PSI - Issue 32

I S Lomakin et al. / Procedia Structural Integrity 32 (2021) 117–123 I S Lomakin, A A Tsayukov / Structural Integrity Procedia 00 (2019) 000 – 000

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technological interlayer, is characterized by a thin-layered structure, with the inclusion of clay layers with a thickness of several millimeters to tens of centimeters. Field observations have shown that their presence contributes to intense laminations of the rocks in the interlayer (Asanov et al. 2012; Asanov et al. 2018). Next, the lamination processes lead to caving of the interlayer rocks into the goaf. This is especially true for the chambers of the lower productive layer, since the lamination and caving of the roof rocks here can reach a total of 1 m. Finally, this changes the mine geometry, increases the height of the interchamber pillars (IP), and so decreases their bearing capacity. Advanced computational tools and methods make it possible to detail and bring the formulation of geomechanical problems closer to the realities of mining-geological and mining-technical conditions for the extraction of minerals. In particular, it is possible to simulate the layered structure of the bed saturated with thin clay interlayers by using Goodman joint elements and describe the geometry of the goaf formed using various facilities. 2. Method of Mathematical Modeling To study the influence of the roof lamination on the loading of the interchamber pillars, we carried out the multivariate mathematical modeling of changes in the stress-strain state of the generalized chamber block in the plane strain formulation. The stress state of the two-layer chamber block was described by an ideal elastoplastic medium. The relationship between deformations and stresses at the prelimiting stage was described by Hooke's law, and the ultimate stresses in the compression region were determined by the Mohr-Coulomb criterion, represented as a parabolic envelope of Mohr's circles (Kuznetsov 1947): ൌ ൌ ሺ ൅ ሻ ʹ − ʹ ∙ ൅ ൅ (1) where , are the ultimate uniaxial compression strength and tensile strengths of the rocks, respectively. Shear ሺ ሻ and normal ሺ ሻ stresses are found at the sites, where the relation reaches the maximum value. The use of the plasticity criterion in the form (1) leads to significant computational difficulties. In this regard, the parabolic envelope of Mohr's circles (1) was approximated by a two-link straight line. Its description is reduced to the classic form of the Mohr-Coulomb law: ൌ ൌ ൅ (2) with the cohesion coefficient and the inner friction coefficient –ƒ . In expression (2), the stresses and are calculated via the values of the primary stresses: ൌ ͳ − ͵ ʹ ൌ ͳ ൅ ͵ ʹ In the tensile region, the ultimate stress was limited by the ultimate tensile strength. ͳ ൌ Goodman joint elements (Goodman 1974; Groth 1980) were used to numerically model the deformation of the clay contacts between the layers. Therelationbetweenthenormalstress ( σ  ) and the corresponding deformation ( ) was described with the linear equation Nomenclature VSD Verkhnekamskoye salt deposit