Determination of concrete strength and toughness from notched 3 PB specimens of same depth but various span-depth ratios

Notched three-point-bending (3 PB) tests of small concrete samples with a fixed depth/size but various span/depth ratios can be performed in almost every laboratory. Additional usefulness is added to the flexibility of those fixed-depth 3 PB tests in this study by providing a simple closed-form solution for determination of the depth and span independent tensile strength f(t) and fracture toughness K-IC measurable from 3 PB samples with any span-depth ratio. Material constants, f(t) and K-IC, only existed asymptotically for large concrete structures are determined by the simple fracture mechanics model regardless the span-depth ratio. Recent results of notched 3 PB tests with 6 span-depth ratios (2, 2.5, 3, 4, 5 and 6) were analysed again by the closed-form model and compared with the effective fracture toughness in the previous study (without f(t)). A good agreement in K-IC values was obtained. That is the two different fracture models have affirmed the usefulness of small notched 3 PB tests of a fixed depth/size but with flexible choices of the span/depth ratio. Moreover, the weight of specimens is suggested to be considered when the span/depth ratio is greater than 4.0 for 3 PB tests. Finally, fracture statistics analysis, not considered by the previous method, was included in this study, which provided the 95% reliability band besides the mean f(t) and K-IC values.

Automated summary

This study provides a simple closed-form solution for determining the depth and span independent tensile strength and fracture toughness of small concrete samples with various span-depth ratios. It is suggested to consider specimen weight when the span-depth ratio is greater than 4.0 in 3 PB tests. The inclusion of fracture statistics analysis in the study adds reliability to the mean f(t) and K-IC values.