Page 394 - Mechanics of Asphalt Microstructure and Micromechanics

386 Ch a p t e r E l ev e n

Temperature drop will make compaction more difficult due to the larger stiffness
for particle contacts and/or a stiffer top layer.

11.3.4 CAP Viscoplasticity Modeling
Xia and Chi (2008) adapted a rate-independent crushable foam plasticity model into a
viscoplasticity model. They developed a user’s material subroutine for ABAQUS and
simulated the roller compaction process. The essential features of the model include non-
associated flow represented by the yielding function F and the potential function g.

− + − + − − − + (11-15)

Where p is the first stress invariant, and S is the deviatoric stress tensor. It is an exten-
sion of the CAP model. They used the additive strain decomposition and the Perzyna
(1966) viscoplastic strain versus potential gradient relation, Equations 11-16 and 11-17.
e
˙ e = ˙ e + ˙ e vp (11-16)
⎛ ⎞ F ∂
·
vp
ε η Φ ⎜ F ⎟ (11-17)
⎝ σ y ⎠ ∂ σ

No comparison between simulation results and experimental observations is
available.

11.4 Empirical Measurements of Compactibility
While the previous sections discussed the theories and backgrounds of compaction,
this section summarizes some literature on the historical development of empirical
measurements of compactibility. Although most of these measurements do not fall into
the rigorous scheme of mechanics, they may help guide developing simple mechanics
models.
11.4.1 The C Value Approach
Kezdi (1969) developed an empirical formulation that associates the densities of the
material at different compaction stages with the accumulative compaction energies.
S
ρ S() = ρ − ρ ( − ρ ) e [kg/m ] (11-18)
3
C
A A• A• A0
and r A0 are the final and initial densities, and
Where S is the compaction energy, r A•
C is a measurement of the compactibility. For C = 10, the material is easy to compact,
while C = 30 is difficult to compact. Renken (1980) and Arand (1985, 1987) have also
employed this approach.
11.4.2 The R Approach
f
Nijboer (1948) used Mohr-Coulomb failure criterion and triaxial tests to characterize
the compactibility of asphalt concrete. He assumed that the internal friction angle, the
“cohesion” resistance, and the viscosity of the mixture can be used to measure the