A statistical approach to scaling size effect on strength of concrete incorporating spatial distribution of flaws

Abstract

The spatial distribution of flaws in a solid has a direct impact on the cumulative probability of failure due to brittle fracture. Accordingly, two composite parameters incorporating the cumulative probability of failure and the volume of fracture process zone are identified and adopted to characterize the size effect on the strength of concrete. Instead of being pre-assumed a specific function, the cumulative distribution function of fracture strength, namely the cumulative probability of fracture, is inferred for either the Poisson or the uniform spatial distributions of flaws from the synchronized analysis of multiple strength data sets measured from different sized specimens of geometrical similarity under a same loading mode (proportional scaling). This approach is validated for the case of proportional scaling by evaluating three representative sets of published strength data of concrete from uniaxial tension, uniaxial and equibiaxial flexure tests. Depending on the specific specimen size, the spatial flaw distribution may follow either the Poisson postulates or the uniform law, while the strength distribution of concrete does not necessarily always follow the Weibull statistics.