Mixed mode fracture resistance of asphalt concrete mixtures

$Page 1: Mixed mode fracture resistance of asphalt concrete mixtures$
Engineering Fracture Mechanics 93 (2012) 153–167

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Engineering Fracture Mechanics

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Mixed mode fracture resistance of asphalt concrete mixtures

M. Ameri a,b,c, A. Mansourian b,⇑, S. Pirmohammad d, M.R.M. Aliha d,e, M.R. Ayatollahi d

a School of Civil Engineering, Iran University of Science and Technology, Iranb Transportation Research Institute, Iran University of Science and Technology, Iranc Center of Excellence of PMS, Transportation and Safety, Irand Fatigue and Fracture Lab., School of Mechanical Engineering, Iran University of Science and Technology, Irane Welding and Joining Research Center, School of Industrial Engineering, Iran University of Science and Technology, Iran

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

Article history:Received 20 December 2011Received in revised form 23 May 2012Accepted 24 June 2012

Keywords:Fracture resistanceHot mix asphalt (HMA)Semi-circular bend (SCB)Mixed mode I/II fracture

0013-7944/$ - see front matter � 2012 Elsevier Ltdhttp://dx.doi.org/10.1016/j.engfracmech.2012.06.015

⇑ Corresponding author. Tel.: +98 2188384181; faE-mail address: [email protected] (A. Man

Fracture resistance of hot mix asphalt (HMA) is an important parameter for characterizingthe asphalt concrete probable performance in cold climates. In this research study, twotypes of semi-circular bend (SCB) specimens containing an edge vertical crack are usedand subjected to asymmetric three-point bending load to measure the critical load neededfor calculation of HMA fracture resistance. The numerical and experimental results indicatethat the proposed test specimens would allow the measurement of critical loads undercomplete combinations of mixed mode deformation ranging from pure mode I to puremode II and therefore can be used as suitable specimens for investigating mixed modecrack deformation of HMA mixtures at low temperatures.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Hot mix asphalt (HMA) concrete is perhaps the most complicated material in flexible pavement system since its proper-ties depend upon temperature and loading conditions. Cracking is a common mode of failure in asphalt concrete pavementsespecially in cold regions. Therefore, investigation of crack growth behavior in pavements is an important issue for design,construction and maintenance of pavements in cold climates. To investigate the crack growth behavior of HMA, fracturetoughness is considered as one of the most important properties of HMA mixtures.

Experimentally, fracture toughness of HMA can be computed using a single edge notched specimen loaded in three-pointbending in accordance with Eqs. (1) and (2) [1].

K IC ¼Pf

tW32� f

aW

� �ð1Þ

fa

W

� �¼

3 aW

� �12 1:99� a

W 1� aW

� �2:15� 3:93 a

W

� �þ 2:7 a

W

� �2n oh i

2 1þ 2 aW

� �1� a

W

� �32

ð2Þ

In Eqs. (1) and (2), Pf is the critical load to failure, t and W are the specimen thickness and width respectively. a is the initialcrack length and KIC is a fundamental material property that measures material resistance against crack growth due to ther-mal or external mechanical loads. A higher value of KIC indicates that an asphalt mixture has a better resistance to crackgrowth and propagation of pre-existing flaws in real pavement structures.

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x: +98 2188344182.sourian).

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Nomenclature

a crack lengthB specimen heightHMA hot mix asphaltKI stress intensity factor for mode IKIf critical stress intensity factor for Mode IKII stress intensity factor for mode IIKIIf critical stress intensity factor for Mode IIL distance of vertical crack from center of specimenP critical load to failurePcr fracture loadR radius of specimenS1, S2 distances of supports from vertical crack positionSCB semi-circular bend speciment thickness of specimenW Width of specimenYI Shape factor for mode IYII Shape factor for mode II

Greek symbolsa crack angle

154 M. Ameri et al. / Engineering Fracture Mechanics 93 (2012) 153–167

At subzero and very low temperatures, HMA mixture behavior may be considered linear elastic [2–5]. Force–displace-ment diagrams obtained experimentally by Li and Marasteanu [4] as well as the experimental research works conductedby Kim et al. [5] show that at very low temperatures, HMA behaves in linear elastic manner up to the maximum loadand thus the framework of linear elastic fracture mechanics (LEFM) would be applicable to this type of material at verylow temperatures [4,6]. In a recent numerical study conducted by authors, it was shown that cracked pavement experiencesmixed mode I/II (tensile-shear) deformation when a vehicle passes from the neighborhood of crack [7]. Consequently, alldeformation modes can affect the fracture behavior of real cracked asphalt pavement. For such conditions, stress intensityfactors can be used as fundamental parameters to characterize pavement failure due to brittle fracture and/or fatigue crackgrowth deformation.

