An extended search method for identifying optimal parameters of the generalized Maxwell model

Abstract Viscoelastic constitutive relations based on Prony series are generally employed to the finite element modeling analysis of asphalt pavement performance. However, little attention has been paid to the selection of target relaxation time constants, which is a key step in the determination of the Prony series coefficients. According to the approximate relationship between the relaxation time and the relaxation strength, an extended search method was developed to determine the optimal relaxation time range (ORTR) in this study. A large number of data points collected from “Master E* Database” were used to validate the universality and accuracy of Prony series model with the ORTR. Besides, the relationship between the reduced frequency range (RFR) of the master curves of viscoelastic parameters and the ORTR was investigated by calculating the difference between the upper limit values Δ up and the difference between the range width values Δ w . The results showed that: (1) the Prony series model with the ORTR had a reasonable number of terms and provided excellent model fitting; (2) the distribution of Δ up , as well as the distribution of Δ w , satisfied the normal distribution at a significance level of 0.05; and (3) the modified RFR-based relaxation time range was easy-to-use for the construction of Prony series model with high R 2 values.