Asymptotic prediction of energetic-statistical size effect from deterministic finite-element solutions

Zdeněk P. Bažant*, Miroslav Vořechovsky, Drahomir Novák

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

80 Scopus citations


An improved form of a recently derived energetic-statistical formula for size effect on the strength of quasibrittle structures failing at crack initiation is presented and exploited to perform stochastic structural analysis without the burden of stochastic nonlinear finite-element simulations. The characteristic length for the statistical term in this formula is deduced by considering the limiting case of the energetic part of size effect for a vanishing thickness of the boundary layer of cracking. A simple elastic analysis of stress field provides the large-size asymptotic deterministic strength, and also allows evaluating the Weibull probability integral which yields the mean strength according to the purely statistical Weibull theory. A deterministic plastic limit analysis of an elastic body with a through-crack imagined to be filled by a perfectly plastic "glue" is used to obtain the small-size asymptote of size effect. Deterministic nonlinear fracture simulations of several scaled structures with commercial code ATENA (based on the crack band model) suffice to calibrate the deterministic part of size effect. On this basis, one can calibrate the energetic-statistical size effect formula, giving the mean strength for any size of geometrically scaled structures. Stochastic two-dimensional nonlinear simulations of the failure of Malpasset Dam demonstrate good agreement with the calibrated formula and the need to consider in dam design both the deterministic and statistical aspects of size effect. The mean tolerable displacement of the abutment of this arch dam is shown to have been approximately one half of the value indicated by the classical deterministic local analysis based on material strength.

Original languageEnglish (US)
Pages (from-to)153-162
Number of pages10
JournalJournal of Engineering Mechanics
Issue number2
StatePublished - Feb 2007


  • Dam safety
  • Damage
  • Dams
  • Finite element method
  • Predictions
  • Simulation
  • Size effects
  • Stochastic models

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Asymptotic prediction of energetic-statistical size effect from deterministic finite-element solutions'. Together they form a unique fingerprint.

Cite this