A review of past experimental research works indicates that Bahgat and Herrin, Majidzadeh, Monismith et al. and Witczakand his coworkers were of the pioneered researchers who have conducted experimental works to obtain fracture resistanceof asphaltic materials [8]. They all have used prismatic rectangular beam specimens with a vertical edge crack at the centersubjected to three or four-point bending loads. In recent years, Molenaar and his coworkers [9–11] conducted both exper-imental and numerical studies to investigate crack growth resistance of various asphalt mixtures. They used different testspecimens such as the semi-circular bend (SCB) specimen, the vertical edge cracked rectangular prismatic beam specimensubjected to four-point bending loads and the center crack plate under tension. Chen et al. [12] also employed the SCB spec-imen to study the effect of temperature on the tensile strength and fracture toughness of HMA mixtures. Some researchershave also investigated the crack growth in asphaltic materials using some other test samples such as rectangular and discshape compact tension specimens [1,13]. In most of the mentioned studies, crack growth of asphalt mixtures has been inves-tigated only under mode I or tensile loads. Among the few available investigations in this area, Braham and Buttlar [14] stud-ied the pure Mode II or shear mode crack growth resistance of an asphalt mixture experimentally using prismatic beamspecimens with two opposing vertical edge cracks on each side of the beam subjected to nonsymmetrical four-point bendingloads. They conducted their experimental study at�10 �C and concluded that at this temperature, the HMA behavior for puremode II fracture is linear elastic. In another experimental study conducted by Braham and his coworkers [15], to evaluate thecrack growth resistance of HMA under pure mode I and pure mode II loading, they concluded that 4 to 5 times more fractureenergy is required to promote the crack extension in pure mode I than it is needed for pure mode II fracture. There are gen-erally two approaches for investigating the mechanical behavior of asphalt mixtures: (1) micro-structural models in whichthe aggregates, voids, and in some extent, randomicity have to be considered. (2) macro-structural models in which the bulkmaterial is often assumed to behave like a uniform or homogeneous material. While many papers (including the present pa-per) have adopted the second approach when dealing with asphalt mixture in macro-scale, some researchers have also at-tempted to study the crack growth behavior of HMA under mixed mode I/II loading using micro- and meso-mechanicalfracture models (see for example [16,17]).

Since finite element method is a powerful tool for simulating and investigating crack growth of HMA mixtures, Ameriet al. [7] recently performed several 3D finite element analyses of a pavement structure to configure predominant modesof deformation in an asphalt layer that contains a top-down transverse crack [7]. They found that depending on the vehiclelocation relative to the crack plane, shear modes sometimes play an important role in the crack deformation. Therefore, it is

M. Ameri et al. / Engineering Fracture Mechanics 93 (2012) 153–167 155

important to investigate mixed mode I/II fracture in cracked asphalt samples using appropriate test specimens. In this paper,two new SCB specimens are used to conduct a series of mixed mode I/II fracture tests on an asphalt mixture sample. Thecrack parameters are calculated for these specimens using finite element method and the advantages of new specimensare discussed.

2. Selection of appropriate specimen geometry

Selection of appropriate compacted HMA test specimen that would properly simulate the real status of crack growth in apre-cracked asphalt layer is essential. The advantage of using SCB specimen to conduct fracture tests is that its fabrication issimple and the edge crack may be cut vertically or at any inclined angle. One may use cored specimen taken from pavementstructure or fabricate it using conventional Gyratory Compactor Machine. Ayatollahi and Aliha [18] numerically investigatedthe classical SCB specimen containing an inclined edge crack subjected to three-point bending (shown in Fig. 1a) under dif-ferent combinations of mode I and mode II loading. For wide ranges of crack lengths and crack angles, they performednumerous finite element analyses and calculated the stress intensity factors for pure mode I, pure mode II and mixed modeI/II crack deformations. They also obtained geometric shape factors for each of these fracture modes and concluded that theSCB specimen shown in Fig. 1a is a good candidate for conducting experimental tests to measure fracture resistance of brittleand quasi-brittle materials like rock. However, cutting an inclined edge crack in asphalt mixtures is often difficult and some-times leads to breakage of some aggregates in the sharp corner at the center of semi-circle. Therefore, cutting an edge cracknormal to the flat side of the SCB specimen is preferred for HMA mixtures. Two types of modified SCB specimens are sug-gested here in which crack is normal to the diametral edge of specimen (see Fig. 1b and 1c). In these specimens, the modemixity is controlled through the positions of the two bottom supports. Fig. 1 shows the loading configurations that wouldsimulate mixed mode I/II (tensile-shear) deformation in the SCB specimen that contain a vertical or an inclined crack. Fromthis Figure, it can be observed that by changing the crack angle or by changing the distance of a bottom support from thevertical crack position, or by cutting an off-centered vertical notch, status of the mixed mode I/II deformation changes. Puremode I deformation occurs when inclination of the crack line to the applied load is zero (a = 0) (or the supporting distancesare symmetric with respect to the loading position and also position of the vertical crack). By gradually increasing inclinationof the crack angle from zero or by changing one of the two supports distance from the vertical crack position, mixed modedeformation occurs. At a specific inclination angle (or supporting distance from the vertical crack position) pure mode IIdeformation will occur.

