A comprehensive model for predicting thermal cracking events in asphalt pavements

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International Journal of Pavement Engineering

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A comprehensive model for predicting thermal cracking events in asphalt pavements

MohammadZia Alavi, Elie Y Hajj & Peter E Sebaaly

To cite this article: MohammadZia Alavi, Elie Y Hajj & Peter E Sebaaly (2015): A comprehensive model for predicting thermal cracking events in asphalt pavements, International Journal of Pavement Engineering, DOI: 10.1080/10298436.2015.1066010

To link to this article: http://dx.doi.org/10.1080/10298436.2015.1066010 Published online: 27 Jul 2015.

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A comprehensive model for predicting thermal cracking events in asphalt pavements

MohammadZia Alavi, Elie Y Hajj^§ and Peter E Sebaaly

Civil and environmental engineering Department, university of nevada, reno, nv, uSa

ABSTRACT

A compressive model for predicting thermal cracking events in asphalt pavements that accounts for the continuous evolution of the asphalt mixture properties with oxidative ageing over time has been developed. The model also considers temperature-dependent coefficient of thermal contraction (CTC) for the calculation of thermal strain in the asphalt layer. An improved pavement temperature profile estimate has been employed in the model to predict the required hourly pavement temperature data. The temperature data at the desired depth in the asphalt layer are then used in a kinetic-based ageing model to predict growth in the carbonyl (CA) of the asphalt binder over time. Using a refined one-dimensional constitutive linear viscoelastic relationship, the hourly thermal stress is then computed considering the changes in the viscoelastic and thermal contraction properties of the asphalt mixture with the increase in CA of asphalt binder used in the mix. The required age-dependent relaxation modulus is obtained from the dynamic modulus (E^*) of asphalt mixtures (i.e. in complex domain) at various ageing levels. Also, the required age and temperature-dependent CTC is obtained from thermal strain measurements of varied aged asphalt mixtures using the uniaxial thermal stress and strain test (UTSST). The cracking events are detected over the service life by comparing the predicted thermal stress with the age-dependent crack initiation stress (CIS) of the asphalt mixture. The age-dependent CIS is obtained from the UTSST results for different ageing periods. Preliminary analysis of the model revealed the accuracy of the model in a realistic prediction of the accumulative thermal cracking events for the asphalt pavement with different air void levels (4, 7 and 11%) and with unmodified (PG64-22) and polymer-modified (PG64-28) asphalt binders in a selected location.

KEYWORDS

thermal cracking; oxidative ageing; carbonyl; relaxation modulus; thermal contraction; crack initiation stress

ARTICLE HISTORY received 10 may 2015 accepted 23 may 2015

CONTACT elie Y Hajj [email protected]

§Current affiliation: Pavement Research Center, Civil and Environmental Engineering Department, University of California, Davis, 2001 Ghausi Hall, 1 shields Ave, Davis, California, USA, 95616.

Introduction

Low temperature or thermal cracking is associated with the volumetric change in asphalt concrete layer when the pavement temperature drops. Since the asphalt concrete layer is continuous, thermal transverse cracks will then be developed due to the excessive induced thermal strains and stresses within the asphalt concrete layer. The development of stresses is generally greater at the surface where the pavement experience the lowest overall temperature and/or the highest temperature fluctuation (Jung and Vinson 1994). With the decrease in temperature, the magnitude of the induced tensile stress increases up to a point where it reaches the damage or cracking limit (e.g. tensile strength) of the asphalt mixture. For extremely cold temperatures or very fast cooling rates, thermal cracks may propagate through the full depth of the asphalt concrete layer after one or few cooling cycles; this is generally referred to as a single-event low-temperature cracking. For milder temperatures or slower cooling rates, cracks advance at a slower rate by accumulation of damage, and hence, the full depth crack only occurs after several thermal cycles; this mechanism is usually referred to as a thermal fatigue cracking.

The resistance of asphalt pavements to thermal cracking is generally influenced by the pavement structure or geometry,

environmental conditions and asphalt mixture properties (Jung and Vinson 1994). The most important pavement structural factor is the thickness of the asphalt concrete layer, which influ- ences the rate of crack propagation. The environmental factors include pavement temperature and rate of cooling. The rate- and temperature-dependent stiffness, contraction and strength properties of the asphalt mixture influence the resistance of the pavement to thermal cracking. These asphalt mixture properties are highly dependent on the asphalt binder type and amount, the aggregate source and gradation, and the mixture volumetrics (i.e. air voids, film thickness, etc.). Furthermore, the mixture properties can significantly change over time due to asphalt binder ageing. With time, the asphalt binder within the mixture becomes hard and brittle as a result of forma- tion of high polar compounds (i.e. carbonyl functional groups, associated with oxidation reaction) Oxidative ageing can significantly influence stiffness, contraction and strength properties of asphalt mixtures so that the occurrence of thermal cracking generally becomes more prevalent with the age of pavement.

The rate of asphalt binder ageing in the mixture (i.e. increased carbonyl) has been observed to be dependent on the asphalt binder composition and some significant mixture characteristics (Morian et al. 2013).

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(3) Assuming a constant value for the asphalt mixture CTC with respect to temperature contradicts the real behaviour of the asphalt material.

(4) Relaxation modulus of the asphalt mixture does not necessary need to be determined from the creep compliance measurements.

(5) Significant errors in the prediction of pavement temperature profiles with the EICM model could be resulted.

Objective

The overall objective of this study was the development of a comprehensive model for the prediction of thermal cracking events in asphalt concrete pavements. Based on the phenom- enological understanding of the thermal cracking mechanism, the new model aims to remedy some of the limitations in the currently available models by considering some of the critical thermal cracking influential factors. It should be noted that the model is not intended to predict the amount (or frequency) of thermal cracking, but it can be used to predict accumulated thermal cracking events over the analysis period. The outcomes of the model can assist in selecting the appropriate material properties for the mitigation of thermal cracking.

