## 2 Existing Brittleness Indices
### Log-Based Brittleness Indices (LBs)  
Well logging data are usually used to predict a number of properties of well surrounding rock masses, including brittleness. In a situation closely resembling the discussion on MBIs, LBs used in practice generally represent correlations for brittleness evaluation, rather than strict physical definitions of brittleness index. The question of scaling procedure remains actual as well, due to the difference between well logging data and results of experimental studies in laboratory conditions. A number of different correlations to evaluate brittleness index profile along the well from logging data have been proposed. As it has been mentioned, porosity is an important factor influencing brittleness. As a result, while mineralogical brittleness is not correlated well with the density porosity, it is claimed to be in good correlation with the neutron porosity, leading to emergence of a set of correlations based on neutron porosity _NPHI_[20]  
\[LBI_{1}=\alpha NPHI+\beta, \tag{2}\]  
where \(\alpha\) and \(\beta\) are two empirical parameters. Compressional wave slowness can be used as input data in similar linear correlations as well. Once again, empirical parameters are obtained from taking the results of laboratory tests into consideration. Some studies use compressional slowness log response \(DTC\) in a similar way [20]  
\[LBI_{2}=\gamma DTC+\delta, \tag{3}\]  
where \(\gamma\) and \(\delta\) are still empirical parameters. A set of methods to introduce brittleness without using laboratory tests results were proposed to overcome the need to find empirical parameters. [PERSON] et al., 2008 have suggested evaluating brittleness from normalized elastic moduli [16]  
\[LBI_{3}=\frac{E_{norm}+v_{norm}}{2}, \tag{4}\]  
where \(E_{norm}\) and \(v_{norm}\) are normalized [PERSON]'s modulus and Poisson ratio respectively  
\[E_{norm}=\frac{E-E_{\min}}{E_{\max}-E_{\min}},\ \ \ v_{norm}=\frac{v-v_{\max}}{v_{ \min}-v_{\max}}\ \, \tag{5}\]  
where \(E_{\max}\) and \(E_{\min}\) are the maximum and minimum [PERSON]'s moduli in the formation, \(v_{\max}\) and \(v_{\min}\) are maximum and minimum Poisson ratios in the formation. Equation (4) was proposed for static elastic moduli, yet we still consider brittleness index \(LBI_{2}\) a log-based, as it was obtained from initial data on dynamic elastic moduli through the correlation between static and dynamic elastic moduli. Although Equation (4) is widely used in practice for brittleness evaluation, the other LBIs have been proposed as well: [PERSON] and [PERSON], 2012 and [PERSON] et al., 2013 have incorporated rock bulk density \(\rho\) to suggest two more brittleness indices [25; 26]  
\[LBI_{4}=\rho E_{dyn},\ \ \ LBI_{5}=\rho\frac{E_{dyn}}{v_{dyn}}\ \,\ \ \ LBI_{5^{ \prime}}=\frac{E_{dyn}}{v_{dyn}}\ \, \tag{6}\]  
where absolute values of dynamic elastic moduli are still obtained from well logs. \(LBI_{5}\) and \(LBI_{5^{\prime}}\) are both used in practice to evaluate brittleness; they differ by taking rock density \(\rho\) into account. An attempt to incorporate mechanical failure of the rock into brittleness index determination from well logs has been made by [PERSON] et al., 2014 [21]. Critical strain energy release rate--fracture energy independent of the applied load and geometry of the body [27]--was considered as a parameter connecting elastic moduli and failure process. It should be noted that hydraulic fracturing was the main focus of the study, so failure of planar I-mode fracture was analyzed. It was noted that critical energy release rate \(G_{c}\) had been established for such fracture propagation, resulting in the existence of a relationship between [PERSON]'s modulus and a certain fracability.