Abstract
Based on the elastic wave propagation and scattering theories, it is introduced acoustical and electromagnetical multiple scattering solutions. With wave function expansion and coordinates translation methods, it is solved the every order of scattering complex coefficients with boundary conditions. The iteration relation of high order to lower order of scattering coefficients is established, the multiple scattering wave and total wave field are determined as well. It is innovatively calculated the elastic wave multiple scattering and dynamic stress response problems of arbitrarily arranged deep cavities subjected to incident P waves. The numerical example shows the value of Dynamic Stress Concentration Factor (DSCF) which the cavities group is arranged as hexagon is approximately the same as the ones linearly arranged meanwhile the separation between cavities is narrower than the former one.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Pao Y H, Mow C C. (1973). Diffraction of elastic waves and dynamic stress concentrations [M]. New York, Crane and Russak.
Lee V W. and Trifunac, M. D. (1979). Response of tunnels to incident SH waves [J]. Journal of the Engineering Mechanics Division, 105 (4): 643–659.
Nasser M, Trifunac M D. (1981). A note on the vibrations of a semi-circular canal excited by plane SH-wave [J]. Bulletin of the Indian Society of Earthquake Technology, 18 (2): 88–100.
Lee V W. (1984). Three dimensional diffraction of plane P, SV and SH waves by a hemispherical alluvial valley [J]. Soil Dynamics and Earthquake Engineering, 3 (3):133–144.
Lee V W, Cao H. (1989). Diffraction of SV waves by circular cylindrical canyons of various depths [J]. Journal of Engineering Mechanics, 115(9): 2035–2056.
Lee V W, Karl J. (1993). Diffraction of SV waves by underground, circular, cylindrical cavities [J]. Soil Dynamic and Earthquake Engineering, 11 (8): 445–456.
Lee V W, Karl J. (1993). Diffraction of elastic plane P waves by circular, underground unlined tunnels [J]. European Journal of Earthquake Engineering, 1 (1): 29–36.
Luco J E, Barros de F C P. (2001). Seismic response of a cylindrical shell embedded in a layered viscoelastic half-space. I: Formulation [J]. Earthquake Engineering and Structural Dynamics, 23 (5): 553–567.
Liang J W, Ji X D. (2006). Amplification of Rayleigh waves due to underground lined cavities [J]. Earthquake Engineering and Engineering Dynamics, 2006, (04): 024–31.
Wang S S, Gao B, Shen Y S, et al. (2014). Study on the mechanism of resistance and damping technology of deep soft rock tunnels subjected to incident plane SH waves [J]. China Civil Engineering Journal, 47 (Sup.1): 280–286.
Gao B, Wang S S. (2016). Dynamic response study on shallow circular composite-lining tunnels [J]. Journal of Southeast Jiaotong University, 51(4): 599–606.
Wang S S, Gao B. (2016). Damping mechanism and shaking table test on mountain tunnel linings with buffer layers [J]. Chinese Journal of Rock Mechanics and Engineering, 35 (3): 592–603.
T D Xia, M M Sun, C Chen, et al. (2011). Analysis on multiple scattering by an arbitrary configuration of piles as barriers for vibration isolation [J]. Soil Dynamics and Earthquake Engineering, 31 (3): 535–545.
M M Sun, G Q Liang, T D Xia, et al. (2014). Ground vibration isolation of multiple scattering by using rows of tubular piles as barriers [J]. Shock and Vibration, 2014: 1–20.
Acknowledgements
The work described in this paper was supported by the National Science Foundation of China (Grant No. 51408549), the Natural Science Foundation of Zhejiang Province, China (Grant No. LY16E090005) and the Research Fund of ZUCC Teachers (Grant No. J-15018).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte. Ltd. and Zhejiang University Press
About this chapter
Cite this chapter
Sun, M., Fang, H., Zhang, S., Wei, X. (2018). Dynamic Stress Distribution of Arbitrarily Arranged Deep Cavities Subjected to Incident Plane P Waves by Multiple Scattering Method. In: Bian, X., Chen, Y., Ye, X. (eds) Environmental Vibrations and Transportation Geodynamics. ISEV 2016. Springer, Singapore. https://doi.org/10.1007/978-981-10-4508-0_33
Download citation
DOI: https://doi.org/10.1007/978-981-10-4508-0_33
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-4507-3
Online ISBN: 978-981-10-4508-0
eBook Packages: EngineeringEngineering (R0)