Abstract

Lining is gaining acceptance in underground excavations because of its reinforcing and protecting capacities. The purpose of this paper was to derive an analytic expression based on the complex variable method to describe the behaviour of a tunnel with a liner of finite thickness. The stress functions have been expressed as Laurent series where the infinite undetermined coefficients are obtained using force and displacement boundary conditions at the inner face, liner–rock interface and far-field boundaries. The finite element method has been used to verify the proposed solution; a good agreement has been obtained both in the surrounding rock mass and within the liner. In addition, based on the verified solution, the liner effect on the critical position of the interface has been investigated by applying Mohr-Coulomb’s failure criterion. A detailed parametric study shows that the relative liner thickness, relative stiffness and lateral stress coefficient have a great influence on the failure position, while the internal friction angle of the rock has a slight effect on the results. The proposed analytical solution is not restricted to the liner thickness, and the stress distribution within the liner is obtained accordingly; the solution can be generalised to other applications such as backfill analysis by setting the liner thickness equal to the radius of the opening.

摘要

衬砌因其加固和保护能力而在地下挖掘中得到认可。本文的目的是推导出一个基于复变量法的解析表达式来描述具有有限厚度衬砌的隧道的行为。应力函数已表示为 Laurent 级数，其中无限未定系数是使用内表面、衬层-岩石界面和远场边界处的力和位移边界条件获得的。有限元方法已用于验证所提出的解决方案；在围岩体和衬管内都获得了良好的一致性。此外，在验证解的基础上，应用 Mohr-Coulomb 失效准则研究了线性对界面临界位置的影响。详细的参数研究表明，相对衬层厚度、相对刚度和侧向应力系数对破坏位置影响很大，而岩石的内摩擦角对结果影响较小。所提出的解析解不限于衬里厚度，并据此得到衬里内的应力分布；通过将衬垫厚度设置为开口半径，该解决方案可以推广到其他应用，例如回填分析。并据此得到衬里内的应力分布；通过将衬垫厚度设置为开口半径，该解决方案可以推广到其他应用，例如回填分析。并据此得到衬里内的应力分布；通过将衬垫厚度设置为开口半径，该解决方案可以推广到其他应用，例如回填分析。