This article was downloaded by: [University of Windsor]On: 11 July 2014, At: 00:10Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Road Materials and Pavement DesignPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/trmp20

Investigation of size effect in asphaltmixture fracture testing at lowtemperatureEyoab Zegeye a , Jia-Liang Le a , Mugur Turos a & Mihai Marasteanua

a University of Minnesota, Department of Civil Engineering , 500Pillsbury Drive S.E, Minneapolis , MN , USAPublished online: 18 Apr 2012.

To cite this article: Eyoab Zegeye , Jia-Liang Le , Mugur Turos & Mihai Marasteanu (2012)Investigation of size effect in asphalt mixture fracture testing at low temperature, Road Materialsand Pavement Design, 13:sup1, 88-101, DOI: 10.1080/14680629.2012.657064

To link to this article: http://dx.doi.org/10.1080/14680629.2012.657064

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Road Materials and Pavement DesignVol. 13, No. S1, June 2012, 88–101

Investigation of size effect in asphalt mixture fracture testingat low temperature

Eyoab Zegeye*, Jia-Liang Le, Mugur Turos and Mihai Marasteanu

University of Minnesota, Department of Civil Engineering, 500 Pillsbury Drive S.E, Minneapolis, MN, USA

The Semi-Circular Bending (SCB) fracture test is commonly used to evaluate the lowtemperature fracture properties of asphalt mixtures. The present work investigates the presenceof a size effect in SCB fracture testing of asphalt mixtures. Un-notched and notched geomet-rically similar SCB specimens of various sizes are tested at −24◦C loaded by crack-mouthopening displacement (CMOD). The effect of specimen size on the nominal strength is inves-tigated through the well-established size effect theories and conclusions are drawn regardingthe fracture behaviour of mixtures at low temperature.

Keywords: semi-circular bending (SCB); asphalt mixture; size effect; nominal strength;fracture energy; fracture process zone

1. IntroductionLow-temperature cracking is the main distress in asphalt pavements built in cold regions. Asthe temperature drops to extreme values, significant tensile stresses develop in the upper lay-ers of the pavement structure, and ultimately lead to the initiation and propagation of cracks.Transverse cracks form at regular intervals on the pavement surface, and if left unrepaired, theygradually widen and allow water and moisture to penetrate into the entire pavement structure andaccelerate failure.

Finding a lasting solution for reducing or eliminating the occurrence of thermal cracking inasphalt pavements requires a good understanding of the fracture properties of paving materials.Traditionally, the indirect tensile test (IDT), AASHTO T 322 (2007), has been used to characterizeasphalt mixtures at low temperatures. However, the IDT does not provide fracture parametersthat can be related to the initiation and propagation of cracks in pavements. Recent studies haveshown that fracture-mechanics based tests and analyses are better suited to discriminate pavementmaterials with better resistance to thermal cracking (Li & Marasteanu, 2004; Marasteanu, Dai,Labuz, & Li, 2002; Mobasher, Mamlouk, & Lin, 1997; Molenaar & Molenaar, 2000; Wagoner,Buttlar, & Paulino, 2005a; 2005b). Among them, the semi-circular bending (SCB) test has gainedsubstantial attention due to its simplicity: the notched SCB specimen can be easily prepared fromstandard laboratory-compacted or field-cored asphalt mixture cylinders of diameter 150 mm.Depending on the orientation of the initial notch, the test can be used to study both mode I andmode II fracture (Chong & Kuruppu, 1988).

Asphalt mixtures behave as quasi-brittle materials at temperatures close to the glass transition ofthe component asphalt binder. A salient feature of structures that consist of quasi-brittle materials

*Corresponding author. Email: zegey001@umn.edu

ISSN 1468-0629 print/ISSN 2164-7402 online© 2012 Taylor & Francishttp://dx.doi.org/10.1080/14680629.2012.657064http://www.tandfonline.com

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

Road Materials and Pavement Design 89

is that there exists an intricate size effect on the structural strength. The existence of such sizeeffect is mainly attributed to the presence and the stable growth of a relatively large fractureprocess zone (FPZ) that develops ahead of the crack tip prior to failure (maximum load) of thestructure. This inelastic region is characterized by non-linear material deformation and fractureenergy dissipation (aggregate interlocking, inelastic deformation, micro-cracking, relaxation ofstresses etc.) that ultimately generate stress redistribution and govern the strain-softening of thematerial. Understanding this size effect is crucial for two purposes: (a) extrapolation of small-scalelaboratory testing results to full-scale design, and (b) identification of material fracture properties.

