“rheology of asphalt binders and implications for...

1

Dr. David AndersonConsultant and Professor EmeritusPenn State [email protected]

“Rheology of Asphalt Binders and Implications for Performance”

November 10, 2009

Dr. Geoffrey RowePresidentAbatech Inc. (Consultants)[email protected]

mailto:[email protected]�


-2-

Today’s Program

Introduction and Purpose Model types – Continuous and discrete Background to CA Interpretation of CA/CAM Parameters Temperature dependency Inter-conversions Models – what do they tell us Summary

-3-

Today’s Program

Introduction and Purpose Model types – Continuous and

discrete Background to CA Interpretation of CA/CAM

Parameters Temperature dependency

Inter-conversions Models – what do they tell us Summary

-4-

Focus of Today’s Webinar

Overview of different rheological models• Assumptions upon which models are based• Applicability and limitations of the models

Use of models in relation to pavement performance Webinar is only an introduction to the topic

• Complete coverage would require many hours• Topic is complicated – concepts may seem unfamiliar• Rigor will be deferred today for the sake of simplicity

-5-

Rheology – What Does It Imply?

Study of a material with a stress-strain response that depends on the temperature and rate or time of loading• Modulus (ratio of stress to strain) is function of

temperature and rate or time of loading Moduli for asphalt binders and mixtures are loading time

and temperature dependent• Expect materials to exhibit viscous and elastic behavior• Refer to such materials as “viscoelastic”

Deal today with linear viscoelastic materials only• “Linear viscoelastic” implies that the modulus is

independent of applied stress or strain• Non-linear viscoelasticity is VERY complicated

-6-

Let’s Get Started!

-7-

Today’s Program


-8-

Why Do We Need Models?

Provide mathematical representation of behavior• Parameters can be useful for monitoring aging and

general implications for performance Used to generate master curves

• Mechanism for interpolation and extrapolation• Used in performing complex calculations

Calculation of low temperature cracking parameter• Used to relate binder and mix behavior

Models are needed in order to relate mechanical properties to performance

-9-

Summary: Test measurements and moduli

OscillatoryComplex modulus: Shear, G*(ω) = τ(ω)/γ(ω)Compression/Tension, E*(ω) = σ(ω)/ε(ω)

CreepCompliance (Modulus):Shear, J(t) = γ(t)/τ [Stiffness, S(t) = 1/J(t)]Tension/Compression, D(t) = ε(t)/σ

RelaxationRelaxation Modulus:Shear, G(t) = γ(t)/τ Tension/Compression, E(t) = σ(t)/ε

-10-

Simple Models Are In Common Use

Polynomial to fit BBR data• Calculate S and m at 60 seconds• Valid over short loading time only

Determination of continuous grading temperature• G* and S interpolated between two temperatures• Assume Log S and G* vs. T linear over 6ºC• Assume m vs. T linear over 6ºC

A model is simply an algorithm that relates a modulus to loading time and temperature• Models are not mysterious visions from the clouds –

but some are complicated!

-11-

Models for Asphalt Binders - Overview

Point measurements• e.g. dynamic viscosity at 60ºC and 10 Hz• Describes behavior at single time-temperature point• Limited use for predicting performance

Indices• e.g. PI, PVN, etc • Typically confound loading time and temperature

Discrete models (e.g. Prony Series)• Built using analogies with springs and dashpots

Continuous models (e.g. CA Model)• Usually based on relaxation modulus

-12-

Temperature Susceptibility Parameters

Multiple methods• PI – based on penetration and SP• PVN – based on penetration and viscosity• Others using multiple pen or vis measurements

Basic problem with these parameters• pen/vis, pen/SP confound test temperature and shear

rate• These parameters are questionable predictors of

temperature susceptibility • Literature indicates poor relationship between various

“temperature susceptibility” parameters• Need to adopt more rational models/parameters!

-13-

Viscosity Temperature Susceptibility (VTS)

Viscosity temperature susceptibility is used in MEPDG Assumes linear relation between log log “viscosity” and

log temperature• Viscosity traditionally measured with capillary

viscometers• Binders, especially modified are shear rate dependent

within measurement range Conclusion: VTS is a questionable measure of

temperature susceptibility

-14-

Rheological Models, General Applications

Rheological models have been used many materials for more than 100 years – nothing new!

