Abstract

The time dependency of tunnelling results mainly from the rheological properties of the rock mass, the sequential excavation and the construction process of liner. This study focuses on the construction of lined circular tunnels in viscoelastic rock mass subjected to non-hydrostatic far-field stresses. The analytical solutions of stress and displacement for both rock mass and liner are developed. In the derivation, several linear viscoelastic models are adopted to analyse the rheological properties of the host rock, and the tunnel radius is regarded as time-dependent to simulate the excavation process of tunnel cross-section.

Two time-dependent potentials with undetermined coefficients are first introduced to express the displacements and stresses of the rock mass by using the complex potential theory and the Laplace transform technique. According to the boundary and compatibility conditions, a set of equations can be built in the Laplace space for these undetermined coefficients, where no-slip and full-slip rock-liner interface conditions are both considered. The time-dependent displacements and stresses for the rock mass and liner are finally achieved by solving these equations. The proposed solutions are verified by comprising with the results of finite element method. A comprehensive parametrical analysis is then conducted to investigate the influence of the lateral pressure coefficient, the installation time and stiffness of the lilner on the resulting displacements and stresses.

摘要

隧道掘进的时间依赖性主要来自于岩体的流变特性、顺序开挖和衬砌的施工过程。本研究的重点是在受到非静水静力远场应力的粘弹性岩体中建造衬砌圆形隧道。开发了岩体和衬砌应力和位移的解析解。推导中采用多种线性粘弹性模型对围岩流变特性进行分析，并以隧道半径为时变模拟隧道断面开挖过程。

首先利用复势理论和拉普拉斯变换技术，引入两个系数未定的时变势来表达岩体的位移和应力。根据边界条件和相容条件，可以在拉普拉斯空间中为这些待定系数建立一组方程，其中既考虑了无滑移也考虑了全滑移的岩衬界面条件。通过求解这些方程，最终得到岩体和衬砌的随时间变化的位移和应力。所提出的解决方案通过包含有限元方法的结果进行了验证。然后进行综合参数分析以研究侧压系数的影响，