A hybrid deterministic-probabilistic approach for the characteristic crack widths and crack spacings in reinforced concrete tension and flexural members

Abstract

Crack control is an important serviceability design criterion for reinforced concrete members. In this paper a new model is proposed that directly incorporates the deterministic and probabilistic aspects of cracking behaviour. The approach defines the minimum crack spacing and the relationship between crack-spacing and crack-width as a function of the bond between the reinforcement and the concrete using partial-interaction mechanics. This deterministic model is then used as a basis for a probabilistic analysis to identify mean crack-spacing and crack-width allowing for uncertainty in the deterministic model. The fitted variables are estimated using a Bayesian approach drawing upon 463 observations of crack-spacing and 3409 observations of crack-width. Using the hybrid deterministic-probabilistic model the importance of spatial variability of material properties is identified and simulated. The probability distributions for the mean crack spacing and the distribution of cracks are then combined to give parsimonious expressions for the characteristic crack-spacing according to a specified probability of exceedance. The same approach is then applied to determine the characteristic crack-width.