Engineering Fracture Mechanics 78 (2011) 1817–1826

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Engineering Fracture Mechanics

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Cracked asphalt pavement under traffic loading – A 3D finiteelement analysis

M. Ameri a, A. Mansourian b, M. Heidary Khavas c, M.R.M. Aliha c,d, M.R. Ayatollahi c,⇑a School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iranb Transportation Research Institute, Iran Ministry of Road and Transportation, Tehran, Iranc Fatigue and Fracture Lab., School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Irand Welding Research Center, School of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran

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

Article history:Available online 6 January 2011

Keywords:Cracked asphalt pavement3D finite element analysisStress intensity factorsT-stressMixed modeTraffic loading

0013-7944/$ - see front matter � 2011 Elsevier Ltddoi:10.1016/j.engfracmech.2010.12.013

⇑ Corresponding author. Tel.: +98 21 7724 0201;E-mail address: m.ayat@iust.ac.ir (M.R. Ayatollah

An asphalt pavement containing a transverse top-down crack is investigated under trafficloading using 3D finite element analysis. The stress intensity factors (SIFs) and the T-stressare calculated for different distances between the crack and the vehicle wheels. It is foundthat all the three Modes (I, II and III) are present in the crack deformation. The signs andmagnitudes of KI, KII, KIII and T are significantly dependent on the location of the vehiclewheels with respect to the crack plane. The magnitude of T-stress is considerable, if com-pared to the stress intensity factors, when one of the wheels is very close to the crack plane.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

A huge amount of money is annually spent for the design, construction and maintenance of asphalt pavements [1,2] par-ticularly in the countries having large networks of roads and highways. Cracking is a common mode of deterioration and oneof the main causes for the overall failure in asphalt pavement of roads and highways, especially in the cold regions [3–5].Under subzero and very low temperatures, asphalt pavements often behave as a brittle material and, hence, the risk of sud-den fracture from pre-existing cracks in the pavement increases. For such conditions, the stress intensity factors can be usedas fundamental parameters in order to characterize the pavement failure due to brittle fracture or fatigue crack growth.Top-down cracks in the surface of asphalt pavements initiate due to daily or seasonal cyclic thermal loads and then extendprimarily because of mechanical traffic loading, causing a noticeable increase in the maintenance and rehabilitation cost ofpavement [6]. Since cracking of asphalt layers is inevitable, the investigation of crack growth behavior in asphalt pavementsis important for estimating the suitable rehabilitation time of pavements and service capability of the roads and highways.

There have been some experimental and numerical studies for investigating the crack growth behavior of asphaltpavements. For example, the fracture resistance of various asphalt mixtures has been investigated experimentally andnumerically by Molennar and coworkers [7–9] using different test specimens such as the semi-circular bend (SCB) specimen,the edge cracked rectangular beam specimen subjected to four-point loading, and the center crack plate under tension. Chenet al. [10] also employed the SCB specimen to study the effect of temperature on the tensile strength and fracture toughnessof asphalt materials. Other researchers have also investigated the crack growth in asphalt materials using different testconfigurations such as the rectangular and disc shape compact-tension specimens [11,12], three-point bend beam specimen[13–15] and the modified indirect tensile disc specimen [16].

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Nomenclature

a depth of rectangular crackD transverse distance between the vehicle center and the crack planed half length between front wheelsE Young’s modulusHMA hot mix asphaltKI Mode I stress intensity factorKII Mode II stress intensity factorKIII Mode III stress intensity factorKshear eff effective shear stress intensity factorL longitudinal distance between the vehicle center and the crack planel half length between the front and rear wheelsP weight of vehicleSCB semi-circular bend specimenSIF stress intensity factorT T-stresst thickness of asphalt pavement layersw width of rectangular crack