Poynting and Thomson (1902)• Maxwell model - spring and dashpot analogy

Weichert (1893) and Thomson (1888)• Concept of a distribution of relaxation times

Boltzmann (1878)• Superposition principle

Continued development is basis of considerable research in polymer industry• Not specific to asphalt binders!

-15-

Mastercurve – What Is It?

A representation of the stress-strain response over a wide range of test temperatures and loading times

Mastercurves are generated by combining data obtained at different loading times and temperatures to generate a single curve• May be represented graphically or with an algorithm

(mathematically)• Algorithms vary according to intended use

Mastercurves may be generated for different functions• e.g. Shear, tension, modulus, phase angle, strength,

etc.

-16-

Idealized Viscoelastic ResponseLo

g M

odul

us,

G*

Log Frequency

Log

Mod

ulus

, J

Log Time

Dynamic Creep

G∝

Jo

η = J(t)/t

η* = G*/ω

-17-

Asymptotes – Asphalt Binders

1. Glassy plateau, common value for all bindersGg = 1/Jo

2. Location of viscous asymptote is specific to binderOn the 1:1 asymptote (log-log plot)

η0 = t/J(t), η* = G*(ω)/(ω), and η0 = η* ` Shape of curve in the transition between two asymptotes is

binder specific• In this region compliance is not inverse of modulus

Need technique for interconverting modulus and compliance in transition region

)(/1)(* tJG ≠ω

-18-

Models for Binders – Historical

van der Poel nomograph (Journal Appl. Chem., vol. 4 1954)• Underlying development involved modeling• Concept of equi-stiffness

Jongepeir and Kuilman (AAPT, vol. 38, 1968)• Involved calculation of relaxation spectra• Assumed Gaussian distribution of relaxation time• Used WLF for time-temperature shifting

Dobson (AAPT, vol. 38, 1968)• Relates tan δ to log G*/log ω• Used WLF for shifting

Several other 1970’s and 1980’s

-19-

Two Approaches to Modeling Binders

Model where mastercurve functions are described by continuous function • Function has limited number of parameters• Parameters have intuitive meaning• CA model is an example

Discrete model based on mechanical-electrical analogy• Model consists of series of springs and dashpots• Comprehensive model may require multiple elements• Element coefficients have little intuitive meaning

Both models require statistical curve fitting

-20-

Dobson’s Model

Based on empirical observations:• Log-log slope of complex modulus versus frequency is

a function of loss tangent and relaxation spectrum• Explicit relationship between loss tangent and complex

modulus Results in a “universal mastercurve”

Impractical because gives frequency as function of modulus instead of modulus as function of frequency

−+−−=

−

3.230

5.20)1log(1loglog

brb

rrr

GG

bGω

-21-

Dickinson and Witt’s Model

Represented mastercurve as a hyperbola

Coefficients are obtained by iteration• Not user friendly

( ) ( )[ ]{ }5.022* 2loglog5.0log βωω +−= rrrG

[Dickinson and Witt, Trans. Soc. Rheology, vol. 18, 1974]

( ) ( ) gr GGG /** ωω =

gor GTa /)(ωηω =

-22-

CA Model

Christensen-Anderson –CA model (1993)

Three parameter model to describe G*(ω)• Glassy modulus, Gg

• Location parameter, ωc

• Shape parameter, R Parameters have

intuitive meaning Model may be extended to

phase angle and creep compliance

-23-

Discrete Models

Discrete models (e.g. Prony Series)• Springs and dashpots in parallel or series

• Spring and dashpot coefficients (Ei and ηi) have little rational or intuitive meaning (except for E and η)

Primary application is for calculation purposes• Coefficients are determined via curve fitting• Resulting Prony series is easy to manipulate

mathematically

ηt

Eg

-24-

Summary: Continuous vs. Discrete Models

Discrete model results in Prony series which can be easily manipulated mathematically but coefficients have little meaning• Discrete models to be discussed later

