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Road Materials and Pavement Design
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Comprehensive evaluation of low-temperaturefracture indices for asphalt mixtures
Yuefeng Zhu, Eshan V. Dave, Reyhaneh Rahbar-Rastegar, Jo Sias Daniel &Adam Zofka
To cite this article: Yuefeng Zhu, Eshan V. Dave, Reyhaneh Rahbar-Rastegar, Jo Sias Daniel& Adam Zofka (2017): Comprehensive evaluation of low-temperature fracture indices for asphaltmixtures, Road Materials and Pavement Design, DOI: 10.1080/14680629.2017.1389085
To link to this article: http://dx.doi.org/10.1080/14680629.2017.1389085
Published online: 27 Oct 2017.
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Road Materials and Pavement Design, 2017https://doi.org/10.1080/14680629.2017.1389085
Comprehensive evaluation of low-temperature fracture indices for asphaltmixtures
Yuefeng Zhua, Eshan V. Dave b∗, Reyhaneh Rahbar-Rastegarb, Jo Sias Danielb andAdam Zofka c
aSchool of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang, People’s Republicof China; bDepartment of Civil and Environmental Engineering, University of New Hampshire, Durham,USA; cRoad and Bridge Research Institute (IBDiM), Warsaw, Poland
(Received 15 August 2016; accepted 25 October 2016 )
For performance-based specifications and design processes, a number of cracking-relatedindex parameters have been proposed for asphalt mixtures in recent years. A number of theseparameters have been developed to utilise results from fracture tests. This study conducteda comprehensive evaluation of various fracture index parameters including fracture energy,Illinois flexibility index, stress intensity factor and toughness index. Over 200 tests from 61distinct test data sets representing 21 asphalt mixtures are included. The focus of this study ison low-temperature cracking and all indices were evaluated using test results from the disk-shaped compact tension fracture tests conducted at low temperatures. The objective of thisstudy was to determine if there is a relationship between various fracture index parameters aswell as to determine typical measurement variability associated with each parameter. Com-parisons were made between different indices and correlations were determined for the mixrankings provided by individual indices. The results indicate that fracture energy successfullycaptured the mix rankings and showed a strong correlation with other indices. In order to bet-ter capture post-peak softening behaviour of asphalt mixtures, the flexibility and toughnessindices have been utilised; however, these parameters were found to have high variability. Anew index called fracture strain tolerance has been proposed that was shown to provide thesame level of distinction between mixtures as the flexibility and toughness indices while hav-ing considerably lower variability. Finally, several areas were identified for future extensionof this research.
Keywords: low-temperature cracking; fracture indices; laboratory testing; variability; flexi-bility index
1. Introduction and backgroundThermal and fatigue cracking are major distresses observed in asphalt pavement structures. In thecurrent practice, asphalt mix design process is primarily focused on preventing rutting failure.Rutting is addressed through stringent aggregate gradation and angularity requirements togetherwith the air-void-level criteria. While prevention of rutting is important, explicit considerationof fatigue and thermal cracking is equally important. Field performance of the asphalt pave-ments constructed recently as well as 10 + years ago demonstrates that premature cracking isa real issue and most likely it is not properly addressed in the current design practice. One ofthe potential reasons is that thermal cracking has been considered in the mix design through the
*Corresponding author. Email: [email protected]
© 2017 Informa UK Limited, trading as Taylor & Francis Group
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binder property testing such as Frass breaking point, bending beam rheometer (BBR) and directtension test (DTT). As demonstrated in numerous studies (Dave, Braham, Buttlar, Paulino, &Zofka, 2008; Marasteanu et al., 2007; Marasteanu et al., 2012; Zofka & Braham, 2009), thermalcracking is a far more complex phenomenon and it does not solely depend on the binder prop-erties. The same is true for fatigue cracking performance (Rahbar-Rastegar & Daniel, 2016).Cracking is also a function of aggregate skeleton, aggregate mineralogy, binder adhesion andcorresponding overall cohesion of the entire mix (Judycki et al., 2015). Thus, the balanced mixdesign requires that thermal and fatigue cracking should be evaluated directly on the asphalt mix-ture specimens. It is necessary to establish appropriate parameter limits thus the susceptibility tocracking is addressed at the mix design stage, i.e. resistance to crack initiation and propagationis evaluated under the laboratory conditions. Testing of asphalt mix specimens is also more prac-tical for contractors and highway agencies and allows focus on the final material rather thanindividual components.
As mentioned earlier, thermal cracking has been indirectly assessed by the binder properties.But in fact there are also several experimental protocols that employ asphalt mix specimens inorder to evaluate their thermal cracking performance, i.e. Thermal Stress Restrained SpecimenTest (Monismith, Secor, & Secor, 1965), Asphalt Concrete Cracking Device (Kim, Sargand, &Wargo, 2009) and BBR (Velasquez, Zofka, Marasteanu, & Turos, 2011). These tests allow deter-mination of laboratory-based critical cracking temperature that can be used for the qualitativeevaluation of different asphalt mixes. However, such protocols require relatively complex speci-men preparation and experimental set-up, rigorous testing conditions and appropriate parameterinterpretation procedures.
