Fractal characteristics of rock fragmentation at strain rate of 10⁰ – 10² s⁻¹

Abstract

The fragmentation test of granite subjected to strain rate of 10⁰ – 10² s⁻¹ was carried out using split Hopkinson pressure bar(SHPB) whose diameter is 75 mm, where half-sine loading waveform was performed. The sieving statistics results of the fragments show that the distribution of the fragments is a fractal, and the fractal dimension values fall into the range of 1.2–2.4. The correlation analysis between the fractal dimension and the logarithm of the energy density shows that they have approximately linear relation. Finally, based on damage theory and scale invariant principle, the fragmentation model with renormalization method was put forward, and the fractal dimension value predicted with the model was compared with the test results. It is found that the fractal dimension value obtained from the improved fragmentation model is more reasonable.

Keywords

SHPB test / rock fragmentation / fractal / damage / renormalization

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