Distribution of stresses near underground cylindrical and spherical cavities created by an explosion
Abstract
Distribution of stresses near underground cylindrical and spherical cavities created by an explosion
Incoming article date: 28.02.2025The paper considers the problem of the stress state of a rock array with continuous inhomogeneity. This type of inhomogeneity can be observed in rock arrays with cavities created by explosion. In this case, the dependence was chosen when the main mechanical characteristics depend only on one coordinate - the radius. It was also taken into account that the chosen dependence gives an opportunity to obtain relatively simple methods of solving the problems. The chosen calculation scheme of the problem allows to reduce it to the solution of one-dimensional task. For the case of the centrally symmetric problem we consider the solving equation, which is an ordinary inhomogeneous differential equation of the second order with variable coefficients. Using the substitution of variables, we can proceed to the solution of the hypergeometric equation. Solutions of hypergeometric equations are given in the form of hypergeometric series, which are known to converge. Using inverse substitutions, the stresses are found. The stress state of the rock array at different degrees of its heterogeneity is determined. The results are presented in the form of graphs. Comparison with similar solutions for homogeneous arrays is carried out. The presented results allow us to conclude that when solving problems on the stress state of rock arrays with cavities, it is necessary to take into account the heterogeneity of the arrays obtained in the process of creating such cavities with the help of explosion.
Keywords: heterogeneity of the medium, rock array, spherical cavity, stress state