Researchers have argued that the length of the fracture ligament in a standard SCB specimen istoo short compared with the size of the FPZ that occurs near the crack tip (Wagoner et al., 2005b),and the test method does not fully satisfy the assumption of linear elastic fracture mechanics(LEFM). However, in the only study in which the FPZ was estimated using acoustic emission(AE) techniques (Li & Marasteanu, 2010), the authors concluded that in the SCB specimen thesize of FPZ ranges between 3–6 mm in width and 20–30 mm in length. Based on these findings,the length of SCB initial fracture ligament could be of concern.

The aim of the present work is to investigate the nature of failure observed in SCB fracture testsof asphalt mixtures tested at a low temperature. A set of geometrically similar SCB specimenswith a sufficiently large range of sizes were prepared in the laboratory and tested. The results wereanalyzed using the concept of size effect in quasi-brittle materials.

2. Review of size effect of quasi-brittle materialsThis section presents a brief summary of the size effect theories of quasi-brittle structures. Thereview is not intended to be all-inclusive, but rather introduce the notions used to analyze theresults of the present work. Further details can be found in (Bažant & Planas, 1998). So far, twotypes of size effects have been distinguished.

(1) Type I size effect: the structure attains its peak load when a macro-crack initiates from onerepresentative volume element (RVE), which often happens to structures with a smoothboundary, such as flexural failure of beam under bending and tensile fracture of bar underuniaxial tension. For small and medium size structures, the Type I size effect can be derivedbased on the Taylor series expansion of the energy release function at zero crack length.At large size limit, the size effect is governed by the Weibull statistics. The statisticalsize effect can be amalgamated with the energetic size effect to form the complete TypeI size effect (Bažant, 2005). Recent studies also showed that the Type I size effect can bealternatively derived from a finite weakest link model where the structure is statisticallyrepresented by a finite chain of RVEs and the probability distribution of RVE strength isderived from fracture mechanics of nano-cracks propagating by small, activation-energycontrolled, random jumps through a nano-structure (Bažant & Le, 2009; Le, Bažant &Bazant, 2011). The type I size effect can be expressed as:

σN = σ∞[(

Db

D

)r n/m

+ r Db

D

]1/r

(1)

where σN is the nominal strength and is given by P/bD or P/D2, respectively, for scalingin two or three dimensions; P = maximum applied load; D = characteristic size; b =thickness of the structure; m = Weibull modulus; n = scaling dimension; and σ∞, r, andDb are positive material constants. Db is an index parameter related to the effective lengthof the boundary layer.

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

90 E. Zegeye et al.

Figure 1. Type I and Type II size effect laws.

(2) Type II size effect: the maximum load of the structure is reached once a single large crackis formed. The Type II size effect is typically applied to quasi-brittle structures containinga large notch or a large stress-free (fatigued) crack formed prior to maximum load. Thissize effect can be derived by using the asymptotic approximation of the energy releasefunction or the J-integral for the propagating crack:

σN = Bf ′t

(1 + D

D0

)−1/2

(2)

where D0 represents a constant called transitional size; B is a dimensionless constantstructure-geometry dependent; f ′

t is the tensile strength. The ratio D/D0 is commonlyreferred to as the brittleness number, β. Large values of β indicate that the structurebehaves in a more brittle manner.

Figure 1 presents these two size effect laws (Bažant & Yu, 2009).The large-size asymptote of Type I size effect follows a power law, which is consistent with

classical Weibull size effect. The large-size asymptote of Type II size effect follows a power lawwith an exponent equal to −1/2, which is consistent with LEFM. Type I and Type II size effectsrepresent two different failure mechanisms. The large-size asymptote of Type I size effect is purelystatistical because the fracture can occur anywhere in the structure. By contrast, for Type II sizeeffect, which usually applies to structures with pre-existing crack, the fracture must occur at thecrack tip. Therefore, the size effect must be governed by the energy release at the crack tip, notby the statistics of material strength.

The small-size asymptotes for Type I and Type II size effects are also different, although bothcan be derived using the equivalent linear elastic fracture mechanics method. The key differencebetween them is that, for Type I size effect, the initial energy release rate is zero (i.e. zero cracklength) whereas for Type II size effect, there is a finite energy release rate (i.e. finite crack length).