Methodology

Figure 1 illustrates the flowchart of the proposed comprehensive thermal cracking model. The model includes four main steps: (1) pavement temperature profile prediction, (2) oxidative ageing prediction, (3) thermal stress calculation and (4) thermal cracking event prediction. These components are further described in the following sub-sections:

Pavement temperature profile prediction

Accurate pavement temperatures data at various depths of the asphalt concrete surface layer and over time are required to estimate the oxidation level of the asphalt binder and to calculate thermally induced stresses within the asphalt concrete surface layer. An improved model has been developed and employed to predict pavement temperatures at various depths of pavement (up to 3 metres below the surface) and over time. The development of the proposed model was mainly benefited from the efforts being conducted at Texas A&M University (Han et al.

2011) and Arizona State University (Gui et al. 2007). The proposed model requires hourly air temperature, solar radiation, wind speed and thermal diffusivity properties of the pavement layer materials (i.e. conductivity, density and heat capacity), as well as monthly variable pavement surface radiation properties (i.e. albedo, emissivity and absorption coefficients) to perform the calculation. In this particular study, the hourly air temperature and wind speed data were obtained from the EICM database while the synchronised solar radiation data were gathered from the national solar radiation database (NSRD). Numerical calculations of the proposed heat transfer model are completed using the finite control volume method (FCVM) in a fully implicit scheme. The improved time-dependent surface boundary condition accounts for a variation in the surface radiation properties, allowing for a better simulation of heat transfer mechanism in the pavement and thus more realistic predictions of pavement temperatures. The discontinuity in the thermal Over the years, several models have been developed to

analyse the thermal cracking performance of asphalt pavements and to assist in the selection of appropriate materials for mitigation of cracking occurrence over the pavement in-service life. These models have been continuously advanced towards mechanistic-empirical (ME) approaches.

TCMODEL is the most widely used ME-based thermal cracking model that is originally developed during the Strategic Highway Research Program (SHRP) by Hiltunen and Roque (1994). The model has been advanced in the National Coopera- tive Highway Research Program (NCHRP) 1-37A (Hallin 2004) and incorporated into the AASHTO ME design guide; currently employed in AASHTOW are Pavement ME design tool. This model calculates thermal stresses in the asphalt concrete layer based on the one-dimensional constitutive viscoelastic model (i.e. Boltzmann equation), using asphalt mixture relaxation modulus and thermal strain rate. Thermal strain is estimated using an estimated constant value for the asphalt mixture coefficient of thermal coefficient (CTC) and predicted hourly pavement temperatures at the selected depth in the asphalt concrete layer. The pavement temperature profile is predicted using the enhanced integrated climate model (EICM). The hourly for- mat calculated thermal stresses are then used to compute crack growth based on the linear elastic fracture mechanics theory (i.e. Paris Law). Consequently, a probabilistic model is used to relate the growth of the representative crack to the amount of cracks over the analysis period. The indirect creep compliance and the indirect tensile strength are the required asphalt mixture properties in the TCMODEL.

Recently, Illi - TC model has been developed, with its associated graphical user interface (GUI), at the University of Illi- nois at Urbana, Champaign Dave et al. (2013), Marasteanu et al. 2012, )The model first estimates probable critical cracking events by comparing the thermal stress at the pavement surface with the 80% of the asphalt mixture indirect tensile strength.

The propagation of cracking during each of the critical events is calculated using the cohesive zone 2-D linear viscoelastic fracture mechanic model, with the aid of a finite element compu- tation engine. Similar to the TCMODEL, a probabilistic model is used to convert computed crack depth of the representative crack to an amount of thermal cracking occurring during the analysis period. The required hourly pavement temperature in Illi-TC model is also obtained from the EICM model. The indirect creep compliance, indirect tensile strength and fracture energy (currently from DCT test) of the asphalt mixture are required to perform the thermal cracking analysis. Moreover, in the current version of Illi-TC model, asphalt mixture CTC is estimated as a constant value with respect to temperature.

While acknowledging the efforts and improvements associated with the existing models, there are limitations recognised that could adversely affect realistic modelling of thermal cracking in asphalt pavements. These limitations may be listed as follows:

(1) Effect of asphalt binder oxidative ageing on the continuous change of asphalt mixture viscoelastic, contraction and strength properties is overlooked.

(2) Evolution of asphalt mixture tensile strength with temperature is neglected.

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diffusivity properties of the various pavement layers can be handled unconditionally with FCVM by assigning specific thermal diffusivity properties to each control volume. The bottom boundary condition in this model is defined independent of the pavement location by assuming a constant heat flux instead of a constant temperature boundary condition (e.g. EICM). Fur- thermore, the numerical solution of the model in implicit time scheme results in a significant reduction in the required time of calculation. The model was validated for different LTPP sections, located in Kingman, Arizona, and Great Fall, Montana.

Details of the model components, calculation approach and validation results are available in a separate literature by Alavi et al. (2014). Currently, efforts are being undertaken at the Uni- versity of Nevada, Reno, to further optimise this model with the development of a stand-alone calculation tool, called as Tem- perature Estimate Model for Pavement Structure (TEMPS).

Oxidative ageing prediction

Oxidative ageing of asphalt binders can be quantified by the increase in carbonyl functional groups (CA). An asphalt mixture becomes harder, brittle and less durable due to the increase in the asphalt binder CA with oxidative ageing. The constant-rate oxidative ageing model developed at Texas A&M University (Han et al. 2013) is employed in the comprehensive thermal cracking model to predict the CA of asphalt binder at any depth of the asphalt concrete layer over the analysis period. The inputs for the ageing model are as follows:

(1) Predicted hourly pavement temperatures at the selected depth in the asphalt concrete layer.

Figure 1. flowchart of the comprehensive model for thermal cracking analysis.

(2) Asphalt binder ageing kinetics (E_a and A)¹ and hardening parameters (HS and m)².

(3) Asphalt binder initial carbonyl at the beginning of constant-rate ageing (CA₀).

(4) Average representative air void radius and effective ageing distance (e.g. asphalt binder film).

