Page 73 - MODELING OF ASPHALT CONCRETE

Modeling of Asphalt Binder Rheology and Its Application to Modified Binders 51

where e = accumulated permanent strain
a
I = intercept with permanent strain axis (arithmetic strain value, not log value)
N = number of load applications
S = slope of the linear portion of the logarithmic relation
It is rather difficult to use the parameter of creep rate S as a specification parameter
because it is an experimental parameter that is affected by a few testing attributes such
as stress, loading time, and number of cycles. A better choice for a specification parameter
is to use rheological models that combine fundamental behaviors to understand the
performance of the material. Although several models have been used to describe the
behavior of asphalt binders, the “four-parameter” (Burgers) model, shown in Fig. 2-21,
was shown to offer a good representation of the binder behavior (Bahia et al. 2001).
This model is a combination of a Maxwell model and a Voigt model. The total shear
strain versus time is expressed as follows:
τ τ τ
1
t
γ () = γ + γ + γ = 0 + 0 ( − e τ / t − ) + η 0 t (2-9)
1
2
3
G
0 G 1 0
By normalizing the strain to the stress applied, the following equation representing
the creep compliance, J(t), in terms of its elastic component (J ), the delayed-elastic (J ),
e de
and the viscous component (J ) could be defined:
v
Jt () = J + J + J v (2-10)
de
e
The viscous component is inversely proportional to the viscosity (h) and directly
proportional to stress and time of loading. Based on this separation of the creep response,
the compliance could be used as an indicator of the contribution of binders to rutting
resistance. Instead of using the compliance (J ), which has a strange unit of 1/Pa, and to
v
be compatible with the concept of stiffness introduced during SHRP, the inverse of the
compliance (G ) could be used. This term is defined as the viscous component of the
v

FIGURE 2-21 Four-element (burgers) model and its response.