Greek symbolsm Poisson’s ratio

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In most of the mentioned research studies, fracture of asphalt material has been investigated only under pure Mode I ortensile loads. In practice since the cracks in the asphalt pavement can initiate in various locations and orientations with re-spect to the traffic direction, the crack growth may occur in a mixed mode manner. In other words, most of the cracks in thesurface of the asphalt layer usually experience a combined opening-sliding deformation due to tensile-shear loads. A reviewof the literature indicates that shear mode or mixed mode (tension-shear) fracture behavior of cracked asphalt pavementshas received little attention for the top-down cracks. Among the few available investigations in this area, Buttlar and Braham[17] studied the Mode II or shear mode fracture resistance of an asphalt material experimentally using the beam specimensubjected to anti-symmetric four-point loading. Artamendi and Khalid [18] have also conducted very limited mixed Modes I/II fracture experiments on asphalt materials. On the other hand, most of the research studies related to the fracture behaviorof asphalt materials have mainly focused on the laboratory test samples, whereas the fracture behavior of real road pave-ments in the presence of a crack has not been investigated in detail.

As is well known, one of the main causes of crack growth in pavements is traffic loading [19]. Hence, a cracked asphaltlayer is investigated in this paper using numerous 3D finite element analyses under different traffic loading conditions. It isshown that the analyzed cracked asphalt pavement is generally subjected to mixed mode loading, and all the three Modes I,II and III can be significantly present in the flawed asphalt layer depending on the location of the applied loads (induced fromthe wheels) with respect to the crack plane.

2. Description of crack in asphalt pavement

Asphalt pavements which are used for roads and highways often consist of four main layers (Fig. 1) namely (i) asphaltconcrete layer (ii) base layer, (iii) sub-base layer and (iv) sub-grade or soil layer (listed from top to bottom). These layersare usually made of a mixture of bitumen and fine or coarse aggregates. Although several types of cracks can be found inan asphalt pavement, the aim of this research is to study the behavior of a top-down crack that exists in the surface ofthe asphaltic upper layer. The crack plane is assumed to be perpendicular to the traffic direction and, therefore, the crackcan be called the top-down transverse crack. The top layer is usually made of hot mix asphalt (HMA) and its thickness rangesbetween 10 and 20 cm. Top-down cracks in the asphalt surface layer often initiate because of severe aging of the HMA nearthe surface or due to low cycle thermal fatigue. They may then propagate due to tensile and shear stresses induced by thevehicle wheels.

Indeed, the experimental observations show that once a top-down crack takes shape normal to the free surface of theasphalt layer, its crack front propagates both normal and parallel to the asphalt surface due to the traffic loads. Since thethickness of upper layer is much less than its width, the propagation of crack parallel to the top surface should be faster thanits downward propagation through the more confined asphalt material. Therefore, the shape of a well-developed crack canbe roughly simulated by a wide but relatively shallow crack of rectangular shape with round bottom corners. Fig. 1 showsschematically a 3-dimensional description of different layers of an asphalt pavement and a rectangular transverse surfacecrack (with respect to the traffic direction) initiated from the surface of the upper layer. Fig. 1b shows the side view sectionof the crack with width w significantly larger than its depth a.

Asphalt Concrete Base Layer

Sub-base Layer

Sub-grade Layer

Traffic direction

DCrack 2d

2l c.g.

w

a

Crack Plane

Sub-base Layer

Sub-grade

Base Layer

AAsphalt Concrete Layer

(a)

(b)

L

Fig. 1. Schematic representation of an asphalt pavement containing a surface rectangular crack perpendicular to the traffic loading direction. (a) 3D viewand (b) Front view.

M. Ameri et al. / Engineering Fracture Mechanics 78 (2011) 1817–1826 1819

The four wheels shown in Fig. 1a are a simplified representation of the total loads transferred from the vehicle to the roadsurface. The four-wheel model of the vehicle load can be considered to be located at different distances from the crack planeby changing the distances D and L shown in Fig. 1a. By moving the wheels towards the crack plane, the crack can be sub-jected to different combinations of opening and sliding deformations.

As is shown in Fig. 2, a crack in the asphalt layer may generally experience three different types of deformation dependingon the loading conditions. If crack faces open without any sliding, the crack is subjected to pure Mode I deformation. PureMode II deformation takes place when the crack faces slide normal to the crack front without any opening. Pure Mode IIIcorresponds to the loading conditions where crack faces slide parallel to the crack front without any opening. For complexloading conditions, a combination of two or three modes of deformation takes place. The relative contributions of thesemodes in crack deformation can be determined by numerical methods like the finite element method. In next section, thefinite element method is employed to analyze the effect of the vehicle load position on the crack deformation.