In summary, CA values at various layers in the asphalt binder film are predicted by knowing the oxygen partial pressure at these layers and the oxidative ageing kinetics of the asphalt binder. The oxygen partial pressures are estimated from a numerical solution of a partial differential equation with age- dependent diffusivity. The oxygen diffusivity of the binder cor- relates well with the low shear viscosity (LSV) of the binder.

The age-dependent diffusivity is defined by relating the asphalt binder LSV to the hardening susceptibility properties (HS and m) of the binder. Details of the ageing model are out of the scope of this article and can be found in the respective literatures (Han et al. 2013, Alavi 2014).

The ageing model can be simplified if the gradient of oxygen pressure into the asphalt binder film is neglected. In this case, the model only requires pavement temperature profile, asphalt binder kinetic parameters (E_a and A) and CA₀. Numerical com- putation of the ageing model is also performed using FCVM in implicit time scheme. Oxidative ageing kinetics and hardening parameters of the model can be determined through measurements of CA and low shear viscosity (LSV) of the asphalt binder after being aged (mix-ageing or pan-ageing) at various combinations of time and temperature. The CA of the asphalt binder is measured by Fourier Transform Infrared (FT-IR)

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asphalt mixture is expressed by the Prony series Equation (4), which is the mathematical representation of the generalised Maxwell model.

where E_r(𝜉): relaxation modulus at reduced time ξE_i and 𝜆_i: Prony series coefficients (E_i is the relaxation strength (spring constant) and 𝜆_i is the relaxation time for the Maxwell element i); 𝜆_i= ^𝜂ⁱ

E_i

An alternative sound approach has been implemented in this study for determining the asphalt mixture relaxation modulus from the complex modulus (E^∗) test result. For an ideal generalised Maxwell model with infinity numbers of Maxwell arms (i.e.

m is infinity), the relationship between the relaxation strength (E_i) and the relaxation time (𝜆_i) is defined with a continuous relaxation spectrum function. In the proposed approach, the continuous spectrum function is determined through the inverse- Fourier Laplace transformation as expressed in Equation (5).

The complex modulus, E^*, in Equation (5) is defined by the 2S2P1D (2 springs, 2 parabolic elements and one dashpot) model introduced by Olard and Di Benedetto (2003), which is expressed in Equation (6).

where i: complex number defined by i2 = −1, 𝜔, the radian frequency, 2𝜋×f(Hz); E₀ : static (equilibrium) modulus when → 0; E_∞: limit of complex modulus when → ∞; h; k: exponents such as 1 > h > k > 0; 𝛿: dimensionless constant; β: dimensionless constant, β = τ^-1/(E_∞ − E₀); when → 0, then E^∗(i𝜔𝜏) ∼E0+i𝜔𝜂

; η: dashpot coefficient; 𝜏: characteristic time, which varies with temperature.

Substituting the complex modulus (E^*) in Equation (6) into the Equation (5), the continuous spectrum function can be calculated. The effect of oxidative ageing is taken into account by correlating changes in the asphalt mixture relaxation spectrum shape parameters (i.e. 2S2P1D coefficients) to the increase in carbonyl (CA − CA₀) of the recovered asphalt binder. Such regression equations facilitate incorporating the effect of asphalt binder oxidative ageing directly into the constitutive equation to calculate thermal stresses in the asphalt concrete layer over time. During development of this comprehensive model, these correlations have been studied for various asphalt mixtures with different aggregate sources and gradations, asphalt binder types and amount, and mixture volumetrics (i.e. air void).

Consistent correlations were found between the 2S2P1D model coefficients (i.e. spectrum shape parameters) and the increase in carbonyl (CA – CA₀) of the recovered asphalt binders. The relationships between the 2S2P1D coefficients and (CA – CA₀) have been typically found to be represented with the increasing exponential functions for E₀, E_∞ and τ₀ coefficients and with the decreasing exponential functions for the remaining coefficients (4) E(𝜉) =

N+1

∑

i=1

E_ie

−𝜉 𝜆i

(5) H(𝜆) =FLT⁻¹[(

E_∞−E^∗(𝜔)) ,𝜌]

𝜌=1∕𝜆= ±𝜋⁻¹ImE^∗(𝜆⁻¹×e^(±i𝜋))

(6) E^∗(i𝜔𝜏) =E0+ E_∞−E0

1+ (i𝜔𝜏)^−k+ (i𝜔𝜏)^−h+ (i𝜔𝛽𝜏)⁻¹ Spectroscopy, and the LSV is determined from the com-

plex modulus, which is measured using the Dynamic Shear Rheometer (DSR).

Having the predicted value of CA over the analysis period, changes in the asphalt mixture mechanical properties (i.e. viscoelastic, coefficient of thermal contraction and crack initiation properties) can be estimated using regression functions that relates asphalt mixture properties to the increase in carbonyl (i.e. CA − CA₀). Therefore, oxidative ageing can be incorporated into the pavement response model to calculate thermal stresses and subsequently to predict thermal cracking events.

Thermal stress calculation

Calculation of thermal stresses at any depth in the asphalt concrete layer is based on the modelling of the asphalt layer with several one-dimensional viscoelastic rods (beams), similar to the TCMODEL. The thermal stress in each beam is calculated based on the one-dimensional linear viscoelastic constitutive relationship. Modifications have been introduced into the constitutive relationship to account for the ongoing oxidative ageing of asphalt binder and the temperature dependency of CTC.

Equation (1) represents the employed constitutive equation.

where 𝜎(CA,t): thermal stress at time t' and ageing level CA;

E(CA,𝜉(t) − 𝜉( t^�)

): relaxation modulus at reduced time 𝜉(t) − 𝜉(

t^�)

and ageing level CA.

𝜀(CA,t^�): thermal strain at time t and ageing level CA Due to the temperature dependency of CTC, the thermal strain will be numerically calculated from the integral in Equa- tion (2). T₀ is the equilibrium temperature at which stress and strain are zero.

