Bayesian Statistical Prediction of Concrete Creep and Shrinkage

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Title: Bayesian Statistical Prediction of Concrete Creep and Shrinkage

Author(s): Zdenek P. Bazant and Jenn-Chuan Chern

Publication: Journal Proceedings

Volume: 81

Issue: 4

Appears on pages(s): 319-330

Keywords: Bayes theorem; concretes; confidence limits; creep properties; er-rors;probability theory; regression analysis; shrinkage; statistical analysis; structural analysis; structural design.

Date: 7/1/1984

Abstract:
In present design practice, the statistical approach is used for strength but not for deformations, including creep and shrinkage. However, predicting concrete creep properties from design strength and concrete composition involves a large uncertainty, much larger than that of strength. It is shown that by carrying out some short-time creep measurements, even rather limited ones, the uncertainty can be drastically reduced, and extrapolation of short-time measurements can be made much more reliable. This is accomplished by developing a Bayesian approach to creep prediction. Prior information consists of the coefficient of variation of deviations from the creep law for concrete in general, as determined in a recent statistical analysis of the numerous creep data that exist in literature. This information is combined, according to Bayes’ theorem, with the probability of a given concrete’s creep values to yield the posterior probability distribution of the creep values for any load duration and age at loading. Only a linear creep case is considered, and a normal distribution of errors is assumed for the given concrete as well as for the prior information. To demonstrate and verify the method developed, various creep data reported in literature are considered. Predictions made on the basis of only a part of the test data are compared with the rest of the data, and very good agreement is found. The effects of various amounts of measured data, and of various degrees of uncertainty in the prior information, are also illustrated. The present approach is recommended for concrete structures for which the creep deflections, creep-induced cracking, or creep buckling are of special concern, e.g., nuclear reactor vessels and containments, certain very large bridges, shells, or building frames.