The International Journal of Geomechanics

Volume 2, Number 3, 353–376 (2002)

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A Study of Nonlinear Tire Contact

Pressure Effects on HMA Rutting
J. Hua and T. White*

Received

Engineer, Lin Engineering, Ltd., 210 West Chestaut,

Chatham, IL 62629
E-mail: jianfenghuakhotmail.com

Professor and Head, Department of Civil Engineering,

Mississippi State University, Box 9546,
Mississippi State, MS 39762
E-mail: Tdwhite@enjzr.msstate.edu

ABSTRACT. The Indiana Department of Transportation/Purdue University accelerated pavement testing

(APT) facility has been utilized in a number of studies of hot mix asphalt (HMA) rutting performance. The
benefit of using APT is that rutting performance can be established in a few days of testing.
Finite element (FE) models have been developed for relating APT to in-service pavement perfor-
mance. Factors addressed in the models include pavement geometry, boundary conditions, materials, loads,
test conditions, and construction variables. Determining the effects of these factors provides a means for
better interpreting APT test results and HMA rutting performance. A detailed analysis using 3D and 2D FE
has been made of tire/pavement contact pressure effects on rutting. The analyses include tread pattern and
constant and varying contact pressure.
A creep model is used to represent the HMA time-dependent material behavior. Based on test data,
the material constants in the creep model were back calculated. Results of the FE studies show that the creep
model can successfully characterize pavement material behavior through a reasonable approximation of
loading and other factors.

I. INTRODUCTION

Asphalt mixture rutting is time dependent and rutting of a well-designed asphalt mixture on
an in-service pavement may take years to develop. Accelerated pavement testing (APT) can

Key Words and Phrases: FE, accelerated pavement testing, tire contact pressure, hot mix asphalt, rutting.

* Corresponding author.

© 2003 ASCE DOI: 10.1061/(ASCE)1532-3641(2002)2:3(353)

ISSN 1532-3641

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 354 J. Hua and T. White

compress the time to obtain asphalt pavement performance data. Several factors can be controlled
to magnify damage per load application. For example, high testing temperature and slow speed
result in significant damage for each wheel pass on an asphalt pavement.
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To take advantage of accelerated pavement testing principles an APT facility was developed
by Purdue University for the Indiana Department of Transportation (INDOT). Prototype scale
pavement sections (a total of four lanes, 5 ft wide by 20 ft long each) can be installed in the test
pit in this facility. The APT loading system has the capability of applying moving wheel loads
to pavement test sections installed in the facility. Also, wheel wander can be explicitly simulated.
The APT is designed to apply up to a 89 kN (20,000 lb) load on a dual wheel or super single wheel
assembly. Traffic can be applied in one or two directions. The load carriage travels at 8 km/h (5
mph). The total time for a section cycle is approximately 15 s.
In large part, applications of accelerated pavement test results have been limited to relative
comparison of materials or pavement sections or empirical analysis. These approaches limit
application of APT results. On the other hand, FE (FE) analysis can expand the APT test results.
For example, FE analysis can be applied to provide a rational analysis of the time-dependent
material properties; load magnitudes, configurations, repetitions and duration; physical geometry
of pavement test sections; boundary conditions, and other important features.

II. ACCELERATED PAVEMENT TESTS

During APT tests, transverse profiles for nine locations are recorded as shown in Figure 1.
Transverse profiles are referenced to a horizontal beam spanning test sections. A small wheel
attached to the beam is lowered to the pavement and rolled across the surface. Transducers
determine the wheel’s horizontal and vertical movement. This data is recorded electronically. An
initial profile is measured. The difference in the initial profile and subsequent profiles at various
levels of wheel passes is used to compute rutting components. The average of three transverse
profiles (Locations 4, 5, and 6) is used for analysis and to compare with rut depth predictions.
Two modes of surface rutting have been observed and are shown in Figure 2.
One mode is compactive rutting and the other mode is uplift rutting. Compactive rutting
includes compressive deformation and shear flow and is identified where the deformed surface

FIGURE 1. Transverse profile locations.