3. Analysis of the cracked pavement

Since the cracks in the surface of roads are usually subjected to complex and variable states of traffic loads, the finiteelement method can be used as a powerful tool for simulating and investigating their deformations. Furthermore, 3D finiteelement models provide more realistic simulations for the cracked asphalt pavements in comparison with the simple 2Dmodels. Hence, a 3D semi-rigid asphalt pavement structure is here analyzed using the finite element code ABAQUS. Although

Sub Layer Pavement

Crack in Surface Layer

Asphalt Layer

KI

KII KIII

Out-of-Plane Shear Mode In-Plane Shear Mode Opening Mode (KI) (KII) (KIII)

Fig. 2. Different types of crack deformation in an asphalt pavement.

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asphalt is a composite material, it is often modeled by an equivalent isotropic and homogenous material. Moreover, atsubzero temperatures, asphalt of pavements usually behaves as a linear elastic and brittle material (see e.g. [20–23]). Forexample, the force–displacement diagrams obtained experimentally by Li and Marasteanu [22] and Kim et al. [23] show thatthe asphalt pavements at low temperature behave in a linear elastic manner, up to the maximum load. Hence, most of theresearchers have used the hypothesis of linear elastic fracture mechanics for modeling the cracked asphalt pavement underlow temperature conditions [20–26].

Therefore, for each layer of asphalt pavement, the construction material is generally assumed to be isotropic, homogenousand linearly elastic. The elastic constants and the thickness of each layer used in our simulations for the asphalt pavementare given in Table 1. These properties correspond to those of the asphalt materials commonly used in Iran highways androads.

Fig. 3 shows the finite element mesh used for modeling the pavement in which a zoomed view of the crack front region isalso represented. A large rectangular area from the road pavement is considered in the finite element modeling. In order toapply the boundary conditions, the side faces of the model (i.e. front, rear, left and right faces) are fixed normal to the cut faces,while the other two degrees of freedom are free. The bottom face of the model (i.e. the bottom of the sub-grade layer) is alsocompletely fixed in all directions. The interfaces between different layers of the pavement are also assumed to be perfectlybonded. The vehicle weight is considered to be equal to 40 tons. The four-wheel model of the vehicle weight is applied atthe top surface of the asphalt layer with different longitudinal and transverse distances from the crack plane. One fourth ofthe vehicle weight P is assumed to be transferred from each wheel to the surface of asphalt layer over a small rectangular con-tact area. The distance between the front and rear wheels (i.e. the distance 2l in Fig. 1a) and the distance between each pair ofthe front or rear wheels (i.e. the distance 2d in Fig. 1a) are assumed to be 3.5 m and 2 m, respectively. A rectangular surfacecrack of width w = 1 m and depth a = 40 mm is assumed to exist in the middle of the top asphaltic layer perpendicular tothe road axis. The width w = 1 m was selected arbitrarily, since in practice cracks of different widths can be found in the surfaceof asphalt layer. The depth a was taken 40 mm based on the practical range reported in previous studies, e.g. Collop and Cebon[27]. A total number of 37,788 solid brick elements are used in the finite element model. In order to produce a square root sin-gularity of stress field, singular (quarter point) elements are used in the first ring of finite elements surrounding the crack front.

For fixed crack dimensions, the Mode I, Mode II and Mode III stress intensity factors KI, KII and KIII are functions of thewheel loads and the vehicle distance from the crack plane (L, D). Therefore, they can be generally written as follows:

Table 1Mechanical properties and the thicknesses of the pavement layers used for finite element modeling.

Layer Young’s modulus, (E) (MPa) Poisson’s ratio, (m) Layer thickness (t) (cm)

Asphalt concrete 2760 0.35 14Base 276 0.35 20Sub-base 104 0.35 25Sub-grade 34.5 0.45 200

Fig. 3. Finite element mesh created for modeling the transverse top-down crack in the asphalt pavement.

