Abstract
The application of the method, i.e. component expansion of hoop and radial coordinate displacement vectors into trigonometric and generalized power series, helped obtain a new exact analytical solution for a heavy transversally-isotropic combined sphere in the equilibrium state of gravity forces. Uniformly distributed pressure was set on the internal surface, the external surface was considered to be rigidly fixed; stress and strain expressions are shown. The obtained new analytical solution helped analyze the influence of geometry on the distribution of independent invariants of stress tensor in the cross-sections of concrete monolithic supports for spherical mine workings and sedimentary rock mass surrounding mine; besides, a comprehensive multicriterion approach enabled the description of damage mechanisms.
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Acknowledgements
The authors acknowledge the support of the Russian Foundation for Basic Research (Grant RFBR–Urals No 17–41–590148).
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Zaitsev, A.V., Fukalov, A.A., Sokolkin, Y.V. (2019). Initial Strength Analysis of Anisotropic Concrete Supports for Spherical Mine Workings in a Sedimentary Rock Mass. In: Karev, V., Klimov, D., Pokazeev, K. (eds) Physical and Mathematical Modeling of Earth and Environment Processes (2018). Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-11533-3_46
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DOI: https://doi.org/10.1007/978-3-030-11533-3_46
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