A Framework to Quantify the Effect of Healing in Bituminous Materials using Material Properties

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A Framework to Quantify the Effect of Healing inBituminous Materials using Material PropertiesAmit Bhasin a , Dallas N. Little b , Rammohan Bommavaram a & Kamilla Vasconcelos aa Texas Transportation Instituteb Zachry Department of Civil Engineering, Texas Transportation Institute, Texas A&MUniversity MS 3135, College Station, TX, 77843, USA E-mail:Published online: 19 Sep 2011.

To cite this article: Amit Bhasin , Dallas N. Little , Rammohan Bommavaram & Kamilla Vasconcelos (2008): A Frameworkto Quantify the Effect of Healing in Bituminous Materials using Material Properties, Road Materials and Pavement Design,9:sup1, 219-242

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Road Materials and Pavement Design. EATA 2008, pages 219 to 242

A Framework to Quantify the Effectof Healing in Bituminous Materials usingMaterial Properties

Amit Bhasin* — Dallas N. Little** — Rammohan Bommavaram*Kamilla Vasconcelos*

* Texas Transportation Institute

** Zachry Department of Civil Engineering and Texas Transportation InstituteTexas A&M University MS 3135College Station, TX 77843USA{a-bhasin; [email protected]

ABSTRACT. Significant evidence exists in the literature that healing has a substantial effect onthe performance of asphalt mixtures and therefore asphalt pavements. The incorporation ofthe healing mechanism in tandem with the crack growth mechanism is necessary forcomprehensive modeling of the fatigue or fracture processes in asphalt mixtures. This paperpresents a new framework that combines material and mechanical properties of the bitumento predict the effect of healing on mechanical properties and performance of the asphaltmixture. This framework is based on an analytical approach that will allow it to beincorporated with future analytical models of crack growth and damage. The paper alsopresents a new test method using the dynamic shear rheometer to obtain some of the materialproperties related to the healing mechanism that are required in the proposed framework.Results from preliminary tests conducted on selected materials support the hypothesis used inthe development of the framework and the DSR based test method.KEYWORDS: Healing, Fatigue, Bitumen, Asphalt.

DOI:10.3166/RMPD.9HS.219-242 © 2008 Lavoisier, Paris

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220 Road Materials and Pavement Design. EATA 2008

1. Introduction

Damage in asphalt pavements is affected by the quality of the bitumen and masticincluding its cohesive strength, ability to resist fracture, and the ability of micro cracksin the bitumen or mastic to heal during rest periods. The fatigue damage process isinfluenced by fracture in which crack growth is induced and micro crack healing inwhich micro crack surfaces, at least partially, re-bond. The healing process affects thefatigue process most profoundly when the micro cracks are small.

Evidence in the literature demonstrates the significance of healing on theperformance and durability of asphalt mixtures. Shift factors that are required totranslate from laboratory predicted to field observed fatigue cracking demonstratethat laboratory data under-predicts field observations. Lytton et al. (1993) expressedthat the shift factor is dominated by healing and is a function of the number of restperiods between load cycles and the duration of the rest period. Another examplethat highlights the importance of the healing process is the interruption of microcrack growth due to a dispersed filler that interrupts or “pins” crack tip energy. Suchprocesses typically impede the growth of micro cracks and keep them small, whichin turn promotes the healing process.

Typically laboratory based test methods used to quantify healing entail damagingthe sample in a fatigue or partial fracture mode and then allowing it to recover overtime. Such an approach can be used very effectively to differentiate among thehealing characteristics of different types of bitumen or asphalt mixtures. However,one drawback of this approach is that the magnitude of healing is dependent on thetest method (e.g., duration of the rest period and specimen geometry). Therefore,healing as quantified using this approach cannot be used to analytically orcomputationally model the behavior of an asphalt mixture under laboratory or fieldconditions. This drawback can be overcome by using intrinsic material propertiesthat are related to the healing process used within an analytical solution based onthese properties to quantify healing. This approach can be used to model and predictthe healing that is observed in laboratory fatigue tests or field.

This paper is divided into seven sections. Section 2 provides a brief backgroundand review of literature pertaining to the evidence and measurement of healing.Section 3 presents a novel framework to quantify healing using an analytical solutionthat is based on fundamental material properties. This framework combines theapproaches used by Schapery (1989) to model crack wetting and Wool and O’Connor(1981) to model crack healing. Section 4 describes methodologies to obtain some ofthe important material properties identified in Section 3. A new and simplemethodology to obtain some of the parameters required to model healing is presentedalong with results for selected materials in Section 4. Section 5 briefly describes themethodology used to quantify the effect of healing on the fatigue cracking life alongwith results for selected asphalt mixes. Section 6 compares the material propertiesrelated to healing obtained in Section 4 to the measured effect of healing on the fatiguecracking life measured in Section 5. Section 7 presents the summary and conclusions.

