It 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

The software package, realizing the calculation and graphics visualization of asymptotic behavior at big time of dominant terms of velocity vector components at 2D motion of rotating stratified liquid, is developed. The mathematical model, which lies at the basis of the software package, is presented. The structure of the software package is described. The application of the software package in the study of fluctuations in stratified fluid is shown.

Keywords: stratified rotating liquid, mathematical model, software package, asymptotic behavior, dominant terms of the asymptotic forms