# Study of the Relationship between Mode I Fracture Toughness and Rock Brittleness Indices
## 1 Introduction
For CB and SR methods, tests can be carried out while recording only maximum load, i.e., level I, or while recording the load and displacement, i.e., level II, to account for rock non-linearity [11]. Tests for K\({}_{\text{IC}}\) determination are sometimes demanding because of the absence of suitable samples in terms of number and size, challenging sample preparation procedures as well as complicated, expensive and time-consuming testing procedures. Hence, K\({}_{\text{IC}}\) prediction, in terms of rock properties, can substitute testing when needed [7; 14; 15]. Many researchers have suggested empirical formulas for the K\({}_{\text{IC}}\) estimation, in terms of rock properties such as Tensile Strength (TS) [9; 16], Uniaxial Compressive Strength (UCS) [14; 17], point Load Strength [18], Young's modulus [17; 19], Poisson's ratio [17], P-wave velocity [14; 17; 20], S-wave velocity, density [14; 17; 21], porosity [17] and permeability [6]. Moreover, researchers have investigated the correlation between K\({}_{\text{IC}}\) and rock brittleness [22; 23; 24]. Rock brittleness can be defined as \"Failure by fracture at or only slightly beyond the yield stress\" [22] or \"it is a property of materials that rupture or fracture with little or no plastic flow\" [23]. Rock brittleness plays an important role in assessing the performance of several rock engineering applications. A rock brittleness index (i.e., the ratio of UCS to TS) was utilized at Sanshandao gold mine, in China, as an empirical indicator of rock burst possibility where a strong burst tendency was reported [25]. Moreover, this index was used to assess rock burst for 102 case studies from fourteen hard rock mines located in Italy, Russia and China [26]. However, it was recommended that this index cannot be solely used in rock burst tendency prediction, because it considered only the rock's strength properties and it had low prediction accuracy [26; 27]. The effect of ornamental stones' brittleness on the production rate of circular sawing machines for seventeen different Iranian granitic and carbonate stones was investigated in [28]. The stones' brittleness was assessed using three different strength-based indices in terms of UCS and TS. Although good correlations were found between the three indices and the production rate, it was concluded that the brittleness index (represented as 0.5\"UCS*TS) was the best index to predict the production rate. Because, unlike the other indices, this brittleness index showed good correlation with the production rates of the combined data for granitic and carbonate ornamental stones, it can be used to predict the production rates for all types of Iranian ornamental stones [28]. The correlation between rock brittleness indices and the penetration rate of four different types of drilling operations, i.e., Tunnel Boring Machine (TBM), diamond, percussive and rotary, was investigated using literature data in [29]. Varying correlation significances were reported that depended on the used index and drilling methods. So, it was concluded that assessing the performance of rock excavation operations using a rock brittleness index depended on the practical application, e.g., brittleness index, that considered that impact strength parameters may be more suitable for the prediction of percussive drilling penetration rate [29]. Similarly, the effect of rock brittleness on the penetration rate for percussive, rotary and Down The Hole (DTM) drilling operations was investigated using literature data for different types of rocks having varying strength in [30]. Using multiple regression, three equations were proposed, one for each drilling type, to predict the penetration rate using three strength-based brittleness indices [30]. KIC test methods assumed that rock fractures followed LEFM principles, which applied only to brittle fracturing that has a very small Fracture Process Zone (FPZ) at the fracture tip. Rocks generally exhibit quasi-brittle fracturing (a general type of brittle fractures), which has a significant FPZ [31,32].