流变岩体中椭圆洞室断面开挖过程的力学分析

王华宁; 蒋明镜; 何平

流变岩体中椭圆洞室断面开挖过程的力学分析 English Version

1. 同济大学航空航天与力学学院,上海 200092; 2. 同济大学土木工程学院地下建筑与工程系,上海 200092

基金项目: 上海市自然科学基金项目(11ZR1438700)

详细信息

作者简介:
王华宁(1975- )，女，副教授，主要从事岩土工程中数值与解析方法研究。E-mail: wanghn@ tongji.edu.cn。

中图分类号: TU452；TB12
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出版历程
- 收稿日期: 2013-01-13
- 发布日期: 2013-11-19

Analytical solutions for elliptical tunnels in rheological rock considering excavation

1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China; 2. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 给出了黏弹性流变岩体中深埋椭圆隧洞断面开挖过程中力学响应的解析解答。通过设定长短半轴随时间变化的函数可模拟施工过程。首先,结合变边界黏弹性问题对应关系和平面弹性复变方法,求得岩体应力及开挖引起位移的统一表达。在推导中,通过建立逆映射函数,分离出参与Laplace变换的时间。然后,对模拟为Boltzmann黏弹模型的岩石材料,给出了积分形式的位移表达式。最后,针对不同类型岩石进行不同开挖方式和速度下无量纲位移及应力的参数分析。分析表明,施工方式对位移与应力有明显影响。给出的解析解答可用于地下椭圆孔型隧道在开挖过程中的力学分析,并可作为实际工程初步设计的手段。
- 流变岩体 /
- 椭圆洞室 /
- 黏弹性 /
- 开挖 /
- 解析解
Abstract: Sequential excavation is often adopted in construction of large tunnels. The analytical solutions for deeply buried elliptical tunnels in rheological rock considering the time-dependent excavation are derived. In order to simulate the design process of excavation, the values of the major and the minor axes are assumed to be arbitrarily time-dependent functions. First, the general expressions for the stresses and the additional displacements due to excavation are derived by using the complex variable method and the corresponding principle of time-dependent boundary problem. In the derivation, the inverse mapping function is introduced to detach the time variable which should participate in the Laplace transformation. Then, the explicit analytical expressions in integral form are obtained by simulating the rock mass in the Boltzmann viscoelastic model. Finally, the parametric analysis of the stresses and displacements is then performed to investigate the influence of the excavation process and the rate for different types of rock. The results show that the stresses and displacements are greatly affected by the excavation process. The proposed solutions can be used in the mechanical analysis of excavation of elliptical tunnels, and are valuable in the preliminary design of underground tunnels.
- rheological rock /
- elliptical tunnel /
- viscoelasticity /
- excavation /
- analytical solution

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参考文献(20)

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