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Advances in Civil Engineering
Volume 2018, Article ID 8401482, 14 pages
Research Article

Using the Schwarz Alternating Method to Identify Critical Water-Resistant Thickness between Tunnel and Concealed Cavity

1International Joint Research Laboratory of Henan Province for Underground Space Development and Disaster Prevention, Jiaozuo, Henan 454003, China
2School of Civil Engineering, Henan Polytechnic University, Jiaozuo, Henan 454003, China
3School of Highway, Chang’an University, Xi’an 710064, China
4College of Chemistry and Chemical Engineering, Henan Polytechnic University, Jiaozuo, Henan 454003, China

Correspondence should be addressed to Jianxun Chen; nc.ude.dhc@9691xjnehc

Received 25 August 2016; Revised 11 July 2017; Accepted 27 July 2017; Published 29 January 2018

Academic Editor: Cumaraswamy Vipulanandan

Copyright © 2018 Jiaqi Guo et al. 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.


This paper aims to estimate the stability of the water-resistant strata between the tunnel and the small-medium-sized concealed cavity filled with high-pressurized water or other fillings at optional position around tunnel through solving the double-hole problem. The analytical method to identify the critical water-resistant thickness is proposed based on the Schwarz alternating method and Griffith strength criterion, and the program to calculate the critical thickness was prepared according to this method using mathematical software. Parametric study of the critical thickness indicates that the critical water-resistant thickness will increase with the buried depth of the tunnel and cavity size; the lateral pressure coefficient has more complicated influence on the critical thickness, which is affected by cavity position; when the cavity is filled with sand or gravel, the critical water-resistant thickness will decrease with the increase of the filling pressure; and when the cavity is filled with the high-pressurized water, the critical thickness will decrease as the water pressure initially and increase afterwards. The analytical result of the critical thickness is consistent with that obtained by numerical simulation using the user-defined program based on FLAC3D, demonstrating the rationality and feasibility of the proposed method in this study.