Equation (3) expresses the CTC function. In this equation, CTC_l and CTC_g are the coefficients of thermal contraction corresponding to temperatures warmer and colder than the glass transition temperature ‘T_g’. R is the curvature parameter defining the transition from CTC_l to CTC_g with temperature. The CTC function also changes with ageing level (CA).

Overall, age-dependent relaxation modulus of the asphalt mixture, E(CA, t), and temperature- and age-dependent CTC(CA,T), are the required inputs for the calculation of the thermal stress. Experimental methods for determining the required input of the model are briefly described below.

Relaxation modulus

Typically, to facilitate the numerical solution of the linear viscoelastic constitutive equation, the relaxation modulus of the

(1) 𝜎(CA,t) =∫

t

o

E(CA,𝜉(t) − 𝜉(t^�)

) × 𝜕𝜀(CA,t^�)

𝜕t^� dt^�

(2) 𝜀(

CA,T(t^�))

=

∫T

T₀CTC(CA,T�(t�)) ×dT�

(3) CTC(CA,T(t�)) =CTC_g(CA)

+ (CTC_l(CA) −CTC_g(CA)) ×e (T(t�

)−Tg(CA) R

) (1+e

T(t�)−Tg(CA)

R )

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Numerical calculation of thermal stress

In the proposed comprehensive model, the convolution integral in Equation (1) is solved numerically by modifying the finite difference solution developed by Soules et al. (1987). Equa- tion (8) expresses the numerical solution of the thermal stress.

Thermal stresses are calculated from the pavement temperature profile while considering an hourly increment in asphalt ageing with time. During the hourly incremental ageing, the asphalt mixture properties, including the relaxation modulus and CTC, remain constant with ageing, but change by the hourly pavement temperature.

where Δ𝜀_Th: change in thermal strain over time t− Δt to t Δ𝜉: change of the reduced time over time t− Δt to t E_i and ρ_i: Prony coefficients of asphalt mixture relaxation modulus; m: numbers of Maxwell arms in Prony series of relaxation modulus

It should be noted that based on the comparison of predicted thermal stresses vs. the measured thermal stresses in the restrained UTSST specimens, it was revealed that the thermal stress can be predicted fairly well if an adjustment factor is considered for the obtained relaxation modulus from the dynamic complex modulus. This adjustment factor mainly defines anisotropic nature of the asphalt mixture as well as possible existing variability between the dynamic modulus (E^∗) and UTSST samples. The anisotropic effect is critical since the aggregates orientation in the E^∗ and UTSST specimens are very likely to be different. The E^∗ test specimen is cored from a superpave gyratory-compacted (SGC) mixture along the axis of compaction, whereas, the UTSST specimens are cored from the SGC mixture perpendicular to the compaction direction. Hence, the adjustment factor adapts the relaxation modulus obtained from the E^∗ test to represent the modulus of the material for the UTSST specimen. In the case of an asphalt pavement layer, thermal stresses are also developed within the asphalt layer perpendicular to the direction of field compaction, similar to the UTSST specimen geometry. Based on the several evaluated mixtures during the development of the model, this adjustment factor was found to be in range of 0.4 to 0.7. More related

(8) 𝜎Th(t,CA) =

m

∑

i=1

[

e^−Δ𝜉�𝜌i𝜎Th(t− Δt,CA)

+ Δ𝜀Th(CA)E_i(CA)𝜌i

Δ𝜉(1−e

−Δ𝜉 𝜌i )

] (δ, k and h). The coefficient β was found to be constant for all

evaluated mixtures at varied levels of ageing. No relationship was found between the Williams–Landel–Ferry³ (WLF) shift factor (Williams et al. 1955) parameters with (CA - CA₀). WLF function defines the shift factor which is required to convert the real time (or frequency) at different testing temperatures to the reduced time (or frequency) at the reference temperature based on the time-temperature superposition principal, which is valid for the thermo-rheologically simple materials. More information regarding this proposed approach can be found in the respective literatures (Alavi et al. 2013a and Alavi 2014).

Coefficient of thermal contraction

Asphalt mixture temperature-dependent CTC is obtained from the measured thermal strain using the uniaxial thermal stress and strain test (UTSST) test. In the UTSST, the restrained and unrestrained samples of asphalt mixtures were subjected to cooling at a constant rate (typically10 °C per hour) from an initial temperature (typically 20 °C) to measure the thermally induced stress and strain, respectively. The set-up has been developed during this study with enhancement of the traditional thermal stress restrained specimen test (TSRST), at the Univer- sity of Nevada, Reno. More information regarding the test set- up and the interpretation of the results can be found in the respective literatures by authors (Alavi et al. 2013b, Alavi and Hajj 2014). Figure 2 shows a typical thermal strain vs. temperature curve obtained from the UTSST. The thermal strain measurement under constant cooling rate is fitted to the Equation (7). C is the intercept value with no physical meaning and other terms in this equation were previously defined. The CTC(T) function Equation (3) is consequently determined from the first derivative of the Equation (7) with respect to temperature.

The effect of oxidative ageing on CTC can potentially be considered by correlating changes in CTC_l, CTC_g, R and T_g with the increased CA of the aged asphalt binder. From the results of the several evaluated asphalt mixtures in this study (Alavi 2014 and Morian 2014), the evolution of these parameters with ageing (i.e. carbonyl growth) was found to be mixture specific.

(7) 𝜀_Th=C+CTC_g(

T−T_g) +R(

CTC_l−CTC_g)

×ln(1+e(^T−Tg)

R )

Figure 2. typical thermal strain vs. temperature measurement in utSSt.

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cracking events over the analysis period can provide information regarding the thermal cracking resistant properties of the mixture for using at the specific location. Moreover, reporting the accumulative thermal cracking events up to each level of ageing (i.e. years of serving) may provide guidelines for selecting appropriate type and time for the preventive maintenance of pavement to minimise occurrence of thermal cracking over the service life. In the next section of this article, examples of performed analysis for few asphalt mixtures are presented.

