Page 287 - Mechanics of Asphalt Microstructure and Micromechanics

F inite Element Method and Boundar y Element Method 279

Sangpetngam (2003) adopted a crack growth model developed by Zhang et al.
(2001) into a DD-BEM-based pavement fracture simulator. He used crack tip elements
ahead of crack tips to improve accuracy of stress distribution and replaced the process
zone with yield elements. The upgrade model requires the determination of four fun-
damental mixture parameters that can be obtained from less than one hour of testing
using the SuperPave IDT. These parameters can account for micro-damage, crack prop-
agation, and healing for stated loading conditions, temperatures, and rest periods. The
implementation of crack growth model in the numerical scheme increases the applica-
tion of fracture mechanics for predicting crack growth in asphalt mixture for various
geometries, loading, and boundary conditions.
Using the validated DD-BEM method with a proper tessellation scheme, Birgisson
et al. (2003) observed that cracks in AC could start as micro-cracks and later propagate
and coalesce to form macro-cracks as the mixture is subjected to sustained tensile
stresses, shear stresses, or a combination of both. Using the same model, Birgisson et
al. (2004) simulated the IDT tests and showed agreement with laboratory observations.
The improved understanding of the mechanism of cracking can be expected to lead to
more reliable prediction of the field performance of asphalt mixtures. Recognizing that
both crack initiation and propagation processes are directly related to stress-strain
fields in asphalt layers, researchers recently have focused on developing more realistic
constitutive law that can describe the cracking response of asphalt mixtures under re-
alistic traffic conditions composed of multiple load levels and random rest periods.
Sangpetngam et al. (2004) extended the DD-BEM to simulating layered asphalt pave-
ments. Birgisson et al. (2006, 2007, 2008) compared the DD-BEM predicted crack pat-
terns in hot mix asphalt (HMA) mixtures to those measured using a digital image cor-
relation (DIC) system that could accurately obtain displacement and strain fields and
detect crack patterns. The comparisons indicated the promising features of the DD-
BEM simulations.
In summary, the DD-BEM approach shows potential applicability in identifying
critical factors that determine the cracking mechanism of asphalt mixture, and therefore
can be used for optimizing or improving the crack resistance of asphalt mixtures. Nev-
ertheless, only very few researchers are engaging in BEM applications research. A com-
bined FEM and BEM approach may demonstrate significant advantages.

Suggested Readings
The theory part of Section 8.2 and Section 8.8 are based on consolidated teaching
notes of the author. These notes are prepared following the presentation from an ex-
cellent book by Gaul et al. (2003). In this chapter, the presentation for general dynam-
ics problems in Gaul et al. (2003) is reduced to the statics problems for simplification.
If readers need more backgrounds, please read this book. For convenience and con-
nections, the symbols adopted in these two sections are consistent with those used in
Gaul et al. (2003).

References
ABAQUS (1984). Abaqus User’s Manual, Hibbett, Karlsson and Sorenson, Inc.
Banthia, V. and Mukherjee, S. (1985). On an improved time integration scheme for stiff constitu-
tive models of inelastic deformation. Journal of Engineering Materials, Vol.107, pp.282–285.