As already explained in Chapters 1 to 3, there are two basic types of quasibrittle failure and size effect, types 1 and 2. They have different large-size asymptotes of the size effect and different statistical contributions of material randomness. Type 1 (Bažant & Li 1995b; Bažant 1997; Bažant & Novák 2000a, 2000b; Bažant 2005) occurs when the maximum load is attained already at macrocrack initiation, and type 2 (Bažant 1984a; Bažant & Pfeiffer 1987; Bažant & Kazemi 1990a, 1990b; Bažant 2005) occurs when, at maximum load, there is a large notch or a large stress-free (or fatigued) crack (note that in Bažant 2005 Type 1 is called Case 2, and Type 2 Case 1).

If the structure is much larger than the size of the representative volume element (RVE) or, equivalently, the size of the fracture process zone (FPZ), type 1 exhibits a large statistical effect of material randomness on the mean of structural strength, particularly on its coefficient of variation (CoV), while at small sizes the type 1 size effect is essentially deterministic. By contrast, the type 2 size effect on the mean structural strength is essentially deterministic at all sizes, owing to energy release and the associated stress redistribution, while the material randomness affects only the CoV of structural strength.

Progress in the modeling of concrete fracture and introduction of fracture concepts into the design codes and practice has been impeded by the unavailability of a comprehensive database for fracture. The literature features a vast amount of fracture data (e.g., Sabnis & Mirza 1979; Petersson 1981; Nallathambi 1986; Bažant & Pfeiffer 1987; Malvar & Warren 1988; Carpinteri, Chiaia, & Ferro 1995a; Rocco 1995; Tang, Bažant, Yang, & Zollinger 1996; Bažant & Planas 1998; Becq-Giraudon 2000; Bažant & Becq- Giraudon 2002; Karihaloo, Abdalla, & Xiao 2003, Hoover et al. 2013). But all these data except the last cover only rather limited ranges of specimen size, initial notch depth, and post-peak response, and have been performed on different concretes, on different batches of supposedly the same concrete, at different ages, at different environmental conditions, at different rates, with different test procedures, and on specimens of different types and dimensions.