Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load

Zhang Xin; Zhang Xiangping; Wang Zhang; Lang Min; Zhao Suzhi; Du Yuxiang; Sun Jinshan

doi:doi:10.11648/j.ajce.20210902.11

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Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load

Zhang Xin, Zhang Xiangping, Wang Zhang, Lang Min, Zhao Suzhi, Du Yuxiang, Sun Jinshan

Published in American Journal of Civil Engineering (Volume 9, Issue 2)

Received: 5 January 2021 Accepted: Published: 12 April 2021

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Abstract

The elastoplastic analysis of the surrounding rock of a circular tunnel is a very classic rock and soil mechanics problem. Previous scholars usually studied the situation under axisymmetric load, and they usually did not take the non-axisymmetric load distribution under the influence of ground stress and lateral pressure into account, which greatly affected its application in engineering practice. Approximate analytical solutions for calculating the plastic zone range, stress field and displacement field of the surrounding rock of a circular tunnel are inseparable from the consideration of the strength reduction and volumetric dilatancy characteristics of the rock material. The elastic-softening-residual plastic triple linear stress-strain model and the Mohr-Coulumb failure criterion are involved. The approximate analytical solutions of the residual stress field, strain field, displacement field and radius of the plastic zone in the elastic zone, plastic softening zone and surrounding plastic zone of the circular tunnel surrounding rock under axisymmetric load are deduced. The analytical solutions are valid only when the plastic zone is large and the lateral pressure coefficients 1≤λ<3. The approximate analytical method is close to the calculation result of finite element method and can replace the finite element method to carry out simple elastic-plastic analysis of surrounding rock.

Published in	American Journal of Civil Engineering (Volume 9, Issue 2)
DOI	10.11648/j.ajce.20210902.11
Page(s)	31-38
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Circular Tunnel, Asymmetrical Load, Strain Softening, Dilatancy, Elastoplastic Analysis

References

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[3]	Yu MH. Advances in strength theory of materials under complex stress state in the 20th century [J]. Applied Mechanics Reviews, 2002, 55 (3): 169-218.
[4]	Fan W, Yu MH, Chen LW, et al. Unified Elastoplastic Solution for Surrounding Rocks of Openings with Consideration of Material Dilatancy and Softening [J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23 (19): 3213-3220.
[5]	Yu XF, Zheng Y. Stability analysis of surrounding rock of underground engineering [M]. Beijing: China Coal Industry Publishing House, 1983.
[6]	Sun GZ. Rock mass mechanics foundation [M]. Beijing: Science Press, 1983.
[7]	Cai XH, Cai YP. Calculation of structural stress of hydraulic pressure tunnel [M]. Beijing: China Water Power Press, 2004.
[8]	Park KH, Kim YJ. Analytical solution for a circular opening in an elastic–brittle–plastic rock [J]. International Journal of Rock Mechanics & Mining Sciences, 2006, 43: 616–622.
[9]	Kargar AR. An analytical solution for circular tunnels excavated in rock masses exhibiting viscous elastic-plastic behavior [J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 124: 104–128.
[10]	Wang SL, Wu ZJ, Guo MW, Ge X. Theoretical solutions of a circular tunnel with the influence of axial in situ stress in elastic–brittle–plastic rock [J]. Tunn Undergr Space Technol, 2012, 30: 155–168.
[11]	Zhou XP, Li JL. Hoek–Brown criterion applied to circular tunnel using elastoplasticity and in situ axial stress [J]. Theor Appl Fract Mech, 2011, 56: 95–103.
[12]	Carranza-Torres, C., Fairhurst, C. The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek–Brown failure criterion [J]. Int. J. Rock. Mech. Min. Sci, 1999, 36: 777–809.
[13]	R. Jimenez, A. Serrano, C. Olalla. Linearization of the Hoek and Brown rock failure criterion for tunnelling in elasto-plastic rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45 (7) 1153– 1163.
[14]	Sharan S. Elastic–brittle–plastic analysis of circular openings in Hoek–Brown media [J]. Int J Rock Mech Min Sci. 2003; 40 (6): 817–824.
[15]	Lu AZ, Zhang XL, Wang SJ. Analytic method for elasto-plastic analysis of circular tunnels under non-axisymmetric stresses [J]. Chin J Rock Mech Eng, 2018, 37: 14–22.
[16]	Ma SJ. The softening deformation analysis and stimulation calculation of dilatancy in the soft rock tunnel [D]. Shenyang: Liaoning Technical University, 2001.