3. Experimental detailsIn the following section, a detailed description of the experimental work is given, and the criteriaand factors considered in selecting the materials and testing procedure are discussed.

3.1. Sample preparationThe first step of the experimental work consisted of identifying the size of the SCB specimensthat can be produced and tested in the laboratory. Based on limitations imposed by specimen

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

Road Materials and Pavement Design 91

preparation, test set up, and size of the environmental chamber used for low temperature con-ditioning, the lower and upper limits for the specimen diameter were found to be 75 mm and300 mm, respectively.

The second step consisted of identifying the largest aggregate size that can be used to prepare thesmallest mixture specimen. The concept of minimum specimen dimensions is strictly correlatedto the representative volume element (RVE) of the tested material. The RVE can be describedas the smallest volume of the material that contains all the information required to describe themechanical properties of the global structure; therefore, it must be sufficiently large to includethe largest aggregate size. A rule of thumb recommends specimen dimensions should be at leastfour times the RVE. The smallest SCB specimen tested has a diameter of 75 mm and a fractureligament length of approximately 37 mm. An accurate fracture test would necessitate an RVEfour times smaller than the fracture ligament dimension, which is approximately 9 mm.

Based on these considerations, a mixture with a nominal maximum aggregate size (NMAS) of4.75 mm was selected. The mixture contains a blend of ISPAT taconite tailings, MINTAC taconitetailings, and locally produced sand, and was used in test cell 6 at MnROAD (Clyne, Johnson &Worel, 2010). The performance grade (PG) of the asphalt binder was PG 64-34 and the asphaltcontent was 7.4%.

The specimens were prepared from loose mix, sampled at MnROAD during construction ofcell 6, at Iowa State University using a Linear Kneading Compactor (LKC). A total of 10 slabsof standard dimensions (381 × 210 × 75 mm) were prepared with 7% air void content.

Coring of cylindrical specimens from the slabs was performed at the University of Minnesota,as illustrated in Figure 2. The coring machine consisted of a motor driven head and a water coolingsystem. The largest size samples were obtained from six different slabs. The remaining slabs wereused to cut cylinders for the three small size samples.

To account for slab to slab variability, and to reduce the effect of non-uniform density thatoccurs along the compaction line, the small size samples were cored from different slabs anddifferent regions of the slab, as shown in Figure 2.

The cored specimens were cut into two cylindrical slices of target thickness of 31 mm. SCBspecimens were then obtained by cutting in two the cylindrical slices. The final diameter of theSCB specimen was determined by the interior diameter size of the coring bits. Therefore, thefollowing SCB diameter sizes were obtained: 76.4 mm, 101 mm, 147 mm and 296 mm. This is

Figure 2. Coring of cylindrical specimens from slabs.

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

92 E. Zegeye et al.

Figure 3. SCB specimens of different size.

Table 1. Experimental design.

No. of replicates

SCB Specimen D [m] a/r = 0∗ a/r = 0.05∗ a/r = 0.2∗∗∗ Loading rate [mm/s] T [◦C]

Small 76.4 6 6 6 0.0003 −24Medium 101 4 4 4 0.0034 −24Standard 147 3 3 3 0.0005 −24Large 296 3 3 3 0.001 −24

(∗) notchless.(∗∗) shallow notch.(∗∗∗) deep notch.

equivalent to a 1: 1.32: 1.92: and 3.87 size ratio among the specimens. The final SCB slices areshown in Figure 3.

Each size was then divided into three subsets of different notch length. In order to take intoaccount the slab to slab variability, each subset included specimens obtained from different slabsand different regions of the slab. The first subset of specimens was designed to be tested withoutnotch. Specimens of the other two subsets were notched in the middle of the span, using awater-cooled masonry saw with a 1-mm-wide blade. Notch length to specimen radius (a/r) ratiosof 5% and 20% were used, respectively, in the second and third subset. Table 1 presents theinitial experimental design. Due to testing problems, the number of tested specimens ended upbeing higher.

3.2. Experimental setupA typical SCB fracture test scheme is shown in Figure 4. The specimen is simply supported bytwo rollers with span, S, equal to 0.8 times the diameter of the specimen, and loaded in a three-point bending configuration. All tests were conducted at −24◦C, equivalent to the low servicetemperature limit of the PG 64-34 binder plus 10◦C. Prior to testing, all samples were conditionedfor 2 hours in a controlled chamber at the test temperature using liquid nitrogen.

