Rheology of Asphalt Binders and Implications for Performance

Transcription

1 Rheology of Asphalt Binders and Implications for Performance November 10, 2009 Dr. David Anderson Consultant and Professor Emeritus Penn State University Dr. Geoffrey Rowe President Abatech Inc. (Consultants) 1

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 -2-

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 -3-

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 -4-

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 -5-

6 Let s Get Started! -6-

7 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 -7-

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 -8-

9 Summary: Test measurements and moduli Oscillatory Creep Relaxation Complex modulus: Shear, G*(ω) = τ(ω)/γ(ω) Compression/Tension, E*(ω) = σ(ω)/ε(ω) Compliance (Modulus): Shear, J(t) = γ(t)/τ [Stiffness, S(t) = 1/J(t)] Tension/Compression, D(t) = ε(t)/σ Relaxation Modulus: Shear, G(t) = γ(t)/τ Tension/Compression, E(t) = σ(t)/ε -9-

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! -10-

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 -11-

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! -12-

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 -13-

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! -14-

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. -15-

16 Idealized Viscoelastic Response Dynamic Creep Log Modulus, G* G η* = G*/ω Log Modulus, J η = J(t)/t J o Log Frequency Log Time -16-

17 Asymptotes Asphalt Binders 1. Glassy plateau, common value for all binders G g = 1/J o 2. Location of viscous asymptote is specific to binder On the 1:1 asymptote (log-log plot) η 0 = t/j(t), η* = G*(ω)/(ω), and η 0 = η* ` Shape of curve in the transition between two asymptotes is binder specific In this region compliance is not inverse of modulus G *( ω) 1/ J ( t) Need technique for interconverting modulus and compliance in transition region -17-

18 Models for Binders Historical van der Poel nomograph (Journal Appl. Chem., vol ) 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 -18-

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 -19-

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 logω r = logg r 1 log(1 G b b r 20.5 G ) b r Impractical because gives frequency as function of modulus instead of modulus as function of frequency -20-

21 Dickinson and Witt s Model Represented mastercurve as a hyperbola log G * r [( ) ( ) ] 2 2 logω 2β { 0.5} logω + = 0.5 r r * r * ( ω ) = G ( ω) Gg G / ω = ωη a ( T ) / G r o Coefficients are obtained by iteration Not user friendly g [Dickinson and Witt, Trans. Soc. Rheology, vol. 18, 1974] -21-

22 CA Model Christensen-Anderson CA model (1993) Three parameter model to describe G*(ω) Glassy modulus, G g Location parameter, ω c Shape parameter, R Parameters have intuitive meaning Model may be extended to phase angle and creep compliance -22-

23 Discrete Models Discrete models (e.g. Prony Series) Springs and dashpots in parallel or series ηt Spring and dashpot coefficients (E i and η i ) 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 E g -23-

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 -24-

25 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 -25-

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 -26-

27 Jongepier and Kuilmann Model Relaxation spectra assumed log normal in shape: H ( τ ) = β G g lnτ / τ exp π β 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 -27- m 2

28 -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] 1 exp 1 exp ) ( + = m b a x b a x b m x F + = b a x x P exp 1 1 ) (

29 CA Model for G*(ω) Substituting rheological parameters: G *( ω) = G*(ω) = Measured complex modulus G g R ω ω c G g 1 + = Glassy modulus = Rhelogical Index (shape factor) = Test frequency ω ωc (log 2 / R) R / log 2 = Crossover frequency (location parameter) -29-

30 CA Model for δ(ω) Rewriting and substituting rheological parameters: δ ( ω) = 90 / 1 + ω ωc (log 2) / R δ(ω) = Measured phase angle -30-

31 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 -31-

32 CA Model G g and η 0 are asymptotes as discussed previously G g = 10 9 Pa all binders η 0 represents 1:1 slope ω c locates the curve on the time R, Rheological Index, defines shape of curve Related to relaxation spectra -32-

33 Parameter Changes With Lab Aging 1.E+09 Complex Modulus, G* ( Pa) 1.E+08 1.E+07 1.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 Note: With aging, R increases making curve flatter while ω c shifts curve to left Original: R = 1.16 ωc = 1932 RTFOT: R = 1.27 ωc = 824 PAV: R = 1.35 ωc = E+00 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) -33-