M. Ameri et al. / Engineering Fracture Mechanics 78 (2011) 1817–1826 1821

K I ¼ fIðL;D; PÞ ð1ÞK II ¼ fIIðL;D; PÞ ð2ÞK III ¼ fIIIðL;D; PÞ ð3Þ

where P is the vehicle weight. A contour-integral based method which is readily available in ABAQUS is used for obtainingdirectly the stress intensity factors and the T-stress. A total number of 125 three-dimensional finite element models withdifferent L and D distances are analyzed, and the corresponding values of KI, KII, KIII and T are computed. It can be noted thatthe crack parameters KI, KII, KIII and T can vary along the crack front. In order to avoid dealing with excessive numerical re-sults, the calculated crack parameters are displayed only for the middle point A (Fig. 1b) along the crack front. The numericalresults are presented and discussed in the next section.

4. Results and discussion

Figs. 4–6 show the Mode I, Mode II and Mode III stress intensity factors (SIFs) obtained from the finite element analyses interms of the normalized loading distances L/l and D/d (i.e. the vehicle position with respect to the crack plane). From thesefigures, we can note that the states of crack deformation, and consequently the stress intensity factors are strongly affectedby the distances L and D.

For example, when the vehicle moves from the far distances in the left towards the crack location, first the Mode I stressintensity factor (KI) increases until the ratio of L/l is about �1.7. Then, by moving the wheels further towards the crack plane(typically for the range of �1.7 < L/l < �1), KI dramatically decreases and its sign switches from positive to negative. Thismeans that the crack flank deformation changes from opening to closing implying that, for such loading distances (wherethe front wheels locate very close to the crack), a downward deformation tends to close the crack flanks. Then, by increasingL/l from approximately �1 to zero, KI increases again noticeably, and its sign turns again from negative into positive. WhenL/l becomes zero (i.e. when the crack is located exactly in the middle of the distance between the front and rear wheels), KI

reaches its maximum value. In this loading situation, the tensile stresses along the crack plane are the highest and tend toopen the crack flanks. Hence, for L/l = 0 and D/d = 0, pure Mode I deformation is achieved due to symmetry conditions with

-200

-150

-100

-50

0

50

100

150

-4 -3 -2 -1 0 1 2 3 4

KI

(kP

a.m

)

L / l

D/d=0D/d=0.25D/d=0.5D/d=0.75D/d=1D/d=1.25D/d=1.5D/d=1.75

0.5

Fig. 4. Variations of Mode I stress intensity factor (KI) for different wheel locations (L/l and D/d) in the analyzed asphalt pavement.

-100

-80

-60

-40

-20

0

20

40

60

80

100

-2.2 -1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 1 1.4 1.8 2.2

KII

L / l

D/d=0D/d=0.25D/d=0.5D/d=0.75D/d=1D/d=1.25D/d=1.5D/d=1.75

(kP

a.m

)

0.5

Fig. 5. Variations of Mode II stress intensity factor (KII) for different wheel locations (L/l and D/d) in the analyzed asphalt pavement.

-80

-60

-40

-20

0

20

40

60

80

-4 -3 -2 -1 0 1 2 3 4

KII

I

L / l

D/d=0D/d=0.25D/d=0.5D/d=0.75D/d=1D/d=1.25D/d=1.5D/d=1.75

(kP

a.m

)

0.5

Fig. 6. Variations of Mode III stress intensity factor (KIII) for different wheel locations (L/l and D/d) in the analyzed asphalt pavement.

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respect to the crack. Moreover, the results obtained for L/l > 0 are exactly mirror reflection of the results obtained for L/l < 0,because of symmetry in the loading conditions.

The trend observed for the switching sign of KI can be found for Mode II and Mode III stress intensity factors as well (seeFigs. 5 and 6). However, the maximum values of KII and KIII occur at about L/l = (±1.3, ±0.75) and L/l = (±1.2), respectively. Fur-thermore, while the opening deformation (i.e. Mode I SIF) is still high for large distances from the crack plane, the sheardeformation (or Mode II and Mode III SIFs) becomes significant only when the wheels are close to the crack plane. The resultspresented in Fig. 5 for different values of D/d reveal that, in the middle point of the crack front, the maximum KII occurs forD/d = 1 i.e. when the nearest wheel passes directly over the center point of the crack. Similarly, Fig. 6 shows that the max-imum KIII occurs when the ratio of D/d is equal to about 1.25. It is noteworthy that the values of KII (or KIII) obtained for thetwo cases of D/d = 0.75 and D/d = 1.25 are not symmetric. This is due to the effects of the other three wheels of vehicle thatinteract with the results related to the effects of nearest wheel.

