Recent Progress in Energetic Probablistic Scaling Laws for Quasi-Brittle Fracture

  • Zdeněk P. Bažant
  • Jia-Liang Le
Conference paper
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)


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 and Weibullian, 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.


Probabilistic mechanics extreme value statistics structural strength cohesive fracture scaling size effect 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Zdeněk P. Bažant
    • 1
  • Jia-Liang Le
  1. 1.McCormick Institute Professor and W.P. Murphy Professor of Civil Engineering and Materials ScienceNorthwestern UniversityCEE/A135 EvanstonUSA 60208

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