Scale dependence of tensile strength of concrete specimens: a multifractal approach

The tensile strength is a parameter that is usually very difficult to determine. Nevertheless, knowledge of its effective value is of strategic importance, as materials are often used at the limit of their performance. In all tensile experiments done in the last few decades (direct tensile test, splitting test, pull-out test, double punch test) it is evident that the tensile strength varies with the dimension of the specimen. Increasing the specimen size results in a decrease in the nominal tensile strength. The authors propose a new size-effect law, the multifractal scaling law, which describes satisfactorily the relationship between the strength parameter and the structural size for disordered materials. The law considers the geometrical multifractality of the resisting section at the peak load, as a consequence of the decreasing influence of the disorder with increasing size. Extensive application of this law to various experimental results reported in the literature, and concerning direct and indirect tensile tests, is presented. A simpler version of this law is introduced and a comparison between the linear and nonlinear best-fits is discussed. (A)