基于非局部Biot理论下饱和土中深埋圆柱形衬砌对平面弹性波的散射

徐长节; 丁海滨; 童立红; 杨园野

doi:10.11779/CJGE201809001

基于非局部Biot理论下饱和土中深埋圆柱形衬砌对平面弹性波的散射 English Version

徐长节^{1, 2},
丁海滨¹,
童立红^1, ,,
杨园野¹

1. 江西省岩土工程基础设施安全与控制重点实验室（华东交通大学）,江西南昌 330013;
2. 浙江大学滨海和城市岩土工程研究中心,浙江杭州 310058

基金项目: 国家重点基础研究发展计划（“973”计划）项目（2015CB057801）; 海底盾构隧道关键设计理论与工程对策项目（51338009）; 江西省青年科学基金项目（20171BAB216047）

详细信息

作者简介:
徐长节(1972- ),男,教授,博士生导师,主要从事地下空间及隧道工程研究。E-mail: xucj@zju.edu.cn。

通讯作者:
童立红，E-mail：lhtong@ecjtu.edu.cn

中图分类号: TU435
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出版历程
- 收稿日期: 2017-02-26
- 发布日期: 2018-09-24

Scattering waves generated by cylindrical lining in saturated soil based on nonlocal Biot theory

1. Jiangxi Key Laboratory of Infrastructure Safety Control in Geotechnical Engineering, East China Jiaotong University, Nanchang 330013, China;
2. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China

摘要

摘要: 基于Biot饱和多孔介质理论和非局部弹性理论,构建了非局部Biot运动方程及本构方程。利用波函数展开法及饱和土与衬砌边界连续条件和衬砌内边界自由边界条件,求解了饱和土体中圆柱形衬砌对平面波散射问题的解析解。并通过将该解退化为单相介质中及经典Biot理论下衬砌对平面P波散射稳态解,验证了计算结果的正确性。研究结果表明,衬砌内边界及外边界动应力集中因子均随非局部因子的增大而减小;隧道内边界动应力集中因子分布曲线随非局部因子的减小而扩大;当入射波频率大于0.045 MHz时,饱和土中空隙尺寸及空隙动力的影响将不可忽略;非局部因子一定时,衬砌外径与内径比越大则衬砌内边界动应力集中因子越大,且当衬砌较薄时,衬砌内边界动应力集中因子可能产生负值。
- 非局部弹性理论 /
- Biot理论 /
- 饱和土 /
- 动应力集中系数 /
- 圆柱形衬砌 /
- 散射
Abstract: Based on the Biot theory and the nonlocal elastic theory, the nonlocal Biot governing equations are proposed. The analytical solutions to the scattering wave fields generated by the cylindrical lining structure under incident plane waves are obtained utilizing the wave function expansion method under specific boundary conditions. The solutions are verified by degenerating the two-phase materials into single-phase ones and by comparing with the classical Biot theory as well. It is shown that the dynamic stress concentration factors on the inner and outer surfaces of the lining decrease with the increasing nonlocal factor. The distribution curves of dynamic stress concentration factor on the inner surface of the tunnel increase with the decrease of nonlocal factor. The influences of pore size and porosity dynamics in saturated soils cannot be ignored when the frequency of incident waves is greater than 0.045 MHz. For a certain nonlocal factor, the dynamic stress concentration factor increases with the increase of the ratio of outer radius to inner radius of the lining. The dynamic stress concentration factor may be negative on the inner surface of the lining for a thin lining.
- nonlocal elasticity theory /
- Biot theory /
- saturated soil /
- dynamic stress concentration factor /
- cylindrical lining /
- scattering

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参考文献(18)

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