Problems with Hu-Duan Boundary Effect Model and Its Comparison to Size-Shape Effect Law for Quasi-Brittle Fracture

Recent disagreements on the mathematical modeling of fracture and size effect in concrete and other quasi-brittle materials are obstacles to improvements in design practice, and especially in design codes for concrete structures. In an attempt to overcome this impediment to progress, this paper compares the Hu-Duan boundary effect model BEM expounded since 2000 to the size-shape effect law SEL proposed at Northwestern University in 1984 and extended to the geometry or shape effects in 1990. It is found that within a rather limited part of the range of sizes and shapes, the fracture energy values identified by BEM and SEL from the test data on maximum loads are nearly the same. But in other parts of the range the BEM is either inferior or inapplicable. The material tensile strength values identified by BEM have a much larger error than those obtained from the SEL after calibration by the cohesive crack model. From the theoretical viewpoint, several hypotheses of BEM are shown to be unrealistic. DOI: 10.1061/ ASCE EM.1943-7889.89 CE Database subject headings: Cracking; Concrete; Structural failures; Data analysis; Size effect. Author keywords: Fracture scaling; Fracture energy; Concrete; Asymptotics of fracture; Cohesive cracks; Failure of structures; Evaluation of experimental data.