
Research Article


Analysis of Asphalt Pavement under Nonuniform Tirepavement Contact Stress using Finite Element Method 

M.H. Nahi,
A. Ismail
and
A.K. Ariffin



ABSTRACT

Tirepavement contact stress is traditionally assumed to be uniformly distributed over a circular contact area. In this study, the tirepavement contact pressure has been modeled to be nonuniform. A new tire model is developed for the analysis based on the geometry of the tire footprint because the contact area between the tire and the pavement is not exactly rectangular or circular. The objective of this study is to develop a finite element model based on viscoplastic theory for simulating the laboratory testing of asphalt mixes in Hamburg Wheel Rut Tester (HWRT) for rutting and to model insitu pavement performance. The creep parameters C_{1}, C_{2} and C_{2} are developed from the triaxial repeated load creep test at 50°C and at frequency of 1 Hz. Viscoplastic model (creep model) is adopted and a commercially available Finite Element (FE) program, ANSYS, is used in this study, in order to predict the rutting for insitu pavement under nonuniform contact pressure. In the simulation, the used element has an eightnode with a three degrees of freedom per node translations in the nodal x, y and z directions. Dual wheel system of a standard axle load of 80 kN is used in the 2D pavement insitu performance analysis. Reasonable agreement has been obtained between the predicted rut depths and the measured one. Moreover, it is found that creep model parameter C_{1}, strongly influences rutting than the parameter C_{3}. Finally it can be concluded that creep model based on finite element method can be used as an effective tools to analyze rutting of asphalt pavements.





