ASTM D6816-11(2016)

Standard Practice for Determining Low-Temperature Performance Grade (PG) of Asphalt Binders

SIGNIFICANCE AND USE
5.1 Estimated critical cracking temperature, as determined by this practice, is a criterion for specifying the low-temperature properties of asphalt binder in accordance with Specification D6373.  
5.2 This practice is designed to identify the temperature region where the induced thermal stress in a typical HMA subjected to rapid cooling (1 °C/h) exceeds the fracture stress of the HMA.  
5.3 For evaluating an asphalt binder for conformance to Specification D6373, the test temperature for the BBR and DTT data is selected from Table 1 of Specification D6373 according to the grade of asphalt binder.
Note 3: Other rates of elongation and test temperatures may be used to test asphalt binders for research purposes.
SCOPE
1.1 This practice covers the calculation of low-temperature properties of asphalt binders using data from the bending beam rheometer (see Test Method D6648) (BBR) and the direct tension tester (see Test Method D6723) (DTT). It can be used on data from unaged material or from material aged using Test Method D2872 (RTFOT), Practice D6521 (PAV), or Test Method D2872 (RTFOT) and Practice D6521 (PAV). It can be used on data generated within the temperature range from +6 °C to –36 °C. This practice generates data suitable for use in binder specifications such as Specification D6373.  
1.2 This practice is only valid for data on materials that fall within the scope of suitability for both Test Method D6648 and Test Method D6723.  
1.3 This practice can be used to determine the following:  
1.3.1 Critical cracking temperature of an asphalt binder, and  
1.3.2 Whether or not the failure stress exceeds the thermal stress in a binder at a given temperature.  
1.4 This practice determines the critical cracking temperature for a typical asphalt binder based on the determination of the temperature where the asphalt binder's strength equals its thermal stress as calculated by this practice. The temperature so determined is intended to yield a low temperature PG Grade of the sample being tested. The low temperature PG grade is intended for use in purchase specifications and is not intended to be a performance prediction of the HMA (Hot Mix Asphalt) in 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 to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
Note 1: The algorithms contained in this standard require implementation by a person trained in the subject of numerical methods and viscoelasticity. However, due to the complexity of the calculations they must, of necessity, be performed on a computer. Software to perform the calculation may be written, purchased as a spreadsheet, or as a stand-alone program.2

General Information

• Status: Historical
• Publication Date: 14-Dec-2016
• ICS: 93.080.20 - Road construction materials
• Technical Committee: D04 - Road and Paving Materials
• Drafting Committee: D04.44 - Rheological Tests

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: D6816 − 11 (Reapproved 2016)
Standard Practice for
Determining Low-Temperature Performance Grade (PG) of
Asphalt Binders
This standard is issued under the fixed designation D6816; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
NOTE 1—The algorithms contained in this standard require implemen-
1. Scope
tation by a person trained in the subject of numerical methods and
1.1 This practice covers the calculation of low-temperature
viscoelasticity. However, due to the complexity of the calculations they
propertiesofasphaltbindersusingdatafromthebendingbeam must, of necessity, be performed on a computer. Software to perform the
calculationmaybewritten,purchasedasaspreadsheet,orasastand-alone
rheometer (see Test Method D6648) (BBR) and the direct
program.
tension tester (see Test Method D6723) (DTT). It can be used
on data from unaged material or from material aged usingTest
2. Referenced Documents
Method D2872 (RTFOT), Practice D6521 (PAV), or Test
2.1 ASTM Standards:
Method D2872 (RTFOT) and Practice D6521 (PAV). It can be
C670Practice for Preparing Precision and Bias Statements
used on data generated within the temperature range from
for Test Methods for Construction Materials
+6°Cto–36°C.Thispracticegeneratesdatasuitableforusein
D8Terminology Relating to Materials for Roads and Pave-
binder specifications such as Specification D6373.
ments
1.2 This practice is only valid for data on materials that fall
D2872Test Method for Effect of Heat andAir on a Moving
withinthescopeofsuitabilityforbothTestMethodD6648and
Film of Asphalt (Rolling Thin-Film Oven Test)
Test Method D6723.