In parallel, recent years brought more advanced experimental procedures based on the fracturemechanics concept, such as semi-circular bending (SCB), disk-compact tension (DCT) and Sin-gle Edge Notch Beam (Li & Marasteanu, 2004; Wagoner, Buttlar, & Paulino, 2005a; Wagoner,Buttlar, & Paulino, 2005b). These tests are direct proxies of the field behaviour where crack-ing evolves with time and temperature changes. One could relate the fracture mechanism to thethermodynamics process of energy balance, where energy applied to the system (i.e. at the cracktip) is contrasted with the energy/resistance stored in the material. In general, low-temperaturecracks develop/grow/expand with time so it is not only the case of crack initiation but it is equallyimportant to assess how quickly it will propagate through the material. Asphalt mixes with a lowresistance to cracking will develop more cracks and their severity will increase quicker whencompared with the mixes with high resistance. In order to assess such a behaviour, it is beneficialto conduct fracture-mechanics-based tests in the crack mouth opening displacement (CMOD)-controlled mode, i.e. force applied to a specimen is adjusted according to the opening rate of thecrack mouth. Data recorded and processed in such tests allow calculation of the energy storedin a specimen and preparation of input parameters for advanced simulations and predictions ofthermal cracking (Dave & Buttlar, 2010; Dave, Buttlar, Leon, Behnia, & Paulino, 2013; Dave& Behnia, 2017). As shown in the recent study (Marasteanu et al., 2012), such advanced mod-els allow for more accurate predictions and can be eventually employed in the pavement designprocess.
In order to transition to performance-based specifications as well as to include performancemeasures during the material selection process, a lab measured parameter that can reliably distin-guish between good- and poor-performing asphalt mixtures is necessary (Dave & Koktan, 2011).A number of lab measured indices have been proposed and the recent NCHRP 9-57 study con-ducted a comprehensive review of different cracking performance tests and measures (Zhou, Im,Hu, Newcomb, & Scullion, 2017). Several similar studies are currently underway with the intentto develop a lab measured index parameter for pavement cracking. Use of a performance indexfrom the fracture tests has generated a lot of attention and has shown very promising results
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(Al-Qadi et al., 2015; Dave, Hanson, Helmer, Dailey, & Hoplin, 2015; Van Deusen et al., 2015).A number of parallel efforts have led to creation of different indices from fracture tests, for exam-ple, flexibility index, toughness index (TI), fracture energy, N flex and stress intensity factor (SIF).There is a need to compare these parameters using a large data set to determine the differencesbetween mix ranking provided by these indices as well as to quantify the anticipated level ofvariability in the measurement of each. This needs motivated research study and correspondingresults described in this paper. The goals of the work presented herein are to:
– provide a brief review of different fracture index parameters;– develop a database of fracture indices calculated for a wide range of asphalt mixtures,
specimen conditioning levels and testing temperatures;– use the database and correlate different fracture indices as well as compare the ranking
of mixtures provided by individual indices; and finally,– compare variability of different indices to gauge their suitability for routine usage, such
as the required parameter for the mix acceptance.
The above goals were realised through the development of a fracture index database from over200 DCT fracture energy tests conducted on 21 distinct mixtures tested at different conditioninglevels, temperatures and air void levels in three independent laboratories. In addition to the abovegoals, this study also evaluated the effects of test temperature and air void levels on fractureindices.
This paper is organised into seven sections. A review of different fracture indices is presentednext, and this is followed by a description of the materials used in the development of thedatabase. The subsequent section provides comparisons between different fracture indices andrankings provided by individual indices. Variability associated with the measurement of eachindex is discussed and the effects of test temperature and specimen air void levels for selectedindices are presented. Finally, a summary of the research is presented along with pertinentconclusions as well as recommendations.
2. Fracture indices for asphalt mixture low-temperature crackingAs briefly discussed in the Introduction, a number of different fracture index parameters havebeen recently developed and proposed as cracking performance indicators for asphalt mixtures. Afracture index is defined here as any parameter that is calculated using laboratory measurementsfrom a fracture test on an asphalt mixture. Fracture tests are typically conducted on notched spec-imens and the primary lab measurements for such tests include displacements and the requiredforce or load to generate those displacements. This study focuses on low-temperature fracturecharacteristics of asphalt mixtures for applications to thermal cracking distresses in asphaltpavements and overlays. At present, DCT fracture test is specified as ASTM D7313 for low-temperature fracture characterisation of asphalt mixtures. A typical test set-up and test specimenare shown in Figure 1. In the test procedure, a notched disk-shaped specimen is initially pre-loaded with 0.1 kN of seating load; thereafter, the test control is switched over to achieve aconstant CMOD rate of 0.167 mm/s. As with any fracture test, the load initially increases as thestress concentration and formation of a non-linear fracture process zone (FPZ) occur near thenotch tip (Anderson, 2005). Once the FPZ is fully formed and the level of micro-cracking at thecrack tip reaches the point where cracks begin to coalesce to form a macro-crack, the requiredforce capacity of the specimen begins to decrease and crack propagation starts to occur. Recently,Dave and Behnia (2016) used cohesive zone fracture modelling of DCT to show that the macro-crack formation and propagation occurs in this test at approximately 90% of peak load on the
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post-peak side of the load–CMOD curve. The test is continued until the load decreases to theseating load level of 0.1 kN, at which point the test ends.
Figure 2 shows some typical load–CMOD curves obtained from DCT fracture testing. Eachof these is from a different asphalt mixture. As seen from this plot, the shape of curves (peakload, pre-peak and post-peak slopes, and the ultimate CMOD at test termination) varies betweendifferent mixtures.
One example load–CMOD result from a DCT test is selected for the purpose of discussing var-ious fracture indices studied in this paper. Discussions of different indices are divided into threecategories: energy indices, normalised energy indices and strength and stress-intensity factormeasurements.
Figure 1. DCT fracture test set-up and test specimen.
Figure 2. Load–CMOD results from three distinct asphalt mixtures.
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Figure 3. Typical load–CMOD results from the DCT test (pre-peak and post-peak fracture work is shownusing different shading patterns).
