of the bending stiffness within the tire structure. The restricted inwardmovement of the tire ribs causes transverse stresses to develop, and thelongitudinal stresses are primarily controlled by the tire–pavementfriction forces (2). The three-dimensional (3-D) tire contact stressesresult in a complex stress state near the pavement surface, whichincreases the potential for pavement damage, including top-downcracking, near-surface cracking, and hot-mix asphalt (HMA) rutting.In addition, stress rotations and loading rates induced by movingloads accelerate pavement deterioration.

Many researchers have analyzed the effects of 3-D tire contactstresses on flexible pavement damage. De Beer et al. (3) found thatpavement responses of thin HMA pavements are sensitive to verticalload shape and distribution. Drakos et al. (4) concluded that the 3-Dtire contact stresses increase HMA rutting potential. Romanoschi andMetcalf (5) and Al-Qadi and Yoo (6) reported that the effect of surfacetangential stresses on pavement response is significant. However,limited investigations were conducted on the effect of 3-D contactstresses on perpetual pavement responses.

The perpetual pavement concept is to prevent cracks from begin-ning at the bottom of the HMA layer through increasing HMAthickness. The design method of perpetual pavement is usually basedon mechanistic–empirical approaches. In the conventional pavementdesign method, the dynamic moving transient load is considered asa stationary uniform stress distribution on a circular contact area.When the wheel load increases, the contact stress or the area or bothincrease uniformly. This situation is inconsistent with field-basedexperience. The effect of this assumption on resulting pavementresponses may be minimal when considering the responses far fromthe surface, but the resulting errors could be high near the pavementsurface. To achieve a realistic mechanistic–empirical design method,the effects of a moving wheel load and 3-D tire contact stresses ona pavement system need to be considered.

OBJECTIVE AND SCOPE

Tire–pavement interaction was analyzed by using the measured3-D tire contact stresses at various load levels (35, 44, and 53 kN)and constant tire pressure (720 kPa). The combined effect of a movingwheel load and 3-D tire contact stress on perpetual pavement responsewas analyzed with a 3-D finite element (FE) model. This modelincorporates the measured 3-D tire contact stresses and continuousmoving load using implicit dynamic analysis. A perpetual pavementdesign having 254-mm HMA placed on 300-mm lime-modified sub-grade was exposed to dual tire loading. HMA linear viscoelasticitywas characterized by the relaxation modulus from creep complianceobtained by the indirect tensile test. The subgrade elastic modulus

Combined Effect of Moving Wheel Loadingand Three-Dimensional Contact Stresseson Perpetual Pavement Responses

Hao Wang and Imad L. Al-Qadi

53

Tire–pavement interaction was analyzed with measured three-dimensional(3-D) tire contact stresses at various load levels (35, 44, and 53 kN) andconstant tire pressure (720 kPa). The combined effect of moving wheelload and 3-D contact stresses on flexible pavement response was evaluatedwith a developed 3-D finite element (FE) model, which incorporated themeasured 3-D tire contact stresses, hot-mix asphalt (HMA) viscoelasticity,and continuous moving load by using implicit dynamic analysis. InFE modeling, a perpetual pavement design with 254-mm HMA placedon 305-mm lime-modified subgrade was exposed to dual tire loading.The critical pavement responses under two loading conditions (uniformcontact stresses and measured 3-D contact stresses) at various load levelswere calculated and compared. The 3-D tire contact stresses inducedgreater pavement stresses and strains at the pavement near surface (shearstrains and octahedral shear stresses) and at deeper depths (transversetensile strains and compressive strains) comparable to the uniform contactstresses; these results suggest that using uniform contact stresses couldunderestimate pavement damage, especially near-surface cracking poten-tial and shear flow in perpetual pavement. The transverse tangentialstresses induce the outward shear flow from the tire center and shearstrain concentration at the pavement near surface. Increasing the wheelload mostly increases contact stresses at the tire edge and the correspond-ing shear strains and octahedral shear stresses. The difference betweenpavement responses caused by uniform contact stresses and 3-D contactstresses decreases when wheel load increases.

