## 1 Introduction  
Exploration and development of hydrocarbon reservoirs are related to many fields of applied sciences and mechanics in particular. Filtration processes, well drilling, well log data obtaining and assessment, and hydraulic fracturing are all closely related to hydrodynamics and rock mechanics [1]. It is natural that methods used in these fields are being developed to answer industrial needs: for example, failure mechanics has been developed a lot to understand and optimize hydraulic fracturing procedures. Consideration of hydrocarbon fields' exploration and development makes emergence of specific problems evident. Some of these problems have their analogs in the other fields, so ideas regarding the ways to solve them are available. Nevertheless, some problems not typical for other branches of science arise as well, leading to the need of creating new principal approaches to deal with them. The current study is aimed at one of such problem--rock brittleness estimation. Brittleness of the medium is a very complicated topic in its nature [2; 3; 4; 5]. Many mechanical concepts have clear physical and mathematical meaning: elastic moduli are defined with respect to stress and strain changes; strength properties are defined as conditions standing for failure, and so on. Brittleness is somewhat unique among these concepts. It is generally easy to understand what brittleness is in general. Comparison of two materials, for instance, glass and clay, leads to a clear understanding that one of them (glass) is brittle, and the other one (clay) is not [6]. Brittleness has been historically introduced in many different ways, including qualitative definitions, such as lack of ductility [6; 7], rock failure with lack of preceding plastic flow [8], and destruction of internal cohesion [9]. Nevertheless, whenever one tries to introduce brittleness as a certain physical property with mathematical definition, a number of problems become evident [2]. While the example of glass and clay reveals a clear distinction between brittle and ductile material, it is very difficult to claim that glass is several times more brittle than clay and answer how many times in particular. Lack of a strict mathematical definition of brittleness brings brittleness discussions from the quantitative to the qualitative plane [9]. While qualitative discussions of brittleness and drawn conclusions may be enough for some practical problems, the other problems highlight the need to develop mathematical approaches to evaluate brittleness. Hydraulic fracturing is among such problems: it is preferable to initiate hydraulic fracture growth in a brittle zone of a hydrocarbon reservoir, but not in a ductile zone [5]. Given the complicated conditions of hydrocarbon reservoirs being in development nowadays, brittle zones should be analyzed with numbers, but not with qualitative discussions [5]. As a result, numerous studies are carried out to develop mathematical ways to estimate brittleness of rock masses from data obtained from hydrocarbon fields [3; 4; 5]. Quantitative definitions of rock brittleness have been developed a lot since the first concepts mentioned above, as new techniques of dealing with stress-strain deformation curves characterizing various materials have been emerging. Such concepts as total strain at the point of failure [2; 10] and ratio between reversible and total energy at failure [11; 12] were proposed to overcome the problem of quantitative brittleness evaluation. Although these definitions are mathematically correct and have solid physical background, a problem arises from of the need to analyze deformation curves. Keeping in mind that hydrocarbon reservoirs are the focus of many practical studies, deformation curves can only be obtained from laboratory tests on extracted rock samples. At the same time, rock sample experiments are complicated and costly, so alternative ways of dealing with brittleness have been developed with regard to various geophysical data.