多排弹性空心管桩屏障对平面SV波的隔离
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摘要
假定土体和管桩为各向同性的均质弹性体,将多排空心管桩构成的非连续屏障对入射平面SV波的隔离问题简化成二维平面问题,运用复变函数的保角映射方法和波场位移势函数展开法,根据管桩与周围土体介质完全联结(即应力和位移连续)以及管桩内侧自由的边界条件,得到了所研究问题的理论解。通过与有限元软件ABAQUS的模拟结果进行对比,验证了上述理论解及其计算程序的正确性,并进一步分析了管桩的壁厚、排数、数量以及入射SV波的频率等因素对隔离效果的影响,结论表明:隔离效果随着管桩壁厚的减小而提高;管桩由一排增加到两排时,最佳隔离区域向远处扩展,而由两排增加到三排时,最佳隔离区域则向两侧扩展;管桩排数不变,而数量增多时,屏障宽度范围内的隔离效果明显提高;入射频率增大时,隔离效果有所减小。这为多排桩屏障的隔振设计提供了理论依据和参考。
The soils and pipe piles are considered as homogeneous isotropic elastic media,and the isolation of incident plane SV waves by the discontinuous barriers composed of several rows of hollow pipe piles is simplified as a two-dimensional plane problem.The conformal mapping method of complex functions and the expansion method of wave functions are adopted,the stresses and displacements at the boundaries between the pipe piles and their adjacent soils are considered to be continuous and the inner sides of the pipe piles to be free,and then the theoretical solutions are obtained for the isolation problem.They are compared with the results simulated by FEM software of ABAQUS and proved to be correct.Finally,some factors that influence the isolation effects are studied,such as the wall depths,rows and total number of pipe piles and frequencies of incident plane SV waves.The results show that: the isolation effects increase when the wall depths of the pipe piles decrease;the best isolation areas develop to the far side when the number of rows increases from one to two,while they develop to the bilateral sides when the number of rows increases from two to three;the isolation effects increase obviously in the barrier width with the total number of pipe piles as to the same number of rows;and the isolation effects decrease when the incident frequencies of SV waves increase.These conclusions will provide some theoretical bases and references for the design of vibration isolation with several rows of pipe piles.
The soils and pipe piles are considered as homogeneous isotropic elastic media,and the isolation of incident plane SV waves by the discontinuous barriers composed of several rows of hollow pipe piles is simplified as a two-dimensional plane problem.The conformal mapping method of complex functions and the expansion method of wave functions are adopted,the stresses and displacements at the boundaries between the pipe piles and their adjacent soils are considered to be continuous and the inner sides of the pipe piles to be free,and then the theoretical solutions are obtained for the isolation problem.They are compared with the results simulated by FEM software of ABAQUS and proved to be correct.Finally,some factors that influence the isolation effects are studied,such as the wall depths,rows and total number of pipe piles and frequencies of incident plane SV waves.The results show that: the isolation effects increase when the wall depths of the pipe piles decrease;the best isolation areas develop to the far side when the number of rows increases from one to two,while they develop to the bilateral sides when the number of rows increases from two to three;the isolation effects increase obviously in the barrier width with the total number of pipe piles as to the same number of rows;and the isolation effects decrease when the incident frequencies of SV waves increase.These conclusions will provide some theoretical bases and references for the design of vibration isolation with several rows of pipe piles.
引文
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[12]杨在林,闫培雷,刘殿魁.SH波对浅埋弹性圆柱及裂纹的散射与地震动[J].力学学报,2009,41(2):229–235.(YANG Zai-lin,YAN Pei-lei,LIU Dian-kui.Scattering of SH-waves and ground motion by an elastic cylindrical inclusion and a crack in half space[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(2):229–235.(in Chinese))
[13]刘晶波,王振宇,杜修力,等.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46–51.(LIU Jing-bo,WANG Zhen-yu,DU Xiu-li,et al.Three-dimensional visco-elastic artificial boundaries in time domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46–51.(in Chinese))
[2]WOODS R D.Screening of surface waves in soils[J].Journal Soil Mechanics and Foundation Division,ASCE,1968,94(4):951–979.
[3]AVILéS J,SáNCHEZ-SESMA F.Piles as barriers for elastic waves[J].Journal of the Geotechnical Engineering Division,ASCE,1983,109(9):1133–1146.
[4]AVILéS J,SáNCHEZ-SESMA F.Foundation isolation from vibrations using piles and barriers[J].Journal of the Geotechnical Engineering Division,ASCE,1988,114(11):1854–1870.
[5]KATTIS S E,POLYZOS D,BESKOS D E.Modeling of pile wave barriers by effective trenches and their screening effectiveness[J].Soil Dynamics and Earthquake Engineering,1999,18(1):1-10.
[6]KATTIS S E,POLYZOS D,BESKOS D E.Vibration isolation by a row of piles using a 3-D frequency domain BEM[J].International Journal for Numerical Methods in Engineering,1999,46(5):713–728.
[7]徐平,夏唐代,周新民.单排空心管桩屏障对平面SV波的隔离效果研究[J].岩土工程学报,2007,29(1):131–136.(XU Ping,XIA Tang-dai,ZHOU Xin-min.Study on the effect of barrier of a row of hollow pipe piles for the isolation of incident plane SV wave[J].Chinese Journal of Geotechnical Engineering,2007,29(1):131–136.(in Chinese))
[8]GAO G Y,LI Z Y,YUE Z Q.Three-dimensional analysis of rows of piles as passive barriers for ground vibration isolation[J].Soil Dynamics and Earthquake Engineering,2006,26(11):1015–1027.
[9]LU J F,XU B,WANG J H.A numerical model for the isolation of moving-load induced vibrations by pile rows embedded in layered porous media[J].International Journal of Solids and Structures,2009,46(21):3771–3781.
[10]LIU D K,GAI B Z,TAO G Y.Applications of the method of complex function to dynamic stress concentration[J].Wave Motion,1982,4(4):293–304.
[11]VEKSLER N,IZBICKI J L,CONOIR J M.Elastic wave scattering by a cylindrical shell[J].Wave Motion,1999,29(3):195–209.
[12]杨在林,闫培雷,刘殿魁.SH波对浅埋弹性圆柱及裂纹的散射与地震动[J].力学学报,2009,41(2):229–235.(YANG Zai-lin,YAN Pei-lei,LIU Dian-kui.Scattering of SH-waves and ground motion by an elastic cylindrical inclusion and a crack in half space[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(2):229–235.(in Chinese))
[13]刘晶波,王振宇,杜修力,等.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46–51.(LIU Jing-bo,WANG Zhen-yu,DU Xiu-li,et al.Three-dimensional visco-elastic artificial boundaries in time domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46–51.(in Chinese))
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