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Complex Modulus fr om the Indir ect Tension Test 131

testing for 25 Hz. Following each loading frequency, a 5-minute rest period was allowed
before the next frequency was applied.
Averaged deformations were used to calculate the dynamic modulus and phase
angle. In the uniaxial case, readings from four LVDTs spaced at 90° intervals were
averaged. In IDT, the vertical deformations and horizontal deformations from two
surfaces were averaged to determine the deformation in each axis.

Comparison of Dynamic Moduli Values

Graphical Comparison
The IDT test data of the 24 mixtures were analyzed using the viscoelastic solutions in
Eq. (5-26). The resulting dynamic modulus mastercurves from these analyses are plotted
in Figs. 5-4 to 5-6 for the 12 representative mixtures. The reference temperature of 10°C
was used as the basis of shifting the data. The data presented in these figures are the
averages of the three replicates. The rest of the data can be found in Kim et al. (2005).
It can be observed from these figures that the dynamic modulus mastercurves
developed from the IDT test using the biaxial linear viscoelastic solution are generally
in good agreement with those determined from the axial compression test. It was also
found that the time-temperature shift factors obtained during the construction of the
mastercurves are essentially identical for the axial compression and IDT tests.

Statistical Analysis

Using P-Value
Recognizing that a sample-to-sample variation exists, a statistical analysis was
conducted using the unequal variance t-test for each mixture at two frequencies for
each testing temperature. In this analysis, all the individual replicates (three from the
axial compression and three from the IDT tests) were used. The null hypothesis is that
the dynamic modulus from the IDT test is the same as that from the axial compression
test. The P-value was calculated and compared with the critical value of 0.05 to reject or
accept the null hypothesis. The P-value indicates the extent to which a computed test
statistic is unusual in comparison with what would be expected under the null
hypothesis. Therefore, in this study a P-value greater than 0.05 indicates that the
dynamic modulus from the IDT test is statistically the same as that from the axial
compression test.
A summary of the P-values for 144 tests (2 frequencies × 3 temperatures × 24
mixtures) is given in Table 5-3. About 19% of the tests indicate that the dynamic modulus
from the IDT test is statistically different from the dynamic modulus from the axial
compression test.

Using Percent Difference
In addition to the statistical analysis, the percent difference was calculated for the
dynamic moduli determined from the axial compression and IDT tests for 288
combinations of temperature and frequency (8 frequencies × 3 temperatures × 12 mixes).
These values are also summarized in Table 5-3. A comparison of the data in this table
and further investigation of individual test data resulted in several important
observations.