Continuous model results in multiple parameter model which may be difficult to manipulate mathematically but coefficients intuitive meaning• Parameters provide links between asphalt composition,

rheology and performance

-25-

Today’s Program


-26-

Models Based on Relaxation Spectrum

Relaxation spectrum can be thought of as a graphical representation of the relaxation process• Represented by a mathematical function• All other viscoelastic functions can be derived

from the mathematical representation of the relaxation spectrum

Two models of note based on relaxation considerations• Jongepier and Kuilmann• CA, CAM, and CAS models

-27-

Jongepier and Kuilmann Model

Relaxation spectra assumed log normal in shape:

Viscoelastic functions can be derived based on this function• Equations for viscoelastic functions, G*, G’, G”, etc. are

very complex integral functions• β parameter gives a series of mastercurves each with a

characteristic shape • Equations provide reasonable fit to data, however their

complexity minimizes practical use

( )2/lnexp

−=β

ττπβ

τ mgGH

-28-

CA Model Derivation

Based on observation that relaxation spectra is not symmetric• Assumed skewed logistic function:

Cumulative distribution function becomes:

[Christensen, AAPT, vol. 61, 1992]

1exp1exp)(

−−

−

+

−

=m

bax

bax

bmxF

−

+−=b

axxP exp11)(

-29-

CA Model for G*(ω)

Substituting rheological parameters:

G*(ω) = Measured complex modulusGg = Glassy modulusR = Rhelogical Index (shape factor)ω = Test frequency

ωc = Crossover frequency (location parameter)

2log/)/2(log1)(*

RR

cgGG

−

+=ωωω

-30-

CA Model for δ(ω)

Rewriting and substituting rheological parameters:

+=R

c

/)2(log1/90)(

ωωωδ

δ(ω) = Measured phase angle

-31-

Program


-32-

CA Model

Gg and η0 are asymptotes as discussed previously• Gg = 109 Pa all binders • η0 represents 1:1 slope

ωc locates the curve on the time

R, Rheological Index, defines shape of curve• Related to relaxation spectra

-33-

Parameter Changes With Lab Aging

Note: With aging, R increases making curve flatter while ωc shifts curve to left

1.E+001.E+011.E+021.E+031.E+041.E+051.E+061.E+071.E+081.E+09

1.E

-05

1.E

-04

1.E

-03

1.E

-02

1.E

-01

1.E

+00

1.E

+01

1.E

+02

1.E

+03

1.E

+04

1.E

+05

1.E

+06

1.E

+07

1.E

+08

1.E

+09

1.E

+10

1.E

+11

1.E

+12

Frequency, ω (rad/s)

Com

plex

Mod

ulus

, G*

( Pa)

Original: R = 1.16 ωc = 1932

RTFOT: R = 1.27 ωc = 824

PAV: R = 1.35 ωc = 123

-34-

R for Different Binders and Aging Conditions

[Source: SHRP-A-669]

-35-

Mastercurve Shape Related to PI


-36-

Field Aging


-37-

Shortcut Determination of η0

Extrapolation to determine η0


-38-

Shortcut Determination of R


-39-

Shortcut Determination of ωc


-40-

How Do Parameters Affect Mastercurve?

Above: R held constant, as ωc decreases the curve shifts to left but retains its shape

1.E+001.E+011.E+021.E+031.E+041.E+051.E+061.E+071.E+081.E+09

1.E

-05

1.E

-04

1.E

-03

1.E

-02

1.E

-01

1.E

+00

1.E

+01

1.E

+02

1.E

+03

1.E

+04

1.E

+05

1.E

+06

1.E

+07

1.E

+08

1.E

+09

1.E

+10

1.E

+11

1.E

+12

Frequency, ω ( rad/s)

Com

plex

Mod

ulus

, G*

( Pa)

R = 2 ωc = 1000

R = 2 ωc = 100

R = 2 ωc = 10

1.E+001.E+011.E+021.E+031.E+041.E+051.E+061.E+071.E+081.E+09

1.E

-05

1.E

-04

1.E

-03

1.E

-02

1.E

-01

1.E

+00

1.E

+01

1.E

+02

1.E

+03

1.E

+04

1.E

+05

1.E

+06

1.E

+07

1.E

+08

1.E

+09

1.E

+10

1.E

+11

1.E

+12

Frequency, ω ( rad/s)