Received: March 26, 2011;
Accepted: May 02, 2011;
Published: June 07, 2011


INTRODUCTION
Finite element method is wide common used now days. Zaoui
et al. (2008) presented a contribution to the reinforced concrete
beams modelling using the Castem 2000 finite element software. Finite element
method is evaluated as a useful approach to recognize the critical points and
fatigue life time of the reciprocating components such as connecting rod (Omid
et al., 2008). The fatigue life prediction was carried out by Rahman
et al. (2008) study using finite element based fatigue code. Lots
of money is spend on the maintenance of asphalt pavements roads (Awwad,
2007), rutting is one of the wide common deformations for flexible pavement
roads. For proper pavement design and better understanding of materials behaviours
it is necessary to predict asphalt pavement rutting. Rutting phenomenon is the
longitudinal depressions along the wheel paths caused by the movement of asphalt
pavement materials under high traffic loading based on consolidation or plastic
flow ( Suo and Wong, 2009). Excessive amount of asphalt
cement is one of reasons for plastic flow (Walker et al.,
2004). Rutting in asphalt pavement is mainly occurs due to its nonlinear
viscoplastic nature (Uzarowski, 2007). The high wheel
loads and high tire pressures are the main cause for Increasing of asphalt pavement
rutting phenomenon (Mukhtar, 2006). Magdy
(1996) presented three rutting mechanisms wear rutting, structural rutting
and instability rutting. This study deals with the last type, which is the most
dangerous type of surface rutting. An eightnode, threedimensional stress displacement
element was used in the finite element analysis. Pirabarooban
et al. (2003) developed a finite element model to simulate the laboratory
testing of asphalt mixes in Asphalt Pavement Analyzer (APA) test for rutting
and to relate the test results to basic material properties, a viscoelastoplastic
model (creep model) has been used to represent the timedependent characteristics
of the asphalt mixture. The objective of this study is to develop a finite element
model to simulate the laboratory testing of asphalt mixes in (HWRT) for rutting
and to develop a finite element model to analyze insitu pavement performance.
Nonuniform contact pressure for dual wheel system of a standard axle load of
80 kN is used in the 2D pavement insitu performance analysis. The nonlinear
viscoplastic behaviour analysis of asphalt mixes was adopted in this study.
It was found that creep model parameters C_{2} and C_{1} have
a strong relationship with rutting. However, among these two the parameter C_{1}
strongly influences rutting than the parameter C_{3}.
ASPHALT VISCOPLASTIC BEHAVIOUR
The hotmix asphalt materials plays a major role in asphalt pavement rutting.
Most paving materials are not elastic, but if the load is small compared to
the strength of the material and is repeated for a large number of times, the
deformation under each load repetition is nearly completely recoverable and
can be considered elastic (Huang, 2004). The recoverable
(elastic and viscoelastic) and nonrecoverable (plastic and viscoplastic) strain
components are determined in the analyses. The viscoplastic strain component
is the major contributor to the asphalt mixture rutting and only this component
is used in the development of the material creep parameters. If the creep model
is used to describe the time dependant material behaviour, the repeated loading
and continuous loading have the same effect on the predicted creep strain as
long as the total loading times are the same (Texas DOT,
2003).
HAMBURG WHEEL RUT TESTER
The Hamburg Wheel Tracking Device (HWTD) is well known in Canada as the Hamburg
Wheel Rut Tester employed The HWRT for asphalt mix accelerated performance testing
in terms of its rutting resistance. The wheels can be either steel 47 mm wide
or solid rubber 50 mm wide and the load applied to the wheels is 710 N (FHWA,
2002). The customary temperature for the HWRT test in Canada and the United
States is 50°C; this temperature is also typically used in Europe for a
climate close to a Superpave high temperature PG of 58. The test path is (230
mm) long and the average speed of each wheel is approximately 1.1 km h^{1}
(53±2 wheel passes per min). All the HWRT testing was carried out at
a temperature of 50°C. Five asphalt mixes were used by Uzarowski
(2007); these mixes present a wide range of applications, from high traffic
to low volume roads. All five mixes were obtained from paving projects in Ontario.
In total, about one ton of asphalt mixes was used in the research and the designs
for all five mixes were provided by the contractors who supplied the mixes.
The mixes incorporated the aggregate types and asphalt cements listed in Table
1.
LOADING TIME CALCULATING
The footprint of the HWRT solid rubber wheel on the surface of asphalt mix
samples, measured at a testing temperature of 50°C, is shown in Fig.
1. The average length of the wheel footprint of 28.5 mm is used to calculate
the loading time and the contact pressure. For the load of 710 N applied in
the HWRT testing, a uniform loading pressure of 500 kPa is used in the analysis.
The test path in the HWRT is 230 mm long and typically, 53±2 passes are
completed in 1 min. For the average wheel footprint length of 28.5 mm, the time
of loading in one pass is about 0.14 sec. The time of loading conversion described
by Hua (2000) and shown in Fig. 2 is
used in this research. The T1T2 time is 0.14 sec. And the T0T1 and T2T3 time
periods are 0.07 sec. The converted loading time in one pass is 0.21 sec. The
time of loading for 20,000 passes is 4,200 sec. ANSYS simulations are completed
for 4, 10, 20 and 30 million ESAL’s traffic loading. The assumed average
speed of commercial vehicles is 60 km h^{1}. The effective time of
loading in one tire pass for the 175 mm long outside tread areas, is 0.0126
sec. For the traffic loading of 30 million ESAL’s applied over 20 years,
the total loading time is 156,000 sec.

Fig. 1: 
Footprint of HWRT solid rubber wheel 
Table 1: 
Asphalt mix ingredients (Uzarowski, 2007) 

*Both PG 7028 PM asphalt cements were polymer modified 
Table 2: 
Loading time used in pavement insitu performance
simulation 

