Investigation of the Relationship Between Rock Brittleness and Brittle Fragmentation
Authors: Khadivi Babak , Heidarpour Amin , Masoumi Hossein 
Published: September 2022

ABSTRACT:
Fragmentation characteristics can provide a good basis for identifying the brittleness level and failure mode in rock materials. Investigating the rock fragmentation is important in many rock mechanics applications such as evaluating the blasting efficiency, wear of cutting tools in mechanized excavation, mineral processing recovery, and rock bursting intensity. Fragments generated from rock failure and through each rock mechanics application are different in size and morphology. The purpose of this research is to find the relationship between fragmentation characteristics and brittleness under static compressive loading. Thus, the fragmentation features including size, mass and shape for Gosford sandstone and granite were analyzed. The fractal dimensions were calculated through the mass-size statistical distribution and then compared with the brittleness levels obtained from various methods. It was found that the rock types with different brittleness values possess different fragmentation properties. The highest quantity of fragments generated from granite owing to its higher level of brittleness. An inverse relationship was found between the fractal dimension and brittleness index that can be used as an effective approach in understanding of rock failure mechanisms.

1. INTRODUCTION
Evaluation of fragmentation process is important in many disciplines to better understand the behaviour of materials under complex loading states (Perfect, 1997). Fractals are hierarchical geometric systems generated through iterative algorithms with simple scaling rules (Mandelbrot, 1982, Feder, 1988). The fractal theory is widely used in rock mechanics for understanding of fragments characteristics. Xie et al. (2011) deployed the fractal concept and proposed a model to analyze the fractal properties of the spatial distribution of acoustic emission (AE) during the damage and failure of salt rock under uniaxial compressive and indirect tensile loadings. Xie and Gao (2000) developed a general statistical formula for rock strength under complex stress state based on the fractal distribution of cracks and theory of the weakest link. The influence of cracks orientation distribution and irregularity of crack growth on rock strength was considered in their approach (Xie and Gao, 2000). Babadagli and Develi (2003) studied the fractal properties of rock fracture surface generated under tension for different rock types, declaring that relationships exist amongst fractal dimension, loading rate, grain size and porosity. Lai and Wang (2015) conducted a study to delineate the pore network characteristics in sandstone and concluded that the fractal theory is an effective method to quantify the complex and irregular pore structure of rocks. Peng et al. (2015) studied the behavior of coal under conventional triaxial loading to identify the relationship between energy transmission and coal failure. Peng et al. (2015) developed a fractal model for describing the size distribution of coal fragments as well as a damage evolution model for determining the initial and critical damage variables. Zhang et al. (2000) performed measurements on the fracture surface of gabbro and concluded that the fractal dimensions of fracture surfaces increase with a rise in the loading rate. Several studies have been conducted to understand the relationships between fracability and brittleness (Jin et al., 2014, Rybacki et al., 2016, Guo et al., 2015, Yang et al., 2021). Although, large number of brittleness indices (BI) was proposed based on different approaches (Altindag, 2002, Munoz et al., 2016b, Munoz et al., 2016a, Zhang et al., 2016), lack of universal agreement between scholars for both definition and measurement principle, makes the correct evaluation of brittleness very challenging (Khadivi Boroujeni et al., 2021). In this study, a research was carried out on the fragmentation characteristics and their relationships with various brittleness approaches for Gosford sandstone (Roshan et al., 2016) and granite under uniaxial compressive loading. Results revealed that the fragmentation characteristics can be used as an effective indicator to describe the level of brittleness in rock materials. Moreover, the deployment of brittleness and fractal dimension were found to be effective at micro and macro scale levels in understanding of rocks fracture behaviour and failure mechanisms.