D6373 Specification for Performance Graded Asphalt
Binder
1.3 This practice can be used to determine the following:
D6521Practice for Accelerated Aging of Asphalt Binder
1.3.1 Criticalcrackingtemperatureofanasphaltbinder,and
Using a Pressurized Aging Vessel (PAV)
1.3.2 Whether or not the failure stress exceeds the thermal
D6648Test Method for Determining the Flexural Creep
stress in a binder at a given temperature.
Stiffness of Asphalt Binder Using the Bending Beam
1.4 This practice determines the critical cracking tempera-
Rheometer (BBR)
ture for a typical asphalt binder based on the determination of
D6723Test Method for Determining the Fracture Properties
the temperature where the asphalt binder’s strength equals its
of Asphalt Binder in Direct Tension (DT)
thermalstressascalculatedbythispractice.Thetemperatureso
determined is intended to yield a low temperature PG grade of
3. Terminology
the sample being tested. The low temperature PG grade is
3.1 Definitions—Fordefinitionsofgeneraltermsusedinthis
intended for use in purchase specifications and is not intended
standard, refer to Terminology D8.
to be a performance prediction of the HMA(Hot MixAsphalt)
3.2 Definitions of Terms Specific to This Standard:
in which the asphalt binder is used.
3.2.1 Arrhenius parameter, a ,n—this is the constant coef-
1.5 ThedevelopmentofthisstandardwasbasedonSIunits.
ficient in the Arrhenius model for shift factors: ln(a)=
T
In cases where units have been omitted, SI units are implied.
a ·((1/T) − (1/T )).
1 ref
1.6 This standard may involve hazardous materials,
3.2.2 coeffıcient of linear thermal expansion, α,n—the
operations, and equipment. This standard does not purport to
fractional change in size in one dimension associated with a
address all of the safety concerns, if any, associated with its
temperature increase of 1°C.
use. It is the responsibility of the user of this standard to
establish appropriate safety and health practices and deter-
The sole source of supply of the software package TSAR known to the
mine the applicability of regulatory limitations prior to use.
committee at this time is Abatech, Incorporated. If you are aware of alternative
suppliers, please provide this information to ASTM International Headquarters.
This practice is under the jurisdiction of ASTM Committee D04 on Road and Your comments will receive careful consideration at a meeting of the responsible
Paving Materials and is the direct responsibility of Subcommittee D04.44 on technical committee, which you may attend.
Rheological Tests. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Dec. 15, 2016. Published December 2016. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2002. Last previous edition approved in 2011 as D6816– 11. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/D6816-11R16. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D6816 − 11 (2016)
3.2.3 creep compliance, D(T,t), n—the reciprocal of the 3.2.12 relaxation modulus, E(T,t), n—the modulus of a
stiffness of a material, 1/S(T,t), at temperature T and time t, material determined using a strain-controlled (relaxation) ex-
which may also be expressed using reduced time, ξ,as periment at temperature T and time t, which may also be
D(T ). expressed using reduced time as E(T ,ξ).
ref,ξ ref
3.2.4 critical cracking temperature, T ,n—thetemperature, 3.2.13 shift factor, a ,n—the shift in the time or frequency
cr
T
estimated using this practice, at which the induced thermal domain associated with a shift from temperature T to the
stress in a material exceeds its fracture stress; the critical reference, T .
ref
cracking temperature is a “single event cracking” limit predic-
3.2.14 stiffness modulus, S(T,t), n—the modulus (stress/
tion which does not include the effect of low temperature
strain) of a material at temperature T and time t, which may
thermal fatigue.
also be expressed using reduced time as S(T ,ξ).
ref
3.2.5 failure stress,σ,n—thetensilestressvalueatthepoint
f
3.2.15 specification temperature, T ,n—the specified
spec
of failure obtained from Test Method D6723.
low-temperature grade of the binder being verified.
3.2.6 glassy modulus, n—the modulus at which the binder
exhibits glass-like behavior, which is assumed to be equal to
4. Summary of Practice
3×10 Pa.
4.1 This practice describes the procedure used to calculate
3.2.7 induced thermal stress, σ ,n—the stress induced in a
the relaxation modulus master curve and subsequently the
th
material by cooling it while it is restrained so that it cannot
thermally induced stress curve for an asphalt binder from data
contract.
generated on the BBR.
