Near-surface stress states in exible pavements usingmeasured radial tire contact stresses and ADINA

Marc Novak, Bjorn Birgisson *, Reynaldo Roque

Department of Civil and Coastal Engineering, University of Florida, P.O. Box 116580, Gainesville, FL 32611-6580, USA

Abstract

The nite element code ADINA was used to identify the three-dimensional stress states in a typical exible pavement

conguration, resulting from measured radial tire contact stresses. The predictions show that measured radial tire

contact stresses result in stress states being both larger in magnitude and more focused near the surface than those

obtained from traditional uniform vertical loading conditions. In terms of eects of possible pavement damage

mechanisms, predicted high near-surface shear stresses may be a part of an explanation for near-surface rutting failure

modes, as supported by near-surface slip planes seen in the eld.

2003 Elsevier Science Ltd. All rights reserved.

Keywords: Tire contact stresses; Contact surfaces; Instability rutting; Pavement analysis

1. Introduction

Instability rutting in asphalt pavements occurs within

wheel paths and is due to the lateral displacement of

material within the pavement layer. It occurs when the

structural properties of the compacted pavement are

inadequate to resist the stresses imposed upon it. Despite

instability rutting being the predominant mode of pre-

mature rutting failures in modern exible pavements,

current pavement structural design approaches do not

deal with rutting in the asphalt concrete layer [18].

Recent studies have shown that instability rutting is

primarily a near-surface phenomenon, aecting only the

top 13 in. of the asphalt concrete layer, with visible slip

surfaces associated with the rutting failure [9,10]. Simi-

larly, studies by Myers et al. [11] and de Beer et al. [12]

have shown that tire contact stresses in this near-surface

region are greatly inuenced by the structural charac-

teristics and design of radial truck tires. Measured radial

tire contact stresses are both distributed highly non-

uniformly over the tire footprint and larger in magni-

tude than the traditional uniform circular load used in

pavement design. Dealing appropriately with instability

rutting for both the design of asphalt mixtures and for

the structural design of pavements, will require a com-

plete understanding of the mechanisms that induce rut-

ting within the surface layer and the identication of the

key factors that aect these mechanisms.

Currently, more than 98% of trucks use radial tires,

because of the associated fuel savings, and higher reli-

ability of newer tire structures [13,14]. Radial tire con-

tact stresses are highly complex, with non-uniform

vertical stresses throughout the tire contact area, as well

as large lateral contact stress components in both the

transverse and longitudinal (along wheel path) direc-

tions. The eects of these complex tire contact stresses

have not been widely analyzed. Myers et al. [15] and

Roque et al. [16] present the results of a series of

two-dimensional nite element analyses where a two-

dimensional cross-section of measured three-dimensional

tire contact stresses was applied on a layered half plane.

The two-dimensional nite element analysis results show

that the predicted stress state is signicantly dierent

from that of a uniform vertical strip load. Similar results

were also reported based on three-dimensional layered

*Corresponding author. Tel.: +1-352-392-9537x1462; fax:

+1-352-392-3394.

E-mail address: bbirg@ce.u.edu (B. Birgisson).

0045-7949/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0045-7949(02)00413-3

Computers and Structures 81 (2003) 859870

www.elsevier.com/locate/compstruc

elastic theory solutions. However, because of the limi-

tations of the semi-analytical layered elastic solution

approach, a number of simplifying assumptions were

made regarding the application and distribution of

measured tire loads. These results were based on a tire

contact measurement system developed by Pottinger

[17], which was especially developed for tire research,

and consists of 1200 distinct measurement points, which

register contact stresses in the x, y and z direction. Todate, no detailed three-dimensional nite element anal-

ysis of the eects of tire contact stresses has been per-

formed, using the results from Pottingers tire contactmeasurement system [17]. A part of the challenge in

modeling actual tire stresses is that the radial tire contact

area is rather small (4060 square inches (in.2)) and

highly non-uniform. Typical exible pavement struc-

tures also consist of a relatively thin layer (48 in.) of

asphalt concrete, overlying a granular base course (812

in. thick), which rests on a semi-innite foundation.

