# Study of the Relationship between Mode I Fracture Toughness and Rock Brittleness Indices
## 4 Discussion
Moreover, the notch-length-to-radius ratio was found to greatly affect KIC for SCB, CSTBD and SECRBB test methods [57; 73; 74]. The variations in notch type between test methods affected the crack propagation and fracturing mechanics of samples. In general, sample geometries with straight notches are characterized by the  
Figure 15: KIC – rock brittleness (B9) relationships considering only CB test method. unstable crack propagation, such as in SCB samples, unlike chevron-notched specimens [33]. This may be due to the larger FPZ associated with straight notches as reported in [75] for SCB and Cracked Chevron Notched Semi-Circular Bend test methods. In fact, sample size, particularly ligament length (i.e., area above the notch), should be large enough such that the FPZ size formed under loading has an insignificant effect on the fracturing mechanism and in turn on the obtained K\({}_{\text{IC}}\) value [74; 76]. Moreover, FPZ size varied between different rocks for the same test method, due to the variation in petrological properties, e.g., grain size heterogeneity and micro-crack-induced anisotropy [77; 78]. Hence, we concluded that the inconsistencies in the values of rock strength properties and the different K\({}_{\text{IC}}\) test methods could explain the weaker correlations between K\({}_{\text{IC}}\) and strength-based rock brittleness indices B3, B4 and B9 reported in this paper compared to the relationships reported in the literature. On the other hand, the K\({}_{\text{IC}}\)--index B10 relationship (Equation (16) in Table 3) showed an overall closer trend to Equation (19) in Table 5. Equation (16) overestimated K\({}_{\text{IC}}\) at values lower than nearly 15 at B10, compared to Equation (19), and underestimated K\({}_{\text{IC}}\) at values above 15 (see Figure 16). These differences were lower than those observed in Figures 11 and 12 for indices B4 and B9, respectively. It should be noted that Equations (16) and (19) were proposed using two distinct datasets. Equation (19) was proposed using K\({}_{\text{IC}}\) data obtained mostly from the CB test [24], unlike this paper. This suggested that K\({}_{\text{IC}}\)--index B10 relationships were not greatly influenced by the K\({}_{\text{IC}}\) test method. However, K\({}_{\text{IC}}\)--index B10 relationships, considering only CB data from Table 1, were more significant (see Figure 17). Moreover, less stiff rocks, i.e., rocks having lower Young's modulus values, were considered in this paper compared to those in [24] (see the skewness of Young's modulus in Table 6). Nonetheless, a significant correlation between K\({}_{\text{IC}}\) and index B10 was reported in this paper. For rocks that exhibit significant plastic deformation before fracturing (i.e., soft rocks), it was believed that both ultimate strength and elastic parameters must be considered in the rock brittleness index. In fact, the effect of Young's modulus on the brittleness of such rocks was found to be more critical than \(\sigma_{\text{c}}\)[24]. Figure 16: Comparison between the deduced K\({}_{\text{IC}}\)–rock brittleness index B10 relationships, i.e., Equation (16) in Table 3, and relationship from [24], i.e., Equation (19) in Table 5.  
For the elastic-based indices, i.e., B5, B6, B7 and B8 in Table 2, there were weak correlations with KIC in contrast to the strength-based indices. The reason may be that the elastic-based brittleness indices were proposed for softer rocks, such as shale [43]. Although this paper considered more soft rock types, stiff rocks were also considered (see the skewness of [PERSON]'s modulus in Table 6). Another possible reason may be the elastic parameters' calculation technique. Strength parameters are determined experimentally, when samples fail. Typical stress strain curves have four regions before failure, i.e., macro-cracking; 1--crack closure, 2--elastic, 3--micro-cracks initiation and 4--unstable crack propagation that ends with failure [9; 79].