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Fundamental and applied issues of mining

2019 year, number 1

MATHEMATICAL MODELING OF STRESS-STRAIN STATE OF THE ROCK MASS IN THE VICINITY OF SUPPORTED CIRCULAR OPENING NEAR THE INTERFACE OF ROCKS WITH DIFFERENT DEFORMATION CHARACTERISTICS

A. S. Sammal, S. V. Antsiferov, N. S. Pavlova
Tula State University, Tula, Russia
Keywords: Горный массив, математическая модель, компьютерное моделирование, напряженное состояние, выработка, крепь, расчет, собственный вес пород, Rock mass, mathematical model, computer modeling, stress state, opening, support, calculation, rocks own weight

Abstract

A new analytical method for estimating the stress state of a rock mass composed of two types of rocks with a straight-line boundary near a supported circular opening is proposed. The method is based on a strict solution of the plane problem of elasticity theory for an infinite weighty medium composed of two different materials and weakened near the rock interface by supported circular opening. The obtained solution is based on the theory of analytical functions of complex variables, properties of Cauchy-type integrals and complex series. An example of stress distribution in the rock mass near the opening is considered. A comparative analysis of the calculation results obtained in accordance with the proposed method and the data of FEM computer simulation are discussed.