: Polymer modifier; Dynamic modulus; Master curve; Witczak |E�| model.
Introduction
The life span of roads is shortened due to cracks, rutting defor-mation, and stripping. These main damages of asphalt pavementare brought on by heavy vehicles, adverse weather, and high vol-ume traffic. Among these damaging factors, plastic deformation isone of the most serious for asphalt pavement. Specifically, theeffect of heavy vehicles on roads is generating plastic deforma-tion during the summer season, making roads lose their intrinsicfunctions. Moreover, unfavorable temperature conditions, heavytraffic, and the trend toward larger and heavier vehicles in China,particularly in its southern areas, are making the plastic deforma-tion even worse. Under such circumstances, apart from encourag-
1Ph.D. Candidate, School of Transportation, Southeast Univ., Sipailou2#, Nanjing 210096, People’s Republic of China �corresponding author�.E-mail: [email protected]
2Professor, School of Transportation, Southeast Univ., Sipailou 2#,Nanjing 210096, People’s Republic of China; and, Dept. of Civil Engi-neering, Catholic Univ. of America, 620 Michigan Ave. NE, Washington,D.C. 20064. E-mail: [email protected]
3Professor, School of Transportation, Southeast Univ., Sipailou 2#,Nanjing 210096, People’s Republic of China. E-mail: [email protected]
4M.E., Zhejiang Provincial KEWE Engineering Consulting Co., Ltd.,Hangzhou 310002, People’s Republic of China. E-mail: [email protected]
5M.E., School of Transportation, Southeast Univ., Sipailou 2#, Nan-jing 210096, People’s Republic of China. E-mail: [email protected]
Note. This manuscript was submitted on November 18, 2009; ap-proved on June 22, 2010; published online on January 14, 2011. Discus-sion period open until July 1, 2011; separate discussions must besubmitted for individual papers. This paper is part of the Journal ofMaterials in Civil Engineering, Vol. 23, No. 2, February 1, 2011.
©ASCE, ISSN 0899-1561/2011/2-131–137/$25.00.JOURNAL OF MA
J. Mater. Civ. Eng. 201
ing the use of more road-friendly vehicles, it is urgent to makestudies on the application of high-quality paving materials to im-prove the rutting-resistance performance of asphalt pavement.Polymer modifier is one of those materials.
Polymer modifier is an additive used to effectively improvethe high temperature performance of asphalt mixture throughtackling, reinforcing, filling, modifying the base asphalt, and elas-tic recovery. Polymer modifier can also improve moisture stabilityfor asphalt mixtures as well as its crack resistance at low tem-peratures �Yang 2009; Meng and Zhang 2006; Li and Qiu 2007;Zhang and Peng 2008�. Polymer modifiers are widely used; forexample, most PG76-22 binders in the United States are polymer-modified binders.
Stiffness �dynamic modulus� is a key property of the materialthat determines strains and displacements in pavement structures.The 2002 Design Guide, abbreviated for Design of New and Re-habilitated Pavement Structures, developed under NCHRP Project1-37A, uses dynamic modulus ��E��� of hot mix asphalt �HMA� asthe design stiffness parameter and the �E�� test for all three levelsof hierarchical input for the HMA characterization �AASHTO2002 �. Thoroughly, for Level 1 input �the most comprehensivedesign input level�, the Guide uses laboratory �E�� data. For Level2 input �with some laboratory test data� and Level 3 input �withno laboratory data�, �E�� values are calculated from the Witczak�E�� predictive equation �Andrei et al. 1999�.