Fig. 2 shows a typical finite element mesh used for modeling the SCB specimen with about 2800 eight-node rectangularplane stress elements. Considering the subzero working temperature, a linear elastic material model with homogenous prop-

a-Classical SCB specimen b-Modified specimen SCB-1 c-Modified specimen SCB-2

Fig. 1. Different loading configurations that simulate mixed mode I/II for three types of SCB specimens.

Fig. 2. Typical finite element mesh used for modeling SCB specimen and crack tip region.


erties was assumed for the modeled HMA. The Young’s modulus and Poisson’s ratio of the SCB material were taken as12500 MPa and 0.35, respectively. The specimen was subjected to a 1 kN concentrated static load as a reference value ap-plied at mid-span on the top surface of the specimen.

The boundary conditions for this model is considered in such a way that displacements in both directions are constrainedin the left support and is vertically constrained in the right support. Finally, the stress intensity factors were directly derivedfrom the results of the numerical analyses performed by ABAQUS software which uses the properties of path-independentcontour integrals for calculating the stress intensity factors.

In each numerical analysis, knowing the values of S1,S2 and the crack length, the values of stress intensity factors are cal-culated by changing the relative position of the crack to the disc center (i.e. the length L in the Fig. 1b).

2.1. SCB-1 specimen

For most modeling cases, mixed mode I/II loading takes place. There exist some specific situations of loading that puremodes occur. The corresponding situations are presented in Table 1 for the SCB-1 specimen. For this specimen, the stressintensity factors (KI and KII) can be written as:

Table 1Pure m

Load

(S1,S(S1,S(S1,S(S1,S(S1,S(S1,S

K I ¼P

2Rt

ffiffiffiffiffiffipap

Y IaR;LR;S1

R;

S2

R

� �

K II ¼P

2Rt


Y IIaR;LR;S1

R;S2

R

� �:

ð3Þ

In which YI and YII are the shape factors of mode I and mode II, respectively. Other parameters are shown in Fig. 1b. Knowingthe loading condition, geometry and also the stress intensity factors obtained from the software, the shape factors of modes Iand II were calculated in accordance with Eq. (3). Selected numerical results are presented in Figs. 3–8 as examples. Moredetails of numerical results can be found in [19].

2.2. SCB-2 specimen

The finite element analyses were also conducted for calculating the shape factors of the SCB-2 shown in Fig. 1c. This caseis actually a special situation in the SCB-1 specimen which was addressed earlier. All the modeling procedures of the twocases are the same, except that in the SCB-2 specimen the crack is considered in the center of the semicircle and only thesupports are moved. After calculating the stress intensity factors, the shape factors are calculated by the following equation:

ode I and pure mode II situations in the SCB-1 specimen and the respective values of stress intensity factors for P = 1 kN.

ing conditions and geometry Situation of pure mode I (mm) K IðMPaffiffiffiffiffimpÞ Situation of pure mode II (mm) K IIðMPa

ffiffiffiffiffimpÞ

2) = (30,30) and a/R = 0.2 L = 0 0.945 L = 27.2 �0.6502) = (30,30) and a/R = 0.4 L = 0 1.570 L = 28.8 �0.9102) = (40,20) and a/R = 0.2 L = �6.4 0.864 L = 17 �0.7882) = (40,20) and a/R = 0.4 L = �7.1 1.337 L = 18.7 �1.0082) = (40,10) and a/R = 0.2 L = �11.2 0.524 L = 4.8 �0.6482) = (40,10) and a/R = 0.4 L = �14.3 0.815 8.5 �0.959

Fig. 3. Mode I shape factor in the SCB-1 specimen for loading condition (S1,S2) = (30,30).