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APA Style

Zhang Xin, Zhang Xiangping, Wang Zhang, Lang Min, Zhao Suzhi, et al. (2021). Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load. American Journal of Civil Engineering, 9(2), 31-38. https://doi.org/10.11648/j.ajce.20210902.11

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ACS Style

Zhang Xin; Zhang Xiangping; Wang Zhang; Lang Min; Zhao Suzhi, et al. Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load. Am. J. Civ. Eng. 2021, 9(2), 31-38. doi: 10.11648/j.ajce.20210902.11

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AMA Style

Zhang Xin, Zhang Xiangping, Wang Zhang, Lang Min, Zhao Suzhi, et al. Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load. Am J Civ Eng. 2021;9(2):31-38. doi: 10.11648/j.ajce.20210902.11

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@article{10.11648/j.ajce.20210902.11,
  author = {Zhang Xin and Zhang Xiangping and Wang Zhang and Lang Min and Zhao Suzhi and Du Yuxiang and Sun Jinshan},
  title = {Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load},
  journal = {American Journal of Civil Engineering},
  volume = {9},
  number = {2},
  pages = {31-38},
  doi = {10.11648/j.ajce.20210902.11},
  url = {https://doi.org/10.11648/j.ajce.20210902.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajce.20210902.11},
  abstract = {The elastoplastic analysis of the surrounding rock of a circular tunnel is a very classic rock and soil mechanics problem. Previous scholars usually studied the situation under axisymmetric load, and they usually did not take the non-axisymmetric load distribution under the influence of ground stress and lateral pressure into account, which greatly affected its application in engineering practice. Approximate analytical solutions for calculating the plastic zone range, stress field and displacement field of the surrounding rock of a circular tunnel are inseparable from the consideration of the strength reduction and volumetric dilatancy characteristics of the rock material. The elastic-softening-residual plastic triple linear stress-strain model and the Mohr-Coulumb failure criterion are involved. The approximate analytical solutions of the residual stress field, strain field, displacement field and radius of the plastic zone in the elastic zone, plastic softening zone and surrounding plastic zone of the circular tunnel surrounding rock under axisymmetric load are deduced. The analytical solutions are valid only when the plastic zone is large and the lateral pressure coefficients 1≤λ<3. The approximate analytical method is close to the calculation result of finite element method and can replace the finite element method to carry out simple elastic-plastic analysis of surrounding rock.},
 year = {2021}
}

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TY  - JOUR
T1  - Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load
AU  - Zhang Xin
AU  - Zhang Xiangping
AU  - Wang Zhang
AU  - Lang Min
AU  - Zhao Suzhi
AU  - Du Yuxiang
AU  - Sun Jinshan
Y1  - 2021/04/12
PY  - 2021
N1  - https://doi.org/10.11648/j.ajce.20210902.11
DO  - 10.11648/j.ajce.20210902.11
T2  - American Journal of Civil Engineering
JF  - American Journal of Civil Engineering
JO  - American Journal of Civil Engineering
SP  - 31
EP  - 38
PB  - Science Publishing Group
SN  - 2330-8737
UR  - https://doi.org/10.11648/j.ajce.20210902.11
AB  - The elastoplastic analysis of the surrounding rock of a circular tunnel is a very classic rock and soil mechanics problem. Previous scholars usually studied the situation under axisymmetric load, and they usually did not take the non-axisymmetric load distribution under the influence of ground stress and lateral pressure into account, which greatly affected its application in engineering practice. Approximate analytical solutions for calculating the plastic zone range, stress field and displacement field of the surrounding rock of a circular tunnel are inseparable from the consideration of the strength reduction and volumetric dilatancy characteristics of the rock material. The elastic-softening-residual plastic triple linear stress-strain model and the Mohr-Coulumb failure criterion are involved. The approximate analytical solutions of the residual stress field, strain field, displacement field and radius of the plastic zone in the elastic zone, plastic softening zone and surrounding plastic zone of the circular tunnel surrounding rock under axisymmetric load are deduced. The analytical solutions are valid only when the plastic zone is large and the lateral pressure coefficients 1≤λ<3. The approximate analytical method is close to the calculation result of finite element method and can replace the finite element method to carry out simple elastic-plastic analysis of surrounding rock.
VL  - 9
IS  - 2
ER  -

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Author Information

Zhang Xin

China Railway 18 Bureau Group Co., Ltd, Tianjin, China
Zhang Xiangping

China Railway 18 Bureau Group Co., Ltd, Tianjin, China
Wang Zhang

Hubei Key Laboratory of Blasting Engineering, Jianghan University, Wuhan, China
Lang Min

