Improved methodology for identifying Prony series coefficients based on continuous relaxation spectrum method

The Prony series models have been widely utilized in characterizing the linear viscoelastic properties of asphalt mixtures. However, the determination of the time coefficients, as a crucial step in identifying the Prony series coefficients, is based on empirical adjustments and time-consuming selections. In order to overcome the drawbacks of the existing methods, this study proposes a method for determining the optimal relaxation time range (ORTR) based on the continuous relaxation spectrum method, which is then utilized to identify the Prony series coefficients. There are four major steps in the proposed method: (1) establish the continuous relaxation spectrum by applying the inverse Stieltjes transform to the storage modulus model; (2) set trial groups of the relaxation time range on the basis of the relaxation time corresponding to the peak value of the continuous relaxation spectrum; (3) identify the ORTR through comparing the characteristic number of terms of each trial group; and (4) determine the Prony series coefficients based on the relationship between the relaxation strength and the relaxation time. The proposed method is validated by using complex modulus data of two types of asphalt mixtures at four test temperatures and six loading frequencies. The results show that: (1) the midpoint of the ORTR is close to the relaxation time corresponding to the peak point of the continuous relaxation spectrum; and (2) the total number of terms in the Prony series model developed from the ORTR is less than 30 and the model errors are less than 3.2%.