ON THE STRESS-STRAIN STATE OF THE ROCK MASS AROUND THE EXCAVATION LOCATED NEAR A ROCK SLOPE

Abstract

A mathematical model has been developed for the formation of the stress-strain state of a rock mass around a circular cross-section mining mine constructed in a closed manner along a slope in close proximity to the inclined earth's surface. The proposed model is based on theoretical propositions and hypotheses of geomechanics and continuum mechanics, which allow us to use modern ideas of mechanics of underground structures about the joint work of elements of a single deformable system "slope – rock mass – mining". The design schemes of the model allow us to take into account the influence of the
main physical, mechanical and geometric factors under the action of static loads – such as the own weight of
rocks and internal pressure. Since the sections of sufficiently extended workings are considered, the statements of plane problems of elasticity theory for a semi-infinite medium weakened near a rectilinear boundary by a circular hole under appropriate boundary conditions are used. Rigorous solutions to the problems of elasticity theory were obtained using the mathematical apparatus of the theory of functions of a complex variable, Kolosov – Muskhelishvili complex potentials, characterizing the stress-strain state of the half-plane, the analytical continuation of complex potentials across the boundary of the half-plane, the Sokhotsky – Plemel theory, the properties of Cauchy-type integrals, Laurent series and the modified Aramanovich method. The solutions are implemented in the form of design algorithms and computer programs that allow performing multivariate calculations when design underground structures and performing scientific research. The results of the design can be used to assess the stability of the slope based on the application of the Coulomb – Mohr strength condition, comparison and evaluation of the results of determining the stress-strain state of the rock mass around the workings in the slope by numerical methods, including FEM. Calculated stress plots are given.