Recent progress in energetic probablistic scaling laws for quasi-brittle fracture

Zdeněk P. Bažant*, Jia Liang Le

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Rational determination of safety factors necessitates establishing the probability density function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf's of the nominal strength of structure are known to be Gaussian andWeibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. The recent results are reviewed, and then mathematically extended in two ways: (1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and (2) to a mathematical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Finally, recent experimental data are analyzed and applicability of the present theory is verified.

Original languageEnglish (US)
Title of host publicationIUTAM Symposium on Scaling in Solid Mechanics - Proceedings of the IUTAM Symposium
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9781402090325
StatePublished - 2009
EventIUTAM Symposium on Scaling in Solid Mechanics - Cardiff, United Kingdom
Duration: Jun 25 2007Jun 29 2007

Publication series

NameSolid Mechanics and its Applications
ISSN (Print)1875-3507


OtherIUTAM Symposium on Scaling in Solid Mechanics
CountryUnited Kingdom


  • Cohesive fracture
  • Extreme value statistics
  • Probabilistic mechanics
  • Scaling
  • Size effect
  • Structural strength

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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