Construction and Building Materials 23 (2009) 3144–3151

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Construction and Building Materials

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Fatigue behavior of rubberized asphalt concrete mixturescontaining warm asphalt additives

Feipeng Xiao a,*, P.E. Wenbin Zhao b, Serji N. Amirkhanian b

a Asphalt Rubber Technology Service, Department of Civil Engineering, Clemson University, Clemson, SC 29634-0911, USAb Department of Civil Engineering, Clemson University, Clemson, SC 29634-0911, USA

a r t i c l e i n f o

Article history:Received 7 December 2008Received in revised form 18 May 2009Accepted 18 June 2009Available online 16 July 2009

Keywords:Rubberized asphalt concreteWarm asphalt additiveMixing and compaction temperatureStiffnessDissipated energyFatigue life

0950-0618/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.conbuildmat.2009.06.036

* Corresponding author. Tel.: +1 864 6566799; fax:E-mail address: feipenx@clemson.edu (F. Xiao).

a b s t r a c t

The long-term performance of pavement is associated with various factors such as pavement structure,materials, traffic loading, and environmental conditions. Improving the understanding of the fatiguebehavior of the specific rubberized warm mix asphalt (WMA) is helpful in recycling the scrap tires andsaving energy. This study explores the utilization of the conventional fatigue analysis approach in inves-tigating the fatigue life of rubberized asphalt concrete mixtures containing the WMA additive. The fatiguebeams were made with one rubber type (�40 mesh ambient crumb rubber), two aggregate sources, twoWMA additives (Asphamin� and Sasobit�), and tested at 20 �C. A total of eight mixtures were performedand 29 fatigue beams were tested in this study. The test results indicated that the addition of crumb rub-ber and WMA additive not only reduced the mixing and compaction temperatures of rubberized asphaltmixtures offset by crumb rubber but also effectively extended the long-term performance of pavementwhen compared with conventional asphalt pavement. In addition, the exponential function forms areefficient in achieving the correlations between the dissipated energy and load cycle as well as mixturestiffness and load cycle.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Fatigue cracking, called alligator cracking and associated withrepetitive traffic loading, is considered to be one of the most signifi-cant distress modes in flexible pavements. The fatigue life of anasphalt pavement is directly related to various engineering proper-ties of a typical hot mix asphalt (HMA). The complicated micro-structure of asphalt concrete is related to the gradation of aggregate,the properties of aggregate–binder interface, the void size distribu-tion, and the interconnectivity of voids. As a result, the fatigue prop-erty of asphalt mixtures is very complicated and sometimes difficultto predict [1–3].

Understanding the ability of an asphalt pavement to resist frac-tures from repeated loading condition is essential for developingsuperior HMA pavement designs. Previous studies have been con-ducted to understand the occurrence of fatigue and how to extendpavement life under repetitive traffic loading [3,4]. However,reaching a better understanding of fatigue behavior of asphaltpavements continues to challenge researchers worldwide, particu-larly as newer materials with more complex properties are beingused in the field.

The recycling of scrap tires has been of interest to the domesticand international asphalt industry for over 40 years. The utilization

ll rights reserved.

+1 864 6566186.

of crumb rubber modifier (CRM) in asphalt binders has proven tobe beneficial from many stand points. The use of CRM, expandedto HMA, continues to evolve since the CRM binders enhance theperformance of asphalt mixtures by increasing the resistance ofthe pavements to permanent deformation and thermal and fatiguecracking. Many researchers have found that utilizing crumb rubberin pavement construction is both effective and economical [5–9].

Recently, the ‘‘warm mix asphalt” (WMA) is widely being usedin the hot HMA industry as a mean of reducing energy require-ments and lowering emissions. WMA can significantly reduce themixing and compacting temperatures of asphalt mixtures, byeither lowering the viscosity of asphalt binders, or causing foamingin the binders. Reduced mixing and paving temperatures decreasesthe energy required to produce HMA, reduces emissions and odorsfrom plants, and makes for better working conditions at both theplant and the paving site [10–15].