Thermal cracking analysis for selected asphalt mixtures

Comprehensive thermal cracking analysis were completed for few asphalt mixtures containing a laboratory-produced mixture with same materials and compacted at three air voids levels and two field-produced laboratory-compacted mixtures obtained from local projects in Reno. The Moana mixtures were obtained from the top lifts of the Moana Lane extension project in Reno, Nevada, in 2006. The Sparks mixtures were obtained from the reconstruction project that took placed in Sparks Boulevard in Sparks, Nevada, in 2008. Table 1 provides the list of evaluated mixtures with their general properties.

The asphalt mixtures were supposed to be used at the surface of a pavement located in Reno, NV. The pavement structure was assumed to have three layers with properties (i.e. thicknesses, density, specific heat capacity and thermal conductivity) as shown in Table 2. The pavement surface radiation properties were assumed to be constant (i.e. no seasonal variation), and reasonable default values were used (albedo = 0.20, emissivity = 0.85 and absorption = 0.70). The required climatic/meteorological data for predicting pavement temperatures were obtained from EICM and NSRD database. Since, EICM data were only available for the time span from 1 August 1996 to 31 December 2005 (i.e. 9 years and 5 months), the required values for the times beyond this period were obtained by repeating the available values (start- ing from 1 January 1997) as needed to eventually have the required input for 20 years (i.e. from August 1996 to suppos- edly 31 July 2016). The prediction of the temperature profile was completed for various depths in the pavement structure (i.e. up to 3 metres below the pavement surface). Figure 4 shows an example of predicted hourly pavement temperatures for one year of analysis (i.e. 1 August 1996 to 31 July 1997) at various depths in the asphalt concrete surface layer.

information is presented in the respective literature (Alavi 2014 and Alavi et al. 2015).

Prediction of thermal cracking event

The criterion selected for determining possible events of thermal cracking is based on the crack initiation stress (CIS) threshold of the asphalt mixture. The CIS is determined from the results of the UTSST. Using the measured thermal stress and strain curves, the modulus of the asphalt mixture at various temperatures can be calculated from the linear viscoelastic constitutive equation. Figure 3 illustrates a typical modulus–temperature curve derived from the UTSST results. The crack initiation stage is defined as the point at which the maximum value of the modulus appears. Right after this point, a prompt reduction in the material modulus can be observed, caused by development of considerable micro-cracks in the mixture (i.e. the initiation of cracking). In fact, it is revealed that the thermal fracture of the asphalt mixture is happening due to the propagation of micro-cracks in the specimen. In addition to the crack initiation stage, other characteristics properties of the asphalt mixture including fracture, glassy hardening, viscous-glassy transition and viscous softening points can be detected from the modulus-temperature curve (Figure 3). Details of relevant to these fracture and thermo-viscoelastic properties can be obtained in other literatures by authors (Alavi et al. 2013b and Alavi and Hajj 2014). The key advantage of this criterion compared to the typical indirect tensile strength limit is the measurement of the stress threshold from the testing of a material under the thermal loading condition (with UTSST) instead of the mechanical loading at the isothermal condition. Therefore, the critical limit of the stress occurs at any temperature, depending on the stiffness and contraction properties of the asphalt mixture. In addition, from an extensive supportive laboratory study, the reduction in the CIS with the increase in oxidative ageing of the asphalt binder has been observed for most of the evaluated mixtures. The relationship between CIS and increase in carbonyl (CA − CA₀) has been found to be well represented using a fast-rate or a slow-rate decaying exponential functions, depending on the mixture ingredient properties and volumetrics. More information on the evolution of the asphalt mixture thermo-viscoelastic and fracture properties with oxidative ageing can be found in the respective literature (Morian et al. 2014).

The critical cracking event can be detected when the thermal stress reaches a defined percentage of CIS. The accumulative

Figure 3. typical modulus–temperature relationship with associated thermo-viscoelastic and fracture characteristic stages obtained from utSSt.

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air void and effective ageing distance within an asphalt mixture have been evaluated by Han (2011) using X-ray CT technique and image processing. The values used in this study are within the range of observed values for a typical asphalt mixture.

The kinetics and hardening parameters for the laboratory- produced NV19I28-5.22 mixtures at 4, 7 and 11% air void were obtained from the asphalt binders recovered from the aged asphalt specimens. The NV asphalt mixtures (i.e. laboratory-produced mixtures) were aged at different combination of times and temperatures in order to determine the kinetic properties. The mixtures were aged at 60 °C for durations of 0, 3, 6 and 9 months and at 85 °C for 0.5, 1 and 3 months using forced draft oven. Mixtures with 0 month ageing only experience loose Oxidative ageing (carbonyl) predictions were completed

over the analysis period at 0.015 m below the pavement surface using the predicted hourly pavement temperature at the corresponding depth as well as the asphalt binder oxidation properties shown in Table 3. The variation in ageing properties of PG64-28 binder when aged in NV19I28 mixtures revealed critical influence of air void level on binder oxidation kinetics and hardening properties. More information on the significance of mixture parameters on asphalt binder ageing properties is available in the respective literature (Morian et al.

2013). The representative air void radius and effective ageing distance (e.g. asphalt binder film) were assumed to be 0.5 and 1 mm, respectively. It should be noted that the distributions of

(% TWM) (%)

nv19I28_5.22_4%^a (lab produced) lockwood,

nevada Pg64-28 (SBS modified), Paramount Petro-

leum 5.22 4

nv19I28_5.22_7% (lab produced) lockwood,

leum 5.22 7

nv19I28_5.22_11% (lab pro-

duced) lockwood,

leum 5.22 11

moana Pg64-22 (Plant produced) lockwood,

nevada Pg64-22 (unmodified), Paramount Petroleum 4.90 7

Sparks Pg64-28 (Plant produced) lockwood,

leum 4.80 7

anv19I28_5.22_X%: Nevada aggregate, 19 mm nominal maximum aggregate Size (nmaS), Intermediate gradation, 5.22% asphalt binder content tWm, and X%

air voids.

Table 2. Pavement structure properties used for pavement temperature profile prediction.