3.2.8 master curve, n—a composite curve at a single refer-
4.2 The stiffness master curve is calculated from the stiff-
ence temperature, T , which can be constructed by shifting,
ref ness versus time data measured in the BBR at two tempera-
along the log time or log frequency axis, a series of overlap-
tures. The fitting procedure follows Christensen-Anderson-
ping modulus data curves at various test temperatures; the
Marasteanu (CAM) rheological model for asphalt binder. The
modulus data curve at the reference temperature is not shifted;
stiffness master curve is then converted to the creep compli-
the shifted smooth curve is called the master curve at the
ance curve by taking its inverse.
reference temperature.
4.3 The creep compliance is converted to relaxation modu-
3.2.9 pavement constant, C, n—a constant factor that serves
lususingtheHopkinsandHammingmethod (3),whichisfitted
as a damage transfer function to convert the thermal stresses
to the CAM model. The Hopkins and Hamming method is a
calculated from laboratory data to the thermal stresses gener-
numerical solution of the convolution integral.
ated in the pavement. The damage transfer function is needed
4.4 The thermally induced stress is calculated by numeri-
to account for the differences in the strain rates experienced by
cally solving the convolution integral.
the distribution of binder films in the pavement and the bulk
strain rate used in the Test Method D6723 DTT test. Full
4.5 The thermal stress calculations are based on Boltz-
details on the determination of the pavement constant may be
mann’s Superposition Principle for linear viscoelastic materi-
foundinRefs (1) and (2),copiesofwhichareonfileatASTM
als. The calculated thermally induced stress is then multiplied
International. After extensive analysis, the most appropriate
by the Pavement Constant to predict the thermal stress pro-
pavement constant was determined to be 18. The pavement
duced in the hot-mix asphalt pavement. A value of 18 (eigh-
constant of 18 is based on the most current available pavement
teen) is used for the Pavement Constant.
performance data. The Federal Highway Administration
4.6 The calculated thermal stress is then compared to the
(FHWA)andtheTransportationResearchBoard(TRB)Binder
failure stress from DTT to determine the critical cracking
ExpertTask Group (ETG) continue to collect and analyze field
temperature of the pavement.
performance data. In the future, based on these analyses, the
pavement constant will be adjusted as appropriate. The pave-
5. Significance and Use
ment constant is an empirical factor required to relate binder
5.1 Estimated critical cracking temperature, as determined
thermal stress to the pavement thermal stress.
by this practice, is a criterion for specifying the low-
NOTE 2—Research suggests that changing the pavement constant from
temperature properties of asphalt binder in accordance with
16 to 24 results ina2to4°C change in the critical cracking temperature,
Specification D6373.
which is less than one low temperature grade interval (6°C).
5.2 This practice is designed to identify the temperature
3.2.10 reduced time, ξ,n—the computed loading time at the
region where the induced thermal stress in a typical HMA
reference temperature, T , equivalent to actual loading at
ref
subjected to rapid cooling (1°C⁄h) exceeds the fracture stress
temperature T, which is determined by dividing actual loading
of the HMA.
time, t, at temperature T, by the shift factor, a , ξ = t/a .
T T
3.2.11 reference temperature, T ,n—the temperature at
5.3 For evaluating an asphalt binder for conformance to
ref
which the master curve is constructed. Specification D6373, the test temperature for the BBR and
DTT data is selected from Table 1 of Specification D6373
according to the grade of asphalt binder.
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof NOTE 3—Other rates of elongation and test temperatures may be used
this standard. to test asphalt binders for research purposes.
D6816 − 11 (2016)
6. Methodology and Required Data t dt'
ζ~t! 5 (3)
*
a
T
6.1 This practice uses data from both BBR and DTT
measurements on an asphalt binder.
