Page 122 - MODELING OF ASPHALT CONCRETE

100 Cha pte r F o u r

Most likely mixtures that have binder as a dominating stiffness contributor will be
ranked similarly, while mixtures that have different gradations, such as dense graded
versus SMA, may be ranked differently.
The recommended provisional stiffness parameter for fatigue cracking was also
found to be the unconfined compressive dynamic modulus of the mix. However, this
conclusion is based on limited data. The dynamic modulus of asphalt mixtures was not
an adequate performance indicator for thermal cracking.
∗
∗
|E | versus |E |/sinj
The Superpave binder specification defines and places requirements on a rutting factor,
∗
|G |/sind, which presents a measure of the high-temperature stiffness or rutting
∗
resistance of asphalt binder. |G | is a shear modulus of binder and d is the phase lag
between stress and strain. According to Bahia and Anderson (1995), the work W
dissipated per loading cycle is inversely proportional to the parameter |G |/sind:
∗
⎡ 1 ⎤
W = πσ 2 ⎥ (4-9)
*
⎣ ⎢ | G |/sin δ ⎦
To minimize permanent deformation, the work dissipated during each load cycle
∗
should be minimized. In a similar manner, a rutting factor, |E |/sinj, can be defined
for asphalt mixtures, where j is the phase angle of the mix. For fatigue cracking, a
∗
performance factor in the Superpave binder specification is |G |sind. Thus, the
∗
equivalent performance factor for the mix is |E |sinj. The Superpave binder
∗
specification has a minimum value for the |G |/sind parameter against rutting, and a
∗
maximum value for the |G |sind for fatigue cracking.
∗
2
The correlation between rutting and rutting factor |E |/sinj was R = 0.91, and
∗
between rutting and |G |/sinj only R = 0.74, although the modulus itself gave similar
2
correlations. As discussed earlier, Fig. 4-7(b), the correlation between phase angles of
the axial and shear modulus was poor to fair, which may explain the poorer correlation
∗
of |G |/sinj and rutting. However, it should be noted that these results apply only to
the dense graded mixtures used in the testing program.
∗
The reason that the |E |/sinj was not recommended as the SPT, regardless that it
gave better correlation to rutting than modulus itself, is that the phase angle of the asphalt
mix is dependent of frequency and temperature differently than the phase angle of the
conventional binder. For conventional binders, the phase angle is an increasing function of
temperature, while the asphalt mix phase angle first increases as temperature increases and
then starts to decrease. This is illustrated in Fig. 4-9 that shows binder and mix data in the
Black space. The binder phase angle approaches 90° at high temperatures when the mix
phase angle approaches some limiting value initiated by the damping of aggregate skeleton.
This occurs because the elastic effect of aggregate skeleton pushes through the viscous effect
of binder at high temperatures. Therefore, if the phase angle decreases it may be due to
more elastic binder or more viscous binder that allows the elastic effect of aggregate skeleton
∗
to influence the phase angle value. Therefore |E |/sinj is not a stable performance
parameter for asphalt mixtures. This same phenomenon can also be seen for some of the
modified binders for which the phase angle is not an increasing function of temperature.
Effect of Confinement and High Stress Levels
One potential limitation of using stiffness measurements as a performance indicator at low
stress/strain test applications is that the effect of aggregate shape and hence internal