周期分布群桩屏障对平面弹性波隔振效应的解析求解

doi:10.13722/j.cnki.jrme.2019.1201

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摘要基于平面波入射下周期分布散射体周围波场的周期分布特性，创造性地提出一种求解无限周期分布群桩屏障对弹性波隔振效应的解析方法。方法首先推导适用于任意坐标系间波函数转换的Graf加法定理，进而采用波函数展开法，充分利用不同周期单元周围的波场完全相同但仅因位置的不同而在频域内相差一个相位的特征，仅需选取一个周期单元分析即可求解整个群桩屏障的散射波场。该解析方法弥补了以往理论分析中桩数较多时难以求解的不足，同时具有精度高、计算量低和显著降低求解时间的优点，便于分析桩体数量较多的群桩屏障隔振规律。重点讨论桩排数、桩体间距和群桩排列方式等因素对隔振效果的影响，结果表明：(1) 群桩屏障对SH波的隔离效果主要体现在归一化频率0.2～1.2的较低频段，对SV波的隔离效果主要体现在0.6～1.8的中等频段，对P波的隔离效果主要体现在1.2～1.5和2.2～2.8左右的中等和较高频段；(2) 桩排数的增加对SH波隔离效果的提高随每排桩的增加能够提高至50%，对SV波隔离效果的提高随每排桩的增加能够提高至33%，而对P波隔离效果的提高随每排桩的增加提高不超过10%；(3) 减小桩体间距有助于提高群桩屏障的隔振效果，但减小排间距的影响较小，而减小列间距则提升明显；(4) 整体上梅花形排列的隔振效果优于矩形排列，仅在入射波频率h = 0.7～1.8的一个小频段内矩形排列优于梅花形排列。

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	巴振宁1
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	刘世朋1
	吴孟桃1
	梁建文1
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关键词 ：桩基础, 群桩隔振, 周期分布, 弹性波, 波函数展开法, Graf加法定理

Abstract：Based on the periodic characteristics of wave field around the periodically distributed scatters under incident plane wave，an analytical method is creatively proposed to solve the vibration isolation effect of infinite periodically distributed group piles barrier against elastic wave. Graf addition theorem which is suitable for wave function transformation between arbitrary coordinate systems is derived firstly. Then，the wave function expansion method and one different phase in the frequency domain around different period units is used，so that only one periodic unit needs to be selected for analysis to solve the scattering wave field of the whole pile group barrier. This analytical method makes up for the shortcomings of the previous theoretical analysis when there are a number of piles，and at the same time， has the advantages of high accuracy，low calculation amount and significantly reducing the solution time，which is convenient to analyse the vibration isolation law of pile group barrier with a large number of piles. In this paper，the influence of pile row number，pile spacing and arrangement on the vibration isolation effect is discussed. The results show that the isolation effects of group piles barrier on SH，SV and P waves are mainly reflected in the lower frequency band (0.2–1.2)，in the middle frequency band of (0.6–1.8)，and in the middle and higher frequency bands (1.2–1.5 and 2.2–2.8)，respectively. With increasing one row piles，the isolation effects against SH，SV and P waves can be respectively increased by 50%，33% and not more than 10%. Reducing the distance between piles is helpful to improve the vibration isolation effect of pile group barrier，and compared with reducing the distance between rows，the effect of reducing the distance between columns is more obvious. On the whole，the vibration isolation effect of the quincunx arrangement is better than that of the rectangular arrangement except for the case of the incident wave frequency h = 0.7–1.8.

Key words： pile foundations;group piles¢')" href="#">

pile foundations;group piles¢

')" href="#">vibration isolation;periodic distribution;elastic waves;wave function expansion method;Graf addition theorem

引用本文:

巴振宁1，2，3，刘世朋1，吴孟桃1，梁建文1，2，3. 周期分布群桩屏障对平面弹性波隔振效应的解析求解[J]. 岩石力学与工程学报, 2020, 39(7): 1468-1482.
BA Zhenning1，2，3，LIU Shipeng1，WU Mengtao1，LIANG Jianwen1，2，3. Analytical solution for isolation effect of periodically distributed pile-group barriers against plane elastic wave#br#. , 2020, 39(7): 1468-1482.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2019.1201 或 http://rockmech.whrsm.ac.cn/CN/Y2020/V39/I7/1468

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