However, the influence of crumb rubber and WMA additivesmixed with virgin mixtures together has not yet been identifiedclearly. The interaction of modified mixtures is not well under-stood from the standpoint of binder properties and field perfor-mance. It has been shown that the WMA additives reduce themixing and compaction temperatures and achieve ideal workabil-ity of HMA without significantly affecting the engineering proper-ties of the mixtures [10–13]. While the addition of crumb rubberincreases the demand of asphalt binder and increases the mixingand compacting temperatures, it is helpful in resisting the high

F. Xiao et al. / Construction and Building Materials 23 (2009) 3144–3151 3145

temperature deformation and extending the long-term perfor-mance of HMA. Because of the complicated relationships of thesetwo materials in the modified mixtures, detailed information willbe beneficial to help obtain an optimum balance in the use of thesematerials. Very few fatigue studies of modified asphalt mixtures,including crumb rubber and warm asphalt additives, have beenperformed in recent years [16]. However, the utilization of thesematerials will enable the engineers to find an environmentallyfriendly method to deal with these materials, save money, energy,and furthermore, protect the environment.

The objective of this study was to gain an improved under-standing in the long-term performance characteristics (fatiguebehavior) of the rubberized asphalt concrete mixtures containingWMA additives through a series of experimental tests. Experi-ments were carried out to evaluate rheological properties of themodified binder (unaged and aged binders) as well as the engineer-ing properties of the mixture, such as the stiffness and fatigue lifeperformed by HMA flexural testing.

0

20

40

60

80

100

Perc

ent p

assi

ng (

%)

Sieve size (mm)

Agg. AAgg. BLow RangeUp Range

0.075 0.60 2.36 4.750.15 9.5 12.5 19.0

Fig. 1. Gradations of aggregates A and B.

2. Background

The fatigue characteristics of asphalt mixtures are usuallyexpressed as relationships between the initial stress or strain andthe number of load repetitions to failure-determined by usingrepeated flexure, direct tension, or diametral tests performed atseveral stress or strain levels. The fatigue behavior of a specificmixture, characterized by the slope and relative level of the stressor strain versus the number of load repetitions to failure, may bedefined using the following equation [17]:

Nf ¼ að1=e0Þbð1=S0Þc or Nf ¼ að1=r0Þbð1=S0Þc ð1Þ

where Nf is the number of load application or crack initiation; e0, r0,the tensile strain and stress, respectively; S0, the initial mix stiff-ness; and a, b, c are the experimentally determined coefficients.Inrecent years, several researchers have used the energy approachfor predicting the fatigue behavior of the asphalt mixtures. The dis-sipated energy per cycle, Wi, for a linearly viscoelastic material isgiven by the following equation [18–22]:

W ¼Xn

i¼1

Wi ¼Xn

i¼1

priei sinðdiÞ ð2Þ

where W is the cumulative dissipated energy to failure, Wi is thedissipated energy at load cycle i, ri is the stress amplitude at loadcycle i, ei is the strain amplitude at load cycle i, and di is the phaseshift between stress and strain at load cycle i.

Research has shown that the dissipated energy approach makesit possible to predict the fatigue behavior of mixtures in the labo-ratory over a wide range of conditions based on the results of a fewsimple fatigue tests. Such a relationship can be characterized in theform of the following equation [18–22]:

W ¼ AðNfÞZ ð3Þ

where Nf is the fatigue life, W is the cumulative dissipated energy tofailure, and A, Z are the experimentally determined coefficients.

Table 1Aggregate property of mixtures.

Aggregate source LA abrasion loss (%) Absorption (%) Specific gravity

Dry (BLK) SSD (BLK)

A 51 0.80 2.740 2.770B 34 0.60 2.780 2.800

3. Experimental program and procedures

3.1. Materials

One virgin binder (PG 64-22) and one crumb rubber modified(CRM) binder (PG 64-22 + 10% �40 mesh rubber) were used in thisstudy. The PG 64-22 binder was a mixture of several sources thatcould not be identified by the supplier. One type of rubber, �40mesh ambient rubber, was used in this study. Previous researchand field projects conducted in South Carolina indicated that the�40 mesh ambient rubber is effective in improving the engineer-ing properties of rubberized mixtures.

