Pseudo-variables method to calculate HMA relaxation modulus through low-temperature induced stress and strain

Thermal cracking is a critical failure mode for asphalt pavements. Relaxation modulus is the major viscoelastic property that controls the development of thermally induced tensile stresses. Therefore, accurate determination of the relaxation modulus is fundamental for designing long lasting pavements. This paper proposes a reliable analytical solution for constructing the relaxation modulus master curve by measuring stress and strain thermally induced in asphalt mixtures. The solution, based on Boltzmann's Superposition Principle and pseudo-variables concepts, accounts for time and temperature dependency of bituminous materials modulus, avoiding complex integral transformations. The applicability of the solution is demonstrated by testing a reference mixture using the Asphalt Thermal Cracking Analyzer (ATCA) device. By applying thermal loadings on restrained and unrestrained asphalt beams, ATCA allows the determination of several parameters, but is still unable to provide reliable estimations of relaxation properties. Without them the measurements from ATCA cannot be used in modeling of pavement behavior. Thus, the proposed solution successfully integrates ATCA experimental data. The same methodology can be applied to all test methods that concurrently measure stress and strain. The statistical parameters used to evaluate the goodness of fit show optimum correlation between theoretical and experimental results, demonstrating the accuracy of this mathematical approach.