An analytical method for determining the crack extension resistance curve of concrete

Owing to its importance in evaluating the fracture behaviour of concrete, crack extension resistance has been studied based mainly on experimental results. In this paper, an analytical method is developed for determining the crack extension resistance curve of concrete. It is assumed that, when the difference in stress intensity factor caused by external forces and by the cohesive stress within the fracture process zone is equal to the initial cracking toughness, crack propagation is initiated. According to this assumption, the crack extension resistance curve of concrete is expressed analytically as either the stress intensity factor caused by external forces, or the sum of the initial cracking toughness and the stress intensity factor by the cohesive stress within the fracture process zone. One advantage of this method is that, unlike other methods, the experimentally measured load–crack mouth opening displacement curve is not required in calculating the crack extension resistance curve. Based on numerical results, it is found that the crack extension resistance curve is independent of initial crack length. Also, for a given fracture energy, the shape of the cohesive stress–crack opening displacement curve exhibits no significant effect on the crack extension resistance curve. It is concluded that the proposed method can predict the crack extension resistance curve of concrete with reasonable accuracy.