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A Framework to Quantify Healing 221

2. Important previous studies related to healing

Some of the most recent, significant documentation of healing in the laboratorywas demonstrated by Kim et al. (2001), by Little et al. (2001), by Maillard et al.(2004), Kim and Roque (2006), and by Carpenter and Shen (2006). Data from theselaboratory studies clearly demonstrate the evidence for existence of healing and itssignificant impact on the fatigue cracking life of asphalt mixtures. Little et al. (2001)demonstrated that rest periods (of 24-hour duration) applied in traditional flexuralbeam bending experiments increased the fatigue life by more than 100 percentdepending on the type of binder used. Kim et al. (2003b) used torsional loading onasphalt mastics to demonstrate that rest periods of between 30-seconds and 2-minutes extend fatigue life and decrease the rate of accumulation of the dissipatedenergy that actually causes damage (measured as pseudo strain energy). Their workalso showed that the impact of healing is by far the greatest when rest periods areapplied before significant damage occurs. Carpenter and Shen (2006) skillfullyverified this conclusion by demonstrating that the application of short rest periodsbetween each load cycle not only extends fatigue life but is also responsible for theextension of so called “endurance limit” of some asphalt mixtures. Carpenter andShen used dissipated energy between load cycles to quantify healing. Kim and Roque(2006) used a similar approach to quantify the healing characteristics of asphaltbinders used in different asphalt mixtures. They quantified healing in terms of therecovered dissipated creep strain energy per unit time.

Maillard et al. (2004) conducted tensile tests on films of asphalt binders lodgedbetween steel spheres to simulate an asphalt film that is bound by aggregates. Theymeasured the rate of healing in the asphalt film by transmitting ultrasonic wavesthrough the sample. A decrease in the amplitude of the ultrasonic signal correspondsto damage in the film. An increase in the amplitude of the ultrasonic signal for anundisturbed sample after applying a tensile load corresponds to the healing process.

The effect of healing during rest periods is also evidenced in the permanentdeformation characteristics of asphalt mixtures. For example, Bhairampally et al.(2000) demonstrated that the inclusion of rest periods between compressive loadcycles extended the time to tertiary damage and that this extension depended on thetype of asphalt. Their work concluded that the transition from the secondary phase tothe tertiary phase of dynamic compressive creep is related to development andgrowth of micro cracks. Further work by Song et al. (2005) has shown this to be trueusing computer assisted tomography. Bhairampally et al. (2000) also demonstratedthat addition of a filler (in this case hydrated lime) resulted in reduced rates ofdamage in the compressive mode of loading because of crack pinning andaccentuated the effect of healing of micro cracks in the mastic.

In addition to laboratory evaluations, there is evidence in the literature todemonstrate the presence of healing in asphalt field pavements. Williams et al.(2001) presented some convincing field data related to healing. They selected fourpavement sections at the Turner Fairbanks accelerated load facility (ALF)

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considering a full factorial of two thicknesses and two asphalt layer types over ahomogeneous subgrade. Surface wave measurements were made to assess pavementstiffnesses before, immediately after, and 24-hours after loading passes. Regardlessof the pavement type, the trend was that more healing (quantified in terms of therecovery of stiffness) was recorded closer to the centerline suggesting that morefatigue damage results in a greater potential for and a greater amount of microdamage healing. Williams et al. (2001) reported other convincing support forhealing using surface wave analysis of pavements at Mn/ROAD pavement sectionsand on U.S. Highway 70 in North Carolina using designed experiments.

Nishizawa et al. (1997) used data from four thick pavements to demonstrate thatfatigue cracking did not occur because healing effects at the low strain and lowdamage levels compensated for (off set) crack growth. Little and Bhasin (2007)presented a more detailed review on the evidence of healing as well asmethodologies used to quantify the effect of healing on the performance ofbituminous materials.

3. A Framework to characterize healing in bituminous materials

In order to accurately characterize and predict the damage caused in asphaltpavements, it is essential to characterize the healing process in tandem with thefatigue cracking or fracture process. The impact of healing on the performance ofasphalt mixtures cited in the literature supports this contention. Significant researchhas been conducted in the past to identify fundamental material properties thatcontrol the fatigue cracking and fracture process. Several analytical models based onfracture mechanics have also been developed. These models utilize fundamentalmaterial properties to predict the damage in bituminous materials.

It is important to characterize the healing process using a similar approach thatcombines material properties with analytical models to predict the effect of healingunder any given condition. This will greatly facilitate future efforts to integratefracture and healing into a single comprehensive model. This section presents aframework in which material properties related to healing can be measured and usedwith an analytical model to predict the effect of healing. Section 4 of this paperpresents a methodology by which to obtain some of the important properties utilizedin this framework. Section 6 of this paper demonstrates a correlation of some ofthese material properties with the effect of healing on fatigue cracking life. Thecomplete and exhaustive evaluation of all elements in this framework is work inprogress and beyond the scope of this paper.

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3.1. Healing mechanism

A precursor to the growth of a crack in a viscoelastic medium is the developmentof a fracture process zone at the crack tip (Schapery, 1981). The fracture processzone can be considered to be comprised of a number of micro or nano cracks. Animportant distinction between the crack and the fracture process zone is as follows.A crack cannot support an external tensile load (considering Mode I failure);whereas, the capacity of the fracture process zone to support external tensile loadvaries from the end of the crack (zero ability) to that of the intact material. Acommon example of a fracture process zone is the formation of craze fibrils inthermoplastic polymers. Craze fibrils form following loss of entanglement of themolecular chains. At low temperatures and high strain rates, crazing occursprimarily due to scission of molecular chains, whereas at higher temperatures itoccurs primarily due to disentanglement of molecular chains (Berger and Kramer1987). One might argue that the entanglement of long chains is not likely in asphalt,but work by Kim et al. (1990), demonstrated the importance of asphalt functionalgroup morphology and size on the healing process.

