Page 61 - Mechanics of Asphalt Microstructure and Micromechanics

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54 Ch a p t e r w o

number of gyrations can be adjusted to simulate field compaction equipment and traf-
fic conditions. The applied vertical pressure is 828 kPa, which is similar to truck tire
inflation pressures. For strength measurement, the pressure required for producing the
desired gyration angle is determined and then converted to shear strength. Typically,
one degree is used for the gyration angle and 300 revolutions for compaction. Also, the
gyratory shear index (GSI), which is determined by dividing the intermediate gyration
angle by the initial angle, is a measure of mixture stability as it is related to permanent
deformation.
GSI values around 1 indicate stable mixtures, while values above 1.1 indicate un-
stable mixtures.

2.4.13 Continuum Damage Mechanics Approach
Continuum damage mechanics is used for modeling the changes in the stress-strain
behavior of AC. In this approach, the state of a damaged body, represented as a homo-
geneous continuum, is quantified based on internal state variables (ISVs). The scale
for this representation is much larger than the defect sizes in the damaged body. Typ-
ically, a suitable damage evolution law is controlling the growth of damage. The ma-
terial’s stiffness is determined by fitting the theoretical model to the existing experi-
mental data, being a function of the internal state variables and depending on the ex-
tent of the damage.
To describe the deformation behavior and performance of AC, a viscoelastoplastic
continuum damage (VEPCD) model was developed that is based on the theory of
viscoelasticity, continuum damage mechanics, and the theory of viscoplasticity.
Through this model the AC behavior is studied in tension and compression.

2.4.14 VEPCD Model Calibration in Tension
The VEPCD model is based on the strain decomposition principle developed by
Schapery in 1999, which states that the total strain can be comprised of viscoelastic and
viscoplastic strain (Kim, 2009). Also, linear viscoelasticity (LVE), viscoelastic continuum
damage (VECD) model and viscoplastic (VP) models are employed for the calibration
of the VEPCD model. The LVE characterization is based on complex modulus testing at
various temperatures and frequencies. The time-temperature shift factor from this test-
ing is used in converting the physical time to reduced time, while the relaxation modu-
li, obtained from the dynamic modulus and phase angle master curves, are used in the
pseudostrain calculation.
To calibrate the VECD model, constant crosshead rate monotonic test results are
used as stress-strain data with minor viscoplasticity required. The data are obtained for
four loading rates at 5 and 40°C. The calibration procedure involves calculation of pseu-
dostrains and relaxation modulus in the Prony series as well as damage parameter (S)
and normalized pseudo-secant modulus (C). The C-S relationship represents the dam-
age characteristic relationship on which the VECD model is based.
For VP model calibration, the permanent strains after the rest periods in monotonic
cycling loading can be considered viscoplastic strain. Monotonic testing was performed
–5
at temperatures ranging from –10°C to 40°C and strain rates of 10 /s to 0.1/s.
The VEPCD model (developed for the Maryland Superpave mixture) is validated
by the thermal strain restrained specimen tensile (TSRST) tests performed on AC beam
specimens (250 50 50 mm) at the Turner-Fairbanks Highway Research Center.