Page 75 - MODELING OF ASPHALT CONCRETE

Modeling of Asphalt Binder Rheology and Its Application to Modified Binders 53

FIGURE 2-22 Application of rate of change of energy dissipation concept to binder strain-
controlled testing data.

Applying this concept to binder data, it is observed that the approach is useful for
the stress-controlled testing, but is not useful for the strain-controlled testing. As shown
in Fig. 2-22, the strain-controlled measurements result in scattered points, which makes
it almost impossible to clearly define the N value. Conceptually, it is difficult to apply
p
this approach for most binders because of the nature of the strain-controlled test. Since
the test is strain-controlled, the rate of energy dissipation will stabilize when the damage
starts accumulating because the material will soften due to damage resulting in reduction
in stress required to cause same strain. The test can, therefore, take a long time to result
in transition of material from the crack initiation stage to the propagation stage.
Cumulative Dissipated Energy Ratio
Pronk (1995) defined the dissipated energy ratio as follows:
n
∑ W i
Dissipated energy ratio = i=1 (2-14)
W
n
n
where Σ W is the total sum of the dissipated energy up to cycle n and W is the
n=1
i
n
dissipated energy at cycle n.
Figure 2-23 shows examples of applying this concept to binder data. The results
shown indicate that binders can be evaluated effectively using this method. The curves
of the binder data are similar to the mixture data published earlier by other researchers,
which is very promising. This also implies that the main factor in the fatigue behavior
of mixtures could be well related to the fatigue damage in the binder.
It is also observed that the slope of the relationship between the energy ratio and
the number of cycles to failure is equal to 1.0 when the material is not undergoing