As the three middle areas are longer by about 15 percent, an additional loading time of 24,000 sec is used for these areas. The loading time used in the ANSYS simulations are given in Table 2. CREEP MODEL PARAMETERS
Five material parameters may affect the rutting predicted by the finite element
method. These parameters include three creep model parameters (C_{1},
C_{2} and C_{3}) and the elastic parameters, modulus of elasticity
and Poison’s ratio. However, predicted rut depth is not sensitive to modulus
of elasticity and Poison’s ratio since these two factors only define the
elastic behavior which is not directly related to the permanent deformation,
therefore, the sensitivity study was kept limited to the creep model parameters
(Pirabarooban et al., 2003). In this analysis,
the modulus of elasticity obtained from the triaxial repeated load creep test
based on Uzarowski (2007) study has been used. The triaxial
repeated load creep test done at a temperature of 50°C and at a frequency
of 1 Hz. The creep parameters C_{1}, C_{2} and C_{3}
have been calibrated based on the rutting measured in the HWRT. The parameter
is stress related. The rut resistance testing in the HWRT is conducted at a
constant loading stress of 500 kPa, the C_{3} parameter is fixed at
the initial level shown in Table 3. Parameter C_{1}
is the value of the yaxis intercept while parameter C_{2} is related
to the slope of the straintime relationship curve in a loglog scale. The elastic
and final creep parameters used in the simulation are shown in Table
3 and the same parameters are used in the modeling of the insitu
pavement performance.
ANSYS MODELING
ANSYS is a suite of powerful engineering simulator based on the finite element
method. Many researcher have been used ANSYS in their studies. The finite element
based software ANSYS models are employed to evaluate the transient temperature
and the residual stress fields during welding. Also, in this study the variations
of the physical and mechanical properties of the material with temperature have
been taken into account (VakiliTahami and Sorkhabi, 2009).
ANSYS has an extensive library of finite elements and an extensive list of material
models.
Table 3: 
Asphalt mix elastic and creep parameters 

Analysis in ANSYS includes two stages, starting level and processing level,
Starting level includes converting a mechanical problem to Finite Element Model
(FEM). Processing level includes three steps Preprocessing, Solve and Postprocessing.
The geometry of problem, material properties, element type and boundary conditions
has been defined in Preprocessing step. While in the solve step, the type of
analysis have been chosen. Finally the result of solving the problem has been
observed in the Postprocessing step (ANSYS, 2004). There
are lots of equations embedded in commercial finite element analysis software
(ANSYS). In order to model primary and secondary stages of creep characteristics,
the presented creep model used in this research can be written in the form of
creep strain rate. The material is assumed to be isotropic, and the basic solution
technique used is the initialstiffness NewtonRaphson method as in Eq.
1 :
where,ε_{cr} is the creep strain rate, r is the equivalent stress,
t is the time at end of substeps. C_{1}, C_{2} and C_{3}
are the parameters related to material properties. As the temperature in the
analysis is fixed at 50°C, the parameters C_{1}, C_{2},
and C_{3} are developed from the triaxial repeated load creep test at
50°C and the modulus of elasticity and Poisson’s ratio determined at
the same temperature. The elastic parameters modulus of elasticity and Poisson’s
ratio and creep parameters C_{1}, C_{2}, and C_{3} are
required for finite element simulator (ANSYS) in order to calculate the rutting
for various mixes under a uniform loading pressure of 500 kPa.
FINITE ELEMENT SIMULATION FOR HWRT The structure and the auxiliary conditions in the finite element simulation have to be properly odellin to obtain reasonable results. This includes the finite element model’s components such as include element type, boundary conditions, load conditions, material properties and geometry of the model As shown in Fig. 3, 150x300 mm (in width) and 63 mm (in height) rectangular bituminous mixture structure was constructed to simulate the Hamburg Wheel Rut Test. The dual wheel loading configurations in the HWRT testing are symmetrical. To reduce the elements number and the required time for each analysis, only one wheel and half of the HWRT sample was included in the finite element modeling. The load magnitude was 710 N with 500 kPa tire pressure. The material creep model discussed above was used to characterize the permanent deformation properties of the bituminous mixture. The parameters used in the creep model were derived from the triaxial repeated load creep test result. The bottom and the four surrounding vertical boundaries were set to be confined with restricting displacement in all directions except the axisymmetric side which is surrounding is x direction only. SOLID45 is used for the 3D modelling of solid structures and this element is defined by eight nodes having three degrees of freedom at each node translations in the nodal x, y and z directions. The element has plasticity, creep, swelling, stress stiffening, large deflection and large strain capabilities. MODELING PAVEMENT insitu PERFORMANCE
The material parameters developed from the laboratory testing and HWRT testing
analysis, shown in Table 3, are used to model pavement insitu
performance in ANSYS. It is assumed in the model that a single 63 mm of asphalt
placed over a Portland cement concrete base so that rutting could occur only
in the asphalt layer. It is also assumed that the layer of HMA is fully bonded
with the underlaying Portland cement concrete layer so that no movement of the
HMA layer can occur on the surface of the concrete base. A dual wheel system
of a standard axle load of 80 kN is used in the pavement insitu performance
analysis. The system is shown in Fig. 4 a load of 20 kN is
applied by each wheel in the system. Tirepavement contact stress is traditionally
assumed to be uniformly distributed over a circular contact area. The tire modeled
in this research is a standard Goodyear G159A11R22.5 (Fig. 5).
The wheel load is applied through the tire treads to the surface of the asphalt
layer. A new tire model shown in Fig. 6 is developed for the
analysis based on the geometry of the tire footprint, because the contact area
between the tire and the pavement is not exactly rectangular or circular.

