排桩对柱面SH波散射问题研究:解析求解  

Study on Scattering of Cylindrical SH Waves by a Row of Piles:Analytical Solution

作　　者：巴振宁[1,2,3] 刘博佳 付继赛 Ba Zhenning;Liu Bojia;Fu Jisai(School of Civil Engineering,Tianjin University,Tianjin 300072,China;Laboratory of Earthquake Engineering Simulation and Seismic Resilience(Tianjin University),China Earthquake Administration,Tianjin 300350,China;Key Laboratory of Coast Civil Structure Safety(Tianjin University),Ministry of Education,Tianjin 300350,China;Tianjin International Engineering Institute,Tianjin University,Tianjin 300072,China)

机构地区：[1]天津大学建筑工程学院,天津300072 [2]中国地震局地震工程综合模拟与城乡抗震韧性重点实验室(天津大学),天津300350 [3]滨海土木工程结构与安全教育部重点实验室(天津大学),天津300350 [4]天津大学国际工程师学院,天津300072

出　　处：《吉林大学学报（地球科学版）》2021年第5期1306-1315,共10页Journal of Jilin University：Earth Science Edition

基　　金：国家自然科学基金项目(51778413)。

摘　　要：采用波函数展开法结合Graf加法定理,利用桩体与土体之间的位移和应力连续边界条件,给出了全空间单排桩对柱面SH波散射解析解,并采用傅里叶逆变换,求得时域结果。该方法考虑了入射波曲率的影响,在频域内分析了柱面SH波入射时排桩散射的频谱规律,给出了时域排桩柱面SH波散射位移云图,讨论了桩数与桩间距对柱面SH波入射时排桩散射的影响。研究表明:在振源距排桩较近(d/a=10)时,低频段(η=0~1.0)排桩对柱面SH波的隔离作用显著;振源距排桩较远时,各频段排桩对柱面SH波的隔离作用均较为显著。桩间距固定时,增加桩数,排桩后方首次出现的最大位移响应相应减小,排桩散射的影响范围随之增大;对柱面SH波进行阻隔时,为提高阻隔效率的同时节约成本,不仅需要考虑桩数,还应考虑波源与桩体、桩间空隙相对位置的影响;排桩分布宽度固定时,由于入射波曲率对排桩散射的影响,减小桩间距,排桩后方首次出现的最大位移响应有可能会出现放大的情况,故应采用合理的桩间距对柱面SH波进行阻隔。The wave function expansion method as well as the Graf addition theorem, combined with the continuous boundary conditions of displacements and stresses between the piles and the soil, are addressed to obtain the analytical full-space solutions of the cylindrical SH waves scattering by a single row of piles, and the time-domain solutions are gained by the inverse Fourier transform. In this method, the influence of the curvature of the incident waves is taken into account. In the frequency domain, the spectrum laws of the scattering wave fields due to piles under cylindrical SH waves incidence are analyzed. In the time domain, the contour maps of displacements near the piles due to the scattered cylindrical SH waves are given, and the influence of the number of piles and the distance between the piles on the scattering by the piles are discussed. The results show that: 1) The isolation effects of the piles on the low-frequency band(η=0-1.0) of the cylindrical SH waves are significant when the vibration source is close to the pile(d/a=10), while those on each frequency band are significant when the vibration source is far from the piles;2) When the pile spacing is fixed, the first-appearing maximum displacement behind the row of piles decreases with increasing the number of piles, as well as the range of influence of the scattering of the row of piles increases accordingly;3) In order to improve the efficiency of isolation and save cost at the same time, the relative position of the vibration source to the piles and to the gap between the piles should also be considered;4) When the row piles distribution width is fixed, the first-appearing maximum displacement behind the row of piles may be amplified with the reduction of pile spacing, due to the effect of incident wave curvature on the scattering of the row pile, so that a reasonable pile spacing should be used to block the cylindrical SH waves.

关 键 词：柱面SH波 波函数展开法 排桩散射 时域 

分 类 号：TU473[建筑科学—结构工程]