The fracture tests were performed under constant crack-mouth opening displacement (CMOD)rates in a closed-loop servo-hydraulic testing machine. For the notched specimens, in which crackinitiates at the tip of the notch, an Epsilon clip gauge with 10 mm gauge length was used. For thenotchless specimens, in which cracks can initiate randomly at any location near the mid-span,

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

Road Materials and Pavement Design 93

D

S

a

CMOD clip gage

P

Figure 4. Typical scheme of a notched SCB test.

CMOD clip gage

Knife edges

Figure 5. Installation of CMOD clip gage on a notchless specimen.

a clip gauge and two long-armed knife edges, glued to the specimens, were used as shown inFigure 5. In this way, it was possible to perform CMOD controlled fracture tests on notchlessSCB specimens, as long as the crack started in a region within the ends of the knife edges.

In the current SCB fracture procedure, a CMOD rate of 0.0005 mm/s is used to test 150-mm-diameter SCB specimens. The low loading rate was selected to reflect the rate of temperaturechange that occurs in real field conditions. In the present work, the same loading rate was appliedfor the 147 mm diameter SCB specimen. The CMOD rates for the other sizes were selected sothat all specimens reached the peak load at approximately similar times. This ensures that the FPZis loaded at the same rate, which eliminates the rate effect on the fracture process (Bažant, 2005;Bažant et al., 1998). Limited preliminary experiments indicated that an average peak time of 3 mincan be achieved using 0.0003 mm/s, 0.00034 mm/s, 0.0005 mm/s, and 0.001 mm/s, respectivelyfor the 76.4 mm, 101 mm, 147 mm and 296 mm SCB specimens. The following measurementswere recorded: displacement of the loading piston, load, CMOD, and time.

4. Inspection of experimental dataSCB fracture tests were successfully performed on all specimens, except for the notchless speci-men of diameter 296 mm. For these specimens, failure occurred at the support, far from the centralregion. Thus, the results were discarded.

For all notched specimens, cracking initiated at the notch tip and almost always the crackpropagated in a straight, Mode I, failure path, as illustrated in Figure 6. In the picture, the surfaceof the specimen was colored in order to highlight the fracture path.

At the end of each SCB test, plots of load vs. CMOD, CMOD vs. time, piston displacementvs. time, and load vs. piston displacement, were generated and visually inspected for any testing

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

94 E. Zegeye et al.

Figure 6. Failure path in SCB fracture test.

0 0.2 0.4 0.6 0.80

2

4

6

CMOD (mm)

Lo

ad (

kN)

SCB fracture test results SCB

0 500 1000 1500 2000 25000

0.5

1

Time (sec)

CM

OD

(m

m)

0 0.2 0.4 0.6 0.80

2

4

6

Piston Disp.(mm)

Lo

ad (

kN)

0 500 1000 1500 2000 25000

0.5

1

Time (sec)

Pis

ton

Dis

p.(

mm

)

Figure 7. Typical SCB test results.

errors, see Figure 7. Both back and front surfaces of the specimen were scanned to allow visualinspection of the crack path.

In a second stage of data processing, the test results generated from similar specimens and testconditions were grouped and analyzed (see Figure 8). In particular, it was verified that the initialslopes of the load-CMOD curves were similar and represented similar material behaviour.

Finally, the times to peak load were checked. The test results that passed all the indicatedinspections were considered valid and used in the analysis.

5. Test resultsPlots representing average nominal stress versus average relative CMOD are presented inFigures 9 to 11. The nominal stress is computed as P/bD. The relative CMOD refers to theCMOD measurements normalized by the radius of the specimen.

In all plots, a gradual reduction of the post peak softening curves can be observed accom-panied by steeper and steeper slopes as the size of specimen increases. This indicates that therange of specimen sizes considered accurately captures the transition from ductile behaviour

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

Road Materials and Pavement Design 95

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.00 0.50 1.00 1.50

Loa

d (k

N)

CMOD (mm)

300-5-1

300-5-2

300-5-3

Figure 8. Load-CMOD for SCB D = 296 mm with notch a/r = 0.05.

0.00

0.50

1.00

1.50

2.00

2.50

0.000 0.003 0.005 0.008 0.010

Nom

inal

str

ess

(MP

a)

Relative CMOD

smallmediumstandard

Figure 9. Nominal stress versus relative CMOD for notchless specimens.