Crack healing occurs immediately after removal of the external load. Figure 1illustrates the crack tip with the zone of interest where the healing process isconcentrated. The terminology used to describe the geometry and stresses in thehealing process zone are borrowed from Schapery (1989). The length of the crack orhealing process zone over which the intermolecular forces across the crack surfacesare effective in causing healing is denoted by β . The tensile stress between the

crack surfaces in the healing process zone is denoted by bσ . The rate at which thetip advances in the healing process zone to cause wetting between the crack surfacesis denoted by ba .

Figure 1. Crack propagation and fracture process/healing zone in mode I loading

Crack closing speed

Healing process zone

Crack surface

ba

β

bσ

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Based on the extensive work done in polymer healing by Wool and O’Connor(1981) three primary stages of the healing process can be identified:

– wetting of the two faces of a nano crack,– instantaneous strength gain due to interfacial cohesion between the crack faces,

and– long term strength gain due to diffusion and randomization of molecules from

one face to the other.

De Gennes (1971) proposed the reptation model to explain the movement of apolymer molecule in a worm like fashion inside a cross linked polymeric gel. Bergerand Kramer (1987) demonstrated that the disentanglement time for chains in thecrazing zone during the crack growth process was in agreement with the reptationmodel. Wool and O’Connor (1981) used the same reptation model but reversed theapproach to determine the time required for healing caused by the inter diffusion ofmolecules between crack faces. They also realized that the overall rate of strengthgain of a fractured interface due to healing is the net effect of the wetting andstrength gain processes related to cohesion and inter diffusion. Based on this findingthey ingeniously described net macroscopic recovery or healing in a material bycombining an intrinsic healing function of the material with a wetting distributionfunction using a convolution integral as follows:

( ) ( )∫=

−∞=

−=t

h dd

dtRRτ

τ

τττφτ [1]

In Equation [1], R is the net macroscopic healing function, ( )tRh is the

intrinsic healing function of the material, ( )Xt,φ is the wetting function, and τ isthe time variable. Succinctly stated, the convolution integral implies that the rate atwhich a crack regains its ability to carry load or heal is the net effect of: i) the rate atwhich the two cracked surfaces wet and ii) the rate at which a wetted crack surfaceregains strength due to cohesion and inter diffusion.

Lytton et al., (2001) determined cumulative macroscopic healing as a function oftime using a form very similar to the Ramberg-Osgood relationship. This is anexcellent example of the macroscopic healing function R over time, which is theresult of the two processes described above. A more detailed description of the twofunctions that describe the two processes related to healing follows.

The wetting distribution function, ( )Xt,φ , defines wetting at the contact of thetwo crack surfaces in a domain X over time t . Fundamental properties such as thesurface free energy, viscoelastic properties, and fracture toughness of the bitumendictate the rate at which the two crack surfaces wet each other. For example, abitumen with higher surface free energy will have stronger intermolecular forces ofattraction between the two cracked surfaces and will consequently wet at a faster

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rate. The analytical form for the wetting function can be simplified by consideringwetting that occurs at a constant rate, or for instantaneous wetting. The wettingfunction reduces to a constant for the former case and to a Dirac-delta function forthe latter. The domain in which wetting occurs is dictated by the geometricconsiderations for crack growth within the material. The following sub-sectionpresents an analytical form for the healing function. This analytical form relates thewetting function or rate of wetting to the material properties of the bitumen.

The intrinsic healing function, ( )tRh , defines the rate at which two crack facesthat are in complete contact with each other (are wetted) regain strength due to theinterfacial work of cohesion between the crack faces and inter diffusion andrandomization of the molecules from one face to the other. Material properties suchas the surface free energy and coefficient of self diffusion dictate the magnitude andrate at which a wetted crack interface regains strength. For example, a bitumen withhigher surface free energy and hence higher work of cohesion will have higherinstantaneous strength gain. Also, a bitumen with a higher coefficient of self diffusionwill facilitate faster inter diffusion of molecules and promote the rate of strength gain.

3.2. Wetting function

The first step in the healing process, i.e., wetting of the two faces of a nano crackis represented by a wetting distribution function ( )Xt,φ as described in theconvolution integral (Equation [1]). This section presents an explicit relationshipbetween the wetting distribution function and material properties related to thewetting for a one dimensional case. Schapery (1989) developed a relationshipbetween the work of cohesion and the material properties related to the wetting ofcrack surfaces. Based on this relationship, the wetting distribution function or rate ofwetting of a crack surface can be shown as follows:

( )( )

m

b

c

mb DW

kDa

dtXtd

1

0221 141,

−

−−

==βσν

πβφ[2]

In Equation [2], cW is the work of cohesion; ν is the Poisson’s ratio; 0D , 1D ,

and m are creep compliance parameters obtained by fitting ( ) mtDDtD 10 += ; and

mk is a material constant that can be computed from m. The terms, bσ , β , and

ba are as described before (Figure 1). The wetting function described inEquation [2] represents a case of wetting that occurs at a constant rate. The value ofthe constant rate at which wetting occurs is determined by mechanical, viscoelasticand material properties of the bitumen.

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The dimensional consistency of Equation [2] can easily be verified. The righthand side of Equation [2] contains mechanical and viscoelastic properties of thematerial, i.e., Poisson’s ratio and creep compliance parameters. These properties canbe easily determined using laboratory tests. The right hand side of Equation [2] alsocontains three material properties, i.e, the work of cohesion ( cW ), the length of the

healing process zone ( β ), and the tensile stresses that cause the crack faces to close

( bσ ).