Hence, the combination of a small, highly non-uni-

formly loaded contact area and relatively thin surface

layers, connecting to a semi-innite half plane requires a

large number of elements.

In this study, the nite element code ADINA [18] is

used in modeling the three-dimensional eects of mea-

sured tire contact stresses in a typical pavement cong-

uration. Although exible pavement materials are

generally non-linear in nature, a rm understanding of

the linear elastic stress states should precede any further

analysis. All pavement layers are assumed to be linear

elastic, and dynamic eects are ignored in favor of

promoting a basic understanding of static stress states

before complicating the analysis with dynamic eects.

Due to the complicated nature of the measured radial

tire contact stresses, contact surfaces were used exten-

sively to control the size of the problem.

The results presented show that the predicted stress

states obtained with measured radial tire loads are dif-

ferent from those resulting from circular uniform verti-

cal loads. In particular, high transverse near-surface

shear stresses are observed in the pavement, which are

not present in the traditional approach, which may

partly explain the near-surface instability rutting failure

modes recently reported in the literature [9,10].

In the following, an overview of the tire contact

measurement system is provided, followed by the de-

scription of the nite element modeling, and the pre-

sentation of the modeling results.

2. Measurement of radial tire contact stresses

Based on contact stress measurements, Pottinger [17]

has identied two distinct types of contact stress eects

that exist under truck tires. These are generally referred

to as the pneumatic eect and Poissons eect [13]. The

overriding eect induced under radial truck tires is the

Poissons eect. This is a direct result of tire construc-tion. Radial tires are constructed to have sti treads and

exible sidewalls, to minimize the deformation of the tire

during rolling. Thus, the lateral stresses induced on the

road by the radial truck tire will tend to push out from

the center of the tire ribs. In contrast, bias-ply tires tend

to have high wall stiness and a exible tread, resulting

in smaller lateral contact stresses. Modern radial truck

tires also can withstand higher ination pressures and

higher loads than bias-ply tires, resulting in higher

contact stresses [13].

By using triaxial load pin transducers inserted onto a

at steel test track, Pottinger [17] was able to measure

tire-interface forces and displacements for vertical, lon-

gitudinal, and transverse axes. The experimental setup

used was also capable of determining the rolling tire

footprint shape. Fig. 1 shows the test track conguration

that was used. The experimental setup consisted of a

rolling steel treadmill device in which the tire was held in

one location, while the bed was moved longitudinally,

causing the tire to roll over a row of 16 transducers.

Stresses and displacements were recorded every 0.20 in.

longitudinally (parallel to wheel path) and every 0.15 in.

transversely (perpendicular to wheel path) by varying

the transverse position of the sensors resulting in over

1200 contact points, at which contact stresses in the x, y,and z directions were recorded. This resulted in 3600distinct stress measurements for a radial tire with ve

ribs and a gross contact area of 47 in.2 with an ination

pressure of 115 psi. The measurements provided a high

denition of actual tire contact stresses.

The other available measurement system, developed

by de Beer et al. [12], also measures contact stresses in

the x, y, and z directions, but uses only 13 triaxial straingauge steel pins, mounted on a steel plate and xed ush

with the road surface.

Because of the complexities involved in measur-

ing contact stresses under tires, it is not possible to ob-

tain these measurements directly on real pavements. In

particular, the question arises as to whether stresses

measured under a tire on a rigid foundation with em-

bedded sensors are similar to the contact stresses that a

exible pavement will experience. Roque et al. [16] pre-

sented a two-dimensional nite element model of a ra-

dial tire, using the nite element program ABAQUS

[19]. The results showed that contact stresses were nearly

identical whether the contact surface was rigid or had

properties similar to an asphalt pavement. Eectively,

the stiness of the tire is so much less than the pavement,

that the resulting contact stresses are similar to those

obtained from a rigid steel bed. It was concluded that

contact stress measuring devices, such as the one used in

this study, with rigid foundations are suitable for the

prediction of response of exible highway pavements

[16].