Fig. 3: 
Geometry of the model and finite element mesh of wheel tracking
test specimen 

Fig. 4: 
Dual wheel system used in pavement insitu performance
analysis 
The wheel load is transferred to the pavement through five rectangular areas.
The three middle areas are narrower and longer than the two outsideareas. The
different lengths of the areas are reflected in the 2D finite element analysis
by using a longer time of loading for the middle three areas. The contact pressure
is not uniform. It ranges from 517 kPa for the outside areas to 586 kPa for
the central area. The pressure in the remaining two areas in the middle is 552
kPa. As the dual wheel system is symmetric, only half of the system is modeled.
The distance between the two wheel tires in a dual wheel system is 120 mm.
The density of the mesh under the load and directly next to it is twice the
density in the 300 mm wide zone outside the loaded part.

Fig. 5: 
Wheel tire model used in ABAQUS simulation 
RESULTS AND DISCUSSION
The creep parameters have been used in the 3D simulation, were derived from
the triaxial repeated load creep test’s results. The simulation results
for the HWRT shows different amount of rutting and Different shape of rutting
versus time curve for different mixes. Figure 6 shows that
dense graded mix, HL3, is the worse mix with higher rutting, there was a good
agreement between the finite elemnt results and the measured one. The gap graded
mix, SMA L, shows a good resistance to rutting, Fig. 7 shows
the rutting versus time for SMA L mix. It’s clear from Figure
8 that SMA L mix has a better resistance than SMA G. The SP 19 E mix has
significantly higher asphalt cement content than the SP 19 D mix, 4.60 percent
and 4.35%, respectively that’s why SP 19 D mix has a higher resistance
to rutting. Figure 9 shows that SP 19 D mix looked much leaner
than the SP 19 E mix which shown in Fig. 10, SP 19 E mix
has the beast rutting resistance among all the five mixes as shown in Fig.
10. The difference between the shapes of the permanent deformation curves
is clear. Uzarowski (2007) noted that there is a significant
difference between the curve’s shapes of the gap graded mixes and dense
graded mixes. Figure 7 and 8 shows that
the densification of the gap graded mixes SMA L and SMA G is high at the beginning
of the loading and then the rutting curve flattens to reach the constant slope
after about 1500 sec. The densification of the dense graded mixes is gradual,
proportionally small at the beginning of the loading and then the deformation
reaches a constant slope after about 1700 sec, as shown in Fig.
6, 9 and 10.

