# ASTM D6816-11 (Reapproved 2016)

Designation D6816 − 11 Reapproved 2016Standard Practice forDetermining Low-Temperature Perance Grade PG ofAsphalt Binders1This standard is issued under the fixed designation D6816; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon ´ indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the calculation of low-temperatureproperties of asphalt binders using data from the bending beamrheometer see Test D6648 BBR and the directtension tester see Test D6723 DTT. It can be usedon data from unaged material or from material aged using Test D2872 RTFOT, Practice D6521 PAV, or Test D2872 RTFOT and Practice D6521 PAV. It can beused on data generated within the temperature range from6 °C to –36 °C.This practice generates data suitable for use inbinder specifications such as Specification D6373.1.2 This practice is only valid for data on materials that fallwithin the scope of suitability for both Test D6648 andTest D6723.1.3 This practice can be used to determine the following1.3.1 Critical cracking temperature of an asphalt binder, and1.3.2 Whether or not the failure stress exceeds the thermalstress in a binder at a given temperature.1.4 This practice determines the critical cracking tempera-ture for a typical asphalt binder based on the determination ofthe temperature where the asphalt binder’s strength equals itsthermal stress as calculated by this practice.The temperature sodetermined is intended to yield a low temperature PG Grade ofthe sample being tested. The low temperature PG grade isintended for use in purchase specifications and is not intendedto be a perance prediction of the HMA Hot Mix Asphaltin which the asphalt binder is used.1.5 The development of this standard was based on SI units.In cases where units have been omitted, SI units are implied.1.6 This standard may involve hazardous materials,operations, and equipment. This standard does not purport toaddress all of the safety concerns, if any, associated with itsuse. It is the responsibility of the user of this standard toestablish appropriate safety and health practices and deter-mine the applicability of regulatory limitations prior to use.NOTE 1The algorithms contained in this standard require implemen-tation by a person trained in the subject of numerical s andviscoelasticity. However, due to the complexity of the calculations theymust, of necessity, be pered on a computer. Software to per thecalculation may be written, purchased as a spreadsheet, or as a stand-aloneprogram.22. Referenced Documents2.1 ASTM Standards3C670 Practice for Preparing Precision and Bias Statementsfor Test s for Construction MaterialsD8 Terminology Relating to Materials for Roads and Pave-mentsD2872 Test for Effect of Heat and Air on a MovingFilm of Asphalt Rolling Thin-Film Oven TestD6373 Specification for Perance Graded AsphaltBinderD6521 Practice for Accelerated Aging of Asphalt BinderUsing a Pressurized Aging Vessel PAVD6648 Test for Determining the Flexural CreepStiffness of Asphalt Binder Using the Bending BeamRheometer BBRD6723 Test for Determining the Fracture Propertiesof Asphalt Binder in Direct Tension DT3. Terminology3.1 DefinitionsFor definitions of general terms used in thisstandard, refer to Terminology D8.3.2 Definitions of Terms Specific to This Standard3.2.1 Arrhenius parameter, a1,nthis is the constant coef-ficient in the Arrhenius model for shift factors lnaTa1·1/T − 1/Tref.3.2.2 coeffıcient of linear thermal expansion, α,nthefractional change in size in one dimension associated with atemperature increase of 1 °C.1This practice is under the jurisdiction of ASTM Committee D04 on Road andPaving Materials and is the direct responsibility of Subcommittee D04.44 onRheological Tests.Current edition approved Dec. 15, 2016. Published December 2016. Originallyapproved in 2002. Last previous edition approved in 2011 as D6816 – 11. DOI10.1520/D6816-11R16.2The sole source of supply of the software package TSAR known to thecommittee at this time is Abatech, Incorporated. If you are aware of alternativesuppliers, please provide this ination to ASTM International Headquarters.Your comments will receive careful consideration at a meeting of the responsibletechnical committee1, which you may attend.