860 M. Novak et al. / Computers and Structures 81 (2003) 859870

3. Pavement structure and loading conditions

A typical three-layer (asphalt concrete, base, and

foundation) pavement structure was used in this analy-

sis, used previously by Myers et al. [15] and Drakos et al.

[10]. The thickness of the asphalt concrete layer was 8

in., overlying a 12-in. thick granular base course. The

foundation was assumed to consist of a 52-in. thick

layer. The properties of each layer were assumed to be

isotropic, homogenous, and linear elastic. Table 1 lists

the elastic moduli, Poissons ratio and the layer thicknessfor each of the pavement layers. The asphalt concrete

layer modulus corresponds to that experienced on a

warm summer day on a fairly new pavement, and the

base and foundation values were chosen based on typi-

cal measured values in the State of Florida [10,15].

4. ADINA nite element model

A part of the challenge with three-dimensional

modeling of a pavement system with measured tire

contact stresses is that the resulting nite element model

needs to combine a small, highly non-uniformly loaded

contact area with relatively thin surface layers, con-

necting to a semi-innite half space, resulting in a large

number of elements. The measured contact area under

the radial tire used in this study is 47 in.2. The radial tire

used was the same one used by Myers [15] and Drakos

[10] and has been determined to be typical for radial

truck tires currently used in the Unites States of Amer-

ica.

An initial assessment of the grid size requirements

based on using a uniform stress distribution demon-

strated that the three-dimensional model should be at

least 72 in. deep and extend laterally at least 60 in. in

each direction from the center of the tire contact load to

adequately represent the semi-innite half space condi-

tions associated with pavement problems. Because of the

size of this model, the renement needed near the tire

contact area, and the desire to remain within the 3:1

element length to width ratio, the resulting memory re-

quirements for the Silicon Graphics Multiprocessor

computer available for this analysis exceeded the 1300

MB RAM memory available. To overcome the limita-

tions associated with building a traditional mesh, con-

tact surfaces were introduced, where a ne graded mesh

representing the loaded surface was attached (glued)

onto a coarse-graded mesh. This allowed for the intro-

duction of coarse meshes at distances further away from

the loaded area where the change in stress was more

gradual, and far eld stresses dominated the response.

The use of contact surfaces was further justied based

on the primary area of interest being the near-surface

area under and immediately surrounding the loaded tire,

thus negating any possible negative numerical eects of

far away contact surfaces.

The measured tire contact measurements reported

tire contact stresses as uniform stresses acting over areas

of 0.03 in.2 in size. Three dierent stresses were pro-

vided, namely vertical normal stresses, transverse shear

stresses, and longitudinal shear stresses. Ideally, each

Fig. 1. Schematic of system developed by Pottinger [17] used to measure tire contact stresses.

Table 1

Material properties and layer thicknesses of pavement structure

used in the nite element analysis

Layer Modulus

(psi)

Poissonsratio

Thickness

(in.)

Asphalt concrete 100,000 0.45 8

Base 40,000 0.45 12

Foundation 15,000 0.45 52

M. Novak et al. / Computers and Structures 81 (2003) 859870 861

uniform stress should be applied to a single element.

Unfortunately, the number of elements needed would

have again exceeded the memory of the Silicon Graphics

multiprocessor computer available for the analysis.

Thus, the use of fewer elements was required under the

contact area, which subsequently required the determi-

nation of the equivalent nodal forces to be applied to

each node. The appropriate nodal forces for each ele-

ment were determined by converting each uniform stress

into an equivalent concentrated force. These forces were

then applied to each element and distributed over the

element nodes according to the rules described below.