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 A Study of Nonlinear Tire Contact Pressure Effects on HMA Rutting 355
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FIGURE 2. Rutting modes.

is lower than the original undisturbed surface. Uplift rutting is evidenced where the deformed
surface is higher than the original surface. Typically uplift is observed between dual tires and
outside of the wheel path. “String-line” rutting as shown in Figure 2 is taken as the difference
in the lowest point on a profile and an imaginary straight edge resting on the test lane surface and
spanning the wheel paths. Ultimately, only the compressive rut depth is used in order to be
compatible with the rut depth recorded in the Purdue University laboratory wheel track test
device (PURWheel).

III. FINITE ELEMENT ANALYSIS

The initial step in applying the FE method is to define the physical model. The model should
include major features in enough detail to provide a reasonable and reliable solution. In addition
to boundary conditions, element types, and material models, load models and wheel path wander
have to be defined. Acceptability of the model is judged from sensitivity studies and comparison
of predicted and measured responses.

A. Model Geometry and Finite Element Type

The APT facility test pit is 6.1 m (20 ft) wide by 6.1 m (20 ft) long and 1.8 m (6 ft) deep
[1]. The test pit walls are reinforced concrete. Typical pavement sections built in the test pit

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 356 J. Hua and T. White

include 1.4 m (57 in.) of pea gravel, a 0.31-m (12-in.) reinforced concrete slab and a 76-mm (3-
in.) asphalt overlay on top of the concrete slab.
Because of the test section configuration, traffic induced densification and plastic shear flow
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occurs only in the asphalt overlay. The underlying concrete slab acts as a rigid foundation. A test
lane is 1.5 m (5 ft) wide and 6.1 m (20 ft) long.
Huang [1] studied effects of model section length and number of element layers in 3D (3D)
FE analyses for the same problem. Predicted rut depths become asymptotic with a model length
of more than 1.14 m (44.8 in.) and three or four element layers. Therefore, a length of 1.27 m
(50 in.) was selected for the 3D FE model. Initially, four element layers were used to model the
76 mm (3 in.) asphalt layer.
The 3D mesh used in single wheel path analyses is shown in Figure 3. Only one half of the
test lanes were modeled due to both test lane and dual wheel assembly symmetry. Figure 4 shows
the mesh cross-section and assumed boundary conditions.

IV. LOAD MODELS

A. Tire Contact Area

Traditionally, pavement structural or rutting analysis has utilized either a circular or rectan-
gular contact area of constant pressure. However, pneumatic tires have treads. And the wheel load
is applied through these treads to the pavement surface. The contact area between a tire and the
pavement surface is not rectangular or circular. As a result, it was felt that the tire print should
be modeled explicitly to obtain an accurate near-surface rutting response prediction.
In reality, contact pressure between the tire and test slab is not uniform. The actual pressure
distribution will depend on the tire stiffness, size, tread pattern, and load as well as stiffness and

FIGURE 3. 3D FE mesh for asphalt overlay.

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 A Study of Nonlinear Tire Contact Pressure Effects on HMA Rutting 357
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FIGURE 4. Side views of FE mesh together with boundary conditions.

deformed shape of the pavement. Some of these issues will be examined below. In preliminary
analysis it is assumed that the wheel load is uniformly distributed over the tread contact area. The
contact pressure is calculated by dividing the total load by the net total contact area.

B. Load Model
Modeling the APT moving wheel load explicitly results in extended computational time. An
alternate load model was adopted consisting of a single step load function for the entire wheel
path. Huang [1] and Pan [2] used this approach. In this method, the loading time for each wheel
pass is summed to produce a total cumulative loading time for the elements. Thus, instead of
applying a large number of analysis steps, only a single load step is needed. The result of applying
this load model is shown in Figure 5.
Both vertical and horizontal permanent deformations in the longitudinal direction were
examined. As shown later in Figures 9 and 10, these deformations were uniform in the central
portion of the lane. For this reason, the analysis could be reduced to a 2D plane-strain problem.
A 2D model was developed using plane-strain element CPE4 in the ABAQUS element
library [3a,3b]. Figure 6 shows the 2D FE model and its overall dimensions. Symmetry is not
used in developing the 2D model since wheel path wander will be incorporated in subsequent
analyses. The model has six element layers in order to maintain a good aspect ratio (length of
element/height of element = 0.8 in this model). The mesh size in the transverse direction is
selected to match the dimensions and configuration of the tire print.