The �E�� test is also a leading member of the simple perfor-mance test �SPT�, developed under NCHRP Project 9-19, andapplied in the Superpave mix design procedure. Thus, the �E�� testwill play a dominating role in the material characterization andbehavior of all dense-graded HMA mixtures in the future techno-logical methodologies. Many researchers measured the dynamicmodulus of HMA and discovered that the dynamic modulus wasaffected by a combined effect of asphalt binder stiffness and ag-
gregate size distribution. Clyne et al. �2003� reported that theTERIALS IN CIVIL ENGINEERING © ASCE / FEBRUARY 2011 / 131
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mixtures with a softer asphalt binder exhibited a lower dynamicmodulus than those with a stiffer asphalt binder. Brown et al.�2004� measured the dynamic modulus of asphalt mixtures withvarious aggregate structures but failed to find certain relationshipsbetween the dynamic modulus values and the aggregate struc-tures. Witczak and Bari �2004� demonstrated that the 2002 DesignGuide can be used effectively for lime-modified asphalt and de-veloped a new revised predictive model for the dynamic modulus�Bari and Witczak 2006�. Gedafa et al. �2010� conducted the dy-namic modulus tests on asphalt concrete cores and compared it tothe laboratory-compacted samples. Kim et al. �2009� conductedthe dynamic modulus tests to evaluate the performance character-istics of cold, in-place recycling mixtures using foamed mixturesover a wide range of loading and temperature conditions.The Department of Transportation of Yunnan Province insouthwest China takes an array of measures to improve the ruttingresistance of asphalt pavement, and plans to use polymer modifi-ers in Mengzi-Xinjie Expressway. Taking this project into consid-eration, the major objective of this study is to conduct dynamicmodulus tests and develop master curves to evaluate the influenceof polymer modifiers on the performance of asphalt mixtures.These results from the research will be of great guidance in se-lecting modifier materials for this project.
Methodology
For linear viscoelastic materials �HMA mixes are often supposedas such materials�, the stress-to-strain relationship under a con-tinuous sinusoidal loading is defined by its complex dynamicmodulus �E��. This complex number relates stress to strain forlinear viscoelastic materials subjected to continuously applyingsinusoidal loading in the frequency domain. The complex dy-namic modulus is defined as the ratio of the amplitude of thesinusoidal stress �at any given time t and angular load frequency��, �=�0 sin��t� to the amplitude of the sinusoidal strain �=�0 sin��t−��, at the same time and frequency, which results ina steady response as shown in Fig. 1.
The complex dynamic modulus �E�� can be mathematicallyexpressed as follows:
E� =�
�=
�0ei�t
�0ei��t−�� =�0 sin �t
�0 sin��t − ���1�
where �0=peak �maximum� stress; �0=peak �maximum� strain;�=phase angle, degrees; �=angular velocity, degrees per second;and t=time, seconds. The “dynamic modulus” is defined as theabsolute value of the complex modulus; i.e., �E��=�0 /�0. Thestiffness data of a HMA mix obtained from the �E�� test are sig-nificantly informative on the linear viscoelastic behavior of thatparticular mix over a wide range of temperature and loading fre-
Fig. 1. Dynamic �complex� modulus
quency.
132 / JOURNAL OF MATERIALS IN CIVIL ENGINEERING © ASCE / FEBRU
J. Mater. Civ. Eng. 201
In the new 2002 Design Guide, the stiffness of HMA at alllevels of temperature and time rate of loading is determined by amaster curve constructed at a reference temperature. Mastercurves are constructed; following the principle of time-temperature superposition. The data at various temperatures areshifted in line with time �frequency� until the curves merge into asingle smooth function. The master curve of modulus, functioningas frequency and formed in this manner, describes the frequencydependency of the material. The amount of shifting at each tem-perature required to form the master curve describes the tempera-ture dependency of the material. In general, the master moduluscurve can be mathematically modeled by a sigmoidal functiondescribed as
log�E�� = � +�
1 + e�+�log fr��2�
where fr=reduced frequency at reference temperature, Hz; �=minimum value of �E��; �+�=maximum value of �E��; and �,=parameters, describing the shape of the sigmoidal function.
The shift factor can be shown in the following form:
��T� =fr
f�3�
where ��T�=shift factor as the function of temperature; f=loading frequency at desired temperature, Hz; fr=reduced fre-quency at reference temperature, Hz; and T=temperature of inter-est, °C.
For the sake of precision, a second-order polynomial relation-ship between the logarithm of the shift factor, i.e., log ��Ti� andthe temperature, is used. The relationship can be expressed asfollows:
log ��Ti� = aTi2 + bTi + c �4�
where ��Ti�=shift factor as the function of temperature Ti; Ti
=temperature of interest, °C; and a, b, and c=coefficients of thesecond-order polynomial.
Before shifting the �E�� data, the relationship between binderviscosity and temperature is established by the following equa-tions:
=�G��10
� 1
sin �b�4.8628
�5�
log log = A + VTS log TR �6�
where =viscosity of binder, cP; �Gb��=complex shear modulus of
binder, Pa; �b=phase angle of binder associated with �Gb��, degree;
A, VTS=regression parameters; and TR=temperature, °Rankine.