If it is assumed that the concentrated forces ff g hascomponents fx, fy , and fz, then the element load vector,freg, acting on a surface of an element, is dened by:freg

ZSe

N TfUgdS 1

where N T is the transpose of the shape function matrix,and fUg is the surface traction vector. The contributionof ff g to freg can be determined by viewing the con-centrated force as a large traction, fUg, acting over asmall area, dS. Subsequently, the concentrated forcevector ff g can be denoted as:ff g fUg dS 2The integral of N TfUgdS thus becomes N Tff g, re-sulting in Eq. (1), with n concentrated forces, becoming:

freg Xni1

N Ti ff gi 3

where N i is the value of N at the location of ff gi.The nal three-dimensional mesh consisted of

204,185 nodes with three degrees of freedom per node,

resulting in a total of 612,555 degrees of freedom. The

elements under the radial contact area had uniform di-

mensions of 0.30 by 0.40 in. Contact surfaces were used

for the transition from the asphalt layer to the base,

from the base to the foundation, and from the ne mesh

near the tire contact area to the peripheral areas. Fig. 2

illustrates the nal three-dimensional mesh, with Fig. 3

showing a plan view of the contact area of the three-

dimensional mesh.

Finally, Fig. 4 shows a plan view of the radial tire

contact stresses applied as nodal forces onto the pave-

ment model surface at locations consistent with ve tire

ribs. Fig. 5 shows a cross-sectional prole of the tire

contact stresses. It is apparent from Figs. 4 and 5 that

the measured tire contact stresses are highly non-sym-

metric, thus forcing the modeling of the whole tire

contact structure.

4.1. Solution process

There are four dierent types of solution schemes

available in ADINA, namely, (1) direct solver, (2) sparse

solver for very large problems, (3) iterative solver, for

non-linear problems, and (4) multigrid solver, for par-

allel processing solutions. The direct solver requires a

large amount of storage and is not recommended for

large three-dimensional models [17]. The multigrid sol-

ver is intended for large three-dimensional problems

with very large systems of equations, but when contact

Fig. 2. Three-dimensional nite element mesh used in the

pavement response analysis.

Fig. 3. Plan view of the contact area of the three-dimensional

mesh used in the pavement response analysis.

862 M. Novak et al. / Computers and Structures 81 (2003) 859870

surfaces are used, ADINA does not allow for the use of

the multigrid solver. The best solver for large memory

limited problems is the sparse solver. Unfortunately, for

the number of equations anticipated, the system requires

a 64-bit version solution solver, with only the 32-bit

version currently available for this research. Hence,

since the iterative solver is also recommended for large

problems, it was used by default.

The equilibrium equations to be solved in a non-

linear static analysis of a nite element model with

contact surfaces in ADINA are:

tDtR tDtF 0 4

where tDtR is the vector of the external nodal loads andtDtF is the force vector equivalent to the element stressesat time t Dt [18]. In non-linear analysis three iterationmethods/schemes are available in ADINA, namely, (1)

full Newton method, with or without line searches, (2)

modied Newton method, with and without line sear-

ches, and (3) the BroydenFlectherGoldfarbShanno

(BFGS) matrix update method. In this study, the full

Newton method with lines searches was employed,

based on its ability to converge and obtain accurate

solutions [18]. The iterative solution process required

1295 MB of RAM memory, with a resulting solution

time of 9000 s, using a single processor.

5. Predicted stress states

In the following, a comparison will be made between

predicted near-surface stress states predicted from: (1)

an axisymmetric uniform vertical load, to simulate cur-

rent practice, (2) a three-dimensional uniform vertical

load applied over measured gross tire contact area, to

evaluate the eects of the tire footprint shape, and (3) a

three-dimensional radial tire load with vertical, tangen-

tial and longitudinal contact stresses, to represent full

measured radial truck tire loading eects. Near-surface

vertical stresses, horizontal stresses, shear stresses, and

conning stresses are presented and compared between

the three dierent surface loading conditions used.

5.1. Axisymmetric model

Current practice in pavement engineering uses solu-

tions based on three-dimensional layered elastic theory,

in which the tire load is modeled as a circular uniform

vertical load. Typical pavement engineering analysis and

design programs that use this loading conguration in-

clude BISAR [20], ELSYM5 [21], and WESLEA [22]. A

two-dimensional axisymmetric model was generated in

ADINA [18] to provide a comparison between the

stresses induced by a circular uniform vertical load and

the more complicated radial tire loading eects. Fig. 6

displays the two-dimensional axisymmetric nite ele-

ment mesh used in the analysis. Because of the sym-

metric nature of the problem, only one half of the loaded

area is modeled. The nite element model is 72 in. tall

and 30 in. wide, with a uniform vertical surface load of

115 psi, distributed over a radius of 4 in. The elements

used consist of eight-noded isoparametric elements, with

72 vertical rows of elements, each containing 99 ele-

ments, for a total of 7128 elements. The layer thicknesses

and elastic properties are the same as in the three-

dimensional nite element model, discussed previously.

