Page 239 - Mechanics of Asphalt Microstructure and Micromechanics

Models for Asphalt Concrete 231

Where AGE = the age of the pavement after overlay, in years; FI = the freezing index;
N temp = the number of temperature load applications to failure; n i = the actual number of
axle passes for axle weight; i, and N i = the allowable number of axle passes according to
the following equation. The N i was developed based on Paris’s crack growth law that
was used to model the relationship between crack propagation in AC and their stress
intensity factors and other material fatigue properties.

h
N = OL (7-86)
i 10 −12 K 2 4 .
C
Where K C = the stress intensity factor; h OL = the thickness of the AC overlay.

Non-Linear Fracture Mechanics
For non-linear fracture mechanics, plastic deformation is considered. A commonly
used parameter for characterization of non-linear behavior is the J contour path inde-
pendent integral, which can be used as both an energy parameter and a stress inten-
sity parameter.
u ∂
∫
J = ( Wdy −σ ij n j x ∂ i ds) (7-87)
Γ

Where W = the strain energy density, Γ = any contour, and ds = a length increment

along the contour (see Chapter 6). Like the stress intensity factor K in linear elastic me-
chanics, the growth rate of crack is a function of J instead of K in non-linear fracture
mechanics. If the material is viscoelastic, strain rates, stress rates, displacement rates
and work rates should be used in the above formulas (see Chapter 6).

Smith and Hesp Model
Smith and Hesp (2000) also modeled the crack propagation phase using Paris’s law,
which relates the rate of crack growth to fundamental properties of the material and
experimental conditions and stress intensity factor K.

7.10.4 Damage-Based Models
The models falling in this category rest on the accumulative damage concept.

Castro and Sanchez Model
Castro and Sanchez (2008) proposed a phenomenological model based on the continu-
um damage theory. The three point bending fatigue test was used to determine the pa-
rameters in the equation shown below:

N =⋅ε b ⋅ D c (7-88)
a
0
N is the number of loading cycles and e 0 is the initial strain; a, b and c are the param-
eters of asphalt concrete determined experimentally; D is the damage parameter,