Construction and Building Materials 25 (2011) 4079–4087

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Construction and Building Materials

journal homepage: www.elsevier .com/locate /conbui ldmat

Three dimensional distribution of the mastic in asphalt composites

Amit Bhasin ⇑, Anoosha Izadi, Swapneel BedgakerThe University of Texas at Austin, Austin, TX 78717, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 10 November 2010Received in revised form 1 April 2011Accepted 14 April 2011Available online 6 May 2011

Keywords:Asphalt mixturesX-ray CTMicrostructure

0950-0618/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.conbuildmat.2011.04.046

⇑ Corresponding author.E-mail addresses: a-bhasin@mail.utexas.edu (A. Bh

(A. Izadi), bedagkarswap@gmail.com (S. Bedgaker).

The microstructure of the fine aggregate matrix has a significant influence on the mechanical propertiesand evolution of damage in an asphalt mixture. This paper presents the findings from a study conductedto identify a quantitative method to characterize the three-dimensional microstructure of the matrix inan asphalt mixture. The influence of binder content, coarse aggregate gradation, and fine aggregategradation on the microstructure of the matrix was also investigated. Results indicate that for a givenaggregate type, binder content and aggregate gradation influence the degree of anisotropy whereasgradation of the coarse aggregate has the most influence on the direction of anisotropy of the asphaltmastic. Addition of asphalt binder or adjustments to the fine aggregate gradation also resulted in a moreuniform spatial distribution of the asphalt mastic.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Motivation

Mechanical tests under controlled laboratory conditions aretypically performed to quantify the resistance of asphalt mixturesto distresses such as fatigue cracking (e.g., beam fatigue test). Theadvantage of this approach is that candidate mixtures can beranked based on a direct measure of laboratory performance. How-ever, this holistic approach does not provide information that canbe used to explain why certain mixtures perform better than oth-ers. To alleviate some of these shortcomings, several research stud-ies have investigated the properties and performance of asphaltmixtures at multiple length scales. For example, properties of theconstituent materials (e.g., binder, aggregate, and fines) are evalu-ated in order to quantify their contribution to the properties of themixture. Properties of mastics (fines mixed with asphalt binder)are evaluated to understand filler-binder interactions. Evaluationof sand-asphalt mortars or the fine aggregate matrix providesinformation on the evolution of damage, role of fines to arrest crackgrowth, and moisture damage. In addition to the material proper-ties, the internal structure of the asphalt mixture strongly influ-ences its mechanical properties and performance.

There is significant literature on the spatial distribution of aggre-gates in an asphalt mixture. However, most of this work is limited tothe distribution of coarse aggregate particles or air voids. Althoughthe spatial distribution of aggregates indirectly reflects the micro-structure of the asphalt matrix, there is very little work done to

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asin), aizadi@mail.utexas.edu

directly characterize the microstructure of the matrix at higher res-olutions. This is especially important because evolution of damagesuch as fatigue crack growth is concentrated in the matrix thatholds the aggregates together. By quantifying the microstructureof the matrix and its relationship to mixture properties one can bet-ter explain the stress-state and damage evolution within the as-phalt mixture. This paper presents the findings from a studyconducted to establish a quantitative method to characterize thethree-dimensional microstructure of the matrix within the asphaltmixture.

1.2. Definitions and scope

The term internal structure refers to the content and spatial dis-tribution of asphalt, aggregates and air-voids [13]. Thus, the inter-nal structure of the mixture is dictated by the proportions andproperties of its constituent materials and method of compaction.In the context of this paper, the term mastic refers to the asphaltbinder mixed with fines (aggregates that pass a 75 lm sieve).The term matrix refers to the mastic combined with fine aggregateparticles (aggregates that pass a 1.2 mm sieve) that hold the coarseaggregates together as a composite. The objective of this paper is toquantify the microstructure of the matrix, i.e., the spatial distribu-tion of the mastic within the matrix. Although the methodologydiscussed in this paper is applied to characterize the internalmicrostructure of the asphalt matrix, it can also be used to charac-terize the three-dimensional microstructure of any component inthe mixture (e.g., air voids, aggregates, mortar).

