Theoretical Solutions of a Circular Tunnel with the Influence of the Out-of-Plane Stress Based on the Generalized Hoek–Brown Failure Criterion
Publication: International Journal of Geomechanics
Volume 16, Issue 3
Abstract
The effect of out-of-plane stress on theoretical solutions of stress, displacement, and plastic radius for a circular tunnel were studied by using the generalized Hoek–Brown (HB) failure criterion and nonassociated flow rule in elastic–brittle–plastic rock masses. A technique of using equivalent Mohr–Coulomb and generalized HB strength parameters was adopted to compare results of the developed method and published results. The presented solution was validated by existing theory. The results of the developed method were found to be larger than those previously published, which were determined through programming.
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Acknowledgments
The authors are grateful to the National Basic Research 973 Program of China (2013CB036004), National Natural Science Foundation of China (No. 51208523), and the China Postdoctoral Science Foundation (No. 2003034468) for the financial support.
The following symbols are used in this paper:
- parameter of HB failure criterion for peak strength ();
- parameter of HB failure criterion for residual strength ();
- integration constant ();
- HB constants for the rock mass ();
- Young’s modulus of the rock mass ();
- elastic parts of strain ();
- parameter of HB failure criterion for peak strength ();
- parameter of HB failure criterion for residual strength ();
- plastic parts of strain ();
- critical internal pressure with as the major principal stress ();
- critical internal pressure with as the intermediate principal stress ();
- critical internal pressure with as the minor principal stress ();
- internal pressure ();
- out-of-plane stress along the axis of the tunnel ();
- plastic radius ();
- radial distance from the center of opening ();
- radius of the tunnel opening ();
- parameter of HB failure criterion for peak strength ();
- parameter of HB failure criterion for residual strength ();
- radial displacement ();
- radial displacement at the interface of plastic and elastic zones ();
- dilation coefficient ();
- unit weight of water ();
- radial strain ();
- axial strain ();
- circumferential strain ();
- hydrostatic stress ();
- uniaxial compressive strength of the rock ();
- uniaxial compressive strength of the rock for residual strength ();
- radial stress at the elastic–plastic interface ();
- radial stress () the parameter of HB failure criterion for residual strength ();
- radial stress at the interface between internal and out plastic zones ();
- out-of-plane stress along the axis of the tunnel ();
- circumferential stress ();
- major principal stresses ();
- minor principal stresses ();
- Poisson’s ratio of the rock mass (); and
- dilation angle ().
References
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Published In
International Journal of Geomechanics
Volume 16 • Issue 3 • June 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Aug 19, 2014
Accepted: May 7, 2015
Published online: Oct 16, 2015
Discussion open until: Mar 7, 2016
Published in print: Jun 1, 2016
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