Theory of cyclic creep of concrete based on Paris law for fatigue growth of subcritical microcracks

Recent investigations prompted by a disaster in Palau revealed that worldwide there are 69 long-span segmental prestressed-concrete box-girder bridges that suffered excessive multi-decade deflections, while many more surely exist. Although the excessive deflections were shown to be caused mainly by obsolescence of design recommendations or codes for static creep, some engineers suspect that cyclic creep might have been a significant additional cause. Many investigators explored the cyclic creep of concrete experimentally, but a rational mathematical model that would be anchored in the microstructure and would allow extrapolation to a 100-year lifetime is lacking. Here it is assumed that the cause of cyclic creep is the fatigue growth of pre-existing microcracks in hydrated cement. The resulting macroscopic strain is calculated by applying fracture mechanics to the microcracks considered as either tensile or, in the form of a crushing band, as compressive. This leads to a mathematical model for cyclic creep in compression, which is verified and calibrated by laboratory test data from the literature. The cyclic creep is shown to be proportional to the time average of stress and to the 4th power of the ratio of the stress amplitude to material strength. The power of 4 is supported by the recent finding that, on the atomistic scale, the Paris law should have the exponent of 2 and that the exponent must increase due to scale bridging. Exponent 4 implies that cyclic creep deflections are enormously sensitive to the relative amplitude of the applied cyclic stress. Calculations of the effects of cyclic creep in six segmental prestressed concrete box girders indicate that, because of self-weight dominance, the effect on deflections absolutely negligible for large spans (>150m). For small spans (<40m) the cyclic creep deflections are not negligible but do not matter since the static creep causes in such bridges upward deflections. However, the cyclic creep is shown to cause in bridges with medium and small spans (<80m) a significant residual tensile strain which can produce deleterious tensile cracking at top or bottom face of the girder.