Scaling of energy dissipation in crushing and fragmentation: a fractal and statistical analysis based on particle size distribution

An extensive experimental investigation on concrete specimens under crushing and fragmentation over a large scale range (1:10) – exploring even very small specimen dimensions (1 cm) – was carried out to evaluate the influence of fragment size distribution on energy density dissipation and related size effect. To obtain a statistically significant fragment production as well as the total energy dissipated in a given specimen, the experimental procedure was unusually carried out up to a strain of approximately −95%, practically corresponding to the initial fragment compaction between the loading platens. The experimental fragment analysis suggests a fractal law for the distribution in particle size; this simply means that fragments derived from a given specimen appear geometrically self-similar at each observation scale. In addition, clear size effects on dissipated energy density are experimentally observed. Fractal concepts permit to quantify the correlation between fragment size distribution and size effect on dissipated energy density, the latter being governed by the total surface area of produced fragments. The experimental results agree with the proposed multi-scale interpretation satisfactorily.