In most cases healing is quantified in terms of the percentage of strength gainedbefore and after the rest period. To represent such a case, the wetting distributionfunction must be modified in order to represent the fraction of the newly formedcrack surface that wets during the healing process. For a one dimensional case, thiscan be done by eliminating the domain X and normalizing the crack growth functionin Equation [2] with the length of the crack that has grown in N cycles, NR∆ , asfollows:

( )( )

m

b

c

mN

DWkDRdt

td1

0221 141'

−

−−∆

=βσν

πβφ[3]

where,

'β = β , when NR∆<β

= NR∆ , when NR∆≥β .

The substitution for β in Equation [2] to obtain Equation [3] provides a formthat is consistent with the observed healing behavior in asphalt mixtures. Consider acase when rest periods are provided very frequently such that the incremental crackgrowth is small and the incremental length of the crack does not exceed the length ofthe healing process zone ( NR∆≥β ). For example, Carpenter and Shen (2006)evaluate the effect of healing on endurance limit by providing a rest period afterevery load cycle. A similar effect can also be obtained by adding fine well dispersedfiller in the asphalt mastic. For example, Kim et al., (2003a) demonstrate the effectof introducing hydrated lime filler particles on the healing of asphalt mastics. Insuch a case the wetted length is maximized simply because the incremental crackprogression is kept within a certain critical limit and the entire crack can heal(although it might not gain the same strength as the original binder). This isdiscussed in the following sub section on the intrinsic healing function, ( )tRh . Onthe other hand, if rest periods are spaced apart so that significant crack growthoccurs before a rest period is provided, i.e., NR∆<β , then the maximum healinglength of the crack is limited to the length of the healing process zone.

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The tensile stresses that cause the crack faces to close ( bσ ) can be considered tobe directly proportional to the surface free energy or the work of cohesion of thematerial ( cW ). This is a reasonable assumption since materials with higher surfacefree energy would also have a higher affinity to cohere and develop greater tensilestresses between the two surfaces. Based on the typical order of magnitudes of thevarious parameters, the contribution of the creep compliance parameter, 0D , can beneglected. Based on this consideration, it is easy to see from Equation [2] thatmaterials with significantly higher work of cohesion will have a higher rate ofwetting and consequently healing.

3.3. Intrinsic healing function

The second and third steps of the healing process, i.e., strength gain due tointerfacial cohesion and inter diffusion of molecules between the wetted surfaces isrepresented by the intrinsic healing function ( )tRh as described in the convolutionintegral (Equation [1]). This section presents a functional form for the intrinsichealing function along with a brief discussion on the significance of the parametersused in the functional form. Section 4 of this paper presents a new and simple testmethod to obtain the parameters for the intrinsic healing function.

Based on Einstein’s relation for a ‘one dimensional random walk in the tube’,Wool and O’ Conner (1981) demonstrated that the intrinsic healing function is bestrepresented using the following form:

( ) ( )ttKRtRh ϕ•+= 25.00 [4]

In Equation [4], t is the time, and ( )tϕ is used to represent the effect of timesurface rearrangement of molecules. The symbol • represents the convolutionprocess. This model was developed for simple polymer molecules and for short timehealing. Wool and O’ Conner also report that for longer duration the power factorchanges from 0.25 to 0.5.

The healing function represents the sum effect of: i) instantaneous strength gaindue to interfacial cohesion at the crack interface, represented by the parameter 0R ,and ii) time dependent strength gain due to inter diffusion of molecules between thecrack surfaces, represented by ( )tKt ϕ•25.0 . In this study, a sigmoid function wasused to represent the latter. The sigmoid function for time dependent strength gain orhealing is similar to the form that is used to model other processes such as kineticsof phase transformations in solids (Callister 2007). The form of the healing functionthat was used is shown below (Equation [5]).

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( ) ( )rqth epRtR −−+= 10 [5]

( )tRh is a time dependent dimensionless function that represents the increase in amechanical property of the wetted crack interface, typically as a fraction orpercentage of the same property for the intact material. This function can be used torepresent any mechanical property of interest, for example, shear modulus. The term

0R represents the effect of instantaneous healing of wetted surfaces that is primarilydue to the interfacial cohesion driven by surface free energy. The second part ofEquation [5] represents the kinetics of a phase transformation type of phenomenonthat is due to the migration and randomization of molecules across the interface. Theterms q and r are time independent constants for a particular phenomenon. The lastterm in Equation [5] is also referred to as the Avrami equation that is generallyapplied to rate of change of phase or chemical reactions. In a case where a detailedknowledge of molecular properties and structures is available, one can potentiallydetermine the rate of surface rearrangement of molecules, ( )tϕ and use it with therandom walk model in Equation [4] to determine the intrinsic healing function.Alternatively, as in the case of this study, a mechanical test can be used withEquation [5] to determine the various material constants that can be used to describethe intrinsic healing phenomenon.

Based on the above reasoning, it is expected that the magnitude of 0R isproportional to the work of cohesion or surface free energy of the material.Section 6.1 demonstrates the validity of this hypothesis. Since this parameterdepends on the surface free energy of the material, it would also depend on extrinsicproperties such as temperature. The parameters, p, q, and r, represent the effect ofhealing that is due to the inter diffusion of molecules between the crack surfaces.Therefore, these parameters will be dictated by intrinsic material properties such asmolecular weight, and activation energy for diffusion. In addition, these parameterswill also depend on extrinsic properties such as pressure and temperature. By testingdifferent materials under similar conditions the effect of extrinsic properties on thehealing function parameters can be eliminated.

