Page 112 - MODELING OF ASPHALT CONCRETE

90 Cha pte r F o u r

Introduction
Pavement design using the elastic layer theory needs two elastic parameters for each
material layer used: Young’s modulus (stiffness) and Poisson’s ratio. One of the more
widely used stiffness parameters for asphalt mixtures employed in mechanistic-
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empirical structural pavement design procedures has been the dynamic modulus |E |.
The dynamic modulus has also been selected to characterize the asphalt mixtures in the
new AASHTO 2002 Guide for the Design of Pavement Structures, which has been in
development in the NCHRP 1-37A project at Arizona State University (ASU).
Additionally, the importance of dynamic modulus for mechanistic modeling will be
discussed in other chapters in this book. Dynamic modulus will replace the resilient
modulus test currently used for pavement design. This chapter discusses a new test
protocol development for the dynamic modulus test and presents some considerations
of the analysis of imperfect sinusoidal cyclic test data. Also, stiffness as a performance
indicator for hot mix asphalt (HMA) will be discussed.
A key feature in the material characterization is to construct a mastercurve of the
mix. Through the mastercurve it is possible to integrate traffic speed, climatic effects,
and aging for the pavement response and distress models. A new method to construct
an asphalt mix mastercurve by using a sigmoidal fitting function and experimental
shifting is discussed and a stress-dependent master-curve construction method is
introduced.
There are two complex modulus tests that have been used for characterization of
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asphalt mixtures in the United States: The dynamic modulus |E | test and the shear
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modulus |G | test. Differences of these two tests are discussed related to the mix design
and pavement design applications.

Complex Modulus
Complex mathematics gives a convenient tool to solve the viscoelastic behavior of the
asphalt mixtures and binders in cyclic loading. The sinusoidal one-dimensional loading
can be represented by a complex form:

σ = σ e ω it (4-1)
∗
0
and the resulting strain
ϕ
∗
ε = ε e i( ω − ) (4-2)
t
0
∗
The axial complex modulus E (iw) is defined as the complex quantity
σ ∗ ∗ ⎛ σ ⎞ ϕ i
0
(
ε ∗ = Ei ω =) ⎜ ⎝ ε ⎠ ⎟ e = E 1 +iE 2 (4-3)
0
in which σ is the stress amplitude, e is strain amplitude, and w is angular velocity,
0 0
which is related to the frequency by
π
ω = 2 f (4-4)
∗
In the complex plane, the real part of the complex modulus E (iw) is called the storage
or elastic modulus E while the imaginary part is the loss or viscous modulus E , shown
1 2