Approximate linear analysis of concrete fracture by R-curves

Zdeněk P. Bažant, Luigi Cedolin

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Using linear elastic fracture analysis, the energy consumed per unit length of fracture (fracture energy) varies with the crack length, as described by the resistance curve (R-curve). This concept, originally proposed for metals, is developed here into a practical, applicable form for concrete. The energy release rate is determined by an approximate linear elastic fracture analysis based on a certain equivalent crack length, which differs from the actual crack length, and is solved as part of structural analysis. It is shown that such an analysis, coupled with the R-curve concept, allows achieving satisfactory fits of the presently existing fracture data obtained with three-point and four-point bent specimens. Without the R-curve, the use of an equivalent crack length in linear analysis is not sufficient to achieve a satisfactory agreement with these data. The existing data can be described equally well with various formulas for the R-curve, and the material parameters in the formula can vary over a relatively broad range without impairing the representation of test data. Only the overall slope of the R-curve, the initial value, and the final value are important. A parabola seems to be the most convenient shape of R-curve because the failure load may then be solved from a quadratic equation. For the general case, a simple algorithm to calculate the failure load is given. Deviations from test data are analyzed statistically, and an approximate relationship of the length parameter of the R-curve to the maximum aggregate size is found.

Original languageEnglish (US)
Pages (from-to)1336-1355
Number of pages20
JournalJournal of Structural Engineering (United States)
Issue number6
StatePublished - Jun 1984

ASJC Scopus subject areas

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


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