## 2 Existing Brittleness Indices
### Test-Based Brittleness Indices (TBIs)
Hence, all brittleness evaluations were normalized with respect to these two extreme cases. [PERSON] et al., 2021 [27] have shown that performance of the normalization procedure described here leads to an increase in correlation between brittleness and confining pressure obtained from loading tests performed on Bazhenov Formation rock samples. It should be mentioned that normalization procedure was established for TBI\({}_{2}\), but not to TBI\({}_{3}\) and TBI\({}_{4}\) proposed by Equation (12) to analyze post-peak behavior. The proper normalization procedure for these indices is yet to be established. The problem of upscaling TBI was also considered for TBI\({}_{1}\): [PERSON], 1981 [40] proposed the following procedure to evaluate effective brittleness of the layered formation: if the formation being investigated is not uniform in structure, a geological log is made, and for each layer of significance, a sample is taken and brittleness is determined in the laboratory. An average brittleness index value for the whole vertical section is then calculated as follows [40]  
\[TBI_{aver}=\sum_{i}h_{i}TBI^{i}\Big{/}\sum_{i}h_{i}, \tag{13}\]  
where \(E\) is tangential static Young's modulus obtained from the linear zone of stress-strain curve, and \(M\) is unloading modulus--the slope of the sector \(BQ\) in Figure 3 corresponding to post-peak rupture associated with increase in strain and decrease in differential stress. Is it worth mentioning that this result is similar to well-known Backus averaging used for layered formations [41]. The final remark is devoted to anisotropy of rocks: it is clear that results of laboratory tests performed at oriented samples can be used to evaluate brittleness indices in different directions. Nevertheless, there are limited ways to incorporate these oriented measurementsinto discussed LBIs and MBIs: [PERSON] et al., 2014 [42] have proposed a method to evaluate brittleness with respect elastic moduli anisotropy. LBI\({}_{5}\) was used to obtain brittleness from elastic moduli measured in the laboratory--it is a complicated task to properly incorporate energy concept into brittleness determination. To sum up, laboratory tests provide an opportunity to evaluate brittleness of rock samples with regard to physically meaningful concepts. Yet there are still various ways to introduce brittleness index from experiments performed on rock samples, there is an opportunity to check whether the suggested index is suitable for the studied rock. The criterion is related to presence of correlation between brittleness and confining pressure. There are problems of proper brittleness normalization and upscaling: they are solved for the classic approach to measure brittleness from pre-peak behavior, but post-peak behavior is yet to be analyzed. Upscaling problem appears to be essential for brittleness evaluation from rocks: existing ways to reconstruct brittleness profiles using well logs or mineral composition use results of laboratory tests to establish the empirical parameters used in Equations (1)-(10). Although data used for estimation of TBIs and LBIs usually belong to different spatial scales--log scale for LBI, and core scale for TBI--there is an opportunity to solve the problem of rescaling. In fact, laboratory tests make it possible to estimate both static and dynamic elastic moduli. As a result, LBIs can be calculated using data obtained from laboratory tests, making the scales with possibility of LBI determination cover core scale as well. Yet, it is still necessary to use proper effective medium theory methods to solve the problem of upscaling. The following section provides the first ideas regarding the algorithm for brittleness upscaling, starting with analysis of the effect the inner structure of the rock (often called as microstructure) has on its brittleness.