Comparison of boundary and size effect models based on new developments

Hoover, Bazant and colleagues have published a number of papers in recent years (Bazant and Yu, 2009; Yu, 2010; Hoover and Bazant, 2013a, 2013b, 2014) on comparisons between Bazant size effect model (SEM) and Hu-Duan boundary effect model (BEM) for quasi-brittle fracture of concrete. With the recent developments of BEM (Wang et al., 2016; Guan et al., 2016; Wang and Hu, 2017) on irregular and discrete crack growth in concrete shaped by coarse aggregate structures, it is time to clarify issues on the SEM and BEM comparison raised by Bazant and Yu (2009), Yu (2010), Hoover and Bazant (2013a, 2013b, 2014). The experimental results of Hoover and Bazant (2013a, 2013b, 2014) are analyzed again using BEM, and new findings and in-depth understandings that have not been achieved by SEM are presented in this study. BEM is one concise equation, containing only two fundamental material constants, tensile strength ft and fracture toughness KIC, applicable to both notched and un-notched concrete specimens. Most importantly, BEM explains the inevitable influence of coarse aggregate structures on quasi-brittle fracture of concrete through modeling irregular and discrete crack formations and by considering the critical role of the maximum aggregate dmax. In contrast, SEM has three different equations, one for notched, one for un-notched, and one for shallow-notch specimens, containing total 18 empirical parameters to be determined from curve fitting. Despite with the staggering 18 parameters, the three SEM equations still overlook the crucial role of coarse aggregate structures in concrete fracture; dmax and discrete crack formation are not considered. After establishing the relation between discrete fictitious crack formation Δafic and dmax at the peak load Pmax based on four different sets of independently obtained experimental results of concrete and rock with dmax from 2 to 10 and 19 mm, BEM becomes a predictive design model which only needs strength ft and toughness KIC.