Experiment
Materials and Mixtures
In this study, limestone aggregate and filler were used, the prop-erties of which meet the requirements of “Aggregate Tests Guide”�JTJ058-2000 in China�. The properties of Esso AH-70 importedfrom Singapore are listed in Table 1. Four kinds of polymer modi-fier, styrene butadiene styrene �SBS� �made in China�, PRPLAST.S �PR� �made in France�, Domix �made in Germany�, andRad Spunrie �RS� �made in China�, were selected in this study.PR, Domix, and RS are products of polymer additives designed to
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rutting resistance, which are directly mixed with aggregates dur-ing construction. This is different from the application ofpolymer-modified binders such as SBS. They mainly take theeffects of tackling, reinforcing, filling, and modifying the baseasphalt in mixtures. They are often used in heavily traveled roads,long steep slope sections, slow lanes, and urban intersections inhigh temperature areas. The properties of the polymer modifierare listed in Table 2.
Gradation Sup-20 showed in Table 3 was designed in accor-dance with the Superpave volumetric mix design procedure, andits optimum asphalt content �Ac� is 4.2%, air void �Va� is 4.0%,voids in mineral aggregates are 13.1%, voids filled with asphaltare 69%; and effective binder content �Vbeff� is 8.9%.
The addition content of PR, RS, and Domix is 0.4% of thetotal weight of asphalt mix, which is recommended by manufac-turers and has been applied in some real projects. Modifiers weremixed with aggregates first, and then Esso AH-70 and filler wereadded. SBS was mixed with Esso AH-70 before being mixed withaggregates and filler was added last. The ratio of SBS to EssoAH-70 is 5:95.
Test Specimen Preparation
The mixing and compaction temperatures were determined usingconsistency test results, and the viscosity-temperature relationshipwas determined for the chosen asphalt. The HMA mixtures werethen aged for 2 h at 170°C in a short-term oven before compac-tion.
The test sample was then compacted with a “Superpave gyra-tory compactor” into a 150-mm-diameter mold to approximately160 mm in height. The test specimen was cored from the center ofthe gyratory compacted sample. Approximately 5 mm was sawn
Table 1. Properties of Esso AH-70
Properties Value
Penetration �25°C, 100 g, 5 s� �0.1 mm� 60.9
Ductility �5 cm/min, 15°C� �cm� 161
Softening point �ring and ball method� �°C� 50.4
Density �15°C� �g /cm3� 1.04
Flash point �°C� 272
Wax content �%� 2.1
Solubility �%� 99.8
Table 2. Properties of Polymer Modifier
Modifiers Color and shapeDiameter
�mm�Density�g /cm3�
Melting range�°C�
PR Black granule �5 0.91–0.97 140–180
Domix Taupe granule 1–6 1.042 130–180
Rad Spunrie Black granule �6 0.92–0.96 150–160
SBS Yellowy granule �10 0.94–1.13 150–230
Table 3. Gradation of Sup-20
Mass
Gradation 25.0 19.0 16.0 12.5 9.5
Sup-20 100.0 94.0 85.7 70.3 56.7
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J. Mater. Civ. Eng. 201
from each sample end to have the final 100-mm-diameter�150-mm-height E� test specimen. All the test specimens werecompacted to about 4% air voids.
Dynamic Modulus Testing
The dynamic modulus test was conducted in a SPT testing sys-tem, a special test machine used for SPTs, made in IPC Global inAustralia, shown in Fig. 2. This machine consists of a confiningpressure system, which is capable of providing a constant pres-sure up to 210 kPa and an environmental chamber to controltemperatures, ranging from 4 to 70°C. First, place the test speci-men in the environmental chamber and make it equilibrate to thespecified testing temperature. Then place the specimen on top ofthe lower end treatment, and mount the axial LVDTs to the gaugepoint previously glued to the specimen. Adjust the LVDT to nearthe end of its linear range to control the full range to be availablefor the accumulation of compressive permanent deformation.Place the upper friction reducing end treatment and platen on topof the specimen. Center the specimen with the load actuator vi-sually in order to avoid eccentric loading. Apply a contact load�Pmin� equal to 5% of the dynamic load, which will be later ap-plied to the specimen, and a haversine loading �Pdynamic� adjustedto obtain axial strains between 85 and 115 microstrains to thespecimen without impact in a cyclic manner. All the test data areautomatically measured and recorded with operation software.For each mix, three replicates were prepared for testing. Sincethis paper mainly focused on the mixture performance at hightemperatures, each specimen in this study was tested at 20, 30, 40,50, 60, and 70°C, without being applied at low temperatures. Theloading frequencies were 25, 20, 10, 5, 1, 0.5, and 0.1 Hz, respec-
tage passing sieve size�mm, %�
5 2.36 1.18 0.6 0.3 0.15 0.075
24.4 16.4 11.4 8.1 5.9 4.7
Fig. 2. Photo of the IPC test machine
percen
4.7
37.9
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tively. In order to help some specimen recover before applying anew loading at a lower frequency, a 60-s rest period was usedbetween each frequency.