3.4. Additional considerations in applying the healing framework

The effect of healing on strength gain at crack surfaces is apparent when restperiods are applied. However, healing properties of a material can significantlyaffect the fatigue cracking life of a bituminous material even when there are no restperiods. A stress or strain reversal can occur due to the nature of the cyclic loadingin laboratory based fatigue cracking tests. For example, this is most readilyvisualized in a tension-compression type of cyclic test where the cracks are forced toclose for a certain part of each load cycle. In such cases, the rate and extent of crackclosure will be dictated by the nature of the applied load cycles, and this must beaccounted for in the wetting function shown in Equation [3]. Similarly, the strength

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gain function in Equation [4] is a material property and remains the same withoutchanging.

4. Measurement of material properties related to healing

The healing mechanism in bitumen is driven by material properties that control,i) the rate at which the crack surfaces wet each other and ii) the rate at which awetted crack surface gains strength. This section presents methodologies used toobtain the values of some of the important material properties related to the healingmechanism.

4.1. Selection of materials and test methods

Three different types of bitumen were selected for this study. The selectedbitumens were originally a part of the Superpave Highway Research Program(SHRP) in the United States and denoted by the label. The selected bitumens werethen evaluated by selected test methods to determine the material propertiesassociated with the healing mechanism.

Table 1. Summary of selected materials and test methods

Materialtype

Testmethod Purpose of the test method Selected materials

WilhelmyPlate test

To determine work of cohesion(material property) related to rateof wetting and instantaneoushealing

Bitumen

DSR test To determine the healing function

Three different types ofbitumen, AAD, AAM,and ABD

FineAggregateMatrix

DMA

To quantify the effect of healingon fatigue cracking life andverify predictions based onmaterial properties

Six different types ofFAM using the threebitumen, AAD, AAM,and ABD with the twodifferent types ofaggregates RA and RL

The effect of healing on fatigue cracking life was quantified by conductingrepeated load tests with and without rest periods on six different types of fineaggregate matrices. A fine aggregate matrix (FAM) is comprised of a mixture ofbitumen and fine aggregates (smaller than sieve size 1.18 mm). The three selectedbitumen and two different types of aggregates were used to produce six different

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FAMs. Table 1 summarizes the materials selected in this study, the type of testconducted on the materials, and the purpose of the test. The three bitumen, AAD,AAM, and ABD have a performance grade specification of PG 58-28, PG 64-16,and PG 58-10, respectively. The aggregate RA is primarily granite and RL isprimarily siliceous gravel. A more detailed description of the properties of theselected material can be found in the literature (Jones 1993; Robl et al., 1991).

4.2. Surface free energy and work of cohesion

By definition, the work of cohesion is twice the magnitude of surface free energyof a material. As discussed in the Sections 3.2 and 3.3, the work of cohesion due tothe surface free energy of bitumen has two important roles in the healing process.First, the rate and extent to which a sharp crack tip heals in a viscoelastic medium isdictated by the work of cohesion (in addition to viscoelastic properties of thematerial). Second, upon wetting of the two crack surfaces, the instantaneous strengthgained by the crack is equal to its work of cohesion. The instantaneous strengthgained by the material is also reflected in the DSR based test method that is used todetermine the intrinsic healing function and will be discussed in section 4.3.Therefore, the role of surface free energy and concomitant work of cohesion in thehealing process cannot be understated.

The Wilhelmy plate method was used to measure the advancing contact angle ofthe asphalt binder with five different probe liquids. The acid-base theory of surfacefree energy components (van Oss, 1994) was used with the measured contact anglesto determine the surface free energy components and concomitant work of cohesionfor each selected bitumen. Details of the methodology to determine the surfaceenergy components and compute the work of cohesion are described in anotherpublication (Hefer et al., 2006). Table 2 presents the three surface energy components,the total surface energy, and the work of cohesion for the three selected bitumen.

Table 2. Surface free energy and work of cohesion of selected bitumen

Surface free energy (mJ/m2)

ComponentsBitumen

LW* Acid BaseTotal

Work ofcohesion, Wc

(mJ/m2)

AAD 18.5 0.1 0.1 18.6 37.2

AAM 24.8 0.2 0.0 24.8 49.6

ABD 32.5 0.4 0.0 32.5 65.0

* LW = Lifshitz van der Waals.

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4.3. Measurement of intrinsic healing function

The Dynamic Shear Rheometer (DSR) was used in a novel way to obtain theparameters of the healing function. In summary, two 28 mm diameter and 3.5 mmthick bitumen specimens are fixed onto the two end plates of the DSR. The surfacesof the two specimens are then brought into contact with each other and the change inthe shear modulus is recorded by applying a few small strain cyclic loads at differenttime intervals. The change in the shear modulus is then normalized with respect to asingle intact specimen of equivalent size. The equivalency in size eliminates theeffect of creep during the test. A more detailed description of the test procedure ispresented below.

The selected bitumen is heated in an oven at 100°C for 30 minutes and pouredinto a silicon rubber mold. The liquid bitumen is allowed to gradually cool andsolidify in the mold at room temperatures. Four test specimens of 28 mm diameterand 3.5 mm in height were prepared for two sets of replicate measurements. Inaddition two test specimens of 28 mm diameter and 5 mm height were prepared toobtain two replicate measurements for the reference property. Consistency in thedimensions of the test specimen is ensured.