2.1. Energy indicesUse of energy-based approaches for fracture characterisation of quasi-brittle materials such asasphalt mixtures has been extensively discussed (Roque, Birgisson, Drakos, & Dietrich, 2004;Wagoner et al., 2005a). Use of an energy approach, as opposed to strength-based approach,allows for a better characterisation of the cracking processes in asphalt mixtures. Energy-basedapproaches also alleviate a major issue of having to make a decision between stress- or a strain-based parameters, as the energy measurement is comprehensive and encompasses both stressand strain parameters in the calculation. The fracture energy of material is defined as the energyneeded to create a new unit fracture surface in the body (Anderson, 2005). Following the ASTMD7313 procedure, which is built upon a similar test for metals (ASTM E399, 2006), the DCTfracture energy denoted as “Gf” is determined by first calculating the work of fracture, Wf. Workof fracture is defined as the area under the load–CMOD curve. This fracture work can be dividedinto pre-peak (WPre-peak
f ) and post-peak fracture work (WPost-peakf ) as shown in Figure 3. Fracture
energy can be calculated by normalising the fracture work by the area of fracture surface that isgenerated during the test. This area can be estimated as a product of the thickness of the specimen(t) and the length of the new crack formed during the test. This crack length is often referred toas ligament length (a). Fracture energy calculation is shown as follows:
Gf = Wf
t × a. (1)
The fracture work (Wf) can be mathematically expressed as follows:
Wf = WPre-peakf + WPost-peak
f =∫ �Fmax
0F · du +
∫ �Final
�Fmax
F · du, (2)
where u is the CMOD, F is the force or load and �i are CMOD thresholds as shown in Figure 3.DCT fracture energy or total DCT fracture energy (Gf) has been extensively studied for its
application to reflective cracking in asphalt overlays (Wagoner, Buttlar, Paulino, & Blankenship,2006) and thermal cracking in asphalt pavements (Dave, Helmer, Hanson, Munch, & Johanneck,
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2016; Marasteanu et al., 2007, 2012). This parameter has been compared with field thermalcracking performance and threshold values have been developed through field calibration andvalidation efforts. After an extensive multi-laboratory repeatability and reproducibility campaign,Minnesota Department of Transportation (MnDOT) has moved to pilot implementation of Gf asa thermal cracking performance parameter (McCarthy, Callans, & Scott, 2016; Van Deusen et al.,2015). In the pilot implementation phase, a minimum Gf value of 400 J/m2 is required for mixdesign acceptance and verification testing is conducted during the mix production and pavementconstruction phases. Due to extensive previous research on this parameter, as well as its currentusage in actual paving projects, Gf is used as the baseline fracture index in the initial comparisonsfor this study.
The other energy index that was chosen in this study is the post-peak fracture energy, GPost-peakf .
This parameter can be calculated using Equation (1) by substituting Wf with WPost-peakf . The
choice of this parameter is on the basis of the mechanism of FPZ formation in the quasi-brittlematerials. As discussed previously, the majority of energy in the pre-peak region is dissipatedin the formation of FPZ and the post-peak region represents the energy dissipation that occursduring the crack propagation phase (Anderson, 2005; Song, Paulino, & Buttlar, 2006). Thus, inorder to distinguish the crack propagation process from the complete test, it is worthwhile toassess the post-peak fracture energy (GPost-peak
f ).A potential drawback of Gf or GPost-peak
f as an asphalt mixture low-temperature cracking (LTC)performance parameter is the inability of energy measurement to distinguish between mixtureswith high peak load and steep post-peak slope (commonly referred to as high-strength low-toughness materials) and mixtures with low peak load and shallow post-peak slope. This topichas been a motivational factor behind the development of normalised energy indices such asthe Illinois flexibility index parameter (Al-Qadi et al., 2015). Normalised energy indices arediscussed next.
2.2. Normalised fracture energy indicesIn order to better distinguish fracture resistance between mixtures with very high peak load andsteep post-peak softening slopes and vice versa conditions, normalisation of fracture energies canbe conducted using a parameter that considers the shape of the post-peak portion. A parametercalled the Illinois flexibility index has been proposed recently for the characterisation of asphaltmixtures using the SCB test at intermediate temperatures. This parameter normalises the fractureenergy (Gf) with the slope of the post-peak softening curve at an inflection point near the middleof the post-peak region. This type of parameter is not possible using DCT results, as the inflectionpoint that is used in SCB test results from indirect loading mode between load application andcrack opening (vertical loading direction and horizontal crack opening displacement). In caseof DCT, the direction of loading is the same as the direction of crack opening, thus there isthe absence of such an inflection point in the post-peak region. The loading direction has alsobeen hypothesised as a reason for lower test variability in DCT configuration over SCB at lowtemperatures. In this paper, three different post-peak slopes were used to calculate three types offlexibility indices. The post-peak slope is indicated by symbol “m”. The three slopes used in thisstudy are graphically depicted in Figure 4.