Asphamin� and Sasobit� were used in this study as two WMAadditives. Asphamin� is Sodium–Aluminum–Silicate which ishydro thermally crystallized as a very fine powder. It containsapproximately 21% crystalline water by weight. By adding it toan asphalt mix, the fine water spray is created as all the crystallinewater is released, which results in volume expansion in the binder,therefore increasing the workability and compactability of the mixat lower temperatures. Sasobit� is a long chain of aliphatic hydro-carbons obtained from coal gasification using the Fischer–Tropschprocess. After crystallization, it forms a lattice structure in the bin-der which is the basis of the structural stability of the binder con-taining Sasobit� [10,11].

Two aggregate sources (A and B) were used for preparing thesamples (Table 1). Aggregate A, a type of granite, is predomi-nantly composed of quartz and potassium feldspar while aggre-gate B (schist) is a metamorphic rock. Hydrated lime, used asan anti-strip additive, was added at a rate of 1% by dry mass ofaggregate. A total number of eight mixtures were evaluated inthis research. In this paper, the mixtures made from aggregatesA and B without rubber and WMA additive are referred to asACO and BCO; and the mixtures with rubber but no WMA addi-tive are referred to as ARO and BRO. In addition, the mixtureswith rubber and Asphamin� are designated as ARA and BRA,

Soundness % loss at five cycles Sand equivalent Hardness

Apparent 1 ½ to 3/4 3/4 to 3/8 3/8 to #4

2.800 0.2 0.1 0.1 – 52.830 0.4 0.6 0.9 35 5

3146 F. Xiao et al. / Construction and Building Materials 23 (2009) 3144–3151

and the mixtures with rubber and Sasobit� are labeled as ARS andBRS, respectively.

3.2. Superpave mix design

The combined aggregate gradations for the 12.5 mm mixtureswere selected in accordance with the specification set by the SouthCarolina Department of Transportation (SCDOT). The gradations foreach aggregate source (A and B) are shown in Fig. 1, which showsthat the design aggregate gradations for each aggregate source arethe same when using different WMA additives (Asphamin� andSasobit�) at the same percentages of rubber (0% or 10% rubber),while the gradations are similar when comparing mixtures fromboth aggregate sources.

Superpave mix design defines that the laboratory mixing andcompaction temperatures can be determined by using a plot ofviscosity versus temperature. While there are no previous specifi-cations available regarding the mixing and compaction tempera-tures for rubberized mixture containing WMA additives, someresearchers have developed guidelines for mixing and compactiontemperatures when using either WMA or rubber [10,11,23]. Thetemperatures, shown in Table 2, were determined in accordancewith previous research projects [16,23]. Though the mixing andcompaction temperatures increase as the percentage of crumb rub-ber increases, these can be reduced by adding either Asphamin� orSasobit�.

Table 2Mixing and compaction temperatures of mixtures.

Mixing temperature (�C) Compaction temperature (�C)

ACO/BCO 152–158 132–138ARO/BRO 170–176 152–158ARA/BRA 145–155 135–145ARS/BRS 145–155 135–145

Note: ACO/BCO; ARO/BRO; ARA/BRA; and ARS/BRS-control; rubberized; rubberizedAsphamin�; and rubberized Sasobit� from aggregates A and B, respectively.

Fig. 2. Fatigue bea

Table 3Binder properties.

Unaged binder

135 �C (64 �C)

Viscosity (Pa s) Std. (Pa s) G*/sin d (kPa) Std. (k

PG 64-22 0.41 0.0 1.2 212.1PG 64-22R 1.60 0.0 3.7 60.8PG 64-22RA 1.48 0.1 4.7 631.9PG 64-22RS 1.44 0.1 5.2 469.4

Note: R, rubberized; A, Asphamin�; S, Sasobit�.

3.3. Fatigue beam fabrication and test procedures

Fatigue beams were made in the laboratory and two–four beamsof each mixture were tested for this study (Fig. 2). All tests wereperformed in a temperature-controlled chamber at 20 ± 0.5 �C. Inthis study, a repeated sinusoidal loading at a frequency of 10 Hzwas used; in addition, the controlled strain mode was employed.The control and data acquisition software measured the deflectionof the beam specimen, computed the strain in the specimen andadjusted the load applied by the loading device (AASHTO T321).