Results and Analysis
Master Curves
The calculated shift parameters and master curves can be used forviscoelastic analysis of materials, and as the inputs of the 2002Design Guide. They are the basic data for viscoelastic mechanicalanalysis of asphalt pavement structure.
Fig. 3 is a plot of �E�� versus loading frequency, where the �E��data are shifted using a nonlinear optimization by simultaneouslysolving shift parameters, and then the seven parameters of mastercurve model are fitted by least-squares method with Matlab pro-gram in this study. In this paper, 40°C is taken as the referencetemperature. Fig. 4 is a plot of the logarithm of the shift factors,log ��Ti� and the temperature. These seven parameters are thenused in Eq. �2� to calculate �E�� of the particular mix at anytemperature and loading frequency within the range used in the�E�� testing.
�E�� master curves of all mixtures were constructed at the ref-erence temperature of 40°C following the principle of time-temperature superposition. The data at various temperatures wereshifted in line with frequency until the curve merges into a singlesigmoidal function, representing the master curve, using asecond-order polynomial relationship between the logarithm ofthe shift factors, log ��Ti� and the temperature, shown in Fig. 4.The time-temperature superposition was done by simultaneouslysolving the four coefficients of the sigmoidal function ��, �, �,and �, as described in Eq. �2�, and the three coefficients of thesecond-order polynomial �a, b, and c� as Eq. �4� with least-squares method. The seven parameters of each mixture are listedin Table 4, and the fitted master curves of each mixture are shown
100
1000
10000
100000
0.1 1 10 100Loading frequency, Hz
|E*|,MPa
20℃30℃40℃50℃60℃70℃
Fig. 3. Plot of �E�� versus loading frequency
134 / JOURNAL OF MATERIALS IN CIVIL ENGINEERING © ASCE / FEBRU
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in Fig. 5.
Effect of Polymer ModifiersOn the basis of this research, it is found that different polymermodifiers vary in their influences on the stiffness of mixture. Fig.6 compares the effects of four different modifiers on the dynamicmodulus �E�� of mixture. The figure shows that mixture with theDomix modifier has the largest dynamic modulus �E��. The �E�� ofmixture with the RS modifier is close to that with the Domixmodifier at intermediate frequency, while smaller at lower orhigher frequency. According to the principle of time-temperaturesuperposition, it implies that the �E�� of mixture with the RSmodifier is close to that with the Domix modifier at intermediatetemperature, but smaller at correspondingly higher or lower tem-perature. The �E�� of mixture with the PR modifier is a little bitsmaller than that with the Domix modifier in any case. However,the �E�� of mixtures with each modifier mentioned above are ex-ceptionally larger than that with the SBS modifier, especially athigh temperature and at low frequency, which shows that all threemodifiers can strengthen the mixture stiffness significantly. Ac-cording to Witczak et al. �2002� and Zhou and Scullion �2003�, awell-fitted relationship exists between dynamic modulus �E�� andthe rutting resistance performance �Witczak et al. 2002; Zhou andScullion 2003�. Hence, all three polymer modifiers, especially theDomix modifier, can effectively improve the rutting resistanceperformance. Since these three polymer modifiers are mixed withaggregates directly during construction, they not only modify theproperties of base asphalt, but also tackle, fill, reinforce, and elas-tically recover the mixture, thereby strengthening its stiffness.