The initial post-peak softening curve slope (minitial) was calculated as the average slope of theload–CMOD curve between 90% and 70% of peak load. These load thresholds were selectedon the basis of the simulations of DCT fracture energy tests by Dave and Behnia (2016). Asdiscussed previously, 90% peak load corresponds to the complete formation of FPZ in this testand 70% represents the initial propagation of the crack. Based on the analysis of over 50 test
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Road Materials and Pavement Design 7
Figure 4. Different post-peak softening slopes and displacement thresholds used in flexibility index andTI calculations.
results, it was found that this slope corresponds well with the upper asymptote for the post-peakload–CMOD softening curve. The final post-peak slope (mfinal) is the reverse of the initial slopeand is estimated by taking the average slope over the latter 20% CMOD in the test. This sloperepresents the final asymptote portion of the load–CMOD curve. Finally, an average softeningslope (maverage) is also calculated. Mathematically, this slope equals the average of tangent slopesalong each point on the softening curve. Once again, the purpose of using these parameters tonormalise fracture energy is in fact to develop a fracture index that has more information aboutthe softening behaviour of the material in addition to the required fracture energy to form a crack.The three variants of flexibility index discussed in this paper are Gf/minitial, Gf/(minitial – mfinal) andGf/maverage. A recent study by West (2016) has proposed a similar flexibility index called N flexthat utilises normalised energy from indirect tensile strength test. In that procedure, the fractureenergy used in the calculation is limited to a portion of the post-peak region (up to inflectionpoint). As this study focuses on the use of fracture test results, this parameter was not includedin the evaluation.
Also with the intent to capture the post-peak fracture behaviour of asphalt mixtures, Pérez-Jiménez, Botella, Martínez, and Miró (2013) proposed a normalised fracture energy parametercalled TI. Instead of using slope as a normalising parameter, TI is calculated by multiplyingpost-peak fracture energy (GPost-peak
f ) with displacement between peak load and 50% peak load.The choice of 50% peak load to select displacements is arbitrary in this index. Using the CMODdisplacement thresholds for DCT test as shown in Figure 4, TI can be calculated as shown below:
TI = (GPost−peakf ) · (�mdp − �F max) · 10−3. (3)
2.3. Fracture strength and stress-intensity factorDue to the presence of singular fields at the tip of a crack, it is not possible to measure stress atthe crack tip. It is common practice to characterise the crack tip stress states using a parametercalled the critical SIF (commonly denoted as K IC). The calculation of K IC relies on linear elasticfracture mechanics which is not applicable to quasi-brittle materials such as asphalt mixtures. TheASTM E399 specification provides formulation for estimation of K IC using DCT test geometry.
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Recently, Amirkhanian, Spring, Roesler, and Paulino (2016) utilised this formulation for fracturecharacterisation of Portland cement concrete using the DCT fracture test. The calculation of K ICis as follows:
KIC = Fmax
t
√π
Lf (L/t), (4)
where t is the specimen thickness and L is the distance from loading location to specimen’sboundary. The geometric factors, f, is a function of the ratio of ligament length (L) to specimenthickness (t). As can be seen in the above equation, the only pertinent parameter from fracturetests that is used in the calculation is the peak load (Fmax). Apeagyei, Buttlar, and Dempsey(2006) proposed a similar parameter called fracture strength (Sf) for the study of moisture damagein asphalt mixtures using the DCT fracture test. This parameter was developed by modifying thestandard strength ratio calculation from ASTM E399 and eliminating the normalisation usingmeasured tensile strength. Fracture strength (Sf) can be calculated using peak load (Fmax) andspecimen geometry by the following equation:
Sf = 2Fmax(3L − a)
t × a2 , (5)
where all symbols are the same as defined previously. While neither K IC nor Sf allows for captur-ing post-peak fracture behaviour of asphalt mixtures, these parameters provide a geometricallynormalised measure of the peak stress resistance of asphalt mixtures. Thus, by themselves theseparameters may not be sufficient in capturing the quasi-brittle cracking response of asphalt mix-tures that is encountered in asphalt pavements at low temperatures, but by combining them withthe fracture energy they can provide a similar effect as the normalised energy indices. Since bothK IC and Sf are direct functions of Fmax with geometric normalisations, only Sf was evaluated inthis study for simplicity.
2.4. Summary of fracture measuresA brief tabular summary of various fracture measures is presented in Table 1. The table presentsthe symbols for various measures as used in this paper as well as a brief description of theparameters.
3. MaterialsThis study utilised DCT fracture energy test results from measurements conducted in three lab-oratories. Over 200 distinct test results were included in the analysis. These tests represent 61distinct specimen conditioning and test temperature combinations for 21 types of asphalt mixesas shown in Table 2. This study encompasses a broad range of asphalt mixture types in termsof binder grades, mix ageing and conditioning types, air void levels, geography and recycling.It is necessary to include such a variety of factors to ensure that the resultant findings are notbiased due to the similarity between mixtures. Brief descriptions of three sources of mixtures arepresented next.
The first set of nine mixtures are from the Phase-II of the LTC pooled fund study (Marasteanuet al., 2012). The component materials for these mixes were obtained from Minnesota (MN),New York (NY) and Wisconsin (WI). All test specimens were fabricated using lab mixed andcompacted gyratory samples. Minnesota mixtures also provided a good variation of binder mod-ification systems including polyphosphoric acid (PPA), styrene butadiene styrene (SBS) andElvaloy®. All mixtures from the pooled fund study were tested at 4% and 7% air void levels
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Table 1. Summary of various fracture indices.