The test apparatus also recorded load cycles, applied load, andbeam deflections. Failure is assumed to occur when the stiffnessreaches half of its initial value, which is determined from the loadat approximately 50 repetitions; the test is terminated automati-cally when this load has diminished by 50%. The flexural stiffnessand dissipated energy of fatigue beam are determined as follows(AASHTO T321):

1. Flexural stiffness (Pa):

m and

Pa)

S ¼ r=e ¼ aPð3l2 � 4a2Þ4bDh3 ð4Þ

where r is the tensile stress in Pa; e, the maximum tensilestain in m/m; P, the applied peak-to-peak load in N; a, thespace between inside clamps in m; b, the average beam widthin m; h, the average beam height, in m; D, the beam deflectionat neutral axis, in m; and l, the length of beam between out-side clamps, in m.

2. Dissipated energy (J/m3) per cycle:

D ¼ pre sinð360f hÞ ð5Þ

where f is the load frequency in Hz; h, the time lag betweenPmax and dmax, in s.

3. Cumulative dissipated energy (J/m3):

W ¼Xi¼n

i¼1

Di ð6Þ

where Di = D for the ith load cycle.

testing.

Aged binder (RTFO + PAV)

(25 �C) (�12 �C)

G*/sin d (kPa) Std. (kPa) Stiffness (MPa) Std. (MPa)

2970.0 572.8 221.0 20.51705.6 66.1 128.5 2.52042.1 3.9 148.0 1.22160.3 170.2 150.5 0.6

Table 4Typical analyzed fatigue test results (BCO-B).

Period number (cycles) Stress (Pa) Strain (m/m) Dynamic stiffness (Pa) Phase angle (degree) Dissipated energy (J/m3) Cumulative energy (J/m3)

50 1860.89 1.42E�04 1.31E+07 72 0.21 63.70100 2110.50 1.53E�04 1.37E+07 72 0.26 130.03250 2050.47 1.73E�04 1.19E+07 72 0.28 207.84500 1706.07 1.25E�04 1.36E+07 72 0.17 308.911000 1864.05 1.72E�04 1.08E+07 72 0.26 361.951600 2074.17 1.74E�04 1.19E+07 72 0.29 382.902500 1875.11 1.65E�04 1.14E+07 72 0.25 445.515000 1750.30 1.66E�04 1.06E+07 72 0.23 484.1110,000 1728.18 1.79E�04 9.68E+06 72 0.25 537.0715,850 1497.53 1.91E�04 7.84E+06 72 0.23 567.4719,954 1289.00 1.66E�04 7.78E+06 72 0.17 581.3725,120 980.96 1.56E�04 6.29E+06 72 0.12 594.70

0

Fatig

ue li

fe (

cycl

e)

Aggregate A Aggregate B

2x10 5

0

4x10 5

8x10 5

6x10 5

0

Stif

fnes

s (k

Pa)

Aggregate A Aggregate B

2.0x10 7

0.5x10 7

1.5x10 7

1.0x10 7

0

0

200

400

600

800

1000

CO RO RA RS

Cum

ulat

ive

diss

ipat

ed e

nerg

y (J

/m3)

Mixture type

CO RO RA RS

Mixture type

CO RO RA RS

Mixture type

Aggregate A Aggregate B

(a)

(b)

(c)

Fig. 3. Mechanical properties: (a) fatigue life; (b) stiffness; (c) cumulative energy.

F. Xiao et al. / Construction and Building Materials 23 (2009) 3144–3151 3147

4. Analysis of test results

4.1. Statistical considerations

Results of the stiffness, cumulative dissipated energy, and fati-gue life values were statistically analyzed with 5% level of signifi-cance (0.05 probability of a Type I error) with respect to theeffects of aggregate sources and WMA additive types. For thesecomparisons, it should be noted that all specimens were producedat optimum binder content.

4.2. Binder analysis

Table 3 shows that the viscosity of rubberized asphalt binderdecreases while the high temperature performance (G*/sin d) ofoverall binders increase with the addition of WMA additive. Theunaged binder test result shows that the Asphamin� and Sasobit�

can improve the workability (viscosity) and rutting resistance(G*/sin d) of mixtures. While the aged rubberized binders showthat the G*sin d values decrease with the addition of rubber, thesevalues increase slightly as the WMA additives are added. It also canbe seen that the stiffness values of binders have similar trends withG*sin d values due to the addition of these materials. Aged binderproperties show that the WMA additives produce a slightly effecton the long-term performance of asphalt binder.