Fig. 6. Mode II shape factor in the SCB-1 specimen for loading condition (S1,S2) = (40,20).



K I ¼P

2Rt

ffiffiffiffiffiffiffipap

Y IaR;S1

R;S2

R

� �

K II ¼P

2Rt

ffiffiffiffiffiffiffipap

Y IIaR;S1

R;S2

R

� � ð4Þ




For brevity, only the final FE results which contain the geometry shape factors are presented. The variations of mode I andmode II shape factors in the SCB-2 specimen are shown in Figs. 9–12 for a/R = 1/2 and 1/3. More numerical results can befound in [19].

As it can be seen from Figs. 9–12, the SCB-2 specimen can develop different cases of mixed mode loading conditions frompure mode I to pure mode II. In this specimen, moving from symmetric loading (S1=S2), the crack deformation state changes

a/R=1/2

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7S2/R

Y I S1/R=2/3

S1/R=1/2

S1/R=1/3

S1/R=1/6

Fig. 9. Mode I shape factor in the SCB-2 specimen for crack length ratio of a/R = 1/2.

a/R=1/2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

S2/R

S1/R=2/3

S1/R=1/2

S1/R=1/3

S1/R=1/6Y II

Fig. 10. Mode II shape factor in the SCB-2 specimen for crack length ratio of a/R = 1/2.

a/R=1/3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8

S2/R

S1/R=2/3

S1/R=1/2

S1/R=1/3

Y I

Fig. 11. Mode I shape factor in the SCB-2 specimen for crack length ratio of a/R = 1/3.

a/R=1/3

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8

S2/R

S1/R=2/3

S1/R=1/2

S1/R=1/3Y II

Fig. 12. Mode II shape factor in the SCB-2 specimen for crack length ratio of a/R = 1/3.


to a mixed case of opening and shearing and finally to pure shear deformation mode. Also by increasing the crack length andS1, the dimensionless value of YI increases. Increasing S2 will decrease YII. Therefore, the two proposed SCB specimens canpotentially be appropriate for assessing the crack growth behavior in tensile-shear mode deformation of asphalt mixtures.


The practical capability and performance of these specimens in measuring fracture resistance of asphalt mixtures should beinvestigated through laboratory experiments on these specimens.

3. Shape factors for test specimens

The laboratory specimens were 15 cm in diameter and the crack length was 2 cm. It should be mentioned that Molenaarand Molenaar [9] have shown that the critical stress intensity factor in asphalt mixtures is independent of the thickness ofthe specimen in the range of 25–75 mm. Therefore, in this research study the thickness of SCB specimens was about 30 mmin order to fall within this range. Molenaar and Molenaar [9] also performed a series of experiments on the SCB specimens ofdiameters 10, 15 and 22 cm at subzero temperatures and showed that the specimen size has negligible effects on the fractureresistance of asphalt mixtures under the mentioned conditions. Thus, no size limitation study was performed in the presentresearch and the diameter of 15 cm was adopted for the SCB specimens based on the results reported in [9].

The values of shape factors of the selected specimens tested in this research study were obtained through finite elementanalysis of the specimens with specific dimensions mentioned above.

In addition to pure mode I and pure mode II loading, four cases of mixed mode I/II loading were also evaluated. The valuesof S1,S2 and the parameter of distance between crack and middle line of specimen (L) together with the values of shape fac-tors for the SCB-1 specimens are presented in Table 2. Table 3 shows the values of S1 and S2 used for creating different load-ing cases for the SCB-2 specimens. The shape factors obtained through finite element (FE) analyses are also presented inTable 2. As shown in Tables 2 and 3, in all experiments S1 was fixed and equal to 50 mm. The SCB-1 tests were also performedall with S2 = 20 mm. Different mixed mode conditions were provided by changing L in the SCB-1 specimen and by changingS2 in the SCB-2 specimens. For easy understanding, the specimens are designated as SCB-x-y in which x indicates the type ofspecimen (i.e. 1 or 2) and y indicates the values of L in the SCB-1 and S2 in the SCB-2 specimens. The SCB-x-y designation hasbeen used in Tables 2 and 3 and Tables 5–7 for describing the specimens tested under pure mode I, pure mode II and mixedmode I/II loading. In the mentioned Tables, Me is the mixity parameter and is defined by the Eq. (5) [18].