Fracture indices SymbolPhysical interpretation/
definition
Energy indices Fracture energy Gf Energy needed to create anew unit fractured surfacein the material
Pre-peak fracture energy GPre−peakf Energy during the pre-peak
part of the load-CMODcurve. Typically associatedwith energy needed toinitiate crack
Post-peak fracture energy GPost−peakf Energy during the pre-peak
part of the load–CMODcurve. Typically associatedwith energy necessary topropagate a crack
Fracture strength andstress-intensityfactor
Fracture strength Sf Measure of peak loadin fracture test that isnormalised for specimengeometry
Normalised fractureenergy indices
Toughness index TI Post-peak fracture energyweighted by the displace-ment between maximumload and 50% of maximumpost-peak load
Initial post-peak slopeflexibility index
Gf/minitial minitial is defined as theaverage slope of load-CMOD curve between90% and 70% of peak load
Average post-peak slopeflexibility index
Gf/maverage maverage is defined as averageof tangent slopes alongeach point on the softeningcurve
Flexibility index usingthe difference betweeninitial and finalpost-peak slopes
Gf/(minitial − mfinal) mfinal is defined as averageslope over the latter 20%CMOD
Fracture strain tolerance FST Gf/Sf, normalised fractureenergy with respect tofracture strength
as well as with laboratory short-term and long-term ageing. All ageing was conducted using theAASHTO R35 protocol. Testing was conducted at the asphalt binder low-temperature perfor-mance grade (PGLT) and 10°C warmer than PGLT. More details on the DCT testing and resultsfor these mixtures can be found elsewhere (Dave, Behnia, Ahmed, Buttlar, & Reis, 2011).
The second data set includes nine plant-produced mixtures fabricated by Pike Industries, Inc.at two drum plants in New Hampshire during the 2013 and 2014 construction seasons. The testingwas a part of a project funded by NHDOT to assess performance impacts of a different amountof recycled asphalt pavement (RAP) and recycled asphalt shingles (RAS) in asphalt mixtures.Six of the mixtures were placed and compacted in the field along New Hampshire State Route 12near Westmoreland. The mixtures are varied in binder PG grade (PG52-34, PG58-28, PG64-28),binder source, nominal maximum size of aggregate (12.5 and 9.5 mm), recycled material type
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Table 2. Mixture source, origin, attributes and test conditions.
Mix source Mix originVirgin binder
grade
Bindermodification/
additiveRAP/ RAS
content Air void Test temperatures Conditioning
LTC pooled fundstudy
MN PG58-28 Unmodified 30%RAP 4%; 7% PGLT; PGLT + 10°C Short-term oven aged;long-term oven aged
PG58-28 30%RAPPG58-34 30%RAPPG58-34 PPA 0%PG58-34 PPA + SBSPG58-34 SBSPG58-34 PPA + Elvaloy®
WI PG64-22 UnmodifiedNY PG64-22 Unknown
NHDOT recyclingstudy
NH PG52-34 (2sources)
Unknown 18.9%RAP 7.6% PGLT + 10°C Plant mixed plantcompacted
20.4%RAP/RAS 6.5%31.3%RAP 6.9%
PG58-28 (2sources)
21.3%RAP 6.7%
22.4%RAP 7%28.3%RAP 8.4%20.4%RAP/RAS 7%31.3%RAP 7.1%
PG64-28 16.4%RAP 7.2%CT WMA study CT PG64-22 Unmodified 0% 6.5% PGLT − 2°C;
PGLT + 10°C;PGLT + 22°C
Plant mixed labcompacted
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Figure 5. Total CMOD fracture energy (Gf) and post-peak CMOD fracture energy (GPost−peakf ).
and binder replacement amount. DCT testing was performed at − 18°C (PGLT + 10°C) for allthe mixtures as the specified binder grade for all of these mixtures was PG58-28.
The last data set is from the pilot warm mix asphalt (WMA) project in the state of Connecticut(Bernier, Zofka, Josen, & Mahoney, 2012). One of the major concerns was the thermal crackingof the constructed experimental sections. The results presented in this paper were obtained onthe laboratory-compacted specimens prepared with the asphalt mixes collected during the con-struction of experimental sections. All testing was conducted for the control hot-mix asphalt andtwo WMA technologies (foamed asphalt and Sasobit additive) at three test temperatures. Moreinformation on these sections and their performance is presented elsewhere (Bernier et al., 2012;Bernier, 2012).
4. Comparison of different low-temperature fracture indices for asphalt mixturesVarious fracture index parameters were calculated for the data set discussed in the previoussection and are compared in this section. Comparisons are made using two approaches: graphicalcomparisons with fitted functions and statistical comparisons of mixture rankings. Graphicalcomparisons are presented next, followed by statistical mix ranking correlations.
4.1. Graphical comparisons of fracture indicesUsing the data from 61 sets of DCT fracture tests on 21 asphalt mixtures, comparisons are madeby plotting of average values for different fracture indices against each other. For brevity, onlyselect plots and discussions are presented here. Post-peak CMOD fracture energy (GPost−peak
f )is plotted against total CMOD fracture energy (Gf) in Figure 5. A linear function fitted to thedata shows that total and post-peak energies follow a highly linear relationship with each other.For the varied data set used in this study, representing different mix types, testing temperatures,ageing levels and testing labs, the post-peak energy appears to be approximately 85% of thetotal energy. Once again, the post-peak energy is considered by many researchers as the energydissipated in the propagation of the crack during the fracture test.
Fracture energy (Gf) is compared with TI in Figure 6. Since the data set includes results at ahigh fracture energy (above 800 J/m2), it is difficult to visualise the relationship between Gf andTI in the typical range (below 800 J/m2). For this reason, a magnified plot (smaller range for Gf
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Figure 6. Total CMOD fracture energy (Gf) and TI (left: full range; right: small range).
Figure 7. Total CMOD fracture energy (Gf) and initial post-peak slope flexibility index (Gf/minitial) (left:full range; right: small range).
and TI) is shown for better visualisation. A power relationship fitted to the data set shows a veryhigh coefficient of correlation. Note that the same function is fitted on both linear and log plots.A high correlation power function relationship indicates that both Gf and TI would rank asphaltmixtures in a similar manner. Furthermore, TI values would change at greater than quadraticrate with the change in Gf. This could be useful in helping provide greater distinction betweenmixtures when using TI for comparison purposes.
