Characterization of the Tensile Viscoelastic Properties of an Undamaged Asphalt Mixture

All characterization of asphalt mixtures must begin with the properties of the mixture in an undamaged state. Subsequent tests of the mixture in different stress or strain states at a level to cause damage can be referred to this undamaged state to assess the degree to which the mixture has been changed. All forms of such change from an original state by such damaging processes as fatigue, plasticity, healing, moisture damage, and aging can only be properly assessed by comparison with an accurately measured undamaged state. This is particularly the case with the use of pseudostrain dissipated energy to characterize the departure of a material from an original linear viscoelastic state. This paper presents a new test and data analysis protocol based on linear viscoelasticity theory to characterize the master curves of the viscoelastic properties of an asphalt mixture. Instead of running a relaxation modulus test in which controlling the test apparatus is a serious challenge, the proposed test protocol applied a uniaxial monotonically increasing tensile stress to the test specimen. The axial and radial deformations of the specimen were recorded and used to calculate the axial and radial strains. The uniaxial tensile loading rate and time were carefully controlled to assure that the strain of the specimen was limited to the small-strain condition $\left(<100\mu \epsilon \right)$ under which the specimen was assumed not to be damaged during the test. The applied stress and measured strain were fitted with functions of time. Applying the Laplace transform to the stress and strain functions, the relaxation modulus as a function of time was determined using the Boltzmann superposition principle and the convolution theorem. The relation between the relaxation modulus and the complex modulus was used to determine the complex modulus as a complex function of frequency. Then the magnitude and phase angle of the complex modulus were obtained from the real part and imaginary part of the complex modulus. The proposed test and data analysis protocol were performed on the same specimen at three temperatures, 10, 20, and $30°\text{C}$ , so master curves of the magnitude and phase angle of the complex modulus were constructed using the time-temperature superposition principle. The master curves of the magnitude and phase angle of the complex modulus were fitted with mathematical functions that were reported in the literature and were modified to be more comprehensive. The parameters in the mathematical functions were searched simultaneously using the Solver Function built into the Microsoft Excel. Compared to the traditional relaxation modulus and the dynamic modulus test protocols, the newly developed test protocol was more efficient to characterize the viscoelastic properties of asphalt mixtures. The newly developed test method did not introduce any damage to the specimen so the same specimen may be retested for its fatigue, healing, and other properties.