0.00

0.50

1.00

1.50

2.00

0.000 0.003 0.005 0.008 0.010

Nom

inal

str

ess

(MP

a)

Relative CMOD

small

medium

standard

large

Figure 10. Nominal stress versus relative CMOD for specimens with a/r = 0.05.

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

96 E. Zegeye et al.

0.00

0.50

1.00

1.50

0.000 0.003 0.005 0.008 0.010

Nom

inal

str

ess

(MP

a)

Relative CMOD

small

medium

standard

large

Figure 11. Nominal stress versus relative CMOD for specimens with a/r = 0.2.

Table 2. Test results.

a/r = 0 a/r = 0.05 a/r = 0.2

Diameter (mm) σN (MPa) Diameter (mm) σN (MPa) Diameter (mm) σN (MPa)

76.4 2.41 76.4 1.69 76.4 1.00101 2.06 101 1.37 101 0.99147 1.99 147 1.17 147 0.78296 296 1.22 296 0.91

for small-size specimens, to brittle behaviour for large-size specimens. The peak loads of thelarge specimens, however, were higher than expected and almost similar to those obtained fromstandard specimens (147 mm).

The peak loads obtained from the SCB tests were used to compute the nominal strength σN .The average nominal strength results are reported in Table 2.

The nominal strength for 296 mm diameter specimens were considerably larger than expected.In Figures 9 to 11, the largest specimens had relatively short and steep strain-softening curves thatsuggest a relatively brittle behaviour compared with the other sizes. Thus, it would be expected thatthe nominal strength of large specimens falls within the LEFM region. Instead, the large specimensprovided nominal strength values similar to those provided by the standard SCB specimens. It ishypothesized that the specimen fabrication process affected the largest specimens’ results. Onlyone specimen could be cored from each slab (see Figure 2) from the same location within theslab. For all other specimen sizes, the location varied within each slab and the specimens weremore representative of the distribution of air voids within the slabs.

The following considerations and size effect investigations include only the results forspecimens with diameters 76.4 mm, 101 mm, and 147 mm.

5.1. Effect of notch lengthThe effect of notch length on the nominal strength is illustrated in Figure 12. It can be observedthat the strength decreases with increasing notch length. In particular, the small and standard sizespecimens show a similar rate of strength decrease.

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

Road Materials and Pavement Design 97

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.05 0.10 0.15 0.20

Nom

inal

str

ess

(MP

a)

a/r

small

medium

standard

Figure 12. Nominal strength as a function of notch length.

-0.15

-0.05

0.05

0.15

0.25

0.35

0.45

1.8 2.0 2.2 2.4

Log

sN

Log D

Shallow notched

Notchless

Deep notched

Figure 13. Nominal strength data for shallow notch SCB specimens.

The highest nominal strength values are observed for the small specimens, and the valuesgradually decrease as the size of the specimen increases. A closer look at the results for eachspecimen size can help identify the type of size effect involved.

5.2. Size effectIn Figure 13, the mean nominal strength vs. size is plotted for the notchless, shallow notch, anddeep notch specimens, respectively. The results obtained from the notchless specimens indicate atrend consistent with the Type I size effect. It is clear that the RVE size is not negligible comparedwith the structure size. The size effect of the deep notch specimens indicate the Type II size effect.This can be attributed to the relatively small fracture ligament of these specimens. Assuming thesize of the FPZ remains constant (regardless the size of specimen), its size gains relevance as thefracture ligament length decreases. Small fracture ligaments do not allow full development ofthe FPZ, and thus the material deviates from the LEFM behaviour as the specimen size decreases.For shallow notch specimens, the small-asymptote of size effect curve is similar to the case ofnotchless specimens, whereas the large-asymptote of size effect curve is close to the size effectof deep notch specimens. Such a phenomenon agrees well with the universal size effect equationrecently proposed by Bažant & Yu (2009).

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

98 E. Zegeye et al.

-0.10

0.00

0.10

0.20

0.2 0.4 0.6 0.8 1.0

Log

(s N

/s•

)

Log (D/Db)

Test Data

Type I SEL

•= 1.80 MPaDb = 28.5 mmr = 0.48n=2m = 26

Figure 14. Nominal strength data for notchless SCB specimens.

