无源环境振动的有限元分析方法及在北京光源工程应用

顾晓强; 余宽原; 黄茂松; 刘鑫; 闫芳; 吴德顺

doi:10.11779/CJGE202212011

无源环境振动的有限元分析方法及在北京光源工程应用 English Version

顾晓强^{1, 2},
余宽原¹,
黄茂松^{1, 2, ,},
刘鑫¹,
闫芳³,
吴德顺¹

1.
同济大学土木工程学院地下建筑与工程系, 上海 200092
2.
同济大学岩土与地下工程教育部重点实验室, 上海 200092
3.
中国科学院高能物理研究所, 北京 100049

基金项目:

上海市教育发展基金会和上海市教育委员会“曙光计划”资助项目 20SG22

中央高校基本科研业务费专项资金资助项目 02002150144

详细信息

作者简介:
顾晓强(1981—)，男，浙江桐乡人，博士，教授，主要从事土动力学与岩土地震工程等方面的研究

通讯作者:
黄茂松, E-mail: mshuang@tongji.edu.cn

中图分类号: TU43
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出版历程
- 收稿日期: 2021-11-20
- 网络出版日期: 2022-12-13
- 刊出日期: 2022-11-30

Finite element method for analyzing environmental vibration without apparent sources and its application in Beijing High-Energy Photon Source

1.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
2.
Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China
3.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

摘要

摘要: 无源环境微振动是指工程场地中没有明显振源时存在的微小振动，其可能导致高精密科学装置无法正常工作，如何准确分析无源条件下结构的环境微振动是此类工程亟需攻克的难题。系统介绍了一种无源环境条件下微振动的有限元分析方法。首先采用实测与理论方法得到地表任意点的振动时程，再利用传递矩阵法计算土层瑞利波弥散曲线及各频率振动沿深度衰减因子，再结合地表振动时程可计算出任意深度处的振动时程。将上述方法计算得到的每个节点的振动时程施加到有限元模型边界的相应节点上，使有限元模型的边界振动场与实际环境微振动场趋于一致。最终将该方法应用于国家“十三五”重大科技基础设施北京高能同步辐射光源工程(HEPS)地基基础的环境微振动分析，结果表明该方法能很好地反映无源振动的特性，为类似高精密科学装置的无源环境微振动分析提供了重要参考。
- 环境振动 /
- 动力有限元 /
- 传递矩阵法 /
- 瑞利波 /
- 振动随深度衰减
Abstract: The environmental vibration without apparent sources refers to the vibration with very small amplitude in the field where there are no apparent excitation sources. It may significantly affect the normal operation of high-precision scientific apparatuses, and therefore appropriate methods are needed to analyze such environmental vibration precisely. A dynamic finite element method is introduced to analyze the environmental vibration without apparent sources in this study. Firstly, the time histories of vibration at the soil surface are obtained through the field measurements. Then, the transfer-matrix method is utilized to calculate the dispersion curve of the Rayleigh waves and the vibration attenuation factors with depth for each frequency. With the measured time histories on the ground and the attenuation factors, the time histories at different depths can be calculated. The calculated time history at each node is applied to the corresponding node on the finite element model boundary, which ensures the similarity of vibration conditions in the model and the reality. Finally, the proposed method is adopted to analyze the environmental vibration of the raft foundation of High-Energy Photon Source (HEPS). The results indicate that the proposed method can successfully capture the characteristics of vibration without apparent sources and provide useful reference for similar projects.
- environmental vibration /
- dynamic finite element method /
- transfer-matrix method /
- Rayleigh wave /
- vibration attenuation along depth

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图 1 无源振动分析模型示意图

Figure 1. Schematic diagram of analysis model for vibration without apparent sources

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图 2 地面振动确定方法的流程图

Figure 2. Flow chart for determining ground surface vibration

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图 3 计算某一深度处位移时程的流程图

Figure 3. Flow chart for calculating vibration at a certain depth

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图 4 北京光源效果图^[15]

Figure 4. Schematic diagram of HEPS ^[15]

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图 5 北京光源工程有限元模型图

Figure 5. Finite element model for HEPS

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图 6 北京光源工程场地实测振动位移时程

Figure 6. Time histories of measured displacement at HEPS site

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图 7 北京光源分层地基瑞利波弥散曲线

Figure 7. Dispersion curve of Rayleigh waves at HEPS site

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图 8 北京光源地基各频率位移随深度衰减因子

Figure 8. Attenuation factors of Rayleigh waves at HEPS site

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图 9 各深度处的计算位移时程

Figure 9. Time histories of calculated displacement at different depths

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图 10 纯地基模型地表各节点位移振幅

Figure 10. Amplitudes of surface vibration displacement at different positions for model without structures

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图 11 北京光源工程场地和基础振动位移RMS值

Figure 11. RMS values of vibration of soil and foundation

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表 1 高精密科学装置对基础振动的控制标准^{[2, 8, 10]}

Table 1 Control criteria of vibration of foundation of high-precision scientific equipments ^{[2, 8, 10]}

装置名称	1~100 Hz竖向振动位移均方根/nm
上海光源	< 150(安静时段)，< 300(嘈杂时段)
软X射线自由电子激光	< 500
硬X射线自由电子激光	< 150
北京高能同步辐射光源	< 25
注：安静时段系指0：00—4：00；嘈杂时段系指4：00—24：00。

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表 2 北京光源工程地基土层分布及参数

Table 2 Soil profile and parameters at HEPS site

土层	厚度/m	密度 /(kg·m^-3)	压缩波速/(m·s^-1)	剪切波速/(m·s^-1)	泊松比	弹性模量 /MPa
①素填土	1	1910	636	173	0.460	166.9
②₁卵石	11	2200	952	344	0.425	742.0
②₂卵石	6	2200	1451	492	0.435	1528.4
④全风化基岩	8	2250	1962	777	0.407	3822.5
⑤强风化基岩	4	2350	2253	1011	0.374	6600.7
⑥中风化基岩	21	2590	3616	1547	0.388	17206.8
⑦微风化基岩	49	2680	4302	1936	0.373	27583.3

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