Also a comparison between the results shown in Figs. 4–6 for the considered asphalt pavement, indicates that the influ-ence of opening mode deformation (KI component) is more pronounced than the other two modes of crack deformation,although the magnitudes of KII and KIII are still significant. Fig. 7 comprises the variations of all the three Modes (I, II andIII) stress intensity factors for various values of L/l and D/d = 0.75. Note that, for a constant value of D/d, the Mode I stressintensity factor KI varies in a wider range and with larger amplitude in comparison with KII and KIII.

However, for some of the loading distances L/l and D/d, the influence of shear deformations becomes significant. This canbe seen more clearly in Fig. 8 which shows the variations of the ratio KI/Kshear eff for different locations of wheels with respectto the crack plane, where Kshear eff is the effective shear stress intensity factor defined as follows:

Kshear eff : ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiK2

II þ K2III

qð4Þ

Note that the effective shear SIF is significant for considerable ranges of L/l and D/d. According to Fig. 8, three separate statesof crack deformation can be observed when a vehicle passes in the neighborhood of a crack. For far distances from the crackplane (region 1 in Fig. 8), the influence of KI is more pronounced than that of Kshear eff. By moving the wheels towards the

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0

50

100

150

-2.2 -1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 1 1.4 1.8 2.2

SIF

(kP

a*m

)

L / l

D / d=0.75

KIKIIKIII

0.5

Fig. 7. Comparison of stress intensity factors (KI, KII and KIII) obtained for D/d = 0.75 and different values of L/l.

-20

0

20

40

60

80

100

120

140

160

180

-2.2 -1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 1 1.4 1.8 2.2

KI

/ K

She

ar e

ff

L / l

D/d=0D/d=0.25D/d=0.5D/d=0.75D/d=1D/d=1.25D/d=1.5D/d=1.75

Region 2K shear eff

dominant

Region 1 KI dominant

Region 3KI dominant

Region 2K shear eff

dominant

Region 1 KI dominant

Fig. 8. Variations of KI/Kshear eff ratio for various locations of wheels relative to the crack plane.

M. Ameri et al. / Engineering Fracture Mechanics 78 (2011) 1817–1826 1823

crack plane (typically for �1.6 < L/l < �0.5), the shear mode deformation becomes more pronounced than the Mode I com-ponent (region 2 in Fig. 8). In this region, KI has a negative value and tends to compress the crack faces to each other, imply-ing that the Mode I component has little effect on crack growth. Hence, only the shear mode components can play the majorrole in the crack growth. It should be noted that, when KI < 0, the Mode I stress intensity factor in Fig. 8 is assumed to be zero.For those situations where the wheels are nearly symmetric with respect to the crack plane, the Mode I component becomesagain dominant (region 3 in Fig. 8). Although the crack is generally subjected to a combination of all the three modes ofdeformation, pure mode deformations can also be observed in specific wheel locations. Table 2 presents the loading locationsthat correspond to pure Mode I, pure Mode II and pure Mode III conditions.

It has been well established that, in addition to the singular stress terms defined by the stress intensity factors, the firstnon-singular stress term (often called the T-stress) can also influence the fracture behavior of a crack especially under mixedmode loading conditions (see e.g. [28–33]). In particular, the T-stress can affect the path of mixed mode crack growth and theonset of fracture. Hence, the T-stress has also been computed for the cracked asphalt pavement from the same finite elementmodels used previously for determining the stress intensity factors. Similar to the stress intensity factors, the T-stress in acracked asphalt pavement is also a function of the induced wheel loads and the locations of vehicle wheels with respect tothe crack plane, and can be written as follows:

T ¼ fTðL;D; PÞ ð5Þ

The variations of the T-stress with the vehicle location (i.e. with L/l and D/d) are obtained directly from ABAQUS code for thegiven cracked asphalt pavement. Fig. 9 shows the numerical results obtained for the T-stress in terms of L/l and D/d. Similar

Table 2Wheel locations corresponding to pure Mode I, II and III conditions.