The test results obtained from the notchless specimens were used in the Type I size effectlaw, shown in equation (1), to identify the material parameters σ∞, Db, and r. Weibull modulusm = 26 was used based on an ongoing size effect research study conducted on the same mixturetested in a three-point bending test configuration. A non-linear optimization method based onthe Levenberg-Marquardt algorithm was used to fit the test data. The fitting procedure consistsof several iterative optimization steps in which the value of Db was varied between four and sixtimes the NMAS. The optimum material parameters found were σ∞ = 1.80 MPa, r = 0.46, andDb = 28.5 mm. Figure 14 shows comparison of the Type I size effect law and the data obtainedfrom notchless specimens.

The nominal strength results of the deep-notch specimens were fitted using the size effectlaw in equation (2). In order to determine the material parameters Bf ′

t and D0, equation (2) wasrearranged in a linear function of the following form:

Y = AX + C (3)

where X = D and Y = 1/σ 2N . The intercept and slope (A and C) of the linear equation were

determined by means of linear regression analysis. Consequently, the parameters were computedas Bf ′

t = 1/√

C and D0 = C/A. Figure 15 illustrates the fitted Type II size law and the dataobtained from deep notched specimens.

5.3. Determination of fracture parametersOne important application of the size effect law in equation (2) is that it can be used to determinethe fracture properties of the mixture (Bažant, 2005). The test results obtained from the deep notchspecimens were employed to evaluate a size-independent fracture energy, Gf , and the effectivesize of the fracture process zone, cf . Constants A and C in equation (3) can be further related toGf and cf (Bažant & Planas, 1998)

Gf = k2(α2)

EA(4a)

cf = k(α0)

k ′(α0)

CA

(4b)

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

Road Materials and Pavement Design 99

-1

-0.9

-0.8

-0.7

-0.6

-0.5

1 1.2 1.4 1.6 1.8 2

log

(sN

/ Bft

')

log (D/D0)

Data

Type II SEL

LEFM

B ft' = 4.62 MPaD0 = 4.2 mmGf = 216 J/m2

cf = 17 mm

Figure 15. Nominal strength data for deep notch SCB specimens.

Figure 16. Initial fracture energy Gf and total fracture energy GF .

where k(α0) represents the dimensionless stress intensity factor. k(α0) for the semi-circular notchspecimen is given by Lim, Johnston, & Choi (1993).

k(α0) = 4.782 − 1.219α0 + 0.063 exp(7.045α0) (5)

The mixture’s Young modulus, E, at test temperature −24◦C, was determined to be approxi-mately 9.5 GPa. The fracture energy computed by the size effect law, equation (3), was 216 J/m2.The same mixture was SCB tested at the same test conditions and using standard SCB speci-mens. The fracture energy computed from the area below the load versus load line displacement(LLD) curve was almost three times larger than that obtained in this work. Similar behaviourwas observed in recent study by Wagoner & Buttlar (2007), in which the authors applied thesize effect law on data obtained from the Disk-Shaped Compact Tension (DCT) fracture tests andcompared it to the fracture energy computed from the load versus CMOD plots. This differencecan be attributed to the fact that the fracture energy calculated by the present size effect anal-yses represent only the initial fracture energy, whereas the fracture energy calculated from theload-deflection curve represents the total fracture energy GF (see Figure 16).

The computed FPZ length was 17 mm. In the study conducted by Li & Marasteanu (2010) usingthe AE technique, the length of the FPZ was approximately 30 mm. However, in this previousresearch, asphalt mixtures with NMAS of about 12 mm were tested, approximately three timesthe NMAS used in the present work.

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

100 E. Zegeye et al.

6. Summary and conclusionSCB fracture tests were conducted on geometrically similar taconite asphalt mixture specimens.The size range of the specimens was approximately 1:4 and included specimens of diameter76.4 mm, 101 mm, 147 mm and 296 mm. The specimens were grouped in three categories, accord-ing to the length of the initial crack notch, and tested at low temperature. The tests were run underCMOD controlled loading rate in order to capture the strain-softening behaviour of the material.The loading rate was determined such that the time to peak for all specimens was about the same.In general, the results obtained in this experimental study can be explained by the size effecttheories. The results of this study are summarized as follow:

(1) The nominal strength is highest for the smallest specimens, and then gradually decreasesas the size of the specimen increases. Deviations from this trend were observed for thelargest specimens.

(2) The nominal strength considerably decreases with an increase in relative length of notch.The rates of decrease observed were similar for the medium and standard size specimens.

(3) In testing large asphalt mixture specimens, several difficulties were encountered. Thenotchless large specimens always failed at the support, far from the middle region wherethe CMOD gauge was installed.

