Frequency determination from vehicular loading time pulse to predict appropriate complex modulus in MEPDG

The Mechanistic-Empirical Pavement Design Guide (MEPDG) makes use of the complex modulus to simulate the time and temperature dependency of hot-mix asphalt (HMA). Since the complex modulus is measured in the frequency domain while vehicular loading is applied in the time domain, the correctness of the design process essentially depends on the accuracy of the conversion from the time domain to the frequency domain. The current MEPDG approach assumes that the frequency is calculated as the inverse of the loading time. Another approach suggests that the frequency be determined from the angular frequency. This paper analyzes these two techniques and demonstrates that they only represent approximations for specific cases not encountered in pavement systems. A novel approach is presented to accurately determine the frequency of vehicular loading based on a detailed Fourier analysis. The proposed Fourier approach provides a direct and reliable technique to obtain the frequency spectrum of moving load based on the time pulse data. To evaluate and validate this approach, data from the Virginia Smart Road were used. The field loading frequency spectra under various vehicle speeds and at different depths were analyzed. Results of this analysis indicated that the MEPDG approach is associated with an error ranging from 40 to 140% in frequency estimation depending on the vehicle speed and depth of calculation. Based on this analysis, the natural frequency of an HMA layer is estimated and the delayed-response associated with HMA viscous properties during the unloading phase is investigated.