Pure Mode I D/d = 0 L/l = 0Pure Mode II D/d = 0 L/l � �1.5Pure Mode III D/d = 1.75 L/l � �1.5

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0

50

100

150

200

-4 -3 -2 -1 0 1 2 3 4

T (

kPa)

L / l

D/d=0D/d=0.25D/d=0.5D/d=0.75D/d=1D/d=1.25D/d=1.5D/d=1.75

Fig. 9. Variations of the T-stress for different wheel locations (L/l and D/d) in the analyzed asphalt pavement.

1824 M. Ameri et al. / Engineering Fracture Mechanics 78 (2011) 1817–1826

to the stress intensity factors, the magnitude of T-stress varies significantly, and its sign switches several times by passingthe vehicle wheels close to the crack region. When the front wheels approach the crack plane from the left side, the T-stressin the region L/l < �1.4 is negative. On the other hand, when the front wheels approach and then pass close to the crack plane(roughly for �1.4 < L/l < �1), the sign of the T-stress switches to positive, and its value increases rapidly. For �1 < L/l < 0, thevalue of T-stress dramatically decreases and its sign becomes again negative.

According to previous fracture studies [29–32], a negative T-stress increases the load bearing capacity of cracked bodiessubjected to mixed mode loading and, conversely, the mixed mode fracture resistance decreases for crack problemscharacterized by a positive T-stress. Therefore, it is expected that the load bearing capacity of the cracked asphalt pavementdecreases for 0.7 < |L/l| < 1.4 (i.e. when the front wheels are very close to the crack plane), due to very large positive T-stres-ses that exist in these locations. However, for other L distances, the negative T-stress reduces the risk of mixed mode fracture,because a higher load is required for the onset of fracture.

It should be noted that a 3D finite element model of the crack in asphalt pavements requires more analysis efforts andexpertise for its complex modeling but, in comparison with a 2D model, it provides a more accurate simulation of the actualconditions that a cracked asphalt pavement experiences under traffic loading. Some researchers have performed 2D finiteelement analyses to investigate the crack growth behavior of asphalt pavements [24–26]. For example, Fakhri et al. [24] ana-lyzed a 2D asphalt layer containing an edge crack in the top layer of pavement. They computed the Mode I and Mode II stressintensity factors resulting from the effect of only one vehicle wheel by applying a pressure load at only four different lon-gitudinal distances from the crack line. However, their simplified model is not able to describe precisely the actual stressesand deformations that a cracked asphaltic pavement experiences. The results obtained from a 3D finite element model in thepresent research, have shown that all four wheels can influence the state of stress and crack deformation and hence consid-ering the effects of one wheel only (i.e. the nearest wheel to the crack) may introduce significant errors in estimating thefracture behavior and the service life of the cracked asphalt pavement. Further, the significant contribution of the ModeIII stress intensity factor which has been observed in this research for a transverse top-down crack had not been reportedin the past. This is mainly because previous researchers had studied the pavement cracks only by a two-dimensional crackmodel which is not able to detect any Mode III crack deformation.

There are two possible failure modes for a top-down transverse crack in an asphalt pavement under traffic loading. Atsubzero temperatures and in the very cold regions, asphalt materials behave in a brittle manner, and hence a cracked asphaltpavement is very likely to fail by brittle fracture. For such environments, the calculation of the load bearing capacity of thecracked asphalt pavements requires a mixed mode fracture criterion which can take into account the influence of the frac-ture parameters KI, KII, KIII and T-stress.