When T is constant with time, this reduces to the following
6.1.1 The DTT data required is stress at failure obtained by
equation:
testing at a strain rate of 3%⁄min. For continuous grade and
t
PG grade determination, DTT results are required at a mini-
ξ~t! 5 (4)
a
T
mum of two test temperatures. The DTT tests shall be
conducted at Specification D6373 specification test tempera- 7.1.6 For all 12 values S(T,t) obtained then becomes
tures at the 6°C increments that represent the low temperature S(T ,ξ) with time being replaced by reduced time.
ref
binder grade. For pass-fail determination, DTT results are
7.1.7 The values are fitted to the Christensen-Anderson-
required at a single temperature that is the low temperature Marasteanu (CAM) (5) model for asphalt master curves in the
grade plus 10°C.
following equation:
6.1.2 Two BBR data sets at two different temperatures are
β 2κ/β
ξ
S T ,ξ 5 S 11 (5)
~ !
required with deflection measurements at 8, 15, 30, 60, 120, F S D G
ref glassy
λ
and 240 s. The BBR test temperatures T and T minus 6°C
where:
(T–6) are selected such that S(T,60) < 300 MPa and S(T–6,
60) > 300 MPa. T shall be one of the Specification D6373 S = theassumedglassymodulusforthebinder: S =
glassy glassy
3×10 Pa.
specification test temperatures at the 6°C increments that
represent the low temperature binder grade.
7.1.8 Fit the resulting master curve data to this equation
using a nonlinear least squares fitting method to achieve a root
7. Calculations
mean square error, rms(%), of less than or equal to 1.25%.
7.1 Calculation of the Stiffness Master Curve: Appendix X1 contains an example calculation of this error
7.1.1 BBR Compliance Data—D(T, t) = compliance at time criterion.
t and temperature T – D(T, 8), D(T, 15), D(T, 30), D(T, 60),
7.2 Convert Stiffness Master Curve to Tensile Relaxation
D(T, 120), D(T, 240), D(T–6, 8), D(T–6, 15), D(T–6, 30),
Modulus Master Curve:
D(T–6, 60), D(T–6, 120), D(T–6, 240).
7.2.1 UseHopkinsandHamming’smethodtoconvertcreep
7.1.2 BBR Stiffness Data is calculated as S(T, t)=1/D(T, t)
compliancevalues D(T ,ξ)=1⁄S(T ,ξ)torelaxationmodulus
ref ref
7.1.3 Lettheshiftfactoratthereferencetemperature a =1.
T
E(T ,ξ).
ref
Determine a , the shift factor for the data at temperature
T–6
NOTE 6—This procedure is described in Ref (3).
T–6°C, numerically using Gordon and Shaw’s method to
produce master curves. The reference temperature shall be the
7.2.2 The glassy modulus value of 3×10 Pa shall be
–8 –8
higher of the two test temperatures. The linear coefficient of
adopted in the analysis for S(T ,1×10 s) = E(T ,1×10
ref ref
thermal expansion, above and below the glass transition
s). Calculate relaxation modulus data points using the follow-
–8 7
temperature, shall be 0.00017 m/m/°C. The glass transition
ing iterative formula from t = 1×10 to t = 1×10 s with
temperature is taken as –20°C.
intervalsof4pointsperdecade—1.000,1.778,3.162and5.623
0.0 0.25 0.5 0.75
(10 ,10 ,10 ,10 ).
NOTE 4—This procedure is described in Gordon and Shaw (4)—the
n21
master curve procedure is the SHIFTT routine found in Chapter 5. The
t 2 E t 1 ƒ t 2 t 2 ƒ t 2 t
value of –20°C is used for the glass transition temperature but has no @ ~ ! ~ !#
S D
n11 ( i n11 i n11 i11
i50
effect on the calculation as the linear expansion coefficient is assumed to
E t 1 5
~ n1 !
ƒ t 2 t
2 ~ !
be the same either side of this temperature. Although a constant value of n11 n
the linear coefficient of thermal expansion alpha is assumed, asphalt (6)
binders may have variable values of alpha.The alpha for mixes, however,
where,
has been shown by various researchers to be approximately constant and
does not vary with asphalt binders.