Section 2 of this paper presents the relevant background on theimportance of characterizing the internal structure of a compositeas well as on the metrics that can be used to quantify the internalstructure of a selected component within the composite. Section 3

4080 A. Bhasin et al. / Construction and Building Materials 25 (2011) 4079–4087

presents a description of the materials and methods used to obtainthree-dimensional digital images of the selected asphalt mixtures.Section 4 presents the analysis conducted on these images to quan-tify the internal microstructure of the asphalt matrix. Section5 presents the conclusion drawn from these analyses withdiscussion.

2. Background

2.1. Influence of internal structure on properties of the composite

The relationship of internal microstructure and mechanicalproperties has been long recognized and used for materials otherthan asphalt mixtures. For example, according to Ryan and Ket-cham [21] the relationship between the trabecular bone morphol-ogy and skeletal loads was first investigated in 1867. Cowin [2]investigated the relationship between the stiffness tensor of a tra-becular bone to its ‘‘fabric’’. He introduced the term fabric as ameasure of the local anisotropy of a material’s microstructure.Duxson et al. [3] demonstrated a correlation between mechanicalstrength and Young’s modulus of geopolymers and theirmicrostructure.

The internal structure of an asphalt mixture has a significantinfluence on its mechanical properties and resistance to major dis-tresses including rutting, fatigue cracking, thermal cracking andlow temperature cracking. Most mixture design methods recognizethe importance of internal microstructure by imposing require-ments for aggregate size, gradation, shape, volumetrics and limitson density during compaction [15].

Several researchers have used imaging tools and analysis toinvestigate the influence of internal microstructure on the engi-neering properties and performance of asphalt mixtures. For exam-ple, Yue et al. [29] used image analysis to quantify anisotropy in anasphalt mixture based on the orientation of aggregates. Directionaldistribution of aggregates was quantified based on the ratio ofaverage area per aggregate in horizontal sections to the averagearea per aggregate in vertical sections. Wang et al. [25] demon-strated that field cores with similar volumetric properties exhib-ited different internal microstructure that correlated better withthe observed field performance. They measured the void content,void distribution, and mean solid path on sectional imagesobtained using X-ray tomography. Masad et al. [17] and Tashmanet al. [23] used two dimensional image analysis to quantify aggre-gate distribution on cut sections of asphalt mixtures to determinethe level of anisotropy. They then used this as one of the modelparameters to improve the predictions of viscoplastic deformationin asphalt concrete mixtures. Arambula et al. [1] demonstratedthat the aggregate gradation and compaction effort influence thesize and distribution of air voids within an asphalt mixture. Thesize and distribution of air voids were shown to have a stronginfluence on the rate of moisture damage in the asphalt mixtures.Kutay et al. [11] and Kutay and Aydilek [10] also used image anal-ysis to evaluate the distribution of voids and interconnected voidswithin an asphalt mixture. They used 19 velocity vectors tocomputationally characterize the three-dimensional flow withindifferent asphalt mixtures and compared the results to experimen-tal data.

Image analysis has also been used to investigate the influence ofcompaction on the internal microstructure of asphalt mixtures. Forexample, Masad et al. [16] used X-ray tomography to establish therelationship between aggregate orientation, aggregate gradation,air void distribution and the compaction effort. They determinedthe aggregate and air void distributions by measuring the areaon two-dimensional sectional images obtained using X-ray tomog-raphy. Since the measurements were not in 3D, they had to use

Monte-Carlo simulations to correct for the bias while comparingmeasurements from 2D sections to actual aggregate gradations.In another study, Masad et al. [16] quantified the internal structureof the asphalt mixtures in terms of the aggregate orientation,points of contact and distribution of air voids. These characteristicswere compared for mixtures compacted using the SGC and the lin-ear kneading compactor (LKC). The erosion operation techniquewas used to determine the number of contact points. Hunteret al. [6] investigated the change in the internal microstructureof asphalt mixtures as influenced by the method of compaction.Radial and circumferential particle alignment and area of particlesin fixed radial quadrants were used to examine variations in aggre-gate orientation and distribution within the asphalt mixture.

