To study the linear viscoelastic (LVE) of crumb rubber-modified asphalt mixtures before and after the warm mix additive was added methods of obtaining the discrete and continuous spectrum are presented. Besides, the relaxation modulus and creep compliance are constructed from the discrete and continuous spectrum, respectively. The discrete spectrum of asphalt mixtures can be obtained from dynamic modulus test results according to the generalized Maxwell model (GMM) and the generalized Kelvin model (GKM). Similarly, the continuous spectrum of asphalt mixtures can be obtained from the dynamic modulus test data via the inverse integral transformation. In this paper, the test procedure for all specimens was ensured to be completed in the LVE range. The results show that the discrete spectrum and the continuous spectrum have similar shapes, but the magnitude and position of the spectrum peaks is different. The continuous spectrum can be considered as the limiting case of the discrete spectrum. The relaxation modulus and creep compliance constructed by the discrete and continuous spectrum are almost indistinguishable in the reduced time range of 10⁻⁵ s–10³ s. However, there are more significant errors outside the time range, and the maximum error is up to 55%.

Warm-mix asphalt technology has been applied to recycled rubber asphalt binder (RAB), which forms warm-mixed crumb rubber-modified asphalt binder (W-RAB) as a “green” material for environmental conservation and to enhance road performance. Furthermore, low-temperature cracking is one of the major distresses for asphalt pavement, which drastically restricts ride quality and service level. Therefore, the main objective of this study is to comparatively analyze the low-temperature properties of W-RABs based on thermal stress and the simple fractional model. W-RABs were obtained by mixing 60 mesh recycled rubber (CR) and two different types of warm-mix additives, namely viscosity reducer (1, 2, and 3%) and surfactant (0.4, 0.6, and 0.8%). First, Hopkins and Hamming’s numerical algorithm and the Boltzmann superposition principle were used for obtaining thermal stress $\sigma \left(T\right)$. Subsequently, critical cracking temperature $T_{cr}$ was derived using the single asymptote procedure (SAP) theory. Second, the simple fractional viscoelasticity model was used to calculate the creep compliance, damping ratio, and dissipation energy ratio, and the results were compared with the Superpave protocol results obtained with bending beam rheometer (BBR) tests. The results showed that a combination of CR and warm-mix additives could slightly improve the thermal crack resistance of the asphalt binder. The addition of 0.6% surfactant yielded the optimum performance, while only a high dosage (3%) of viscosity reducer provided a marked improvement in efficiency, which decreased with a decrease in temperature. This study recommends the use of RAB composited with 0.6% surfactant for areas with extremely low temperature.