The next set of comparisons are made using different types of flexibility indices. As discussedearlier, flexibility index can be calculated in different ways depending on the choice of the post-peak slope parameter. Fracture energy (Gf) is first compared with the flexibility index calculatedusing the initial post-peak slope (minitial). Figure 7 demonstrates graphical comparisons betweenGf and Gf/minitial. Once again, both full-range and small-range (magnified) plots are provided toensure that full scale of data is visualised. Exponential relationship best describes the relationshipbetween these parameters with a high correlation coefficient of 0.88.
Flexibility index is compared with the fracture energy calculated using average post-peakslope (maverage) in Figure 8. Similar to the initial slope flexibility index (Gf/minitial), a high corre-lation is also observed between fracture energy and average slope flexibility index (Gf/maverage)using an exponential function. Please note that only 52 sets of mixture tests were included in this
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Figure 8. Total CMOD fracture energy (Gf) and average post-peak slope flexibility index (Gf/maverage).
Figure 9. Total CMOD fracture energy (Gf) and flexibility index using the difference between initial andfinal post-peak slopes (Gf/minitial − mfinal).
analysis as the remaining 9 sets of mixture tests did not consist of the necessary load–CMODdata near the very end of the test to calculate the average post-peak slope (maverage).
Figure 9 shows the comparison between fracture energy and the flexibility index calculatedusing the difference between initial and final post-peak slopes (minitial – mfinal). In this case aswell, exponential function describes the fracture energy and flexibility index with reasonablecorrelation coefficient. However, the quality of fit is not as good as the other two flexibilityindices.
Since a number of studies have utilised either SIF or fracture strength (Sf) as a cracking per-formance index, fracture energy (Gf) and fracture strength (Sf) are compared in Figure 10. Pleasenote that the estimate of SIF follows a very similar procedure as Sf and hence the trends wouldbe similar if SIF was compared with Gf. As can be seen from the figure, there is not a strongcorrelation coefficient between these two parameters. This is not entirely surprising, as the frac-ture strength is primarily a function of the peak load during the fracture test and the specimengeometry, whereas fracture energy is calculated using the total fracture work, which is a functionof both the load and the displacement. For the sake of completeness, a power function is fittedto the data to represent the general trend of decreasing fracture strength with increasing fracture
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Figure 10. Total CMOD fracture energy (Gf) and fracture strength (Sf).
Figure 11. Flexibility index using initial slope (Gf/minitial) and TI (left: full range; right: small range).
energy. Please note that there is substantial data scatter and thus this general trend cannot beutilised for purposes of drawing conclusions regarding material behaviour.
Both flexibility indices and TI combine the fracture energy with some measure to capturepost-peak behaviour in the fracture test. In the case of flexibility indices, these parameters aremeasures of post-peak slope, whereas TI utilises measures of CMOD or displacement. Sincethese sets of parameters are aimed at capturing similar material behaviour, their comparison ispresented next. Comparison between initial softening slope flexibility index (Gf/minitial) and TI isshown in Figure 11. As with the previous figures, to present a full scale of data both full-range andsmall-range (zoomed-in) plots are provided. A linear correlation between these parameters witha very high correlation coefficient verifies the hypothesis presented earlier that these parameterscapture similar aspects of fracture test results. The linear function is intentionally fitted withan intercept value of zero because from a theoretical perspective when an asphalt mixture’sflexibility index is zero, its TI should also be zero.
Flexibility index calculated using average post-peak slope (Gf/maverage) is compared with TIin Figure 12. Once again a very good linear correlation is seen between these parameters. Asdiscussed before, the data for calculation of flexibility index with average post-peak slope wereonly available for 52 test sets.
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Figure 12. Flexibility index using average slope (Gf/maverage) and TI.
Figure 13. Flexibility index using initial slope (Gf/minitial) and fracture strain tolerance (FST) (left: fullrange; right: small range).
A major challenge associated with both flexibility indices and TI is high test variability; this isdiscussed further in a later section. A new parameter for the characterisation of fracture behaviourin asphalt mixtures is introduced here. This new parameter is referred to as fracture strain tol-erance (FST). FST is calculated by normalising the fracture energy of mixture with the fracturestrength (Gf/Sf).
Comparison of FST with different flexibility indices and TI is presented to show that all ofthese parameters rank asphalt mixtures in a similar manner. Figure 13 shows a very high correla-tion between initial post-peak slope flexibility index and FST. The relationship between the twoparameters is best represented by a power function. Similar results are seen for flexibility indexcalculated with average post-peak slope (Gf/maverage) and FST in Figure 14.
A comparison between TI and FST is shown in Figure 15. As with flexibility indices, FSTshows very good correlation with flexibility index for a power function relationship. Compar-isons of various fracture indices have been presented so far using graphical representation andon the basis of the quality of fit between the two parameters using linear, power or exponential
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Figure 14. Flexibility index using average slope (Gf/maverage) and fracture strain tolerance (FST).
Figure 15. TI and FST (left: full range; right: small range).
functions. It is important to recognise that this is not sufficient to fully confirm whether two frac-ture indices would provide a similar ranking of mixtures or not. Statistical analysis of rankingsis presented next.
4.2. Statistical comparison of mix rankings determined using different fracture indicesTo compare different fracture indices in terms of their ranking of mixtures and test conditionsthe best to worst, a statistical analysis was conducted. The analysis was performed using JMP®
software to determine how similar or dissimilar the indices rank the mixtures. In order to evaluatedependency between the indices, the correlation factors between the ranking from each pair ofvariables were determined. This statistical parameter shows the goodness of linear relationshipbetween each pair of index parameters, so that when the correlation factor of 1 equals the indicesranking results identical manner. The maximum and minimum values of the correlation factor are1 and − 1 for a perfect direct (increasing) linear relationship and a perfect inverse (decreasing)linear relationship, respectively.