ƒ~t ! 5 ƒ~t !1 @D~t !1D~t !#@t 2 t # (7)
n11 n n11 n n11 n
7.1.4 From a calculate theArrhenius parameter from the
T-6 2
following equations:
Use the same time in
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D6816 − 11 D6816 − 11 (Reapproved 2016)
Standard Practice for
Determining Low-Temperature Performance Grade (PG) of
Asphalt Binders
This standard is issued under the fixed designation D6816; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice covers the calculation of low-temperature properties of asphalt binders using data from the bending beam
rheometer (see Test Method D6648) (BBR) and the direct tension tester (see Test Method D6723) (DTT). It can be used on data
from unaged material or from material aged using Test Method D2872 (RTFOT), Practice D6521 (PAV), or Test Method D2872
(RTFOT) and Practice D6521 (PAV). It can be used on data generated within the temperature range from +6°C+6 °C to
-36°C.–36 °C. This practice generates data suitable for use in binder specifications such as Specification D6373.
1.2 This practice is only valid for data on materials that fall within the scope of suitability for both Test Method D6648 and Test
Method D6723.
1.3 This practice can be used to determine the following:
1.3.1 Critical cracking temperature of an asphalt binder, and
1.3.2 Whether or not the failure stress exceeds the thermal stress in a binder at a given temperature.
1.4 This practice determines the critical cracking temperature for a typical asphalt binder based on the determination of the
temperature where the asphalt binder’s strength equals its thermal stress as calculated by this practice. The temperature so
determined is intended to yield a low temperature PG Grade of the sample being tested. The low temperature PG grade is intended
for use in purchase specifications and is not intended to be a performance prediction of the HMA (Hot Mix Asphalt) in 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 to address all
of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate
safety and health practices and determine the applicability of regulatory limitations prior to use.
NOTE 1—The algorithms contained in this standard require implementation by a person trained in the subject of numerical methods and viscoelasticity.
However, due to the complexity of the calculations they must, of necessity, be performed on a computer. Software to perform the calculation may be
written, purchased as a spreadsheet, or as a stand-alone program.
2. Referenced Documents
2.1 ASTM Standards:
C670 Practice for Preparing Precision and Bias Statements for Test Methods for Construction Materials
D8 Terminology Relating to Materials for Roads and Pavements
D2872 Test Method for Effect of Heat and Air on a Moving Film of Asphalt (Rolling Thin-Film Oven Test)
D6373 Specification for Performance Graded Asphalt Binder
D6521 Practice for Accelerated Aging of Asphalt Binder Using a Pressurized Aging Vessel (PAV)
D6648 Test Method for Determining the Flexural Creep Stiffness of Asphalt Binder Using the Bending Beam Rheometer (BBR)
D6723 Test Method for Determining the Fracture Properties of Asphalt Binder in Direct Tension (DT)
This practice is under the jurisdiction of ASTM Committee D04 on Road and Paving Materials and is the direct responsibility of Subcommittee D04.44 on Rheological
Tests.
Current edition approved July 1, 2011Dec. 15, 2016. Published August 2011December 2016. Originally approved in 2002. Last previous edition approved in 20022011
as D6816– 02 which was withdrawn 2007 and reinstated in July 2011. DOI: 10.1520/D6816-11. – 11. DOI: 10.1520/D6816-11R16.
The sole source of supply of the software package TSAR known to the committee at this time is Abatech, Incorporated. If you are aware of alternative suppliers, please
provide this information to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of the responsible technical committee , which
you may attend.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D6816 − 11 (2016)
3. Terminology
3.1 Definitions—For definitions of general terms used in this standard, refer to Terminology D8.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 Arrhenius parameter, a , n—this is the constant coefficient in the Arrhenius model for shift factors: ln(a ) = a ·((1/T) −
1 T 1
(1/T )).
ref
3.2.2 coeffıcient of linear thermal expansion, α, n—the fractional change in size in one dimension associated with a temperature
increase of 1°C.1 °C.
3.2.3 creep compliance, D(T,t), n—the reciprocal of the stiffness of a material, 1/S(T,t), at temperature T and time t, which may
also be expressed using reduced time, ξ, as D(T ).
ref,ξ
3.2.4 critical cracking temperature, T ,n—the temperature, estimated using this practice, at which the induced thermal stress
cr
in a material exceeds its fracture stress; the critical cracking temperature is a “single event cracking” limit prediction which does
not include the effect of low temperature thermal fatigue.
