A Fractal Study of the Size Effect of Concrete Fracture Energy

The three-dimensional crack structure of concrete, which is divergent, discontinuous and comp le~ is quantitatively described with fractal theory, and the calculation formula of total crack surface area deduced. accord~nce with the definition 9f fracture energy by TC50-FMC, a is built between fracture energy and the parameters of micro of structure in micro crack zone, and hence the size effect problem energy solved theoretically. The relation was also proved by experiments. Results show that: concrete strength increases with the increase of fracture surface energy y 8; concrete strength increases and the significance of the size effect of fracture energy Gf decreases with the decrease of the structure parameter Dc of the micro crack zone; the structure of the micro crack zone changes with varying specimen size, so does the value of Dc~ thickness of specimen also causes the size effect of G f 597 1 Theoretical proof Relation between fracture energy and ligament height The different fracture toughness of various part of concrete is caused by large amount of discontinuous pores and micro cracks widely and randomly dispersed, as well as heterogeneity of internal structure of the material. Stress intensity factors of different parts also vary even under the same applied force. The part with lower fracture toughness or higher stress intensity factor always begins to crack first. Therefore, micro cracks caused by external force are also discontinuous and randomly distributed. Like the main macro crack, micro cracks are extremely tortuous and branching. Such a complex and irregular micro crack system can be simulated with a fractal model. Suppose the micro crack dispersion in micro crack zone is a dendritic structure as shown in Fig. la, and assume the length of each broken line segment of the generator (Fig.