A correlation matrix for ranking of asphalt mixtures by various fracture parameters assessed inthis study is presented in Table 3. Please note that the correlations for flexibility index calculatedusing average softening slope (Gf/maverage) were calculated for the 52 sets of results, all other
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Table 3. Correlation matrix for different fracture indices.
Fractureenergy, Gf
(J/m2)
Post-peakfracture energy,GPost−peak
f (J/m2)
Flexibilityindex initialslope, Gf/
minitial
Flexibilityindex average
slope, Gf/maverage
Toughnessindex
Fracturestrength, Sf
(MPa)
Fracture straintolerance, FST
(10−6 m)
Fracture energy, Gf(J/m2)
0.993 0.952 0.881 0.973 − 0.089 0.963
Post-peak fractureenergy, GPost−peak
f(J/m2)
0.993 0.959 0.940 0.985 − 0.244 0.971
Flexibility index initialslope, Gf/minitial
0.952 0.959 0.950 0.975 − 0.523 0.972
Flexibility indexaverage slope,Gf/maverage
0.881 0.940 0.950 0.964 − 0.457 0.990
Toughness index 0.973 0.985 0.975 0.964 − 0.455 0.990Fracture strength, Sf
(MPa)− 0.089 − 0.244 − 0.523 − 0.457 − 0.455 0.759
Fracture straintolerance (10−6 m)
0.963 0.971 0.972 0.990 0.990 0.759
correlations use the 61 sets of results. The correlation information in this table can be summarisedwith the following key points:
– Total fracture energy (Gf) and post-peak fracture energy (GPost−peakf ) are expected to rank
asphalt mixture results in an almost identical manner (correlation coefficient is 99.7%).– Total fracture energy (Gf) as well as post-peak fracture energy (GPost−peak
f ) ranks asphaltmixtures in a similar manner as the flexibility indices and TI.
– Ranking of mixtures on the basis of fracture strength does not correlate well with rankingprovided by other fracture indices.
– FST (Gf/Sf) parameter ranks mixtures similar to other normalised fracture energyparameters, i.e. flexibility indices and TI.
The correlation analysis of the mixture rankings confirms the findings discussed earlier in thepaper where graphical comparisons were presented between various fracture indices.
5. Variability of different fracture indicesConsideration of measurement variability is critical for any material property. It is an impor-tant consideration when selecting an asphalt mixture performance index that is to be used formaterials selection, material comparison and specification purposes. In this section, a study ofvariability for various fracture indices is presented.
Data from the replicate samples for each mix type, air void level and laboratory conditioningwere used to assess the variability of the different fracture indices. Various fracture parameterswere calculated for each specimen and using this information, average, standard deviation andcoefficient of variation (CV) were calculated for each of the 61 sets of values. The overall CVvalues for all 61 sets are summarised in Table 4. The flexibility indices and TI have relativelyhigh measurement variability with greater than 20% average and median values. Both total (Gf)and post-peak (GPost-peak
f ) fracture energies have low variability, whereas the fracture strength isthe least variable parameter with less than 10% average and median values. The new parameterintroduced in this paper, FST, has variability comparable to that of total fracture energy (Gf).
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Table 4. Coefficient of variation (CV) summery for various fracture indices.
Coefficient of variation, CV (%)
Fracture index Average (%) Median (%) Maximum (%) Minimum (%)
Fracture energy, Gf (J/m2) 12.2 11.7 31.4 0.9Post-peak fracture energy, GPost−peak
f (J/m2) 11.7 10.7 28.7 1.4Flexibility index initial slope, Gf/minitial 25.8 21.3 118.2 4.5Flexibility index average slope, Gf/maverage 25.8 26.0 72.6 0.5Toughness index 23.6 21.9 90.5 0.8Fracture strength, Sf (MPa) 8.4 6.6 28.1 0.6Fracture strain tolerance (10−6 m) 12.4 10.9 59.2 0.9
Figure 16. Frequency distribution of CV for different fracture indices.
In order to further distinguish the measurement variability of various fracture indices, thefrequency distribution plot for CV has been generated (c.f. Figure 16). This plot reaffirms thefindings discussed above on the basis of average, median, maximum and minimum values. Frac-ture strength (Sf) is the least variable parameter with 70% results in less than 10% range asopposed to flexibility indices and TI where over 40% of test sets exhibited more than 20% vari-ability. Fracture energy (Gf) shows very few test sets to be over 20% variable with the majorityin the 5–20% range. Variability distribution for FST shows that 67% of tests are under 15%CV range and 88% are under 20% range. These numbers are substantially lower as compared toother normalised energy measures. For example, the high variability measurement expressed bygreater than 25% CV shows that only 3% results for FST fall in this category, whereas 40% ofresults for flexibility and TI are located in this range.
In summary, evaluation of the CV of different fracture indices indicated that total (Gf) andpost-peak fracture energies (GPost−peak
f ), fracture strength (Sf), and FST parameters are in low-to-intermediate variability ranges. Other fracture indices that utilise normalised fracture energies(flexibility indices and TI) show high variability.
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6. Effects of test temperature and air void level on fracture indicesFracture testing data used in this research provide an opportunity to also assess the variation ofdifferent fracture parameters with respect to the test temperature and specimen air void levels.To assess general effects of how measured values of a fracture index changes with temperature,frequency distribution plots were employed. Please note that the frequency distributions are onlypresented for the results where multiple temperature or multiple air void data were available.
