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Mathematical Problems in Engineering
Volume 2017, Article ID 9523267, 10 pages
Research Article

Plastic Zone Analysis of Deep-Buried, Noncircular Tunnel and Application on the High-Speed Railway in the Karst Area

1School of Civil Engineering, Beijing Jiaotong University, Beijing, China
2Beijing Key Laboratory of Track Engineering, Beijing, China

Correspondence should be addressed to Hai Shi; moc.qq@665915615

Received 16 January 2017; Revised 26 March 2017; Accepted 11 April 2017; Published 13 August 2017

Academic Editor: Francesco Marotti de Sciarra

Copyright © 2017 Hai Shi and Mingzhou Bai. 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.


With the conformal mapping function provided by Verruijt, the outland of a noncircular tunnel can be mapped to a circular unit in the complex plane and then spread the analytic function into a Laurent series. The stress unified solution of oval and horseshoe cross section can be determined using Muskhelishvili’s complex variables function method. Subsequently, the solution can be taken into the Griffith strength failure criterion and determine the scale and shape of plastic zone in the tunnel surrounding rock. Aiming at the critical safety thickness between a concealed cave and tunnel in the karst area and determining whether the plastic zone of tunnel surrounding rock is connected with the plastic zone of cave as a judgment standard, the model of critical safety thickness among the concealed caves and tunnels is established. The numerical model is established in comparison with the computing method of rock plate critical safety thickness in actual engineering based on the Doumo tunnel engineering of Shanghai-Kunming (Guizhou segment) high-speed railway. The following conclusions can be drawn: the analytical approximation method has less indexes, and the output of this method is approximately close to actual engineering and numerical analysis, in which it is reliable and rational.