Evolution of the Modulus of Asphalt Concrete in Four-Point Beam Fatigue Tests

The four-point beam (4PB) test is extensively used to characterize the fatigue behavior of asphalt concrete mixtures. But the inhomogeneity of the deformation in the beam is not given due consideration in traditional analyses of these tests. During bending, the strain in the beam varies both along the length and depth of the beam. Consequently, different parts of the beam would experience different levels of damage when subjected to repeated loading. The modulus obtained from traditional calculation procedures do not take into account this variation, and therefore, the calculated modulus is essentially an overall weighted modulus. In this study, a new methodology is proposed with which the evolution of local modulus and local phase angle with loading cycles can be determined. The methodology does not assume any specific constitutive relationship among the stress, strain, and extent of damage. It was developed by considering the modulus of the material to depend on only the amplitude of the applied strain and the number of cycles of load repetition. With this methodology, the evolution of local modulus at any particular strain level can be obtained, provided the 4PB tests are conducted at a sufficient number of strain levels. Based on the evolution of local modulus, a new fatigue failure criterion is proposed. The number of repetitions at which the local modulus reduces to zero is taken to be the point of failure. This fatigue life criterion is more meaningful than the old 50% reduction in stiffness criterion. The fatigue life obtained using this criterion is also comparable to that obtained using the new stiffness ratio criterion.