Abstract
In structural engineering, it is necessary to design structures with incomplete knowledge of the creep and shrinkage characteristics of the concrete to be used. Therefore, prediction based on concrete strength and composition is required. After summarizing the criteria for a sound prediction model, we discuss in detail the theoretical justification of model B3, including the thermodynamic restrictions, reasons for using power functions, consequences of microprestress relaxation and of activation energy, problems of characterizing aging by strength gain, consequences of diffusion of pore water for size and shape effects on shrinkage and drying creep and their asymptotics, and separation of cracking effects. Then, we focus on unbiased fitting of the existing worldwide database, which is characterized by limited range and complicated by variable data density. We present a statistical evaluation of models B3 and B4 and their statistical comparisons to other prediction models, and we describe the procedure that was used for calibration of the constitutive parameters by fitting a combined database of several thousand laboratory curves of limited time range and of about seventy histories of excessive multidecade deflections of large-span prestressed bridges. Finally, we briefly mention analytical methods for prediction of creep and shrinkage via homogenization.
Notes
- 1.
This conclusion is reinforced by a comparison with rocks, which all creep on the geologic scale. All the creep of concrete treated in this book is the primary creep, which, after a time called the Maxwell time, always gradually transits into the secondary creep, characterized by a constant rate. The Maxwell time could be thousands of years. A nanoscale mechanism explaining why this transition is necessary for shale was proposed in [305]. It may also apply to concrete.
- 2.
The same is true for a variant of the second method, popular with concrete researchers, where the ratio \(r_k = y_k /Y_k\) is plotted versus time, for which, if the model were perfect and the tests scatter-free, one would ideally get a horizontal plot \(r_k =1\) (see Fig. 11.9a). For problems with such kind of statistics, see the comments on Eqs. (K.8)–(K.9) in Appendix K. Although the plots of residuals reduced to population statistics (Fig. 11.9a) have been popular in the literature, the plots showing the data trend, as in Fig. 11.9b, are far more informative.
- 3.
The European classification of cements is selected for model B4 since it is directly related to the reaction rate of the cement instead of the type of application, which is the basis of other classification systems. It should be noted, though, that the class labels used by B4 (RS \(=\) rapid hardening, R \(=\) normal, and SL \(=\) slow hardening) are somewhat different from the class labels used in Eurocode 2 (R \(=\) rapid hardening, N \(=\) normal, and S \(=\) slow hardening) and in CEB Model Code 1990 (RS \(=\) rapidly hardening high-strength concrete, R \(=\) rapid hardening, N \(=\) normal, and SL \(=\) slow hardening).
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Bažant, Z.P., Jirásek, M. (2018). Physical and Statistical Justifications of Models B3 and B4 and Comparisons to Other Models. In: Creep and Hygrothermal Effects in Concrete Structures. Solid Mechanics and Its Applications, vol 225. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1138-6_11
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DOI: https://doi.org/10.1007/978-94-024-1138-6_11
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