Size Effects Quasibrittle Fracture : Apercu of Recent Results

The paper consists of two parts. In view of length limitations, a.nd because several comprehensive reviews behind the present lecture were already published in journals, the first part is limited to listing various recent adva.nces that are surveyed in the conference lecture. The second, much longer, part then complements this survey by presenting in ma.thematical terms several new results that are only outlined in the lecture. These results concern: 1) a deriva.tion of the first two terms of the small-size a.symptotic expa.nsion of size effect of the cohesive cra.ck model; 2) a review of the deriva.tion of the first two terms of the large-size asymptotic expa.nsion of size effect ensuing from the smeared-tip method; a.nd 3) a size effect formula for a very broad size ra.nge, unifying the fracture energies measured by the size effect method a.nd the work-of-fracture method. 1. OVERVIEW OF SOME RECENT RESULTS The size effect represents the most important pra.ctical consequence of fra.cture behavior as well as the clue to uncovering various fundamental characteristics of concrete fra.cture. Interest in the quasibrittle size effect, which started in the 1970s and surged throughout the 1990s, continues unabated and will probably persist for some time because significant open questions remain and applications in design, especially in terms of revisions of design code specifications, are still deplorably limited. The conference lecture addressing this broad subject reviews some selected recent results, dealing with: • amalgamation of the deterministic (energetic) theory of quasi brittle size effect with the Wei bull probabilistic theory of brittle size effect; • derivation of small-size asymptotic properties of size effect ensuing from the cohesive cra.ck model; • size effect law for a very broad size range, explaining the difference between the fracture energies obtained by the work-of-fra.cture method (Hillerborg 19.85a,b) and the size effect method (proposed by BaZant in 1987, see Bazant and Planas 1998) or Jenq and Shah's (1985) method; • approximate statistical prediction of the fracture properties of concrete from its simple design characteristics; • size effect in redundant beam structures failing by softening inelastic hinges; and • size effect hidden in excessive dead load factor in the design codes (BaZant and Frangopol 2000). In the closing of the lecture, it is pointed out that the size effect must have played a major, yet previously unrecognized, role in a host of famous structural catastrophes (e.g., Malpasset Dam, St. Francis Dam, Schoharie Creek Bridge, Sleipner Oil Platform, Hanshin Viaduct and Cypress Viaduct). Since the aforementioned subjects have recently been reviewed in several journal articles of various foci and scopes (BaZant and Chen 1997, BaZant 1999a,b, 2000, 200la), it would be superfluous, and inevitably duplicative, to devote this paper to still another review. Therefore, the rest of this paper will focus on several new, still unpublished, results that are outlined in the conference lecture. 2. NEW RESULTS ON ASYMPTOTIC SIZE EFFECT PROPERTIES 2.1 Small-Size Asymptotics of Cohesive Crack