PSI - Issue 32

Ivan Pankov et al. / Procedia Structural Integrity 32 (2021) 166–172 Author name / StructuralIntegrity Procedia 00 (2019) 000 – 000 Karman were conducted according to ͳ ൐ ʹ ൌ ͵ , and those by Becker used this one ͳ ൌ ʹ ൐ ͵ . The experiment results presented in the works (Von Karman, 1911;Boker, 1915) showed that the influence of ʹ on the rock strength was insignificant. These conclusions contradicted the Mohr – Coulomb theory which postulates that the influence of ʹ on the rock strength is independent. For this reason, the further studies in this area were aimed at the development of testing the equipment which could allow an independent control of the principal stresses in order to study the influence of the intermediate component on the rock strength. One of the first machines was constructed by Kuznetsov and was used to test equivalent isotropic materials, which modeled the properties of rocks (Kuznetsov and Budko, 1968). Based on the experiment results, it was concluded that ʹ does not influence their strength in case of volume compression. Around the same time, Mogi developed a true triaxial compression apparatus for testing rock strength, which he used to demonstrate that the influence of σ 2 on the rock strength did exist (Mogi, 1967a, 1970). Beron and Chirkov noted that ʹ does influence the rock strength under volume compression (Beron and Chirkov, 1969). Later Chirkov showed that the influence of ʹ on the rock strength is greater for anisotropic materials than for isotropic ones (Chirkov, 1976). Studies on the rock strength and deformation were conducted by many researchers using different types of the true triaxial compression apparatuses (Alekseev and Nedodaev, 1982; Takahashi and Koide, 1989;Chang and Haimson, 2000; Kwasniewski et al., 2003; Chen and Feng, 2006; Lee and Haimson, 2011; Descamps et al., 2012; Ingraham et al., 2013). Another method allowing the variation of ʹ was described by Jagger and Cook and consisted in testing hollow cylindric samples loaded with external and internal pressure (Jaeger and Cook, 1969). The data presented by them indicated that there was a significant influence of ʹ on the rock strength. Despite the obtained experimental data, it can be said that the issue whether ʹ has an influence on the rock strength remains open. At the present time, computer modeling of the stressed condition of mined rocks is one of the most effective tools of solving problems related to geomechanical technologies to ensure safety when mining the rocks in difficult mining and geological conditions. New computing technologies allow solving three-dimensional problems to determine all the principal stresses. This approach means that when assessing the rock formation condition, one must apply strength criteria, the mathematical expression of which includes not only the maximum and minimum, but also the intermediate principal stresses. Despite the fact there are numerous criterial dependences suggested by different researchers (Litvinsky, 2008), the list of criteria most often used to solve this type of problems is quite limited. First of all, such criteria include the Mogi empirical criterion (Mogi, 1967b) and its exponential modification proposed by Colmenares and Zoback (Colmenares and Zoback, 2002). Also, satisfactory results for various rock types are obtained using the generalized variant of the Drucker – Prager linear criterion proposed by Pariseau (Pariseau, 2007), which is essentially a result of generalizing the Mises energy strength theory (Ma et al., 2011). It is necessary to note that one of the main factors considerably complicating the strength criteria researches is a considerable difficulty to experimentally determine the strength indicators of the rocks under true triaxial stress, as well as a high cost of the equipment for such tests. For this reason, it is considered relevant to develop the strength criteria of rocks in the true stress condition based on results of simple experimental studies, which allows for a significant increase of the reliability of recommendations on ensuring safety during mining in difficult geological conditions. 2. Complex Determination of Rock Strength Properties As for the applicability and use of the strength criteria in current problems of geomechanics, their equations are to meet the following basic requirements: - the strength criterion is to be written as a combination of the principal stresses, and its equation should include not only the maximum and minimum components of the principal stresses, but also the intermediate principal stress; - it is to have a simple mathematical formula allowing an expression of any component of the principal stresses using simple algebraic transformations; - the parameters of the strength criterion are to be easily computed based on results of comparatively simple experimental studies, for example, studies using a complex determination of the rock strength indicators, according to which the ultimate strength for uniaxial tensile, uniaxial compression and biaxial compression is determined. Drawings of tests aimed at determining the complex rock strength indicator, as well as the occurrence of 167 2