The DSR manufactured by TA Instruments, USA, (model AR 2000) was used inthis study. Before the specimens were attached to the device, the normal force andgap in the DSR was zeroed for the two 25 mm flat circular end plates. The loadingaxis of the DSR was then raised to gain access to the bottom and top plates.Two 3.5 mm thick bitumen specimens were then gently affixed to the top andbottom plates (Figure 2a). It was ensured that the specimens were centered along thevertical axis of the instrument. The loading axis was then lowered to reach a targetthickness of 5 mm and excess bitumen outside the plate was trimmed. This ensuredthat the bitumen surfaces of the two specimens would come into intimate contactwith each other (Figure 2b). This is referred to as the two-part specimen. Followingthis, the instrument then readjusts the gap to achieve a constant normal forceor 0.4±0.1 N and maintains it throughout the remainder of the test.

The initial adjustments to bring the bitumen surfaces into intimate contact witheach other and readjustment of the normal force by the instrument takes about oneminute. Following this initial setup, the DSR is programmed to measure and recordthe dynamic shear modulus (G*) at 0, 2, 4, 6, 8, 10, 15, 20, 25, 30, 40, 50and 60 minutes for the two-part bitumen specimen. The contact normal force ismaintained throughout the test. Although, this resulted in a small change in the gapbetween the metal plates as the test progressed, this change was not significant. Ateach instance, the dynamic shear modulus is measured at 0.001 % strain by applying50 cycles at a frequency of 10 Hz. The same test procedure is repeated using a one-part or single 5 mm thick test specimen of the bitumen. All tests were conducted atambient temperature (23°C). The percentage healing at any given time is computedas the ratio of the value of G* obtained using the two-part specimen test to the valueof G* obtained using the one-part or specimen test at each time interval. This

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normalization offsets the effect of secondary changes, such as creep due to the smallnormal force, on the measured value of G*. The evidence of the healing that occursat the interface of the two bitumen specimens is clearly visible upon the removal ofthe specimens after the test (Figure 2c).

Figure 2. Illustration of the test method to obtain parameters for the healingfunction using a DSR

At this point, it is necessary to briefly comment on the relevance of theaforementioned test protocol to the healing frame work described in Section 3.0.Healing between two bitumen surfaces in contact with each other is modeled by theconvolution (Equation [1]) of wetting (Equation [3]) and healing or strength gainover time (Equation [5]). The objective of this test method is to obtain the healingfunction described in Equation [5]. By bringing the two bitumen surfaces in intimatecontact with each other within a short duration of time, the condition ofinstantaneous wetting is achieved. In this case, the wetting distribution functionreduces to a Dirac-delta function:

( ) ( )τδττφ

=d

d[6]

As a result, the healing function in Equation [1] reduces to the following form:

( )tRR h= [7]

a) Two bitumen specimensaffixed to the two end platesof the DSR.

b) Bitumen specimen afterbeing brought into contact witheach other to measure changein composite G* over time.

c) Separation of the testspecimens after completionof the test.

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In other words, the macroscopic healing function measured over time can be usedto obtain the healing function. The procedure assumes that the inter diffusion thatoccurs during the first minute of the test is minimal and is accommodated in theinstantaneous healing parameter of the healing function. This assumption may not bevalid if the test is conducted at elevated temperatures that entail significant interdiffusion within short time periods.

Also note that the bitumen specimens were prepared by pouring liquid binderand gradually allowing it to cool at room temperature. This process ensures that thesurfaces of the bitumen that come into contact with each other are smooth and freefrom any irregularities to facilitate immediate wetting. G* was measured at lowstrain amplitudes and for a small number of cycles to avoid significant disruption ofthe healing process at the interface. Although, the normal force that was utilizedthroughout the test was small (0.4 N) it is likely to have some influence on the rateof healing. The authors are currently refining the test procedure to obtain similarmeasurements at close to 0 normal load.

The amount of healing measured using this test method was then used inEquation [5] to obtain the healing function parameters 0R , p, q, and r. Theparameters were determined using an optimization procedure to obtain a leastsquares error solution using Matlab© software. Figure 3 and Table 3 present theresults from these measurements.

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Time (minutes)

Heal

ing,

R (%

)

AAD data AAD Equation-5AAM data AAM Equation-5ABD data ABD Equation-5

Figure 3. Healing function for selected bitumen obtained using the DSR data

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Table 3. Parameters for the healing function

Bitumen 0R p* q r

AAD 39 60 2.E-03 1.73AAM 55 66 7.E-05 2.01ABD 60 1728 1.E-03 0.69

Note: p* denotes asymptotic or final healing at infinite time. Longer durations of healing andmore data points are required to make robust estimates for this term, as currently beingpursued by the authors.

5. Effect of healing on fatigue life

The most apparent impact of healing of bitumen is the extension of fatiguecracking life of asphalt mixtures. A common approach to quantify the propensity ofdifferent types of asphalt mixtures to heal is by comparing the fatigue cracking lifeof the mixture with and without the opportunity to heal or to compare the rate ofaccumulation of dissipated pseudo strain energy before and after rest periods. It isimportant to reiterate the distinction between measurement of material propertiesrelated to healing (as discussed earlier in Section 4) and quantifying healing basedon the results of a laboratory based fatigue test. The aim of the former is todetermine intrinsic properties by which to quantify the healing characteristics ofdifferent bitumens. By definition, these properties are largely independent of the testmethod or geometry used to determine these properties. Intrinsic material propertiescan be used to make a general assessment of the healing character for different typesof bitumens. They can also be used to predict the magnitude of healing that occursunder a given laboratory test or field condition. In contrast, the magnitude of healingquantified using fatigue tests is restricted by the test method and geometry used toconduct the test.

