Page 238 - Mechanics of Asphalt Microstructure and Micromechanics

230 Ch a p t e r Sev e n

7.10.3 Fracture Mechanics Models
The fracture models made use of the cracking propagation law for both linear elastic
fracture mechanics and the non-linear fracture mechanics. For LEFM the Paris law is
often used. For the non-linear elastic mechanics, the J integral is often used.

The Uzan Model
Uzan (2007) modeled the fatigue cracking as a two-stage process consisting of crack
initiation and crack propagation. The crack initiation stage is characterized by conven-
tional laboratory fatigue tests; while the crack-propagation stage is described using the
Paris-Erdogan law.
Uzan adopted the model developed by Tayebali et al. in SHRP Project A-003A as the
crack-initiation model (Equation 7-79).
dc
The Paris-Erdogan law = AK)Δ n was used as the crack-propagation model for
(
dN
evaluating the number of load repetitions needed to propagate the crack. Where, c = crack
length; N = number of load repetitions; ΔK = difference between maximum and minimum
stress intensity factor K; and A, n = Paris law fracture parameters for AC.
In the case of ΔK = K, it is given by the following equation:

N = 1 ⋅ c ∫ h dc = 1 I ⋅ (7-83)
p A 0 K n A K

Where N p is number of load repetitions to propagate a crack of initial length c 0 to the
surface; h is layer thickness; c 0 is initial crack length; K is stress-intensity factor (K I for
Mode I and K II for Mode II); n , A, are material properties; and I K = N p A.

Owusu-Antwi Model
Owusu-Antwi et al. (1998) used the principles of fracture mechanics and developed a
mechanistic-based performance model for predicting the amount of reflective cracks in
composite AC/PCC pavements. It is illustrated that a mechanistic-based model can be
developed to closely model the real-life behavior of composite pavements and predict
the amount of reflective cracks. Because of the mechanistic nature of the model, it is
particularly effective for performance prediction for design checks and pavement man-
agement. Also, the model has great potential for application in cost allocation since it
can take into account the relative damaging effect of the actual axle loads in any traffic
distribution.
For a 1-kilometer long section, the number of reflective cracks can be determined
from the following equation:

RCRACKS = DAMTOT 19 . * 1000 + S (7-84)
DAMTOT 19 . + 1 S
Where S is the joint spacing; the total damage (DAMTOT) from both temperature
and traffic loading can be calculated using the following equation:

*
.
.
I
DAMTOT = 0 0132 ∑ n 1 + AGE ( 8 79 + 0 000795 * FI AGE) (7-85)
.
N N
i temp