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FIGURE 5. Deformed mesh after loading.

FIGURE 6. 2D FE mesh for APT with dual wheel assembly.

Analyses were conducted to compare responses from 3D and 2D models of an APT test lane.
The predicted transverse surface profiles for the two models corresponding to 5,000 wheel passes
are plotted in Figure 7. Difference in predicted maximum rut depths is less than 2%. Based on
the minimal difference, the 2D model is used in subsequent analyses.

C. Material Model
In the analysis, a creep model is used to represent the viscoplastic strain as sole contributor
to permanent deformation. Instantaneous plastic strain is neglected. Lai and Anderson [4] and
Perl et al. [5] used the following models to represent creep test results:

( )
Lai: ε˙ p = 0.7580σ − 0.004078σ 2 × 10 −5 t −0.75 (1)

Perl: ε˙ p = (0.2882σ − 0.000879σ ) × 10 2 −5 −0.78

t (2)

Regression analyses were conducted to convert these polynomial functions to a stress power
law of the form ε·p = Aσ nt m. The result is:

Lai: ε˙ p = 1.03 × 10 −5 σ 0.8477t −0.75 (3)

Perl: ε˙ p = 0.47116 × 10 −5 σ 0.8159t −0.78 (4)

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FIGURE 7. Comparison of 2D and 3D model responses.

The A value derived from experiments ranged from 0.47116 × 10–5 to 1.03 × 10–5 and the
constant n ranged from 0.819 to 0.8477. The constant m ranged from –0.75 to –0.78. It is noted
that the range of stresses at which the creep tests were conducted were from 69kPa (10 psi) to
345kPa (50 psi) in Lai’s experiment and from 100 kPa (14.5 psi) to 800 kPa (116 psi) in Perl’s
experiment. The APT tire contact stress pressure is within Perl’s experimental stress level.
Therefore the stress function in Perl’s equation is more appropriate for this study.
According to Huang [1], the parameter n is associated with the tire contact pressure. Huang
selected a value for n of 0.8 for tests with 620 kPa tire pressure. Since the current analysis was
also conducted with a tire pressure of 620 kPa, the same value of n was utilized.

D. Nonuniform Tire Pressure Distribution

Results of single wheel path APT tests show the tire tread imprinted in the rutted asphalt
surface. An analysis was conducted to examine the effect of tire contact pressure on predicted
rutting.
De Beer, et al. [6] measured contact stresses with the Vehicle-Road Surface Pressure
Transducer Array (VRSPTA) system. The VRSPTA system is in essence a “stress-in-motion”
system because it was developed to quantify tire/pavement contact stresses. The VRSPTA system
was originally developed in South Africa for use with the South African Heavy Vehicle Simulator
(HVS). The basic principle of the VRSPTA is that the vertical, transverse, and longitudinal forces
are measured in one line across the tire print in real time. The contact stresses are then calculated
during post-processing of the data. In making the measurements, a loaded wheel is rolled across
the instrumented array of pins at a known speed and the loads are measured with a fixed sampling
frequency until the total contact area has traversed the VRSPTA surface. The VRSPTA is