Validation of Witczak Model Predicted E� Data withLaboratory E� DataDynamic modulus is adopted as the primary material property ofHMA mixtures in the M-E Pavement Design Guide 2002. Theguide uses Witczak �E�� predictive model as Eq. �7� to predict thedynamic modulus �Andrei et al. 1999�.
y = 0.0011x2 - 0.1955x + 5.9929R2 = 0.9981
-3
-2
-1
0
1
2
3
0 10 20 30 40 50 60 70 80
Temperature,℃
logα(T)
Fig. 4. Plot of shift factor log ��T� versus temperature
Table 4. Master Curve and Shift Parameters
Modifiers � � � a b c
PR 2.3081 2.2745 0.5272 0.6109 0.0007 0.1475 4.7757
SBS 1.7113 2.8829 0.3826 0.5786 0.0009 0.1514 4.7529
Domix 2.3511 2.2219 0.4268 0.6247 0.0012 0.1885 5.5957
RS 2.0464 2.5774 0.1507 0.5181 0.0011 0.1955 5.9929
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log�E�� = − 1.249 937 + 0.029 232�200 − 0.001 767�2002 + 0.002 841�4 − 0.058 097Va − 0.802 208
Vbeff
Vbeff + Va
+3.871 977 − 0.002 1�4 + 0.003 958�38 − 0.000 017�38
2 + 0.054 7�34
1 + e�−0.603 313−0.313 351 log f−0.393 532 log � �7�
-4 -3 -2 -1 0 1 2 3 4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
Log reduced frequency,Hz
Log|E*|,Mpa
Master curve of Domix
20℃30℃40℃50℃60℃70℃master curve
(a)
-4 -3 -2 -1 0 1 2 3 4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
Log reduced frequency,Hz
Log|E*|,Mpa
Master curve of PR
20℃30℃40℃50℃60℃70℃master curve
(b)
-4 -3 -2 -1 0 1 2 3 42
2.5
3
3.5
4
4.5
Log reduced frequency,Hz
Log|E*|,Mpa
Master curve of RS
20℃30℃40℃50℃60℃70℃master curve
(c)
-4 -3 -2 -1 0 1 2 3 41.5
2
2.5
3
3.5
4
4.5
Log reduced frequency,Hz
Log|E*|,Mpa
Master curve of SBS
20℃30℃40℃50℃60℃70℃master curve
(d)
Fig. 5. �a� Fitted master curve of Domix mixture; �b� fitted master curve of PR mixture; �c� fitted master curve of RS mixture; and �d� fittedmaster curve of SBS mixture
where �E��=dynamic modulus, 105 psi; =viscosity of binder,106 P; f =loading frequency, Hz; �200=aggregates passingthrough the 0.075-mm sieve, %; �4=cumulative aggregates re-tained on the 4.75-mm sieve, %; �38=cumulative aggregates re-tained on the 9.5-mm sieve, %; �34=cumulative aggregatesretained on the 19.0-mm sieve, %; Va=air voids, %; and Vbeff
=effective binder content, %.Use the criteria developed by NCHRP-report-465 �Witczak et
al. 2002� to evaluate the prediction accuracy. The subjective clas-sification of the goodness of fit is shown in Table 5. R2 is thecoefficient of determination, Se is standard error, and Sy is stan-dard deviation. A good model would have a high R2 �close tounity� and a small Se /Sy.
These Witczak model predicted �E�� and the laboratory mea-sured �E�� data are presented in Fig. 7. It is shown that the Witc-zak model predicted �E�� can produce well-fitted results whencompared to laboratory �E�� test data. Hence, for practical pur-poses, Witczak �E�� predictive model may be applicable for dy-
namic modulus prediction for polymer-modified asphalt mixtures.JOURNAL OF MA
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Effect of Other Variables
The effects of loading frequency, temperature, and confining pres-sure on the stiffness of modified mixture are discussed.
Loading FrequencyTake the �E�� at reference temperature of 40°C, for example, asshown in Fig. 8. The figure obviously shows that with the in-crease in frequency, the dynamic modulus �E�� of mixture in-creases; and conclusions come to that through using the principleof time-temperature superposition, dynamic modulus �E�� is smallat the conditions of high temperature and low frequency, while itincreases under the contrary conditions.