While the aforementioned studies have recognized the impor-tance of microstructure of the binder, very little work has beendone to directly quantify its distribution in the mix. For example,in 1930s Hveem introduced the concept of film thickness to designasphalt mixtures. The methods used to calculate the film thickness(that would result in optimal performance of the mixture) wereapproximate and relied on several unrealistic assumptions. Morerecently, Elseifi et al. [4] used reflective light microscopy and scan-ning electron microscopy to demonstrate that a uniform film coat-ing the aggregates did not actually exist in the asphalt mix. Theydemonstrated that film thickness varied greatly within the samespecimen and around the same aggregate. They also reported thatmineral fillers and finer aggregates were embedded in the asphaltbinder such that the behavior of the binder itself may not be ascritical as the behavior of the mastic.

In summary, distribution of air voids, solid path between airvoids, orientation and points of contacts between coarse aggre-gates were typically used as the metrics to describe the internalmicrostructure of asphalt mixtures. In most cases, these metricswere obtained using individual 2D sectional images of a mixturespecimen. Three-dimensional techniques, such as those reportedby Kutay et al. [11] and Kutay and Aydilek [10] were applied tocharacterize fluid flow using limited number of velocity vectorswithin air voids. However, to the best of the authors knowledge,there is very little work done to directly characterize the threedimensional distribution of the matrix that holds the aggregateparticles together. This is especially important to understand thestate of stress and evolution of damage in the matrix. The method-ology presented in this paper attempts to overcome some of theseshortcomings.

2.2. Image analysis

This section presents a brief background on the methods usedto acquire, process and analyze images to characterize the internalmicrostructure of the asphalt mixture. The internal microstructureof a mixture is characterized using two-dimensional (2D) or three-dimensional images (3D) of the composite. Digital cameras can beused to acquire 2D image of a cross-section or a series of images forcross-sections that are obtained by physically dissecting the spec-imen into several slices. An alternative approach is to use non-destructive techniques such as 3D X-ray computed tomography(CT) that provide a stack of 2D images for a volume of interest atvarying resolutions. The latter was used in this study.

The acquired digital images must be processed prior to use forany kind of analysis. Image processing involves steps such asreduction of noise and thresholding. Thresholding involves conver-sion of a gray scale image to a binary or trinary image, that reflectthe two or three different components of interest in the asphaltmixture. Median filtering and thresholding based on known volu-metric properties have been frequently used to process imagesof asphalt mixtures [26,28,30]. Russ [20] presents a detaileddescription of several of algorithms that can be used to remove

A. Bhasin et al. / Construction and Building Materials 25 (2011) 4079–4087 4081

noise from digital images and distinguish between individualparticles.

Image analysis entails the use of processed images to character-ize the internal structure of the composite. A continuous quantitythat varies with orientation can be used to quantify the orientationand distribution of material objects or entities within a composite.Examples of such quantities that have typically been used in theliterature are mean intercept length (MIL), chord length, starlength, and star volume.

One of the simplest direction dependent quantities that can beused to characterize the microstructure of a two-component com-posite is the mean intercept length (MIL) [5]. The MIL along a direc-tion is obtained as follows: grid lines are drawn at specific intervalson an image of a two-component composite. The intersectionsbetween the grid lines and the interface of the two-componentsare counted. The mean intercept length is then defined as the totallength L of the line grid divided by the number of intersections(Fig. 1). The MIL can be obtained along several different directions.A drawback of the MIL is that it determines the orientation of theinterface rather than the material itself and it may underestimatethe anisotropy of the material. An alternative and similar approachis the chord length density distribution. The chord length distribu-tion along a direction is obtained as follows: grid lines are drawnon an image of the two-component composite and lengths ofchords between the intersections of grid lines are measured(Fig. 1). The chord length distribution (CLD) function p(z) indicatesthat the probability of finding a chord of length between z andz + dz is p(z)dz [24].