Com

plex

Mod

ulus

, G*

( Pa)

R = 1 ωc = 100

R = 2 ωc = 100

R = 3 ωc = 100

Below: Cross-over frequency ωc (ω where G” = G’) is held constant, as R increases the curve flattens

-41-

Cautions With CA Model

Model does not fit well as approach viscous asymptote• CAM Model adds parameter to account for this

discrepancy Model does not accommodate plateau region for

polymer modified binders• Reasonable fit at lower temperatures

[Marasteanu,

-42-

Today’s Program


-43-

Time-Temperature Superposition

Observation of experimental data shows that changing temperature shifts the modulus versus time or frequency curve along time or frequency axis but does not change shape of the curve• Andrews and Tobolsky 1950

Such materials are called thermo-rheologically simple

Shifting along the time axis is called time-temperature superposition

Log

Mod

ulus

Log Frequency

T1<T2<T3

-44-

Time-temperature superposition

A material is thermo-rheologically simple if the principles of time-temperature superposition apply

Do not confuse with linear visco-elastic behavior Neat asphalt binders can generally be considered as

“thermo-rheologically simple linear visco-elastic liquids”

Of course if we add lots of polymer and fillers we end up with materials which are outside this definition

-45-

Time-Temperature Superposition –Why do we need it?

To obtain a test result at some condition where it would be difficult to conduct a test• Shift measurement to a temperature or time

where it would be difficult to test• e.g.. BBR where measurement is at Tdes + 10ºC at

60s rather than 2 hr• Low temperature specification based on 2-hr

Stiffness at low pavement temperature• S after 60 s at T + 10ºC approximates S after 2 hr

at T To develop a better understanding of material

behavior To generate mastercurves

-46-

Steps in MC construction

Perform frequency sweep at different temps Slide frequency sweeps along time axis to produce single

curve• This gives us the mastercurve

Determine relationship between amount of slide (shift factor) and temperature as a function of temperature• This gives us our shift function

Onerous task and poorly repeated when done manually• Done painlessly and very accurately in computer

software

-47-

MC Construction – Software Generated

Shift factor

Shift factor

-48-

Modeling the Shift Factor

WLF equation• Log a(T) = -C1(T-TR)/C2+T-TR)

Arrhenius equation• Log a(T) = a1(1/T – 1/TR)

Polynomial representation• Log a(T) = a + bT + cT2 + dT3

-49-

T-TS: Applicable to Other Measurements?

Applicable to moduli obtained in tension, compression or shear? • Yes – Use to generate mastercurves

Applicable to strength properties where strength is measured at different loading rates and temperatures? • Yes – Use to generate mastercurves

Applicable tom fatigue parameters? • Likely – Under consideration in mixture studies

-50-

Today’s program


-51-

Measurement Interconversions

Can convert dynamic data to time based data and vice-versa

Useful since experimentation can be targeted to give best possible measurements – avoiding problems with compliance etc.

Detailed numerical consideration is needed

-52-

Simple conversions

Poisson’s ratio, μ commonly taken as 0.50 for asphalt binders

• This corresponds to an incompressible liquid

• If μ is 0.5 we have:

D(t) = J(t)/3 E(t) = 3G(t) If we consider mixes the Poisson’s ratio will can

be taken function of E*

-53-

Conversion options

Approximations Via relaxation/retardation spectra

-54-

Conversion typically needed

G* to E(t) S(t) to G*

-55-

Approximate relationships

Dynamic to time - Ninomiya-Ferry Time to dynamic - Yagii-Makawa

These can be done in a spreadsheet with ease so are quite useful for a basic understanding

-56-

Ninomiya-Ferry

Approximation works for converting data collected in the frequency domain to time domain

)10("014.0)40.0("40.0)(')( ωωω GGGtG +−=

)10("014.0)40.0("40.0)(')( ωωω GJJtJ +−=

t1=ω

-57-

Yagii-Makawa

The approximation is used from converting time data to that in the frequency domain.

