Statistical prediction of fracture parameters of concrete and implications for choice of testing standard

Zdeněk P. Bažant*, Emilie Becq-Giraudon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

288 Scopus citations


This article shows how the fracture energy of concrete, as well as other fracture parameters such as the effective length of the fracture process zone, critical crack-tip opening displacement and the fracture toughness, can be approximately predicted from the standard compression strength, maximum aggregate size, water-cement ratio, and aggregate type (river or crushed). A database, consisting of 238 test data, is extracted from the literature and tabulated, and approximate mean prediction formulae calibrated by this very large data set are developed. A distinction is made between (a) the fracture energy, Gf, corresponding to the area under the initial tangent of the softening stress-separation curve of cohesive crack model, which governs the maximum loads of structures and is obtained by the size effect method (SEM) or related methods (Jenq-Shah two-parameter method and Karihaloo's effective crack model, ECM) and (b) the fracture energy, GF, corresponding to the area under the complete stress-separation curve, which governs large postpeak deflections of structures and is obtained by the work-of-fracture method (WFM) proposed for concrete by Hillerborg. The coefficients of variation of the errors in the prediction formulae compared to the test data are calculated; they are 17.8% for Gf and 29.9% for GF, the latter being 1.67 times higher than the former. Although the errors of the prediction formulae taking into account the differences among different concretes doubtless contribute significantly to the high values of these coefficients of variation, there is no reason for a bias of the statistics in favor of Gf or GF. Thus, the statistics indicate that the fracture energy based on the measurements in the maximum load region is much less uncertain than that based on the measurement of the tail of the postpeak load-deflection curve. While both Gf and GF are needed for accurate structural analysis, it follows that if the testing standard should measure, for the sake of simplicity, only one of these two fracture energies, then Gf is preferable.

Original languageEnglish (US)
Pages (from-to)529-556
Number of pages28
JournalCement and Concrete Research
Issue number4
StatePublished - Apr 2002


  • Concrete
  • Fracture
  • Fracture energy
  • Prediction
  • Randomness
  • Scatter
  • Si ze effect
  • Standards
  • Statistics
  • Testing
  • Uncertainty

ASJC Scopus subject areas

  • Building and Construction
  • Materials Science(all)


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