Two additional direction dependent quantities are the StarLength Distribution (SLD) and Star Volume Distribution (SVD)[19]. The star length distribution is calculated by randomly select-ing several points in the material of interest within the compositeand measuring the length of lines emanating from these points invarious directions until the lines encounter a boundary. By doingso, the distribution of the material of interest is obtained. The ori-entations along which the lines emanate from the points are typi-cally pre-defined by selecting a homogeneous distribution ofpoints on a unit sphere. Increasing the number of points reducesthe uncertainty and is more efficient than increasing the numberof orientations. The average star length along any given orientationis computed as:

Sw ¼1n

Xn

i¼1

Li ð1Þ

where L is the length of measured intercept through point i at ori-entation w and n is the number of points. The SLD can be obtained

Fig. 1. Schematic of MIL measurements in two dimensions in a two componentcomposite.

for any single material that is of interest within a multi-componentcomposite. Fig. 2 illustrates the measurement of SLD at four pointsin two dimensions (in practice the measurements are carried out inthree dimensions). The Star Volume Distribution (SVD) is similar toSLD with the only difference that instead of the length of a straightline along a particular direction, the volume of a cone emanatingfrom a point in a predefined orientation is measured. The averagestar volume along any given orientation is computed as:

Uw ¼p3n

Xn

i¼1

L3i ð2Þ

where L and n are as described before. The difference between SVDand SLD is that SVD tends to amplify the differences between majorand minor components, enhancing the effect of anisotropy. For amore detailed description of these two methods, the readers are re-ferred to Odgaard [18].

The aforementioned parameters (MIL, CLD, SLD, and SVD) pro-vide the distribution and mean of a characteristic quantity alongdifferent orientations in a composite. A 2D or 3D rose diagram ofthe mean of any one of these characteristics along different orien-tations provides an excellent visual representation of the internalmicrostructure. However, it is also important to use this informa-tion to quantitatively derive parameters that relate to the mechan-ical properties of the composite. One such parameter, that will beused later to characterize the microstructure of the asphalt mastic,is the fabric tensor based on the moment of inertia. Consider thatthe star lengths are measured at n points along w orientations toproduce a data set of N vectors represented by ai, where i = 1 to N.

ai ¼axi

ayi

azi

264

375 ð3Þ

Watson [27] proposed that the orientation matrix or fabric tensorfor this data are mathematically obtained as follows:

T ¼XN

i¼1

aiaTi ¼

PNi¼1a2

xi

PNi¼1

axiayiPN

i¼1axiazi

PNi¼1axiayi

PNi¼1a2

yi

PNi¼1ayiazi

PNi¼1axiazi

PNi¼1ayiazi

PNi¼1a2

zi

266664

377775

ð4Þ

The orientation matrix or fabric tensor T has three eigenvaluess1 > s2 > s3 and corresponding eigen vectors u1, u2, u3 [27,8]. Forany axis represented by vector u, the moment of inertia I(u) is givenby Eq. (5).

Fig. 2. Schematic of SLD measurements in two dimensions in a two componentcomposite.

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IðuÞ ¼XN

i¼i

jaij2 � uT Tu ð5Þ

Finally, the eigen vectors u1 and u3 also represent the direction vec-tors along which the moment of inertia is minimized and maxi-mized, respectively. The eigen vectors can be used to deriveparameters that reflect the properties of the composite. For exam-ple, the degree of anisotropy can be computed as s1=s3 and elonga-tion index as 1� ðs2=s1Þ [8]. For this research metrics based on theSLD, i.e., the fabric tensor and the degree of anisotropy were used tocompare the microstructure of different asphalt mixtures.

