Taking into account the influence of the centrally symmetric thermal field on the stress state of a inhomogeneous rock mass with a spherical cavity

Abstract

The problem of calculating the stress-strain behavior of a rock mass in the vicinity of a spherical cavity, taking into account the radial inhomogeneity of the rock material mass is considered. The solution takes into account the technological inhomogeneity of the soil and the inhomogeneity caused by the influence of the thermal field. The axially symmetric problem of determining the stresses and displacements was solved with a joint action of an asymmetric load (ground reaction) and hyper-thermal fields on the rock mass. Similar problems tend to arise during the creation of underground cavities and their exploitation for storing various self-heating products. To solve the initial simultaneous equations in displacements, the Fourier series of Legendre polynomials were used. Then by the separation of variables, the problem was reduced to 2 ordinary differential simultaneous equations with variable coefficients, which can be solved numerically.