A Novel Closed-Form Solution for Circular Openings in Generalized Hoek-Brown Media

Qing Xiang Meng,Wei Wang

doi:10.1155/2014/870835

Abstract

A novel closed-form solution is presented in this paper for the estimation of displacements around circular openings in a brittle rock mass subject to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic media governed by the generalized Hoek-Brown yield criterion. The present closed-form solution was validated by employing the existing analytical solutions. Results of several example cases are analyzed to show that, with the simplified assumption, a novel closed-form solution is derived and found to be in an excellent agreement with those obtained by using the exact integration method with mathematical software. Parametric sensitivity analysis is carried out and the parameterartends to be the sensitive factor. As a closed-form solution that does not require transformation technique and the use of any numerical method, this work can provide a better choice in the preliminary design for circular opening.

Highlights

Analysis for the stress and displacement around a circular opening is a common problem widely used in geotechnical, petroleum, and mining engineering
A large number of analyses of circular tunnel in an infinite medium subjected to a hydrostatic in situ stress have been presented by considering different models of material behavior, such as the ideal plastic, brittle plastic, strain-softening models, with the different yield criteria like the linear Mohr-Coulomb yield criterion and the nonlinear Hoek-Brown criteria
The Hoek-Brown failure criterion is an empirical criterion based on triaxial behavior of rock mass, large scale tests, and experience [12]

Summary

Introduction

Analysis for the stress and displacement around a circular opening is a common problem widely used in geotechnical, petroleum, and mining engineering For this reason, a large number of analyses of circular tunnel in an infinite medium subjected to a hydrostatic in situ stress have been presented by considering different models of material behavior, such as the ideal plastic, brittle plastic, strain-softening models, with the different yield criteria like the linear Mohr-Coulomb yield criterion and the nonlinear Hoek-Brown criteria. Based on the elastic stress-strain relationship, this note proposed a closed-form solution for the prediction of displacement around a circular opening in an elastic-brittleplastic rock mass compatible with a nonlinear Hoek-Brown yield criterion and a nonassociate flow rule. Comparing the closed-form solutions presented by Sharan [7], the results of this work were found to have a better performance

Analysis of Stresses and Displacements

Validation and Sensitivity Analysis

Conclusions