3. Materials, data collection and processing

3.1. Selection of materials and specimen fabrication

The primary objective of this study was to identify metrics thatcan be used to quantify the shape characteristics and variability inthe structure of the mastic in an asphalt mixture. To achieve theobjective of this study, a typical dense graded asphalt mixturewas selected. Three additional variations of this mixture were pro-duced in the laboratory by changing the binder content, coarseaggregate gradation, and fine aggregate gradation to produce atotal of four different mixtures. The four mix designs were labeledas control, high binder, coarse adjusted, and fine adjusted. The aggre-gate used in all mixtures was a limestone.

Fig. 3 shows the gradation and binder content for these fourmixtures. The gradation limits are based on specifications followedby the Texas Department of Transportation (TxDOT), USA, for TypeC mixtures and all variations of the control mix were designed tobe within these limits. The control mix had 4.2% binder contentby weight of aggregates, and the high binder mix had 4.7% bindercontent but the same aggregate gradation as the control mix. Thecoarse adjusted mix had the same binder content and fine aggregate(passing #16 sieve) gradation as the control mix but the gradationof the coarser aggregates (retained on #16 sieve) was modified.Similarly, the fine adjusted mix had the same binder content andcoarse aggregate gradation as the control mix but the fine aggre-gate gradation was modified. The control and the coarse adjustedmix had approximately 11.5% mastic by volume in the mix. Simi-larly, the fine adjusted and high binder mix had approximately13% and 15.5% mastic by volume, respectively.

It is important to emphasize that in terms of the composition,the only difference between the control and other mixes was eitherthe binder content or the gradation. The rationale for selectingthese four mixtures was not to establish a correlation betweenthe micro structure of the mastic and mixture characteristics(although this is the eventual long term goal). Rather, these fourmixtures were selected to evaluate whether or not the metricsused to quantify the mastic micro structure are sensitive tochanges in mixture characteristics.

The maximum specimen size that can be used with the threedimensional X-ray CT scanner is dictated by the resolution re-quired for micro structure characterization. A resolution in therange of 15 lm per voxel was considered as appropriate for thisstudy. At this resolution, combined with the use of median filter(discussed in the following section), it is possible to detect and dif-ferentiate features that are of 75 lm or more in size. This is also themaximum size of the particles in the mastic. A cylindrical speci-men approximately 12.5 mm in diameter was considered as appro-priate to achieve this resolution. Asphalt mixture specimens thatwere 150 mm in diameter and 100 mm in height were compactedfor each of the four different mixtures using the Superpavegyratory compactor (SGC). The ends of the SGC compacted speci-men were cut using a diamond blade saw to achieve a finished

specimen height of two inches. A diamond coring bit was used tocore approximately ten specimens that were 12.5 mm in diameterand 50 mm in height. Two specimens cored from the SGC com-pacted specimen for each type of mixture were selected for X-rayCT scanning. The two cored specimen were selected such that theyhad similar air void content as compared to the average air voidcontent of the SGC compacted specimen.

3.2. Scanning and image processing

The finished specimens were used to obtain high resolution sec-tional images for a volume of interest. The scanning was performedat the high-resolution X-ray CT Facility at the University of Texas atAustin (UTCT). Ketcham and Carlson [9] provide a more detaileddescription of the principles of X-ray tomography and methodsused to acquire images and correct artifacts. In summary, high-resolution X-ray CT scanning (HRXCT) is based on the principlethat an X-ray fan beam (or cone beam) is directed at an object fromall orientations in a plane (or volume), and the decrease in X-rayintensity caused by passage through the object is measured by alinear array of detectors. The resulting data are then reconstructedto create cross-sections of the object. The gray scales in suchimages reflect the relative linear X-ray attenuation coefficient l,which is a function of density, atomic number, and X-ray energy.For this study, the energy source used was adjusted to 80 kV and10 W to obtain the best resolutions.

