# Study of the Relationship between Mode I Fracture Toughness and Rock Brittleness Indices
## 1 Introduction  
Rock fracture toughness is an essential property in fracture mechanics [1]. It represents the rock's resistance to fractures' propagation. Following fracture mechanics principles, structures' safety depends mainly on three factors: applied stresses, construction material's fracture toughness and material flaws' size [2]. In general, rocks are inhomogeneous, non-continuous and anisotropic, and they contain macro-scale and micro-scale flaws. Thus, studying rock fracture toughness is vital in many engineering applications, particularly where the role of natural discontinuities or generated fractures is significant. Rock fracture toughness was used to predict the power consumption of cone crushers for twelve rocks [3]. Moreover, rock fracture toughness plays an important role in the extraction of ornamental stone blocks, particularly hard stones such as granite, using Soundless Cracking Demoition Agents (SCDAs). The optimum hole spacing, in drilling patterns, was investigated in order to optimize the extraction process [4]. Compared to the empirical equations where spacing is determined in terms of hole diameter, it was concluded that additional rock properties such as Young's modulus and fracture toughness must be considered. Moreover, the fracture growth between two holes filled with SCDAs was investigated in [5]. Considering Linear Elastic Fracture Mechanics (LEFM) principles, an algorithm was suggested to estimate the first fracture length due to the increasing expansive pressure, in terms of rock fracture toughness, in [5]. The effect of thermal cycling, up to 300 \({}^{\circ}\)C and 20 cycles, on the fracture characteristics of Suzhou granite (from China) located at a potential site for an EnhancedGeothermal System (EGS) was investigated in [6]. In the EGS, a fluid is injected into a fracture network artificially formed in a low-porosity and impermeable hot dry rock, such as granite. Hence, the rock is subjected to repeated heating-cooling thermal cycles. It was found that fracture toughness decreased with the number of thermal cycles and the temperature due to thermally induced micro-damages. Similarly, the variation in fracture toughness with temperature, up to 600 \({}^{\circ}\)C, was studied for three crystalline rocks collected from Deccan Volcanic Province, Western India where there was an interest in developing geothermal energy projects [7]. A negative effect of temperature on rock fracture toughness was reported due to the development of micro-cracks as a result of the differential stresses at the grain boundaries. As the treatment temperature increased, micro-crack density increased and pre-existing cracks became wider, resulting in irreversible thermal damages and leading to an extreme reduction in stiffness [7]. Propagation modes of fractures include mode I (opening or tension), mode II (in plane shear) and mixed mode or mode III (out of plane shear) [2]. It was believed that, in practical applications, fractures propagate under the mixed mode [8]. However, mode I fracture toughness (K\({}_{\text{IC}}\)) was the most critical parameter because rocks were more vulnerable to tensile loads compared to shear loads [9]. Many K\({}_{\text{IC}}\) test methods have been suggested in the scientific literature. They are classified into non-core and core test methods. Non-core methods include three-point and four-point bending tests. These methods, unlike core test methods, need relatively large rectangular samples that cannot be usually obtained within a usual rock testing program [10]. In this paper, only core test methods are considered, because their geometry is the easiest obtainable geometry particularly at great depths. The most commonly known core test methods are those suggested by the ISRM: Chevron Bend (CB) [11], Short Rod (SR) [11], Cracked Chevron Notched Brazilian Disc (CCNBD) [12]; and Semi-Circular Bend (SCB) [13].