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 360 J. Hua and T. White

designed to measure directly the 3D loads acting on each pin during the tire movement. Contact
stresses are determined using a diamond shaped area covered by each pin. The diamond shaped
area is a direct result of the diagonal pattern of the pins.
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De Beer, et al. [6] tested six types of tires with the VRSPTA. The measurements show that
the vertical contact stresses can be more than double the tire inflation pressure in certain cases.
Distribution of vertical stresses across the tire width was shown to be highly nonuniform. It was
also found that relatively large shear stresses might occur.
The closest tire matching the Michelin 11R 24.5 XTA radial tire used in the APT tests is the
Goodyear G159A 295/75 R22.5. Table 1 shows the 295/75R22.5 VRSPTA tire test matrix. The
APT tire has an inflation pressure of 620 kPa (90 psi) with a load of 20 kN (4500 lb). Tire/
pavement contact pressure for the APT tire was interpolated from VRSPTA test data for tire
inflation pressures of 520 kPa (75 psi) and 690 kPa (100 psi).
Contact pressure distribution histories for the 520 kPa (75 psi) and 690 kPa (100 psi) tire
inflation pressures are plotted in Figures 8 and 9, respectively. Because of test data variation,
average values of the tire contact pressures over the middle 20 samples were plotted instead of
using the maximum value for a pin.
The tire contact pressure distributions are highly irregular and closely related to the tire tread
patterns. There are four gaps between the treads of the tires tested. Due to test pin spacing, only
one or two pins contact any single tread. The contact pressure for a tread was taken as the average
value of pressure for the pins in contact with it. In making the interpolation for the APT tires,
advantage was taken of tire tread symmetry. The numbers of treads on the Goodyear tire and the
APT tire are different as shown in Figure 10. The Nos. 2 and 3 tire treads on the tire used in the
APT and Nos. 2, 3 and, 4 tire treads on the tire tested were assumed to have the same pressure
contact, and the APT Nos. 1 and 4 tire treads and Nos. 1 and 5 treads of the tested tire were
assumed to have the same tire contact pressure. Also, it was assumed that the ratio of tire contact
pressure of the middle treads to that of the edge treads is the same for both tires. Based on these
assumptions and measured tire print dimensions, the APT tire contact pressures were calculated
and are shown in Figure 11.
Rutting was predicted using uniform tire contact pressure on the gross tire contact area as
well as uniform tire contact pressure and nonuniform tire contact pressures on the net tread areas.
Loading for these three cases is shown in Figure 12. Two sets of material properties were used,
one representing a very “hard” material (Type 1) and the other representing a very “soft” material

TABLE 1
Test Matrix for the 295/75 R22.5 Radial Tire

Single Tire Load

kPa 420 520 690 820
kN lbs. Psi 61 75 100 119

20 4496 Yes Yes Yes Yes

25 5620 Yes Yes Yes Yes
30 6744 Yes Yes Yes Yes
35 7868 Yes Yes Yes Yes

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FIGURE 8. Transverse tire contact pressure distribution history (517 kPa, 20 kN). (After De Beer, et al. [6].)

FIGURE 9. Transverse tire contact pressure distribution history (690 kPa, 20 kN). (After De Beer, et al. [6].)

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 362 J. Hua and T. White
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FIGURE 10. Tire prints of Goodyear 295/75R22.5 (left) and APT (right) tires.

FIGURE 11. APT tire contact pressure distribution and tire print dimensions.

(Type 2). The material properties utilized are listed in Table 2. Deformed surface profiles of the
APT test lane corresponding to 5000 wheel passes are plotted in Figures 13 and 14, respectively,
for the two material property sets. The uniform tire pressure produces a predicted deformed
surface with rut depth greater under tire edges than in the middle, which is not the case for the
measured profile, although the difference is not large compared to the total rut depth.
When the tire print is explicitly modeled the predicted profile matches the deformed profile
of the APT test lane and clearly reflects the tire tread pattern as shown in Figure 15. However,

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FIGURE 12. Tire prints and contact pressures used in analyses.

TABLE 2
Material Properties
Material Type 1 Material Type 2

E 450,000 psi
Elastic Properties Poisson’s Ratio 0.3

Creep model Parameters A 0.5 × 10–4 1 × 10–4

n 0.8 0.8
m 0 –0.7

as will be shown later, when wheel path wander is involved, differences of predicted rutting using
nonuniform tire pressure distribution and uniform tire pressure distribution will be further
reduced and can be neglected without significant effect.

