Page 221 - Mechanics of Asphalt Microstructure and Micromechanics

CHAPTER7

Models for Asphalt Concrete

7.1 Introduction
There are many rational models developed in the past 20 years for asphalt concrete
(AC). Detailed descriptions of these models is beyond the scope of this book. Due to
page limitations, only those complete models are presented. Works on empirical mod-
els and/or some components of a model are not summarized. Elasticity models and
viscoelasticity models are not reviewed. Models reviewed in this chapter are mainly
those viscoplasticity models that consider 1) viscoelasticity; 2) yielding; 3) hardening;
and 4) failures. Most of the fatigue models are actually fatigue failure criteria.
The total strains in AC can be decomposed into elastic, viscoelastic, and viscoplastic
components. Depending on the ways of the individual components or a combination of
several components (viscoelastic, viscoplastic, elastoplastic), a large number of models
have been proposed. The interpretation of the mechanism regarding the plastic defor-
mation and the viscoplastic deformation will add more varieties including the damage
mechanics mechanism.

7.2 Viscoplasticity with Damage
Richard Kim (Kim et al., 1995, 2004, 2009) and his group (Chehab et al., 2005; Chehab
and Kim, 2005; Daniel and Kim, 2002) devoted significant efforts to the modeling of AC
using viscoelastoplastic continuum damage (VEPCD) mechanics. Their models fol-
lowed a series of publications by Schapery (1975, 1981, 1984, 1987a, 1987b, 1990, and
1999). Major features of their models are summarized as follows.
7.2.1 Strain Components
ε = ε + ε (7-1)
Total ve vp
where e Total = total strain
e ve = viscoelastic (VE) strain
e vp = viscoplastic (VP) strain

7.2.2 Viscoelastic Stress-Strain Relationship
The stress-strain equation for linear viscoelastic materials can be represented as:

ξ ε ∂
−
σ = E ( ξ τ) kl τ d (7-2)
ij ∫ 0 ijkl τ ∂

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