# Study of the Relationship between Mode I Fracture Toughness and Rock Brittleness Indices
## 1 Introduction
FPZ size is controlled by several factors such as rock petrological properties, specimen geometries, test method and loading conditions [31,33]. Accordingly, the obtained KIC values from tests may not represent the true KIC. For Mancos shale (from the USA), the LEFM assumption was invalid due to its inelastic behavior, so level II testing was carried out to estimate a fracture toughness correction factor. A significant inelasticity was reported such that the fracture toughness correction factor varied from 1.49 to 1.83 [34]. The Mode I failure mechanism of five rock types was investigated in [35]. It was concluded that KIC measurement was more accurate for brittle rocks compared to soft rocks; therefore, two KIC--tensile strength formulas were proposed corresponding to brittle and inelastic behaviors, because a significantly large FPZ, compared to the sample size, could result in failure due to loss of strength rather than fracture propagation [36,37]. A size effect law was suggested to quantitatively represent the FPZ effect on the failure mechanism of samples, in order to obtain the true size-dependent KIC [38]. The size law effect was applied to different geo-materials in [36,39,40]. Moreover, the effect of samples' size on the fracturing behavior of concrete was investigated in [41]. Rock brittleness can assess how brittle rock fractures would be and hence how applicable the LEFM assumption would be. Many researchers have suggested various brittleness indices for different rock engineering applications. Rock brittleness indices can be classified based on the parameters used in their estimation such as strength parameters, stress-strain curve parameters, elastic parameters, mineralogy and indentation characteristics [42,43]. Moreover, various formulas of a non-dimensional parameter called \"brittleness number\" were suggested in [36,37,44]. These formulas described the brittleness behavior of geo-materials quantitatively taking into account either the sample size or the FPZ size. The brittleness number suggested in [36] was independent of the sample geometrical shape unlike [PERSON]'s brittleness number proposed in [44] that was suggested for a notched beam sample under three-point bending (i.e., non-core test method) [36]. These brittleness numbers were not considered in this paper, because only core test methods were considered, and sample dimensions and peak loads were not available. Furthermore, there were not enough data available for each rock considering each test method to estimate the brittleness number suggested in [36]. In the literature, a few studies have focused on the relationship between KIC and rock brittleness indices. The correlations between KIC and two strength-based indices were investigated using two separate literature datasets [22]. In these datasets, KIC results were obtained from two different test methods, i.e., CB and SR. Significant relationships between KIC and a brittleness index represented as (0.5*UCS*TS) were reported [22]. The relationships between KIC and three strength-based rock brittleness indices were studied in [23] using the same literature data used in [22]. There were good correlations between KIC and only one brittleness index represented as (\(\surd\) (0.5*UCS*TS)); however, more investigationswere recommended to obtain a general relationship for other rock types. It should be noted that, in [22; 23], the literature datasets were analyzed separately, and thus the effect of the K\({}_{\text{IC}}\) test method on the K\({}_{\text{IC}}\)-rock brittleness relationship was considered explicitly. Moreover, the correlations between K\({}_{\text{IC}}\) and four strength-based indices were investigated in [24]. Three of these strength-based indices were the same as those investigated previously in [22; 23]. Similar to [22; 23], literature data were used to investigate the correlations, although this was a different dataset with most of the K\({}_{\text{IC}}\) data obtained from the CB test [24].