TemperatureTake the �E�� at a loading frequency of 5 Hz, for example, asshown in Fig. 9. The figure obviously shows that with the in-
crease in temperature asphalt binder is softened and finally dy-TERIALS IN CIVIL ENGINEERING © ASCE / FEBRUARY 2011 / 135
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namic modulus �E�� of mixture is decreased. The �E�� at lowtemperature of 20°C is about twice as large as that at high tem-perature of 70°C.
Confining PressureTake the �E�� of RS and PR modified mixtures at temperature of50°C. Results with and without 100-kPa confining pressure arecompared, as shown in Fig. 10. The figure shows that under thetest conditions in this study, confining pressure has influenced thestiffness of mixture so significantly that the confined dynamicmodulus �E�� is notably larger than the unconfined. The �E�� atconfining pressure of 100 kPa is about 20–40% more than that atan unconfined condition.
Table 5. Subjective Classification of the Goodness-of-Fit Statistical Pa-rameters
Rank R2 Se /Sy
Excellent �0.90 �0.35
Good 0.70–0.89 0.36–0.55
Fair 0.40–0.69 0.56–0.75
Poor 0.20–0.39 0.76–0.90
Very Poor �0.19 �0.90
-4 -3 -2 -1 0 1 2 3 41.5
2
2.5
3
3.5
4
4.5
Log reduced frequency,Hz
Log|E*|,Mpa
Master curves
PRSBSDomixRS
Fig. 6. Master curves of four different mixtures
y = 0.8532x + 0.452Se=0.2414, Se/Sy=0.4422, R2 = 0.7893
1.5
2
2.5
3
3.5
4
4.5
5
1.5 2 2.5 3 3.5 4 4.5 5
log|E*| from Model
log|E*|fromlab
Fig. 7. Plot of Witczak model predicted versus laboratory measured�E��
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Comparison of Master Curve �E�� Data with Laboratory�E�� Data
The �E�� of each mix at six test temperatures and seven test load-ing frequencies were also calculated using the master curve andshift coefficients. These “master curve obtained �E��” and “thelaboratory measured �E��” data are presented in Fig. 11. Accord-ing to the criteria in Table 5, it is shown that master curve ob-tained �E�� produced nearly identical results when compared tolaboratory �E�� test data. Hence, for practical purposes, the �E��values obtained from a master curve may be substituted for thelaboratory �E�� test data.
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20 25 30
Loading frequency, Hz
|E*|,MPa
PRSBSDomixRS
Fig. 8. Plot of loading frequency versus �E��
0
2000
4000
6000
8000
10000
12000
14000
16000
20 30 40 50 60 70 80
Temperature, °C
|E*|,MPa
PRSBSDomixRS
Fig. 9. Plot of temperature versus �E��
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30
Loading frequency, Hz
|E*|,MPa
RS-100kPaPR-100kPaRS-0kPaPR-0kPa
Fig. 10. Plot of confining pressure versus �E��
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Conclusions
Based on the laboratory test results and analysis made in thisresearch study, the following conclusions can be obtained.1. All the polymer modifiers used in this research study can
strengthen the mixture stiffness notably, and the modifyingeffect rank is Domix�RS�PR�SBS in view of the projectin this research.
2. The �E�� of Domix, RS, and PR modified mixtures are excep-tionally larger than that of SBS modified mixture, especiallyat a high temperature and at a low frequency. This is becausethese three polymer modifiers are mixed with aggregates di-rectly so that they do not only modify the properties of baseasphalt, but also tackle, fill, reinforce, and elastically recoverthe mixture and thereby strengthen its stiffness.
3. Through using the principle of time-temperature superposi-tion, dynamic modulus �E�� is small at the conditions of hightemperature and low frequency, while it increases under thecontrary conditions.
4. Under the test conditions in this study, confining pressureinfluences the stiffness of mixture so significantly that theconfined dynamic modulus �E�� is extremely larger than theunconfined.
5. Dynamic modulus can be obtained as nearly identical to thelaboratory results by using master curves, and Witczak modelmay be applicable to predict the dynamic modulus ofpolymer-modified asphalt mixtures.
