Vibration Isolation of Plane Waves by Periodic Pipe Pile Barriers in Saturated Soil
Publication: Journal of Aerospace Engineering
Volume 32, Issue 1
Abstract
Pile barriers as an effective method for isolating ambient vibration have been used in practical engineering for many decades. However, the study of multiple rows of pile barriers in saturated soil is rare, especially of periodic pipe pile barriers in saturated soil. Based on a new method called the COMSOL partial differential equation (PDE) method, this paper investigates the vibration isolation of plane waves by periodic pipe pile barriers in saturated soil. First, through some comparisons with results from related works, the COMSOL PDE method is validated. Second, the first complete attenuation zone (CAZ) of pipe piles embedded periodically in saturated soil is studied; the effects of parameters such as the filling fraction, arrangement configuration, and filling materials on the first CAZ are discussed. Two kinds of formation mechanism of the first CAZ for periodic filled pipe pile barriers, the Bragg scattering mode and the locally resonant mode, are investigated comprehensively. Both two-dimensional (2D) and three-dimensional (3D) models with multiple rows of periodic pipe piles in saturated soil are built, and the displacement responses behind the pile barriers are analyzed in the frequency domain. This study provides a sound background for the application of periodic pipe pile barriers in saturated soil to isolate ambient vibration in engineering practice.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant Nos. 51878030 and 51678046).
References
Achaoui, Y., A. Khelif, S. Benchabane, and V. Laude. 2010. “Polarization state and level repulsion in two-dimensional phononic crystals and waveguides in the presence of material anisotropy.” J. Phys. D Appl. Phys. 43 (18): 185401. https://doi.org/10.1088/0022-3727/43/18/185401.
Atalla, N., R. Panneton, and R. Debergue. 1998. “A mixed displacement-pressure formulation for poroelastic materials.” J. Acoust. Soc. Am. 104 (3): 1444–1452. https://doi.org/10.1121/1.424355.
Avilés, J., and F. J. Sánchez-Sesma. 1983. “Piles as barriers for elastic waves.” J. Geotech. Eng. 109 (9): 1133–1146. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:9(1133).
Avilés, J., and F. J. Sánchez-Sesma. 1988. “Foundation isolation from vibrations using piles as barriers.” J. Eng. Mech. 114 (11): 1854–1870. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:11(1854).
Biot, M. A. 1956a. “Theory of propagation of elastic waves in a fluid-saturated porous solid. I: Low-frequency range.” J. Acoust. Soc. Am. 28 (2): 168–178. https://doi.org/10.1121/1.1908239.
Biot, M. A. 1956b. “Theory of propagation of elastic waves in a fluid-saturated porous solid. II: Higher-frequency range.” J. Acoust. Soc. Am. 28 (2): 179–191. https://doi.org/10.1121/1.1908241.
Cai, Y. Q., G. Y. Ding, and C. J. Xu. 2008. “Screening of plane S waves by an array of rigid piles in poroelastic soil.” J. Zhejiang Univ. Sci. A 9 (5): 589–599. https://doi.org/10.1631/jzus.A071494.
Cai, Y. Q., G. Y. Ding, and C. J. Xu. 2009. “Amplitude reduction of elastic waves by a row of piles in poroelastic soil.” Comput. Geotech. 36 (3): 463–473. https://doi.org/10.1016/j.compgeo.2008.08.015.
Chen, Y. Y., and G. L. Huang. 2015. “Active elastic metamaterials for subwavelength wave propagation control.” Acta Mech. Sin. 31 (3): 349–363. https://doi.org/10.1007/s10409-015-0402-0.
Chen, Y. Y., G. L. Huang, and C. T. Sun. 2014. “Band gap control in an active elastic metamaterial with negative capacitance piezoelectric shunting.” J. Vib. Acoust. 136 (6): 061008. https://doi.org/10.1115/1.4028378.
COMSOL Software. 2015. COMSOL multiphysics reference manual (Version: COMSOL 5.1). Burlington, MA: COMSOL Inc.