)}]398.0()25.0({159.0)}50.2()59.1({08.1)([)(' tGtGtGtGtGG −+−+=ω

)}]159.0()100.0({794.0)}()631.0({70.2[)(" tGtGtGtGG −+−=ω

)}]398.0.0()25.0({159.0)}50.2()59.1({08.1)([)(' tJtGtJtJtJJ −+−+=− ω)}]159.0()100.0({794.0)}()631.0({70.2[)(" tJtJtJtJJ −+−=− ω

t1=ω

-58-

From discrete spectra/Prony series

By fitting a discrete spectra to the data interrelationships may be determined directly

Consider spring dashpot analogy

-59-

Simple springs and dashpots

OK – lets get some equations for these

-60-

Simple visco-elastic model

Maxwell Element

ConsiderSpring constant, stiffness, gRelaxation time, viscosity/stiffness, λ= η/g

λ/)( tgetG −=

22

22

1)('

λωλωω

+= gG

221)("

λωωλω

+= gG

STATIC LOAD

DYNAMIC LOADViscosity -η

Elastic - g

-61-

Simple visco-elastic model (1)

Generalized Maxwell Model

ConsiderSpring constant, stiffness, giRelaxation time, viscosity/stiffness, λi= ηi/gi

…

i=1 to nit

n

iiegtG λ/

1)( −

=∑=

22

22

1 1)('

i

in

iigG

λωλωω

+= ∑

=

221 1

)("i

in

iigG

λωωλω

+= ∑

=

EQUATIONS FOR VISCO-ELASTIC LIQUID

-62-

Simple visco-elastic model (1)

Generalized Maxwell Model

ConsiderSpring constant, stiffness, giRelaxation time, viscosity/stiffness, λi= ηi/gi

…

i=1 to n

221 1

)("i

in

iigG

λωωλω

+= ∑

=

EQUATIONS FOR VISCO-ELASTIC SOLID

itn

iie eggtG λ/

1)( −

=∑+=

ge22

22

1 1)('

i

in

iie ggG

λωλωω

++= ∑

=

-63-

Relaxation/retardation spectra

Can do same thing for Voigt element (also called Kelvin) in series Voigt Element

-64-

Spectra (discrete)

n

n

Relaxation Spectra Model

Retardation Spectra ModelAlso called

Prony series

-65-

Binder conversions

Why?

BBR data useful to define cold region of master curve

DTT can also be used in same region

-66-

Binder - example

DSR

BBR

-67-

Range of measurement

Generally DSR cannot get to the same high stiffness that BBR can

Crude ranges• BBR – 10 to 1000 MPa• DSR <10 MPa• Typically can measure with both instruments

10 to 1,000,000,000 Pa – or – 0.00001 to 1,000 MPa

-68-

Mix conversions

Why?

Can combine SST and IDT to make mix mastercurve

Can combine IDT and E* (MEPDG) to make mastercurve

-69-

Mix - example

Example data set –IDT data combined with SST data

IDT converted to shear format

SST

IDT

-70-

Mix – notes on conversion

Need to make assumption on Poisson’s ratio if going from G to E – or E to G

-71-

Conversion of BBR data

• BBR is time based data• S(t) or 1/D(t) – not E(t)• Note E(t) ≠ 1/D(t)• Typically between

10MPa and 1,000 MPa

-72-

BBR S(t) to G’G” conversion (1 of 3)

Fit the BBR data is fitted with the CA, CAS and CAM model and determine the fit with the lowest error. This master-curve is adopted.• If material is a filled product then fit will most likely be

CAS – enables higher glassy modulus• For most neat binders fit most likely will be CAM

Hopkins and Hamming method is used to convert the master curve to the relaxation modulus E(t).

-73-


Fit the E(t) data with a CAM model using the Glassy modulus determined from the previous fitting. This gives a function which describes a E(t) fit and essentially allows for a different glassy modulus if considered necessary from the earlier step.

Calculate the discrete spectra for the E(t) fitted function.

The reciprocal of the observed times are the substituted into the function to estimate the E', E" data points.

-74-


The data points are shifted using the original shift values obtained along with a reverse density correction (Rouse) to obtain dynamic isotherms corresponding to the original data.

Extensional data is then obtained by converting to G with a Poisson's ratio of 0.5. This basically assumes no volume change which is reasonable for a liquid binder.