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume ination, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.3 creep compliance, DT,t, nthe reciprocal of thestiffness of a material, 1/ST,t, at temperature T and time t,which may also be expressed using reduced time, ξ,asDTref,ξ.3.2.4 critical cracking temperature, Tcr,nthe temperature,estimated using this practice, at which the induced thermalstress in a material exceeds its fracture stress; the criticalcracking temperature is a “single event cracking” limit predic-tion which does not include the effect of low temperaturethermal fatigue.3.2.5 failure stress, σf,nthe tensile stress value at the pointof failure obtained from Test D6723.3.2.6 glassy modulus, nthe modulus at which the binderexhibits glass-like behavior, which is assumed to be equal to3109Pa.3.2.7 induced thermal stress, σth,nthe stress induced in amaterial by cooling it while it is restrained so that it cannotcontract.3.2.8 master curve, na composite curve at a single refer-ence temperature, Tref, which can be constructed by shifting,along the log time or log frequency axis, a series of overlap-ping modulus data curves at various test temperatures; themodulus data curve at the reference temperature is not shifted;the shifted smooth curve is called the master curve at thereference temperature.3.2.9 pavement constant, C, na constant factor that servesas a damage transfer function to convert the thermal stressescalculated from laboratory data to the thermal stresses gener-ated in the pavement. The damage transfer function is neededto account for the differences in the strain rates experienced bythe distribution of binder films in the pavement and the bulkstrain rate used in the Test D6723 DTT test. Fulldetails on the determination of the pavement constant may befound in Refs 14and 2, copies of which are on file atASTMInternational. After extensive analysis, the most appropriatepavement constant was determined to be 18. The pavementconstant of 18 is based on the most current available pavementperance data. The Federal Highway AdministrationFHWA and the Transportation Research Board TRB BinderExpert Task Group ETG continue to collect and analyze fieldperance data. In the future, based on these analyses, thepavement constant will be adjusted as appropriate. The pave-ment constant is an empirical factor required to relate binderthermal stress to the pavement thermal stress.NOTE 2Research suggests that changing the pavement constant from16 to 24 results ina2to4°Cchange in the critical cracking temperature,which is less than one low temperature grade interval 6 °C.3.2.10 reduced time, ξ,nthe computed loading time at thereference temperature, Tref, equivalent to actual loading attemperature T, which is determined by dividing actual loadingtime, t, at temperature T, by the shift factor, aT, ξ t/aT.3.2.11 reference temperature, Tref,nthe temperature atwhich the master curve is constructed.3.2.12 relaxation modulus, ET,t, nthe modulus of amaterial determined using a strain-controlled relaxation ex-periment at temperature T and time t, which may also beexpressed using reduced time as ETref,ξ.3.2.13 shift factor, aT,nthe shift in the time or frequencydomain associated with a shift from temperature T to thereference, Tref.3.2.14 stiffness modulus, ST,t, nthe modulus stress/strain of a material at temperature T and time t, which mayalso be expressed using reduced time as STref,ξ.3.2.15 specification temperature, Tspec,nthe specifiedlow-temperature grade of the binder being verified.4. Summary of Practice4.1 This practice describes the procedure used to calculatethe relaxation modulus master curve and subsequently thethermally induced stress curve for an asphalt binder from datagenerated on the BBR.4.2 The stiffness master curve is calculated from the stiff-ness versus time data measured in the BBR at two tempera-tures. The fitting procedure follows Christensen-Anderson-Marasteanu CAM rheological model for asphalt binder. Thestiffness master curve is then converted to the creep compli-ance curve by taking its inverse.4.3 The creep compliance is converted to relaxation modu-lus using the Hopkins and Hamming 3, which is fittedto the CAM model. The Hopkins and Hamming is anumerical solution of the convolution integral.4.4 The thermally induced stress is calculated by numeri-cally solving the convolution integral.4.5 The thermal stress calculations are based on Boltz-mann’s Superposition Principle for linear viscoelastic materi-als. The calculated thermally induced stress is then multipliedby the Pavement Constant to predict the thermal stress pro-duced in the hot-mix asphalt pavement. A value of 18 eigh-teen is used for the Pavement Constant.4.6 The calculated thermal stress is then compared to thefailure stress from DTT to determine the critical crackingtemperature of the pavement.5. Significance and Use5.1 Estimated critical cracking temperature, as determinedby this practice, is a criterion for specifying the low-temperature properties of asphalt binder in accordance withSpecification D6373.5.2 This practice is designed to identify the