To evaluate the results from the axisymmetric nite

element model, a comparison was performed between

predicted shear stresses at the edge of the loaded area and

those obtained from a semi-analytic layered-elastic the-

ory solution, using the program BISAR [20]. Fig. 7

shows that the shear stress predictions obtained with

ADINA [18] and BISAR [20] are very similar for the

exact same loading conditions, meaning that the axi-

symmetric model adequately captures the loading re-

sponse due to the circular uniformly loaded vertical load.

5.2. Comparison of vertical stress states

Figs. 8 and 9 show the near-surface vertical stress

contours obtained from the measured radial truck tire

Fig. 4. Illustration of the contact area and the radial tire nodal

forces used in the pavement response analysis.

Fig. 5. Cross-sectional view of applied radial tire nodal forces used in the pavement response analysis.

M. Novak et al. / Computers and Structures 81 (2003) 859870 863

loads and the corresponding three-dimensional uniform

vertical load, respectively. The contour plots are ob-

tained under the left-most rib of the three-dimensional

radial tire, and the corresponding location for the uni-

form vertical load. The radial tire produces new surface

vertical stresses that are higher in magnitude than those

produced by the uniform vertical load. Fig. 10 shows a

comparison between predicted vertical stresses at the

edge of the radial tire and those obtained from the three-

dimensional vertical load and the axisymmetric loading

case. Below 1.0 in., the radial tire loading case ap-

proaches the uniform vertical and the axisymmetric

loading cases.

Fig. 6. A cross-sectional view of the axisymmetric nite ele-

ment mesh used for comparison purposes.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0Shear Stress (psi)

Dep

th (i

nche

s)

BISAR

ADINA

Fig. 7. Comparison of shear stresses under the edge of a two-dimensional axisymmetric circular uniform vertical load predicted with

BISAR and ADINA.

Fig. 8. Predicted vertical stress contours under left edge of

three-dimensional radial tire load.

864 M. Novak et al. / Computers and Structures 81 (2003) 859870

The three-dimensional uniform vertical and two-

dimensional axisymmetric results show very similar

vertical stress proles at the edge of the tire, implying

that for uniform loading conditions, the circular uni-

form vertical loading condition is suciently detailed in

many cases, negating the need for three-dimensional

modeling. However, the addition of lateral surface

tractions, as in the radial tire case, signicantly changes

the near-surface vertical stress proles, thus requiring a

full three-dimensional analysis of loading eects.

5.3. Comparison of horizontal stress states

Figs. 11 and 12 show the near-surface horizontal

stress contours obtained under the left-most rib of the

three-dimensional radial tire, and the corresponding

location for the uniform vertical load. The radial tire

contact stresses produce horizontal compressive stresses

that are both higher in magnitude and more intense in

the top 0.25 in. than the corresponding uniform vertical

load. These high very near-surface stress states may be

partly due to the discrete nature of the tire contact

Fig. 9. Predicted vertical stress contours under left edge of

three-dimensional uniform vertical tire load acting over mea-

sured tire contact surface.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0

Stress (psi)

Dep

th (i

nche

s)

AxisymmetricRadialUniform

Fig. 10. A comparison of predicted vertical stress with depth at the left edge of loaded area.

Fig. 11. Predicted horizontal stress contours under left edge of

three-dimensional radial tire load.

M. Novak et al. / Computers and Structures 81 (2003) 859870 865

measurement system and the constraints associated with

applying the measured tire contact stresses as discrete

nodal forces in the nite element model. However, the

general pattern of stresses should be representative,

discounting the higher local peaks in stress under dis-

crete nodal locations. Fig. 13 shows a comparison of

horizontal stress with depth at the edge of the tire load.

