Concrete fracture models: testing and practice

The existing fracture models for concrete and the testing methods for fracture energy and other fracture characteristics are reviewed and some new results on the relationship between fracture testing and size effect are presented. The limitations of the cohesive crack model are discussed. The discrepancy between the fracture energy values measured by Hillerborgʹs work-of-fracture method and the size effect method is explained and mathematically described by the recently proposed broad-range size effect law. The implications of the recently identified large statistical scatter of the fracture energy values measured by the work of fracture, compared to those measured by the size effect method or Jenq–Shah method, are discussed. Merits of various testing methods are analyzed. A testing procedure in which the maximum loads of notched beams of only two different sizes in the ratio 2:1 and two different notch depths are tested is proposed and a least-square procedure for calculating the fracture parameters is given. A simplified testing procedure with an empirical coefficient, in which only the maximum loads of identical notched and unnotched beams of one size are tested, is also proposed as an alternative. To improve the size effect description for small sizes, the small-size asymptotics of the cohesive crack model is determined and a formula matching this asymptotics, as well as the large-size linear elastic fracture mechanics asymptotics, is presented. Finally, various arguments for introducing fracture mechanics into concrete design practice are reviewed and put into the perspective of safety factors.