The pavement–tire contact stress distribution arising from the movingwheel load carried by each tire depends largely on tire geometry andloading conditions. Results from tire–pavement contact stress mea-surements indicate that different tire contact stress patterns developwhen the tire load changes while the tire inflation pressure is constant(1). For better understanding of the behavior of flexible pavementsunder real traffic loading, it is necessary to incorporate moving wheelload and tire–pavement contact stresses into the vehicle–pavementinteraction analysis.

When a tire loading is applied to a pavement surface, three contactstress components are generated: vertical, transverse, and longitudinal.The vertical contact stresses are not uniformly distributed because

H. Wang, Department of Civil and Environmental Engineering, and I. L. Al-Qadi,Illinois Center for Transportation, University of Illinois at Urbana–Champaign,205 North Mathews Avenue, MC-250, Urbana, IL 61801. Corresponding author:I. L. Al-Qadi, alqadi@uiuc.edu.

Transportation Research Record: Journal of the Transportation Research Board,No. 2095, Transportation Research Board of the National Academies, Washington,D.C., 2009, pp. 53–61.DOI: 10.3141/2095-06

was backcalculated from the falling weight deflectometer test. Thecritical pavement responses for different failure mechanisms werecalculated and compared for two loading conditions (uniform contactstresses and 3-D measured contact stresses) at various loading levels.

TIRE–PAVEMENT INTERACTION

Tire–Pavement Contact Area

Two important factors are at play when considering the tire–pavement interaction mechanism: contact area and contact stress.Many researchers used the circular or equivalent rectangular contactarea in the pavement loading analysis (7). However, the contact areaof a truck tire is, in reality, closer to a rectangular than to a circularshape, especially for a wide-based tire (8). In addition, both thecircular and equivalent rectangular contact areas overestimate thenet contact area without considering the tread pattern of the tire orthe localized stress distribution under each tire rib.

Figure 1a shows the measured tire imprint for one tire of a dual tireassembly. The rectangular contact area of each rib is clearly indicated.Figure 1b shows the contact areas and contact lengths of the middlerib at three loading levels for 275/80R22.5 dual tires. The patternsof increased contact area and contact length with increased tire loadcan be clearly observed. As load increases, the increase in contactlength is more significant for the middle rib than for other ribs. Thecontact widths are almost constant under various loading levels.

3-D Tire–Pavement Contact Stress

The measured longitudinal distributions of contact stresses (vertical,transverse, and longitudinal) under the center rib of a 275/80R22.5dual tire at a tire pressure of 720 kPa and various wheel loads on flatpavement surface are shown in Figure 2a. Both the vertical com-pression stresses and transverse tangential stresses have a convexshape along the longitudinal contact length. The longitudinal tan-gential stresses vary significantly between the entrance and exit partsof a tire imprint, with backward stresses in the front half and forwardstresses in the rear half. The location of a point where the longitudi-nal stress directions change is determined by the rolling conditionof the tire.

54 Transportation Research Record 2095

The transverse distributions of contact stresses under each rib atvarious loading levels are shown in Figure 2b and c for the verticalcontact stresses and transverse tangential stresses, respectively. Thevertical contact stress is usually greater underneath inner tire ribs(crown) than outer tire ribs, and the middle point of each rib has thelowest vertical stress. The maximum vertical stress under the centerrib is about 1.6 times the tire inflation pressure.

The transverse tangential stresses show the distinct asymmetricdistribution beneath each rib. If averaged over the tire width, the totaltransverse stress is near zero. However, the transverse stresses maybe either tension or compression at different positions along each tirerib. In addition, the transverse tangential stresses range from about24% of vertical stress at the center rib to 35% to 52% of vertical con-tact stress at edge ribs. Thus, the localized surface tangential stressesunder each rib should be considered for predicting the pavementresponse at the near surface.