Table 2FE resu

Spec

SCB-SCB-SCB-SCB-SCB-

Table 3FE resu

Spec

SCB-SCB-SCB-SCB-SCB-SCB-

Me ¼ 2p tan�1 K I

K II

� �ð5Þ

The mixity parameter Me defines the relative contribution of modes I and II. For pure mode I, Me = 1 and for pure mode II theparameter Me is zero.

For each test specimen, the finite element analysis was performed for a reference load of P = 1000 N, thickness t = 30 mm,specimen radius R = 75 mm and crack length a = 20 mm. The stress intensity factors KI and KII were obtained directly fromABAQUS. The shape factors YI and YII were then calculated by Eq. (6). The results are given in Tables 2 and 3 for both labo-ratory test specimens.

Y I ¼K Iffiffiffiffiffiffipap 2Rt

P

Y II ¼K IIffiffiffiffiffiffipap 2Rt

P

ð6Þ

lts of shape factors for the SCB-1 specimens used in experiments.

imen Loading mode S (mm) Shape factor for mode I (YI) Shape factor for mode II (YII) Me

1-0 Mixed mode I/II (S1,S2) = (50,20) and L = 0 1.522 0.688 0.731-3 Mixed mode I/II (S1,S2) = (50,20) and L = 3 1.196 0.945 0571-7 Mixed mode I/II (S1,S2) = (50,20) and L = 7 0.874 1.359 0361-11 Mixed mode I/II (S1,S2) = (50,20) and L = 11 0.612 1.794 0.21-17 Pure mode II (S1,S2) = (50,20) and L = 17 0 2.489 0

lts of shape factors for the SCB-2 specimens used in experiments.

imen Loading mode S (mm) Shape factor for mode I (YI) Shape factor for mode II (YII) Me

2-50 Pure mode I ðS1; S2Þ ¼ ð50;50Þ 3.734 0 12-22 Mixed mode I/II ðS1; S2Þ ¼ ð50;22Þ 1.766 0.578 0.82-18 Mixed mode I/II ðS1; S2Þ ¼ ð50;18Þ 1.229 0.894 0.62-15 Mixed mode I/II ðS1; S2Þ ¼ ð50;15Þ 0.802 1.179 0.382-12 Mixed mode I/II ðS1; S2Þ ¼ ð50;12Þ 0.421 1.446 0.182-9 Pure mode II ðS1; S2Þ ¼ ð50;9Þ 0 1.772 0

Table 4HMA aggregate gradation.

Sieve size(mm) Requirements Percent passing

Min Max

19 100 100 10012.5 90 100 959 67 87 774.75 44 74 592.36 28 58 431.18 20 46 330.5 13 34 230.3 5 21 130.15 4 16 9.50.075 2 10 8.4

Table 5Results of pure mode I fracture tests on asphalt mixture using SCB-2 specimen.

Specimen type Me t (cm) Pcr (kN) K If MPaffiffiffiffiffimp

K IIf MPaffiffiffiffiffimp

Average

KavIf MPa

ffiffiffiffiffimp

KavIIf MPa

ffiffiffiffiffimp

SCB-2-50 1 3.4 3.561 0.6535 0 0.8575 03.2 4.400 0.8580 03.3 5.388 1.0188 03.1 4.682 0.9424 03.1 3.768 0.7584 03.1 3.851 0.7752 03.3 4.681 0.8851 03.2 4.967 0.9685 0

Table 6Critical stress intensity factors KIIf for HMA specimens under pure mode II loading.

Specimen types Me t (cm) Pcr (kN) K If MPaffiffiffiffiffimp


Average

KavIf MPa

ffiffiffiffiffimp

KavIIf MPa

ffiffiffiffiffimp

SCB-1-17S1 = 50 mmS2 = 20 mmL = 17 mm

0 3.2 7.433 0 0.9661 0 0.90293.1 6.606 0 0.88633.2 6.371 0 0.82813.1 6.906 0 0.92663.2 6.566 0 0.85343.1 7.827 0 1.05023.3 6.787 0 0.85543.3 6.803 0 0.8574

SCB-2-9S1 = 50 mmS2 = 9 mm

0 3.2 * * * 0 0.98443.1 * * *

3.2 9.144 0 0.84613.1 13.442 0 1.24393.2 * * *

3.2 9.328 0 0.8632

* Test results are not reported because the mode II fracture tests conducted are not valid (because fracture did not initiate from the crack tip).


4. Material and testing procedure

Asphalt cement with penetration grade of 60–70 (widely used in the Iran pavement systems) was utilized as a binder.The nominal maximum aggregate size of 12.5 mm and the air void content of 4% were used for preparing the HMA mixture.Table 4 shows the aggregate gradation of the asphalt concrete specimens.

