Chapter 2 - Asymptotic Analysis of Size Effect

Abstract

The scaling properties for the nominal strength σN of a structure containing a notch or a stably grown large crack can be generally deduced by an asymptotic analysis of the energy release. The chapter discusses the asymptotic analysis of size effect in structures with notches or large cracks. It illustrates large-size and small-size asymptotic expansions of size effect (clashed curves) and the size effect law as their asymptotic matching, and explains the characteristics matching to the asymptotic energetic size effect law. The asymptotic analysis can be made more general by considering function of ģ or ģ to be a smooth function of θr or ήr , rather than θ or ή, where r is some constant. The derivations presented simplifies linear regressions (according to the size effect law) of the nominal strength values of notched concrete specimens measured by Bazant and Pfeiffer (1987), Bazant and Gettu (1992), and Gettu et al. Moreover, the size effect method is adopted as a standard recommendation for concrete fracture testing by RILEM.