Ding, G. Y., Y. Q. Cai, J. Wang, and P. Wang. 2010. “Isolation of obliquely incident elastic waves by an array of pipe piles in saturated soil.” [In Chinese.] J. Vib. Shock 29 (3): 121–124.
Eslami, H., and B. Gatmiri. 2010. “Two formulations for dynamic response of a cylindrical cavity in cross-anisotropic porous media.” Int. J. Numer. Anal. Methods Geomech. 34: 331–356.
Gao, G. Y., Z. Y. Li, C. Qiu, and Z. Q. Yue. 2006. “Three-dimensional analysis of rows of piles as passive barriers for ground vibration isolation.” Soil Dyn. Earthquake Eng. 26 (11): 1015–1027. https://doi.org/10.1016/j.soildyn.2006.02.005.
Gatmiri, B., and H. Eslami. 2007. “Scattering of harmonic waves by a circular cavity in a porous medium: Complex functions theory approach.” Int. J. Geomech. 7 (5): 371–381. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:5(371).
Huang, J. K., and Z. F. Shi. 2013a. “Application of periodic theory to rows of piles for horizontal vibration attenuation.” Int. J. Geomech. 13 (2): 132–142. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000193.
Huang, J. K., and Z. F. Shi. 2013b. “Attenuation zones of periodic pile barriers and its application in vibration reduction for plane waves.” J. Sound Vib. 332 (19): 4423–4439. https://doi.org/10.1016/j.jsv.2013.03.028.
Huang, J. K., and Z. F. Shi. 2015. “Vibration reduction of plane waves using periodic in-filled pile barriers.” J. Geotech. Geoenviron. 141 (6): 04015018. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001301.
Jensen, J. S. 2003. “Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures.” J. Sound Vib. 266 (5): 1053–1078. https://doi.org/10.1016/S0022-460X(02)01629-2.
Kattis, S. E., D. Polyzos, and D. E. Beskos. 1999a. “Modelling of pile wave barriers by effective trenches and their screening effectiveness.” Soil Dyn. Earthquake Eng. 18 (1): 1–10. https://doi.org/10.1016/S0267-7261(98)00032-3.
Kattis, S. E., D. Polyzos, and D. E. Beskos. 1999b. “Vibration isolation by a row of piles using a 3-D frequency domain BEM.” Int. J. Numer. Methods Eng. 46 (5): 713–728. https://doi.org/10.1002/(ISSN)1097-0207.
Khelif, A., and A. Adibi. 2016. Phononic crystals fundamentals and applications. New York: Springer.
Liu, J. B., G. Yin, and Y. X. Du. 2006. “Consistent viscous-spring artificial boundaries and viscous-spring boundary elements.” [In Chinese.] Chin. J. Geotech. Eng. 28 (9): 1070–1075.
Liu, Z. Y., X. X. Zhang, Y. W. Mao, Y. Y. Zhu, Z. Y. Yang, C. T. Chan, and P. Sheng. 2000. “Locally resonant sonic materials.” Science 289 (5485): 1734–1736. https://doi.org/10.1126/science.289.5485.1734.
Lu, J. F., and D. S. Jeng. 2008. “Poroelastic model for pile-soil interaction in a half-space porous medium due to seismic waves.” Int. J. Numer. Anal. Methods Geomech. 32 (1): 1–41. https://doi.org/10.1002/(ISSN)1096-9853.
Mavko, G., J. Dvorkin, and T. Mukerji. 2009. The rock physics handbook: Tools for seismic analysis of porous media. New York: Cambridge University Press.
Pu, X. B., and Z. F. Shi. 2017. “A novel method for identifying surface waves in periodic structures.” Soil Dyn. Earthquake Eng. 98: 67–71. https://doi.org/10.1016/j.soildyn.2017.04.011.
Richart, F. E., R. D. Woods, and J. R. Hall. 1970. Vibrations of soils and foundations. Englewood Cliffs, NJ: Prentice Hall.