4.3. Analysis of fatigue test results

Testing data were analyzed using Eqs. (4)–(6) presented earlierto compute the stress, strain, stiffness, phase angle, the dissipatedenergy per cycle as the function of the number of load cycles, andthe cumulative dissipated energy to a given load cycle. In thisstudy, fatigue life was defined as the number of repeated cyclescorresponding to a 50% reduction in initial stiffness, which wasmeasured at the 50th load cycle. Several fatigue beam specimenswere utilized to characterize the fatigue behavior of a mixture inorder to avoid too much or too little loss in stiffness. This proce-dure involved testing control specimens (ACO and BCO samples)at a 500 micro-strain level with the controlled strain mode of load-ing at a frequency of 10 Hz.

Table 4 presents a typical analyzed fatigue test results whichwere computed at various cycles from the raw data. It can be seenthat the stress value and dissipated energy per cycle generally de-crease as the number of cycle increases. That is, at the same strainlevel, the greater stress is needed to reach the desired strain valuesat the beginning of fatigue test than at the end of the test. At thesame time, the dissipated energy per cycle during the first thou-sands of cycles is remarkably greater than those during the finalcycles (50% loss of initial stiffness). As expected, the asphalt pave-ment in the field rapidly releases the potential energy within the

Table 5Statistical analysis of mechanical properties in terms of aggregate sources.

P-value Test properties (agg. A and B)

Cumulative energy Stiffness Fatigue life

Control 0.431 0.059 0.048Rubberized 0.297 0.011 0.030Rubberized + Asphmin 0.293 0.005 0.002Rubberized + Sasobit 0.036 0.205 0.033

Note: P-value < a = 0.05 (significant difference); P-value > a = 0.05 (No significantdifference).

yA = -141.59x + 562241

yB = -19.604x + 96617

11000 2000 3000 4000

Fatig

ue li

fe (

cycl

e)

G*sinδ (kPa)

Aggregate A Aggregate B

10 4

10

10 3

102

0

10 6

105

yA = 4095.5x + 8E+06

yB = -15759x + 2E+07

100 150 200 250

Stif

fnes

s (k

Pa)

Binder stiffness (MPa)

Aggregate A Aggregate B

108

105

106

107

(b)

(a)

Fig. 4. Correlations: (a) fatigue life and G*sin d; (b) mixture stiffness and binderstiffness.

3148 F. Xiao et al. / Construction and Building Materials 23 (2009) 3144–3151

first several years, followed by the further reduction of pavementperformance caused by micro-cracking under repeated traffic load-ing conditions. Previous research also presents this similar long-term performance process [3,4,21,22].

The test results presented in Fig. 3a show that the fatigue life offatigue beams made from aggregate A has a greater value thanthose made from aggregate B, though the aggregate B has a lowerLA abrasion loss and absorption values. Conversely, the standarddeviations of the fatigue test results for each mixture are largesince the variability of fatigue life is generally based upon the mi-cro-structure of beams (e.g. the aggregate–binder interface, thevoid size distribution, the interconnectivity of voids, distributionof aggregate particles, film thickness and the aged status of binder).Through previous research, which also determined that large vari-abilities exist in the fatigue test results, the authors found thatincreasing the number of the repeated specimens reduced the var-iability [23]. Moreover, in comparison with the control fatiguebeam (without rubber and WMA additive), the rubberized fatiguebeam without WMA additive or with Sasobit� additive has aslightly greater fatigue life while the rubberized fatigue beam withAsphamin� additive has a slightly lower fatigue life, regardless ofaggregate sources. Fig. 3a shows that the addition of crumb rubberand/or Sasobit� slightly benefits the long-term performance of as-phalt pavement while the Asphamin� results in a slight decrease ofthe fatigue life, though these additives are critical in reducing themixing and compaction temperatures of mixture. In addition, thestatistical analysis (t-statistics) in Table 5 indicates that, with re-spect to the effect of aggregate source, there is a significant differ-ent fatigue life value between any two aggregate sourcesregardless of mix types. As shown in Table 6, the influence of aWMA additive on the fatigue life is generally not significant (p-va-lue > 0.05) for overall mixtures.