After determining the crack position in the semi-circular test specimens, for each specific mixed mode I/II condition,cracks were generated using rotary blades in lower edge of semi-circular specimens and on appropriate locations designatedthrough the FE calculations. In this way, the SCB laboratory specimens were cracked in the SCB-1 and SCB-2 samples undersix loading conditions noted in Tables 2 and 3.

For each loading condition, at least 6 laboratory specimens were made to be used in the fracture tests and all the spec-imens were maintained in a freezer so the testing temperature would be at -10�C.

Table 7Critical stress intensity factors of HMA specimens (KIf and KIIf) under different cases of mixed mode loading.



Average

KavIf MPa

ffiffiffiffiffimp

KavIIf MPa

ffiffiffiffiffimp

SCB-2-50 1 3.4 3.561 0.6535 0 0.8575 03.2 4.400 0.8580 03.3 5.388 1.0188 03.1 4.682 0.9424 03.1 3.768 0.7584 03.1 3.851 0.7752 03.3 4.681 0.8851 03.2 4.967 0.9685 0

SCB-2-22 0.8 3.2 8.946 0.8250 0.2700 0.7909 0.25893.4 7.280 0.6319 0.20693.2 9.254 0.8534 0.27933.2 8.250 0.7608 0.24903.1 9.713 0.9246 0.30263.2 8.735 0.8056 0.26373.2 8.620 0.7950 0.26023.1 7.680 0.7311 0.2393

SCB-2-18 0.6 3.2 7.298 0.4684 0.3407 0.6895 0.50153.1 13.264 0.8788 0.63923.1 9.762 0.6467 0.47053.1 12.168 0.8061 0.58643.1 10.575 0.7006 0.50963.2 10.566 0.6781 0.49333.3 9.594 0.5971 0.43433.1 11.166 0.7398 0.5381

SCB-2-15 0.38 3.2 9.274 0.3884 0.5710 0.5078 0.74753.1 � � �3.3 � � �3.1 12.718 0.5498 0.80833.1 � � �3.2 10.740 0.4498 0.66123.2 14.381 0.6023 0.88543.2 � � �3.1 13.654 0.5864 0.86783.0 10.522 0.4701 0.69113.2 � � �3.1 � � �

SCB-2-12 0.18 3.2 14.368 0.3159 1.0850 0.2676 0.91913.2 � � �3.1 � � �3.2 10.923 0.2401 0.82483.1 10.872 0.2467 0.84753.4 � � �

SCB-2-9 0 3.2 � � � 0 0.98443.1 � � �3.2 9.144 0 0.84613.1 13.442 0 1.24393.2 � � �3.2 9.328 0 0.8632

SCB-1-0 0.73 3.2 9.180 0.7297 0.3298 0.7425 0.33563.2 7.753 0.6163 0.27853.2 9.837 0.7818 0.35353.2 9.513 0.7561 0.34183.2 9.396 0.7468 0.33763.2 9.499 0.7550 0.34123.2 10.035 0.7976 0.36053.2 9.520 0.7567 0.3421

SCB-1-3 0.57 3.1 � � � 0.5874 0.46413.2 � � �3.3 8.397 0.5086 0.40183.2 9.129 0.5702 0.45053.1 11.783 0.7597 0.60023.2 9.314 0.5817 0.45963.2 8.277 0.5170 0.40853.1 � � �


Table 7 (continued)



Average

KavIf MPa

ffiffiffiffiffimp

KavIIf MPa

ffiffiffiffiffimp

SCB-1-7 0.36 3.2 10.717 0.4891 0.7606 0.4406 0.68513.1 10.193 0.4802 0.74673.2 8.230 0.3756 0.58413.1 7.987 0.3763 0.58513.2 10.419 0.4755 0.73943.1 7.920 0.3731 0.58023.2 10.343 0.4721 0.73403.2 10.577 0.4827 0.7506

SCB-1-11 0.2 3.1 8.478 0.2797 0.8199 0.3045 0.89273.2 10.132 0.3238 0.94923.2 8.768 0.2802 0.82143.2 7.125 0.2277 0.66753.3 11.588 0.3591 1.05273.2 9.310 0.2975 0.87223.2 8.793 0.2810 0.82383.1 11.738 0.3872 1.1351

SCB-1-17 0 3.2 7.433 0 0.9661 0 0.90293.1 6.606 0 0.88633.2 6.371 0 0.82813.1 6.906 0 0.92663.2 6.566 0 0.85343.1 7.827 0 1.05023.3 6.787 0 0.85543.3 6.803 0 0.8574

Fig. 13. Loading frame and a sample path of fracture.


