Quantifying Variability in Assessing the Risk of Early-Age Cracking in Restrained Concrete Elements

Civil Engineers frequently perform calculations based on material properties that represent either the 'worst case' or the 'average' properties. While these approaches are extremely helpful in simplifying computations, they can fail to quantify how variability from different sources combines to influence the overall performance of the system. This paper describes two approaches to quantify the variation in residual stress development and the risk of cracking in concrete. First, the paper illustrates the use of a Monte Carlo simulation procedure to quantify the residual stresses and age of cracking for a restrained concrete element due to variability in material properties, environmental conditions, and construction procedures. Second, the paper illustrates how statistical analysis can be directly applied to the problem using an approach that is similar to that used in the design of steel structures (a Load and Resistance Factor Design approach).This paper begins with a short review of a model that computes residual stress development in a restrained concrete element. The paper then describes a Monte Carlo modeling approach that was added to the model to account for variability in materials, construction practices, and environmental conditions. The results show that even low variability in material inputs results in substantial scatter in the predicted time of cracking.An alternative approach to predict the time of cracking is then presented that is similar to the one used for the design of steel structures (Load and Resistance Factor Design - LRFD). The LRFD approach enables the computation of a reliability index β which can quantify a material's potential for cracking. The results indicate that, as one may expect, as the magnitude of shrinkage coefficient increases, the potential for failure increases. Results also show that when the free shrinkage is reduced to a sufficient level, cracking will no longer be observed. The LRFD method enables the level of shrinkage to be quantified and this can then be used in the development of mixture proportioning procedures for mixtures containing shrinkage reducing admixtures (SRA).