3.2.5 failure stress, σ ,n—the tensile stress value at the point of failure obtained from Test Method D6723.
f
3.2.6 glassy modulus, n—the modulus at which the binder exhibits glass-like behavior, which is assumed to be equal to
3×103 × 10 Pa.
3.2.7 induced thermal stress, σ ,n—the stress induced in a material by cooling it while it is restrained so that it cannot contract.
th
3.2.8 master curve, n—a composite curve at a single reference temperature, T , which can be constructed by shifting, along
ref
the log time or log frequency axis, a series of overlapping modulus data curves at various test temperatures; the modulus data curve
at the reference temperature is not shifted; the shifted smooth curve is called the master curve at the reference temperature.
3.2.9 pavement constant, C, n—a constant factor that serves as a damage transfer function to convert the thermal stresses
calculated from laboratory data to the thermal stresses generated in the pavement. The damage transfer function is needed to
account for the differences in the strain rates experienced by the distribution of binder films in the pavement and the bulk strain
rate used in the Test Method D6723 DTT test. Full details on the determination of the pavement constant may be found in Refs
(1) and (2), copies of which are on file at ASTM International. After extensive analysis, the most appropriate pavement constant
was determined to be 18. The pavement constant of 18 is based on the most current available pavement performance data. The
Federal Highway Administration (FHWA) and the Transportation Research Board (TRB) Binder Expert Task Group (ETG)
continue to collect and analyze field performance data. In the future, based on these analyses, the pavement constant will be
adjusted as appropriate. The pavement constant is an empirical factor required to relate binder thermal stress to the pavement
thermal stress.
NOTE 2—Research suggests that changing the pavement constant from 16 to 24 results in a 2 to 4°C4 °C change in the critical cracking temperature,
which is less than one low temperature grade interval (6°C).(6 °C).
3.2.10 reduced time, ξ, n—the computed loading time at the reference temperature, T , equivalent to actual loading at
ref
temperature T, which is determined by dividing actual loading time, t, at temperature T, by the shift factor, a , ξ = t/a .
T T
3.2.11 reference temperature, T ,n—the temperature at which the master curve is constructed.
ref
3.2.12 relaxation modulus, E(T,t), n—the modulus of a material determined using a strain-controlled (relaxation) experiment at
temperature T and time t, which may also be expressed using reduced time as E(T ,ξ).
ref
3.2.13 shift factor, a ,n—the shift in the time or frequency domain associated with a shift from temperature T to the reference,
T
T .
ref
3.2.14 stiffness modulus, S(T,t), n—the modulus (stress/strain) of a material at temperature T and time t, which may also be
expressed using reduced time as S(T ,ξ).
ref
3.2.15 specification temperature, T ,n—the specified low-temperature grade of the binder being verified.
spec
4. Summary of Practice
4.1 This practice describes the procedure used to calculate the relaxation modulus master curve and subsequently the thermally
induced stress curve for an asphalt binder from data generated on the BBR.
4.2 The stiffness master curve is calculated from the stiffness versus time data measured in the BBR at two temperatures. The
fitting procedure follows Christensen-Anderson-Marasteanu (CAM) rheological model for asphalt binder. The stiffness master
curve is then converted to the creep compliance curve by taking its inverse.
4.3 The creep compliance is converted to relaxation modulus using the Hopkins and Hamming’sHamming method (3), which
is fitted to the CAM model. The Hopkins and Hamming method is a numerical solution of the convolution integral.
The boldface numbers in parentheses refer to the list of references at the end of this standard.
D6816 − 11 (2016)
4.4 The thermally induced stress is calculated by numerically solving the convolution integral.
4.5 The thermal stress calculations are based on Boltzmann’s Superposition Principle for linear viscoelastic materials. The
calculated thermally induced stress is then multiplied by the Pavement Constant to predict the thermal stress produced in the
hot-mix asphalt pavement. A value of 18 (eighteen) is used for the Pavement Constant.
4.6 The calculated thermal stress is then compared to the failure stress from DTT to determine the critical cracking temperature
of the pavement.
5. Significance and Use
5.1 Estimated critical cracking temperature, as determined by this practice, is a criterion for specifying the low-temperature
properties of asphalt binder in accordance with Specification D6373.
