Energy-based method to determine equivalent frequency for HMA

Dynamic modulus (|E*|) master curve is the fundamental material property of asphalt concrete (AC) mixture, which illustrates the time and temperature dependency for hot mix asphalt (HMA), and it is a crucial input to the new ME-PDG, expressed as Witczak´s equation, or sigmoidal function. To obtain the equivalent elastic modulus of the AC layer corresponding to a specific load, the vehicle speed and pavement structure need to be considered together. In this paper, the equivalent frequency in new ME-PDG is briefly introduced first, and then a theoretical formula for the proposed equivalent frequency is derived, based on the principle of energy conservation, or the ParsevaPs theorem. Field Falling Weight Deflectometer (FWD) test is simulated by the Finite Element Method (FEM) software ABAQUS, and deflection history is compared between dynamic response and static response, which is almost identical to the linear layered elastic theory with the elastic modulus of AC layer at equivalent frequency. Followed by the theoretical solution of spectral element method with the interpolation of influence line, a special truck load is applied on typical thick pavement and thin pavement, and the magnitude of longitudinal strain at the bottom of AC and the vertical strain at the top of subgrade are compared with linear elastic solution from KENLAYER. Both results show that the proposed equivalent frequency works well to simply AC layer as visco elastic material with constant elastic modulus and Poisson´s Ratio.