Thermal stress state of rock massif with a spherical cavity taking into account inhomogeneity of the medium

Abstract

Abstract. The case of continuous one-dimensional heterogeneity of deformation characteristics of a material of the pedigree array with the spherical cavity, received by means of explosion, are continuous functions of one of co-ordinates -radius is considered. Solution of an initial set of equations concerning displacements is sought in the form of decomposition in Fourier series in Legendre polynomials. Using the method of separation of variables, we can reduce the problem to a system of two ordinary differential equations with variable coefficients, which can be solved numerically. Stress analysis was performed in the homogeneous and inhomogeneous array surrounding the spherical cavity. A comparative analysis of the results is carried out.

Comparison of the Stress-State Level for the Inhomogeneous Rock Mass with a Spherical Cavity in the Stationary and Non-Stationary Temperature Conditions

“…The axially symmetric problem for a non-homogeneous body in spherical coordinates can be reduced to a system of two partial differential equations with variable coefficients relative to displacement components the algorithm for numerical analytic solution of which is provided in detail in [7].…”

Calculation of a Radial Inhomogeneous Rock Mass with a Spherical Cavity under the Influence of Thermal Field

“…A numerical analytic solution is applied for solving the class of problems on the equilibrium of elastic inhomogeneous bodies in spherical coordinates. An axially symmetric problem of this class can be reduced to a system of two partial differential equations with variable coefficients relative to the displacement components of u n and v n [8,9]. The solution of the derived equations is proposed to be sought in the form of an expansion into Fourier series in Legendre polynomials [10].…”