# Time-Domain Characterization of Linear Viscoelastic Behavior in Asphalt Mixtures: A Comparative Evaluation Through Discrete and Continuous Spectral Techniques

## TL;DR

This study compares discrete and continuous spectral techniques for analyzing the viscoelastic behavior of asphalt mixtures, showing their similarities and differences in predicting material responses over time.

## Contribution

The study provides a systematic comparative evaluation of discrete and continuous spectral methods for viscoelastic characterization of asphalt mixtures.

## Key findings

- Discrete and continuous spectra methods yield consistent predictions of relaxation modulus and creep compliance within conventional time scales.
- Continuous spectra methods produce higher maximum equilibrium values and lower minimum values compared to discrete methods.
- Crumb rubber-modified asphalt mixtures show better low-temperature cracking resistance, while SBS-modified mixtures resist high-temperature deformation better.

## Abstract

This study systematically investigates continuous and discrete spectra methodologies for determining time-domain viscoelastic response functions (creep compliance and relaxation modulus) in asphalt mixtures. Through complex modulus testing of three asphalt mixtures (base asphalt mixture, SBS-modified asphalt mixture, and crumb rubber-modified asphalt mixture), we established unified master curves using a Generalized Sigmoidal model with approximated Kramers–Kronig (K-K) relations. Discrete spectra can be obtained by Prony series of Maxwell/Kelvin modeling, while continuous spectra derived through integral transformation produced complementary response functions by numerical integration. Comparative analysis demonstrated that discrete and continuous spectra methods yield highly consistent predictions of the relaxation modulus and creep compliance within conventional time scales (10−7–105 s), with significant deviations emerging only at extreme temporal extremities. Compared to discrete spectra results, material parameters (relaxation modulus and creep compliance) derived from continuous spectra methods invariably asymptotically approach upper and lower plateaus. Notably, the maximum equilibrium values derived from continuous spectra methods consistently surpassed those obtained through discrete approaches, whereas the corresponding minimum values were consistently lower. This comparative analysis highlights the inherent limitations in the extrapolation reliability of computational methodologies, particularly regarding spectra method implementation. Furthermore, within the linear viscoelastic range, the crumb rubber-modified asphalt mixtures exhibited superior low-temperature cracking resistance, whereas the SBS-modified asphalt mixtures demonstrated enhanced high-temperature deformation resistance. This systematic comparative study not only establishes a critical theoretical foundation for the precise characterization of asphalt mixture viscoelasticity across practical engineering time scales through optimal spectral method selection, but also provides actionable guidance for region-specific material selection strategies.