Mathematical modeling of the stress-strain state of an elastic mass near a spherical cavity taking into account the technological heterogeneity of its mechanical properties
Abstract
Mathematical modeling of the stress-strain state of an elastic mass near a spherical cavity taking into account the technological heterogeneity of its mechanical properties
Incoming article date: 21.08.2018It is considered a centrally symmetric stress-strain state of the rock mass near the underground spherical cavity taking into account the technological heterogeneity of the rocks of the near-edge region. The mathematical model was developed and analytical solutions were found for this problem. The technological heterogeneity of the elastic properties of the rock mass material was modeled by a radially inhomogeneous coefficient of elasticity at a constant Poisson's ratio. The variable coefficient of elasticity for heterogeneous rocks was approximated by a generalized polynomial with undetermined coefficients. On the basis of experimental data, a numerical calculation of the stress-strain state components for the problem was carried out, and characteristic effects were detected.
Keywords: stress-strain state, rock mass with technological heterogeneity, underground spherical cavity, mathematical model