Page 137 - Mechanics of Asphalt Microstructure and Micromechanics

CHAPTER5

Mixture Theory and

Micromechanics Applications

5.1 Mixture Theory and Its Application
Asphalt concrete (AC) is a heterogeneous mixture of three constituents of asphalt binder,
aggregate, and air voids. The local volume fractions of these constituents vary spatially
and therefore result in the spatial gradients of the local volume fractions. The local vol-
ume fractions and their spatial gradients are important field variables in the mixture
theory whose objective is to predict the mixture behavior out of the structure of the mix-
ture and the properties of the constituents. In this section (based on Wang et al., 2003),
the fundamentals of mixture theory and a general method for solving boundary value
problems using mixture theories are presented. A simplified mixture theory for two-con-
stituent mixtures of solids and air voids is presented to model the initial stress distribu-
tion of AC under static loading. The analytical solutions of simple two-dimensional (2D)
and one-dimensional (1D) cases using the simplified theory are also presented to illus-
trate how this theory predicts the effective stress distribution of a heterogeneous mix-
ture. The final part of this section will present a study on using mixture theory to model
the air void reduction (Krishnan and Rao, 2000, 2001).

5.1.1 A Brief Introduction
Mixture theory (Truesdell, 1957, 1969; Green and Naghdi, 1967; Bowen, 1976; Eringen
and Ingram, 1976) was initially proposed for modeling the mixture behavior of fluids,
and the granular flow properties (Goodman and Cowin, 1971, 1972; Passman, 1977;
Kanatani, 1979). Two books (Bear, 1972; Coussy, 1995) offered excellent literature on
mixture theory applications in porous media. In recent years, mixture theory has also
been used in modeling the properties of AC (Krishnan and Rao, 2000, 2001). For solid
state and granular materials, volume-fraction-based mixture theories have been shown
to be more suited than the traditional mixture theories. For this type of mixture theory,
important field variables include the local volume fraction and the spatial gradients of
the local volume fractions of the constituents (i.e., Goodman and Cowin, 1971, 1972).
However, due to the lack of an efficient method to characterize these field variables, ap-
plication of mixture theory to general boundary value problems is limited.
In recent years, X-ray computed tomography (XCT) has become a reliable tool in
obtaining the microstructure of AC and other construction materials (Desruses, 1996;
Shashidhar, 1999; Braz et al., 1999; Rogasik et al., 1999; Shi 1999; Wang et al., 2001;

129