Bibliography: 1. Shankar V., Kumar D., and Subrahmanyam Ds. Impact and severity of deep excavations on stress tensors in mining. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh. 2019, no. 2, pp. 43—48. [In Russ]. DOI: 10.15372/FTPRPI20190205.
2. Vasil’ev L. M. and Vasil’ev D. L. Theoretical ground for origination of normal horizontal stresses in rock masses. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh. 2013, no. 2, pp. 81—90. [In Russ].
3. Gudkov V. M., Katkov G. A. Stability of rock formations. MIAB. Mining Inf. Anal. Bull. 2008, no. 2, pp. 119—121. [In Russ].
4. Nazarov L. A., Nazarova L. A. Estimate of the interchamber pillar stability based on the damage accumulation criterion. Journal of Mining Science. 2007, vol. 43, no. 6, pp. 575—584.
5. Mokhnachev M. P. Ustalost' gornykh porod [Fatigue of rocks], Moscow, Nauka, 1979, 152 p.
6. Rabotnov Yu. N. Equilibrium of an elastic medium with after-effect. Fractional Calculus and Applied Analysis. 2014, vol. 17, no. 3, pp. 684—696. DOI: 10.2478/s13540-014-0193-1.
7. Shermegor T. D. Teoriya uprugosti mikroneodnorodnykh sred [Theory of elasticity of microhomogenic medium], Moscow, Nauka, 1977, 400 p.
8. Shitikova M. V. Fractional operator viscoelastic models in dynamic problems of mechanics of solids: a review. Izvestiya Rossiyskoy akademii nauk. Mekhanika tverdogo tela. 2022, no. 1, pp. 3—40. [In Russ]. DOI: 10.31857/S0572329921060118.
9. Rossikhin Yu. A., Shitikova M. V. Application of fractional calculus for dynamic problems of solid mechanics: Novel trends and recent results. Applied Mechanics Reviews. 2010, vol. 63, no. 1, article 010801. DOI: 10.1115/1.4000563.
10. Mainardi F. Fractional calculus: Some basic problems in continuum and statistical mechanics. Fractals and Fractional Calculus in Continuum Mechanics. CISM Courses and Lectures No. 78, A. Carpinteri and F. Mainardi, eds., Springer, Wien, NY, 1997, pp. 291—348.
11. Fabrizio M., Giorgi C., Morro A. Two approaches to aging and fatigue models in viscoelastic solids. AAPP Atti della Accademia Peloritana dei Pericolanti, Classe di Scienze Fisiche, Matematiche e Naturali. 2019, vol. 97, no. 1. DOI: 10.1478/AAPP.97S1A7.
12. Caputo M., Fabrizio M. Damage and fatigue described by a fractional derivative model. Journal of Computational Physics. 2014, vol. 293, pp. 400—408. DOI: 10.1016/j.jcp.2014.11.012.
13. Amendola G., Fabrizio M., Golden J. M. Thermomechanics of damage and fatigue by a phase field model. Journal of Thermal Stresses. 2016, vol. 39, no. 5, pp. 487—499.
14. Lavrov A. V., Shkuratnik V. L., Filimonov Yu. L. Akustoemissionnyy effekt pamyati v gornykh porodakh [Acoustic-emission memory effect in rocks], Moscow, Izd-vo MGGU, 2004, 450 p.
15. Beltyukov N. L. Studying the Kaiser effect during modeling of rock loading conditions using the NX-borehole jack. Journal of Physics: Conference Series. 2021, vol. 1945, article 012023. DOI: 10.1088/1742-6596/1945/1/012023.
16. Blokhin D. I., Kharchenko A. V. Complex study of acoustoemission and thermomechanical effects in samples of rock salt at their cyclic deformation. MIAB. Mining Inf. Anal. Bull. 2021, no. 4-1, pp. 129—137. [In Russ]. DOI: 10.25018/0236_1493_2021_41_0_129.
17. Miehe C., Hofacker M., Welschinger F. A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering. 2010, vol. 199, pp. 2765—2778. DOI: 10.1016/j.cma.2010.04.011.
18. Hu S., Baskes M., Stan M. Phase-field modeling of microvoid evolution under elastic-plastic deformation. Applied Physics Letters. 2007, vol. 90, no. 8, pp. 1921—1923. DOI: 10.1063/1.2709908.
19. Ohno M., Matsuura K. Quantitative phase-field modeling for two-phase solidification process involving diffusion in the solid. Acta Materialia. 2010, vol. 58, no. 17, pp. 5749—5758. DOI: 10.1016/ j.actamat.2010.06.050.
20. Levitas V. I., Ozsoy I. B. Micromechanical modeling of stress-induced phase transformations. Part 1. Тhermodynamics and kinetics of coupled interface propagation and reorientation. International Journal of Plasticity. 2009, vol. 25, no. 2, pp. 239—280. DOI: 10.1016/j.ijplas.2008.02.004.
21. Voyiadjis G. Z. (ed.). Handbook of damage mechanics: nano to macro scale for materials and structures. New York, Springer, 2015, 1579 p.
22. Stepanova L. V., Igonin S. A. Description of deterioration processes: damage parameter of Y.N. Rabotnov: historical remarks, fundamental results and contemporary state. Vestnik of Samara University. Natural Science Series. 2014, no. 3 (114), pp. 97—114. [In Russ].
23. Uchaykin V. V. Metod drobnykh proizvodnykh: monografiya [The fractional derivative method], Ulyanovsk, Artishok, 2008, 510 p.
24. Sheinin V. I., Blokhin D. I., Maksimovich I. B., Sarana E. P. Experimental research into thermomechanical effects at linear and nonlinear deformation stages in rock salt specimens under cyclic loading. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh. 2016, no. 6, pp. 15—22. [In Russ]. DOI: 10.1134/S1062739116061575.
25. Ogorodnikov E. N., Radchenko V. P., Ungarova L. G. Mathematical models of nonlinear viscoelasticity with operators of fractional integro-differentiation. PNRPU Mechanics bulletin. 2018, no. 2, pp. 147—161. [In Russ]. DOI: 10.15593/perm.mech/2018.2.13.
26. Blokhin D. I., Sheinin V. I. Thermomechancal effects in different geomaterials in limiting behavior of cyclic loading. IOP Conference Series: Earth and Environmental Science. 2021, vol. 773, no. 1, article 012055. DOI: 10.1088/1755-1315/773/1/012055.
27. Vysotin N. G., Vinnikov V. A. A case history of modeling elastic hysteresis of different-genotype rocks based on the Preisach model. MIAB. Mining Inf. Anal. Bull. 2023, no. 11, pp. 5—16. [In Russ]. DOI: 10.25018/0236_1493_2023_11_0_5.
28. Nadai A. Plastichnost' i razrushenie tverdykh tel. T. 1 [Plasticity and destruction of solids, vol. 1], Мoscow, 1954, 648 p.