Technical information

5-27
resilient modulus range of test results), and a base modulus of 6,820 psi (47 MPa)
appears too low for a material compacted to 97% (which is the compaction degree in
the APT experiment). In comparison with the isotropic LET analysis (Table 4.2.1), the
subgrade here is about 2.2 times stiffer; the base modulus here is merely 28% of that
backcalculated in the time-independent isotropic case.
Table 5.2.1: Backcalculated material properties for the layered viscoelastic model
during APT pass #5,000.
#
Layer
Thickness,
in. (mm)
Poisson’s
Ratio
Modulus, psi (MPa)
+ equation 5.2.12 parameters
1 HMA 5 (127) 0.30
=
0
E 5,920,000 (40,825); =
∞
E 23,800 (164);
=
D
τ
21.8 s; =
D
n 0.532
2 Base 6 (152) 0.35 6,820 (47)
3 Subgrade 61 (1,549) 0.40 25,915 (180)
4 Concrete
Semi-
infinite
0.20 4,000,000 (27,580)
As for the HMA, Figure 5.2.3 superimposes the backcalculated relaxation
modulus )(tE , i.e., equation 5.2.12 and parameters from Table 5.2.1, with the
relaxation modulus interconverted from the combined dynamic modulus and phase
angle master curves in Figure 4.3.1. The interconversion from the frequency domain to
the time was performed using the following equation (Levenberg and Shah, 2008):
∫
∞
=
−
∞
⋅⋅+=
0
/
)(ln)()(
τ
τ
ττ dehEtE
t
.................................................................. (5.2.14)
in which )(
τ
h is the relaxation spectrum given in equation 3.3.7 with parameters listed
in Subsection 4.3.1 (calibrated to results in the frequency domain). As can be seen in the
figure, although both curves were derived for a reference temperature of 15.5ºC, and
although the extreme values
0
E and
∞
E
were forced to coincide, the transitions from
0
E to
∞
E
are completely different (faster in the backcalculated case).