The flexural stiffness of an asphalt pavement, associated withrepetitive traffic loading and pavement thickness, is related tothe various aspects of HMA, such as rutting, resilient modulus,and fatigue life. In this study, the fatigue beams were made witha height of approximate 50 mm and the values were competedfrom Eq. (3), defined as the ratio of tensile stress-to-tensile strain.The test results shown in Fig. 3b show that the aggregate A mixturehas greater stiffness values since under the repeated loading theinduced micro-strain of the mixture from aggregate A is smaller.This greater stiffness may be the result of different aggregatesources producing different interfaces among the binder, voids,

Table 6Statistical analysis of mechanical properties in terms of mixture types.

Mixture type (0 – control, 1 – rubberized, 2 – rubberized

0 – 1 0 – 2 0 – 3

Cumulative energy 0.017 0.065 0.036Stiffness 0.372 0.073 0.236Fatigue life 0.194 0.194 0.226

Note: P-value < a = 0.05 (significant difference); P-value > a = 0.05 (no significant differe

and aggregate, thus, affecting the corresponding fatigue behaviorof the pavement. Previous research indicates that while the initialstiffness of rubberized mixture is less than the conventional mix-ture [19], the initial stiffness values of mixtures in this studyshowed no obvious trend when the additional crumb rubber andWMA additive were blended together. Moreover, the statisticalanalysis in Tables 5 and 6 indicates that aggregate source has a sig-nificant influence on the stiffness values generally while the effectsof rubber and WMA additive is not significant for all four types ofmixtures.

The dissipated energy, computed from Eqs. (5) and (6) was usedas an indicator of fatigue cracking in the asphalt layer [19–22]. Asshown in Fig. 3c, the cumulative dissipated energy of mixturemade from aggregate B is slightly higher than that of mixture fromaggregate A. However, the statistical results in Table 5 indicatethat, except for the mixture with Sasobit additive, other mixturesfrom two aggregate sources have no significant different cumula-

+ Asphmin, 3 – rubberized + Sasobit)

1 – 2 1 – 3 2 – 3

0.149 0.346 0.1410.129 0.394 0.1630.125 0.145 0.308

nce).

F. Xiao et al. / Construction and Building Materials 23 (2009) 3144–3151 3149

tive dissipated energy values. With respect to the effect of rubberand WMA additive, Table 6 shows that there is a significant differ-ent value between control and rubberized mixture in general, butthe influence of WMA additive on cumulative dissipated energyis not significant for all rubberized mixture.

4.4. Correlation analysis of fatigue test factors

G*sin d, strongly associated with fatigue life of the mixture, hasbecome a basic parameter used to describe fatigue characteristicsof asphalt binder. Thus, the study of G*sin d is beneficial forresearchers and engineers to analyze fatigue behavior of asphaltpavements. Table 3 indicates the effect of rubber and WMA addi-tive on G*sin d of binder. In Fig. 4a, it can been seen that the fatiguelife decreases remarkably with a corresponding increase of G*sin dregardless of aggregate source. Fig. 4 indicates that the binderaging process, for the materials used in this research, does shortenthe fatigue life of asphalt pavement. However, the addition ofcrumb rubber enhances the long-term performance of asphaltpavement.

The correlations between the stiffness of the beam and binderare shown in Fig. 4b. Similar to Fig. 4a, it can be seen that the stiff-ness values of the beam do not have a large alteration with an in-crease in binder stiffness. Table 3 shows that the rubberizedbinders have lower stiffness values than original asphalt binder.However, the stiffness values of the rubberized mixture do not ex-hibit a similar trend. In addition, as shown in Fig. 4b, two aggregatesources also show the different effects on mixture stiffness interms of binder stiffness in this study.

