Page 206 - MODELING OF ASPHALT CONCRETE

184 Cha pte r Se v e n

such as viscoplasticity, begin to contribute significantly, the performance ranking could
change.

VP Characterization
Calibration of the VP model in Eq. (7-42) first requires the determination of the
viscoplastic strain from the total strain measured from the monotonic data. In cyclic
loading with rest periods, the permanent strains after the rest periods can be used as the
viscoplastic strain. However, in tension where the specimen is glued to the loading
plates, it is difficult to maintain zero stress during the rest periods. In monotonic loading,
although the stress-strain data at high temperatures and slow loading rates would have
greater proportions of viscoplastic strain in the measured strain, it is unclear how high
the temperature and slow the loading rate must be in order to consider the measured
total strain as the viscoplastic strain.
This difficulty is overcome using the strain decomposition principle in Eq. (7-1).
Knowing the damage characteristic curve of the material from the 5°C monotonic
testing, the viscoelastic strain can be predicted for high temperatures using Eq. (7-35).
The viscoelastic strain is then subtracted from the total measured strain to determine
the viscoplastic strain. An optimization algorithm, such as the genetic algorithm, is
used to determine the VP model coefficients (p, q, and Y) in Eq. (7-42) from the extracted
viscoplastic strain and corresponding stress and time.
It is worthwhile, given the strain decomposition nature of the VEPCD model, to
examine the effect of strain rate and temperature on the viscoelastic and viscoplastic
characteristics of the mixtures. Figure 7-12(a) presents the influence of viscoelastic and
viscoplastic effects on the behavior of the Maryland mixture during the constant
crosshead rate tests. This figure shows the percentage of total strain attributed to
viscoelastic and viscoplastic effects as a function of the reduced strain rate at a reference
of 25°C. Each data point in this plot represents the results from a single test conducted
at a particular strain rate and temperature and is obtained at the peak stress. From this
figure one can observe a generally decreasing significance of viscoplastic strain with an
increased reduced strain rate.
As observed from Fig. 7-12(a), after a reduced strain rate of 4 e/s, seen in Region C,
the total strain consists solely of viscoelastic response. In Region B, where the reduced
strain rate ranges from 0.01 to 4 e/s, the viscoelastic strain constitutes about 95% of the
total response. As for Region A, viscoelastic and viscoplastic behavior are both present
with their proportions being equal at a reduced crosshead strain rate of 0.0001 e/s. Now
that the composition percentage of component strains can be known for a particular
loading condition, the conditions required for modeling each strain separately can be
more accurately selected.
Effects of temperature and strain rate on the viscoplastic characteristic of various
mixtures are shown in Fig. 7-12(b). The reference temperature is 5°C. The figure
illustrates that the CR-TB mixture shows the least significant viscoplastic behavior at
lower reduced rates. This behavior is somewhat expected knowing that the high
temperature PG grade of the CR-TB binder is 76°C, which is higher than all the other
binders used in this study. It is also observed that the control mixture shows, by
percentage, less viscoplasticity than the Terpolymer and SBS mixtures over all the tested
conditions. However, the unmodified mixture has a much steeper slope than the
modified mixtures and is expected to show more viscoplasticity at ranges outside those
tested. Due to this increased slope and based on the results of Fig. 7-10, it appears that