Fig. 6: 
Rutting measured in HWRT and predicted in ABAQUS and ANSYS
for the HL 3 Mix 

Fig. 7: 
Rutting measured in HWRT and predicted in ABAQUS and ANSYS
for the SMA L Mix 

Fig. 8: 
Rutting measured in HWRT and predicted in ABAQUS and ANSYS
for the SMA G Mix 

Fig. 9: 
Rutting measured in HWRT and predicted in ABAQUS and ANSYS
for the SP 19 D Mix 

Fig. 10: 
Rutting measured in HWRT and predicted in ABAQUS and ANSYS
for the SP 19 E Mix 
The measured rut depth versus time is predicted in ANSYS and ABAQUS at the
time of loading of 1000, 1800, 2600, 3300 and 4200 sec, the results show that
there is a reasonable agreement of the difference between the predicted and
the laboratory measured rutting and the comparison between the obtained results
from ABAQUS.

Fig. 11: 
Predicted rutting depth versus ESAL of a pavement the five
mixes by ANSYS 
It’s clear that the rutting increasing with the time as the asphalt pavement
is time dependent, Yin et al. (2007) presented
that the loading time has a more significant impact on pavement response in
the fixed temperature. The 2D model for insitu asphalt pavement is successfully
predicted asphalt pavement rutting. Fig. 11 show the predicted
rutting of a pavement versus ESAL for the five mixes. The depth of the rutting
for HL3 mix has increased from 3.5 mm for 4 million ESAL’s to 9.3 mm for
30 million ESAL’s as shown in Fig. 7 while the depth
of the rutting for SMA L mix has increased from 1.7 mm for 4 million ESAL’s
to 2.6 mm for 30 million ESAL’s. It is also clear from Fig.
11 that the rutting depth for the mix SMA G has increased from 2.2 mm for
4 million ESAL’s to 3.4 mm for 30 million ESAL’s, while the depth
of the rutting for mix SP19 D has increased from 1.6 mm for 4 million ESAL’s
to 3.04 mm for 30 million ESAL’s. The rutting depth For SP19 E mix increase
from 2.5 mm for 4 million ESAL’s to 5.3 mm for 30 million ESAL’s.
Load repetition is an important traffic factor which influences rutting resistance
of asphalt pavements (Hofstra and Kolomp, 1972). Phang
(1988) stated that rutting accumulates faster as the load repetition increases.
There are total of five possible factors which may affect the predicted model
response, they are creep model parameters C_{1}, C_{2} and C_{3},
modulus of elasticity and Poisson’s Ratio. Pirabarooban
et al. (2003) stated that the rut depth (magnitude) and the nature
of variation decreases with increasing C_{3}, values, note that C_{3}
is negative. Similar to parameter C_{1}, the parameter C_{3}
also increases with increasing asphalt cement content. The results of this work
simulation shows that the predicted rut depth is not sensitive to modulus of
elasticity and Poisson’s Ratio.

Fig. 12: 
Effect of varying creep model parameter on rut depth 

Fig. 13: 
Effect of varying creep model parameter on rut depth 
This expected since these two factors only define the elastic behaviour which
is not directly related to permanent deformation. It was clear that the parameter
C_{1} strongly influences rutting than the parameter . As can be seen
from Figure 12, predicted rut depth increases with increasing
value. As can be seen from Fig. 13, predicted rut depth increases
with increasing value (noted that is in the range from 1 to 0).
CONCLUSION
The 2D model for insitu asphalt pavement is successfully predicted
asphalt pavement rutting. A new tire model used for the analysis based on the
geometry of the tire footprint and that successfully simulated the tirepavement
contact stress because the contact area between the tire and the pavement is
not exactly rectangular or circular and. The finite element model developed
for HWRT tester was verified by comparing predicted and measured rut depths
and also by comparing the rut depth with ABAQUS result from literature. Reasonable
agreement was found between the predicted and measured rut depths furthermore
it was found that creep model parameters C_{1} and C_{3} have
a strong relationship with rutting and that the parameter strongly influences
rutting than the parameter C_{3}. It was clear that the predicted rut
depth increases with increasing value and with increasing C_{3} value.
The parameters C_{1} and C_{3} are closely related to the amount
of asphalt content and the air void in hot mix asphalt. Finally it can be concluded
that creep model based on finite element method can be used as effective tools
to analyze rutting of asphalt pavements.

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