Fracture energy-based model for average crack spacing of reinforced concrete considering size effect and concrete strength variation

- The crack spacing of RC members is analyzed using the fracture energy criterion.
- The influence of compressive strength on crack spacing is first explained.
- The size effect of the crack spacing is first examined for RC members.
- A simple formula for crack spacing is proposed with a reasonable level of accuracy.

The average crack spacing is a key parameter for an accurate evaluation of the crack width of reinforced concrete (RC) members. According to the test results in the existing literature, both the variations of the concrete strength and the size effect are critical factors influencing the average crack spacing. However, available prediction models for the average crack spacing cannot give satisfactory results in simulating both factors. Based on the finite-element (FE) analysis and the fracture-energy criterion, a theoretical method considering the influence of concrete strength variation and size effect is first proposed. It is assumed that a micro-crack will grow into a visible crack if and only if the energy release exceeds the fracture energy of the effective cracking area. Therefore, the average crack spacing can be predicted by equating the energy release, which is obtained by the three-dimensional FE model of concrete subjected to bond stress, to the fracture energy of the effective cracking area. In addition, from the proposed model, the characteristic length of concrete is found to be the most important material parameter for average crack spacing of RC members. Subsequently, a database including 136 test specimens is established to sufficiently validate the proposed model. The influence of various key factors on the average crack spacing is discussed in detail. Finally, simplified prediction formulas for average crack spacing of RC members are proposed considering both concrete strength variation and size effect. Comparisons indicate that both the proposed theoretical model and the simplified formulas have sufficient accuracy.