Comparing Figure 2a, b, and c, the maximum vertical contactstresses beneath the three center ribs are almost constant as the wheelload increases, and the vertical contact stresses at the two outsideribs increase from around 600 to 800 kPa, probably due to theinfluence of the structural stiffness of the tire sidewalls. The higherthe load, the greater is the contribution of the sidewall, which is mainlytransferred to the outside ribs in the contact area. However, theincreased transverse stress is insignificant as the load increases. Thegeneral shapes of the longitudinal stresses remain relatively constantin spite of the changes in load, with the exception of a slight differencein the exit part. The peak longitudinal stress under each rib increasesas the loading increases. The contact stress data at various loadinglevels are summarized in Table 1.

MATERIAL CHARACTERIZATION

The perpetual pavement design used in the analysis is an existingtest section built as part of a project focused on the extended-lifeflexible pavement study (9), as shown in Figure 3a. The HMA wasprepared in accordance with the Superpave® volumetric design pro-cedure. The laboratory mix–design criterion is based on 90 gyrationsto achieve 4% air voids. Two asphalt binders were used in the HMAlayers: a PG 64-22 for the standard binder course and a styrene–butadiene–styrene PG 70-22 for the polymer-modified binder coursesand dense-graded surface. The asphalt content of the standard and

0

200

400

600

800

1000

35 44 53

Load on Dual-Tire Assembly (kN)

(b)(a)

Con

tact

Are

a (c

m2 )

0

100

200

300

400

Con

tact

Len

gth

(mm

)

Net Contact Area

Contact Length (Middle Rib)

FIGURE 1 The 275/80R22.5 dual tire: (a) measured tire imprint and (b) contact areaand length.

Wang and Al-Qadi 55

-400

-200

0

200

400

600

800

1000

1200

1400

-120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120

Longitudinal Contact Length (mm)

Con

tact

Str

ess

(kP

a)

35kN

44kN

53kNVertical contact stress

Transverse contact stress

Longitudinal contact stress

0

300

600

900

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1500

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Data Points in a Rib

Ver

tical

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tact

Str

ess

(kP

a)

35kN 44kN 53kN

(a)

(b)

(c)

-400

-200

0

200

400

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Data Points in a Rib

Tra

nsve

rse

Con

tact

Str

ess

(kP

a)

35kN 44kN 53kN

FIGURE 2 Distribution of (a) 3-D, (b) vertical, and (c) transverse contact stresses at various loading levels (275/80R22.5 tire under 720-kPa inflation pressure).

polymer-modified binder courses is 4.5%, and the HMA dense-gradedasphalt content is 5.4%. No antistripping was used in the HMA. Theaggregate used in all mixes was limestone. The subgrade was 305-mmlime stabilized to increase the strength of the natural soil.

In this study, an indirect tensile creep compliance test was con-ducted to characterize the three HMA materials used in the perpetualpavement section. The indirect tensile setup was used to allow testingof thin HMA layer cores taken from the field. In addition, this test’stensile stress state is close to stress conditions in the field at the bottomof the HMA layer (10). The relaxation moduli were interconvertedfrom the creep compliance data. The bulk (K) and shear (G) relax-ation moduli were calculated assuming a constant Poisson’s ratioand fitted into the Prony series as a generalized Maxwell solid model(see Equations 1 and 2). The elastic modulus of the subgrade wasbackcalculated from the falling weight deflectometer test.

where

G = shear modulus,K = bulk modulus,t = reduced relaxation time,

G0 and K0 = instantaneous elastic modulus,Gi, Ki, and τi = Prony series parameters,

N = number of terms in the equation, ande = base of natural logarithm.