E. Wander — Wheel Path Distribution

Wheel path distribution refers to the distribution of wheel loads in the transverse direction
across a traffic lane (i.e., wander). Several factors may affect wheel path distribution on in-service
pavements. They include roadway geometry, lateral clearances, traffic conditions, roadway
characteristics, weather conditions, and vehicle type.
In early INDOT/Purdue APT tests, single wheel path traffic was the only option. Therefore,
all asphalt mixtures were tested with single wheel path traffic (centerline of dual wheel assembly
coincides with test lane centerline). Subsequently, controls and software were installed for
incorporating a traffic wander option. Traffic with this wander option was applied to selected,

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364
J. Hua and T. White

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FIGURE 13. Surface rutting for Material Type 1.
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Int. J. Geomech., 2002, 2(3): 353-376

FIGURE 14. Surface rutting for Material Type 2.
A Study of Nonlinear Tire Contact Pressure Effects on HMA Rutting
365
 366 J. Hua and T. White
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FIGURE 15. Comparison of measured and predicted surface profiles.

unused test lanes. When wander is incorporated, the wheels are randomly positioned in a
normally distributed fashion. And the mean position of the wander coincides with the test lane
centerline.
Single wheel path traffic produces significant uplift between and outside of the tires.
However, with wander the deformed surface profiles are much smoother because the tires are
applied over uplifted areas, which are re-compacted. Typical sections seen from lanes subjected
to single wheel path traffic and traffic with wander are shown in Figure 16.
The programmed normal distribution has a certain standard deviations, related to the maxi-
mum wander distance. In this study, when wander is applied, it is assumed that 98% of the wheel
paths will occur within the maximum wander distance, D. As a result,

FIGURE 16. Rutting with and without wander.

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 A Study of Nonlinear Tire Contact Pressure Effects on HMA Rutting 367

D − 0
z = 0.99 (5)
 s 
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where z is the cumulative probability of the standard normal distribution and the standard
deviation, s, is:

D
s= (6)
2.326

If the tire width is W, the loading time on any given point A can be calculated as shown
in Figure 17. Point A is not loaded when the centerline of the tire is outside of the range from
(χ – W/2) to (χ + W/2). Hence, the percent total loading time t(x) for point A relative to the total
cumulative loading time of the tire over the entire width of the lane during the test is the area
under the normal distribution curve within the range (χ – W/2) to (χ + W/2). Therefore, the total
loading time t(x) of any point A on the surface of the test lane can be calculated as follows:

 W 
t( x ) =  F  x +  − F  x −   × T
W
   (7)
 2 2 

where
x = offset distance from the test lane centerline
F(x) = normal cumulative distribution for the specified mean (zero in this study) and
standard deviation, s
T = total loading time of the tire during the test

FIGURE 17. Loading time for any point on the pavement surface.

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 368 J. Hua and T. White

The above equation is valid only for a given point. In the FE method, the load is applied on
the element surfaces, which have a finite width. The element loading time has to be developed
using the above concept.
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We assume that the FE width is a, and a is smaller than the tire width W. This assumption
is reasonable because the actual mesh size has to be small enough to produce accurate results.
Figure 18 shows the loading time for any surface element. Once the tire centerline is in the range
of (x – W/2) to (x + a + W/2), part or all of the element width will be covered by the tire print.
The total loading time over this width can be calculated using the following equation:

 W 
t( x ) =  F  x + a +  − F  x −   × T
W
   (8)
 2 2 

Loading on this element may not be a maximum during the entire loading time, tx. The load
over this width will vary linearly from zero to a maximum and from the maximum to zero once
the centerline of the tire ranges from (x – W/2) to (x + a – W/2) and from (x + W/2) to (x + a +
W/2), respectively. The load positions on this element and within these two ranges will vary from
(x) to (x + a/2) and from (x + a/2) to (x + a), respectively. The varying load magnitude and
position in this width makes it difficult if not impossible to apply the load history. Consequently,
a decision was made to convert the loading time with varying load magnitude and position to a
loading time with a constant maximum load and fixed loading position (center of the element)
during the entire loading period. The assumption used in this conversion is that the constant load
has the same effect as the varying load. As shown in Figure 19, the two triangles under the load-
tire centerline position curve on both sides of the rectangular area can be converted into two
smaller rectangles with the same total area. The converted load will have a fixed load magnitude

FIGURE 18. Loading time for surface element.