temperatureregion where the induced thermal stress in a typical HMAsubjected to rapid cooling 1 °C⁄h exceeds the fracture stressof the HMA.5.3 For uating an asphalt binder for conance toSpecification D6373, the test temperature for the BBR andDTT data is selected from Table 1 of Specification D6373according to the grade of asphalt binder.NOTE 3Other rates of elongation and test temperatures may be usedto test asphalt binders for research purposes.4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.D6816 − 11 201626. ology and Required Data6.1 This practice uses data from both BBR and DTTmeasurements on an asphalt binder.6.1.1 The DTT data required is stress at failure obtained bytesting at a strain rate of 3 ⁄min. For continuous grade andPG grade determination, DTT results are required at a mini-mum of two test temperatures. The DTT tests shall beconducted at Specification D6373 specification test tempera-tures at the 6 °C increments that represent the low temperaturebinder grade. For pass-fail determination, DTT results arerequired at a single temperature that is the low temperaturegrade plus 10 °C.6.1.2 Two BBR data sets at two different temperatures arerequired with deflection measurements at 8, 15, 30, 60, 120,and 240 s. The BBR test temperatures T and T minus 6 °CT – 6 are selected such that ST, 60 300 MPa. T shall be one of the Specification D6373specification test temperatures at the 6 °C increments thatrepresent the low temperature binder grade.7. Calculations7.1 Calculation of the Stiffness Master Curve7.1.1 BBR Compliance DataDT, t compliance at timet and temperature T – DT, 8, DT, 15, DT, 30, DT, 60,DT, 120, DT, 240, DT – 6, 8, DT – 6, 15, DT – 6, 30,DT – 6, 60, DT – 6, 120, DT – 6, 240.7.1.2 BBR Stiffness Data is calculated as ST, t1/DT, t7.1.3 Let the shift factor at the reference temperature aT1.Determine aT –6, the shift factor for the data at temperatureT – 6 °C, numerically using Gordon and Shaw’s toproduce master curves. The reference temperature shall be thehigher of the two test temperatures. The linear coefficient ofthermal expansion, above and below the glass transitiontemperature, shall be 0.00017 m/m/°C. The glass transitiontemperature is taken as –20 °C.NOTE 4This procedure is described in Gordon and Shaw 4themaster curve procedure is the SHIFTT routine found in Chapter 5. Thue of –20 °C is used for the glass transition temperature but has noeffect on the calculation as the linear expansion coefficient is assumed tobe the same either side of this temperature. Although a constant value ofthe linear coefficient of thermal expansion alpha is assumed, asphaltbinders may have variable values of alpha. The alpha for mixes, however,has been shown by various researchers to be approximately constant anddoes not vary with asphalt binders.7.1.4 From aT-6calculate the Arrhenius parameter from thefollowing equationslnaT26 5 a1·S1Tref2 621TrefD1a15lnaT26S1Tref2 6 21TrefD2NOTE 5The Gordon/Shaw uses a shift factor aT in the of a base 10 log log10. However, this specification is based on the naturallog ln or loge.7.1.5 Reduced time, ξ, for data at temperature T, is deter-mined by integrating the reciprocal of the shift factor withrespect to time in the following equationζt 5 *0t dt aT3When T is constant with time, this reduces to the followingequationξt 5taT47.1.6 For all 12 values ST,t obtained then becomesSTref,ξ with time being replaced by reduced time.7.1.7 The values are fitted to the Christensen-Anderson-Marasteanu CAM 5 model for asphalt master curves in thefollowing equationSTref,ξ 5 SglassyF11SξλDβG2κ/β5whereSglassy the assumed glassy modulus for the binder Sglassy3109Pa.7.1.8 Fit the resulting master curve data to this equationusing a nonlinear least squares fitting to achieve a rootmean square error, rms, of less than or equal to 1.25 .Appendix X1 contains an example calculation of this errorcriterion.7.2 Convert Stiffness Master Curve to Tensile RelaxationModulus Master Curve7.2.1 Use Hopkins and Hamming’s to convert creepcompliance values DTref,ξ1⁄STref,ξ to relaxation modulusETref,ξ.NOTE 6This procedure is described in Ref 3.7.2.2 The glassy modulus value of 3 109Pa shall beadopted in the analysis for STref,110–8s ETref,110–8s. Calculate relaxation modulus data points using the follow-ing iterative ula from t 110–8to t 1107s withintervals of 4 points per decade1.000, 1.778, 3.162 and 5.623100.0,100.25,100.5,100.75.Etn1125tn112i50n21ESti112D ƒtn112 ti 2 ƒtn112 ti11ƒtn112 tn6where,ƒtn11 5 ƒtn112Dtn111Dtntn112 tn 7Use the same time intervals as above and use ƒt00.Acubic spline has been found to be suitable for interpolation.7.2.3 Fit the relaxation modulus values to the CAM asdescribe