K t K K eit

i

Ni( ) = − −( )⎛

⎝⎜⎞⎠⎟

−

=∑0

1

1 1 2τ ( )

G t G G eit

i

Ni( ) = − −( )⎛

⎝⎜⎞⎠⎟

−

=∑0

1

1 1 1τ ( )

56 Transportation Research Record 2095

FINITE ELEMENT MODEL DEVELOPMENT

A 3-D FE model was developed using ABAQUS version 6.7 to predictpavement responses under various loading conditions (see Figure 3b).The elements used were eight-node, linear brick elements with reducedintegration (C3D8R). The infinite elements (CIN3D8) were used toreduce the number of far-field elements without significant loss ofaccuracy and to create a “silent” boundary for the dynamic analysis.Sensitivity analysis shows that the dimensions of the element thicknesscan be selected as 9.5 mm for the upper HMA layers, 20 to 50 mmfor the granular base layers, and 200 to 500 mm for the subgrade (11).The element horizontal dimensions along the vehicle loading areawere dictated by the tire rib and groove geometries: 15 to 18 mm lat-erally and 20 mm in the traffic direction. Full interface bonding wasassumed between HMA layers, and the Coulomb friction model wasused at the HMA and subgrade interfaces.

The loading time actually changes at various pavement depthsand the principal stresses rotate in the pavement under the movingwheel loading. A recently developed concept of continuous movingload was used. In this approach, the tire loading imprint is graduallyshifted over the loading area (step loading) until a single tire passis completed. More details about the developed FE model andcontinuous moving load are presented elsewhere (11, 12).

DYNAMIC TRANSIENT ANALYSIS

Three different approaches can be used in pavement analysis: static,quasi-static, and dynamic transient analysis. The static approach tra-ditionally has been used in multilayer elastic analysis. The quasi-staticapproach is based on the concept of moving the load at later positionsalong the pavement for each new time step and assuming the load is

TABLE 1 Contact Stresses at Various Loading Levels

Peak Stress (kPa)

Contact Average Vertical Transverse LongitudinalLoad (kN) Area (cm2) Stress (kPa) Stress Stress Stress

35 507 700 1,205 351 148

44 614 725 1,208 363 190

53 686 779 1,205 372 223

DG Surface 50 mm

Polymer Binder 115 mm

Standard Binder 89 mm

Lime ModifiedSubgrade 305 mm

Infiniteelement

Infiniteelement

Loadingarea

(a) (b)

FIGURE 3 The 3-D FE model: (a) perpetual pavement structure and (b) crosssection (DG � dense-graded).

static at each position. No inertia or damping effects are quantifiedin quasi-static analysis.

Two important factors need to be considered in dynamic transientanalysis of the pavement, including the inertia associated with themoving load and the dependency of the material properties on theloading frequency. Zafir et al. (13) considered the continuum-basedfinite layer approach and concluded that the dynamic effects ofmoving loads on pavement strain responses are important and shouldnot be ignored. Yoo and Al-Qadi (14) found that the dynamic transientanalysis induces greater strain response and residual stress.

The FE method was used in this study for dynamic transientanalysis. This method permits modeling of more complex materialproperties (such as linear or nonlinear viscoelasticity of HMA andnonlinear elasticity of aggregate base) and pavement geometries(discontinuity such as cracking or interface debonding) than is pos-sible with the analytical solution method. In ABAQUS, the dynamicequilibrium equation can be solved by a direct integration methodsuch as implicit or explicit modes.

In pavement analysis, the rise time (loading duration) of the tran-sient dynamic loading, which in this study depends on vehicle speed[e.g., 8 km/h (0.009 s/20-mm element length in traffic direction)],exceeds by a few multiples the time required for a stress wave to speedthrough the flexible pavement structure: 100 to 600 m/s (15). Hence,this problem may be classified as a structure dynamic problem insteadof a wave propagation problem. Using an implicit method is usuallymost effective for a structure dynamic problem such as this one. Thedamping ratio of 5% and the Rayleigh damping scheme were usedfor the subgrade in the implicit dynamic analysis.

EFFECT OF 3-D CONTACT STRESS ON PAVEMENT RESPONSES

To evaluate the effect of 3-D contact stresses on flexible pavementresponses, two groups of analysis were conducted: one using measured3-D contact stress and one using uniform contact stress distribution.The uniform contact stress at each rib was calculated as the total loaddivided by the actual net contact area, as shown in Table 1. Both groupsof analysis were conducted at a vehicle speed of 8 km/h at 25°C.

