Fractal Characteristics of Concrete Fragmentation under Impact Loading

Abstract

This paper aims to investigate the fractal characteristics of concrete fragments produced by impact fragmentation. The dynamic compressive tests for concretes with different static strengths were conducted by split Hopkinson pressure bar apparatus under various strain rates. The results indicate that the fragments size distribution of concrete after impact fragmentation can be statistically regarded as a fractal. The corresponding fractal dimension, as calculated by mass-size relationship, is an ideal indicator to describe the fragmentation degree. Under impact loading, the fractal dimension of impact fragmentation increases with strain rate. For a given loading rate, concrete with a higher static strength is less fragmented and has a smaller fractal dimension. In a word, the more serious the fragmentation is, the larger the fractal dimension obtained. The variation of fractal dimension essentially depends on the development of cracks inside and the compactness of concrete. Moreover, the dynamic compressive strength and impact toughness of concrete demonstrate an increasing trend with fractal dimension of impact fragmentation. Under a given fractal dimension, concrete with a higher static strength exhibits larger dynamic compressive strength and impact toughness. A modified renormalization group model can be used to describe the fractal behavior of impact fragmentation of concrete by taking the strain rate effect into account. To get closer to the real fragmentation process, this model can be further modified by assuming that the subelements produced each time have different sizes. In addition, based on mercury intrusion porosimetry tests, it is found that the pore structure of concrete also possesses obvious fractal characteristics. Concrete with lower porosity and finer pore structure exhibits a larger pore fractal dimension.