Each CT image is termed a ‘slice’, as it corresponds to what onewould see if the object were sliced along the scan plane. By gath-ering a stack of contiguous slices, data for a complete 3D volumecan be obtained. Each slice represents a finite thickness of material,corresponding to the thickness of the collimated X-ray beam anddetector array. Consequently, the pixels in CT images representvolume elements and are referred to as voxels [7]. A total of eightspecimens, two of each mixture type, were scanned using the HRXCT. A volume, approximately 15 mm � 15 mm � 8 mm, enclosingthe middle third of each specimen was scanned to obtain a totalof 562 images each with a resolution of 1024 � 1024 pixels.Fig. 4 shows a typical image of the specimen for the control mix.

As described before, all images acquired using the HRXCT mustbe processed before conducting any kind of analysis. The twodimensional slice images were cropped to a size of 512 � 512 pix-els to obtain the region of interest and remove any unwanted infor-mation from the edges. A median filter was found to be mostsuitable to remove noise while preserving the details in the image.This was also the most preferred technique reported in the litera-ture discussed in the previous section.

A typical mixture composite can be broken down into threecomponents – aggregates, mastic, and air. The objective of thethresholding operation was to identify two pixel intensity valuesin the gray scale image that differentiate between these three com-ponents. The volumetric properties (volume of air void and volumeof mastic) of each specimen were determined. An iterative processwas used to determine the two pixel intensity values that differen-tiated between air voids, mastic, and the aggregates for a stack of520 images that represent a volume of the specimen. The iterationswere designed to minimize the difference between the volumepercent of air voids and mastic computed using the stack of imagesto the values obtained experimentally. This procedure was similarto the procedure reported by Zelelew et al. [30]. The thresholdswere defined when the computed volume of the mastic and airvoids were within a certain tolerance of the known volumes forthe mixtures. The final set of images had air represented by blackpixels (pixel value 0), mastic represented by gray (pixel value150) and aggregate represented by white (pixel value 255).

Fig. 3. Gradations for the four different mixtures.

A. Bhasin et al. / Construction and Building Materials 25 (2011) 4079–4087 4083

4. Analysis and results

4.1. Spatial distribution of mastic

The Quant3D program originally developed by Ketcham andco-workers was used to analyze images and obtain the SLD ofthe mastic [7]. The Quant3D program uses the processed imagesas an input and computes the SLD (or SVD), fabric tensor, eigen val-ues and eigen vectors for the component of interest. The SLD pro-vides the average length of the component of interest (for specifiednumber of points) along different orientations.

For each specimen 512 processed slice images were uploaded. Apixel value of 150 that was assigned to the mastic during

thresholding was selected to obtain the SLD. A total of 513 orienta-tions that represent a uniform distribution on a sphere were se-lected and 1000 points were randomly selected in the mastic tomake these measurements. Selection of too many points resultsin very long computing time. In contrast, selection of too fewpoints will not provide meaningful distributions.

Fig. 5 illustrates the typical three dimensional rose diagram forthe SLD as generated by the Quant3D program. The average SLD isused to compute the fabric tensor using Eq. (4). The eigen vectorand eigen values for this fabric tensor are also computed. Recallthat the eigen vectors with the largest and smallest eigen valuesrepresent the direction vectors along which the moment of inertiais minimized and maximized, respectively. In addition, the ratio of

Fig. 4. Typical specimen used for high resolution X-ray CT scanning along with atypical slice image.

Table 1Typical results from Quant3D for SLD analysis.

Parameter Value

Fabric tensor based on SLD 0:351 0:006 �0:00080:006 0:344 �0:0006�0:0008 �0:0006 0:3042

24

35

Eigen vectors 0:8635 0:5040 �0:0191½ �0:5042 �0:8636 0:0036½ ��0:0147 �0:0128 �0:9998½ �

Eigenvalues 0.35510.34070.3042

Degree of anisotropy 1.1672

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the maximum to the minimum eigen values is a measure of the de-gree of anisotropy. Table 1 lists the fabric tensor, eigenvalues, andeigen vectors based on a typical SLD analysis.

Fig. 6. Typical Weibull distribution for the star length along a given orientation.