Acknowledgments
The writers are very thankful to anonymous reviewers for theirinsightful and constructive comments, which enable the writers toimprove the content of the original manuscript, and to Ms. SiyuanZhou at Nanjing Normal University and Ms. Regina Zolbrod atCatholic University of America, who helped to edit the presenta-tion of the paper. This study is sponsored in part by the National
y = 0.9895x + 0.0366Se=0.0570, Se/Sy=0.1087, R2 = 0.9882
2
2.5
3
3.5
4
4.5
2 2.5 3 3.5 4 4.5
log|E*| from master curve
log|E*|fromlab
Fig. 11. Plot of master curve versus laboratory �E��
Science Foundation �NSF� under Grant No. CMMI-0408390 and
JOURNAL OF MA
J. Mater. Civ. Eng. 201
NSF CAREER Award No. CMMI-0644552, by the AmericanChemical Society Petroleum Research Foundation under GrantNo. PRF-44468-G9, by the Changjiang Scholarship of Ministryof Education of China, by the Huoyingdong Educational Founda-tion under Grant No. 114024, by the Jiangsu Natural ScienceFoundation under Grant No. SBK200910046, by the JiangsuPostdoctoral Foundation under Grant No. 0901005C, by theShandong DOT, by the Shanxi DOT, by the Shanxi DOT underGrant No. 7921000015, and by the Yunnan DOT under Grant No.2007�A�1–03, to which the writers are very grateful.
References
AASHTO. �2002�. 2002 design guide: Design of new and rehabilitatedpavement structures, National Cooperative Highway Research Pro-gram, Transportation Research Board, Washington, D.C.
Andrei, D., Witczak, M. W., and Mirza, W. �1999�. “Development of arevised predictive model for the dynamic �complex� modulus of as-phalt mixtures.” Inter Team Technical Rep. prepared for the NCHRP1-37A Project, Dept. of Civil Engineering, Univ. of Maryland, Col-lege Park, Md.
Bari, J., and Witczak, M. W. �2006�. “Development of a new revisedversion of the Witczak E� predictive model for hot mix asphalt mix-tures.” Electron. J. Assoc. Asph. Paving Technol., 75, 381–423.
Brown, E. R., Prowell, B., Cooley, A., Zhang, J., and Powell, B. �2004�.“Evaluation of rutting performance at the 2000 NCAT test track.”Electron. J. Assoc. Asph. Paving Technol., 73, 287–336.
Clyne, T. R., Li, X., Marasteanu, M. O., and Engene, K. �2003�. “Dy-namic modulus and resilient modulus of Mn/DOT asphalt mixtures.”MN/RC-2003-09, Minnesota Dept. of Transportation, St. Paul, Minn.
Gedafa, D. S., Hossain, M., Romanoschi, S., and Gisi, A. J. �2009�.“Field verification of Superpave dynamic modulus.” J. Mater. Civ.Eng., 22�5�, 485–494.
Kim, Y. J., Lee, H. D., and Heitzman, M. �2009�. “Dynamic modulus andrepeated load tests of cold in-place recycling mixtures using foamedasphalt.” J. Mater. Civ. Eng., 21�6�, 279–285.
Li, J. F., and Qiu, Z. X. �2007�. “PR Plast module additive applied to longand gradient asphalt pavement.” Journal of China and Foreign High-way, 27�4�, 69–72.
Meng, Y. J., and Zhang, X. N. �2006�. “Effects of additives on the prop-erties of asphalt cement.” Journal of Highway and TransportationResearch and Development, 23�12�, 14–17.
Witczak, M. W., et al. �2002�. “Simple performance test for Superpavemix design.” NCHRP Rep. No. 465, National Cooperative HighwayResearch Program, Transportation Research Board, Washington, D.C.
Witczak, M. W., and Bari, J. �2004�. “Development of a master curve �E��database for lime modified asphaltic mixtures.” Final Rep., ArizonaState Univ., Tempe, Ariz.
Yang, J. �2009�. “Research on the rutting resistance performance of ex-pressway asphalt pavement in Yunnan Province.” Final Rep., South-east Univ., Nanjing, China �in Chinese�.
Zhang, C., and Peng, Q. Y. �2008�. “Research on the field performance ofrubber and Domix modified asphalt.” Journal of Highway and Trans-portation Research and Development, 4�11�, 64–68.
Zhou, F. J., and Scullion, T. �2003�. “Case study: Preliminary field vali-dation of simple performance tests for permanent deformation.” 82ndAnnual Meeting of the Transportation Research Board, Transportation
Research Board, Washington, D.C.TERIALS IN CIVIL ENGINEERING © ASCE / FEBRUARY 2011 / 137
1.23:131-137.
