A consistent approach for characterising asphalt concrete based on generalised Maxwell or Kelvin model

The generalised Maxwell (GM) model and generalised Kelvin (GK) model are widely used in characterising the linear viscoelastic (LVE) properties of asphalt concrete. Traditionally, the GM and GK model coefficients are determined by fitting the analytical LVE functions to pre-smoothed storage component data. The loss component data are usually disregarded primarily due to the fact that a well-accepted loss component master curve of asphalt concrete is not available to pre-smooth the experimental results. This study shows that the results obtained from the traditional approach may not satisfy some basic LVE requirements, namely the Kronig–Kramers relation between the storage and loss components, the convolution integral relation between the relaxation modulus and creep compliance and the applicability of the same time-temperature shift factor to various LVE functions. In addition, the relationships between the viscoelastic constants and model coefficients are usually neglected in the traditional approach which may lead to inconsistent LVE functions. A new procedure was proposed in this study to determine the GM and GK model coefficients using the collocation method. The experimental results are pre-smoothed using a complex modulus master curve represented by the modified Havriliak–Negami (MHN) model and then the model coefficients are solved from either the storage or loss component collocation points. The relation between viscoelastic constants and model coefficients is satisfied by introducing an additional linear equation besides those for the collocation points. It is shown that more densely spaced time constants (typically 0.5 decades apart) are necessary to eliminate any oscillation in the loss component master curves. The results show that the proposed approach effectively correct the deficiencies associated with the traditional approach. The GM model and GK model obtained from the approach are equivalent for the same material. The new approach provides a consistent and simple way for determining the coefficients of GM and GK model for asphalt concrete.