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FIGURE 19. Converted Loading time for a certain length in the transverse direction.

and fixed position at the center of the element. The ratio of the converted areas to the total area
under the load-tire centerline position curve can be calculated as follows:

2 ×  × a × Lmax 
1
2  a 1
= =
(W − a) × Lmax W −a W
−1
(9)
a

As W >> a, the value of Equation (9) is minimized. This conversion does not have significant
effect on the calculated results as long as the mesh size is small enough.
The converted total loading time can now be calculated using the following equation:

 W 
t( x ) =  F  x +  − F  x −   × T
W
(10)
  2  2 

Equation (10) is exactly the same as Equation (7). Also, the converted loading time is no
longer related to a as long as a is smaller than the tire print width, W, which is the case in this
study. Hence, the calculated total loading time for a width, which is smaller than the tire width,
is the same as that for a point. And the total loading time distribution over the width of the APT
test lane is not affected by the mesh size. This is useful, as only one loading time distribution
corresponding to a specific level of wander needs to be calculated regardless of the model mesh
size.

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 370 J. Hua and T. White

When duel tires or tires with treads are used, the total loading time can be calculated by
summing (superposition) the total loading time from each single tire or each single tire tread. For
example, if a dual tire assembly is used, the loading time on a point or for a width in the transverse
direction on the test lane will be the sum of the loading times of tire No. 1 and tire No. 2 acting
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separately minus the loading time of tire No. 1 and tire No. 2 acting together on the point or width.
The relation of the loading time is expressed in the following equation:

Totaltime = Time No. 1 ∪ Time No. 2 = Time No. 1 + Time No. 2 − (Time No. 1 ∩ Time No. 2 ) (11)

However, the two tires will not act on a point at the same time. This also is true for a width in
the transverse direction if the width is smaller than the clear distance between the two tires. The
intersection of TimeNo. 1 and TimeNo. 2 will be zero and the total loading time is simply the sum
of the two loading times from each single tire. The same is true if tire treads are considered. The
concept of loading time superposition is shown in Figure 20. The APT tires have four treads
(Figure 10) and hence the load from each tire is transferred to the surface of the test lane from
these four tire treads. The exact tire print patterns have to be used in order to obtain an accurate
result. The tire print of each tire was measured and the average dimensions used in the model.
Layout and dimensions of the APT test lane, dual wheel assembly, and tire prints used in this
study are shown in Figure 21. Rutting was predicted for two wander distances, 130 mm (5.1 in.)
and 260 mm (10.2 in.). Material Type 1 properties were used from Table 2.

FIGURE 20. Superposition of loading time for dual tire assembly.

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FIGURE 21. APT test lane layout and tire print dimensions.

The assumed modulus of elasticity was obtained from results of tests conducted by Huang
[1]. Complex modulus tests in this study were conducted at frequencies of 1, 4, and 8 Hz and at
temperatures of 20, 30, and 40°C, respectively. The modulus of elasticity from tests at 8 Hz and
40°C were utilized since these conditions are in agreement with the 8 km/h loading speed and
38°C (100°F) temperature for APT tests.
Total loading time for any point on the surface will be the sum of the loading times resulting
from each of the eight distinct tire treads of a dual wheel assembly. Every tread will have the same
normal distribution in the transverse direction but with different mean positions (centerline
position of the tread) and the same deviation as that of the centerline of the dual tire assembly.
Calculated total loading times of the APT dual wheel assembly in the transverse for different
wander distances are shown in Figure 22.
The total loading time under the original tire print position decreases with increasing wander.
And, the loading time between the dual tires gradually increases from zero to an amount greater
than the loading time directly under the originaly tire. Also, when the wander distance is larger
than 76 mm (3 in.) the loading time under the tire print is the same as a smooth tire. If the wander
distance is greater than 381 mm (15 in.), which is the approximate centerline distance between
the dual tires, the loading compares to that of a large single tire. The “shape and configuration”
of the dual wheel assembly is totally lost in the deformed surface profile.
Calculated loading times were applied on the FE model. A summary of the deformed surface
profiles with different wander distances is given in Figure 23. Final deformed shapes of the test
lane are plotted in Figure 24. It can be seen that with increasing wander distance the surface uplift
between the dual tires is greatly reduced and the deformed surface profile becomes smoother.
Also, both the maximum rut depth and the total rut depth (compactive rut depth plus uplift rut
depth) are greatly reduced.
It is also interesting to note that the shape of the deformed surface profile is closely related
to the loading time profile. The deformed surface profile together with the corresponding loading
time profile for various wander distances are plotted in Figure 25.

