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Mathematical Problems in Engineering
Volume 2016, Article ID 3698525, 10 pages
Research Article

A Numerical Approach for the Quasi-Plane Strain-Softening Problem of Cylindrical Cavity Expansion Based on the Hoek-Brown Failure Criterion

School of Civil Engineering, Central South University, No. 22, Shaoshan South Road, Central South University Railway Campus, Changsha, Hunan Province 410075, China

Received 12 April 2016; Revised 26 June 2016; Accepted 20 July 2016

Academic Editor: Sebastian Heidenreich

Copyright © 2016 Jin-feng Zou and Jia-min Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper focuses on a novel approach for the quasi-plane strain-softening problem of the cylindrical cavity expansion based on generalized Hoek-Brown failure criterion. Because the intermediate principal stress is deformation-dependent, the quasi-plane strain problem is defined to implement the numerical solution of the intermediate principal stress. This approach assumes that the initial total strain in axial direction is a nonzero constant () and the plastic strain in axial direction is not zero. Based on 3D failure criterion, the numerical solution of plastic strain is given. Solution of the intermediate principal stress can be derived by Hooke’s law. The radial and circumferential stress and strain considering the intermediate principal stress are obtained by the proposed approach of the intermediate principal stress, stress equilibrium equation, and generalized H-B failure criterion. The numerical results can be used for the solution of strain-softening surrounding rock. In additional, the validity and accuracy of the proposed approach are verified with the published results. At last, parametric studies are carried out using MATLAB programming to highlight the influences of the out-of-plane stress on the stress and displacement of surrounding rock.