Tensile Strain

The horizontal tensile strain at the bottom of HMA is thought tobe related to the bottom-up fatigue cracking of flexible pavement.As shown in Figure 4, the longitudinal and transverse tensile straindistributions with depth are similar for the two loading conditions(uniform stress and 3-D measured contact stress): compressive inthe upper half of the HMA layer and inverted to tensile in the lowerpart of the layer. The transverse tensile strain at the bottom of HMAunder 3-D contact stress was found to be 17% greater than thetransverse tensile strain under a uniform contact stress condition.Similar longitudinal tensile strains were obtained at the bottom ofthe HMA layer for the two loading conditions, which suggests that thepavement response in the transverse direction is more sensitive tostress nonuniformity than the response in the longitudinal direction.

Shear Strain

Top-down cracking is recognized as longitudinal or transverse crack-ing, or both, that appears at the pavement surface and propagates

Wang and Al-Qadi 57

downward. Many field studies have proven that top-down crackingis the major cracking mechanism in thick flexible pavement. Severalfactors have been proposed as the cause of top-down cracking: load-induced factors (high tensile and shear stress or strain at the edgesof truck tires or in between truck tires), material factors (low-fractureenergies, HMA aging, and segregation during construction), andtemperature-induced factors (extreme cooling rate) (16).

In this study, the maximum shear strain was found to be greater thanthe tensile strain at the bottom of HMA for both loading conditions,as shown in Figure 5a and b, consistent with the near-surface fatiguecracking phenomenon reported in a recent study (11, 12). At inter-mediate to high temperatures, the vertical shear strains at the shallowdepth (up to 100 mm below the surface) are significantly greaterthan the critical transverse and longitudinal tensile strains at thesurface and bottom of HMA layers for thick flexible pavement. Thisshear strain could induce a new phenomenon of crack developmentknown as near-surface fatigue cracking. The difference betweenmaximum tensile strain and shear strain is 47% to 50% for 3-Dcontact stress and 25% to 37% for uniform contact stress. Hence,the uniform contact stress underestimates the near-surface crackingpotential for thick pavement.

Figure 6 (a and b) shows the schematic distribution of the shearstrain within the HMA layer at 35-kN dual tire loading under uniformcontact stresses and 3-D contact stresses, respectively. The maximumshear strain is concentrated at the upper part of the HMA layer at the

0

50

100

150

200

250

300

-150 -100 -50 0 50 100 150

Transverse Tensile Strain (micro)

Dep

th (

mm

)

Uniform contact stressMeasured 3D contact stress

(a)

-150 -100 -50 0 50 100 1500

50

100

150

200

250

Longtitudinal Tensile Strain (micro)

Dep

th (

mm

)

Uniform contact stressMeasured 3D contact stress

(b)

FIGURE 4 Horizontal tensile strains at bottom ofHMA in (a) transverse direction and (b) longitudinaldirection.

tire edge for both loading conditions. The 3-D contact stress causesgreater shear strain at the pavement near surface than the uniformcontact stress loading condition. The greater shear strain and thelow confinement at the tire edge indicate that the 3-D tire contactstresses could cause significant cracking or shear flow, or both, atthe pavement near surface.

An outward shear flow trend away from the tire center is clearlyobserved under the 3-D contact stress loading condition, probablydue to the effect of transverse surface tangential stresses and thenonuniform distribution of vertical contact stresses. In addition, highshear strain concentration is observed close to the pavement surfaceunder the tire ribs when the 3-D contact stresses are considered. Thisfinding is consistent with the findings of top-down cracking reportedby Myers et al. (17 ).

58 Transportation Research Record 2095

Octahedral Shear Stress

Two types of deformation exist in HMA layer: volume reductioncaused by traffic densification and permanent movement at a constantvolume caused by shear flow. Rutting is caused mainly by shear flowbecause volumetric rutting by postcompaction appears only in theinitial phase.

