Modeling Crack Propagation in Bituminous Binders under a Rotational Shear Fatigue Load using Pseudo J-Integral Paris' Law

Fatigue resistance of bituminous binders plays a critical role in determining the fatigue performance of asphalt pavements. It is reported in the literature that, under a rotational shear fatigue load like a dynamic shear rheometer (DSR) test, the crack grows in the cylindrical bitumen sample as a circumferential crack that is initiated at the periphery of the sample and propagates toward the center of the sample. This study aims to model this crack propagation in bituminous binders under rotational shear fatigue load by time sweep (TS) fatigue test using the DSR. The crack length in the TS test is determined using a damage mechanics-based DSR-C model which is a function of the shear moduli and phase angles under undamaged and damaged conditions. The crack evolution is modeled by a pseudo J-integral based Paris' law. Samples of virgin bitumen 40/60 and polymer-modified bitumen X-70 under unaged and aged conditions are tested by the TS tests at different temperatures, frequencies, and strain levels. Results show that the pseudo J-integral Paris' law is able to predict accurately the crack propagation in bituminous binders under the rotational shear fatigue load. The crack grows faster in aged bitumen or at lower temperatures. The Paris' law model parameters (A and n) are independent of loading frequency or load amplitude. They are fundamental material properties and can be determined at one loading frequency and amplitude, then can be implemented to predict the growth of cracks in bituminous binders at different loading frequencies or amplitudes.