In this section, healing is quantified by conducting fatigue cracking tests on thefine aggregate matrix (FAM) portion of asphalt mixtures with and without restperiod. Results shown in this section will be used to compare the tendency of theseFAMs to heal, and this healing potential or tendency will be compared to thematerial properties measured in Section 4.

5.1. Characterization of fatigue cracking using the DMA

Fatigue cracking and healing in asphalt mixtures is a process that is concentratedmostly in the bitumen – fine aggregate phase (asphalt binder + material passing theNo. 16 or 1.18 mm sieve) of the mixture. Initiation and growth of cracks in the fineaggregate matrix (FAM) depends on several material properties such as the creep

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compliance characteristics of the mix and work of cohesion of the bitumen. Previousstudies have demonstrated that the Dynamic Mechanical Analysis (DMA) is aneffective tool by which to characterize the fatigue cracking and healing in the FAMportion of asphalt mixtures (Kim and Little 2005; Kim et al., 2003c; Masad et al.,2007).

The cylindrical FAM test specimen comprised of the bitumen mixed with fineaggregate (material smaller than 1.18 mm in nominal diameter). The aggregates andthe bitumen were mixed at the specified mixing and compaction temperature using amechanical mixer. After short term aging for two hours, the mix was compactedusing a 152 mm diameter mold under the Superpave gyratory compactor to a heightof 75 mm and target air void content of 13%. The compacted samples were allowedto cool to room temperature. Each side of the compacted sample (top and bottom)was trimmed to obtain a sample height of 50 mm. Approximately 30 FAM testspecimens of 12.5 mm diameter were obtained by coring the 152 mm diametercompacted sample. The air void content of the test specimens was ensured to bewithin 13±1 percent.

Figure 4. Illustration of the DMA test conducted on a fine aggregate matrixspecimen to determine fatigue and healing characteristics

The DMA test was conducted by fixing one end of the mastic specimen andapplying a torsional shear at the other end. A strain amplitude of 0.2 percent wasapplied using a sinusoidal wave form at 10 Hz until specimen failure occurred. Thestress response along with the shear modulus, G*, and phase angle, (φ) werecontinuously recorded throughout the test. Figure 4 illustrates the DMA test setupalong with the type of loading applied for a constant stain amplitude test.

Time

Cyclic Torsion γ0

γ

50 mm height, 12.5 mm diameter fine aggregate matrix test specimen subjected to cyclic torsion

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The fatigue life of the FAM specimen was quantified using two parameters:i) number of load cycles for physical failure of the specimen (Nf), and ii) the rate ofaccumulation of damage (b). The latter parameter was preferred over the formerbecause of its lower variability. The parameter, b, is used in the relationship that wasfound to best describe the change in dissipated pseudo strain energy, WR, withnumber of load cycles, N, from experimental data:

( )NbaWR ln+= [8]

The dissipated pseudo strain energy at any given load cycle i, WR,i, wasdetermined from the area within in the stress – pseudo strain hysteresis loop for anygiven cycle as follows:

( )120

*, sin φφγπ −= iiiR GW [9]

In Equation [9], *iG is the stiffness at the ith load cycle, iφ and 1φ are phase

angles for the ith and 1st load cycles, and 0γ is the applied shear strain amplitude. Alower value of the parameter b obtained using Equations [8] and [9] indicates alower rate of crack propagation and better fatigue cracking resistance.

Details pertaining to the background and adequacy of the parameters discussedabove, as well the methodology used in preparing test specimens, conducting tests,and analyzing data using the DMA are described in other publications (Kim andLittle 2005; Kim et al., 2003a; Masad et al., 2006; Masad et al., 2007; Zollinger,2005).

5.2. Using the DMA to quantify healing

In order to quantify healing for different materials, nine rest periods of fourminutes each during the cyclic test were introduced. The rest periods wereintroduced after cycles that correspond to 2.5, 5, 10, 15, 20, 25, 30, 40,and 50 percent of the fatigue life value for that particular material measured withoutany rest period. When rest periods were applied, the parameter, b, was computed byfitting Equation [6] to the relationship between dissipated pseudo strain energymeasured immediately after the rest period to the corresponding number of loadcycles to failure. The b value determined without rest period was then compared tothe b value determined with rest periods. A relative decrease in the parameter, b, whichwould be associated with positive healing, was then used to quantify the healingpotential for each material. Further details of this methodology and typical results dueto incorporation of rest periods can be found in another publication (Little and Bhasin,2006). Table 4 presents the healing potential for the selected FAM comprising of threedifferent types of bitumen and two different types of aggregates.

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Table 4. Effect of healing during rest periods on the fatigue cracking life of fineaggregate matrix

Asphalt Aggregatefines

b-value(No rest)

b-value(10, rest periods)

% decrease inb-value

AAD 139 130 6%

AAM 281 210 25%RA

ABD 231 181 22%

AAD 202 195 3%

AAM 291 199 32%RL

ABD 313 174 44%

6. Discussion of results

6.1. Work of cohesion vs. healing function

As discussed previously, the parameter Ro in Equation [5] reflects the effect ofinstantaneous healing that is due to the interfacial cohesion between the cracksurfaces. Figure 5 compares the values of Ro and the work of cohesion, Wc for theselected bitumen. As expected, the magnitude of the parameter Ro for the threebitumen follows the same order as the work of cohesion or surface free energydetermined using the Wilhelmy plate method. Although the data are limited, theysupports the consistency of the analytical frame work and test methods used toobtain the material properties related to healing.

