Abstract

Underground openings of different shapes are excavated in rocks for several engineering purposes such as mining of mineral deposits, underground roadways (tunnels), underground power houses, etc. In this paper the analysis of stresses and strains around these excavations are of main concern. There are several methods for their analysis but because of the complexity of loadings and geometries of these openings and also different depths and rock types, the general closed form solutions are technically impossible. Therefore, one of the versatile numerical methods such as finite element, boundary element and finite difference methods or a combination of them should be used for these analyses. In this paper, an indirect boundary element method is used to evaluate the stresses and displacements on the boundary and around the excavations. The strains and tangential stresses are also determined by implementing a finite difference scheme based on the results obtained by the boundary element method. Excavations of different cross-sections (e. g. rectangular and circular shapes) are solved numerically by the proposed method. These results are compared with some existing analytical results which prove the validity of the method. The analytical and numerical results are tabulated in several tables and some of them are shown graphically in the related figures of the text.

1.
Introduction

Underground excavations are designed to solve many complicated problems in mining and civil engineering projects. The stress and strain (or displacement) analysis of these problems is the primary steps of their solution. Several analytical and numerical methods are developed for stress analysis around underground openings. In this research the indirect boundary element method (IBEM) which is a semi-analytical method and can be well matched with other numerical techniques such as finite element, finite difference and boundary collocation methods; is used for the analysis of stress and strain around underground excavations [1, 2]. These indirect boundary element techniques which are divided into two individual methods known as fictitious and displacement discontinuity methods as explain by Crouch and Starfield [3]. As a particular example the fictitious stress method (FSM) is briefly discussed here and for the details of these methods the reader is referred to the references [3–6] at the end of this study. The higher order displacement discontinuity method proposed by Crawford and Curran, and Shou and Crouch can also be used for the stress and displacement analysis of cavity problems [5, 6].

2.
Fictitious stress method

The fictitious stress method concerns with constant resultant tractions x x t = P and P y t = are applied to a finite strip in an infinite body (Figure 1). The problem of a constant traction x x t = P and P y t = applied to the line segment xa, y = 0 in an infinite elastic solid can be solved by integrating the solution to the Kelvin's problem.

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