Layer type Thickness (m) Density (kg/m³) Specific heat capacity (Jol/(kg ° k)) Thermal conductivity (W/(m °k))

asphalt concrete 0.3 2550 921 1.5

Crushed aggregate Base 0.5 2370 805 1.5

Subgrade — 2200 1100 1.7

Figure 4. Predicted pavement temperature at various depths of asphalt mixture surface layer.

Table 3. oxidative ageing model parameters for the evaluated asphalt mixtures.

Required input Mixture ID

NV19I28 _5.22_4% NV19I28 _5.22_7% NV19I28 _5.22_11% Moana PG64-22 Sparks PG64-28

E_a (kJol.mol⁻¹.°k⁻¹) 64.85 72.53 66.80 74.92 85.76

AP^α (ln(Ca/day)) 3.113e+07 4.080e+08 6.544e+07 1.269e+09 1.155e+10

HS (1/Ca) 2.34 2.70 2.87 5.91 4.86

m (ln(poise)) 9.69 9.24 8.97 4.55 5.50

CA₀ 0.815 0.821 0.744 1.129 1.295

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binders. It is worth to mention that although the same PG64- 28 binder was used in all of the NV mixtures, the kinetics and hardening properties of binder were found to be different based on the air void level of the mixtures. More information regarding the ageing process and the impact of mixture properties on asphalt binder ageing can be found in respective literature (Morian 2014 and Morian et al. 2013). For Moana and Sparks mix short-term ageing per AASHTO R30 (i.e. 4 h at 135 °C)

before compaction. After testing of these varied aged mixtures for the dynamic modulus (E^*) and UTSST, the mixtures were processed to extract and recover the asphalt binders. The CA and LSV of the extracted/recovered binders were obtained using FTIR and DSR tests to determine the oxidative ageing kinetics and hardening parameters of the so called mix-aged

Figure 5. Predicted carbonyl (Ca) over 20 years analysis period for the evaluated mixtures.

Table 4. asphalt mixture age-dependent characteristics for the evaluated mixtures.

Properties Mixture ID

NV19I28 _5.22_4% NV19I28 _5.22_7% NV19I28 _5.22_11% Moana PG64-22 Sparks PG64-28 2S2P1D model function coefficients a

A_E

0(ln(mPa)) 4.221 3.742 3.486 4.063 3.808

B_E

0 1.270 1.336 0.036 3.753 1.014

A_E

∞(ln (mPa)) 10.005 9.793 9.372 9.700 9.906

B_E

∞ 0.061 0.225 −0.428 0.748 0.064

A_𝜹 0.375 0.801 0.542 −1.124 0.798

B_𝜹 −0.853 −1.233 −0.455 0.630 −0.974

A_k −0.836 −0.887 −0.819 −0.606 −0.798

B_k −0.173 −0.128 −0.160 −0.743 −0.244

A_h −1.710 −1.798 −1.491 −1.350 −1.684

B_h −0.454 −0.622 −0.984 −1.522 −0.699

A_𝝉

0 −7.104 −6.111 −6.248 −5.806 −5.839

B_𝝉

0 4.022 0.777 0.196 0.880 0.193

𝜷 2000 2000 2000 2000 2000

Wlf Shift factor b

C₁ 14.31 15.90 12.33 12.10 14.28

C₂ 128.62 150.00 117.20 109.00 127.45

T_R (°C) 25 25 25 25 25

Coefficient of thermal Contraction function coefficients c C_CTC

l(e+5/°C) 2.101 2.072 1.975 1.629 2.000

D_CTC

l −1.299 −0.283 0.219 0.862 −0.161

C_CTC

g(e+5/°C) 0.902 0.973 0.841 0.702 1.100

D_CTC

g −0.443 −0.393 −0.169 −0.335 0.537

C_T

g(°C) −26.5 −29.40 −27.70 −26.00 −25.00

D_T

g −5.673 3.404 3.142 6.508 2.150

R 7.5 7.5 8.5 6.5 7.0

Crack Initiation Stress function coefficients d

E_CIS (ln(mPa)) 1.428 1.033 0.603 0.583 1.145

FCIS −0.600 −0.560 −1.113 −0.619 −0.018

a2S2P1Dcoefficint_i=e^Aⁱ^+Bⁱ^(CA−CA⁰⁾

blog(a_T(T))

= ^−C_C¹^(T−T^r⁾

2+T−Tr, t(°C).

cCTCcoefficint

i=C

i+D

i(CA−CA

0)

dCIS

i=e^Eⁱ^+Fⁱ^(CA−CA⁰⁾

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over the analysis period and at 0.015 m below the surface for the evaluated asphalt mixtures. The predicted CA for the Sparks PG64-28 mixture was observed to be different from the other mixtures, which should be considered while evaluating the results. This is due to the different measured kinetics for this specific asphalt binder.

The required asphalt mixture age-dependent characteristics were obtained from testing the mixtures at various ageing levels and quantifying the evolution of properties with the increase in carbonyl from the initial value (i.e. CA - CA₀). The mixtures were tested for the dynamic modulus (E^*) to determine the 2S2P1D then subjected to ageing in pans (with 1-mm film thickness) at

various combinations of times (up to 260 days) and temperatures (50, 60, 85 and 100 °C) using a precise forced draft oven (i.e. ambient pressure)⁴. Similarly, the CA and LSV of the so called pan-aged binders were determined using FTIR and DSR, respectively, to determine kinetics and hardening parameters.

Although, the prediction of CA at various depths in the asphalt binder film was conducted, the values at the exposed surface of the film to air were used. The differences between the predicted CA over 20 years under field condition (i.e. with pavement temperature variation) at the exposed surface of the

Figure 6. Comparison of predicted hourly thermal stress with different percentages of the crack initiation stress for the nv19I28-5.22 asphalt mixture with (a) 4, (b) 7 and (c) 11% air void.

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coefficients) properties of the evaluated mixtures. It is worth men- tioning that the anisotropic adjustment factor was assumed to be 0.6 for these performed analyses.