AASHTO T321 assumes that the fatigue life depends on theaccumulation of dissipated energy from each load cycle. Thus,

yA = 0.1508e -7E-06x

yB = 0.1468e -4E-06x

yC = 0.1249e -2E-06x

0.0

0.1

0.2

0.3

Dis

sipa

ted

ener

gy (

J/m

3)

ACO-AACO-BACO-C

yA = 0.1108e -6E-06x

yB = 0.117e -5E-06x

yD = 0.1499e -2E-06x

yC = 0.1372e -2E-06x

0.0

0.1

0.2

0.3

Cycles

ARO-AARO-BARO-CARO-D

10 104103102 106105

Cycles

10 104103102 106105

Cycles

10 104103102 106105

Cycles

10 104103102 106105

0

0

0

0

yA = 0.1566e -1E-05x

yB = 0.2253e -1E-05x

0.0

0.1

0.2

0.3

Dis

sipa

ted

ener

gy (

J/m

3)

BCO-A BCO-B

yA = 0.1726e -1E-05x

yB= 0.1912e -2E-05x

yC = 0.2157e -1E-05x

yD = 0.2639e -4E-05x

0.0

0.1

0.2

0.3

0.4

BRO-ABRO-BBRO-CBRO-D

(a) (b)

(e) (f)

Fig. 5. Dissipated energy versus load cycles (repetition): (a), (e) control beam (aggregAsphamin� beam (aggregates A and B); (d), (h) rubberized Sasobit� beam (aggregates A

the dissipated energy may be plotted against load cycles for theparticular load cycles where the data was collected. As shown inFig. 5, the correlations between the dissipated energy per cycleswith load cycles indicate that the dissipated energy increases at anegative exponential growth as the number of load cycles increase,in other words, the dissipated energy decreases insignificantly ini-tially and then it reduces rapid prior to reaching the 50% stiffness.For example, as shown in Fig. 5a, the dissipated energy of threefatigue beams exhibits a slightly decrease before the number ofthe repeated loads is less than 10,000 cycles, after that, the dissipatedenergy decreases quickly until the final load cycle accomplishes.

Fig. 5 indicates that the individual fatigue beam from each mix-ture has different dissipated energy values per load cycle, regard-less of the mixture types (i.e. ACO, ARO, etc.) and these valuesare greater when using aggregate B. The results in Fig. 5 also showthat the crumb rubber and WMA additive do not affect the dissi-pated energy per cycle.

The initial stiffness of fatigue beam, determined by the initialtensile stress and strain, can be plotted using stiffness (S) againstload cycles (n) and best fitting the data to exponential functionof the form shown below:

S ¼ Aebn ð7Þ

where e is the natural logarithm to the base e and A, b, the experi-mentally determined coefficients.

As shown in Fig. 6, it can be noted that, in most cases, the stiff-ness values of various fatigue beams from same mixture presentsimilar results, and the mixture from aggregate B has a greaterstiffness value. However, the addition of crumb rubber and WMAadditive do not exhibit a significant effect on the stiffness valuesregardless of aggregate sources.

Cycles

10 104103102 106105

Cycles

10 104103102 106105

Cycles

10 104103102 106105

Cycles

10 104103102 106105

yA = 0.1454e -4E-06x

yB = 0.1647e -8E-06x

.0

.1

.2

.3

ARA-A ARA-B

yA = 0.1663e -3E-06x

yB = 0.1776e -8E-06x

0.0

0.1

0.2

0.3

ARS-A ARS-B

yA = 0.2175e -4E-05x

y B= 0.2378e -1E-05x

0.0

0.1

0.2

0.3

0.4

BRA-A BRA-B

yA = 0.2516e -2E-05x

yB = 0.2455e -6E-06x

0.0

0.1

0.2

0.3

0.4

BRS-A BRS-B

(c) (d)

(g) (h)

ates A and B); (b), (f) rubberized beam (aggregates A and B); (c), (g) rubberizedand B).

yA = 9E+06e-6E-06x

yB = 8E+06e -4E-06x

yC = 8E+06e -2E-06x

Stif

fnes

s (

kPa)

Cycles Cycles Cycles Cycles

ACO-A

ACO-B

ACO-C10 6

10 10 4

10 8

10 310 2

10 7

10 610 5

yA = 9E+06e -6E-06x

yD = 9E+06e -6E-06x

yC = 8E+06e -1E-06x

yB = 8E+06e -5E-06x

ARO-AARO-BARO-CARO-D

10 6

10 10 4

10 8

10 310 2

10 7

10 610 5

yA = 9E+06e-5E-06x

yB = 8E+06e -7E-06x

ARA-A ARA-B106

10 104

108

103102

107

106105

yA = 1E+07e -3E-06x

yB = 9E+06e -5E-06x

ARS-A ARS-B106

10 104

108

103102

107

106105

yA = 1E+07e-1E-05x

yB = 1E+07e -3E-05x

Stif

fnes

s (

kPa)