(4) The strain softening curves, observed in load versus CMOD plots, reasonably capture thetransition from the relatively ductile behaviour of the small specimens to the relativelybrittle behaviour of the large specimens.

(5) The size effect described by the small, medium and standard specimens can be dividedinto the following: the data obtained from notchless specimens revealed the Type I sizeeffect; the results from the shallow notch specimens indicated a size effect whose small-size asymptote is close to the Type I size effect and large-size asymptote is close toType II size effect; and the data from the deep notch specimens demonstrated the Type IIsize effect.

(6) Finally, an application of the type II size effect law to determine non-linear fractureparameters of the mixture was demonstrated. As a result, size independent fracture energyand the effective size of the fracture process zone of the mixture were determined.

AcknowledgementsThe authors gratefully acknowledge the Minnesota Department of Transportation for providing the materialsused in this study and Dr Chris Williams at Iowa State University for kindly providing accesses to theirLinear Kneading Compactor (LKC).

ReferencesAASHTO T 322-07 (2007). Standard method of test for determining the creep compliance and strength of

hot-mix asphalt (HMA) using the indirect tensile test device. American Association of State Highwayand Transportation Officials.

Bažant, Z.P. (2005). Scaling of structural strength. New York: Butterworth-Heinemann.Bažant, Z.P., & Le, J.L. (2009). Size effect on strength and lifetime distributions of quasi-brittle structures.

Proceedings of the ASME Journal of Engineering and Materials Technology, 1–9.Bažant, Z.P., & Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials.

Washington, DC: CRC Press LLC.Bažant, Z.P., & Yu Q. (2009). Universal size effect law and effect of crack depth on quasi-brittle structure

strength. Journal of Engineering Mechanics, 135(78), 78–84.Chong, K.P., & Kuruppu, M.D. (1988). New specimens for mixed mode fracture investigations of

geomaterials. Engineering Fracture Mechanics, 30, 701–712.

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4

Road Materials and Pavement Design 101

Clyne, R.T., Johnson, E.N., & Worel, B.J. (2010). Use of taconite aggregates in pavement applications.Report MN/RC-2010-24, MnDOT.

Le, J.L., Bažant, Z.P., & Bazant, M.Z. (2011). Unified nano-mechanics based probabilistic theory of quasib-rittle and brittle structures: I. Strength, static crack growth, lifetime and scaling. Journal of the Mechanicsand Physics of Solids, 59, 1291–1321.

Li, X., & Marasteanu, M.O. (2004). Evaluation of the low temperature fracture resistance of asphalt mix-tures using the semi-circular bend test. Journal of the Association of Asphalt Paving Technologist, 73,401–426.

Li, X., & Marasteanu, M.O. (2010). The fracture process zone in asphalt mixture at low temperature. Journalof Engineering Fracture Mechanics, 77, 1175–1190.

Lim, I.L., Johnston, I.W., & Choi, S.K. (1993). Stress intensity factors for semi-circular specimens underthree-point bending. Journal of Engineering Fracture Mechanics, 44, 363–382.

Marasteanu, M.O., Dai, S., Labuz, J.F., & Li, X. (2002). Determining the low-temperature fracture toughnessof asphalt mixtures. Transportation Research Record: Journal of the Transportation Research Board,1789(1), 191–199.

Mobasher, B., Mamlouk, M.S., & Lin, H.M. (1997). Evaluation of crack propagation properties of asphaltmixtures. Journal of Transportation Engineering, 123, 405–413.

Molenaar, J.M.M., & Molenaar, A.A.A. (2000). Fracture toughness of asphalt in the semi-circular bend test.Proceedings of the Second Euroasphalt & Eurobitume Congress Barcelona.

Wagoner, M.P., & Buttlar, W.G. (2007). Influence of specimen size on fracture energy of asphalt concrete.Journal of the Association of Asphalt Paving Technologists, 76, 391–418.

Wagoner, M.P., Buttlar, W.G., & Paulino, G.H. (2005a). Development of a single-edge notched beam testfor asphalt concrete mixtures. Journal of Testing and Evaluation, 33, 452–460.

Wagoner, M.P., Buttlar, W.G., & Paulino, G.H. (2005b). Disk-shaped compact tension test for asphaltconcrete fracture. Journal of Experimental Mechanics, 45, 270–277.

Dow

nloa

ded

by [

Uni

vers

ity o

f W

inds

or]

at 0

0:10

11

July

201

4