China Railway 18 Bureau Group Co., Ltd, Tianjin, China
Zhao Suzhi

China Railway 18 Bureau Group Co., Ltd, Tianjin, China
Du Yuxiang

Hubei Key Laboratory of Blasting Engineering, Jianghan University, Wuhan, China
Sun Jinshan

Hubei Key Laboratory of Blasting Engineering, Jianghan University, Wuhan, China

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Plain Text BibTeX RIS

APA Style

Zhang Xin, Zhang Xiangping, Wang Zhang, Lang Min, Zhao Suzhi, et al. (2021). Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load. American Journal of Civil Engineering, 9(2), 31-38. https://doi.org/10.11648/j.ajce.20210902.11

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ACS Style

Zhang Xin; Zhang Xiangping; Wang Zhang; Lang Min; Zhao Suzhi, et al. Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load. Am. J. Civ. Eng. 2021, 9(2), 31-38. doi: 10.11648/j.ajce.20210902.11

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AMA Style

Zhang Xin, Zhang Xiangping, Wang Zhang, Lang Min, Zhao Suzhi, et al. Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load. Am J Civ Eng. 2021;9(2):31-38. doi: 10.11648/j.ajce.20210902.11

Copy | Download

@article{10.11648/j.ajce.20210902.11,
  author = {Zhang Xin and Zhang Xiangping and Wang Zhang and Lang Min and Zhao Suzhi and Du Yuxiang and Sun Jinshan},
  title = {Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load},
  journal = {American Journal of Civil Engineering},
  volume = {9},
  number = {2},
  pages = {31-38},
  doi = {10.11648/j.ajce.20210902.11},
  url = {https://doi.org/10.11648/j.ajce.20210902.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajce.20210902.11},
  abstract = {The elastoplastic analysis of the surrounding rock of a circular tunnel is a very classic rock and soil mechanics problem. Previous scholars usually studied the situation under axisymmetric load, and they usually did not take the non-axisymmetric load distribution under the influence of ground stress and lateral pressure into account, which greatly affected its application in engineering practice. Approximate analytical solutions for calculating the plastic zone range, stress field and displacement field of the surrounding rock of a circular tunnel are inseparable from the consideration of the strength reduction and volumetric dilatancy characteristics of the rock material. The elastic-softening-residual plastic triple linear stress-strain model and the Mohr-Coulumb failure criterion are involved. The approximate analytical solutions of the residual stress field, strain field, displacement field and radius of the plastic zone in the elastic zone, plastic softening zone and surrounding plastic zone of the circular tunnel surrounding rock under axisymmetric load are deduced. The analytical solutions are valid only when the plastic zone is large and the lateral pressure coefficients 1≤λ<3. The approximate analytical method is close to the calculation result of finite element method and can replace the finite element method to carry out simple elastic-plastic analysis of surrounding rock.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Analytical Elastoplastic Solutions for Deep-buried Circular Tunnels Under Asymmetric Load
AU  - Zhang Xin
AU  - Zhang Xiangping
AU  - Wang Zhang
AU  - Lang Min
AU  - Zhao Suzhi
AU  - Du Yuxiang
AU  - Sun Jinshan
Y1  - 2021/04/12
PY  - 2021
N1  - https://doi.org/10.11648/j.ajce.20210902.11
DO  - 10.11648/j.ajce.20210902.11
T2  - American Journal of Civil Engineering
JF  - American Journal of Civil Engineering
JO  - American Journal of Civil Engineering
SP  - 31
EP  - 38
PB  - Science Publishing Group
SN  - 2330-8737
UR  - https://doi.org/10.11648/j.ajce.20210902.11
AB  - The elastoplastic analysis of the surrounding rock of a circular tunnel is a very classic rock and soil mechanics problem. Previous scholars usually studied the situation under axisymmetric load, and they usually did not take the non-axisymmetric load distribution under the influence of ground stress and lateral pressure into account, which greatly affected its application in engineering practice. Approximate analytical solutions for calculating the plastic zone range, stress field and displacement field of the surrounding rock of a circular tunnel are inseparable from the consideration of the strength reduction and volumetric dilatancy characteristics of the rock material. The elastic-softening-residual plastic triple linear stress-strain model and the Mohr-Coulumb failure criterion are involved. The approximate analytical solutions of the residual stress field, strain field, displacement field and radius of the plastic zone in the elastic zone, plastic softening zone and surrounding plastic zone of the circular tunnel surrounding rock under axisymmetric load are deduced. The analytical solutions are valid only when the plastic zone is large and the lateral pressure coefficients 1≤λ<3. The approximate analytical method is close to the calculation result of finite element method and can replace the finite element method to carry out simple elastic-plastic analysis of surrounding rock.
VL  - 9
IS  - 2
ER  -

Copy | Download