Shi, Z. F., Z. B. Cheng, and H. J. Xiang. 2017a. Periodic structures: Theory and applications to seismic isolation and vibration reduction. [In Chinese.] Beijing: Science Press Ltd.
Shi, Z. F., Y. G. Wen, and Q. J. Meng. 2017b. “Propagation attenuation of plane waves in saturated soil by pile barriers.” Int. J. Geomech. 17 (9): 04017053. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000963.
Taiebat, M., B. Jeremic, Y. F. Dafalias, A. M. Kaynia, and Z. Cheng. 2010. “Propagation of seismic waves through liquefied soils.” Soil Dyn. Earthquake Eng. 30 (4): 236–257. https://doi.org/10.1016/j.soildyn.2009.11.003.
Taiebat, M., H. Shahir, and A. Pak. 2007. “Study of pore pressure variation during liquefaction using two constitutive models for sand.” Soil Dyn. Earthquake Eng. 27 (1): 60–72. https://doi.org/10.1016/j.soildyn.2006.03.004.
Tsai, P. H., Z. Y. Feng, and T. L. Jena. 2008. “Three-dimensional analysis of the screening effectiveness of hollow pile barriers for foundation-induced vertical vibration.” Comput. Geotech. 35 (3): 489–499. https://doi.org/10.1016/j.compgeo.2007.05.010.
Tsai, P. H., Z. Y. Feng, and S. Y. Lin. 2011. “A wavelet based method for estimating the damping ratio in statnamic pile load tests.” Comput. Geotech. 38 (2): 205–216. https://doi.org/10.1016/j.compgeo.2010.11.007.
Wang, G., X. S. Wen, J. H. Wen, L. H. Shao, and Y. Z. Liu. 2004. “Two-dimensional locally resonant phononic crystals with binary structures.” Phys. Rev. Lett. 93 (15): 154302. https://doi.org/10.1103/PhysRevLett.93.154302.
Wang, Y. F. 2015. “Bandgap properties and design of phononic crystals with resonant units.” [In Chinese.] Ph.D. dissertation, Institute of Engineering Mechanics, Beijing Jiaotong Univ.
Xia, T. D., M. M. Sun, C. Chen, W. Y. Chen, and P. Xu. 2011. “Analysis on multiple scattering by an arbitrary configuration of piles as barriers for vibration isolation.” Soil Dyn. Earthquake Eng. 31 (3): 535–545. https://doi.org/10.1016/j.soildyn.2010.10.008.
Xu, B., J. F. Lu, and J. H. Wang. 2010. “Dynamic responses of a pile embedded in a layered poroelastic half-space to harmonic lateral loads.” Int. J. Numer. Anal. Methods Geomech. 34 (5): 493–515. https://doi.org/10.1002/nag.v34:5.
Xu, P. 2017. “Analysis of isolation effectiveness of shear waves by a row of hollow pipe piles in saturated Soils.” Transp. Porous Med. 120 (2): 415–432. https://doi.org/10.1007/s11242-017-0931-z.
Xu, P., and T. D. Xia. 2013. “Analysis of isolation effects of P1 waves by barriers composed of a row of hollow pipe piles in saturated soils.” [In Chinese.] Supplement, China Civ. Eng. J. 46 (S2): 152–157.
Xu, P., T. D. Xia, and M. Wu. 2008. “Study on the effect of barrier of a row of rigid hollow pipe piles for isolation of P and SH waves.” [In Chinese.] Eng. Mech. 25 (5): 210–217.
Xu, P., T. D. Xia, and X. M. Zhou. 2007. “Study on effect of barrier of a row of hollow pipe piles on isolation of incident plane SV waves.” [In Chinese.] Chin. J. Geotech. Eng. 29 (1): 131–136.
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jan 24, 2018
Accepted: May 24, 2018
Published online: Sep 13, 2018
Published in print: Jan 1, 2019
Discussion open until: Feb 13, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.