Page 237 - MODELING OF ASPHALT CONCRETE

Unified Disturbed State Constitutive Modeling of Asphalt Concr ete 215

approaches. In fact, the DSC allows for the interaction and coupling between the RI and
FA parts and avoids the need for the definition of particle level response (as in the
micromechanics approach), which is difficult or impossible to measure at this time.

Equations
Based on the equilibrium of forces on a material element, the incremental constitutive
equations are derived as (Desai 2001):
dσ = ( − D dσ) i + Ddσ + dD σ( c − σ ) (8-1a)
i
a
c
1
~ ~ ~ ~ ~
c
i
or dσ = ( − D)C i dε + DC c dε + dD σ( i − σ ) (8-1b)
a
i
1
~ ~ ~ ~ ~ ~ ~
a
or dσ = C DSC dε (8-1c)
~ ~ ~
where a, i, and c = observed RI and FA responses, respectively
σ and ε = stress and strain vectors, respectively
~ ~
C = constitutive or stress-strain matrix
~
D = disturbance
dD = increment or rate of D
As a simplification, D is assumed to be a scalar in a weighted sense. It can, however,
be expressed as a tensor, D , if the test data to define the directional values of D is
ij
available (Desai 2001).
Capabilities and Hierarchical Options
Figure 8-5 shows a summary of the capabilities of the DSC model. In the single framework,
the DSC approach is capable of allowing for elastic, plastic, and creep strains,
microcracking, fracture and disturbance (damage), and stiffening under mechanical
and environmental loading. This is considered to be a unique advantage compared to
other available models. A major advantage of the DSC is that various specialized
versions, such as elasticity, plasticity, creep, microcracking, degradation or softening,
and healing or stiffening can be obtained from Eq. (8-1). If there is no disturbance
(damage) due to microcracking and fracture, D = 0 and Eq. (8-1) reduces to the classical
incremental equations as

i
i
dσ = C dε i (8-2)
~ ~ ~
i
where C can represent elastic, elastoplastic, or elasto-viscoplastic response. If D ≠ 0,
~
the model can include damage and softening, and healing, as shown in Fig. 8-6. The
user can choose an appropriate option for a given pavement material and needs to
input only parameters relevant to that option. For instance, the bound asphalt material
can be characterized by using the DSC with elasto-viscoplastic model, whereas the
unbound materials can be treated as elastoplastic.