Comparison Between Exact Solutions and Approximate Solutions of Deep Tunnels

ZHOU Feng-xi; CAO Xiao-lin

doi:10.21656/1000-0887.370196

Volume 38 Issue 10

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ZHOU Feng-xi, CAO Xiao-lin. Comparison Between Exact Solutions and Approximate Solutions of Deep Tunnels[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1166-1179. doi: 10.21656/1000-0887.370196

Citation:

ZHOU Feng-xi, CAO Xiao-lin. Comparison Between Exact Solutions and Approximate Solutions of Deep Tunnels[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1166-1179. doi: 10.21656/1000-0887.370196

Citation:

ZHOU Feng-xi, CAO Xiao-lin. Comparison Between Exact Solutions and Approximate Solutions of Deep Tunnels[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1166-1179. doi: 10.21656/1000-0887.370196

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Comparison Between Exact Solutions and Approximate Solutions of Deep Tunnels

doi: 10.21656/1000-0887.370196

ZHOU Feng-xi^1,2,
CAO Xiao-lin¹

¹School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, P.R.China;²Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou 730050, P.R.China

Funds: The National Natural Science Foundation of China（51368038）

Received Date: 2016-06-21
Rev Recd Date: 2017-03-30
Publish Date: 2017-10-15

Abstract

Abstract

Deep buried tunnels with different cross-section shapes were analyzed through comparison between the analytical solutions and the approximate solutions obtained by the equivalent radii for the surrounding rock stresses. Firstly, according to the basic theory of complex variable functions, the stress components were obtained and the analytical expressions for the surrounding rock stresses of deep tunnels with various section shapes including the circle, the ellipse, the rectangle and the straight-wall arch, were given. Secondly, with the converted forms of the equivalent radii, the section boundary was transformed into a standard circle and the surrounding rock stress components were calculated by means of the Lamé solution. Finally, in view of the variable parameters of the tunnel cross-section shapes, comparisons between the exact solutions and the approximate solutions were conducted based on numerical examples, and the accuracy of the converted equivalent radii was discussed. The accuracy of the analytic solutions of the complex variable functions was proved, and the accuracy of the equivalent radii was verified for different cross-section shapes. The results show that the similarity between the solutions of the converted forms and the exact solutions of the equivalent radii is closely related to the cross-section shapes of the tunnels and the geometrical parameters.
- complex variable function,
- surrounding rock stress,
- deep tunnel,
- equivalent radius

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References(17)

References

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