Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests

The universal size-shape effect law is a law that describes the dependence of nominal strength of specimen or structure on both its size and the crack (or notch) length, over the entire range of interest, and exhibits the correct small-size and large-size asymptotic properties as required by the cohesive crack model (or crack band model). The main difficulty has been the transition of crack length from 0, in which case the size effect is Type 1, to deep cracks (or notches), in which case the size effect is Type 2 and is fundamentally different from Type 1, with different asymptotes. In this transition, the problem is not linearizable because the notch is not much larger than the fracture process zone. The previously proposed universal law could not be verified experimentally for the Type 1-Type 2 transition because sufficient test data were lacking. The current study is based on recently obtained comprehensive fracture test data for three-point bend beams cast from one batch of the same concrete and cured and tested under identical conditions. The test data reveal that the Type 1-Type 2 transition in the previous universal law has insufficient accuracy and cannot be captured by Taylor series expansion of the energy release rate function of linear elastic fracture mechanics. Instead, the size effect for a zero notch and for the transitional range is now characterized in terms of the strain gradient at the specimen surface, which is the main variable determining the degree of stress redistribution by the boundary layer of cracking. The new universal law is shown to fit the comprehensive data quite well, with a coefficient of variation of only 2.3%.