4.2. Variability in the distribution of the mastic

The Quant3D program was modified to provide star lengths ateach one of the 1000 points along the 513 directions used in thisstudy. A frequency histogram of the star lengths along each direc-tion was plotted. It was found that the Weibull distribution was areasonably good representation of the distribution of star lengthsalong any given direction. The Weibull distribution has two param-eters, shape and scale, that can be varied to fit a wide variety ofobserved data. The Matlab program was used to obtain the

Fig. 5. Typical SLD rose diagram reported by the Quant3D program.

Fig. 7. Typical 3D rose diagram for the coefficient of variation in star lengths alongdifferent orientations.

Fig. 8. Average SLD of the mastic in the

A. Bhasin et al. / Construction and Building Materials 25 (2011) 4079–4087 4085

parameters for the Weibull distribution using the 1000 pointsalong each one of the 513 directions. Fig. 6 illustrates the typicalfit to the Weibull distribution that was obtained using Matlabalong one of the 513 directions. The shape and scale parametersfor the Weibull distribution were then used to compute the stan-dard deviation and coefficient of variation of the star length alongeach direction.

The coefficient of variation along different directions were usedto plot a three dimensional rose diagram to assess whether or notany particular direction was more susceptible to variability thanothers (Fig. 7). This is similar to the rose diagram for the star lengthdistribution, with the difference that the coefficient of variationwas used to plot the three dimensional rose diagram. In addition,an average coefficient of variation was also computed for all the512 directions to be used as a metric to compare the variabilityof the microstructure between different mixture types.

4.3. Results

The X-ray CT images of two specimens for each of the four mix-tures illustrated in Fig. 3 were processed and analyzed to obtain

four mixtures used in this study.

Fig. 9. Typical 3D rose diagram for the coefficient of variation illustrating the orientation of the preferred direction.

Table 2Summary of results based on star length analysis of the matrix.

Mix type Degree ofanisotropy

Average star length inpreferred direction (mm)

Average of standarddeviations of star length⁄

Average of coefficientof variations of star lengths (%)⁄

Orientation of thepreferred direction (�)

Control mix 1.20 0.34 0.29 105 0.6High binder 1.28 0.17 0.12 81 3.8Fine adjusted 1.15 0.21 0.15 80 6.9Coarse adjusted 1.31 0.35 0.29 112 42.8

⁄ The standard deviation (or coefficient of variation) along each of the 512 directions was obtained and the value reported in the table is the average of these values.

4086 A. Bhasin et al. / Construction and Building Materials 25 (2011) 4079–4087

the information described in the aforementioned sections. Fig. 8compares the 3D rose diagram for the average star length for thefour different mixtures used in this study. The same color mapand scale is used in the four figures to allow for a direct visual com-parison of the influence of mixture properties on the average SLD.

The microstructure of the matrix for these four mixtures werecompared based on the following four metrics.

1. Degree of anisotropy: This is defined as the ratio of the maxi-mum to the minimum eigen values.

2. Average star length along the preferred direction: The preferreddirection is the principal direction that has the highest eigenvalue. It is also the direction along which the moment of inertiaof the geometry is minimized.

3. Average variation in the star lengths along all directions: Theanalysis was conducted by measuring the star lengths along513 orientations at 1000 points. The average of the 1000 starlengths along each direction is used to obtain the average threedimensional shape of the matrix. Similarly, the coefficient ofvariation along each of these 513 directions can be computedfor the 1000 points. Since the coefficient of variation along dif-ferent directions did not vary significantly, the average of thestandard deviations and average of the coefficient of variationalong the 513 directions were computed and compared for dif-ferent mixes. The high value for the average coefficient of vari-ation indicates high variability in the dimensions of the masticbetween the aggregate particles. This level of variability is notentirely unexpected in a composite such as an asphalt mixture.For example, the coefficient of variation in the void size basedon the distributions presented by Masad et al. [14] can beexpected to be about 80%. In addition, an increase in the volumeof the mastic (binder and/or fine aggregate) resulted in reduced

variability in the dimensions of the mastic between aggregateparticles. This suggests that higher volume fraction of the mas-tic may tend to make it more homogeneously distributed.

