ABSTRACT
Currently, two major completely opposite types of theoretical scaling laws for concrete structures exist. The first type, recently introduced by Carpinteri [4], is based on a multifractal aspects of damage - multifractality of the crack surfaces. Practically, the concept rely on the homogeneity (inhomogeneity) of the material i.e. in small concrete structure the aggregate size is large relative to the structure size and, therefore, the inhomogeneity is maximal and the size effect strong. On the contrary, in large concrete structures the aggregate size is small relative to the structure size and material is close to be perfectly homogeneous. As a consequence the size effect disappear. According to fractal damage concept, the size effect law (MFSL) is of the form [4]:
crN = ( A + ^ (1) where C T A T ^ nominal strength, d-structure size, A and C are two constants obtained by fitting of test or calculated data. As can be seen from (1), if d —• oo the nominal strength yields to a constant value different than zero (strength limit). On the contrary, when d —» 0, O~N —> co. This means that the size effect for any concrete structure is strong only in a limited size range, which may be larger or smaller, depending on the problem type. In (1) the constant C has a meaning of the characteristic structure size. For structures with d > C the size effect tends to disappear i.e. structure fail at crack initiation — brittle failure. However, for d < C, the size effect is strong and the structural response more ductile.
