Analysis of elastic wave scattering and vibration isolation performance of multiple open trenches: SH incident
ZHOU Fengxi1, 2, LIANG Yuwang1, LIU Jia1
1.School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China;
2. Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou University of Technology, Lanzhou 730050, China
Abstract：In foundation vibration control, the use of single open trench makes the isolation efficiency unsatisfactory due to low diffraction efficiency. Therefore, multiple open trenches vibration isolation barriers are set up to block the propagation of vibration waves many times to achieve ideal vibration isolation effect. According to the basic theory of elastic dynamics, the wave function expansion is carried out in the complex number domain, and the infinite-order linear equations are established by the free boundary conditions of the stress around the open trenches and by dint of conformal mapping theory and multi-polar coordinate transformation technology. Analytical solution to elastic SH wave scattering. Taking the double open trenches as an example, the parameters of the influence of factors such as excitation frequency, open trenches length and spacing on the vibration isolation effect are analyzed. The results show that the vibration isolation effect of double open trenches is significantly better than that of single open trench, and as the length and spacing of the open trenches increase, the area of the shielding area increases significantly.
周凤玺1,2，梁玉旺1，刘佳1. 多空沟对弹性波的散射及隔振性能分析：SH波入射[J]. 振动与冲击, 2021, 40(24): 263-268.
ZHOU Fengxi1, 2, LIANG Yuwang1, LIU Jia1. Analysis of elastic wave scattering and vibration isolation performance of multiple open trenches: SH incident. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(24): 263-268.
[1] Barkan D D. Dynamics of Base and Foundations. McGraw Hill, New York, 1962.
[2] Woods R D. Screening of surface waves in soil[J]. Journal of the Soil Mechanics and Foundations Division, ASCE, 1968, 94(4): 951-979.
[3] Ahmad S, Al-Hussaini T M. Simplified design for vibration screening by open and in-filled trenches[J]. Journal of Geotechnical Engineering, ASCE, 1991, 117(1): 67-88.
[4] Klein R , Antes H , D. Le Houédec. Efficient 3D modelling of vibration isolation by open trenches[J]. Computers & Structures, 1997, 64(1-4):809-817.
[5] Haupt W A. Model tests on screening of surface waves[C]. Proceedings of the 10th International Conference in Soil Mechanics and Foundation Engineering, Stockholm, 1981, 3: 215-222．
[6] ÇELEBI E, FIRAT S, BEYHAN G, 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.
[7] Murillo C, Thorel L and Caicedo B. Ground vibration isolation with geofoam barriers: centrifuge modeling[J]. Geotextiles and Geomembranes, 2009, 27(6): 423-434．
[8] D. Ulgen, O. Toygar. Screening effectiveness of open and in-filled wave barriers: A full-scale experimental study[J]. Construction and Building Materials, 2015, 86: 12-20.
[9] 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(1):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 & Soil Mechanics, 2014, 35(1):341-346.
[10] Ankurjyoti Saikia, Utpal Kumar Das. Analysis and design of open trench barriers in screening steady-state surface vibrations [J]. Earthquake Engineering and Engineering Vibration, 2014, 13(3): 545-554.
[11] Shrivastava R K , Kameswara Rao N S V . Response of soil media due to impulse loads and isolation using trenches[J]. Soil Dynamics and Earthquake Engineering, 2002, 22(8):695-702.
[12] Emad K, Manolis G D. Shallow trenches and propagation of surface waves[J]. Journal of engineering mechanical division, ASCE, 1985, 111(2): 279-282.
[13] Beskos D E, Dasgupta G, Vardoulakis I G. Vibration isolation using open or filled trenches, part 1: 2-D homogeneous soil[J]. Computational mechanics, 1986, 1(1): 43-63.
[14] Tsai P H, Chang T S. Effects of open trench siding on vibration-screening effectiveness using the two-dementional boundary element method[J]. Soil Dynamics and Earthquake Engineering, 2009, 29(5): 865-873.
