Page 237 - Mechanics of Asphalt Microstructure and Micromechanics

Models for Asphalt Concrete 229

The Shell Model
⎡ ε ⎤ −5
N = ⎢ t ⎥ (7-77)
f ⎣ ⎢ (.0 856 V + . )1 08 S mix ⎦ ⎥
− .036
b
Where N f = fatigue life; e t = tensile strain; S mix = mixture flexural stiffness; and
V b = asphalt content by volume.

The Asphalt Institute Model
⎣
N = S * 10 ⎡ .484 ( VFB− .069 ) ⎤ ⎦ * .004325 ε − .3291 1 * S − 0 845 (7-78)
.
0
*
f f t mix
Where N f = fatigue life; S f = shift factor to convert laboratory test results to field ex-
pected results (the recommended factor is 18.4 for a 10% cracked area); e t = tensile strain
applied; S mix = flexural stiffness of a mix (psi); and VFB = voids filled with bitumen.
The Tayebali (1996) Model (SHRP Project A-003A)
N = S *.2 738 10 5 e * . 0 077 VFB * ε − .6224 S − " 2720 0 (7-79)
×
.
3
f f 0 0
Where S f = shift factor to convert laboratory results to field expected results (the
recommended factor is 10 for 10% cracked area and 14.0 for 45% cracked area), e = base
of natural logarithm, VFB = percentage of voids filled by bitumen, e 0 = strain level, and
"
S 0 = loss of stiffness as measured in flexure.
The Medani and Molenaar Model (2000)

⎛ 1 ⎞ n
N = k ⎜ ⎟ (7-80)
f 1 ⎝ ε t ⎠
2
n =
.
m 0 541 + 0 346 − 0 03524 V )
.
(.
m a
3209 V V
l logk = . 6 589 3 .762 + + . 2 332 logV + . 0 149 b + 0 928 PI − 0 0721. T (7-81)
−
n
.
&
1 S b V RB
m a
Where k 1 = coefficient; e t = initial tensile strain; m = slope of the mix stiffness master
curve; T R&B = softening point for binder (determined by ring and ball test) (°C); S m =
mixture stiffness (MPa); n = fracture parameter; V a = air void content (%); and V b = vol-
ume of binder (as a percentage).
As it is understood that AC mixtures are typically assumed to exhibit linear-visco-
elastic behavior, their response is dependent on time of loading and test temperature.
This behavior is represented by the following relationship where the stiffness is a func-
tion of temperature and time:
σ
S mix = (, (7-82)
t T)
ε
Where S mix = mixture stiffness; s = stress level; e = strain level; t = time of loading;
and T = test temperature.