5.2 This practice is designed to identify the temperature region where the induced thermal stress in a typical HMA subjected
to rapid cooling (1°C/h)(1 °C ⁄h) exceeds the fracture stress of the HMA.
5.3 For evaluating an asphalt binder for conformance to Specification D6373, the test temperature for the BBR and DTT data
is selected from Table 1 of Specification D6373 according to the grade of asphalt binder.
NOTE 3—Other rates of elongation and test temperatures may be used to test asphalt binders for research purposes.
6. Methodology and Required Data
6.1 This practice uses data from both BBR and DTT measurements on an asphalt binder.
6.1.1 The DTT data required is stress at failure obtained by testing at a strain rate of 3 % ⁄min. For continuous grade and PG
grade determination, DTT results are required at a minimum of two test temperatures. The DTT tests shall be conducted at
Specification D6373 specification test temperatures at the 6°C6 °C increments that represent the low temperature binder grade. For
pass-fail determination, DTT results are required at a single temperature that is the low temperature grade plus 10°C.10 °C.
6.1.2 Two BBR data sets at two different temperatures are required with deflection measurements at 8, 15, 30, 60, 120, and 240
s. The BBR test temperatures T and T minus 6°C6 °C (T-6) – 6) are selected such that S(T,60) 60) < 300 MPa and S(T-6,60) – 6,
60) > 300 MPa. T shall be one of the Specification D6373 specification test temperatures at the 6°C6 °C increments that represent
the low temperature binder grade.
7. Calculations
7.1 Calculation of the Stiffness Master Curve:
7.1.1 BBR Compliance Data—D(T,t) = compliance at time t and temperature T – D(T, 8), D(T, 15), D(T, 30), D(T, 60), D(T,
120), D(T, 240), D(T-6,8), – 6, 8), D(T-6,15), – 6, 15), D(T-6,30), – 6, 30), D(T-6,60), – 6, 60), D(T-6,120), – 6, 120),
D(T-6,240). – 6, 240).
7.1.2 BBR Stiffness Data is calculated as S(T,t) = 1/D(T,t)
7.1.3 Let the shift factor at the reference temperature a = 1. Determine a , the shift factor for the data at temperature
T T-6 – 6
T-6°C, – 6 °C, numerically using Gordon and Shaw’s method to produce master curves. The reference temperature shall be the
higher of the two test temperatures. The linear coefficient of thermal expansion, above and below the glass transition temperature,
shall be 0.00017 m/m/°C. The glass transition temperature is taken as -20°C.–20 °C.
NOTE 4—This procedure is described in Gordon/Shaw Gordon and Shaw (4)—the master curve procedure is the SHIFTT routine found in Chapter 5.
The value of -20°C–20 °C is used for the glass transition temperature but has no effect on the calculation as the linear expansion coefficient is assumed
to be the same either side of this temperature. Although a constant value of the linear coefficient of thermal expansion alpha is assumed, asphalt binders
may have variable values of alpha. The alpha for mixes, however, has been shown by various researchers to be approximately constant and does not vary
with asphalt binders.
7.1.4 From a calculate the Arrhenius parameter from the following equations:
T-6
1 1
ln~a !5 a · 2 (1)
S D
T26 1
T 2 6 T
~ !
ref ref
ln a
~ !
T26
a 5 (2)
S D
T 2 6 2
~ !
ref
T
ref
NOTE 5—The Gordon/Shaw method uses a shift factor (a ) in the form of a base 10 log (log ). However, this specification is based on the natural
T 10
log (ln or log ).
e
7.1.5 Reduced time, ξ, for data at temperature T, is determined by integrating the reciprocal of the shift factor with respect to
time in the following equation:
t dt'
ζ t 5 (3)
~ ! *
0 a
T
When T is constant with time, this reduces to the following equation:
D6816 − 11 (2016)
t
ξ~t! 5 (4)
a
T
7.1.6 For all 12 values S(T,t) obtained then becomes S(T ,ξ) with time being replaced by reduced time.
ref
7.1.7 The values are fitted to the Christensen-Anderson-Marasteanu (CAM) (5) model for asphalt master
...