Inter-conversion of the generalized Kelvin and generalized Maxwell model parameters via a continuous spectrum method

Accurate determination of the Prony series parameters of the generalized Maxwell (GM) model and the generalized Kelvin (GK) model is crucial to the characterization of linear viscoelastic (LVE) properties of asphalt mixture and the prediction of in-service performance of asphalt pavement. However, existing methods may not be able to provide satisfactory accuracy due to their weakness of fully complying with the LVE theory or the involvement of unsolvable high-order nonlinear systems. To identify the Prony series parameters more efficiently and accurately, this paper developed a continuous spectrum method to establish the inter-conversion between the GM and GK model parameters. In the newly developed method, the complex modulus mater curves are first constructed through the conventional master curve models. The continuous relaxation and retardation spectra are then established using the proposed direct or indirect methods. The time and strength constants of the GM and GK models are subsequently calculated via an extended search method, based on which the Prony series parameters and the LVE variables of the asphalt mixture can be finally determined. Accuracy of the new method in determining the LVE variables was validated through a comparison of the calculated and measured LVE variables of asphalt mixture, while the equivalence between the GM and GK models established based on the new method was verified in different domains. Besides, the success implementation of the new method to the generalized Sigmodal model demonstrates the universality of the newly developed continuous spectrum method in determining the LVE variables of asphalt mixture.