Quantification of crack prediction models in reinforced concrete under flexural loading

To date, serviceability limit states (SLS) such as concrete cracking have been treated nominally by structural design standards, without the pertinent estimation of target reliability on the basis of life cycle cost optimization that is applied to the ultimate limit state, see Rackwitz. In structures such as concrete liquid retaining structures (LRS) where serviceability cracking in concrete is the governing design limit state together with more onerous conditions than general structures, this nominal treatment is not necessarily appropriate. In addition, serviceability limit states (SLS) are becoming more important in the design of structures generally, therefore require more attention. A full probabilistic approach is therefore warranted in assessing serviceability cracking in reinforced concrete structures in developing a safe but economical design formulation for crack width control. Uncertainty exists in crack models due to the inherent randomness of cracking mechanisms that cannot be taken into account in the stochastic parameters of the random variables of the probabilistic model. Cracking in concrete has a high degree of randomness which has led to much debate over the cracking mechanisms, and over the resulting models developed to describe this cracking behavior. Various researchers have reported on and compared numerous crack formulations which included design code formulations and improvements. For example, Borosnyόi and Balázs commented on over 40 proposed flexural crack widths models, while Lapi et al. compared 30 flexural crack models, illustrating the extent of the debate. This is also indicative of a significant level of model uncertainty in crack models. Proper assessment of model uncertainty was identified by sources such as Retief as a key issue in structural reliability as this influences the level of treatment of model uncertainty in probabilistic analyses. In quantifying model uncertainty for load-induced crack models, the degree of uncertainty and its associated level of treatment can be determined. Model uncertainty was identified as a significant influence in a reliability analysis of the EN 1992 crack model by McLeod. However, it was found that there is little data on the statistical parameters of model uncertainty needed for probabilistic analysis. This paper reports on efforts to quantify model uncertainty of flexural load-induced crack width prediction models, of both shortand long-term duration, in reinforced concrete, as the first step in performing the probabilistic analysis. Model uncertainty is specific to the model concerned, therefore suitable load-induced crack models are investigated, applicable to structures where serviceability cracking governs the design, such as concrete liquid retaining structures (LRS). The South African industry has historically utilized the now withdrawn British standard BS 8007, and is currently updating the standard SANS 10100-1 on the design of reinforced concrete structures by adopting the corresponding Eurocode, concurrently with the development Discussion on this paper must be submitted within two months of the print publication. The discussion will then be published in print, along with the authors' closure, if any, approximately nine months after the print publication. Received: 25 January 2019 Revised: 9 June 2019 Accepted: 18 July 2019