Influence of Heterogeneity on the Propagation Behavior of Love-Type Waves in a Layered Isotropic Structure
Publication: International Journal of Geomechanics
Volume 16, Issue 2
Abstract
This paper aims to investigate the propagation of Love-type waves in the double layers lying over an isotropic homogeneous half-space. The two layers have been considered of finite width and a different sort of heterogeneities. Debye asymptotic expansion has been used to obtain the closed form of the dispersion equation. It has been found that the heterogeneity and width ratio of layers have a considerable effect on the phase velocity of Love-type waves. In particular, increment in the width ratio decreases the phase velocity of Love-type waves. The established dispersion relation for this study agrees well with the classical results. The comparative study of the present problem with a case in which double layers are homogeneous has been made. Results have been represented graphically, and it has been observed that the dimensionless phase velocity decreases with the increase in dimensionless wave number. It has also been examined that the heterogeneity parameter of uppermost layer and intermediate layer affects the phase velocity substantially.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors convey their sincere thanks to the Indian School of Mines, Dhanbad, for granting access to its best facility and providing a Junior Research Fellowship to Ms. Nirmala Kumari.
References
Bard, P. Y., and Bouchon, M. (1980). “The seismic response of sediment-filled valleys: Part-1.” Bull. Seismol. Soc. Am., 70(5), 1263–1286.
Bhattacharya, J. (1962). “On the dispersion curve for love wave due to irregularity in the thickness of the transversely isotropic crustal layer.” Gerl. Beit. Geophys., 6, 324–334.
Campillo, M. (1987). “Modeling of SH-wave propagation in an irregularly layered medium—Application to seismic profiles near a dome.” Geophys. Prospect., 35(3), 236–249.
Chattopadhyay, A. (1975). “On the propagation of Love type waves in an intermediate nonhomogeneous layers lying between two semi-infinite homogeneous elastic media.” Gerl. Beit. Geophys., 84(3), 327–334.
Chattopadhyay, A., Gupta, S., Chattopadhyay, A., and Singh, A. K. (2010). “The dispersion of shear wave in multilayered magnetoelastic self-reinforced media.” Int. J. Solids Struct., 47(9), 1317–1324.
Chattopadhyay, A., Gupta, S., Kumari, P., and Sharma, V. K. (2012b). “Effect of point source and heterogeneity on the propagation of SH-waves in a viscoelastic layer over a viscoelastic half space.” Acta Geophys., 60(1), 119–139.
Chattopadhyay, A., Gupta, S., Kumari, P., and Sharma, V. K. (2013b). “Torsional wave propagation in harmonically inhomogeneous media.” Int. J. Numer. Anal. Methods Geomech., 37(10), 1280–1291.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2011). “Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer.” Appl. Math. Mech., 32(5), 571–586.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2012a). “Torsional surface waves in a self-reinforced medium over a heterogeneous half-space.” Int. J. Geomech., 193–197.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2013a). “Dispersion of SH waves in an irregular non homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium.” J. Vib. Control, 19(1), 109–119.
Chattopadhyay, A., and Singh, A. K. (2012). “Propagation of magnetoelastic shear waves in an irregular self-reinforced layer.” J. Eng. Math., 75(1), 139–155.
Chattopadhyay, A., Singh, A. K., and Dhua, S. (2014). “Effect of heterogeneity and reinforcement on propagation of a crack due to shear waves.” Int. J. Geomech., 04014013.
Dhua, S., Singh, A. K., and Chattopadhyay, A. (2015). “Propagation of torsional wave in a composite layer overlying an anisotropic heterogeneous half-space with initial stress.” J. Vib. Control., 21(10), 1987–1998
Ge, Z., and Chen, X. (2007). “Wave propagation in irregularly layered elastic models: A boundary element approach with a global reflection/transmission matrix propagator.” Bull. Seismol. Soc. Am., 97(3), 1025–1031.
Gogna, M. L. (1976). “Love waves in heterogeneous layered media.” Geophys. J. R. Astron. Soc., 357–370.
Gubbins, D. (1990). Seismology and plate tectonics, Cambridge University Press, London.
Hartzell, S., Bonilla, L. F., and Williams, R. A. (2004). “Prediction of nonlinear soil effects.” Bull. Seismol. Soc. Am., 94(5), 1609–1629.
Kar, B. K. (1977). “On the propagation of Love-type waves in a nonhomogeneous internal stratum of finite thickness lying between two semi-infinite isotropic media.” Gerl. Beit. Geophys., 86(5), 407–412.
Lee, V. W., and Trifunac, M. D. (1985). “Torsional accelerograms.” Int. J. Soil Dyn. Earthquake Eng., 4(3), 132–139.
Mathematica [Computer software]. Wolfram Research, Champaign, IL.
Santisi d’Avila, M. P., and Semblat, J.-F. (2014). “Nonlinear seismic response for the 2011 Tohoku earthquake: Borehole records versus one-directional three-component propagation models.” Geophys. J. Int., 197(1), 566–580.
Semblat, J. F., et al. (2005). “Site effects: Basin geometry vs soil layering.” Soil Dyn. Earthquake Eng., 25(7–10), 529–538.
Singh, A. K., Kumar, S., and Chattopadhyay, A. (2014). “Effect of irregularity and heterogeneity on the stresses produced due to a normal moving load on a rough monoclinic half-space.” Meccanica, 49(12), 2861–2878.
Singh, A. K., Kumar, S., and Chattopadhyay, A. (2015). “Propagation of torsional waves in a fiber composite layer lying over an initially stressed viscoelastic half-space.” Int. J. Geomech., 04015014.
Todorovska, M. I., and Lee, V. W. (1989). “Seismic waves in building with shear walls or central core.” J. Eng. Mech., 15(12), 2669–2686.
Todorovska, M. I., and Trifunac, M. D. (1990). “Note on excitation of long structures by ground wave.” J. Eng. Mech., 116(4), 952–964.
Watson, G. N. (1958). A treatise on the theory of Bessel functions, Cambridge University Press, New York.
Wolf, J. P., and Obernhuber, P. (1981). “Effects of horizontally propagating waves on the response of structures with a soft first storey.” Earthquake Eng. Struct. Dyn., 9(1), 1–21.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 16 • Issue 2 • April 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jan 14, 2014
Accepted: Apr 28, 2015
Published online: Oct 16, 2015
Discussion open until: Mar 2, 2016
Published in print: Apr 1, 2016
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.