-75-

BBR S(t) to G’G” conversion - result

Process is implemented in software since it is quite numerically intensive

RESULT Can now merge this

with other dynamic data

-76-

Binder - result

DSR

BBR

-77-

IDT D(t) to G’G” or E’E” conversion

Process is similar to BBR conversion

Model fit is power law curve instead of CA, CAM or CAS

-78-

IDT D(t) to G’G” or E’E” conversion

Result

-79-

Today’s program


-80-

Objective of models

Binder models help us to estimate field conditions• E.g. Binder purchase spec.

Binder models help us to define mix models and perform calculations of stress and strain in pavement structures

-81-

Model – spectra or continuous

Remember – spectra has problems if you go outside the data range.

-82-

Temperature or frequency

In this window we can interpolate with good accuracy!In this window we can interpolate with good accuracy!

-83-

Binder specification

Low temperature• Table 2 of M320 shows that thermal stress can

be estimated from BBR data• Table 1 uses the S and m value to arrive at

similar specification valuesm describes the ability of the binder to relax

stresses High temperature – Jnr

• Jnr is effectively related to the isolated dash-pot when testing at a high level of stress

-84-

Low Temperature

Use of thermal stress prediction from BBR Combined with strength from DTT Implemented in MP1a – initial Now Table 2 of M320 PP42 contains method for calculation

-85-

Prediction of Tcr

Temperature

Ther

mal

Stre

ss/S

treng

th

Strength

Stress

TCritical

Single Event Thermal Cracking

-86-

High temperature

-87-

New High Temp Criteria Jnr

D’Angelo, AAPT v. 76, 2007

0

5

10

15

20

25

30

0 20 40 60 80 100Time s

Nor

mal

ized

Stra

in %

?u = Avg. un-recovered strain

Jnr = ?u / ?

? = stress applied during creep

Jnr = non-recoverable compliance

0

5

10

15

20

25

30

0 20 40 60 80 100Time s

Nor

mal

ized

Stra

in %

γu = Avg. un-recovered strain

Jnr = γu / τ

τ = stress applied during creep


0

5

10

15

20

25

30

0 20 40 60 80 100Time s

Nor

mal

ized

Stra

in %

?u = Avg. un-recovered strain

Jnr = ?u / ?

? = stress applied during creep


0

5

10

15

20

25

30

0 20 40 60 80 100Time s

Nor

mal

ized

Stra

in %

γu = Avg. un-recovered strain

Jnr = γu / τ

τ = stress applied during creep


-88-

Jnr

Need to consider tests in non-linear region Linear work on master curves as discussed earlier

will not work with defining Jnr Jnr could be considered to be related to an

isolated dashpot considered by fitting a model to the test performed at a high stress level

-89-

New High Temperature Spec

PG 64 (Standard, Heavy, Very heavy) based on traffic

• PG 64S-XX Jnr > 0.4• PG 64H-XX Jnr > 0.2• PG 64V-XX Jnr > 0.1

-90-

Mix models

-91-

Methods for mixture stiffness prediction

Brown (1978) The Asphalt Institute (1969, 1978) Francken and Verstaeten, 1974 Bonnaure et al. (1977) Hirsch (2002) Witczak, AASHTO (developed 1970’s to now)

-92-

Models for mixes

Two models commonly used in past few years as we head towards the Mechanistic-Empirical Pavement Design Guide (MEPDG)

These are the Witczak and Hirsch models

-93-

Hirsh model

Christensen, Pellinen and Bonaquist, AAPT 2003

where:E* = complex dynamic modulus,VMA = voids in mineral aggregate, %VFA = voids filled with asphalt, %G*b =binder complex shear stiffness modulus

( )