Cycles Cycles Cycles Cycles

BCO-A BCO-B10 6

10 104

10 8

103102

10 7

106105

yA = 8E+06e-7E-06x

yB = 1E+07e -3E-05x

yC = 1E+07e -9E-06x

yD = 2E+07e-3E-05x

BRO-ABRO-BBRO-CBRO-D

106

10 104

108

103102

107

106105

yA = 1E+07e -6E-05x

yB = 2E+07e -2E-05x

6

7

8

BRA-A BRA-B

106

10 104

108

103102

107

106105

yA = 1E+07e-2E-05x

yB = 1E+07e -7E-06x

06

07

BRS-A BRS-B

106

10 104

108

103102

107

106105

(a) (b) (c) (d)

(e) (f) (g) (h)

Fig. 6. Stiffness versus load cycles (repetition) (a), (e) control beam (aggregates A and B); (b), (f) rubberized beam (aggregates A and B); (c), (g) rubberized Asphamin� beam(aggregates A and B); (d), (h) rubberized Sasobit� beam (aggregates A and B).

yA = 63.372x + 243145yB = 163.28x – 40713

100 600 1100

Rep

etiti

on (

cycl

e)

Cumulative dissipated energy (J/m3)

100 600 1100

Cumulative dissipated energy (J/m3)

Aggregate A Aggregate B

10 4

10 3

10 6

10 5

yB = 2121.7x + 3E+06yA = 11.92x + 7E+06

Los

s of

stif

fnes

s (k

Pa)

Aggregate A Aggregate B10 5

10 6

10 7

(a)

(b)

Fig. 7. Cumulative dissipated energy versus: (a) repetition and (b) stiffness.

3150 F. Xiao et al. / Construction and Building Materials 23 (2009) 3144–3151

The correlations between the repetition number of fatiguebeam and cumulative dissipated energy are shown in Fig. 7a.Although these two linear models can be used to determine thepredicted values, it was hard to obtain accurate results due tothe limited test specimens and variability of materials. Similarly,as shown in Fig. 7b, the loss of stiffness under repeated loading,as expected, is also related to the cumulative dissipated energythough they are not highly correlated with each other.

5. Conclusions

The following conclusions were determined based upon thelimited experimental data presented regarding the fatigue life ofthe modified binder and mixtures for the materials tested for thisresearch project:

� The combination of the crumb rubber and WMA additive inasphalt binder is beneficial for improving the rheological prop-erties of both the unaged and aged binders (e.g. increase G*sin dand reduce G*/sin d values), The increase in the mixing and com-paction temperatures due to the addition of crumb rubber canbe offset by adding the warm asphalt additives, which lowersthe mixing and compaction temperatures of rubberized mix-tures comparable to conventional HMA.

� The experimental results indicated that fatigue life and stiff-ness of the rubberized WMA mixture from aggregate A isgreater than aggregate B while the cumulative dissipatedenergy of mixtures made from aggregate A is slightly lower.Moreover, the fatigue life of the mixtures made with crumbrubber and WMA additive is greater than the control mixtures(no rubber and WMA additive), except the mixtures containingAsphamin� additive.

F. Xiao et al. / Construction and Building Materials 23 (2009) 3144–3151 3151

� Statistical analysis results illustrated that there are no signifi-cant differences in the stiffness and cumulative dissipatedenergy values for overall mixtures (control, rubberized, orWMA mixtures) while fatigue life values from control mixturesare significantly different with other rubberized mixtures. Inaddition, statistical results presented the aggregate sources playa key role in determining fatigue life, stiffness and cumulativedissipated energy values of mixtures.

� There are good correlations between the fatigue life and G*sin das well as mixture and binder stiffness values. The exponentialfunction forms are efficient in achieving the correlationsbetween the dissipated energy and load cycle as well as mixturestiffness and load cycles.

Acknowledgments

The financial support of South Carolina Department of Healthand Environmental Control (SC DHEC) is greatly appreciated. How-ever, the results and opinions presented in this paper do not nec-essarily reflect the view and policy of the SC DHEC.

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