The results show that the high horizontal stresses dissi-

pate very quickly over the top 0.25 in. of the pavement,

below which they become similar in magnitude to those

produced by the uniform loading conditions. These re-

sults imply that the contribution from bending may

dominate the response at greater depths for this partic-

ular pavement system, overwhelming the eects from the

lateral tire contact stresses.

5.4. Comparison of shear stress states

Figs. 14 and 15 show the near-surface shear stress

contours obtained under the left-most rib of the three-

dimensional radial tire, and the corresponding location

Fig. 12. Predicted horizontal stress contours under left edge of

three-dimensional uniform vertical tire load acting over mea-

sured tire contact surface.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0

Stress (psi)

Dep

th (i

nche

s)

AxisymmetricRadialUniform

Fig. 13. Comparison of predicted horizontal stress with depth at the left edge of loaded area.

Fig. 14. Predicted shear stress contours in the lateral direction

(yz-plane) under left edge of three-dimensional radial tire load.

866 M. Novak et al. / Computers and Structures 81 (2003) 859870

for the uniform vertical load, respectively. Again, the

radial tire contact stresses produce shear stresses that are

both higher in magnitude and more intense in the top 1

in. than the corresponding uniform vertical load. The

zone of maximum shear is also closer to the surface for

the radial tire contact stress case.

Figs. 16 and 17 show a plot of the near-surface shear

stresses under the edge of the loaded area, as well as 0.15

in. away from the loading. The results show high near-

surface shear stresses (68 psi) under the edge of the

loaded tire for the radial tire contact stress case, dissi-

pating rapidly both vertically and horizontally away

from the tire. In contrast, the uniform vertical loading

cases do not show these high near-surface shear stresses.

5.5. Comparison of hydrostatic pressure states

Since asphalt concrete, like other granular geomate-

rials, is pressure dependent, the eects of tire contact

stresses on the distribution of hydrostatic pressures was

also evaluated. The hydrostatic pressure, herein denoted

simply as pressure, is dened as the sum of the normal

stresses divided by three. Figs. 18 and 19 show contour

plots of pressure obtained under the left-most rib of the

three-dimensional radial tire, and the corresponding

location for the uniform vertical load, respectively. The

radial tire conguration produces much higher pressures

near the edges of the loaded area than the corresponding

uniformly loaded cases, implying a conning eect due

to the radial tire contact stresses.

Figs. 20 and 21 show proles of pressure versus depth

under the edge of the tire and at a distance of 0.15 in.

away from the tire. Again, the results show that pressure

dissipates fast in both the vertical and horizontal direc-

tions away from the loaded area, dropping from a near-

surface high of 158 psi under the edge of the loaded area,

down to 9 psi at a horizontal distance of 0.15 in. away

from the tire.

6. Summary and conclusions

The commercial nite element code ADINA [18] was

used to identify the stress states in a typical exible

pavement conguration, resulting from measured radial

tire contact stresses. Due to the complicated nature of

the measured tire contact stresses used in this paper, the

resulting nite element model consisted of 204,185

nodes, with a total of 612,555 degrees of freedom. An

Fig. 15. Predicted shear stress contours in the lateral direction

(yz-plane) under left edge of three-dimensional uniform verticaltire load acting over measured tire contact surface.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0

Shear Stress (psi)

Dep

th (i

nche

s)

RadialUniformAxisymmetric

Fig. 16. Comparison of predicted shear stresses in the lateral direction (yz-plane) with depth at the left edge of loaded area.

M. Novak et al. / Computers and Structures 81 (2003) 859870 867

iterative solution scheme consisting of the full Newton

method with lines searches was employed. The iterative

solution process required 1295 MB of RAM memory,

with a resulting solution time of 9000 s, using a single

processor. Due to memory limitations, contact surfaces

were used extensively in the three-dimensional nite el-

ement model. The results show clearly that contact

surfaces can be employed successfully if they are su-

ciently far away from the areas of interest, since no

signicant numerical errors were observed in the near-

surface stress states due to the presence of contact sur-

faces.

