借助复变函数的保角变换法将有限长度的空沟映射变换为单位圆，根据空沟四周完全自由的边界条件，运用波动函数展开法得到了空沟对纵波(P波)和剪切波(SV波)隔离的理论解答。引入位移比值(屏障后某点由入射波波、散射波产生的总位移与入射波单独产生的位移之比)，以入射P波为例，计算了沟宽0.4m、沟长分别为3.0m、4.0m、5.0m和6.0m共4条空沟的位移比值，通过比较发现：随着空沟长度的增加，最佳隔振效果明显提高，区域明显增大；当空沟长度达到6.0m时，靠近空沟的区域的隔振效果超过了70%，隔振效果比较理想。最后对比了空沟和单排柱腔列的隔振效果，结果表明：由于单排柱腔列产生波的透射和绕射，而空沟仅产生波的绕射，6.0m长空沟的最佳隔振效果与8根半径1.0m的单排柱腔列相当，因此在场地和施工条件都允许的前提下，宜优先考虑空沟进行隔振。
Abstract
An open trench with finite length was transformed to a unit circle with the conformal mapping method of complex functions,the boundaries of the trench were considered as free,theoretical solutions to isolation problems of longitudinal waves (P waves) and shear waves (SV waves) with an open trench were obtained based the wave function expansion method.The normalized displacement amplitudes were introduced,they were the ratios of displacement amplitudes of soil behind a barrier caused by both incident P or SV waves and scattering P and SV waves to those only by incident P or SV waves.Only incident P waves were taken as examples,and 4 trenches with a width of 0.4 m and lengths of 3.0 m,4.0 m,5.0 m and 6.0 m were analyzed.The results showed that the isolation effect and effective isolation zones increase obviously when the trench length increases from 3.0 m to 6.0 m,and the isolation effect exceeds 70% behind the trench when its length is 6.0 m,it reaches the in-situ test results of an open trench to isolate the impact loads.Finally,the isolation effect of an open trench and that of a discontinuous barrier composed of a row of cylindrical cavities were compared,and the results showed that because wave diffracting and trasmitting occur in a row of cylindrical cavities while only wave diffracting occurs in a trench,so the isolation effect of a trench with length of 6.0 m is equivalent to that of a row of 8 cylindrical cavities with a radius of 1.0 m,and so an open trench is the first and the best choice for the vibration isolation under the permission of field and operation conditions.
关键词
空沟 /
平面纵波 /
隔离效果 /
保角映射 /
隔振设计
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Key words
open trench /
plane longitudinal waves /
isolation effect /
conformal mapping method /
vibration isolation design
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参考文献
[1] 凌育洪, 吴景壮, 马宏伟. 地铁引起的振动对框架结构的影响及隔振研究-以某教学楼为例[J]. 振动与冲击, 2015, 34(4): 184-189. (LING Yu-hong, WU Jing-zhuang, MA Hong-wei. Effects of subway vibration on a frame structure and its vibration isolation[J]. Journal of Vibration and Shock, 2015, 34(4): 184-189. (in Chinese))
[2] Woods R D. Screening of surface waves in soils[J]. Journal of Soil Mechanics and Foundation Engineering. ASCE, 1968, 94 (4): 951-979.
[3] Richart F E, Woods R D. Vibration of soils and foundations[M]. New Jersey: Prentice-Hall, INC, Englewood Cliffs, 1987: 130-142.
[4] Erkan Ç, Seyhan F, Günay B et al. Field experiments on wave propagation and vibration isolation by using wave barriers[J]. Soil Dynamics and Earthquake Engineering, 2009, 29(5): 824-833.
[5] 徐平, 张天航, 石明生, 等. 空沟对冲击荷载隔离的现场试验与数值模拟[J]. 岩土力学, 2014, 35(s1): 341-346. (XU Ping, ZHANG Tian-hang, SHI Ming-sheng, et al. In-situ test and numerical simulation of isolation of impact loads by open trenches[J]. Rock and Soil Mechanics, 2014, 35(s1): 341-346. (in Chinese))
[6] Ulgen D, Toygar O. Screening effectiveness of open and in-filled wave barriers: A full-scale experimental study[J]. Construction and Building Materials, 2015, 86(5): 12-20.
[7] Adam M and Estorff O. Reduction of train-induced building vibrations by using open and filled trenches[J]. Computer Structure, 2005, 83: 1-24.
[8] 淳庆, 潘建吾. 减振沟在强夯施工时的减振效果研究[J]. 振动与冲击, 2010, 29(6): 115-120. (CHUN Qing, PAN Jian-wu. Vibration-isolating effect of vibration-isolating slot in the process of dynamic compaction construction[J]. Journal of Vibration and Shock, 2010, 29(6): 115-120. (in Chinese))
[9] 王晓, 严中保, 杜涵文. 上海自由电子激光工程隔振沟减振数值分析[J]. 振动与冲击, 2012, 31(15): 190-194. (WANG Xiao, YAN Zhong-bao, DU Han-wen. Numerical analysis of vibration-attenuation effect of trenches in the engineering project of Shanghai free electron laser[J]. Journal of Vibration and Shock, 2012, 31(15): 190-194 (inChinese)).
[10] 赵凯, 刘长武, 张国良. 用弹性力学的复变函数法求解矩形硐室周边应力[J]. 采矿与安全工程学报, 2007, 24(3): 361-365. (ZHAO Kai, LIU Chang-wu, ZHANG Guo-liang. Solution for perimeter stresses of rocks around a rectangular chamber using the complex function of elastic mechanics[J]. Journal o f Mining & Safety Engineering, 2007, 24(3): 361-365. (in Chinese))
[11] 徐平. 多排桩非连续屏障对平面弹性波的隔离[J]. 岩石力学与工程学报, 2012, 31(Supp 1): 3159-3166. (XU Ping. Isolation of Plane elastic waves by discontinuous barriers composed of several rows of piles[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(Supp 1): 3159-3166. (in Chinese))
[12] 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): 293 - 304.
[13] 徐平. 多排柱腔列对平面P波和SH波的隔离[J]. 工程力学, 2011, 28(5): 78-83. (XU Ping. Isolations of plane P and SH waves by barriers composed of several rows of cylindrical cavities[J]. Engineering Mechanics, 2011, 28(5): 78-83. (in Chinese)
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