Numerical and theoretical analysis of comprehensive concrete fracture tests

The size-shape effect describes the dependence of the nominal strength of a specimen or structure on both its size and the length of internal flaw (crack or notch). Although hundreds of concrete fracture tests exist, their evaluation is ambiguous because they have limited ranges of specimen sizes, initial notch depths and postpeak response, and refer to different concretes, different batches of concrete, different ages, different environmental conditions, different loading rates and test procedures and different specimen types. Presented is an experimental investigation, of unprecedented comprehensiveness and low scatter, using specimens made from one batch of concrete and kept in the same curing conditions. The results of these tests, supported by finite element simulations with a cohesive crack model and a universal size-shape law, show a strong dependence of the structure strength on the structure size, which is currently lacking in many design codes. A universal size-shape law, anchored in cohesive fracture mechanics, covers over the entire size 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 the universal size-shape law, the size effect for a zero notch and for the transitional range is 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%.