However, at normal temperatures, a cracked asphalt pavement is more vulnerable to fatigue crack growth due to a largenumber of loading cycles associated with passing the vehicles over the crack and its neighborhood. As is mentioned above,the signs of stress intensity factors (SIFs) switch from negative to positive and vice versa depending on the wheels positions.It is seen from Figs. 4–6 that, for a four-wheel loading model, when a vehicle passes over a crack on the surface of road, thesign of each stress intensity factor changes several times. This implies that the transverse cracks in an asphalt layer and un-der traffic loading experience variable fatigue loads due to reversing the state of crack deformation from opening to closingor from positive shear to negative shear. The cumulative damage induced from the complex history of stress/deformationdue to heavy traffic loads can therefore cause the propagation of the crack in a mixed mode manner. Again the use of a mixedmode fatigue crack growth model requires specific crack parameters that have been calculated in the present research for acracked asphalt pavement. Generally speaking, methods that are available for pavement analysis and design are mostlybased on static or moving loads and do not consider the inertia effects due to dynamic loads. For example, Monismith etal. [35] showed that, for asphalt concrete pavements, it was unnecessary to perform a complete dynamic analysis since cur-rent design procedures do not consider the damage caused by pavement roughness. As trucks become larger and heavier,

M. Ameri et al. / Engineering Fracture Mechanics 78 (2011) 1817–1826 1825

some benefits can be gained by designing proper suspension systems to minimize the damage effect. It should be mentionedthat cracks have the least effect on the roughness of a pavement (to produce inertia effect) whereas rutting (permanentdeformation in the wheel track) has the most effect. However, rutting rarely takes place at low temperature where the visco-plastic behavior of asphalt layers is suppressed.

It is worth mentioning that another concern regarding transverse top-down cracking is the ingress of water to the pave-ment structure through the cracks (Marasteanu et al. [34]). From a durability standpoint, the presence of water increases therate of stripping which leads to early deterioration of the asphalt concrete. Additionally, water infiltration promotes pump-ing of unbound fines in the underlying material leading, in some cases, to a depression at the thermal crack. Many research-ers have postulated that an ice lens could form beneath a transverse crack, which would cause an upward lipping or tentingof the crack edges. There is also mounting evidence that transverse cracks can act as stress focal points from which longi-tudinal cracks may form (Marasteanu et al. [34]).

The results presented in this paper reveal the significant roles of Mode II and Mode III stress intensity factors in the totaldeformation of cracked asphalt pavements under traffic loading. Although extensive experiments have been conducted inthe past for determining Mode I fracture toughness of different asphalt materials, very few researchers have dealt with pureMode II, pure Mode III and mixed mode fracture experiments for these materials. Therefore, it would be very useful to con-duct a series of experiments to obtain mixed mode fracture resistance of different asphalt materials in order to determineappropriate parameters which can improve the pavement mechanical properties from the crack growth point of view atlow temperature. These parameters may include (but are not limited to) the type and size of asphalt ingredients and thecompositions of bitumen and aggregates, etc.

5. Conclusions

– Using a large number of 3D finite element analyses, the stress intensity factors (KI, KII and KIII) have been computed for anasphalt pavement containing a transverse top-down crack subjected to traffic loading.

– According to the finite element results, the cracked asphalt pavement is generally subjected to mixed mode loading, andall the three fracture modes may affect the crack propagation behavior.

– It has been shown that the Mode III stress intensity factor KIII, which has been often ignored in the past, can be significantin the deformation of cracked asphalt pavements under traffic loading.

– The location of the four-wheel loading model with respect to the crack plane (represented by L/l and D/d) is the mainparameter affecting the sign and magnitude of the stress intensity factors.

– The T-stress has been also calculated for the cracked asphalt pavement as a function of the normalized loading distancesL/l and D/d. The T-stress significantly varies when a vehicle passes over the cracked area.

– The calculated crack parameters KI, KII, KIII and T-stress can be employed for analyzing the fracture resistance or theremaining life of a cracked asphalt pavement under traffic loading. These parameters should be used with an appropriatemixed mode fracture criterion, particularly in the case of subzero temperatures, or together with a mixed mode fatiguecrack growth criterion in the case of normal temperature conditions.

Acknowledgement

MHK, MRMA and MRA would like to acknowledge the financial support for this research provided by the TransportationResearch Institute (Iran Ministry of Road and Transportation) under the Contract 88B5T2P28 (RP).

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