Research on the fatigue equation of asphalt mixtures based on actual stress ratio using semi-circular bending test

•SCB strength models of asphalt mixtures based on loading rates and temperatures were established.•The fatigue properties of asphalt mixtures were evaluated in aspect of energy consumption and vertical deformation.•Fatigue equations based on real actual stress ratio and nominal stress ratio were developed. The semi-circular bending (SCB) strength test and fatigue test were used in this paper to evaluate the strength property and fatigue performance of asphalt mixtures. The SCB strength test was carried out at 8 loading rates and 3 temperatures, followed by the SCB fatigue test at 5 load levels on one common stone matrix asphalt (SMA) mixture. The time–temperature characteristics of strength from SCB test were studied. The fatigue performance was evaluated based on displacement development and energy consumption during the cyclic loading process. And according to the established strength-loading rate model, the fatigue equation based on actual stress ratio was obtained as well. The results showed that asphalt mixture strength was affected by loading rate and temperature significantly, the relation between strength and loading rate could be approximately expressed as a power function; the relation between fatigue life and stress level (or nominal stress ratio) could also be expressed as a power function. The lower the stress level, the longer the fatigue life was, and the fatigue life and the cumulative energy consumption showed a good linear relationship in the double logarithmic coordinates; the fatigue equation based on actual stress ratio revealed the connection between fatigue failure and strength failure.