MATHEMATICAL INTERPRETATION OF SEISMIC WAVE SCATTERING AND REFRACTION ON TUNNEL STRUCTURES OF CIRCULAR CROSS-SECTION

Elefterija Zlatanović, Vlatko Šešov, Dragan Lukić, Zoran Bonić

DOI Number
https://doi.org/10.2298/FUACE200422018Z
First page
241
Last page
260

Abstract


Mathematical interpretation of the elastic wave diffraction in circular cylinder coordinates is in the focus of this paper. Firstly, some of the most important properties of Bessel functions, pertinent to the elastic wave scattering problem, have been introduced. Afterwards, basic equations, upon which the method of wave function expansions is established, are given for cylindrical coordinates and for plane-wave representation. In addition, steady-state solutions for the cases of a single cavity and a single tunnel are presented, with respect to the wave scattering and refraction phenomena, considering both incident plane harmonic compressional and shear waves. The last part of the work is dealing with the translational addition theorems having an important role in the problems of diffraction of waves on a pair of circular cylinders.



Keywords

circular tunnel, seismic waves, scattering, refraction, Fourier–Bessel series

Full Text:

PDF

References


V. Šešov and K. Talaganov, Soil and Foundation Dynamics – Dynamic Response of Soil, 25th International eleven-week course on aseismic design and construction “CADAC 2006”, Institute of Earthquake Engineering and Engineering Seismology (IZIIS), Skopje, 2006.

C. C. Mow and H. Y. Pao, The Diffraction of Elastic Waves and Dynamic Stress Concentrations, Report No. R-482-PR, Rand, Santa Monica, California, 1971.

J. D. Achenbach, Wave Propagation in Elastic Solids, North Holland Publishing Company – Amsterdam • London, American Elsevier Publishing Company, Inc., New York, 1973.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, United States Department of Commerce, National Bureau of Standards, 1964.

G. N. Watson, A Treatise of the Theory of Bessel Functions, Cambridge University Press, London and New York, 1966.

Ye. A. Ivanov, Diffraction of Electromagnetic Waves on Two Bodies, National Aeronautics and Space Administration, Washington, DC, 1970.

X.-L. Zhou, J.-H. Wang and L.-F. Jiang, “Dynamic response of a pair of elliptic tunnels embedded in a poroelastic medium”, Journal of Sound and Vibration 325, 2009, pp. 816-834, doi:10.1016/j.jsv.2009.04.001.

C. Yi, P. Zhang, D. Johansson and U. Nyberg, “Dynamic response of a circular lined tunnel with an imperfect interface subjected to cylindrical P-waves”, Computers and Geotechnics 55, 2014, pp. 165-171, doi:10.1016/j.compgeo.2013.08.009.

S. M. Hasheminejad and R. Avazmohammadi, “Dynamic stress concentrations in lined twin tunnels within fluid-saturated soil”, Journal of Engineering Mechanics 134(7), 2008, pp. 542-554, doi:10.1061/(ASCE)0733-9399(2008)134:7(542).

E. Zlatanović, Contribution to the methods of seismic analysis of twin-tunnel structures, PhD Dissertation, Institute of Earthquake Engineering and Engineering Seismology (IZIIS) of Skopje, University “Ss. Cyril and Methodius” of Skopje, Skopje, Republic of North Macedonia, 2016.

E. Zlatanović, G. Broćeta and N. Popović-Miletić, “Numerical modelling in seismic analysis of tunnels regarding soil–structure interaction”, Facta Universitatis, Series: Architecture and Civil Engineering 11(3), 2013, pp. 251-267, doi:10.2298/FUACE1303251Z.

E. Zlatanović, D. Lukić and V. Šešov, “Presentation of analytical solutions for seismically induced tunnel lining forces accounting for soil–structure interaction effects”, Building Materials and Structures 57(1), 2014, pp. 3-28, doi:10.5937/grmk1401003Z.

E. Zlatanović, V. Šešov, D. Lukić, Z. Bonić and N. Davidović, “State-of-the-art of seismic design codes for tunnels and underground structures”, Scientific Journal of Civil Engineering 8(2), 2019, pp. 49-54.


Refbacks

  • There are currently no refbacks.


ISSN 0354-4605 (Print)
ISSN 2406-0860 (Online)
COBISS.SR-ID 98807559