Page 235 - Mechanics of Asphalt Microstructure and Micromechanics

Models for Asphalt Concrete 227

More general models should also include the kinematics hardening. The SHRP per-
manent deformation is a good example (see Chapter 8). A good review paper was pre-
sented by Krempl (1987). Other examples in the general models include the ones by
Chaboche (1986) and Krempl and Khan (2003). There are other models such as (Nguyen
et al., 2007). A good literature resource can be found from Kim et al. (2009).

7.9 Generalization of the Models
The elastic strain energy can be stored and recovered. Depending on the dissipation
mechanism, one can assume various dissipation mechanisms to cover plastic deforma-
tion, viscoplastic deformation, and damage (fracture) dissipation. The possibilities of
unifying these models exist. A potential approach is the internal variable method.
A detailed description can be found in Lubliner (1990).

7.10 Fatigue Modeling
7.10.1 Overview
The fundamental mechanisms of fatigue of AC are complicated. In general, fatigue is
the accumulation of damage (in broad sense) in materials under the effect of repeated
loading. Fatigue damage accumulation in AC mixtures results in cracking, which is one
of the main distresses in flexible pavements. A thorough description of damage caused
by fatigue therefore becomes essential if mechanistic-based pavement design principles
are to be applied accurately.
The fatigue properties of AC are usually obtained by repeated-load laboratory test-
ing. The early fatigue models of asphalt mixtures are simple phenomenological formu-
las of fatigue under cyclic loading. Paris’s law plays an important role in linking the rate
of crack growth to tensile strain developed in asphalt mixture. In addition, fatigue mod-
els based on continuum damage or fracture mechanics have been developed. Paris’s
law was also used to link the rate of crack growth to the degradation of fracture tough-
ness indicators such as the stress intensity factor when LEFM is used. Models were also
reviewed involving the concepts of dissipated energy or surface energy that were pro-
posed taking the format of the phenomenological formula or incorporated in the Paris’s
law. Numerical methods using the cohesive zone approach will be briefly reviewed in
this section.

7.10.2 Empirical Phenomenological Models
Models falling into this category were developed based on experimental data to link
fatigue life (maximum allowable number of repetitions N f ) to tensile strain e t and the
dynamic modulus E * (sometimes) of AC. A typical formulation can be represented as:
N = k () − k 2 E * − k 3 (7-73)
ε
f 1 t
In which k 1 , k 2 , k 3 are regression coefficients. A typical failure criterion for fatigue life
at a specific strain is the loading repetition at which AC loses its modulus by 50%. If k 2 ,
σ
= k 3 and for direct tension tests, N = k (ε E ) − k 2 = k ( ) − k 2 .
*
f 1 t 1 t