Conversion from Shear Creep Compliance to Relaxation Modulus of Asphalt Binder Using Cauchy Residue Method and Experimental Validation

The need for conversion between viscoelastic functions arises in that strain-controlled relaxation test is quite difficult to run than a stress-controlled creep test, especially on rigid sample and at low temperatures. A new theoretical method aimed at converting shear creep compliance to relaxation modulus within linear viscoelastic region based on the Cauchy residue theorem was proposed and investigated experimentally in this research. A numerical example was presented and then its effectiveness and accuracy were verified by the experimental results. Prior to the conversion, the oscillatory amplitude sweep test, shear creep test, and shear stress relaxation test were conducted on three asphalt binders to obtain their linear viscoelastic region, creep compliance as well as relaxation modulus data. It was found that polynomial was equally competent as the power law and Prony series in terms of emulating short-term creep behavior of the asphalt, which laid a firm foundation for reasonable conversion. Furthermore, statistics show the converted modulus could give a good description on the measured shear relaxation modulus, suggesting the proposed method was effective in the discussed material and temperature range. Finally, in terms of signal and system theory, the relaxation modulus had three poles and one double zero on the complex plane: one negative real pole and a pair of conjugate complex poles. All the poles lie to the left of the imaginary axis of the complex plane (excepting a simple pole at the origin), which agreed well with the requirement for a linear viscoelastic behavior.