## 5 Discussion  
Behavior of LBI\({}_{6}\) deserves particular discussion. Recall that LBI\({}_{6}\) was proposed with energy concept kept in mind: critical energy release rate was considered as a factor controlling brittleness. Energy concept has been used for introduction of TBIs as well, so it can be used to establish a bridge between TBIs and LBIs. This link can be highlighted after considering of inner structure influence on failure process. Figure 10 represents brittleness index LBI\({}_{6}\) as function of fractures density. Note that the fracture density \(\varepsilon\) is related to the number of fractures \(N_{fp}\) by the linear equation \(N_{fp}=V\varepsilon/a^{3}\), where \(V\) is the volume containing the fractures, and \(a\) is the fracture's half-length. It can be seen that increase in the fracture density and, as a result, in the number of natural fractures in the rock volume leads into an increase in its brittleness. This effect can be explained by detailed analysis of failure process. Each fracture serves as a stress concentrator during loading. Increase in stresses leads to development of natural fractures--the process associated with increase in total free surface existing in fractured rock. Hence, the more fractures are present, the more free surface emerges during loading. As a result, more energy is released during brittle failure. Hence, increase in relative amount of fractures--or fracture density in terms of rock physics modeling--is expected to lead to increase in brittleness index TBI\({}_{1}\) or TBI\({}_{2}\). At the same time, rock physics modeling has been carried out for calculating LBIs, so the tendency shown in Figure 10 is in fact visualization of the connection between energetic concept of brittleness, rock physics model, and log-based empirical correlation for brittleness index evaluation. This rock physics approach can be also applied for changing mineral composition and pore-filling substance thereby providing a link between MBI and LBI indices. Note that this approach for LBI analysis in terms of rock composition and microstructure can be applied at any scale of interest--core, log, or seismic scale. For example, if we have other types of heterogeneities at the log scale, which are much greater than those at the core scale, we should introduce them in the rock physics model considering the effective properties calculated at the core scale as a background medium with effective properties. Thus, subvertical fractures tens of centimeters in size can exist in carbonate rocks or elongated lenses of kerogen or clay. In this case, the rock physics modeling is again suitable for an analysis shown above but for anisotropic rocks of HTI (horizontal transverse isotropy) or VTI (vertical transverse isotropy) symmetry. Note that Equation (14) of self-consistent method is general and applicable to anisotropy of any type not only for HTI or VTI. We try to perform such an analysis and discover that a lot of questions arise when calculating the LBIs to anisotropic rocks. The only exception is LBI\({}_{4}\) that is rather  
Figure 10: Brittleness index LBI\({}_{6}\) versus fracture density and decimal logarithm of aspect ratio. simple, linear dependent on the Young's modulus, and does not require normalization. In this case, we can compare the indices calculated for different directions and distinctly conclude that the index in the symmetry plane is greater than that in the perpendicular plane. However, when considering LBI\({}_{5^{\prime}}\) or LBI\({}_{3}\) that are widely used in practice or other indices the comparison meets some difficulties since it is not clear which minimum and maximum of moduli should be used for the normalization--over all directions or only for the particular direction. The same problem arises when dealing with TBIs--although it is natural to treat TBIs obtained from samples with known spatial orientations as anisotropic indices, construction of a single parameter standing for brittleness in all directions remains a challenge.