70
Temp = test temperature: - 1, 0 and 1 for 15, 20 and 25 ° C, respectively;
Freq = frequency in Hz; and
exp = e: base of natural log.
It can be seen from these models that shear stiffness as well as shear loss stiffness
is sensitive to all mix and test variables considered in this study.
6.4.2 Surrogate models for phase angle
Summary of the regression analysis for shear phase angle is presented in Table
6- 5. It was found in this study that the phase angle is dependent on | G*| and the
frequency. The model with variable frequency is:
f = - 58.75 + 58.45 × log | G* | - 7.87 × ( log | G* |) 2 - 1.41 × log( f ) R2 = 0.77 ( 6.5)
where,
f = phase angle in degree,
| G* | = shear dynamic stiffness, and
f = frequency in Hz, and
log = logarithm to base 10.
For the phase angle at 10 Hz frequency, equation 6.5 reduces to:
f = - 59.86 + 58.45 × log | G* | - 7.87 × ( log | G* |) 2 R2 = 0.77 ( 6.6)
6.5 Relationships between axial and shear stiffness
Summary of the regression analysis between axial and shear stiffness is presented
in Table 6- 6 and Table 6- 7. For mixes considered in this study, the axial stiffness can
reliably be estimated from shear stiffness through the following regression equations: