Zero-brittleness size-effect method for one-size fracture test of concrete

Zdeněk P. Bažant*, Zhengzhi Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


This paper proposes a new and less laborious version of the size-effect method for measuring the fracture energy or fracture toughness of concrete as well as other nonlinear fracture characteristics, such as the effective length of fracture process zone or critical crack-tip opening displacement. The size-effect method, based on the size-effect law, is the simplest to carry out because only the maximum loads of specimens need to be measured. No measurements of postpeak deflection and unloading stiffness, nor observations of crack-tip location, are needed; the testing machine need not be very stiff, and there is no need for closed-loop displacement control. The simplicity of the method makes it suitable not only for the laboratory but also for field quality control. In the original version of the size-effect method, notched specimens of different sizes are tested. The proposed new version further simplifies testing by allowing the use of notched specimens of only one size. The idea is to supplement the one-size notched-beam tests with an evaluation of the maximum load value for specimens with a zero-brittleness number. There are two types of methods that will achieve this. In one type of method, zero-brittleness data are obtained by using plastic limit analysis based on the modulus of rupture or compression strength of concrete to calculate the limiting nominal strength for zero specimen size. In the second type of method, zero-brittleness data are obtained by testing the maximum loads of notchless specimens of the same size. The fȯrmer type leads to simpler calculations but has the drawback that the material strength to calculate the maximum load for zero size depends on specimen geometry. Both types of the zero-brittleness version of the size-effect method are validated by previously reported test data. The proposed method should also be applicable to other quasibrittle materials such as rock, ice, tough ceramics, and brittle composites.

Original languageEnglish (US)
Pages (from-to)458-468
Number of pages11
JournalJournal of Engineering Mechanics
Issue number5
StatePublished - May 1996

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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