Estimation of fracture toughness, driving force, and fracture energy for fractal cracks using the method of imaginary smooth crack

Theoretical expressions of the fracture toughness, driving force and fracture energy are derived for a perfect infinite plate with a solitary self-similar fractal crack of mode I considering the fractal effects of cracks in this work. The specific surface energy per unit fractal measure for concrete is fit based on test data. Thus, behaviors of the above four fracture parameters for concrete are studied as varying the initial length of the fractal crack.