4. Orientation or preferred direction of the mastic: This refers tothe orientation of the eigen vector with the highest eigen valueor lowest moment of inertia. This is also the orientation alongwhich the maximum value of the star length is aligned. The ori-entation or plunge is the angle made by the vector that definesthe preferred direction to the plane perpendicular to the direc-tion of compaction (Fig. 9).

The results based on the above metrics are summarized inTable 2.

5. Conclusions and discussion

The following are some of the conclusions that can be drawnbased on the results presented in Table 2.

1. The asphalt binder matrix has some degree of anisotropy in allmixtures. Increasing the binder content while keeping all otherparameters constant increased the degree of anisotropy (con-trol mix versus high binder mix). Changing the gradation withinthe fine aggregate fraction of the mixture significantly reducedthe level of anisotropy (fine adjusted mix).

2. The average star length of the asphalt mastic in the fine aggre-gate matrix along the preferred orientation was similar for thecontrol and the coarse adjusted mix. This was expected, sincechanges in the coarse aggregate gradation should not have asignificant impact on the internal microstructure of the fineaggregate matrix. The average star length reduced significantlydue to the addition of asphalt binder (high binder mix). All

A. Bhasin et al. / Construction and Building Materials 25 (2011) 4079–4087 4087

other variables remaining constant, contrary to the findings,one would expect that the addition of asphalt binder shouldincrease the average star length as compared to the controlmixture. This apparent contradiction can be explained as fol-lows. The fine aggregate particles in mixtures with higher bin-der content are more likely to be homogeneously distributedresulting in a more dispersed mastic-fine aggregate matrix withrelatively smaller average size of the asphalt mastic. This expla-nation is supported by the reduced standard deviation and coef-ficient of variability in the star lengths for the mixtures withhigher binder content. A change in the fine aggregate gradationalso had a similar impact on SLD as the increase in binder con-tent. This is because similar to the increase in binder, anincrease in fines will also increase the total volume of the mas-tic. It is possible that, uniformly dispersed mastic with smalleraverage dimensions is more effective in crack pinning andhence resisting crack growth [22]. In addition, smaller dimen-sions of the mastic translate into greater confinement andimproved tensile strength [12]. This observation provides aplausible explanation for the improved fatigue cracking resis-tance typically observed with mixtures having higher bindercontent.

3. In most cases, the preferred direction of the asphalt mastic ordirection with the largest star length was perpendicular to thedirection of compaction. This indicates the possibility of com-paction induced anisotropy in addition to inherent anisotropythat may be due to the shape characteristics of the fine aggre-gate particles. For the mixture with the different coarse aggre-gate gradation (coarse adjusted mix), this orientation wasalmost 45� to the direction of compaction and significantly dif-ferent from other mixtures. This observation was consistentbased on the two different replicate specimens. This indicatesthat the coarse aggregate gradation may have a significantinfluence in dictating the direction of anisotropy.

4. Although all test specimens had gradations within the specifica-tion limits, they had widely different internal microstructures.The differences in the internal microstructure are expected toyield very different mechanical and damage characteristics.While the findings reported in this study are based on the useof a limited number of mixtures, the results indicate the impor-tance of understanding the relationship between aggregate gra-dation, internal microstructure, and performance.

In summary, this paper described the use of Star Length Distri-bution (SLD) and concomitant fabric tensor to characterize themicrostructure of the mastic in an asphalt mixture. The methodol-ogy was demonstrated to be sensitive to mixture properties suchas binder content and aggregate gradation. Further study usingthe proposed methodology can provide meaningful insight intothe spatial distribution of the mastic within the mixture, whichin turn dictates the stress-state and damage evolution in the mix(e.g., increase in fines or binder content resulted in smaller butmore homogenous distribution of the mastic). Finally, althoughthe SLD was used to characterize the distribution of the masticwithin the mixture, this technique can easily be extended to char-acterize the spatial distribution of air voids as well.

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