34 R for Different Binders and Aging Conditions [Source: SHRP-A-669] -34-

35 Mastercurve Shape Related to PI [Source: SHRP-A-669] -35-

36 Field Aging [Source: SHRP-A-369] -36-

37 Shortcut Determination of η 0 Extrapolation to determine η 0 [Source: SHRP-A-369] -37-

38 Shortcut Determination of R [Source: SHRP-A-369] -38-

39 Shortcut Determination of ω c [Source: SHRP-A-369] -39-

40 How Do Parameters Affect Mastercurve? Complex Modulus, G* ( Pa) 1.E+09 1.E+08 1.E+07 1.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 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 Above: R held constant, as ω c decreases the curve shifts to left but retains its shape 1.E+04 1.E+05 R = 2 ωc = 1000 R = 2 ωc = 100 R = 2 ωc = 10 1.E+09 1.E+08 1.E+07 1.E+06 Frequency, ω ( rad/s) 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 1.E+06 Complex Modulus, G* ( Pa) 1.E+07 1.E+08 1.E+09 1.E-05 1.E+10 1.E-04 1.E+11 1.E-03 1.E+12 1.E-02 1.E-01 Below: Cross-over frequency ω c (ω where G = G ) is held constant, as R increases the curve flattens 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 Frequency, ω ( rad/s) R = 1 ωc = 100 R = 2 ωc = 100 R = 3 ωc = E+07 1.E+08 1.E+09 1.E+10 1.E E+12

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, -41-

42 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 -42-

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 timetemperature superposition Log Modulus T 1 <T 2 <T 3 Log Frequency -43-

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 -44-

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 T des + 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 -45-

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 -46-

47 MC Construction Software Generated Shift factor Shift factor -47-

48 Modeling the Shift Factor WLF equation Log a(t) = -C 1 (T-T R )/C 2 +T-T R ) Arrhenius equation Log a(t) = a 1 (1/T 1/T R ) Polynomial representation Log a(t) = a + bt + ct 2 + dt 3-48-

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 -49-

50 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 -50-

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 -51-

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* -52-

53 Conversion options Approximations Via relaxation/retardation spectra -53-

54 Conversion typically needed G* to E(t) S(t) to G* -54-

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 -55-

56 Ninomiya-Ferry Approximation works for converting data collected in the frequency domain to time domain G ( t) = G'( ω) 0.40G"(0.40ω) G"(10ω) J ( t) = J '( ω) 0.40J"(0.40ω) G"(10ω) ω = 1 t -56-

57 Yagii-Makawa The approximation is used from converting time data to that in the frequency domain. G' ( ω) = [ G( t) { G(1.59t) G(2.50t)} { G(0.25t) G(0.398t)}] G" ( ω) = [2.70{ G(0.631t ) G( t)} { G(0.100t) G(0.159t)}] J '( ω) = [ J ( t) { J (1.59t) J (2.50t)} { G(0.25t) J ( t)}] J" ( ω) = [2.70{ J (0.631t ) J ( t)} { J (0.100t) J (0.159t)}] ω = 1 t -57-

58 From discrete spectra/prony series By fitting a discrete spectra to the data interrelationships may be determined directly Consider spring dashpot analogy -58-

59 Simple springs and dashpots OK lets get some equations for these -59-

60 Simple visco-elastic model Elastic - g Maxwell Element Viscosity -η Consider Spring constant, stiffness, g Relaxation time, viscosity/stiffness, λ= η/g STATIC LOAD G( t) = ge t DYNAMIC LOAD ω G'( ω) = g 1+ ω G"( ω) / λ 2 2 λ 2 2 λ ωλ = g 1+ ω 2 2 λ -60-

61 Simple visco-elastic model (1) Generalized Maxwell Model i=1 to n Consider Spring constant, stiffness, g i Relaxation time, viscosity/stiffness, λ i = η i /g i G( t) n = i= 1 G'( ω) = G"( ω) = g i e n g i i= 1 1 n g i i= 1 1 t / λ i 2 ω λ + ω ωλ + ω 2 i 2 2 λi i 2 λ 2 i EQUATIONS FOR VISCO-ELASTIC LIQUID -61-

62 Simple visco-elastic model (1) Generalized Maxwell Model G( t) = i=1 to n g e n + g e n 2 2 ω λi G' ( ω) g e + g i 2 = i= 1 g i i= 1 1 e t / λ 2 + ω λ i i Consider Spring constant, stiffness, g i Relaxation time, viscosity/stiffness, λ i = η i /g i G"( ω) = n g i i= 1 1 ωλ + ω i 2 EQUATIONS FOR VISCO-ELASTIC SOLID λ 2 i -62-

63 Relaxation/retardation spectra Can do same thing for Voigt element (also called Kelvin) in series Voigt Element -63-

64 Spectra (discrete) n Relaxation Spectra Model n Retardation Spectra Model Also called Prony series -64-

65 Binder conversions Why? BBR data useful to define cold region of master curve DTT can also be used in same region -65-

