Page 158 - Mechanics of Asphalt Microstructure and Micromechanics

150 Ch a p t e r Fiv e

5.4 Micromechanics Application to Mastics and Asphalt Concrete
When fillers or aggregates are added to binder or mastics, aggregate or filler particles
will reinforce the binder or mastics. For some aggregate/filler binder combinations,
there may be physiochemical reactions at their interfaces, forming a thin layer of as-
phalt binder that becomes stronger due to absorption, adsorption, and selective sorp-
tion. When aggregate/filler volume fractions are large enough so that filler particles are
forming contact and skeleton, the particle interaction effects will take place. The rest can
be attributed to the dilute inclusion situations that can be well addressed by the gener-
alized self-consistent scheme (GSCS).
One of the applications of micromechnics that was widely used dated back to the
70s (Shell, 1978). The Shell nomography actually utilized micromechanics principles to
obtain the stiffness modulus of asphalt mixture from binder stiffness, the volume frac-
tion of mineral aggregates, and the volume fraction of binder. The binder stiffness is
obtained from the penetration index (Equation 5-101), the loading frequency, and tem-
perature in service. More recent systematic studies using micromechanics started from
Buttlar’s group.
PI = 20 − 500 A (5-151)
+
150 A
log( penatT −) log( penatT )
Where A = 1 2 represents the temperature sensitivity of pen-
T − T
1 2
etration of asphalt binder.
Two major publications of Butllar’s research present evaluations of accuracy of var-
ious micromechanics formulations for predicting mastics and mixture modulus, as well
as use of the micromechanics approach to assess the volume fraction of recovered AC.
Buttlar and Dave (2005) applied a) Paul’s Rule of Mixture (Paul, 1960); b) Arbitrary
Phase Geometry (APG) model (Hashin and Shtrikman, 1963); c) GSCS Model (Chris-
tensen and Lo, 1979); d) Mori-Tanaka method (Mori and Tanaka, 1973); and e) Hirsch
Model (Hirsch, 1962). The predictions of the mixture modulus using various models
were compared with experimental results. The Hashin’s APG model was identified as
offering the best potentials in accuracy.
Christensen, et al. (2003) evaluated four alternatives under the general philosophy
of the Hirsch model to combine the parallel and series models differently (Figure 5.5).
The fundamental idea is based on the consideration that AC is a thermal sensitive mate-
rial and the load transfer proportion will vary with temperature; the real distribution
mechanisms are more complicated than the simple combination of the original Hirsch
model.
The formulations corresponding to the four different alternatives are as follows:
(a) Serial version
⎡ Va' (1 − Va') 2 ⎤ −1
Ec = ⎢ + + ⎥ (5-152)
⎣ Ea PcEa VmEm ⎦
(b) Parallel version
⎛ Va' Vm⎞ −1
Ec = VcEa + (1 − Vc) 2 ⎜ + Em⎠ ⎟ (5-153)
⎝ Ea