Frequency distribution plots for fracture energy (Gf), initial post-peak softening slope flexi-bility index (Gf/minitial) and FST are shown in Figure 17, 18 and 19, respectively. As discussedpreviously, the test temperatures are expressed here in terms of the specified asphalt binder low-temperature Superpave performance grade (PGLT). The fracture energy (Gf) of asphalt mixturesincreases with increasing temperatures in the range evaluated in this study. This type of behaviouris anticipated; at warmer temperatures, there is a greater amount of energy required to fractureasphalt mixtures. Comparisons between the distributions at PGLT and PGLT + 10°C reveal agreater extent of variation at PGLT + 10°C, this indicates that at a warmer temperature, the totalfracture energy (Gf) index yields a larger range of differences between different asphalt mixtures.This reaffirms the approach adopted by current MnDOT pilot DCT specification that utilisesPGLT + 10°C as test temperature and not PGLT. At a considerably higher test temperature ofPGLT + 22°C, the fracture energy values are also quite high. The results for the average slopeflexibility index (Gf/maverage) and FST provide the same information as fracture energy, i.e. highervalues at warmer temperatures and a greater range of distribution at PGLT + 10°C as opposedto PGLT.
Frequency distribution plots have also been developed for assessing the effects of specimenair void levels on the calculated fracture indices. Plots for total fracture energy (Gf), initial slopeflexibility index (Gf/minitial) and FST are presented in Figure 20, 21 and 22, respectively. Frac-ture energy frequency distribution shows that while there is a continuous distribution betweenboth 4% and 7% air void levels, in general specimens with 4% air void levels exhibit a slightlyhigher fracture energy. Further analysis of the data using statistical analysis of the distributionis warranted to draw conclusions, but it is outside the scope of the current paper. The frequencydistributions for the flexibility index (Gf/minitial) and FST show a limited variation between 4%and 7% air void levels. Once again, while not in the scope of this study, future studies can takethe data from current work and utilise statistical analysis of frequency distributions of indiceswith respect to the specimen air void levels to confirm these findings.
Figure 17. Frequency distribution of fracture energy (Gf) with respect to test temperature.
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Figure 18. Frequency distribution of average slope flexibility index (Gf/maverage) with respect to testtemperature.
Figure 19. Frequency distribution of FST with respect to test temperature.
Figure 20. Frequency distribution of fracture energy (Gf) with respect to specimen air void level.
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Figure 21. Frequency distribution of initial slope flexibility index (Gf/minitial) with respect to thespecimen air void level.
Figure 22. Frequency distribution of fracture strain tolerance (FST) with respect to the specimen air voidlevel.
7. Summary, conclusions and future research directionThis study conducted a comprehensive assessment of different fracture indices calculated usingmore than 200 low-temperature DCT test results. Various fracture indices were compared witheach other graphically and statistical correlations were calculated for the rankings of mixturesprovided by the indices. In order to assess implementation suitability of different indices in termsof the measurement variability, evaluations of CV were also conducted. Finally, the effects of testtemperatures and air void levels on the measured fracture indices were assessed and discussed.
Based on the results presented in this paper, the following conclusions can be drawn:
• Use of total CMOD fracture energy (Gf) from DCT test is expected to rank the majorityof mixtures similar to other fracture index parameters such as TI or flexibility index. Con-tinued use of Gf is recommended due to the availability of field calibration and validationinformation for this parameter.
• Newly proposed FST parameter has shown better variability as compared to other nor-malised fracture energy parameters. This index is extremely well correlated to flexibilityindices and TI and has a lower variability. Use and further evaluation of FST is encouragedas it does allow distinction between mixtures with similar fracture energies but dissimilarpost-peak softening behaviours.
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• Fracture energy, flexibility index, TU and FST all increase with increasing test tempera-ture. The use of test temperature that is 10°C warmer than the specified low-temperaturebinder grade of the mix (PGLT + 10°C) yields greater distinction between mixes asopposed to using PGLT as the test temperature.
• There was some difference observed between the fracture indices for tests conducted onspecimens with 4% and 7% air void levels; however, more analysis is needed to drawsound conclusions.
This study provides a comprehensive assessment of different fracture indices from low-temperature fracture tests, while a substantial amount of new information were gathered throughthis effort, a number of topics were identified for further investigation. The following extensionsshould be undertaken to augment the conclusions from the present study and to further advancethe knowledge on pavement cracking performance fracture indices and their usefulness:
• The present study compared different fracture indices, assessed their variabilities and cor-related rankings provided by them; however, it was beyond the scope of this study to alsocompare various fracture indices with field thermal cracking performance. Future studiesshould undertake validation of fracture indices through the use of field performance data.
• Data from 21 distinct mixtures were assessed here, to further ensure that findings presentedhere are applicable to most asphalt mixtures, the data set should be expanded with moremixtures and testing conditions.
• The newly proposed index, FST, needs to be further assessed in the context of the fracturemechanics and its usefulness in performance modelling of cracking distress in asphalt mix-tures should be determined. Effects of mix volumetric measures and constituent materialproperties on FST also need to be tested and analysed.
• Analysis similar to that presented in this work should be conducted for other testgeometrics (such as SCB) and other test temperatures.
AcknowledgementsThe authors gratefully acknowledge financial support from China Scholarship Council for visit of Mr Yue-feng Zhu to the University of New Hampshire as a visiting doctoral student. The results and conclusionspresented herein do not reflect views or opinion of the sponsors.
Disclosure statementNo potential conflict of interest was reported by the authors.
ORCIDEshan V. Dave http://orcid.org/0000-0001-9788-2246Adam Zofka http://orcid.org/0000-0002-6541-5966
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