66 Binder - example BBR DSR -66-

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 to 1,000 MPa -67-

68 Mix conversions Why? Can combine SST and IDT to make mix mastercurve Can combine IDT and E* (MEPDG) to make mastercurve -68-

69 Mix - example Example data set IDT data combined with SST data IDT converted to shear format SST IDT -69-

70 Mix notes on conversion Need to make assumption on Poisson s ratio if going from G to E or E to G -70-

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 -71-

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). -72-

73 BBR S(t) to G G conversion (2 of 3) 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. -73-

74 BBR S(t) to G G conversion (3 of 3) 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. -74-

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 -75-

76 Binder - result BBR DSR -76-

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 -77-

78 IDT D(t) to G G or E E conversion Result -78-

79 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 -79-

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 -80-

81 Model spectra or continuous Remember spectra has problems if you go outside the data range. -81-

82 Temperature or frequency In this window we can interpolate with good accuracy! -82-

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 values m describes the ability of the binder to relax stresses High temperature Jnr Jnr is effectively related to the isolated dashpot when testing at a high level of stress -83-

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 -84-

85 Prediction of T cr Single Event Thermal Cracking Thermal Stress/Strength Strength Stress T Critical Temperature -85-

86 High temperature -86-

87 New High Temp Criteria Jnr Normalized Strain % J nr =? γ u /? τ? τ = stress applied during creep J nr = non-recoverable compliance? γ u = Avg. un-recovered strain Time s D Angelo, AAPT v. 76,

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 -88-

89 New High Temperature Spec PG 64 (Standard, Heavy, Very heavy) based on traffic PG 64S-XX J nr > 0.4 PG 64H-XX J nr > 0.2 PG 64V-XX J nr >

90 Mix models -90-

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) -91-

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 -92-

93 Hirsh model Christensen, Pellinen and Bonaquist, AAPT 2003 VMA 1 VMA VFA VMA * 4,200, * ( 1 ) 100 VMA E = Pc + G b + + Pc ,000 4,200,000 3 VFA G * b 1 where: E* = complex dynamic modulus, VMA = voids in mineral aggregate, % VFA = voids filled with asphalt, % G* b =binder complex shear stiffness modulus Pc = VFA 3G * 20 + VMA VFA 3G * VMA b b

94 Witczak Predictive Model for E AC log E * = ( p ) ( p ( V beff ( p ) ( V ) 4 a V + V beff a ( p ) ( p ) ( p ) ( p ) ( log( f ) log( η) 1+ e E* = dynamic modulus, 10 5 psi η = bitumen viscosity, 10 6 Poise f = loading frequency, Hz V a = air void content, % V beff = effective bitumen content, % by volume p 34 = cumulative % retained on 19 mm sieve p 38 = cumulative % retained on 9.5 mm sieve p 4 = cumulative % retained on 4.76 mm sieve p 200 = % passing mm sieve 2 ) Has been modified ) -94-

95 New- Witczak Predictive Model for E AC More data included in regression analysis! -95-

96 Mix vs. binder master curve 1.0E E+04 Mix Mix and Binder Stiffness, MPa 1.0E E E E E E-02 Increase in stiffness due to aggregate volumetrics Binder Remember we are trying to get mix properties from binder properties. - Hirsch uses G * b - Witczak uses viscosity 1.0E E E E E E E E E E E E E+07 Frequency, Hz -96-

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? -97-

98 Example Variation of E* over year for typical day in month at various depths 30,000 25,000 PG76-22 SMA, Depth = 20mm PG76-22 Superpave-19, Depth = 45mm PG70-22 Superpave-25, Depth = 120mm E*, MPa 20,000 15,000 10,000 5,000 0 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Time Interval (24 hr x month Jan to Dec = 288) -98-

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! -99-

100 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 -100-

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 -101-

102 Rheology of binders and performance Temperature dependency We can consider properties as a function of temperature and loading time via the use of shift functions -102-

103 Rheology of binders and performance 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 -103-

104 Rheology of binders and performance 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 -104-

105 Thank you for listening Feel free to call or either of us if you have any post-webinar questions Dave Anderson Geoff Rowe (215)

106 Selected References 1. H.A. Barnes, J.F. Hutton, K. Walters, An Introduction to Rheology, Elsevier, ISBN-13: [Elementary introduction] 2. J. D. Ferry, Viscoelastic Properties of Polymers, John Wiley, ISBN [Classic textbook, comprehensive treatment of viscoelasticity] 3. Ch. W. Macosko, Rheology : Principles, Measurements and Applications, John Wiley, ISBN-13: [Comprehensive textbook] 4. Y. Kim, Modeling Of Asphalt Concrete, McGraw-Hill Construction, ISBN [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 ( [Development of rheological characterization of asphalt binders during SHRP]