Development of Prony series models based on continuous relaxation spectrums for relaxation moduli determined using creep tests

Abstract

Prony series models have been widely utilized to represent relaxation moduli. However, negative model parameters and wavy fitting curves are common observations of Prony series models of relaxation moduli constructed based on creep tests without establishing a continuous relaxation spectrum. This study developed a method of constructing relaxation modulus models in the form of Prony series based on creep test data via establishing continuous spectrums of relaxation times. Uniaxial compressive creep tests were performed on two types of asphalt mixtures at five test temperatures. The measured creep compliances at every test temperature were modeled using the generalized Kelvin model with two Kelvin elements, which provided excellent model fitting with R2 values larger than 0.99. The modeled creep compliances at every temperature were converted into the relaxation moduli according to the constitutive relations of the generalized Kelvin model. Master curves of the relaxation moduli were constructed using the modified power law model. The continuous spectrum of relaxation times was therefore established for each mixture type. The relaxation modulus model in terms of the continuous relaxation spectrum was approximated using the form of Prony series. Prony series models with various terms were constructed for each mixture type; the parameters of these Prony series models were all positive. It was demonstrated that, when specifying one relaxation time per decade equidistantly on a base-10 logarithmic axis, the constructed Prony series model for each mixture type had a reasonable number of terms and generated a fitting curve of the relaxation modulus with negligible waviness and an R2 value larger than 0.99.The method developed in this study provided an effective solution to build a Prony series model of the relaxation modulus with a limited number of terms, guaranteed positive model parameters, an excellent goodness of fit, and a fitting curve with negligible waviness.