# ENERGETIC-STATISTICAL SIZE EFFECT IN QUASIBRITTLE FAILURE AT CRACK INITIATION

The size effect on the nominal strength of quasibrittle structures failing at crack initiation, and particularly on the modulus of rupture of plain concrete beams, is analyzed. First, an improved deterministic formula is derived from the energy release caused by a boundary layer of cracking (initiating fracture process zone) whose thickness is not negligible compared with beam depth. To fit the test data, a rapidly converging iterative nonlinear optimization algorithm is developed. The formula is shown to give an excellent agreement with the existing test data on the size effect on the modulus of rupture of plain concrete beams. The data range, however, is much too limited; it does not cover the extreme sizes encountered in arch dams, foundations, and retaining walls. Therefore, it becomes necessary to extrapolate on the basis of a theory. For extreme sizes, the Weibull type statistical effect of random material strength must be incorporated into the theory. Based on structural analysis with the recently developed statistical nonlocal model, a generalized energetic-statistical size effect formula is developed. The formula represents asymptotic matching between the deterministic-energetic formula, which is approached for small sizes, and the power law size effect of the classical Weibull theory, which is approached for large sizes. In the limit of infinite Weibull modulus, the deterministic-energetic formula is recovered. Data fitting with the new formula reveals that, for concrete and mortar, the Weibull modulus is approximately equal to 24 rather than 12, the value widely accepted so far. This means that, for extreme sizes, the nominal strength (modulus of rupture) decreases, for two-dimensional (2D) similarity, as the -1/12 power of the structure size, and for 3D similarity, as the -1/8 power (whereas the -1/4 power has been assumed thus far). The coefficient of variation characterizing the scatter of many test results for one shape and one size is shown not to give the correct value of Weibull modulus because the energetic size effect inevitably intervenes. The results imply that the size effect at fracture initiation must have been a significant contributing factor in many disasters (for example, those of Malpasset Dam, Saint Francis Dam and Schoharie Creek Bridge.)

• Availability:
• Supplemental Notes:
• Partial funding was received from the U.S. National Science Foundation under Grant N00014-91-J-1109. The visiting scholar appointment of the second author at Northwestern University was initially supported under NSF Grant INT-9531299; his research was funded under Grant 103/97/K003 from the Grant Agency of Czech Republic and Project CEZ:J22/98:261100007 from the Ministry of Education of Czech Republic.
• Corporate Authors:
38800 Country Club Drive
Farmington Hills, MI  United States  48331
• Authors:
• Bazant, Z P
• Novak, Doris
• Publication Date: 2000-5

• English

## Filing Info

• Accession Number: 00795755
• Record Type: Publication
• Contract Numbers: NSF/GER-9023496-02, CMS-9632407, NSC 84-2211-E-009-14
• Files: TRIS
• Created Date: Jul 27 2000 12:00AM