Reliability and scale effect in toughness of concrete structures

In the present work, the distribution of the random toughness characteristics (i.e. critical energy release rate, G_1c) has been evaluated on the basis of experimental observations. Fracture test results from three groups of geometrically similar concrete specimens of size (width×total depth×thickness), 420×420×50–1680×1680×200 mm³, made with different maximum aggregate size of 9.5, 19, 38, and 76 mm were analyzed using a recently proposed distribution of extremes. In applications of probability, it is important to use an appropriate distribution type and adequate techniques for estimating the parameters of distribution. In this study, a new type distribution of minima is employed for probability computations. It was noticed that the entropy of distribution increases with the crack length, i.e. the uncertainty of toughness, G_1c, value increases with crack length. A non-linear reduction of the maximum allowable splitting force with the defect size, a, was noticed. For large specimens, the maximum allowable splitting load is more sensitive to the required reliability level than that for small specimens. Reliability increases with aggregate size when all other conditions were constant.