A new method of developing the master curve for asphalt mixtures was developed
by Pellinen and Witczak (2002), in which the master curves were constructed fitting a
sigmoidal function to the measured complex modulus test data using non-linear least
squares regression techniques. The shift can be achieved by solving the shift factors
simultaneously with the coefficients of the sigmoidal function. The sigmoidal fitting
function for master curve construction used by Pellinen and Witczak (2002) is defined
equation (4-2).
log(E*) = +og (Eq. 4-2)
Where
log(IE*|) = log of dynamic modulus,
6 = minimum modulus value,
fr = reduced frequency,
Uc = span of modulus value,
P, y = shape parameters.
The reduced frequency, fr, is defined as,
f= (Eq. 4-3)
a(T)
or alternatively,
log(fr) = log(f) + log[a(T)]
in which f = testing frequency, and a(T) is the shift factor that defines the required shift at
a given temperature to get the reduced frequency fr. At the reference temperature, the
shift factor a(Tr) = 1. Finally, the parameter y influences the steepness of the function
(rate of change between minimum and maximum) and P3 influences the horizontal
position of the turning point, shown in Figure (6-17).