Using the predicted hourly pavement temperatures, predicted CA values and the age-dependent asphalt mixture properties, the analyses were completed to predict thermal stresses (at the depth of 0.015 m below the pavement surface) in the various asphalt layers. Consequently, possible thermal cracking events over the analysis period were detected by comparing the predicted thermal stresses with the age-dependent CIS values.

model parameters for relaxation modulus calculation. The UTSST test was also conducted to determine the CTC function parameters and the CIS at different ageing levels. For NV mixtures, the relationships were found by measuring the properties of the mixtures after being aged at 60 °C for the periods of 0, 3, 6 and 9 months.

For the Moana and Sparks mixtures, the relationships were found by measuring the properties of the mixtures after being aged for 0, 0.5 and 1 month at 85 °C. Table 4 provides the defined functions\

prime coefficients for the age-dependent viscoelastic (i.e. 2S2P1D coefficients), contraction (i.e. CTC coefficients) and strength (CIS

Figure 7. accumulative cracking event to reach 50% CIS for the nv19I28-5.22 asphalt mixtures at (a) 4, (b) 7 and (c) 11% air void.

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to 12 years from the construction time. After that the difference in the behaviour of the asphalt mixtures with different air void levels can be observed such that the possible events at which thermal stresses reach 50% CIS were observed to be more frequent for the mixtures with higher air void content.

The thermal stress in the asphalt mixture at 4% air voids did not even reach 50% CIS stress over the analysis period. This observation agrees with the expected behaviour of material such that generally mixture with higher air void content prone to damage (i.e. crack) faster and more severe. Hence, this initial observation may preliminarily validate the accuracy of the model to realistically reflect the behaviour of asphalt mixtures with different air void levels.

Effect of polymer modification on thermal cracking performance

Figure 8 illustrates the analyses results, including predicted thermal stress vs. different percentages of CIS over the analysis period, for the Moana PG64-22 (unmodified) and Sparks PG64-28 (SBS modified) field-produced asphalt mixtures. Based on the results, there were no thermal cracking events detected for the Sparks PG64-28 mixture for a 50% or higher of CIS. For this particular mixture, the decay in the Effect of air voids on thermal cracking performance

Figure 6 illustrates the outputs from the comprehensive thermal cracking model analyses, including the predicted thermal stresses vs. different percentages of CIS (i.e. 100, 80, 70, 60 and 50%) over the 20-year analysis period, for the NV19I28_5.22 asphalt mixtures with 4, 7 and 11% air voids. Accordingly, reduction in values of CIS and a gradual increase in the thermal stress with time are observed for all evaluated mixtures due to the effect of oxidative ageing. The critical cracking events can be detected for each percentage of CIS when the thermal stress reaches a defined percentage of CIS. As observed in Figure 6, for all of the NV19I28_5.22 mixtures, the developed thermal stresses could not reach the 100% CIS values over the analysis period. It should be noted that the NV mixtures with the polymer-modified asphalt binder have historically been show- ing a very good resistance to thermal cracking in the northern Nevada environment. The differences in the performance of the asphalt mixtures could be observed by evaluating the events at which thermal stresses reaches a lower percentage of CIS (e.g. 50% CIS). Figure 7 shows the accumulative cracking events at which thermal stress reaches 50% CIS. As shown in Figure 7, the behaviour of asphalt mixtures with different air void contents was predicted to be similar approximately up

Figure 8. Comparison of predicted hourly thermal stress with different percentages of the crack initiation stress for (a) moana Pg64-22 (unmodified) and (b) Sparks Pg64- 28 (SBS modified) asphalt mixtures.

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Effect of oxidative ageing on predicted thermal stresses Hourly thermal stresses were predicted over the analysis period for the evaluated asphalt mixtures without considering the changes in asphalt mixture relaxation modulus and CTC with oxidative ageing. In other words, the asphalt mixture characteristics at the start of analysis were assumed to be preserved over the analysis period. The differences between hourly predicted thermal stresses with considering effect of oxidative ageing and without considering its effect were calculated to determine the increase in thermal stress due to ageing over the analysis period, as shown in Figure 10. In general, higher values of thermal stresses were predicted when oxidative ageing was considered.

The oxidative ageing, quantified by the increase in carbonyl (CA - CA₀), particularly caused the increase in the stiffness of the asphalt mixture, led to the development of greater thermal stresses. The increase in the developed thermal stresses due to oxidative ageing was observed to progressively increase with time. The increase in the thermal stress due to oxidative ageing can be as high as 1.25 MPa, as observed for Moana PG64-22 asphalt mixture.

As shown in Figure 10, the influence of ageing on increasing the thermal stress was found to be higher for the mixtures with lower air voids since overall integrity of the mixture with lower air voids is higher compared to the mixtures with high air void contents. Therefore, an increase in stiffness of the asphalt binder, due to oxidative ageing, has a larger influence on the stiffness of the mixture. Comparing the Moana PG64-22 and Sparks PG64-28, asphalt mixtures revealed that the increase in thermal stress due to the oxidative ageing was higher for the mixture with the unmodified asphalt binder (i.e. Moana PG64-22).

CIS value with ageing was not observed. It should be noted that the results are consistent with the current filed performance of the Sparks Boulevard pavement where no thermal cracking distresses observed 6 years after construction. In the case of the Moana PG64-22 mixture, the thermal stresses reached different percentages of CIS at several events over the analysis period. The occurrence of these events increased with time as a result of oxidative ageing, which caused an increase in the predicted thermal stress and a decrease in the CIS value. Figure 9 shows the accumulative thermal cracking events at which thermal stress reached both 50% and 100% CIS for the Moana PG64- 22 asphalt mixture. Based on the findings, the Moana PG64-22 mixture may have an acceptable thermal cracking performance up to approximately 9 years from the construction date due to the low number of cracking events. Howev- er, after this time, the number of possible cracking events increases drastically due to the effect of oxidative ageing on both stiffening the mixture (i.e. observed by the gradual increase in thermal stresses) and decreasing the stress tolerance of the asphalt mixture (i.e. observed by the gradual decrease in CIS). Overall, these observations from the thermal cracking simulations are in line with the field performance of the corresponding asphalt mixtures especially that the PG64-28 polymer-modified asphalt binder has historically been outper- forming the performance of the PG64-22 unmodified asphalt binder in terms of thermal cracking in northern Nevada. The weak resistance of the PG64-22 asphalt mixtures to thermal cracking under northern environmental conditions led to the mandatory use of the polymer-modified asphalt mixtures on all state highway roads more than 10 years ago.