Octahedral shear stress is independent of the first stress invariant.Thus, it is possible to use octahedral shear stress to evaluate the HMAshear flow potential without considering the volumetric deformation.The crack can also be induced by shear because the shear stress caninduce dilation due to aggregate particle movement and result intensile in the asphalt mastic or the interface between mastic andaggregate (18). Octahedral shear stress is calculated as the equivalentshear stress at the octahedral plane and reflects the ability of ductilematerial to resist shear failure (see Equation 3) (19).

where

τoct = octahedral shear stress;σ1, σ2, and σ3 = maximum, middle, and minimum principal

stresses; andJ2 = second deviatoric stress invariant.

The schematic distribution of octahedral shear stresses within theHMA layer at 35-kN dual tire loading is shown in Figure 7a and b foruniform stress and 3-D contact stress loading conditions, respectively.The octahedral shear stress concentrates near the surface becauseof the effect of 3-D tire contact stresses. This high concentrationof octahedral shear stress indicates that the 3-D contact stresses cancause significant HMA shear flow at the upper part of the HMAlayer and lateral vaults at tire edges compared with the uniformcontact stresses.

EFFECTS OF VARIOUS LOADS ON PAVEMENT RESPONSES

As described in the tire–pavement interaction analysis, the verticalcontact stresses under each rib increase in a nonuniform manner asload increases. In this section, the measured 3-D contact stresses under

τ σ σ σ σ σ σoct = −( ) + −( ) + −( ) =1

3

2

331 2

2

2 3

2

1 3

2

2J ( )

0

60

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180

240

35kN 44kN 53kN

Str

ain

(mic

ro)

Maximum tensile strain Maximum shear strain

(a)

(b)

0

60

120

180

240

Str

ain

(mic

ro)

35kN 44kN 53kN

Maximum tensile strain Maximum shear strain

FIGURE 5 Maximum tensile strains at bottom ofHMA and maximum shear strains for (a) uniformcontact stresses and (b) 3-D contact stresses.

(a)

(b)

FIGURE 6 Schematic distribution of shear strains within HMAfor (a) uniform contact stresses and (b) 3-D contact stresses.

(a)

(b)

FIGURE 7 Schematic distribution of octahedral shear stresseswithin HMA for (a) uniform contact stresses and (b) 3-D contactstresses.

various loading levels were used, and their effects on pavementresponses were analyzed.

Vertical Shear Strain and Octahedral Shear Stress

Figure 8 (a and b) shows the schematic distribution of vertical shearstrain within HMA for 35- and 53-kN dual tire loading, respectively,using measured 3-D contact stresses. As the load increases, themaximum shear strain concentrates at the upper part of the HMAlayer at the tire edge, while the increase of shear strain concentra-tion under tire ribs becomes less significant, possibly because theincrease in wheel load mainly increases the vertical contact stressat the tire edge.

Figure 8 (c and d) shows the schematic distribution of octahedralshear stresses within HMA for 35- and 53-kN dual tire loading,respectively, using the measured 3-D contact stresses. As the loadincreases, octahedral shear stresses increase, and a small concentrationof octahedral shear stress is observed at the inner edge of the dualtire assembly.

The maximum shear strains and octahedral shear stresses at variousload levels were compared for the two loading conditions (uniformand 3-D contact stresses), as shown in Figure 9a and b, respectively.The 3-D contact stress resulted in a 7% to 18% greater maximum shearstrain and a 19% to 25% greater maximum octahedral shear stress thanunder uniform stress loading conditions. The strain differencesbetween the two loading conditions decrease as the load increases,consistent with the fact that the nonuniformity of vertical contactstress distribution at each rib decreases as load increases.

Wang and Al-Qadi 59

Tensile Strain

The transverse and longitudinal tensile strains at the bottom ofHMA at various loading levels were compared for the two loadingconditions (uniform and 3-D contact stresses; see Figure 10a and b).The 3-D contact stresses resulted in 9% to 17% greater transversetensile strains and 1% to 3% greater longitudinal tensile strains thanunder the uniform stress loading condition. Similar to the shear strainsand octahedral shear stresses, the tensile strain differences for thetwo loading conditions decrease as the load increases.