AAD38

AAD39

AAM50

AAM55

ABD65 ABD

60

Wc(ergs/ cm2) Ro (%)

Figure 5. Surface free energy vs. parameter for instantaneous healing from DSRtests

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6.2. Work of cohesion and healing function vs. effect of healing on fatigue life

Equations [1], [3], and [5], constitute a comprehensive framework by which topredict the effect of healing on the fatigue cracking life of asphalt mixtures. Both thewetting and healing functions are required to accurately predict the magnitude ofhealing in the asphalt materials. Due to the limited scope of this study, only theparameters related to the healing function (Equation [5]) were determined. Notwithstanding this limitation, the healing function was used to determine the expectedlevel of healing for the selected bitumen for a healing period of 4 minutes. Thesevalues were then compared to the relative increase in the fatigue cracking life asmeasured on FAM specimens using the DMA. Figures 6 and 7 illustrate thesecomparisons. It is evident from these figures that for aggregate RL, the rank order ofthe mixes in terms of the effect of healing on fatigue cracking life was very similarto the order based on or predicted by the healing function. For aggregate RA, theimpact of healing on fatigue life was the smallest for bitumen AAD. This isconsistent with the prediction based on the healing function. The comparisons of theeffect of healing from the healing function for bitumen AAM and ABD withaggregate RA with the effect of healing on fatigue life as measured by the DMA isnot as clear. We expect that other parameters, which affect the healing function,should be considered, and this is consistent with the plan for refining the healingfunction though still using the same general convolution form.

AAD3

AAD40

AAM32

AAM55

ABD44

ABD65

% increase in fatigue crackingresistance (RL)

%H(t=4 min)Rh (4 min) (%)

Figure 6. Expected healing for wetted surfaces at 4 minutes vs. effect of healing onfatigue cracking life with 4 minute rest period for FAM with RL aggregate

The trends illustrated in Figures 6 and 7 provide reasonable interim support tocontinue the development of the approach developed and described in this paper.

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This is keeping in view that the effect of healing on fatigue cracking life is the netresult of the wetting function and intrinsic healing function, whereas in this caseonly the latter was considered for comparison.

AAD6

AAD40

AAM25

AAM55

ABD22

ABD65

% increase in fatigue crackingresistance (RA)

%H(t=4 min)Rh (4 min) (%)

Figure 7. Expected healing for wetted surfaces at 4 minutes vs. effect of healing onfatigue cracking life with 4 minute rest period for FAM with RA aggregate

An observation from Figure 3 is enlightening. Bitumen AAD, which has thelowest molecular weight of the three bitumen also has the lowest cohesive strengthor bond strength of the three. The latter observation is consistent with the poor initialhealing of AAD, which is ostensibly due to poor wetting. However, over time AADbecomes a better healer, perhaps because of the greater mobility of the smallermolecules.

7. Conclusions

A framework to quantify the effect of healing based on the work of Schapery(1989) and Wool and O’Connor (1981) was developed and presented in this paper.This framework is based on the convolution of two important processes related tohealing. These two processes are represented by the wetting function and the healingfunction.

The wetting function depends on the creep compliance properties of the material,Poisson’s ratio, and intrinsic material properties such as work of cohesion, length ofthe healing process zone, and bonding tensile stresses. The mechanical and creepcompliance properties can easily be measured using laboratory tests. The work ofcohesion can be determined from surface free energy measurements of the bitumen.The authors are currently investigating methods by which to quantify or measure the

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remaining two parameters in the wetting function, i.e., length of the healing processzone and the tensile bonding stresses.

The healing function is comprised of two components: strength gain due toinstantaneous cohesion between the wetted crack faces and strength gain over timedue to inter diffusion of molecules between crack faces. A simple and new testmethod using the DSR was developed to determine the parameters for the healingfunction. The authors are refining this test method as well as investigating othermethods that may be used to determine parameters related to the healing function.

Based on the theory used to develop the healing framework, the parametersrelated to the instantaneous strength gain in the healing function for differentbitumen are expected to follow the same trend as the work of cohesion. This wasindeed shown to be true by comparing the measurements made with the DSR to thesurface free energy measurements of the selected bitumen.

The healing function determined using the DSR test method was used to predictthe effect of healing on the performance of different bitumen. These predictionsshow a reasonable correlation with the relative increase in the fatigue cracking lifedue to the introduction of rest periods. A much better correlation is possible whenthe wetting distribution function is considered in addition to the healing function in aconvolution form as expressed by Equation [1]. The authors believe that the resultsreported in this paper provide an interim validation that warrants further work indeveloping this methodology.

The authors would like to thank Dr. Robert Lytton of Texas A&M University forhis guidance and continued motivation to develop methodologies based onfundamental material properties by which to characterize healing. The authors wouldalso like to acknowledge the Federal Highway Administration (FHWA) of USA forfunding this research under the Asphalt Research Consortium.

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and Paving Mixes”, SHRP-A-357, Strategic Highway Research Program, NationalResearch Council, Washington D.C., 1993.

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A Framework to Quantify the Effect of Healing in Bituminous Materials using Material Properties

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Transcript of A Framework to Quantify the Effect of Healing in Bituminous Materials using Material Properties