Figure 9. accumulative cracking events when thermal stresses reach (a) CIS and (b) 50% CIS for moana Pg64-22 asphalt mixture.

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surface radiation properties as well as any discontinuity in the thermal diffusivity of the various layer materials. The required climatic and meteorological input of the model is the hourly air temperature, wind speed and solar radiation. These inputs were obtained from the EICM and NSRD databases for this study.

A kinetic-based constant-rate oxidative ageing model is employed for the prediction of carbonyl at the selected depths in the asphalt concrete layer over the analysis period. The model account for the main thermal cracking influential factors such

as asphalt binder oxidative ageing and temperature-dependent CTC. The model includes four major steps: (I) pavement temperature profile prediction, (II) oxidative ageing (carbonyl) prediction, (III) thermal stress calculation and (IV) thermal cracking event prediction.

An improved heat transfer model with refined boundary condition is used in the comprehensive model to predict

Figure 10. Increased thermal stress due to oxidative ageing over analysis period for nv19I28_5.22 asphalt mixtures with (a) 4, (b) 7 and (c) 11% air void.

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with respect to the glass transition regime. The CTC function can be obtained through the measurements of the thermal strain in the UTSST device. Possible variations of CTC with ageing can be handled by the regression equations relating the CTC function coefficients with the increase in carbonyl (CA - CA₀).

A thermal cracking event is detected when the predicted thermal stress reaches the crack initiation stress (CIS) of the asphalt mixture. The CIS is defined from the results of thermal stress and strain measurements in the UTSST. The crack initiation in the asphalt mixture is defined as the stage at which the asphalt mixture modulus–temperature curve reaches to a maximum point; an instantaneous drop in the modulus is observed for the temperatures colder than the crack initiation temperature. CIS is the thermal stress corresponding to the crack initiation stage. The CIS was found to decay with the oxidative ageing of the asphalt binder over time. The relationship between CIS and the increase in carbonyl (CA - CA₀) can be used to account for the change of CIS with ageing over the analysis period. The accumulated cracking events over the analysis period, corresponding to different percentages of CIS, can be used to assess the thermal cracking resistant properties of an asphalt mixture used at the location of interest and also to recommend changes requires predictive hourly pavement temperatures at the desired

depth in the asphalt layer, the oxidative ageing kinetics (E_a and A) and, the hardening parameters (HS and m) for the asphalt binder, the initial carbonyl value (CA₀), as well as the represented air void diameter and effective ageing distance (e.g. asphalt binder film). The required kinetics and hardening properties of an asphalt binder can be obtained by ageing the asphalt mixture or the asphalt binder for various combinations of durations and temperatures and testing the aged binder for CA (using FTIR) and LSV (using the DSR).

Thermal stresses are then predicted at each depth of the asphalt concrete layer using the one-dimensional viscoelastic constitutive equation that is refined to account for the effect of continuous ageing with time. The required asphalt mixture properties are the age-dependent relaxation modulus and the age-dependent CTC function. The relaxation modulus at each ageing level is obtained by inter-conversion from the dynamic complex modulus (E^*) based on the continuous relaxation spectrum of the 2S2P1D model. The influence of ageing on the relaxation modulus is modelled by relationships defining the 2S2P1D model coefficients with the increase in carbonyl (CA - CA₀). Temperature-dependent CTC function accounts for the variation of asphalt concrete contraction potential

Figure 11. Increased thermal stress due to oxidative ageing over analysis period for (a) moana Pg64-22 (unmodified) and (b) Sparks Pg64-28 (SBS modified) asphalt mixtures.

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The proposed comprehensive model was used to evaluate the thermal cracking performance of selected asphalt mixtures while simulating a pavement located in Reno, Nevada. The results of the primary analyses showed that the model can realistically differentiate the difference between the thermal cracking potential of asphalt mixtures with various air void levels and asphalt binders. The asphalt mixtures with higher air void contents were found to be more prone to thermal cracking, which followed the expected trend. Also, the mixture with a polymer-modified asphalt binder showed superior performance compared to the mixture with an unmodified asphalt binder in terms of less potential accumulative thermal cracking events.

Historically, polymer-modified asphalt binders have been per- forming well in northern Nevada in terms resistance thermal cracking.

Further research

More studies are required including various types of asphalt mixtures to refine the model output. In addition, a stand-alone software based on the model could potentially facilitate the analysis of thermal cracking based on the developed comprehensive model. Currently, all the calculations are performed using MATLAB computing program. The model can be expand- ed for the evaluation of thermal cracking propagation based on the cohesive zone model similar to the approach implemented by based on actual filed performance of asphalt pavements in various locations of the US.

Notes

1. E_a: Activation energy, A: Pre-exponential factor.

2. HS: Hardening susceptibility, m: hardening function constant.

3. Williams–Landel–Ferry.

4. The ageing durations at each temperature for pan-aged binders were as follows: 60, 120, 180 and 240 days at 50 °C; 30, 60, 100 and 160 days at 60 °C; 8, 15, 25 and 40 at 85 °C; and 2, 4, 6 and 10 days at 100 °C.

Acknowledgements

The content of this article is part of the overall effort in the Asphalt Research Consortium (ARC). However, the contents of this report reflect the views of the authors and do not necessarily reflect the official views and policies of the FHWA. The authors gratefully acknowledge the FHWA support.

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Alavi, M.Z. and Hajj, E.Y., 2014. Effect of cooling rate on the thermo- volumetric, thermo-viscoelastic, and fracture properties of asphalt