Int. J. Geomech., 2002, 2(3): 353-376

 372 J. Hua and T. White
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FIGURE 22. Loading time distribution with different wander distances (1 in. = 2.54 cm).

FIGURE 23. Rut depth with different wander distances.

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 A Study of Nonlinear Tire Contact Pressure Effects on HMA Rutting 373
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FIGURE 24. Deformed test lane with different wander distances (magnified).

Measured and predicted surface profiles for a wander distance of 260 mm after 5000 wheel
passes are shown in Figure 26. There is good agreement between measured and predicted rut
depths.

Int. J. Geomech., 2002, 2(3): 353-376

 374 J. Hua and T. White
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FIGURE 25. Deformed surface profiles of APT test lane and loading time with different wander distances.

Int. J. Geomech., 2002, 2(3): 353-376

 A Study of Nonlinear Tire Contact Pressure Effects on HMA Rutting 375
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FIGURE 26. Predicted and measured surface deformations (5000 wheel passes).

V. CONCLUSIONS

A creep model was used to characterize the time-dependent material properties of HMA. Hot
mix asphalt rutting was closely predicted using the creep model in the FE analyses. Also, from
sensitivity analysis, it was found that the HMA predicted rut depth is not sensitive to the input
values of modulus of elasticity, Poisson’s ratio, and elastic foundation stiffness. This is expected
because these three factors define elastic material properties, which are not related to permanent
deformation.
One of the benefits of using the creep model is that the total cumulative loading time can be
utilized. This concept significantly reduces the FE computational time for repetitive traffic
loading while maintaining the desired accuracy.
Tire print shape and tread pattern influences rutting shape and depth. For single wheel path
APT tests significant uplift is produced between and to the outside of the tires. However, with
wander the deformed surface profiles are much smoother and uplift is greatly reduced. The
loading time distribution corresponding to any tire configuration can be calculated by assuming
a normal distribution of the loading over a pavement surface. By using this loading time
distribution in the model, both the predicted shape of the deformed slab surface and the rut depth
magnitude showed very good agreement with measured values.
The effect of measured nonuniform tire pressure was analyzed. It was found that the
difference in predicted rut depths using uniform and nonuniform tire pressure is minimal. With
wander there is virtually no difference in the predicted maximum rut depth.

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 376 J. Hua and T. White

REFERENCES
[1] Huang, H.M., Analysis of Accelerated Pavement Tests and Finite Element Modeling of Rutting Phenomenon,
Thesis, Purdue University, submitted August, 1995.
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[2] Pan, C.L., Analysis of Bituminous Mixtures Stripping/Rutting Potential, Thesi, Purdue University, submitted
August, 1997.
[3a] ABAQUS Standard User’s Manual, Version 5.7, Hibbit, Karlsson and Sorenson, Inc., 1997a.
[3b] ABAQUS Theory Manual, Version 5.7, Hibbit, Karlsson and Sorenson, Inc., 1997b.
[4] Lai, J.S. and Anderson, D., Irrecoverable and Recoverable Nonlinear Viscoelastic Properties of Asphalt
Concrete, Transportation Research Record, National Research Council, Washington, D.C., pp. 73–88, 1973.
[5] Perl, M., Uzan, J., and Sides, A., Visco-Elasto-Plastic Constitutive Law for a Bituminous Mixture Under
Repeated Loading, Transportation Research Record 911, National Research Council, Washington, D.C.,
pp. 21–27, 1983.
[6] De Beer, M., Fisher, C., and Jooste, F.J., Determination of Pneumatic Tire/Pavement Interface Contact
Stresses Under Moving Loads and Some Effects on Pavements with Thin Asphalt Surfacing Layers, Division
of Roads and Transport Technology, CSIR, 1997.
[7] Hua, J., Finite Element Modeling and Analysis of Accelerated Pavement Testing Devices and Rutting
Phenomenon, Thesis, Purdue University, submitted August, 2000.

Int. J. Geomech., 2002, 2(3): 353-376