Abstract
A simple design model, able to link test results of small concrete samples to failures of large structures, is desirable for fracture analysis of concrete structures, particularly if the model has no special requirements on small samples, e.g., size, notched or un-notched. The linear Boundary Effect Model (BEM, which has evolved over the past 20 years, is able to provide the link between small samples and large structures with fairly reliable predictions and a built-in function of statistical analysis. BEM enables researchers and engineers to model the quasi-brittle fracture behavior of concrete and the associated size effects by focusing on the fracture process zone (FPZ) at the notch tip or at the specimen boundary (for an un-notched case). FPZ and quasi-brittle fracture of concrete are directly influenced by the average aggregate size (dav), but few models mathematically show such critical aggregate influence, except BEM. The aggregate size used in BEM can be accurately estimated separately before fracture experiments. A comprehensive dataset of concrete fracture results from the existing literature, along with a new experimental dataset from three-point bending (3-P-B) tests, involving 138 specimens with varying notch depths (un-notched, 1 mm shallow-notched, and 6 mm deep-notched) was analyzed. The specimens, which present inconsistent dimensions (160 mm span, approximately 40 mm thickness, and 38 mm width/height), were used to estimate FPZ at peak fracture loads and investigate their interactions with structural boundaries. Statistical analyses were integrated into BEM, allowing the model to account for the experimental scatter, thus improving its reliability as a predictive tool for maximum fracture loads of concrete structures. This study confirmed again that the linear BEM is easy to use and provides fairly accurate predictions across concrete specimens and structures of various sizes.