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Asphalt binder has an important role in asphalt mixture behavior. Therefore binder fatigue characterization has been widely investigated. Significant research efforts were focused on developing reliable fatigue prediction models. Those efforts in the beginning were concentrated on relating initial responses, such as strain or stress levels of asphalt mixtures to their fatigue life. Such phenomenological relationships were usually developed by means of testing samples under different loading conditions and generating regression models. Considering different combinations of loading conditions, and the long time duration needed for a single fatigue test, the phenomenological approach requires extensive time and funding. Therefore, the mechanistic approaches which substitute excessive testing with analytic equations, have become more common in the field of fatigue behavior characterization. Viscoelastic continuum damage (VECD) mechanics is one of the well-studied mechanistic approaches to characterize the fatigue life of viscoelastic materials. In this approach an internal state variable (ISV), called damage, is defined to stand as a representative of material structural state. Then the state of the modulus is determined as a function of damage, namely damage function.  Determination of damage function can facilitate asphalt fatigue prediction under different loading patterns. However, VECD analysis has its own complications. The damage parameter needs to be calculated in each cycle during the test, while its calculation needs damage function trend to be known. Thus, damage parameter can only be determined using a procedure of try and error. In this research an inventive method has been introduced that can simplify efforts to yield damage function, requiring less time and fewer samples. A formulation framework has been presented here which is based on an analytical solution of the governing differential equation of damage evolution power-law. The solution is made assuming the ruling conditions of this study. These assumptions which are clarified in the paper could be reconsidered to form new formulations through a similar approach. Using the formulation, developed in this study, damage function can be found, using the data obtained from two constant-strain, or a single incremental-strain tests. According to this method Time Sweep Test can be performed at two different strain amplitudes and the developed models could be fit to the initial responses data of the material to yield VECD parameters needed to constitute the fatigue prediction model. This approach uses a nonlinear regression analysis to determine VECD parameters, even without calculating the values of damage during test. Afterward, the proposed procedure was validated by experimental tests. Time Sweep tests were performed on binder samples modified with SBS polymer. The binder samples were modified using SBS Polymer, due to its popularity among asphalt researchers. Such modification transforms a simple binder to a complex one. Results showed that the try and error procedure can be substituted by regression model to yield damage function in less time. The discrepancies between the data obtained from the two above-mentioned methods were negligible. It was concluded that the similar results are due to the same mechanism, used in try and error and regression methods which is performed through different approaches.
 

Keywords: Asphalt, Fatigue, Viscoelastic Continuum Damage

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