Page 203 - MODELING OF ASPHALT CONCRETE

VEPCD Modeling of Asphalt Concr ete with Gr owing Damage 181

and analysis. Displacements were measured using loose-core LVDTs, two with a 75-mm
gauge length and two with a 100-mm gauge length attached to the middle section of the
specimen at equal distances from the ends. Using two different gauge lengths enables
the determination of the onset of localization because the opening of the major cracks
that start to form in the asphalt matrix between the gauge points would be numerically
divided by two different gauge lengths, thus leading to two different strain values.
Hence, the divergence of the strains corresponding to the different gauge lengths
indicates the onset of localization and macrocracking.
Calibration Test Program
The major strength of the VEPCD model is the simplicity of the calibration testing
requirement. The calibration testing program is composed of three phases: (1) LVE
characterization, (2) VECD characterization, and (3) viscoplastic (VP) characterization.
Complex modulus testing at varying temperatures and frequencies is used for the
LVE characterization. The dynamic moduli and the time-temperature shift factors are
determined using the procedure given in the AASHTO TP 62-03 and then used in the
VECD and VP modeling. The dynamic modulus is converted to the relaxation modulus
using the algorithm presented in Chap. 6.
For the VECD and VP characterizations, constant crosshead rate monotonic tests
are used. Instead of testing several replicates at a limited set of rates and temperatures,
these tests are conducted with few or just one replicate at a wider range of loading rates.
Typically, four different rates are used at 5 and 40°C to calibrate the VECD and VP
models, respectively.
Linear Viscoelastic Characterization
Figures 7-9 and 7-10 present the replicate averaged dynamic modulus and phase angle
mastercurves for all the FHWA ALF mixtures. These figures show that at higher reduced
frequencies (lower temperatures) the unmodified mixture shows substantially greater
stiffness and more elasticity (evidenced by lower phase angles) than any of the other
mixtures. It is also observed that the SBS and CR-TB mixtures show approximately the
same stiffness and elasticity under these conditions. Also, the SBS and CR-TB
mastercurves have smaller slopes during the transition period than the mastercurves of
the control and Terpolymer mixtures. Finally, at the lower reduced frequencies (higher
temperatures), the CR-TB and SBS mixtures are the stiffest, which is the opposite of that
observed at the higher reduced frequencies.
These complicated time and temperature dependencies of different mixtures are
captured in the dynamic modulus and phase angle mastercurves. The conversion
technique presented in Chap. 9 is applied to these LVE properties to obtain relaxation
moduli of the mixtures, which will then be used in the pseudostrain calculation. The
converted relaxation modulus is fit to the Prony series representation in Eq. (7-10).
Another important material property characterized from the complex modulus test is
the time-temperature shift factor. This property is used in converting the physical time
to reduced time in the VEPCD modeling approach.

VECD Characterization
The VECD model calibration requires stress-strain data with negligible viscoplasticity;
therefore, the constant crosshead rate monotonic test results at 5°C are used. The
calibration procedure starts from the calculation of pseudostrains using Eqs. (7-11) to
(7-13) and the relaxation modulus in the Prony series. Once the pseudostrains are