ABSTRACT
The classical applications of Weibull statistical theory of size effect in quasi-brittle structures such as reinforced concrete structures are reexamined in the light of recent test results. The classical Weibull-type approach ignores the stress redistributions and energy release during the stable large fracture growth before failure, which causes a strong deterministic size effect. Furthermore, the classical theory does not agree with recent test data. Therefore, the failure probability of structures must be calculated from the stress field that exists just before failure, rather than the initial elastic field. Accordingly, fracture mechanics stress solutions are utilized to obtain the failure probabilities and formulate an amalgamated theory that combines the size effect due to fracture energy release with the size effect due to random variability of strength having Weibull distribution. For the singular stress field of linear elastic fracture mechanics, the failure probability integral diverges. Convergent solutions, however, can be obtained with the nonlocal continuum concept. This leads to nonlocal statistical theory of size effect. According to this theory, the asymptotic size effect law for very small structure sizes agrees with the classical power law based on Weibull theory, while the asymptotic size effect law for very large structure sizes coincides with that of linear elastic fracture mechanics of bodies with similar large cracks. For very large structures, the failure probability is dominated by the stress field in the fracture process zone, 2 while the stresses in the rest of the structure are almost irrelevant. The size effect predictions agree reasonably well with the existing test data. The failure probability can be approximately calculated by applying the failure probability integral to spatially averaged stresses obtained, according to the nonlocal continuum concept, from the singular stress field of linear elastic fracture mechanics. More realistic is the use of the stress field obtained by nonlinear finite element analysis according to the nonlocal damage concept.
