Skip to main content
Log in

Unified semi-analytical solution for elastic-plastic stress of deep circular hydraulic tunnel with support yielding

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions. The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST). Different major principal stresses in different engineering situations and different support yielding conditions are both considered. The unified solution obtained in this work is a series of results, rather than one specific solution, hence it is suitable for a wide range of rock masses. In addition, parametric study is conducted to investigate the effect of intermediate principal stress. The result shows the major principal stress should be rationally chosen according to different engineering conditions. Finally, the applicability of the unified solution is discussed according to the critical pressures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. JAEGER J C, COOK N G W. Fundamentals of rock mechanics [M]. London: Chapman and Hall, 1979: 252–280.

    Google Scholar 

  2. JIANG Y, YONEDA H, TANABASHI Y. Theoretical estimation of loosening pressure on tunnels in soft rocks [J]. Tunneling and Underground Space Technology, 2001, 16(2): 99–105.

    Article  Google Scholar 

  3. REN Qing-wen, ZHANG Hong-chao. A modification of Fanner formula [J]. Journal of Hohai University, 2001, 29(16): 109–111. (in Chinese)

    Google Scholar 

  4. REN Qing-wen, QIU Ying. Elastic-plastic solution of circular tunnel with liner [J]. Engineering Mechanics, 2005, 22(2): 212–217. (in Chinese)

    Google Scholar 

  5. WANG Y. Ground response of circular tunnel in poorly consolidated rock [J]. Journal of Geotechnical Engineering, ASCE, 1996, 122(9): 703–708.

    Article  Google Scholar 

  6. SHARAN S K. Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(1): 78–85.

    Article  MathSciNet  Google Scholar 

  7. HUANG Fu, ZHANG Dao-bing, SUN Zhi-bin, WU Ben. Influence of pore water pressure on upper bound analysis of collapse shape for square tunnel in Hoek-Brown media [J]. Journal of Central South University of Technology, 2011, 18(2): 530–535.

    Article  Google Scholar 

  8. SONG Li, ZHANG Yong-qiang, YU Mao-hong. Elastic-plastic unified analysis of pressure tunnel [J]. Engineering Mechanics, 1998, 15(4): 57–61. (in Chinese)

    Google Scholar 

  9. ZHANG Chang-guang, WANG Jiang-feng, ZHAO Jun-hai. Unified solutions for stresses and displacements around circular tunnels using the unified strength theory [J]. Science China: Technological Sciences, 2010, 53(6): 1694–1699.

    Article  MATH  Google Scholar 

  10. ZHANG Chang-guang, ZHAO Jun-hai, ZHANG Qing-he, HU Xiang-Dong. A new closed-form solution for circular openings modeled by the unified strength theory and radius-dependent Young’s modulus [J]. Computers and Geotechnics, 2012, 42: 118–128.

    Article  Google Scholar 

  11. ZENG Kai-hua, LI Jian-hua, XU Jia-xiong, YE Qing. Analytical solution for stresses of deep hydraulic tunnel considering linear yielding [J]. Journal of Central South University: Science and Technology, 2012, 43(3): 1131–1137. (in Chinese)

    Google Scholar 

  12. ZHANG Chang-guang, ZHANG Qing-he, ZHAO Jun-hai, XU Fei. Elastic-plastic stress unified solutions of a circular hydraulic with lining [J]. Journal of Tongji University: Natural Science, 2010, 38(1): 50–53, 134. (in Chinese)

    Google Scholar 

  13. ZHANG Chang-guang, HU Yun-shi, ZHAO Jun-hai, YANG Yan-zong. Elastic-plastic unified solutions for stresses and displacements of a deep buried circular tunnel [J]. Chinese Journal of Geotechnical Engineering, 2010, 32(11): 1738–1745. (in Chinese)

    Google Scholar 

  14. CAI M. Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries-Insight from numerical modeling [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(5): 763–772.

    Article  Google Scholar 

  15. ZHANG L. A generalized three-dimensional Hoek-Brown strength criterion [J]. Rock Mechznics and Rock Engineering, 2008, 41(6): 893–915.

    Article  Google Scholar 

  16. YU Mao-hong. Unified strength theory and its applications [M]. Berlin: Springer, 2004: 129–172.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kai-hua Zeng  (曾开华).

Additional information

Foundation item: Project(50969007) supported by National Natural Science Foundation of China; Project(GJJ13753) supported by the Scientific and Technological Research Fund, Department of Education, Jiangxi Province, China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zeng, Kh., Xu, Jx. Unified semi-analytical solution for elastic-plastic stress of deep circular hydraulic tunnel with support yielding. J. Cent. South Univ. 20, 1742–1749 (2013). https://doi.org/10.1007/s11771-013-1667-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-013-1667-8

Key words

Navigation