Each specimen was loaded in a constant rate three-point bending test till its final facture. Fig. 13 depicts the loading andfracture procedure of a typical laboratory specimen. In this research, the loading rate was similar to the one used by Mole-naar and Molenaar [9] for 15 cm diameter specimens and was 3 mm/min. During the tests, the load–displacement curve foreach specimen was recorded by a personal computer. A sample load–displacement curve is presented in Fig. 14. The linearrelationship between the load and displacement and sudden fracture indicate brittle behavior of asphalt mixtures at �10 �C.In this case, the fracture resistance values of each specimen can be calculated by obtaining the critical fracture load.

5. Test results

In this part of research, the purpose of laboratory testing is to obtain the fracture resistance of conventional asphalt con-crete mixtures that is used in construction of Iranian pavement network and assess its strength against cracking. Therefore,

Fig. 14. Load–displacement curve for one of the asphalt concrete specimens.


in this section, the way of calculating critical stress intensity factors based on the value of critical fracture load (obtainedthrough the results of tests conducted on HMA specimens) is explained first. The critical stress intensity factors for modesI and II i.e. KIf and KIIf are computed using Eqs. (7a and 7b):

K If ¼ Y IPcr

2Rt


ð7aÞ

K IIf ¼ Y IIPcr

2Rt


ð7bÞ

in which R is the radius of specimens (R = 7.5 cm), a is the crack length (a = 2 cm) and t is the thickness of specimens given inTables 5–7. Pcr is the fracture load which is obtained from the experiments. The values of YI and YII are given in Tables 2 and3. Therefore, by using these data the values of KIf and KIIf can be calculated.

A total number of 8 SCB-2 specimens cooled in freezer at the temperature of �10 �C were used for pure mode I fracturetests. The specimens were loaded in such a way that the lower supports were symmetric relative to crack position and thecrack was exactly in the center of the bottom edge. The critical load was recorded for each specimen and finally the mode Icritical stress intensity factor (or KIf) was calculated according to Eq. (7a). The values of mode I fracture resistance KIf withtheir average are given in Table 5. A sample specimen fractured under pure mode I is shown in Fig. 15.

Pure mode II fracture tests were performed on both SCB-1 and SCB-2 specimens while frozen at �10 �C. Eight SCB-1 spec-imens and six SCB-2 specimens were used for mode II fracture tests on the HMA mixture. The test specimens were loaded

Fig. 15. A sample HMA specimen fractured under pure mode I loading.

SCB-1 SCB-2

Fig. 16. Samples of HMA specimens fractured under pure mode II loading.

Fig. 17. A mode II fracture test on HMA using SCB-2 specimen with unacceptable fracture trajectory.

SCB-1-3 SCB-1-0

SCB-1-11 SCB-1-7

Fig. 18. Sample SCB-1 specimens fractured under different combinations of mode I and mode II.


SCB-2-18 SCB-2-22

SCB-2-12 SCB-2-15

Fig. 19. Sample SCB-2 specimens fractured under different combinations of mode I and mode II.


using three-point loading fixture according to the geometrical properties mentioned in Tables 2 and 3. For each test sample,the critical fracture load was recorded and the critical stress intensity factor was calculated using Eq. (7b). The values ofmode II fracture resistance (KIIf) together with the average value obtained from each specimen are given in Table 6.

Fig. 16 shows two samples fractured under pure mode II loading for each of the SCB-1 and SCB-2 specimens.In some of the SCB-2 specimens, mode II fracture was not initiated from the crack tip. Instead, a new crack was nucleated

from the bottom right support and propagated towards top loading point. Fig. 17 shows a sample of mode II test specimenswith unacceptable pattern of crack growth. These cases (designated by a ‘‘�’’ sign in Table 6), were considered as invalid tests.

To conduct the experiments under mixed mode loading (tension-shear loading), the specimens were prepared and wereput in freezer at -10�C. The loading was in accordance with the values of S1 and S2, and L given in Tables 2 and 3, and thecritical loads were recorded. Finally the fracture resistance was calculated using Eqs. (7a and 7b). The values of KIf and KIIf

together with their averages for each mixed mode case are given in Table 7.The specimens fractured under mixed mode I/II are shown in Fig. 18 for a SCB-1 specimen and in Fig. 19 for a SCB-2 spec-

imen. It is seen in Table 7 that again in some of the SCB-2 test cases, fracture did not initiated from the crack tip and the testswere invalid. Such invalid tests (designated by ‘‘�’’ sign) were more frequent for mode II dominated loading conditions.Therefore, one may suggest that the SCB-1 specimen is more appropriate for performing mixed mode fracture tests onHMA mixture.

