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Table 8. Vehicle class related to axle and tire categories.
Vehicle Class Single Axle Tandem Axle Tridem Axle Quad Axle
4 3 Single Tire
5 7
5
1
6 Dual Tire
7
8 4
9
10
11 2 6 8
12
13
14
Shaded areas are vehicle classes that use single tires; unshaded areas are vehicle classes that use dual tires.
analysis of the traffic load effect on reflection cracking. Table 8 assumption that heat fluxes at the pavement surface are exactly
shows the categorization of the axles of each vehicle class based balanced by conduction into the ground well below the surface;
on tire configuration. Categories 1, 3, 5, and 7 have single tires inaccuracy of climatic data (especially calculated solar radia-
and the categories 2, 4, 6, and 8 have dual tires. These eight tion); and the assumptions of the constant temperature bound-
categories are used in calculating the traffic stresses which are ary condition and site-independent model parameter values.
partly the cause of reflection cracking. Recently, significant improvement over the EICM model
has been achieved by several groups using a similar one-
Climatic Data Collection dimensional heat transfer model, but with an unsteady-state
surface heat flux boundary condition, measured model input
The climatic data were collected from two principal sources data, and site-specific model parameters that were optimized
in addition to the LTPP database. The hourly solar radiation based on measured pavement temperatures (19, 20, 21).
and the daily air temperature and wind speed were needed to Figure 8 presents a comparison of the temperatures mea-
make accurate estimates of the temperature in the overlay. In sured at different depths below the pavement surface with
addition to these data, the temperature model requires the those calculated with the EICM model (18).
albedo of the pavement surface, its thermal conductivity, and Figure 9 shows a comparison between the measured tem-
emissivity and absorption coefficients. The solar radiation peratures and those calculated with the new model used in
data can be obtained from the internet at METSTAT Model this project (the model is described later in this chapter:
(MeteorologicalStatistical Solar Model) and the SUNY details are provided in Appendix B).
Model for the State University of New York at Albany (http:// The one dimensional heat transfer model employs an
rredc.nrel.gov/solar/old data/nsrdb/). The daily climate data unsteady-state heat flux boundary condition at the pavement
on air temperature and wind speed can be found at http:// surface, a depth-independent heat flux 3 m below the surface,
www.ltpp-products.com/DataPave/. It was necessary to deve- and the ability to estimate site-specific model parameters
lop a different temperature model than the one contained in the using known measured pavement temperatures.
Enhanced Integrated Climatic Model (EICM) in order to cal-
culate the temperatures to a higher degree of accuracy (more
Finite Element Method
detail is provided in Appendix B).
for Calculating SIF
Although temperatures predicted with the EICM model sat-
isfy pavement design needs in general, there have been some In this project, it was found that the computational time to
large differences when compared to measured pavement tem- calculate new stress intensity factors using the finite element
perature (18). These differences are most likely caused by the method at the daily location of the tip of the crack was too

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Figure 8. Typical daily pavement temperature prediction using EICM model (18).
long. Therefore a method was adopted to calculate the SIF for · Asphalt overlay over cracked asphalt surface;
a wide variety of conditions, pavement structures, and crack · Asphalt overlay over compliant interlayer (SAMI) over
lengths using a finite element method and then to model the cracked asphalt surface;
computed results with the computationally efficient ANN · Asphalt overlay with reinforcing geosynthetic layer over
algorithm (the method used to generate these sets of SIF is cracked asphalt surface;
presented in detail in Appendix Q). · Asphalt overlay over jointed concrete surface;
The finite element method is a two-dimensional method · Asphalt overlay with reinforcing geosynthetic layer over
which uses Fourier Series to represent the effects of loads that jointed concrete surface; and
act at some distance from the two-dimensional plane where the · Asphalt overlay over cracked continuously reinforced con-
calculations are made (details are provided in Appendix Q). A crete surface.
comparison of the results obtained using this method with the
results obtained using a true three-dimensional finite element The following three different loading conditions were used
program revealed differences of 2 to 5 percent. Use of a two- in the finite element calculations of the SIF at the tip of the
dimensional finite element program was ruled out because of crack:
the long computational time it required (the time required for
a three-dimensional program is of course much greater). · Thermal stress;
The following six basic pavement structures were used in · Bending stress due to traffic; and
the computations: · Shearing stress due to traffic.
Figure 9. Typical daily pavement temperature prediction using
improved model.

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Table 9. Number of computer runs of SIF.
Pavement Structures Number of Computer Runs of Stress Intensity Factors
Test Sections with Varying Crack Lengths
Thermal Shear Bending
AC/AC OL 233 1,620 25,920 4,320
JCP/AC OL 69 14,580 25,920 4,320
AC/SAMI/AC OL 38 6,480 - -
AC/GRID/AC OL 50 9,720 - -
CRC/AC OL 21 1,620 - -
The following two tire and axles configurations were cases where a compliant interlayer (SAMI) was used, the thick-
included in the traffic stress finite element computations: ness and modulus of that layer were also varied. In those pave-
ment structures in which reinforcing geosynthetics were used,
· Single axle, single tire the thickness and the grid stiffness were used. Because there are
· Single axle, dual tire no uniform industry standards for specifying the properties of
these commercially available products, three levels of geosyn-
Collateral studies with multiple axles showed that the SIF thetic stiffness (high, medium, and low) were used in the com-
beneath one axle is affected by the loads of other axles at stan- puter runs. The appropriate level can be chosen by the user by
dard axle spacings by no more than about 10 percent. This referring to the graph in Figure 10. The user will calculate the
effect was included in the computations of the SIF for tan- reinforcing product stiffness (in MN-mm/m2 units) and enter
dem, tridem, and quadrem axles. the value on the graph in Figure 10 at the corresponding rein-
Table 9 lists the pavement structures and the number of forcing product thickness (in mm). The curved line that is clos-
computer runs performed for developing the SIF. The total est to this point provides the stiffness level that should be used
number of computer runs was 94,500. The number of bending as input to the design program.
SIF computations was reduced because the bending stresses For a geo-grid, the stiffness is computed from its geometric
become compressive only a short distance into the overlay. and material properties as Ea/s where E is the material modulus
The variables included in the finite element computational (MN/m2); a is the rib cross-sectional area, (mm2); s is the rib
runs were the layer thickness, modulus of overlay, surface layer, spacing (mm); and t is the vertical rib thickness (mm). If the
and base course and the crack or joint spacing. In the thermal reinforcing material is a sheet instead of a grid, then the overlay
stress cases, different levels of thermal expansion coefficient reinforcing stiffness in MN-mm/m2 is calculated as Et.
were used. With the jointed concrete pavement structures, dif- Successful use of geo-grids as reinforcing interlayers depends
ferent levels of load transfer efficiency were used. For those upon embedding the grid within the overlay so that there is
Figure 10. Overlay reinforcing stiffness versus reinforcing thickness.