In this paper, measured tire contact stresses are ap-

plied as nodal forces in a three-dimensional nite ele-

ment model. The representation of measured tire contact

stresses at discrete points is currently a function of the

limitations of available tire contact measurement sys-

tems [17]. The authors recognize that some predicted

high concentrations or peaks in local near-surface stress

states under nodal points may be partly due to the dis-

crete nature of the tire contact measurement system and

the constraints associated with applying the measured

tire contact stresses as discrete nodal forces in the nite

element model. However, the general pattern of stresses

Fig. 18. Predicted pressure contours under left edge of three-

dimensional radial tire load.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0

Shear Stress (psi)

Dep

th (i

nche

s)

RadialUniformAxisymmetric

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0

Shear Stress (psi)

Dep

th (i

nche

s)

RadialUniformAxisymmetric

Fig. 17. Comparison of predicted shear stresses in the lateral direction (yz-plane) with depth at 0.15 in. away from the left edge ofloaded area.

Fig. 19. Predicted pressure contours under left edge of three-

dimensional uniform vertical tire load acting over measured tire

contact surface.

868 M. Novak et al. / Computers and Structures 81 (2003) 859870

should be representative, discounting the higher local

peaks in stress under discrete nodal locations.

Even though it has been shown that contact stresses

obtained with the tire contact measurement system used

were nearly identical whether the contact surface was

rigid or had properties similar to an asphalt pavement

[16], it has to be recognized that the an actual tire has

some transverse rigidity [16]. Thus in reality subsequent

application of measured tire contact stresses at discrete

points without incorporating the actual tire structure is

an approximation of the conditions present in a real

situation. However, the current approach represents the

rst attempt to model the eects of measured tire in-

terface stresses in three dimensions. The incorporation

of a full tire model would be signicantly more com-

plicated, with numerous other issues needing to be ad-

dressed, such as the eective stiness of radial tire walls

and treads that are reinforced with steel wiring, and the

net eect of tire bulging and deformation on the redis-

tribution of stresses onto the pavement.

Within the context of the limitations of the current

tire measurement system, the results in this paper still

provide a good starting point for developing the needed

level of understanding of the mechanisms that may in-

duce instability rutting in the near-surface region of an

asphalt concrete layer. Current pavement structural

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0

Pressure (psi)

Dep

th (i

nche

s)

RadialUniformAxisymmetric

Fig. 20. Comparison of predicted pressures with depth at the left edge of loaded area.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0

Pressure (psi)

Dep

th (i

nche

s)

RadialUniformAxisymmetric

Fig. 21. Comparison of predicted pressures with depth at 0.15 in. away from the left edge of loaded area.

M. Novak et al. / Computers and Structures 81 (2003) 859870 869

design approaches do not deal with rutting in the asphalt

concrete layer. The results presented in this paper show

that measured radial tire contact stresses result in near-

surface stress states are dierent from those obtained

using traditional circular uniform-loading conditions.

The resulting stress states appear larger in magnitude

and more focused near the surface than those obtained

from uniform vertical loading conditions. In particular,

higher transverse near-surface shear stresses are ob-

served in the top 1 in. of the pavement, which may partly

explain the near-surface instability rutting failure modes

recently reported in the literature [9,10]. However, at

depths below 12 in., bending eects tended to dominate

the response, minimizing the dierence between the ra-

dial tire stress states and those obtained from uniformly

distributed loading conditions.

In summary, further research is needed, in which more

radial tire congurations are evaluated, along with other

pavement geometries. The eects of variation of modulus

within the asphalt layer and non-linear material behavior

may also be important, and require further study.

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870 M. Novak et al. / Computers and Structures 81 (2003) 859870

Near-surface stress states in flexible pavements using measured radial tire contact stresses and ADINAIntroductionMeasurement of radial tire contact stressesPavement structure and loading conditionsADINA finite element modelSolution process

Predicted stress statesAxisymmetric modelComparison of vertical stress statesComparison of horizontal stress statesComparison of shear stress statesComparison of hydrostatic pressure states

Summary and conclusionsReferences