Compressive Strain

The compressive strains at the pavement near surface and the topof the subgrade at various loading levels were compared for the twoloading conditions (uniform and 3-D contact stresses; see Figure 10cand d). The 3-D contact stresses resulted in 28% to 35% greatercompressive strains at the pavement’s near surface and 7% greatercompressive strains at the top of the subgrade than under the uni-form stress loading condition. The strain differences are significantat the pavement’s near surface and become negligible at a greaterdepth. The pavement responses at greater depth are mainly controlledby total wheel load, suggesting that the 3-D contact stresses maynot be neglected when considering pavement responses at the nearsurface. In addition, the compressive strains at the pavement surfacechange insignificantly as the load increases, because the verticalcontact stresses at the center rib are almost constant as the total wheelload increases.

(a)

(c)

(d)

(b)

FIGURE 8 Schematic distribution within HMA for (a) shear strainunder 35-kN load, (b) shear strain under 53-kN load, (c) octahedralshear stress under 35-kN load, and (d ) octahedral shear stressunder 53-kN load.

Uniform contact stress3D contact stress

Uniform contact stress3D contact stress

0

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35kN 44kN 53kN

Max

imum

She

ar S

trai

n (m

icro

)

(a)

(b)

0

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300

Max

imum

Oct

ahed

ral S

hear

Str

ess

(kP

a)

35kN 44kN 53kN

FIGURE 9 Comparisons of (a) maximum shearstrains and (b) maximum octahedral shearstresses for various loading levels.

CONCLUSION

This study demonstrates that 3-D contact stresses are important whenanalyzing perpetual pavement responses. The following conclusionscan be drawn from this study:

1. The 3-D tire contact stresses induce greater compressive strain,shear strain, and octahedral shear stress at the pavement near surfacethan under the uniform contact stresses, suggesting that uniform con-tact stresses might underestimate the near-surface cracking potentialand shear flow in perpetual pavement.

2. Although the pavement responses at greater depths are mainlycontrolled by wheel loading, the 3-D tire contact stresses induce greatertransverse tensile strains at the bottom of HMA and compressivestrains at the top of the subgrade.

3. The nonuniform distribution of vertical contact stresses andtransverse tangential stresses induce the outward shear flow from thetire center and shear strain concentration under tire ribs at the pavementnear surface.

4. Increasing the wheel loading mostly increases the contactstresses at the tire shoulder and the corresponding shear strain andoctahedral shear stress at the tire edge.

5. The difference in pavement responses for uniform contactstresses and 3-D contact stresses decreases as wheel loading increases.

ACKNOWLEDGMENTS

This publication is partially based on the results of ICT-R59, Eval-uation of Pavement Damage Due to New Tire Designs, conductedin cooperation with the Illinois Center for Transportation; the Illi-

60 Transportation Research Record 2095

nois Department of Transportation, Division of Highways; and theU.S. Department of Transportation, FHWA. The authors acknowledgeDavid Lippert’s support and the assistance of the following membersof the Technical Review Panel for ICT-R59: Mark Gawedzinski,Amy Schutzbach, Bruce Peebles, Charles Wienrank, and RichTelford. Earlier work by J. Yoo and M. A. Elseifi is also greatlyappreciated.

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Uniform contact stress

3D contact stress

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pres

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at N

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(a)

FIGURE 10 Comparisons of (a) transverse tensile strains at bottom of HMA, (b) longitudinal tensile strainsat bottom of HMA, (c) compressive strains at pavement near surface, and (d ) compressive strains at top of subgrade.

8. Al-Qadi, I. L., M. A. Elseifi, and P. J. Yoo. Characterization of PavementDamage Due to Different Tire Configurations. Journal of the Associationof Asphalt Paving Technologists, Vol. 84, 2005, pp. 921–962.

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The contents of this paper reflect the views of the authors, who are responsiblefor the facts and accuracy of the data. The contents do not necessarily reflectthe official views or policies of the Illinois Center for Transportation, the IllinoisDepartment of Transportation, or FHWA. This paper does not constitute a standard,specification, or regulation.

The Flexible Pavement Design Committee sponsored publication of this paper.