JZUS - Journal of Zhejiang University SCIENCE

Journal of Zhejiang University SCIENCE A 2014 Vol.15 No.6 P.395-404

Analytical solutions of stresses and displacements for deep circular tunnels with liners in saturated ground*

Author(s): Peng-fei Li^1,2, Qian Fang³, Ding-li Zhang³
Affiliation(s): 1. Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China; more
Corresponding email(s): lpf@bjut.edu.cn
Key Words: Deep tunnel, Seepage force, Plane strain model, Analytical solution, Numerical simulation

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Peng-fei Li, Qian Fang, Ding-li Zhang. Analytical solutions of stresses and displacements for deep circular tunnels with liners in saturated ground[J]. Journal of Zhejiang University Science A, 2014, 15(6): 395-404.

@article{title="Analytical solutions of stresses and displacements for deep circular tunnels with liners in saturated ground",
author="Peng-fei Li, Qian Fang, Ding-li Zhang",
journal="Journal of Zhejiang University Science A",
volume="15",
number="6",
pages="395-404",
year="2014",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1400023"
}

%0 Journal Article
%T Analytical solutions of stresses and displacements for deep circular tunnels with liners in saturated ground
%A Peng-fei Li
%A Qian Fang
%A Ding-li Zhang
%J Journal of Zhejiang University SCIENCE A
%V 15
%N 6
%P 395-404
%@ 1673-565X
%D 2014
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1400023

TY - JOUR
T1 - Analytical solutions of stresses and displacements for deep circular tunnels with liners in saturated ground
A1 - Peng-fei Li
A1 - Qian Fang
A1 - Ding-li Zhang
J0 - Journal of Zhejiang University Science A
VL - 15
IS - 6
SP - 395
EP - 404
%@ 1673-565X
Y1 - 2014
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1400023

Abstract
Chinese Summary
Academic Network
Reviewer Comment

Abstract: To investigate the displacement and stress distributions for deep circular tunnels with liners in saturated ground, an analytical model is proposed. For a deep tunnel with drainage conditions, plane strain conditions at any cross-section of the tunnel and the elastic regime of the linear elasticity for the remaining liner are assumed, while the ground is assumed to be linearly elastic and perfectly plastic with a failure surface defined by the Mohr-Coulomb criterion. The post-yield behavior of the ground follows the non-associated flow rule defined by the dilation angle. To solve the proposed problem, two procedures are presented. An axisymmetric model for a deep circular tunnel with a steady-state seepage condition is considered, and then a simple closed-form analytical solution is obtained with a common theoretical framework for the boundary conditions of a constant total head along the tunnel circumference. Assuming that certain ground displacements along the tunnel circumference have occurred before the installation of the liner, analytical solutions of stresses and displacements are derived with particular emphasis on the seepage and the stress release effect induced by tunnelling. The proposed analytical model is validated by numerical simulation.

深埋圆形富水隧道应力与位移的弹塑性解

研究目的：推导获得深埋圆形富水隧道应力场与位移场分布的弹塑性解析解。
创新要点：基于弹性力学厚壁圆筒受均布压力的拉姆解答和Mohr-Coulomb屈服条件，推导了考虑渗流作用和应力释放时含衬砌深埋隧道的弹塑性解，并采用FLAC^3D有限差分程序验证了其正确性。
研究方法：通过理论分析建立考虑渗流作用和应力释放的含衬砌深埋圆形隧道的解析模型（图1），然后推导了基于Mohr-Coulomb屈服准则的隧道围岩与衬砌渗流场、位移场和应力场计算的弹塑性解析公式，并通过数值模拟程序（图2）验证了推导公式的正确性。
重要结论：基于前人研究基础，推导获得了深埋富水隧道应力与位移场分布的理论解析解，并通过数值模拟方法验证了其正确性。该解析解一方面可以用于深埋高水头隧道的预设计，如预测隧道周围的水压力、应力场和位移场分布规律，另一方面可用于校核大型复杂数值模型的正确性。

关键词：深埋隧道；渗流力；平面应变模型；应力释放；塑性半径

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深埋圆形富水隧道应力与位移的弹塑性解

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