1

*3000,200,4100

11

000,10*3

1001000,200,4*

−

××+

−++

×+

−=

bb GVFA

VMAVMA

PcVMAVFAGVMAPcE

58.0

58.0

*3650

*320

×

+

×

+=

VMAGVFA

VMAGVFA

Pcb

b

-94-

Witczak Predictive Model for EAC

)log(393532.0)log(313351.0603313.0(1

)34(00547.02)38(000017.0)38(003958.0)4(0021.0871977.3

)(802208.0)(058097.0)4(002841.02)200(001767.0)200(029232.0249937.1||log *

η×−×−−+

+−+−+

+−−−−+−=

fe

pppp

aVbeffVbeffV

aVpppE

E* = dynamic modulus, 105 psi

η = bitumen viscosity, 106 Poise

f = loading frequency, Hz

Va = air void content, %

Vbeff = effective bitumen content, % by volume

p34 = cumulative % retained on 19 mm sieve

p38 = cumulative % retained on 9.5 mm sieve

p4 = cumulative % retained on 4.76 mm sieve

p200 = % passing 0.075 mm sieve Has been modified

-95-

New- Witczak Predictive Model for EAC

More data included in regression analysis !

-96-

Mix vs. binder master curve

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07

Frequency, Hz

Mix

and

Bin

der S

tiffn

ess,

MPa

Binder

Mix

Remember we are trying to get mix properties from binder properties.- Hirsch uses G*

b- Witczak uses viscosity

Increase in stiffness due to aggregate volumetrics

-97-

Mix models

Both these models rely upon a good estimation of binder properties

Witczak model uses a method of estimating the viscosity from the binder stiffness

Both models can be used for estimating the mix stiffness over a wide range of temperatures and frequencies• How are these then used?

-98-

Example – Variation of E* over year for typical day in month at various depths

0

5,000

10,000

15,000

20,000

25,000

30,000

0 24 48 72 96 120 144 168 192 216 240 264 288

Time Interval (24 hr x month Jan to Dec = 288)

E*, M

Pa

PG76-22 SMA, Depth = 20mm

PG76-22 Superpave-19, Depth = 45mm

PG70-22 Superpave-25, Depth = 120mm

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

-99-

Mix model – low temperature

Mixture model is used in similar way to binder specification for calculation of low temperature cracking of a mixture

Mixture calculations should always be more reliable• Note – binder tests regarded as purchase spec

not necessarily as a performance related measure!

-100-

Today’s program


-101-

Rheology of binders and performance

Models• Models not new in asphalt or mix testing• Two basic types of models – continuous and

discrete – each has own advantageous and disadvantageous

• Continuous better when considering a wide range but limited in applicability – we need some underlying functional form

• Discrete has problems when we need to extrapolate

-102-


Temperature dependency • We can consider properties as a function of

temperature and loading time via the use of shift functions

-103-


Interconversions• Use of BBR and IDT to assist with master

curve definition – can make better use of test data collected in different stiffness ranges

• Enables checks on reasonableness of data• Enables master curve to be developed that

covers full range of stiffnesses – a good definition of either binder or mixture rheology

-104-


Models – what do they tell us• Enable estimation of stresses for binder spec,

e.g. Tcr, S and m parameters• Enable understanding of alternate specs, e.g.

Jnr • Enable binder properties to be better related

to mixture properties

-105-

Thank you for listening

Feel free to call or e-mail either of us if you have any post-Webinar questions

Dave Anderson

814-883-1901

[email protected]

Geoff Rowe

(215) 258-3640

[email protected]



Selected References1. H.A. Barnes, J.F. Hutton, K. Walters, An Introduction to Rheology, Elsevier,

ISBN-13: 978-0-444-87140-4 [Elementary introduction]2. J. D. Ferry, Viscoelastic Properties of Polymers, John Wiley, ISBN 0-471-

04894-1 [Classic textbook, comprehensive treatment of viscoelasticity]3. Ch. W. Macosko, Rheology : Principles, Measurements and Applications,

John Wiley, ISBN-13: 9780471185758 [Comprehensive textbook]4. Y. Kim, Modeling Of Asphalt Concrete, McGraw-Hill Construction, ISBN 978-

0-07-146462-8 [Two chapters on asphalt rheology with extensive references]

5. D. A. Anderson et al., Binder Characterization and Evaluation Volume 3: Physical Characterization, SHRP-A-369, ISBN 0-309-05767-1 (http://pubsindex.trb.org/view.aspx?id=404931) [Development of rheological characterization of asphalt binders during SHRP]

http://pubsindex.trb.org/view.aspx?id=404931�

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