6. Conclusions

� In this paper, finite element method was used to calculate the values of shape factors for two types of SCB specimensproposed for measuring the mixed mode fracture resistance of HMA mixtures.

� Cutting a normal crack instead of an inclined crack is one of the advantages of the proposed SCB specimens comparedwith the classical SCB specimens.

� Both types of specimens used in this research study have similar potential for measuring mixed mode fracture resis-tance of HMA, although the SCB-1 specimen was found to be more suitable.

� The testing procedure presented in this research study can be used to determine the mixed mode fracture resistance ofHMA at low temperatures.

� Typical values of KIf and KIIf presented in Table 7, may be used to evaluate the HMA resistance against mixed modecrack growth.

Acknowledgement

The authors would like to acknowledge the financial support for this research provided by the Transportation ResearchInstitute under the contract 88B5T2P28 (RP).


References

[1] Marasteanu M, et al. Low temperature cracking of asphalt concrete pavements. Research Report of Department of Civil Engineering University ofMinnesota; 2007.

[2] Novak M, Birgisson B, Roque R. Near-surface stress states in flexible pavements using measured radial tire contact stresses and ADINA. Comput Struct2003;81(8–11):859–70.

[3] Akbulut H, Aslantas K. Finite element analysis of stress distribution on bituminous pavement and failure mechanism. Mater Des 2004;26(4):383–7.[4] Li XJ, Marasteanu MO. The fracture process zone in asphalt mixture at low temperature. Eng. Fract Mech 2010;77(7):1185–90.[5] Kim H, Wagoner MP, Buttlar WG. Numerical fracture analysis on the specimen size dependency of asphalt concrete using a cohesive softening model.

Constr Build Mater 2009;23(5):2112–20.[6] Li XJ, Marasteanu MO. Using semi-circular bending test to evaluate low temperature fracture resistance for asphalt concrete. Exp Mech

2010;50:867–76.[7] Ameri M, Mansourian A, Heidary Khavas M, Ayatollahi MR. Cracked asphalt pavement under traffic loading – A 3D finite element analysis. Eng Frac

Mech 2011;78:1818–26.[8] Mansourian A. Usage of indirect tensile test for investigation of asphalt-mix fatigue life. PhD. Dissertation. Iran University of science and technology;

2006.[9] Molenaar JMM, Molenaar AAA. Fracture toughness of asphalt in the semi-circular bend test. Eur asphalt and Euro bitume congress. Barcelona, Spain;

2000. p. 509–18.[10] Molenaar AAA, Scarpas A, Liu X, Erkens G. Semi-circular bending test; simple but useful. J Assoc Asphalt Technol 2002;71:794–815.[11] Molenaar JMM, Molenaar AAA, Liu X. Resistance to crack-growth and fracture of asphalt mixture. In: Sixth international RILEM symposium on

performance testing and evaluation of bituminous materials; 2003. p. 618–25.[12] Chen X, Li W, Li H. Evaluation of fracture properties of epoxy asphalt mixtures by SCB test. J Southeast Univ 2009;25(4):527–30.[13] Edwards MA, Hesp SAM. Compact tension testing of asphalt binders at low temperatures. J Transport Res Board 2006;1962:36–43.[14] Braham A, Buttlar W. Mode II cracking in asphalt concrete. Adv Test Charact Bituminous Mater 2009;II:699–706.[15] Braham A, Peterson C, Buttlar W. Mixed-mode cracking in asphalt concrete. Adv Test Charact Bituminous Mater 2009;I:785–93.[16] Yin A, Yang X, Yang S, Jiang W. Multi scale fracture simulation of three-point bending asphalt mixture beam considering material heterogeneity. Eng

Fract Mech 2011;78:2414–28.[17] Kim H, Wagoner MP, Buttlar WG. Micromechanical fracture modeling of asphalt concrete using a single-edge notched beam test. Mater Struct

2009;42:677–89.[18] Ayatollahi MR, Aliha MRM. Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Comput Mater Sci

2006;38(4):660–70.[19] Ayatollahi MR. Investigation of mixed mode fracture in asphalt concretes due to traffic loads. Research Report, Transportation Research Institute, Iran

Ministry of Roads and Transportation; 2011.

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Mixed mode fracture resistance of asphalt concrete mixtures