[15] Banerjee P K, Ahmad S, Chen K. Advanced application of BEM to wave barriers in multi-layered three-dimensional soil media[J]. Earthquake Engineering and Structural Dynamics, 2010, 16(7): 1041-1060.
[16] 巴振宁,王靖雅,梁建文.层状地基中隔振沟对移动列车荷载隔振研究-2.5维IBEM方法[J].振动工程学报,2016,29(05):860-873.
BA Zhen-Ning. Wang Jing-Ya. LIANG Jian-Wen. Reduction of train-induced vibrations by using a trench in a layered foundation[J] Journal of Vibration Engineering, 2016, 29(5):860-873
[17] 巴振宁,梁建文,王靖雅.空沟对层状饱和地基中列车移动荷载的隔振性能研究[J].岩土工程学报,2017,39(05):848-858.
BA Zhen-Ning, LIANG Jian-Wen, WANG Jing-Ya. Isolation effect of an open trench against train-induced vibrations in a saturated layered ground[J]. Chinese Journal of Geotechnical Engineering, 2017,39(05):848-858
[18] Andersen L, Nielsen S R K. Reduction of ground vibration by means of barriers or soil improvement along a railway track[J]. Soil Dynamics & Earthquake Engineering, 2005, 25(7): 701-716.
[19] Adam M, Von Estorff O. Reduction of train-induced building vibrations by using open and filled trenchs[J]. Computers and Structures, 2005, 38: 11-24.
[20] 李伟, 高广运. 二维层状地基空沟主动隔振分析[J]. 地下空间, 2004,24(3):391-394.
LI Wei, GAO Guang-yun. 2D Analysis of Active Isolation Using Open Trench in Layered Medium[J]. Undergroung Space, 2004, 24(3):391-394.
[21] 高广运, 彭争光, 李伟, 等. 三维层状地基空沟主动隔振分析[J]. 西北地震学报, 2006, 28(3): 211-215.
GAO Guang-yun, PENG Zheng-guang, LI Wei, et al. 3-D Analysis of Active Vibration Isolation by Open Trench in Layered Ground. Northwestern Seismological Journal, 2006, 28(3): 211-215.
[22] CAO Z, CAI Y, BOSTRÖM A, et al. Semi-analytical analysis of the isolation to moving-load induced ground vibrations by trenches on a poroelastic half-space[J]. Journal of Sound and Vibration, 2012, 331(4): 947–961.
[23] 徐平, 石明生,等. 空沟对SH波隔离效果的理论解答[J]. 地下空间与工程学报, 2015, 11(3): 647-651.
XU Ping, SHI Ming-sheng, et al. Theoretical analysis of isolation effects of an open trench on incident SH waves[J]. Chinese Journal of Underground Space and Engineering, 2015, 11(3): 647-651.
[24] 徐平. 空沟对平面纵波隔离效果的理论解答[J]. 振动与冲击, 2017, 36(5): 67-101.
XU Ping. Theoretical analysis for isolation effect of an open trench on plane longitudinal waves[J].Journal Of Vibration And Shock, 2017, 36(5): 67-101.
[25] YOUNESIAN D, SADRI M. Performance Analysis of Multiple Trenches in Train-Induced Wave Mitigation[J]. Journal of Low Frequency Noise, Vibration and Active Control, 2014, 33(1): 47-64.
[26] HWANG J H, TU T Y. Ground vibration due to dynamic compaction[J].Soil Dynamic and Earthquake Engineering, 2006, 26(5): 337-346.
[27] 陈志刚, 刘殿魁. 椭圆孔对SH波散射的远场［J］．哈尔滨工程大学学报, 2003, 24(3): 334-338．
CHEN Zhi-gang, LIU Dian-kui. Far field solution of SH-wave scattering by elliptic cavity［J］. Journal of Harbin Engineering University，2003，24(3): 334-338．( in Chinese)
[28] 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 of Mining ＆ Safety Engineering, 2007, 24(3): 361-365
