Statistical justification of Model B4 for drying and autogenous shrinkage of concrete and comparisons to other models

Mija H. Hubler, Roman Wendner, Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


The shrinkage prediction part of Model B4 presented in the preceding paper is here statistically justified by optimal fitting of the new NU database containing 1050 test curves and by statistical comparisons with the existing shrinkage prediction models. Rather than attempting a point-wise constitutive model for free shrinkage, Model B4 predicts the average shrinkage of cross sections of long members, which are affected by nonuniform residual stresses relaxing due to creep and microcracking. The main improvement in Model B4, which extends the 1995 Model B3 (a RILEM recommendation), is that separate formulae are given for: (1) the drying shrinkage, which represents most of the shrinkage observed in normal concretes of high water–cement ratios, and (2) for the autogenous shrinkage, which has a different physical mechanism and is important for modern high-performance concretes with admixtures, additives and low water–cement ratios. The effect of elevated temperature on the shrinkage rate is captured through an equivalent accelerated time based on activation energy. Model B4 is statistically calibrated by the new NU database of laboratory shrinkage tests through a sequential optimization procedure which isolates different physical behaviors. The new shrinkage equations are shown to match the time curves of individual shrinkage tests well, and fit the database with minimum error. Statistics of extensive comparisons with Model B3 and with the models of various engineering societies, including those of ACI and fib, document a superior fit of the new model to the database.

Original languageEnglish (US)
Pages (from-to)797-814
Number of pages18
JournalMaterials and Structures/Materiaux et Constructions
Issue number4
StatePublished - 2015


  • Calibration
  • Concrete
  • Database
  • Prediction
  • Shrinkage
  • Statistical comparisons

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Materials Science(all)
  • Mechanics of Materials


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